Bibliography - Isaac Held

1. Garner, Stephen T., Isaac Held, Thomas R Knutson, and Joseph J Sirutis, in press: The roles of wind shear and thermodynamic stability in past and projected changes of Atlantic tropical-cyclone activity. Journal of Climate. 2/09.
   [ Abstract ]

   Atlantic tropical-cyclone activity has trended upward in recent decades. The increase coincides with favorable changes in local sea-surface temperature and other environmental indices, principally vertical shear and thermodynamic stability. The relative importance of these environmental factors has not been firmly established. A recent study using a high-resolution dynamical downscaling model has captured both the trend and interannual variations in Atlantic storm frequency with considerable fidelity. In the present work, this downscaling framework is used to assess the importance of the large-scale thermodynamic environment relative to other factors influencing Atlantic tropical storms. Separate assessments are done for the recent multi-decadal trend (1980 to 2006) and a model-projected global-warming environment for the late 21st century. For the multi-decadal trend, changes in the seasonal-mean thermodynamic environment (sea-surface temperature and atmospheric temperature profile at fixed relative humidity) account for most of the observed increase in tropical-cyclone frequency, with other seasonal-mean changes (including vertical shear) having a smaller combined effect. In contrast, the model’s projected reduction in Atlantic tropical-cyclone activity in the warm-climate scenario appears driven mostly by increased seasonal-mean vertical shear in the western Atlantic and Caribbean, rather than changes in the SST and thermodynamic profile.

2. Winton, Michael, K Takahashi, and Isaac Held, in press: Importance of ocean heat uptake efficacy to transient climate change. Journal of Climate. 3/09.
3. Zhang, Rong, S M Kang, and Isaac Held, in press: Sensitivity of climate change induced by the weakening of the Atlantic Meridional Overturning Circulation to cloud feedback. Journal of Climate. 2/09.
   [ Abstract ]

   A variety of observational and modeling studies show that changes in the Atlantic Meridional Overturning Circulation (AMOC) can induce rapid global scale climate change. In particular, a substantially weakened AMOC leads to a southward shift of the Intertropical Convergence Zone (ITCZ) in both the Atlantic and the Pacific. However, the simulated amplitudes of the AMOC induced tropical climate change differ substantially among different models. In this paper, we study the sensitivity to cloud feedback of the climate response to a change in the AMOC using a coupled ocean-atmosphere model (GFDL CM2.1). Without cloud feedback, the simulated AMOC-induced climate change in this model is weakened substantially. Low cloud feedback has a strong amplifying impact on the tropical ITCZ shift in this model, while the effects of high cloud feedback are weaker. We conclude that cloud feedback is an important contributor to the uncertainty in the global response to AMOC changes.

4. Zhao, Ming, Isaac Held, Shian-Jiann Lin, and G A Vecchi, in press: Simulations of global hurricane climatology, interannual variability, and response to global warming using a 50km resolution GCM. Journal of Climate. 1/09.
5. Giannini, A, M Biasutti, Isaac Held, and A Sobel, 2008: A global perspective on African climate. Climatic Change, 90(4), doi:10.1007/s10584-008-9396-y.
   [ Abstract ]

   We describe the global climate system context in which to interpret African environmental change to support planning and implementation of policymaking action at national, regional and continental scales, and to inform the debate between proponents of mitigation v. adaptation strategies in the face of climate change. We review recent advances and current challenges in African climate research and exploit our physical understanding of variability and trends to shape our outlook on future climate change. We classify the various mechanisms that have been proposed as relevant for understanding variations in African rainfall, emphasizing a “tropospheric stabilization” mechanism that is of importance on interannual time scales as well as for the future response to warming oceans. Two patterns stand out in our analysis of twentieth century rainfall variability: a drying of the monsoon regions, related to warming of the tropical oceans, and variability related to the El Niño–Southern Oscillation. The latest generation of climate models partly captures this recent continent-wide drying trend, attributing it to the combination of anthropogenic emissions of aerosols and greenhouse gases, the relative contribution of which is difficult to quantify with the existing model archive. The same climate models fail to reach a robust agreement regarding the twenty-first century outlook for African rainfall, in a future with increasing greenhouse gases and decreasing aerosol loadings. Such uncertainty underscores current limitations in our understanding of the global climate system that it is necessary to overcome if science is to support Africa in meeting its development goals.

6. Held, Isaac, and Ming Zhao, June 2008: Horizontally homogeneous rotating radiative–convective Equilibria at GCM resolution. Journal of the Atmospheric Sciences, 65(6), doi:10.1175/2007JAS2604.1.
   [ Abstract ]

   Rotating radiative–convective equilibrium, using the column physics and resolution of GCMs, is proposed as a useful framework for studying the tropical storm–like vortices produced by global models. These equilibria are illustrated using the column physics and dynamics of a version of the GFDL Atmospheric Model 2 (AM2) at resolutions of 220, 110, and 55 km in a large 2 × 10⁴ km square horizontally homogeneous domain with fixed sea surface temperature and uniform Coriolis parameter. The large domain allows a number of tropical storms to exist simultaneously. Once equilibrium is attained, storms often persist for hundreds of days. The number of storms decreases as sea surface temperatures increase, while the average intensity increases. As the background rotation is decreased, the number of storms also decreases. At these resolutions and with this parameterization of convection, a dense collection of tropical storms is always the end state of moist convection in the cases examined.

7. Kang, S M., Isaac Held, D M W Frierson, and Ming Zhao, 2008: The response of the ITCZ to extratropical thermal forcing: Idealized slab-ocean experiments with a GCM. Journal of Climate, 21(14), doi:10.1175/2007JCLI2146.1.
   [ Abstract ]

   Using a comprehensive atmospheric GCM coupled to a slab mixed layer ocean, experiments are performed to study the mechanism by which displacements of the intertropical convergence zone (ITCZ) are forced from the extratropics. The northern extratropics are cooled and the southern extratropics are warmed by an imposed cross-equatorial flux beneath the mixed layer, forcing a southward shift in the ITCZ. The ITCZ displacement can be understood in terms of the degree of compensation between the imposed oceanic flux and the resulting response in the atmospheric energy transport in the tropics. The magnitude of the ITCZ displacement is very sensitive to a parameter in the convection scheme that limits the entrainment into convective plumes. The change in the convection scheme affects the extratropical–tropical interactions in the model primarily by modifying the cloud response. The results raise the possibility that the response of tropical precipitation to extratropical thermal forcing, important for a variety of problems in climate dynamics (such as the response of the tropics to the Northern Hemisphere ice sheets during glacial maxima or to variations in the Atlantic meridional overturning circulation), may be strongly dependent on cloud feedback. The model configuration described here is suggested as a useful benchmark helping to quantify extratropical–tropical interactions in atmospheric models.

8. Kang, S M., D M W Frierson, and Isaac Held, in press: The response of tropical precipitation to extratropical thermal forcing in an idealized GCM. Journal of the Atmospheric Sciences. 9/08.
   [ Abstract ]

   The response of tropical precipitation to extratropical thermal forcing is reexamined using an idealized moist atmospheric GCM, which has no water vapor or cloud feedbacks, simplifying the analysis in an aqua-planet configuration coupled to a slab ocean. As in earlier studies, in response to high latitude forcing, tropical precipitation is skewed towards the warmed hemisphere. Comparisons with a comprehensive GCM in an identical aqua-planet, mixed-layer framework reveal that the tropical responses tend to be much larger in the comprehensive GCM due to positive cloud and water vapor feedbacks that amplify the imposed extratropical thermal forcing. The magnitude of the tropical precipitation response in the idealized model is sensitive to convection scheme parameters. This sensitivity as well as the tropical precipitation response can be understood from a simple theory with two ingredients: first, the changes in poleward energy fluxes are predicted using a one-dimensional energy balance model; second, a measure of the “total gross moist stability” (which is defined to be the total atmospheric energy transport per unit mass transport) of the model tropics converts the energy flux change (mean plus eddy) into a mass flux and a moisture flux change. It can be understood from this theory that the sensitivity of the tropical response to the convection scheme in the idealized model results from different strength of the Hadley mass transport in the control climate.

9. Knutson, Thomas R., Joseph J Sirutis, Stephen T Garner, G A Vecchi, and Isaac Held, 2008: Simulated reduction in Atlantic hurricane frequency under twenty-first-century warming conditions. Nature Geoscience, 1(6), 359-364.
   [ Abstract PDF ]

   Increasing sea surface temperatures in the tropical Atlantic Ocean and measures of Atlantic hurricane activity have been reported to be strongly correlated since at least 1950 (refs 1, 2, 3, 4, 5), raising concerns that future greenhouse-gas-induced warming6 could lead to pronounced increases in hurricane activity. Models that explicitly simulate hurricanes are needed to study the influence of warming ocean temperatures on Atlantic hurricane activity, complementing empirical approaches. Our regional climate model of the Atlantic basin reproduces the observed rise in hurricane counts between 1980 and 2006, along with much of the interannual variability, when forced with observed sea surface temperatures and atmospheric conditions7. Here we assess, in our model system7, the changes in large-scale climate that are projected to occur by the end of the twenty-first century by an ensemble of global climate models8, and find that Atlantic hurricane and tropical storm frequencies are reduced. At the same time, near-storm rainfall rates increase substantially. Our results do not support the notion of large increasing trends in either tropical storm or hurricane frequency driven by increases in atmospheric greenhouse-gas concentrations.

10. Lee, M-I, M J Suarez, I-S Kang, Isaac Held, and D Kim, October 2008: A moist benchmark calculation for atmospheric general circulation models. Journal of Climate, 21(19), doi:10.1175/2008JCLI1891.1.
    [ Abstract ]

    A benchmark calculation is designed to compare the climate and climate sensitivity of atmospheric general circulation models (AGCMs). The experimental setup basically follows that of the aquaplanet experiment (APE) proposed by Neale and Hoskins, but a simple mixed layer ocean is embedded to enable air–sea coupling and the prediction of surface temperature. In calculations with several AGCMs, this idealization produces very strong zonal-mean flow and exaggerated ITCZ strength, but the model simulations remain sufficiently realistic to justify the use of this framework in isolating key differences between models. Because surface temperatures are free to respond to model differences, the simulation of the cloud distribution, especially in the subtropics, affects many other aspects of the simulations. The analysis of the simulated tropical transients highlights the importance of convection inhibition and air–sea coupling as affected by the depth of the mixed layer. These preliminary comparisons demonstrate that this idealized benchmark provides a discriminating framework for understanding the implications of differing physics parameterization in AGCMs.

11. Medeiros, B, B Stevens, Isaac Held, Ming Zhao, D L Williamson, J Olson, and C S Bretherton, October 2008: Aquaplanets, climate sensitivity, and low clouds. Journal of Climate, 21(19), doi:10.1175/2008JCLI1995.1.
    [ Abstract ]

    Cloud effects have repeatedly been pointed out as the leading source of uncertainty in projections of future climate, yet clouds remain poorly understood and simulated in climate models. Aquaplanets provide a simplified framework for comparing and understanding cloud effects, and how they are partitioned as a function of regime, in large-scale models. This work uses two climate models to demonstrate that aquaplanets can successfully predict a climate model's sensitivity to an idealized climate change. For both models, aquaplanet climate sensitivity is similar to that of the realistic configuration. Tropical low clouds appear to play a leading role in determining the sensitivity. Regions of large-scale subsidence, which cover much of the tropics, are most directly responsible for the differences between the models. Although cloud effects and climate sensitivity are similar for aquaplanets and realistic configurations, the aquaplanets lack persistent stratocumulus in the tropical atmosphere. This, and an additional analysis of the cloud response in the realistically configured simulations, suggests the representation of shallow (trade wind) cumulus convection, which is ubiquitous in the tropics, is largely responsible for differences in the simulated climate sensitivity of these two models.

12. Soden, Brian J., Isaac Held, R Colman, K M Shell, J T Kiehl, and C A Shields, 2008: Quantifying climate feedbacks using radiative kernels. Journal of Climate, 21(14), doi:10.1175/2007JCLI2110.1.
    [ Abstract ]

    The extent to which the climate will change due to an external forcing depends largely on radiative feedbacks, which act to amplify or damp the surface temperature response. There are a variety of issues that complicate the analysis of radiative feedbacks in global climate models, resulting in some confusion regarding their strengths and distributions. In this paper, the authors present a method for quantifying climate feedbacks based on “radiative kernels” that describe the differential response of the top-of-atmosphere radiative fluxes to incremental changes in the feedback variables. The use of radiative kernels enables one to decompose the feedback into one factor that depends on the radiative transfer algorithm and the unperturbed climate state and a second factor that arises from the climate response of the feedback variables. Such decomposition facilitates an understanding of the spatial characteristics of the feedbacks and the causes of intermodel differences. This technique provides a simple and accurate way to compare feedbacks across different models using a consistent methodology. Cloud feedbacks cannot be evaluated directly from a cloud radiative kernel because of strong nonlinearities, but they can be estimated from the change in cloud forcing and the difference between the full-sky and clear-sky kernels. The authors construct maps to illustrate the regional structure of the feedbacks and compare results obtained using three different model kernels to demonstrate the robustness of the methodology. The results confirm that models typically generate globally averaged cloud feedbacks that are substantially positive or near neutral, unlike the change in cloud forcing itself, which is as often negative as positive

13. Chen, G, Isaac Held, and W A Robinson, 2007: Sensitivity of the Latitude of the Surface Westerlies to Surface Friction. Journal of the Atmospheric Sciences, 64(8), doi:10.1175/JAS3995.1.
    [ Abstract ]

    The sensitivity to surface friction of the latitude of the surface westerlies and the associated eddy-driven midlatitude jet is studied in an idealized dry GCM. The westerlies move poleward as the friction is reduced in strength. An increase in the eastward phase speed of midlatitude eddies is implicated as playing a central role in this shift. This shift in latitude is mainly determined by changes in the friction on the zonal mean flow rather than the friction on the eddies. If the friction on the zonal mean is reduced instantaneously, the response reveals two distinctive adjustment time scales. In the fast adjustment over the first 10–20 days, there is an increase in the barotropic component of zonal winds and a substantial decrease in the eddy kinetic energy; the shift in the surface westerlies and jet latitude occurs in a slower adjustment. The space–time eddy momentum flux spectra suggest that the key to the shift is a poleward movement in the subtropical critical latitude associated with the faster eastward phase speeds in the dominant midlatitude eddies. The view is supported by simulating the upper-tropospheric dynamics in a stochastically stirred nonlinear shallow water model.

14. Chen, G, and Isaac Held, 2007: Phase speed spectra and the recent poleward shift of Southern Hemisphere surface westerlies. Geophysical Research Letters, 34, L21805, doi:10.1029/2007GL031200.
    [ Abstract ]

    The poleward shift of the Southern Hemisphere surface westerlies in recent decades is examined in reanalysis data and in the output of coupled atmosphere-ocean and uncoupled atmospheric models. The space-time spectra of the eddy momentum fluxes in the upper troposphere reveal a trend that marks an increase in the eastward phase speed of the tropospheric eddies accompanied by a poleward displacement of the region of wave breaking in the subtropics. A dynamical mechanism is suggested that may help explain the connections among the lower stratospheric wind anomalies, the increased eastward propagation of tropospheric eddies and the poleward shift of the tropospheric circulation.

15. Christensen, J H., and Isaac Held, et al., 2007: Regional climate projections In Climate Change 2007: The Physical Science Basis, Cambridge University Press, Cambridge, UK, Cambridge University Press, 847-940.
16. Frierson, D M., Isaac Held, and Pablo Zurita-Gotor, May 2007: A gray-radiation aquaplanet moist GCM. Part II: Energy transports in altered climates. Journal of the Atmospheric Sciences, 64(5), doi:10.1175/JAS3913.1.
    [ Abstract ]

    A simplified moist general circulation model is used to study changes in the meridional transport of moist static energy by the atmosphere as the water vapor content is increased. The key assumptions of the model are gray radiation, with water vapor and other constituents having no effect on radiative transfer, and mixed layer aquaplanet boundary conditions, implying that the atmospheric meridional energy transport balances the net radiation at the top of the atmosphere. These simplifications allow the authors to isolate the effect of moisture on energy transports by baroclinic eddies in a relatively simple setting. The authors investigate the partition of moist static energy transport in the model into dry static energy and latent energy transports as water vapor concentrations are increased, by varying a constant in the Clausius–Clapeyron relation. The increase in the poleward moisture flux is rather precisely compensated by a reduction in the dry static energy flux. These results are interpreted with diffusive energy balance models (EBMs). The simplest of these is an analytic model that has the property of exact invariance of total energy flux as the moisture content is changed, but the assumptions underlying this model are not accurately satisfied by the GCM. A more complex EBM that includes expressions for the diffusivity, length scale, velocity scale, and latitude of maximum baroclinic eddy activity provides a better fit to the GCM’s behavior.

17. Garner, Stephen T., D M W Frierson, Isaac Held, O M Pauluis, and Geoffrey K Vallis, June 2007: Resolving convection in a global hypohydrostatic model. Journal of the Atmospheric Sciences, 64(6), doi:10.1175/JAS3929.1.
    [ Abstract ]

    Convection cannot be explicitly resolved in general circulation models given their typical grid size of 50 km or larger. However, by multiplying the vertical acceleration in the equation of motion by a constant larger than unity, the horizontal scale of convection can be increased at will, without necessarily affecting the larger-scale flow. The resulting hypohydrostatic system has been recognized for some time as a way to improve numerical stability on grids that cannot well resolve nonhydrostatic gravity waves. More recent studies have explored its potential for better representing convection in relatively coarse models. The recent studies have tested the rescaling idea in the context of regional models. Here the authors present global aquaplanet simulations with a low-resolution, nonhydrostatic model free of convective parameterization, and describe the effect on the global climate of very large rescaling of the vertical acceleration. As the convection expands to resolved scales, a deepening of the troposphere, a weakening of the Hadley cell, and a moistening of the lower troposphere is found, compared to solutions in which the moist convection is essentially hydrostatic. The growth rate of convective instability is reduced and the convective life cycle is lengthened relative to synoptic phenomena. This problematic side effect is noted in earlier studies and examined further here.

18. Held, Isaac, Ming Zhao, and Bruce Wyman, January 2007: Dynamic radiative-convective equilibria using GCM column physics. Journal of the Atmospheric Sciences, 64(1), 228-238.
    [ Abstract PDF ]

    The behavior of a GCM column physics package in a nonrotating, doubly periodic, homogeneous setting with prescribed SSTs is examined. This radiative–convective framework is proposed as a useful tool for studying some of the interactions between convection and larger-scale dynamics and the effects of differing modeling assumptions on convective organization and cloud feedbacks. For the column physics utilized here, from the Geophysical Fluid Dynamics Laboratory (GFDL) AM2 model, many of the properties of the homogeneous, nonrotating model are closely tied to the fraction of precipitation that is large-scale, rather than convective. Significant large-scale precipitation appears above a critical temperature and then increases with further increases in temperature. The amount of large-scale precipitation is a function of horizontal resolution and can also be controlled by modifying the convection scheme, as is illustrated here by modifying assumptions concerning entrainment into convective plumes. Significant similarities are found between the behavior of the homogeneous model and that of the Tropics of the parent GCM when ocean temperatures are increased and when the convection scheme is modified.

19. Held, Isaac, 2007: Progress and problems in large-scale atmospheric dynamics In The Global Circulation of the Atmosphere, T. Schneider and A. Sobel, eds., Princeton, NJ, Princeton University Press, 1-21.
20. Jiang, X, Ngar-Cheung Lau, Isaac Held, and Jeff J Ploshay, January 2007: Mechanisms of the Great Plains low-level jet as simulated in an AGCM. Journal of the Atmospheric Sciences, 64(2), doi:10.1175/JAS3847.1.
    [ Abstract ]

    A model diagnosis has been performed on the nocturnal Great Plains low-level jet (LLJ), which is one of the key elements of the warm season regional climate over North America. The horizontal–vertical structure, diurnal phase, and amplitude of the LLJ are well simulated by an atmospheric general circulation model (AGCM), thus justifying a reevaluation of the physical mechanisms for the formation of the LLJ based on output from this model. A diagnosis of the AGCM data confirms that two planetary boundary layer (PBL) processes, the diurnal oscillation of the pressure gradient force and of vertical diffusion, are of comparable importance in regulating the inertial oscillation of the winds, which leads to the occurrence of maximum LLJ strength during nighttime. These two processes are highlighted in the theories for the LLJ proposed by Holton (1967) and Blackadar (1957). A simple model is constructed in order to study the relative roles of these two mechanisms. This model incorporates the diurnal variation of the pressure gradient force and vertical diffusion coefficients as obtained from the AGCM simulation. The results reveal that the observed diurnal phase and amplitude of the LLJ can be attributed to the combination of these two mechanisms. The LLJ generated by either Holton’s or Blackadar’s mechanism alone is characterized by an unrealistic meridional phase shift and weaker amplitude. It is also shown that the diurnal phase of the LLJ exhibits vertical variations in the PBL, more clearly at higher latitudes, with the upper PBL wind attaining a southerly peak several hours earlier than the lower PBL. The simple model demonstrates that this phase tilt is due mainly to sequential triggering of the inertial oscillation from upper to lower PBL when surface cooling commences after sunset. At lower latitudes, due to the change of orientation of prevailing mean wind vectors and the longer inertial period, the inertial oscillation in the lower PBL tends to be interrupted by strong vertical mixing in the following day, whereas in the upper PBL, the inertial oscillation can proceed in a low-friction environment for a relatively longer duration. Thus, the vertical phase tilt initiated at sunset is less evident at lower latitudes.

21. Knutson, Thomas R., Joseph J Sirutis, Stephen T Garner, Isaac Held, and Robert E Tuleya, 2007: Simulation of the Recent Multidecadal Increase of Atlantic Hurricane Activity Using an 18-km-Grid Regional Model. Bulletin of the American Meteorological Society, 88(10), doi:10.1175/BAMS-88-10-1549.
    [ Abstract ]

    In this study, a new modeling framework for simulating Atlantic hurricane activity is introduced. The model is an 18-km-grid nonhydrostatic regional model, run over observed specified SSTs and nudged toward observed time-varying large-scale atmospheric conditions (Atlantic domain wavenumbers 0–2) derived from the National Centers for Environmental Prediction (NCEP) reanalyses. Using this “perfect large-scale model” approach for 27 recent August–October seasons (1980–2006), it is found that the model successfully reproduces the observed multidecadal increase in numbers of Atlantic hurricanes and several other tropical cyclone (TC) indices over this period. The correlation of simulated versus observed hurricane activity by year varies from 0.87 for basin-wide hurricane counts to 0.41 for U.S. landfalling hurricanes. For tropical storm count, accumulated cyclone energy, and TC power dissipation indices the correlation is 0.75, for major hurricanes the correlation is 0.69, and for U.S. landfalling tropical storms, the correlation is 0.57. The model occasionally simulates hurricanes intensities of up to category 4 (942 mb) in terms of central pressure, although the surface winds (< 47 m s^-1 ) do not exceed category-2 intensity. On interannual time scales, the model reproduces the observed ENSO-Atlantic hurricane covariation reasonably well. Some notable aspects of the highly contrasting 2005 and 2006 seasons are well reproduced, although the simulated activity during the 2006 core season was excessive. The authors conclude that the model appears to be a useful tool for exploring mechanisms of hurricane variability in the Atlantic (e.g., shear versus potential intensity contributions). The model may be capable of making useful simulations/projections of pre-1980 or twentieth-century Atlantic hurricane activity. However, the reliability of these projections will depend on obtaining reliable large-scale atmospheric and SST conditions from sources external to the model.

22. Lee, M-I, S D Schubert, M J Suarez, Isaac Held, A Kumar, T L Bell, J-K E Schemm, Ngar-Cheung Lau, Jeff J Ploshay, H-K Kim, and S-H Yoo, May 2007: Sensitivity to horizontal resolution in the AGCM simulations of warm season diurnal cycle of precipitation over the United States and Northern Mexico. Journal of Climate, 20(9), doi:10.1175/JCLI4090.1.
    [ Abstract ]

    This study examines the sensitivity of the North American warm season diurnal cycle of precipitation to changes in horizontal resolution in three atmospheric general circulation models, with a primary focus on how the parameterized moist processes respond to improved resolution of topography and associated local/regional circulations on the diurnal time scale. It is found that increasing resolution (from approximately 2° to ½° in latitude–longitude) has a mixed impact on the simulated diurnal cycle of precipitation. Higher resolution generally improves the initiation and downslope propagation of moist convection over the Rockies and the adjacent Great Plains. The propagating signals, however, do not extend beyond the slope region, thereby likely contributing to a dry bias in the Great Plains. Similar improvements in the propagating signals are also found in the diurnal cycle over the North American monsoon region as the models begin to resolve the Gulf of California and the surrounding steep terrain. In general, the phase of the diurnal cycle of precipitation improves with increasing resolution, though not always monotonically. Nevertheless, large errors in both the phase and amplitude of the diurnal cycle in precipitation remain even at the highest resolution considered here. These errors tend to be associated with unrealistically strong coupling of the convection to the surface heating and suggest that improved simulations of the diurnal cycle of precipitation require further improvements in the parameterizations of moist convection processes.

23. Lee, M-I, S D Schubert, M J Suarez, Isaac Held, Ngar-Cheung Lau, Jeff J Ploshay, A Kumar, H-K Kim, and J-K E Schemm, June 2007: An analysis of the warm-season diurnal cycle over the continental United States and Northern Mexico in general circulation models. Journal of Hydrometeorology, 8(3), doi:10.1175/JHM581.1.
    [ Abstract ]

    The diurnal cycle of warm-season rainfall over the continental United States and northern Mexico is analyzed in three global atmospheric general circulation models (AGCMs) from NCEP, GFDL, and the NASA Global Modeling Assimilation Office (GMAO). The results for each model are based on an ensemble of five summer simulations forced with climatological sea surface temperatures. Although the overall patterns of time-mean (summer) rainfall and low-level winds are reasonably well simulated, all three models exhibit substantial regional deficiencies that appear to be related to problems with the diurnal cycle. Especially prominent are the discrepancies in the diurnal cycle of precipitation over the eastern slopes of the Rocky Mountains and adjacent Great Plains, including the failure to adequately capture the observed nocturnal peak. Moreover, the observed late afternoon–early evening eastward propagation of convection from the mountains into the Great Plains is not adequately simulated, contributing to the deficiencies in the diurnal cycle in the Great Plains. In the southeast United States, the models show a general tendency to rain in the early afternoon—several hours earlier than observed. Over the North American monsoon region in the southwest United States and northern Mexico, the phase of the broad-scale diurnal convection appears to be reasonably well simulated, though the coarse resolution of the runs precludes the simulation of key regional phenomena. All three models employ deep convection schemes that assume fundamentally the same buoyancy closure based on simplified versions of the Arakawa–Schubert scheme. Nevertheless, substantial differences between the models in the diurnal cycle of convection highlight the important differences in their implementations and interactions with the boundary layer scheme. An analysis of local diurnal variations of convective available potential energy (CAPE) shows an overall tendency for an afternoon peak—a feature well simulated by the models. The simulated diurnal cycle of rainfall is in phase with the local CAPE variation over the southeast United States and the Rocky Mountains where the local surface boundary forcing is important in regulating the diurnal cycle of convection. On the other hand, the simulated diurnal cycle of rainfall tends to be too strongly tied to CAPE over the Great Plains, where the observed precipitation and CAPE are out of phase, implying that free atmospheric large-scale forcing plays a more important role than surface heat fluxes in initiating or inhibiting convection.

24. Seager, R, Mingfang Ting, Isaac Held, Y Kushnir, Jian Lu, G A Vecchi, H-P Huang, N Harnik, Ants Leetma, Ngar-Cheung Lau, C Li, Jennifer Velez, and N Naik, 2007: Model projections of an imminent transition to a more arid climate in southwestern North America. Science, 316(5828), doi:10.1126/science.1139601.
    [ Abstract ]

    How anthropogenic climate change will affect hydroclimate in the arid regions of southwestern North America has implications for the allocation of water resources and the course of regional development. Here we show that there is a broad consensus among climate models that this region will dry in the 21st century and that the transition to a more arid climate should already be under way. If these models are correct, the levels of aridity of the recent multiyear drought or the Dust Bowl and the 1950s droughts will become the new climatology of the American Southwest within a time frame of years to decades.

25. Zhang, Rong, Thomas L Delworth, and Isaac Held, 2007: Can the Atlantic Ocean drive the observed multidecadal variability in Northern Hemisphere mean temperature? Geophysical Research Letters, 34, L02709, doi:10.1029/2006GL028683.
    [ Abstract PDF ]

    While the Northern Hemisphere mean surface temperature has clearly warmed over the 20th century due in large part to increasing greenhouse gases, this warming has not been monotonic. The departures from steady warming on multidecadal timescales might be associated in part with radiative forcing, especially solar irradiance, volcanoes, and anthropogenic aerosols. It is also possible that internal oceanic variability explains a part of this variation. We report here on simulations with a climate model in which the Atlantic Ocean is constrained to produce multidecadal fluctuations similar to observations by redistributing heat within the Atlantic, with other oceans left free to adjust to these Atlantic perturbations. The model generates multidecadal variability in Northern Hemisphere mean temperatures similar in phase and magnitude to detrended observations. The results suggest that variability in the Atlantic is a viable explanation for a portion of the multidecadal variability in the Northern Hemisphere mean temperature record.

26. Delworth, Thomas L., Anthony J Broccoli, Anthony Rosati, Ronald J Stouffer, Ventakramani Balaji, J A Beesley, W F Cooke, Keith W Dixon, John Dunne, Krista A Dunne, J W Durachta, Kirsten L Findell, Paul Ginoux, Anand Gnanadesikan, C Tony Gordon, Stephen Griffies, Rich Gudgel, Matthew J Harrison, Isaac Held, Richard S Hemler, Larry Horowitz, Stephen A Klein, Thomas R Knutson, P J Kushner, A R Langenhorst, H C Lee, Shian-Jiann Lin, Jian Lu, S Malyshev, P C D Milly, V Ramaswamy, J L Russell, M Daniel Schwarzkopf, Elena Shevliakova, Joseph J Sirutis, Michael J Spelman, William F Stern, Michael Winton, Andrew T Wittenberg, Bruce Wyman, Fanrong Zeng, and Rong Zhang, 2006: GFDL's CM2 Global Coupled Climate Models. Part I: Formulation and Simulation Characteristics. Journal of Climate, 19(5), doi:10.1175/JCLI3629.1.
    [ Abstract ]

    The formulation and simulation characteristics of two new global coupled climate models developed at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL) are described. The models were designed to simulate atmospheric and oceanic climate and variability from the diurnal time scale through multicentury climate change, given our computational constraints. In particular, an important goal was to use the same model for both experimental seasonal to interannual forecasting and the study of multicentury global climate change, and this goal has been achieved. Two versions of the coupled model are described, called CM2.0 and CM2.1. The versions differ primarily in the dynamical core used in the atmospheric component, along with the cloud tuning and some details of the land and ocean components. For both coupled models, the resolution of the land and atmospheric components is 2° latitude × 2.5° longitude; the atmospheric model has 24 vertical levels. The ocean resolution is 1° in latitude and longitude, with meridional resolution equatorward of 30° becoming progressively finer, such that the meridional resolution is 1/3° at the equator. There are 50 vertical levels in the ocean, with 22 evenly spaced levels within the top 220 m. The ocean component has poles over North America and Eurasia to avoid polar filtering. Neither coupled model employs flux adjustments. The control simulations have stable, realistic climates when integrated over multiple centuries. Both models have simulations of ENSO that are substantially improved relative to previous GFDL coupled models. The CM2.0 model has been further evaluated as an ENSO forecast model and has good skill (CM2.1 has not been evaluated as an ENSO forecast model). Generally reduced temperature and salinity biases exist in CM2.1 relative to CM2.0. These reductions are associated with 1) improved simulations of surface wind stress in CM2.1 and associated changes in oceanic gyre circulations; 2) changes in cloud tuning and the land model, both of which act to increase the net surface shortwave radiation in CM2.1, thereby reducing an overall cold bias present in CM2.0; and 3) a reduction of ocean lateral viscosity in the extratropics in CM2.1, which reduces sea ice biases in the North Atlantic. Both models have been used to conduct a suite of climate change simulations for the 2007 Intergovernmental Panel on Climate Change (IPCC) assessment report and are able to simulate the main features of the observed warming of the twentieth century. The climate sensitivities of the CM2.0 and CM2.1 models are 2.9 and 3.4 K, respectively. These sensitivities are defined by coupling the atmospheric components of CM2.0 and CM2.1 to a slab ocean model and allowing the model to come into equilibrium with a doubling of atmospheric CO2. The output from a suite of integrations conducted with these models is freely available online (see http://nomads.gfdl.noaa.gov/). Manuscript received 8 December 2004, in final form 18 March 2005

27. Frierson, D M., Isaac Held, and Pablo Zurita-Gotor, 2006: A Gray-Radiation Aquaplanet moist GCM. Part I: Static stability and eddy scale. Journal of the Atmospheric Sciences, 63(10), doi:10.1175/JAS3753.1.
    [ Abstract ]

    In this paper, a simplified moist general circulation model is developed and used to study changes in the atmospheric general circulation as the water vapor content of the atmosphere is altered. The key elements of the model physics are gray radiative transfer, in which water vapor and other constituents have no effect on radiative fluxes, a simple diffusive boundary layer with prognostic depth, and a mixed layer aquaplanet surface boundary condition. This GCM can be integrated stably without a convection parameterization, with large-scale condensation only, and this study focuses on this simplest version of the model. These simplifications provide a useful framework in which to focus on the interplay between latent heat release and large-scale dynamics. In this paper, the authors study the role of moisture in determining the tropospheric static stability and midlatitude eddy scale. In a companion paper, the effects of moisture on energy transports by baroclinic eddies are discussed. The authors vary a parameter in the Clausius–Clapeyron relation to control the amount of water in the atmosphere, and consider circulations ranging from the dry limit to 10 times a control value. The typical length scale of midlatitude eddies is found to be remarkably insensitive to the amount of moisture in the atmosphere in this model. The Rhines scale evaluated at the latitude of the maximum eddy kinetic energy fits the model results for the eddy scale well. Moist convection is important in determining the extratropical lapse rate, and the dry stability is significantly increased with increased moisture content.

28. Gnanadesikan, Anand, Keith W Dixon, Stephen Griffies, Ventakramani Balaji, M Barreiro, J A Beesley, W F Cooke, Thomas L Delworth, R Gerdes, Matthew J Harrison, Isaac Held, William J Hurlin, H C Lee, Z Liang, G Nong, Ronald C Pacanowski, Anthony Rosati, J L Russell, Bonita L Samuels, Qian Song, Michael J Spelman, Ronald J Stouffer, C Sweeney, G A Vecchi, Michael Winton, Andrew T Wittenberg, Fanrong Zeng, Rong Zhang, and John Dunne, 2006: GFDL's CM2 Global Coupled Climate Models. Part II: The baseline ocean simulation. Journal of Climate, 19(5), doi:10.1175/JCLI3630.1.
    [ Abstract ]

    The current generation of coupled climate models run at the Geophysical Fluid Dynamics Laboratory (GFDL) as part of the Climate Change Science Program contains ocean components that differ in almost every respect from those contained in previous generations of GFDL climate models. This paper summarizes the new physical features of the models and examines the simulations that they produce. Of the two new coupled climate model versions 2.1 (CM2.1) and 2.0 (CM2.0), the CM2.1 model represents a major improvement over CM2.0 in most of the major oceanic features examined, with strikingly lower drifts in hydrographic fields such as temperature and salinity, more realistic ventilation of the deep ocean, and currents that are closer to their observed values. Regional analysis of the differences between the models highlights the importance of wind stress in determining the circulation, particularly in the Southern Ocean. At present, major errors in both models are associated with Northern Hemisphere Mode Waters and outflows from overflows, particularly the Mediterranean Sea and Red Sea.

29. Held, Isaac, and Brian J Soden, 2006: Robust responses of the hydrological cycle to global warming. Journal of Climate, 19(21), doi:10.1175/JCLI3990.1.
    [ Abstract ]

    Using the climate change experiments generated for the Fourth Assessment of the Intergovernmental Panel on Climate Change, this study examines some aspects of the changes in the hydrological cycle that are robust across the models. These responses include the decrease in convective mass fluxes, the increase in horizontal moisture transport, the associated enhancement of the pattern of evaporation minus precipitation and its temporal variance, and the decrease in the horizontal sensible heat transport in the extratropics. A surprising finding is that a robust decrease in extratropical sensible heat transport is found only in the equilibrium climate response, as estimated in slab ocean responses to the doubling of CO2 , and not in transient climate change scenarios. All of these robust responses are consequences of the increase in lower-tropospheric water vapor.

30. Held, Isaac, and Jian Lu, in press: On the plausibility of drying in the Sahel associated with global warming. Journal of Climate. 10/06.
    [ Abstract ]

    The Geophysical Fluid Dynamics Laboratory’s CM2.1 climate model simulates strong drying in the Sahel in response to increases in greenhouse gases. This response is not sensitive to the detailed spatial structure of the oceanic warming; the atmosphere/land component of this model, AM2.1, simulates a drying of the Sahel in response to a uniform warming of the ocean surface. We train a simple linear statistical model using the 20th century co-variability of Sahel rainfall and Atlantic and Indian sea surface temperatures in both the fully-coupled CM2.1 and in AM2.1 running over observed sea surface temperatures. This statistical model predicts the drying in the coupled model’s 21st century simulations. Comparison with the regressions obtained with observed precipitation and temperature fields supports the plausibility of a drying response over the Sahel as a consequence of increasing greenhouse gases. Repeating this procedure with a model that predicts a much wetter Sahel in the future, MIROC2.3(medres), the linear statistical fit trained on the models’ 20th century correctly predicts the sign of the model’s Sahel rainfall response in the 21st century, but the magnitude of the response is underestimated. The regression explains a much smaller fraction of the variance in the MIROC model as compared to CM2.1. A statistical model capable of reliably predicting a GCM’s 21st century Sahel rainfall from its SST-rainfall co-variability in the 20th century would provide a basis for a more definitive evaluation of model projections.

31. Knutson, Thomas R., Thomas L Delworth, Keith W Dixon, Isaac Held, Jian Lu, V Ramaswamy, M Daniel Schwarzkopf, G Stenchikov, and Ronald J Stouffer, 2006: Assessment of Twentieth-Century regional surface temperature trends using the GFDL CM2 coupled models. Journal of Climate, 19(9), doi:10.1175/JCLI3709.1.
    [ Abstract ]

    Historical climate simulations of the period 1861–2000 using two new Geophysical Fluid Dynamics Laboratory (GFDL) global climate models (CM2.0 and CM2.1) are compared with observed surface temperatures. All-forcing runs include the effects of changes in well-mixed greenhouse gases, ozone, sulfates, black and organic carbon, volcanic aerosols, solar flux, and land cover. Indirect effects of tropospheric aerosols on clouds and precipitation processes are not included. Ensembles of size 3 (CM2.0) and 5 (CM2.1) with all forcings are analyzed, along with smaller ensembles of natural-only and anthropogenic-only forcing, and multicentury control runs with no external forcing. Observed warming trends on the global scale and in many regions are simulated more realistically in the all-forcing and anthropogenic-only forcing runs than in experiments using natural-only forcing or no external forcing. In the all-forcing and anthropogenic-only forcing runs, the model shows some tendency for too much twentieth-century warming in lower latitudes and too little warming in higher latitudes. Differences in Arctic Oscillation behavior between models and observations contribute substantially to an underprediction of the observed warming over northern Asia. In the all-forcing and natural-only forcing runs, a temporary global cooling in the models during the 1880s not evident in the observed temperature records is volcanically forced. El Niño interactions complicate comparisons of observed and simulated temperature records for the El Chichón and Mt. Pinatubo eruptions during the early 1980s and early 1990s. The simulations support previous findings that twentieth-century global warming has resulted from a combination of natural and anthropogenic forcing, with anthropogenic forcing being the dominant cause of the pronounced late-twentieth-century warming. The regional results provide evidence for an emergent anthropogenic warming signal over many, if not most, regions of the globe. The warming signal has emerged rather monotonically in the Indian Ocean/western Pacific warm pool during the past half-century. The tropical and subtropical North Atlantic and the tropical eastern Pacific are examples of regions where the anthropogenic warming signal now appears to be emerging from a background of more substantial multidecadal variability.

32. Soden, Brian J., and Isaac Held, 2006: An Assessment of Climate Feedbacks in Coupled Ocean–Atmosphere Models. Journal of Climate, 19(14), doi:10.1175/JCLI3799.1.
    [ Abstract ]

    The climate feedbacks in coupled ocean–atmosphere models are compared using a coordinated set of twenty-first-century climate change experiments. Water vapor is found to provide the largest positive feedback in all models and its strength is consistent with that expected from constant relative humidity changes in the water vapor mixing ratio. The feedbacks from clouds and surface albedo are also found to be positive in all models, while the only stabilizing (negative) feedback comes from the temperature response. Large intermodel differences in the lapse rate feedback are observed and shown to be associated with differing regional patterns of surface warming. Consistent with previous studies, it is found that the vertical changes in temperature and water vapor are tightly coupled in all models and, importantly, demonstrate that intermodel differences in the sum of lapse rate and water vapor feedbacks are small. In contrast, intermodel differences in cloud feedback are found to provide the largest source of uncertainty in current predictions of climate sensitivity.

33. Stouffer, Ronald J., Thomas L Delworth, Keith W Dixon, Rich Gudgel, Isaac Held, Richard S Hemler, Thomas R Knutson, M Daniel Schwarzkopf, Michael J Spelman, Michael Winton, Anthony J Broccoli, H C Lee, Fanrong Zeng, and Brian J Soden, 2006: GFDL's CM2 Global Coupled Climate Models. Part IV: Idealized Climate Response. Journal of Climate, 19(5), doi:10.1175/JCLI3632.1.
    [ Abstract ]

    The climate response to idealized changes in the atmospheric CO2 concentration by the new GFDL climate model (CM2) is documented. This new model is very different from earlier GFDL models in its parameterizations of subgrid-scale physical processes, numerical algorithms, and resolution. The model was constructed to be useful for both seasonal-to-interannual predictions and climate change research. Unlike previous versions of the global coupled GFDL climate models, CM2 does not use flux adjustments to maintain a stable control climate. Results from two model versions, Climate Model versions 2.0 (CM2.0) and 2.1 (CM2.1), are presented. Two atmosphere–mixed layer ocean or slab models, Slab Model versions 2.0 (SM2.0) and 2.1 (SM2.1), are constructed corresponding to CM2.0 and CM2.1. Using the SM2 models to estimate the climate sensitivity, it is found that the equilibrium globally averaged surface air temperature increases 2.9 (SM2.0) and 3.4 K (SM2.1) for a doubling of the atmospheric CO2 concentration. When forced by a 1% per year CO2 increase, the surface air temperature difference around the time of CO2 doubling [transient climate response (TCR)] is about 1.6 K for both coupled model versions (CM2.0 and CM2.1). The simulated warming is near the median of the responses documented for the climate models used in the 2001 Intergovernmental Panel on Climate Change (IPCC) Working Group I Third Assessment Report (TAR). The thermohaline circulation (THC) weakened in response to increasing atmospheric CO2. By the time of CO2 doubling, the weakening in CM2.1 is larger than that found in CM2.0: 7 and 4 Sv (1 Sv 106 m3 s−1), respectively. However, the THC in the control integration of CM2.1 is stronger than in CM2.0, so that the percentage change in the THC between the two versions is more similar. The average THC change for the models presented in the TAR is about 3 or 4 Sv; however, the range across the model results is very large, varying from a slight increase (+2 Sv) to a large decrease (−10 Sv).

34. Sun, D-Z, T Zhang, C Covey, Stephen A Klein, W D Collins, J J Hack, J T Kiehl, G A Meehl, Isaac Held, and M J Suarez, 2006: Radiative and Dynamical Feedbacks over the Equatorial Cold Tongue: Results from Nine Atmospheric GCMs. Journal of Climate, 19(16), doi:10.1175/JCLI3835.1.
    [ Abstract ]

    The equatorial Pacific is a region with strong negative feedbacks. Yet coupled general circulation models (GCMs) have exhibited a propensity to develop a significant SST bias in that region, suggesting an unrealistic sensitivity in the coupled models to small energy flux errors that inevitably occur in the individual model components. Could this “hypersensitivity” exhibited in a coupled model be due to an underestimate of the strength of the negative feedbacks in this region? With this suspicion, the feedbacks in the equatorial Pacific in nine atmospheric GCMs (AGCMs) have been quantified using the interannual variations in that region and compared with the corresponding calculations from the observations. The nine AGCMs are the NCAR Community Climate Model version 1 (CAM1), the NCAR Community Climate Model version 2 (CAM2), the NCAR Community Climate Model version 3 (CAM3), the NCAR CAM3 at T85 resolution, the NASA Seasonal-to-Interannual Prediction Project (NSIPP) Atmospheric Model, the Hadley Centre Atmospheric Model (HadAM3), the Institut Pierre Simon Laplace (IPSL) model (LMDZ4), the Geophysical Fluid Dynamics Laboratory (GFDL) AM2p10, and the GFDL AM2p12. All the corresponding coupled runs of these nine AGCMs have an excessive cold tongue in the equatorial Pacific. The net atmospheric feedback over the equatorial Pacific in the two GFDL models is found to be comparable to the observed value. All other models are found to have a weaker negative net feedback from the atmosphere—a weaker regulating effect on the underlying SST than the real atmosphere. Except for the French (IPSL) model, a weaker negative feedback from the cloud albedo and a weaker negative feedback from the atmospheric transport are the two leading contributors to the weaker regulating effect from the atmosphere. The underestimate of the strength of the negative feedbacks by the models is apparently linked to an underestimate of the equatorial precipitation response. All models have a stronger water vapor feedback than that indicated in Earth Radiation Budget Experiment (ERBE) observations. These results confirm the suspicion that an underestimate of the regulatory effect from the atmosphere over the equatorial Pacific region is a prevalent problem. The results also suggest, however, that a weaker regulatory effect from the atmosphere is unlikely solely responsible for the hypersensitivity in all models. The need to validate the feedbacks from the ocean transport is therefore highlighted.

35. Vecchi, G A., Brian J Soden, Andrew T Wittenberg, Isaac Held, Ants Leetma, and Matthew J Harrison, 2006: Weakening of tropical Pacific atmospheric circulation due to anthropogenic forcing. Nature, 441(7089), 73-76.
    [ Abstract PDF ]

    Since the mid-nineteenth century the Earth's surface has warmed1, 2, 3, and models indicate that human activities have caused part of the warming by altering the radiative balance of the atmosphere1, 3. Simple theories suggest that global warming will reduce the strength of the mean tropical atmospheric circulation4, 5. An important aspect of this tropical circulation is a large-scale zonal (east–west) overturning of air across the equatorial Pacific Ocean—driven by convection to the west and subsidence to the east—known as the Walker circulation6. Here we explore changes in tropical Pacific circulation since the mid-nineteenth century using observations and a suite of global climate model experiments. Observed Indo-Pacific sea level pressure reveals a weakening of the Walker circulation. The size of this trend is consistent with theoretical predictions, is accurately reproduced by climate model simulations and, within the climate models, is largely due to anthropogenic forcing. The climate model indicates that the weakened surface winds have altered the thermal structure and circulation of the tropical Pacific Ocean. These results support model projections of further weakening of tropical atmospheric circulation during the twenty-first century4, 5, 7.

36. Wyant, M C., C S Bretherton, J T Bacmeister, J T Kiehl, Isaac Held, Ming Zhao, Stephen A Klein, and Brian J Soden, 2006: A comparison of low-latitude cloud properties and their response to climate change in three AGCMs sorted into regimes using mid-tropospheric vertical velocity. Climate Dynamics, 27(2-3), doi:10.1007/s00382-006-0138-4.
    [ Abstract ]

    Low-latitude cloud distributions and cloud responses to climate perturbations are compared in near-current versions of three leading U.S. AGCMs, the NCAR CAM 3.0, the GFDL AM2.12b, and the NASA GMAO NSIPP-2 model. The analysis technique of Bony et al. (Clim Dyn 22:71–86, 2004) is used to sort cloud variables by dynamical regime using the monthly mean pressure velocity ω at 500 hPa from 30S to 30N. All models simulate the climatological monthly mean top-of-atmosphere longwave and shortwave cloud radiative forcing (CRF) adequately in all ω-regimes. However, they disagree with each other and with ISCCP satellite observations in regime-sorted cloud fraction, condensate amount, and cloud-top height. All models have too little cloud with tops in the middle troposphere and too much thin cirrus in ascent regimes. In subsidence regimes one model simulates cloud condensate to be too near the surface, while another generates condensate over an excessively deep layer of the lower troposphere. Standardized climate perturbation experiments of the three models are also compared, including uniform SST increase, patterned SST increase, and doubled CO2 over a mixed layer ocean. The regime-sorted cloud and CRF perturbations are very different between models, and show lesser, but still significant, differences between the same model simulating different types of imposed climate perturbation. There is a negative correlation across all general circulation models (GCMs) and climate perturbations between changes in tropical low cloud cover and changes in net CRF, suggesting a dominant role for boundary layer cloud in these changes. For some of the cases presented, upper-level clouds in deep convection regimes are also important, and changes in such regimes can either reinforce or partially cancel the net CRF response from the boundary layer cloud in subsidence regimes. This study highlights the continuing uncertainty in both low and high cloud feedbacks simulated by GCMs.

37. Galewsky, J, A Sobel, and Isaac Held, 2005: Diagnosis of subtropical humidity dynamics using tracers of last saturation. Journal of the Atmospheric Sciences, 62(9), doi:10.1175/JAS3533.1.
    [ Abstract ]

    A technique for diagnosing the mechanisms that control the humidity in a general circulation model (GCM) or observationally derived meteorological analysis dataset is presented. The technique involves defining a large number of tracers, each of which represents air that has last been saturated in a particular region of the atmosphere. The time-mean tracer fields show the typical pathways that air parcels take between one occurrence of saturation and the next. The tracers provide useful information about how different regions of the atmosphere influence the humidity elsewhere. Because saturation vapor pressure is a function only of temperature and assuming mixing ratio is conserved for unsaturated parcels, these tracer fields can also be used together with the temperature field to reconstruct the water vapor field. The technique is first applied to an idealized GCM in which the dynamics are dry and forced using the Held-Suarez thermal relaxation, but the model carries a passive waterlike tracer that is emitted at the surface and lost due to large-scale condensation with zero latent heat release and no condensate retained. The technique provides an accurate reconstruction of the simulated water vapor field. In this model, the dry air in the subtropical troposphere is produced primarily by isentropic transport and is moistened somewhat by mixing with air from lower levels, which has not been saturated since last contact with the surface. The technique is then applied to the NCEP-NCAR reanalysis data from December-February (DJF) 2001/02, using the offline tracer transport model MATCH. The results show that the dryness of the subtropical troposphere is primarily controlled by isentropic transport of very dry air by midlatitude eddies and that diabatic descent from the tropical upper troposphere plays a secondary role in controlling the dryness of the subtropics.

38. Held, Isaac, 2005: The gap between simulation and understanding in climate modeling. Bulletin of the American Meteorological Society, 86(11), 1609-1614.
    [ Abstract PDF ]

    The problem of creating truly convincing numerical simulations of our Earth's climate will remain a challenge for the next generation of climate scientists. Hopefully, the ever increasing power of computers will make this task somewhat less frustrating than it is at present. But, increasing computational power also raises issues as to how we would like to see climate modeling and the study of climate dynamics evolve in the twenty-first century. One of the key issues we will need to address is the widening gap between simulation and understanding.

39. Held, Isaac, Thomas L Delworth, Jian Lu, Kirsten L Findell, and Thomas R Knutson, 2005: Simulation of Sahel drought in the 20th and 21st centuries. Proceedings of the National Academy of Sciences, 102(50), doi:10.1073/pnas.0509057102.
    [ Abstract ]

    The Sahel, the transition zone between the Saharan desert and the rainforests of Central Africa and the Guinean Coast, experienced a severe drying trend from the 1950s to the 1980s, from which there has been partial recovery. Continuation of either the drying trend or the more recent ameliorating trend would have far-ranging implications for the economy and ecology of the region. Coupled atmosphere/ocean climate models being used to simulate the future climate have had difficulty simulating Sahel rainfall variations comparable to those observed, thus calling into question their ability to predict future climate change in this region. We describe simulations using a new global climate model that capture several aspects of the 20th century rainfall record in the Sahel. An ensemble mean over eight realizations shows a drying trend in the second half of the century of nearly half of the observed amplitude. Individual realizations can be found that display striking similarity to the observed time series and drying pattern, consistent with the hypothesis that the observations are a superposition of an externally forced trend and internal variability. The drying trend in the ensemble mean of the model simulations is attributable to anthropogenic forcing, partly to an increase in aerosol loading and partly to an increase in greenhouse gases. The model projects a drier Sahel in the future, due primarily to increasing greenhouse gases.

40. Tian, B, Isaac Held, Ngar-Cheung Lau, and Brian J Soden, 2005: Diurnal cycle of summertime deep convection over North America: A satellite perspective. Journal of Geophysical Research, 110, D08108, doi:10.1029/2004JD005275.
    [ Abstract ]

    High-resolution (0.1�‹ �~ 0.1�‹) geostationary satellite infrared radiances at 11 ƒÊm in combination with gridded (2.5�‹ �~ 2.0�‹) hourly surface precipitation observations are employed to document the spatial structure of the diurnal cycle of summertime deep convection and associated precipitation over North America. Comparison of the diurnal cycle pattern between the satellite retrieval and surface observations demonstrates the reliability of satellite radiances for inferring the diurnal cycle of precipitation, especially the diurnal phase. On the basis of the satellite radiances, we find that over most land regions, deep convection peaks in the late afternoon and early evening, a few hours later than the peak of land surface temperature. However, strong regional variations exist in both the diurnal phase and amplitude, implying that topography, land-sea contrast, and coastline curvature play an important role in modulating the diurnal cycle. Examples of such effects are highlighted over Florida, the Great Plains, and the North American monsoon region.

41. Grianik, N, Isaac Held, K S Smith, and Geoffrey K Vallis, 2004: The effects of quadratic drag on the inverse cascade of two-dimensional turbulence. Physics of Fluids, 16(1), 73-78.
    [ Abstract ]

    We explore the effects of a quadratic drag, similar to that used in bulk aerodynamic formulas, on the inverse cascade of homogeneous two-dimensional turbulence. If a two-dimensional fluid is forced at a relatively small scale, then an inverse cascade of energy will be generated that may then be arrested by such a drag at large scales. Both scaling arguments and numerical experiments support the idea that in a statistically steady state the length scale of energy-containing eddies will not then depend on the energy input to the system; rather, the only external parameter that defines this scale is the quadratic drag coefficient itself. A universal form of the spectrum is suggested, and numerical experiments are in good agreement. Further, the turbulent transfer of a passive tracer in the presence of a uniform gradient is well predicted by scaling arguments based solely on the energy cascade rate and the nonlinear drag coefficient.

42. Lapeyre, G, and Isaac Held, 2004: The role of moisture in the dynamics and energetics of turbulent baroclinic eddies. Journal of the Atmospheric Sciences, 61(14), 1693-1710.
    [ Abstract PDF ]

    The effects of moisture on nonlinear baroclinic eddies are examined in the context of a horizontally homogeneous two-layer quasigeostrophic model. Using an explicit equation for moisture and a simple parameterization of latent heat release, the present study focuses on how moisture affects the statistically steady state of a baroclinically unstable flow. It is shown that, when latent heating is weak, the flow is dominated by jets and baroclinic waves, just as in the corresponding dry model. In this regime, the concept of an effective static stability can be used, which allows one to interpret some aspects of the moist simulations in terms of an equivalent dry model. It is found that a useful way of diagnosing the effective static stability is by relating it to the eddy fluxes of moisture and moist potential vorticity; no a priori theory for its value is presented here. As the strength of latent heating is increased, the flow rather suddenly becomes vortex dominated, with an asymmetry between strong low-level cyclones and weak anticyclones that has no analog in the dry model. It is argued that this asymmetry develops because of a correlation between low-level vorticity and moisture that results from the correlated horizontal transports of moisture and vorticity. The energetics of the simulations and the efficiency of energy production by latent heat release are discussed.

43. Shell, K M., and Isaac Held, 2004: Abrupt transition to strong superrotation in an axisymmetric model of the upper troposphere. Journal of the Atmospheric Sciences, 61(23), 2928-2935.
    [ Abstract PDF ]

    Abrupt transitions to strongly superrotating states have been found in some idealized models of the troposphere. These transitions are thought to be caused by feedbacks between the eddy momentum flux convergence in low latitudes and the strength of the equatorial flow. The behavior of an axisymmetric shallow-water model with an applied tropical torque is studied here to determine if an abrupt transition can be realized without eddy feedbacks. The upper-tropospheric layer is relaxed to a radiative equilibrium thickness, exchanging mass and thus momentum with the nonmoving lower layer. For low values of the applied torque, the circulation is earthlike; however, for larger values, an abrupt transition to a strongly superrotating state can occur. In some cases, the system remains superrotating as the torque is subsequently decreased. A simple analytical model is used to better understand the system. The bifurcation is caused by a feedback between the applied torque and the strength of the Hadley cell. As the torque increases, the strength of the cell decreases, reducing the damping caused by momentum transfer from the lower layer.

44. Lapeyre, G, and Isaac Held, 2003: Diffusivity, kinetic energy dissipation, and closure theories for the poleward eddy heat flux. Journal of the Atmospheric Sciences, 60(23), 2907-2916.
    [ Abstract PDF ]

    Diffusive eddy closure theory for estimating the poleward heat flux is reexamined and tested in the context of a two-layer homogeneous model. Consideration of the inverse energy cascade induced by baroclinic turbulence on the β plane leads to an expression for diffusivity in terms of the kinetic energy dissipation and the β effect. A key step in the closure is the identification of this diffusivity with that for potential vorticity in the lower of the two layers in the model. This assumption is then combined with an exact expression relating the diffusivity to the baroclinic energy generation and the mean vertical shear. The theory is closed by identifying the kinetic energy dissipation entering the inverse cascade argument with the baroclinic energy production. It is found that the first constraint in isolation based on inverse cascade arguments between the diffusivity of lower-layer potential vorticity and the kinetic energy dissipation is robust and accurate, whereas the final theory relating diffusivity to vertical shear remains useful but has somewhat degraded accuracy and is more sensitive to model parameters, such as numerical resolution and small-scale dissipation. In the limit of large supercriticality, this theory reduces to that of Held and Larichev. However, it is much more accurate in reproducing numerical results from a two-layer homogeneous model on a β plane for the moderate supercriticalities that are typical of model atmospheres. The problems involved in generalizing this result to models with more layers on the vertical or with a continuous stratification are discussed.

45. Schneider, T, Isaac Held, and Stephen T Garner, 2003: Boundary effects in potential vorticity dynamics. Journal of the Atmospheric Sciences, 60(8), 1024-1040.
    [ Abstract PDF ]

    Many aspects of geophysical flows can be described compactly in terms of potential vorticity dynamics. Since potential temperature can fluctuate at boundaries, however, the boundary conditions for potential vorticity dynamics are inhomogeneous, which complicates considerations of potential vorticity dynamics when boundary effects are dynamically significant. A formulation of potential vorticity dynamics is presented that encompasses boundary effects. It is shown that, for arbitrary flows, the generalization of the potential vorticity concept to a sum of the conventional interior potential vorticity and a singular surface potential vorticity allows one to replace the inhomogeneous boundary conditions for potential vorticity dynamics by simpler homogeneous boundary conditions (of constant potential temperature). Functional forms of the surface potential vorticity are derived from field equations in which the potential vorticity and a potential vorticity flux appear as sources of flow quantities in the same way in which an electric charge and an electric current appear as sources of fields in electrodynamics. For the generalized potential vorticity of flows that need be neither balanced nor hydrostatic and that can be influenced by diabatic processes and friction, a conservation law holds that is similar to the conservation law for the conventional interior potential vorticity. The conservation law for generalized potential vorticity contains, in the quasigeostrophic limit, the well-known dual relationship between fluctuations of potential temperature at boundaries and fluctuations of potential vorticity in the interior of quasigeostrophic flows. A nongeostrophic effect described by the conservation law is the induction of generalized potential vorticity by baroclinicity at boundaries, an effect that plays a role, for example, in mesoscale flows past topographic obstacles. Based on the generalized potential vorticity concept, a theory is outlined of how a wake with lee vortices can form in weakly dissipative flows past a mountain. Theoretical considerations and an analysis of a simulation show that a wake with lee vortices can form by separation of a generalized potential vorticity sheet from the mountain surface, similar to the separation of a friction-induced vorticity sheet from an obstacle, except that the generalized potential vorticity sheet can be induced by baroclinicity at the surface.

46. Held, Isaac, Mingfang Ting, and H Wang, 2002: Northern winter stationary waves: theory and modeling. Journal of Climate, 15(16), 2125-2144.
    [ Abstract PDF ]

    A review is provided of stationary wave theory, the theory for the deviations from zonal symmetry of the climate. To help focus the discussion the authors concentrate exclusively on northern winter. Several theoretical issues, including the external Rossby wave dispersion relation and vertical structure, critical latitude absorption, the nonlinear response to orography, and the interaction of forced wave trains with preexisting zonal asymmetries, are chosen for discussion while simultaneously presenting a decomposition of the wintertime stationary wave field using a nonlinear steady-state model.

47. Pauluis, O M., and Isaac Held, 2002: Entropy budget of an atmosphere in radiative-convective equilibrium. Part I: Maximum work and frictional dissipation. Journal of the Atmospheric Sciences, 59(2), 125-139.
    [ Abstract PDF ]

    The entropy budget of an atmosphere in radiative-convective equilibrium is analyzed here. The differential heating of the atmosphere, resulting from surface heat fluxes and tropospheric radiative cooling, corresponds to a net entropy sink. In statistical equilibrium, this entropy sink is balanced by the entropy production due to various irreversible processes such as frictional dissipation, diffusion of heat, diffusion of water vapor, and irreversible phase changes. Determining the relative contribution of each individual irreversible process to the entropy budget can provide important information on the behavior of convection. The entropy budget of numerical simulations with a cloud ensemble model is discussed. In these simulations, it is found that the dominant irreversible entropy source is associated with irreversible phase changes and diffusion of water vapor. In addition, a large fraction of the frictional dissipation results from falling precipitation, and turbulent dissipation accounts for only a small fraction of the entropy production. This behavior is directly related to the fact that the convective heat transport is mostly due to the latent heat transport. In such cases, moist convection acts more as an atmospheric dehumidifier than as a heat engine. The amount of work available to accelerate convective updrafts and downdrafts is much smaller than predicted by studies that assume that moist convection behaves mostly as a perfect heat engine.

48. Pauluis, O M., and Isaac Held, 2002: Entropy budget of an atmosphere in radiative-convective equilibrium. Part II: Latent heat transport and moist processes. Journal of the Atmospheric Sciences, 59(2), 140-149.
    [ Abstract PDF ]

    In moist convection, atmospheric motions transport water vapor from earth's surface to the regions where condensation occurs. This transport is associated with three other aspects of convection: the latent heat transport, the expansion work performed by water vapor, and the irreversible entropy production due to diffusion of water vapor and phase changes. An analysis of the thermodynamic transformations of atmospheric water yields what is referred to as the entropy budget of the water substance, providing a quantitative relationship between these three aspects of moist convection. The water vapor transport can be viewed as an imperfect heat engine that produces less mechanical work than the corresponding Carnot cycle because of diffusion of water vapor and irreversible phase changes. The entropy budget of the water substance provides an alternative method of determining the irreversible entropy production due to phase changes and diffusion of water vapor. This method has the advantage that it does not require explicit knowledge of the relative humidity or of the molecular flux of water vapor for the estimation of the entropy production. Scaling arguments show that the expansion work of water vapor accounts for a small fraction of the work that would be produced in the absence of irreversible moist processes. It is also shown that diffusion of water vapor and irreversible phase changes can be interpreted as the irreversible counterpart to the continuous dehumidification resulting from condensation and precipitation. This leads to a description of moist convection where it acts more as an atmospheric dehumidifier than as a heat engine.

49. Smith, K S., G Boccaletti, C C Henning, I Marinov, C-Y Tam, Isaac Held, and Geoffrey K Vallis, 2002: Turbulent diffusion in the geostrophic inverse cascade. Journal of Fluid Mechanics, 469, 13-48.
    [ Abstract PDF ]

    Motivated in part by the problem of large-scale lateral turbulent heat transport in the Earth's atmosphere and oceans, and in part by the problem of turbulent transport itself, we seek to better understand the transport of a passive tracer advected by various types of fully developed two-dimensional turbulence. The types of turbulence considered correspond to various relationships between the streamfunction and the advected field. Each type of turbulence considered possesses two quadratic invariants and each can develop an inverse cascade. These cascades can be modified or halted, for example, by friction, a background vorticity gradient or a mean temperature gradient. We focus on three physically realizable cases: classical two-dimensional turbulence, surface quasi-geostrophic turbulence, and shallow-water quasi-geostrophic turbulence at scales large compared to the radius of deformation. In each model we assume that tracer variance is maintained by a large-scale mean tracer gradient while turbulent energy is produced at small scales via random forcing, and dissipated by linear drag. We predict the spectral shapes, eddy scales and equilibrated energies resulting from the inverse cascades, and use the expected velocity and length scales to predict integrated tracer fluxes. When linear drag halts the cascade, the resulting diffusivities are decreasing functions of the drag coefficient, but with different dependences for each case. When [beta] is significant, we find a clear distinction between the tracer mixing scale, which depends on [beta] but is nearly independent of drag, and the energy-containing (or jet) scale, set by a combination of the drag coefficient and [beta]. Our predictions are tested via high- resolution spectral simulations. We find in all cases that the passive scalar is diffused down-gradient with a diffusion coefficient that is well-predicted from estimates of mixing length and velocity scale obtained from turbulence phenomenology.

50. Sobel, A, Isaac Held, and C S Bretherton, 2002: The ENSO signal in tropical tropospheric temperature. Journal of Climate, 15(18), 2702-2706.
    [ Abstract PDF ]

    Interannual anomalies in tropical tropospheric temperature have been shown to be related to interannual anomalies in tropical mean sea surface temperature (SST) by a simple moist adiabatic relationship. On physical grounds, it is less obvious than it might at first seem that this should be the case. It is expected that the free-tropospheric temperature should be sensitive primarily to SST anomalies in regions in which the mean SST is high and deep convection is frequent, rather than to the tropical mean SST. The tropical mean also includes nonconvecting regions in which the SST has no direct way of influencing the free troposphere. However, interannual anomalies of SST averaged over regions of high monthly mean precipitation are very similar to interannual anomalies of tropical mean SST. Empirical orthogonal function analysis of the monthly SST histograms for the period of 1982–98 reveals a leading mode, well separated from the others, whose structure is very similar to a simple shift of the annual and climatological mean histogram, without change of shape. As a consequence, many different ways of sampling the histogram will yield similar anomaly time series, and the adequacy of the mean SST for predicting the tropospheric temperature appears coincidental from the point of view of the uncoupled atmospheric problem with given SST. There is a suggestion in the results that changes in the histogram shape may be significant for the tropospheric temperature anomalies associated with some large El Niño events and that in those events it is indeed the SST anomalies in the convective regions that are most important in controlling the tropospheric temperature.

51. Held, Isaac, 2001: The partitioning of the poleward energy transport between the tropical ocean and atmosphere. Journal of the Atmospheric Sciences, 58(8), 943-948.
    [ Abstract PDF ]

    The mass transport in the shallow, wind-driven, overturning cells in the tropical oceans is constrained to be close to the mass transport in the atmospheric Hadley cell, assuming that zonally integrated wind stresses on land are relatively small. Therefore, the ratio of the poleward energy transport in low latitudes in the two media is determined by the ratio of the atmospheric gross static stability to that of the ocean. A qualitative discussion of the gross stability of each medium suggests that the resulting ratio of oceanic to atmospheric energy transport, averaged over the Hadley cell, is roughly equal to the ratio of the heat capacity of water to that of air at constant pressure, multiplied by the ratio of the moist- to the dry-adiabatic lapse rates near the surface. The ratio of oceanic to atmospheric energy transport should be larger than this value near the equator and smaller than this value near the poleward boundary of the Hadley cell.

52. Kushner, P J., Isaac Held, and Thomas L Delworth, 2001: Southern Hemisphere atmospheric circulation response to global warming. Journal of Climate, 14(10), 2238-2249.
    [ Abstract PDF ]

    The response of the Southern Hemisphere (SH), extratropical, atmospheric general circulation to transient, anthropogenic, greenhouse warming is investigated in a coupled climate model. The extratropical circulation response consists of a SH summer half-year poleward shift of the westerly jet and a year-round positive wind anomaly in the stratosphere and the tropical upper troposphere. Along with the poleward shift of the jet, there is a poleward shift of several related fields, including the belt of eddy momentum-flux convergence and the mean meridional overturning in the atmosphere and in the ocean. The tropospheric wind response projects strongly onto the model's "Southern Annular Mode" (also known as the "Antarctic oscillation"), which is the leading pattern of variability of the extratropical zonal winds.

53. Pauluis, O M., Ventakramani Balaji, and Isaac Held, 2001: Reply. Journal of the Atmospheric Sciences, 58(9), 1178-1179.
54. Schneider, T, and Isaac Held, 2001: Discriminants of Twentieth-Century changes in earth surface temperatures. Journal of Climate, 14(3), 249-254.
    [ Abstract PDF ]

    An approach to identifying climate changes is presented that does not hinge on simulations of natural climate variations or anthropogenic changes. Observed interdecadal climate variations are decomposed into several discriminants, mutually uncorrelated spatiotemporal components with a maximal ratio of interdecadal-to-intradecadal variance. The dominant discriminants of twentieth-century variations in surface temperature exhibit large-scale warming in which, particularly in the Northern Hemisphere summer months, localized cooling is embedded. The structure of the large-scale warming is consistent with expected effects of increases in greenhouse gas concentrations. The localized cooling, with maxims on scales of 1000-2000 km over East Asia, eastern Europe, and North America, is suggestive of radiative effects of anthropogenic sulfate aerosols.

55. Stocker, T F., Thomas L Delworth, Stephen Griffies, Isaac Held, V Ramaswamy, and Brian J Soden, et al., 2001: Physical climate processes and feedbacks In Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge, UK, Cambridge University Press, 418-470.
56. Held, Isaac, and Brian J Soden, 2000: Water vapor feedback and global warming. Annual Review of Energy and the Environment, 25, 441-475.
    [ Abstract PDF ]

    Water vapor is the dominant greenhouse gas, the most important gaseous source of infrared opacity in the atmosphere. As the concentrations of other greenhouse gases, particularly carbon dioxide, increase because of human activity, it is centrally important to predict how the water vapor distribution will be affected. To the extent that water vapor concentrations increase in a warmer world, the climatic effects of the other greenhouse gases will be amplified. Models of the Earth's climate indicate that this is an important positive feedback that increases the sensitivity of surface temperatures to carbon dioxide by a factor of two when considered in isolation from other feedbacks, and possibly by as much as a factor of three or more when interactions with other feedbacks are considered. Critics of this consensus have attempted to provide reasons why modeling results are overestimating the strength of this feedback. Our uncertainty concerning climate sensitivity is disturbing. The range most often quoted for the equilibrium global mean surface temperature response to a doubling of CO2 concentrations in the atmosphere is 1.5°C to 4.5°C. If the Earth lies near the upper bound of this sensitivity range, climate changes in the twenty-first century will be profound. The range in sensitivity is primarily due to differing assumptions about how the Earth's cloud distribution is maintained; all the models on which these estimates are based possess strong water vapor feedback. If this feedback is, in fact, substantially weaker than predicted in current models, sensitivities in the upper half of this range would be much less likely, a conclusion that would clearly have important policy implications. In this review, we describe the background behind the prevailing view on water vapor feedback and some of the arguments raised by its critics, and attempt to explain why these arguments have not modified the consensus within the climate research community.

57. Pauluis, O M., Ventakramani Balaji, and Isaac Held, 2000: Frictional dissipation in a precipitating atmosphere. Journal of the Atmospheric Sciences, 57(7), 989-994.
    [ Abstract PDF ]

    The frictional dissipation in the shear zone surrounding falling hydrometeors is estimated to be 2-4 W m-2 in the Tropics. A numerical model of radiative-convective equilibrium with resolved three-dimensional moist convection confirms this estimate and shows that the precipitation-related dissipation is much larger than the dissipation associated with the turbulent energy cascade from the convective scale. Equivalently, the work performed by moist convection is used primarily to lift water rather than generate kinetic energy of the convective airflow. This fact complicates attempts to use the entropy budget to derive convective velocity scales.

58. Delworth, Thomas L., Anthony J Broccoli, Keith W Dixon, Isaac Held, Thomas R Knutson, P J Kushner, Michael J Spelman, Ronald J Stouffer, K Y Vinnikov, and Richard T Wetherald, 1999: Coupled climate modelling at GFDL: Recent accomplishments and future plans. Clivar Exchanges, 4(4), 15-20.
    [ PDF ]
59. Held, Isaac, 1999: The macroturbulence of the troposphere. Tellus, 51A-B(1), 59-70.
    [ Abstract PDF ]

    Eddy length scales, eddy velocity scales, and the amplitude of eddy fluxes in the mid-latitude troposphere are discussed, primarily from the qualitative perspective provided by studies of quasi-geostrophic turbulence. The utility of a diffusive picture for the near surface poleward flux of heat is emphasized, as is the extent to which a full closure theory for the troposphere, including the interior potential vorticity fluxes, must revolve around this theory for the heat flux. A central problem in general circulation theory is then to determine which factors control the horizontal diffusivity near the surface. The baroclinic eddy production problem has distinctive features that make it stand out from other inhomogeneous turbulence problems such as Benard convection and laboratory shear flows, the crucial point being that there can be scale separation between the eddies and the scale of the mean flow inhomogeneity in the direction of the relevant transport. This scale separation makes diffusive closures more compelling. In addition, it allows one to compute diffusivities from models of homogeneous turbulence.

60. Held, Isaac, 1999: Planetary waves and their interaction with smaller scales In The Life Cycles of Extratropical Cyclones, Boston, MA, American Meteorological Society, 101-109.
61. Held, Isaac, and T Schneider, 1999: The surface branch of the zonally averaged mass transport circulation in the troposphere. Journal of the Atmospheric Sciences, 56(11), 1688-1697.
    [ Abstract PDF ]

    The near-surface branch of the overturning mass transport circulation in the troposphere, containing the equatorward flow, is examined in isentropic and geometric coordinates. A discussion of the zonal momentum balance within isentropic layers shows that the equatorward flow at a given latitude is confined to isentropic layers that typically intersect the surface at that latitude. As a consequence of mass transport within the surface mixed layer, much of the equatorward flow occurs in layers with potential temperatures below the mean surface potential temperature. In the conventional transformed Eulerian mean formulation for geometric coordinates, the surface branch of the overturning circulation is represented in an unrealistic manner: streamlines of the residual circulation do not close above the surface. A modified residual circulation is introduced that is free from this defect and has the additional advantage that its computation, unlike that of the convential residual circulation, does not require division by the static stability, which may approach zero in the planetary boundary layer. It is then argued that cold air advection by the residual circulation is responsible for the formation of surface inversions at all latitudes in idealized GCMs with weak thermal damping. Also included is a discussion of how a general circulation theory for the troposphere must be built upon a theory for the near-surface meridional mass fluxes.

62. Kushner, P J., and Isaac Held, 1999: Potential vorticity thickness fluxes and wave-mean flow interaction. Journal of the Atmospheric Sciences, 56(7), 948-958.
    [ Abstract PDF ]

    The use of eddy flux of thickness between density surfaces has become a familiar starting point in oceanographic studies of adiabatic eddy effects on the mean density distribution. In this study, a dynamical analogy with the density thickness flux approach is explored to reexamine the theory of nonzonal wave-mean flow interaction in two-dimensional horizontal flows. By analogy with the density thickness flux, the flux of thickness between potential vorticity (PV) surfaces is used as a starting point for a residual circulation formulation for nonzonal mean flows. Mean equations for barotropic PV dynamics are derived in which a modified mean velocity with an eddy-induced component advects a modified mean PV that also has an eddy-induced component. For small-amplitude eddies, the results are analogous to recent results of McDougall and McIntosh derived for stratified flow. The dynamical implications of this approach are then examined. The modified mean PV equation provides a decomposition of the eddy forcing of the mean flow into contributions from wave transience, wave dissipation, and wave-induced mass redistribution between PV contours. If the mean flow is along the mean PV contours, the contribution from wave-induced mass redistribution is "workless" in Plumb's sense that it is equivalent to an eddy-induced stress that is perpendicular to the mean flow. This contribution is also associated with the convergence along the mean streamlines of a modified PV flux that is equal to the difference between the PV flux and the rotational PV flux term identified by Illari and Marshall. The cross-stream component of the modified PV flux is related to wave transience and dissipation.

63. Zhang, Y, and Isaac Held, 1999: A linear stochastic model of a GCM's midlatitude storm tracks. Journal of the Atmospheric Sciences, 56(19), 3416-3435.
    [ Abstract PDF ]

    A linear stochastic model is used to simulate the midlatitude storm tracks produced by an atmospheric GCM. A series of six perpetual insolation/SST GCM experiments are first performed for each month. These experiments capture the "midwinter suppression" of the Pacific storm track in a particularly clean way. The stochastic model is constructed by linearizing the GCM about its January climatology and finding damping and stirring parameters that best reproduce that model's eddy statistics. The model is tested by examining its ability to simulate other GCM integrations when the basic state is changed to the mean flow of those models, while keeping the stirring and damping unchanged. The stochastic model shows an impressive ability to simulate a variety of eddy statistics. It captures the midwinter suppression of the Pacific storm track qualitatively and is also capable of simulating storm track responses to El Niño. The model results are sensitive to the manner in which the model is stirred. Best results for eddy variances and fluxes are obtained by stirring the temperature and vorticity at low levels. However, a better simulation of the spatial structure of the dominant wave train as defined by covariance maps is obtained by stirring the temperature equation only, and at all levels.

64. Kushner, P J., and Isaac Held, 1998: A test, using atmospheric data, of a method for estimating oceanic eddy diffusivity. Geophysical Research Letters, 25(22), 4213-4216.
    [ Abstract PDF ]

    G. Holloway has proposed a simple method to estimate the effective horizontal eddy diffusivity for oceanic tracers using satellite measurements of sea-surface height variability. In this method, the diffusivity is assumed to scale as the r.m.s. eddy geostrophic streamfunction. This method should apply analogously in an atmospheric context, in which the energetic eddies are well resolved in data sets and models, and in which both the effective diffusivity and tracer fluxes can be directly calculated. We evaluate Holloway's method using lower-tropospheric daily atmospheric reanalysis data, and find that at a given height the method successfully yields estimates of the divergent part of the atmospheric sensible heat flux, to within a fairly uniform scaling factor

65. Swanson, K L., P J Kushner, and Isaac Held, 1997: Dynamics of barotropic storm tracks. Journal of the Atmospheric Sciences, 54(7), 791-810.
    [ Abstract PDF ]

    Longitudinal variations in the upper-troposphere time-mean flow strongly modulate the structure and amplitude of upper-tropospheric eddies. This barotropic modulation is studied using simple models of wave propagation through zonally varying basic states that consist of contours separating regions of uniform barotropic potential vorticity. Such basic states represent in a simple manner the potential vorticity distribution in the upper troposphere. Predictions of the effect of basic-state zonal variations on the amplitude and spatial structure of eddies and their associated particle displacements are made using conservation of wave action or, equivalently, the linearized "pseudoenergy" wave activity. The predictions are confirmed using WKB theory and linear numerical calculations. The interaction of finite-amplitude disturbances with the basic flow is also analyzed numerically using nonlinear contour-dynamical simulations. It is found that breaking nonlinear contour waves undergo irreversible amplitude attenuation, scale lengthening, and frequency lowering upon passing through a region of weak basic-state flow.

66. Treguier, A M., Isaac Held, and V D Larichev, 1997: Parameterization of quasigeostrophic eddies in primitive equation ocean models. Journal of Physical Oceanography, 27(4), 567-580.
    [ Abstract PDF ]

    A parameterization of mesoscale eddy fluxes in the ocean should be consistent with the fact that the ocean interior is nearly adiabatic. Gent and McWilliams have described a framework in which this can be approximated in z-coordinate primitive equation models by incorporating the effects of eddies on the buoyancy field through an eddy-induced velocity. It is also natural to base a parameterization on the simple picture of the mixing of potential vorticity in the interior and the mixing of buoyancy at the surface. The authors discuss the various constraints imposed by these two requirements and attempt to clarify the appropriate boundary conditions on the eddy-induced velocities at the surface. Quasigeostrophic theory is used as a guide to the simplest way of satisfying these constraints.

67. Held, Isaac, and V D Larichev, 1996: A scaling theory for horizontally homogeneous, baroclinically unstable flow on a Beta plane. Journal of the Atmospheric Sciences, 53(7), 946-952.
    [ PDF ]
68. Kushnir, Y, and Isaac Held, 1996: Equilibrium atmospheric response to North Atlantic SST anomalies. Journal of Climate, 9(6), 1208-1220.
    [ Abstract PDF ]

    The equilibrium general circulation model (GCM) response to sea surface temperature (SST) anomalies in the western North Atlantic region is studied. A coarse resolution GCM, with realistic lower boundary conditions including topography and climatological SST distribution, is integrated in perpetual January and perpetual October modes, distinguished from one another by the strength of the midlatitude westerlies. An SST anomaly with a maximum of 4°C is added to the climatological SST distribution of the model with both positive and negative polarity. These anomaly runs are compared to one another, and to a control integration, to determine the atmospheric response. In all cases warming (cooling) of the midlatitude ocean surface yields a warming (cooling) of the atmosphere over and to the the east of the SST anomaly center. The atmospheric temperature change is largest near the surface and decreases upward. Consistent with this simple thermal response, the geopotential height field displays a baroclinic response with a shallow anomalous low somewhat downstream from the warm SST anomaly. The equivalent barotropic, downstream response is weak and not robust. To help interpret the results, the realistic GCM integrations are compared with parallel idealized model runs. The idealized model has full physics and a similar horizontal and vertical resolution, but an all-ocean surface with a single, permanent zonal asymmetry. The idealized and realistic versions of the GCM display compatible response patterns that are qualitatively consistent with stationary, linear, quasigeostrophic theory. However, the idealized model response is stronger and more coherent. The differences between the two model response patterns can be reconciled based on the size of the anomaly, the model treatment of cloud-radiation interaction, and the static stability of the model atmosphere in the vicinity of the SST anomaly. Model results are contrasted with other GCM studies and observations.

69. Pavan, V, and Isaac Held, 1996: The diffusive approximation for eddy fluxes in baroclinically unstable jets. Journal of the Atmospheric Sciences, 53(9), 1262-1272.
    [ Abstract PDF ]

    A series of statistically steady states for baroclinically unstable jets in a two-layer quasigeostrophic model is examined, in order to evaluate diffusive approximation to the eddy potential vorticity or heat fluxes. The flow is forced by thermal relaxation to an unstable "radiative equilibrium" temperature gradient. The statistically steady states are studied as a function of the width of the radiative equilibrium jet. A local diffusive "theory" for the eddy fluxes is obtained from integrations of a homogenous, doubly periodic model with prescribed environmental potential vorticity gradients. The flux-gradient relationship generated by the homogenous model predicts the magnitude and shape fo the eddy fluxes in the unstable jet flows remarkably well, as long as the jet is not too narrow. The results confirm the relevance of diffusive closures for eddy potential vorticity and heat fluxes in such flows. For narrow jets that produce eddy fluxes with a half-width of one to two radii of deformation, this local theory underpredicts the fluxes.

70. Sun, D-Z, and Isaac Held, 1996: A comparison of modeled and observed relationships between interannual variations of water vapor and temperature. Journal of Climate, 9(4), 665-675.
    [ Abstract PDF ]

    The correlations between interannual variations of tropical mean water vapor and temperature in the simulations by a low resolution (R15) GCM are stronger than those in the rawinsonde observations. The rate of fractional increase of tropical mean water vapor with temperature in the model simulations is also larger than that from the observations. The largest discrepancies are found in the region immediately above the tropical convective boundary layer (850-600 mb). The rate of fractional increase of tropical mean water vapor with temperature in the model simulations is close to that for a constant relative humidity. The correlations between variations of water vapor in the upper troposphere and those in the lower troposphere are also stronger in the model simulations than in the observations. In the horizontal, the characteristic spatial patterns of the normalized water vapor variations in the model simulations and observations are similar. The water vapor-temperature relationship in simulations by a GCM with a somewhat higher spatial resolution (R30) is almost identical to that in the simulations by the low resolution (R15) GCM. The implications of these findings for the radiative feedback of water vapor are discussed.

71. Brantstator, G, and Isaac Held, 1995: Westward propagating normal modes in the presence of stationary background waves. Journal of the Atmospheric Sciences, 52(2), 247-262.
    [ Abstract PDF ]

    Eigenvectors and eigenvalues of the nondivergent barotropic vorticity equation linearized about zonally asymmetric wintertime mean flows are calculated to determine which barotropic modes might contribute to westward propagating disturbances observed in nature. Of particular interest are modes that correspond to a recurring pattern concentrated in the Western Hemisphere with a period of about 25 days reported by Branstator and Kushnir. The most unstable modes of November-March means from individual years tend to be westward propogating and have a structure that is similar to the observed 25-day pattern. By following the evolution of each Rossby-Haurwitz mode as the basic state is gradually changed from a state of rest to an observed mean state, it is demonstrated that all but about eight of the Rossby-Haurwitz modes will be modified beyond recognition by the action of the time mean flow. One of these,the second gravest antisymmetric zonal wavenumber-one mode (denoted {1,3} and sometimes referred to as the 16-day wave), has a structure that bears some resemblance to the observed 25-day pattern, but it is typically neutral. The structural similarity between this mode and the 25-day pattern is not as pronounced as the similarity between the most unstable modes and the 25-day pattern. Furthermore, the mode for the observed basic state that {1,3} evolves to depends on the path by which the resting state is transformed into the observed state, suggesting that {1,3} cannot always be thought of as a distinct mode in the presence of a realistic background. The results indicate that even if {1,3} can be considered to exist in wintertime mean flows, it is distinct from the most unstable modes on those flows. By slowly changing the basic states that support the westward propogating unstable modes until they are equal to the climatological January state that earlier studies have shown produces quasi-stationary teleconnection-like modes, it is demonstrated that the unstable westward propagating and quasi-stationary modes are related to each other.

72. Held, Isaac, R T Pierrehumbert, Stephen T Garner, and K L Swanson, 1995: Surface quasi-geostrophic dynamics. Journal of Fluid Mechanics, 282, 1-20.
    [ Abstract PDF ]

    The dynamics of quasi-geostrophic flow with uniform potential vorticity reduces to the evolution of buoyancy, or potential temperature, on horizontal boundaries. There is a formal resemblance to two-dimensional flow, with surface temperature playing the role of vorticity, but a different relationship between the flow and the advected scalar creates several distinctive features. A series of examples are described which highlight some of these features: the evolution of an eliptical vortex; the start-up vortex shed by flow over a mountain; the instability of temperature filaments; the `edge wave' critical layer; and mixing in an overturning edge wave. Characteristics of the direct cascade of the tracer variance to small scales in homogeneous turbulence, as well as the inverse energy cascade, are also described. In addition to its geophysical relevance, the ubiquitous generation of secondary instabilities and the possibility of finite-time collapse make this system a potentially important, numerically tractable, testbed for turbulence theories.

73. Larichev, V D., and Isaac Held, 1995: Eddy amplitudes and fluxes in a homogenous model of fully developed baroclinic instability. Journal of Physical Oceanography, 25(10), 2285-2297.
    [ Abstract PDF ]

    A horizontally homogenous two-layer quasigeostrophic model with imposed environmental vertical shear is used to study eddy energies and fluxes in the regime in which an inverse barotropic energy cascade excites eddies of much larger scale than the deformation radius. It is shown that the eddy potential vorticity flux, "thickness" flux, and the extraction of energy from the background flow are dominated by the largest eddies excited by the cascade, and not by deformation-scale eddies. The role of the latter is a catalytic one of transferring the baroclinic energy cascading downscale into the barotropic mode, thereby energizing the inverse cascade. Based on this picture, scaling arguments are developed for the eddy energy level and potential vorticity flux in statistical equilibrium. The potential vorticity flux can be thought of as generated by a diffusivity of magnitude Uk_d/k²0, where U is the difference between the mean currents in the two layers, k_d is the inverse of the deformation radius, and k₀ is the wavenumber of the energy-containing eddies. This result is closely related to that proposed by Green, although the underlying dynamical picture is different.

74. Held, Isaac, and M J Suarez, 1994: A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bulletin of the American Meteorological Society, 75(10), 1825-1830.
    [ Abstract PDF ]

    A benchmark calculation is proposed for evaluating the dynamical cores of atmospheric general circulation models independently of the physical parameterizations. The test focuses on the long-term statistical properties of a fully developed general circulation; thus, it is particularly appropriate for intercomparing the dynamics used in climate models. To illustrate the use of this benchmark, two very different atmospheric dynamical cores-one spectral, one finite difference-are compared. It is found that the long-term statistics produced by the two models are very similar. Selected results from these calculations are presented to initiate the intercomparison.

75. Kushnir, Y, and Isaac Held, 1994: The wintertime general circulation model response to North Atlantic SST anomalies In The Atlantic Climate Change Program, Proceedings from the principal investigators meeting, NOAA, University Corporation for Atmospheric Research, 121-124.
76. Phillipps, Peter, and Isaac Held, 1994: The response to orbital pertubations in an atmospheric model coupled to a slab ocean. Journal of Climate, 7(5), 767-782.
    [ Abstract PDF ]

    The sensitivity of an atmospheric GCM coupled to a mixed-layer ocean to changes in orbital parameters is investigated. Three experiments are compared. One has perihelion at summer solstice and a large obliquity; another has perihelion at winter solstice and low obliquity. The first of these is favorable for warm summers; the second for cool summers. A third experiment, with perihelion at summer solstice and the lower value of obliquity, is used to examine the relative importance of the changes in perihelion and obliquity. The eccentricity is set at 0.04 in all cases. Surface temperature responses are as large as 15°C, with the largest response over North America in summer. Changes in monsoons and Arctic sea ice are consistent with previous GCM studies. A perpetual summer version of the atmospheric model is used to investigate the positive feedback due to soil moisture. Drying of the soil over North America is found to increase the temperature response by approximately 50% and is also essential to the decrease in summertime precipitation in that region. Soil moisture changes also enhance the precipitation response over central Africa, but have little effect on the model's Asian monsoon. The orbital parameters most favorable for expansion of the Northern Hemisphere glaciers, that is, minimal seasonality, do not produce permanent snow cover. Several model deficiencies that act to accelerate the melting of snow in spring may be responsible.

77. Pierrehumbert, R T., Isaac Held, and K L Swanson, 1994: Spectra of local and nonlocal two-dimensional turbulence. Chaos, Solitons, and Fractals, 4(6), 1111-1116.
    [ Abstract ]

    We propose a family of two-dimensional incompressible fluid models indexed by a parameter a e [0, infinity], and discuss the spectral scaling properties for homogenous, isotropic turbulence in these models. The family includes two physically realizable members. It is shown that the enstrophy cascade is spectrally local for a < 2, but becomes dominated by nonlocal interactions for a > 2. Numerical simulations indicate that the spectral slopes are systematically steeper than those predicted by the local scaling argument.

78. Held, Isaac, 1993: Large-scale dynamics and global warming. Bulletin of the American Meteorological Society, 74(2), 228-241.
    [ Abstract PDF ]

    Predictions of future climate change raise a variety of issues in large-scale atmospheric and oceanic dynamics. Several of these are reviewed in this essay, including the sensitivity of the circulation of the Atlantic Ocean to increasing freshwater input at high latitudes; the possibility of greenhouse cooling in the southern oceans; the sensitivity of monsoonal circulations to differential warming of the two hemispheres; the response of midlatitude storms to changing temperature gradients and increasing water vapor in the atmosphere; and the possible importance of positive feedback between the mean winds and eddy-induced heating in the polar stratosphere.

79. Held, Isaac, Richard S Hemler, and V Ramaswamy, 1993: Radiative-convective equilibrium with explicit two-dimensional moist convection. Journal of the Atmospheric Sciences, 50(23), 3909-3927.
    [ Abstract PDF ]

    Radiative-convective statistical equilibria are obtained using a two-dimensional model in which radiative transfer is interactive with the predicted moisture and cloud fields. The domain is periodic in x, with a width of 640 km, and extends from the ground to 26 km. The lower boundary is a fixed-temperature water-saturated surface. The model produces a temperature profile resembling the mean profile observed in the tropics. A number of integrations of several months' duration are described in this preliminary examination of the model's qualitative behavior. The model generates a QBO-like oscillation in the x-averaged winds with an apparent period of ~60 days. This oscillation extends into the troposphere and influences the convective organization. In order to avoid the associated large vertical wind shears, calculations are also performed in which the x-averaged winds are constrained to vanish. The convection then evolves into a pattern in which rain falls only within a small part of the domain. The moisture field appears to provide the memory that localizes the convection. If the vertical shears are fixed in a modest nonzero value, this localization is avoided. Comparing calculations with surface temperatures of 25°C and 30°C, the planetary albedo is found to decrease with increasing temperature, primarily due to a reduction in low-level cloudiness.

80. Held, Isaac, and Peter Phillipps, 1993: Sensitivity of the eddy momentum flux to meridional resolution in atmospheric GCMs. Journal of Climate, 6(3), 499-507.
    [ Abstract PDF ]

    GCM experiments with zonally symmetric climates are used to demonstrate that the increase in the meridional eddy momentum fluxes and zonal surface winds that occurs when resolution is increased is primarily due to the increase in meridional rather than zonal resolution. It is argued that the sensitivity to meridional resolution reflects the need to resolve the small scales generated in the Rossby wave field as waves radiate from the midlatitude baroclinic eddy source region into regions with small mean winds. Some additional experiments highlight the sensitivity of surface winds and eddy momentum fluxes to the subgrid-scale horizontal mixing formulation in low-resolution models.

81. Lee, S, and Isaac Held, 1993: Baroclinic wave packets in models and observations. Journal of the Atmospheric Sciences, 50(10), 1413-1428.
    [ Abstract PDF ]

    Coherent baroclinic wave packets are present in the Southern Hemisphere, most clearly in the summer season. These coherent packets are also found in a hierarchy of models of nonlinear baroclinic instability - a two-layer quasigeostrophic (QG) model on a beta-plane, a two-level primitive equation (PE) model, and a general circulation model. The flows are chaotic, but the packet itself can remain remarkably coherent, despite the complex evolution of the flow within the packet. In both QG and PE models, the packets become more robust as the supercriticality of the flow is reduced. In both models and the observations, the packets move with a group velocity that is greater than the phase speed of the individual disturbances, so that these disturbances exhibit downstream development. The structure of the baroclinic waves in the packet as a function of longitude resembles the life cycles of sinusoidal baroclinic waves as a function of time. More than one packet can exist in the domain at the same time. In the QG model, the number of packets increases in a systematic way as the length of the channel increases.

82. Stephenson, D B., and Isaac Held, 1993: GCM response of northern winter stationary waves and storm tracks to increasing amounts of carbon dioxide. Journal of Climate, 6(10), 1859-1870.
    [ Abstract PDF ]

    The response of the Geophysical Fluid Dynamics Laboratory (GFDL) coupled ocean-atmosphere R15, 9-level GCM to gradually increasing CO₂ amounts is analyzed with emphasis on the changes in the stationary waves and storm tracks in the Northern Hemisphere wintertime troposphere. A large part of the change is described by an equivalent-barotropic stationary wave with a high over eastern Canada and a low over southern Alaska. Consistent with this, the Atlantic jet weakens near the North American coast. Perpetual winter runs of an R15, nine-level atmospheric GCM with sea surface temperature, sea ice thickness, and soil moisture values prescribed from the coupled GCM results are able to reproduce the coupled model's response qualitatively. Consistent with the weakened baroclinicity associated with the stationary wave change, the Atlantic storm track weakens with increasing CO₂ concentrations while the Pacific storm track does not change in strength substantially. An R15, nine-level atmospheric model linearized about the zonal time-mean state is used to analyze the contributions to the stationary wave response. With mountains, diabatic heating, and transient forcings the linear model gives a stationary wave change in qualitative agreement with the change seen in the coupled and perpetual models. Transients and diabatic heating appear to be the major forcing terms, while changes in zonal-mean basic state and topographic forcing play only a small role. A substantial part of the diabatic response is due to changes in tropical latent heating.

83. Cook, K H., and Isaac Held, 1992: The stationary response to large-scale orography in a general circulation model and a linear model. Journal of the Atmospheric Sciences, 49(6), 525-539.
    [ Abstract PDF ]

    Stationary waves generated over orography in a linear model and a general circulation model (GCM) are cmpared to examine how the atmosphere's response is established for small mountains and how linear theory breaks down over large orographic features. Both models have nine vertical levels and are low-resolution (R15) spectral models. The linear model solves the stationary linear primitive equations. The GCM's control integration uses zonally uniform and hemispherically symmetric boundary conditions, with a global swamp surface. Five experiments are performed by perturbing the GCM with Gaussian mountains of various heights introduced in midlatitudes. The stationary wave model is linearized about zonal mean fields from the GCM climatology. The linear model's response to a Gaussian mountain at 45°N latitude is dominated by a single wave train radiating toward the southeast. For mountain heights between 0.7 and 2 km, the GCM's stationary waves are similar to the linear model response to orography, although amplitudes increase less rapidly than linearly with mountain height. For larger mountains, closed isentropes and distinctly nonlinear flow occur along the surface of the mountain and a large poleward-radiating wave train develops. The development of closed isentropes, and the breakdown of linear theory, can be predicted whenever the slope of the surface exceeds the slope of the isentropes in the unperturbed (no mountain) basic state.

84. Garner, Stephen T., N Nakamura, and Isaac Held, 1992: Nonlinear equilibration of two-dimensional eady waves: a new perspective. Journal of the Atmospheric Sciences, 49(21), 1984-1996.
    [ Abstract PDF ]

    The equilibration of two-dimensional baroclinic waves differs fundamentally from equilibration in three dimensions because two-dimensional eddies cannot develop meridional temperature or velocity structure. It was shown in an earlier paper that frontogenesis together with diffusive mixing in a two-dimensional Eady wave brings positive potential vorticity (PV) anomalies deep into the atmosphere from both boundaries and allows the disturbance to settle into a steady state without meridional gradients. Here we depart from the earlier explanation of this equilibration and associate the PVintrusions with essentially the same kind of vortex "roll-up" that characterizes the evolution of barotropic shear layers. To avoid subgrid turbulence parameterizations and computational diffusion, the analogy is developed using Eady's generalized baroclinic instability problem. Eady's generalized model has two semi-infinite regions of large PV surrounding a layer of relatively small PV. Without boundaries, frontal collapse, or strong diffusion the model still produces equilibrated states, with structure similar to the vortex streets that emerge from unstable barotropic shear layers. The similarity is greatest when the baroclinic development is viewed in isentropic coordinates. The contrast between the present equilibrated solutions, which exhibit no vertical tilt, and Blumen's diffusive frontogenesis model, which allows the wave to retain its phase tilt, is briefly discussed. The equilibration of two-dimensional baroclinic waves differs fundamentally from equilibration in three dimensions because two-dimensional eddies cannot develop meridional temperature or velocity structure. It was shown in an earlier paper that frontogenesis together with diffusive mixing in a two-dimensional Eady wave brings positive potential vorticity (PV) anomalies deep into the atmosphere from both boundaries and allows the disturbance to settle into a steady state without meridional gradients. Here we depart from the earlier explanation of this equilibration and associate the PVintrusions with essentially the same kind of vortex "roll-up" that characterizes the evolution of barotropic shear layers. To avoid subgrid turbulence parameterizations and computational diffusion, the analogy is developed using Eady's generalized baroclinic instability problem. Eady's generalized model has two semi-infinite regions of large PV surrounding a layer of relatively small PV. Without boundaries, frontal collapse, or strong diffusion the model still produces equilibrated states, with structure similar to the vortex streets that emerge from unstable barotropic shear layers. The similarity is greatest when the baroclinic development is viewed in isentropic coordinates. The contrast between the present equilibrated solutions, which exhibit no vertical tilt, and Blumen's diffusive frontogenesis model, which allows the wave to retain its phase tilt, is briefly discussed.

85. Held, Isaac, and E O'Brien, 1992: Quasigeostrophic turbulence in a three-layer model: effects of vertical structure in the mean shear. Journal of the Atmospheric Sciences, 49(19), 1861-1870.
    [ Abstract PDF ]

    A three-layer, horizontally homogeneous, quasigeostrophic model is selected as one of the simplest environments in which to study the sensitivity of baroclinic eddy fluxes in the atmosphere to the vertical structure of the basic-state temperature gradients or vertical wind shears. Eddy statistics obtained from the model are interpreted in terms of linear theory and a modified "baroclinic adjustment" hypothesis. Both linear theory and the baroclinic adjustment construction are found to provide useful predictions for the vertical structure of the eddy potential vorticity flux. For equal values of the mean vertical shear, eddy fluxes and energies are greater when the shear is concentrated at lower levels (d²U / dz² < 0)than when the shear is concentrated at higher levels (d²U / dz² > 0). Eddy fluxes are more sensitive to lower-than to upper-level mean temperature gradients. This relative sensitivity is a function of g = f² l / (b N²H), where l is the mean vertical shear and H is the depth of the fluid. It is enhanced as g is reduced, as the unstable modes become shallower, until the eddies become almost completely insensitive to the strength of the upper-layer wind for g < 0.5.

86. Held, Isaac, and E O'Brien, 1991: Quasi-geostrophic turbulence in a three-layer model In Eighth Conference on Atmospheric and Oceanic Waves and Stability, Boston, MA, American Meteorological Society, 7-8.
87. Lee, S, and Isaac Held, 1991: Baroclinic wave packets in models and observations In Eighth Conference on Atmospheric and Oceanic Waves and Stability, Boston, MA, American Meteorological Society, 71-72.
88. Lee, S, and Isaac Held, 1991: Subcritical instability and hysteresis in a two-layer model. Journal of the Atmospheric Sciences, 48(8), 1071-1077.
    [ Abstract PDF ]

    A two-layer quasi-geostrophic model forced by surface friction and radiative relaxation to a jetlike wind profile can exist in either a wave-free state or in a finite-amplitude wave state, over a substantial region of the model's parameter space. The friction on the lower layer must be much stronger than the thermal relaxation, and the upper layer must be nearly inviscid, for this behavior to be observed. Consistent with this behavior, weakly unstable waves are found that do not stabilize the flow; instead, their growth rate increases with wave amplitude. We attempt to provide a physical explanation for this behavior in terms of 1) the competition between the stabilizing effect of the lower-layer potential vorticity fluxes and the destabilizing effect of nonlinear critical layer formation associated with the upper-layer fluxes, and 2) the tendency of surface drag to restore the vertical shear at the center of the jet by damping the surface westerlies generated by the baroclinic instability.

89. Randel, W, and Isaac Held, 1991: Phase speed spectra of transient eddy fluxes and critical layer absorption. Journal of the Atmospheric Sciences, 48(5), 688-697.
    [ Abstract PDF ]

    Tropospheric zonal mean eddy fluxes of heat and momentum, and the divergence of the Eliassen-palm flux, are decomposed into contributions from different zonal phase speeds. Data analyzed are ECMWF operational global analyses covering 1980-87. Eastward moving medium-scale waves (zonal waves 4-7) dominate the spectra of lower tropospheric heat fluxes in both hemispheres and all seasons. Upper tropospheric wave flux spectra are similar to the low level spectra in midlatitudes, but shift to slower zonal phase speeds as low latitudes are approached. The cause of this shift is the selective absorption of faster moving components in midlatitudes as the waves propagate meridionally. Latitude-phase speed distributions of eddy fluxes are constructed and compared to the zonal mean wind structure. These results demonstrate that upper tropospheric eddies break and decelerate the zonal mean flow approximately 10°-20° in latitude away from their critical line (where phase speed equals zonal wind speed). Comparisons are also made with results from the middle stratosphere.

90. Tao, X, and Isaac Held, 1991: Interaction between the subtropic jet and Rossby waves in a multi-layer isentropic model In Eighth Conference on Atmospheric and Oceanic Waves and Stability, Boston, MA, American Meteorological Society, 47-50.
91. Fyfe, J C., and Isaac Held, 1990: The two-fifths and one-fifth rules for Rossby wave breaking in the WKB limit. Journal of the Atmospheric Sciences, 40(6), 697-706.
    [ Abstract PDF ]

    A stationary Rossby wave, sinusoidal in longitude, is slowly switched on, and the meridional propagation of the resulting wave front through a shear flow is examined. Initially the flow is westerly everywhere and therefore free of critical layers. The transition from reversible to irreversible behavior as the wave amplitude is increased is described. It is shown that under slowly varying conditions in an inviscid quasi-linear model, a steady state is obtained if, and only if, the mean flow is decelerated by less than two-fifths of its initial value as a result of the passage of the wave front. If this passage causes a larger mean flow reduction, a pile-up of wave activity in the shear layer culminates in the generation of a critical layer, qualitatively as in Dunkerton's model of gravity wave-mean flow interaction. This qualitative picture is shown to be preserved in the quasi-linear model when the slowly varying assumption breaks down. Fully nonlinear calculations show that these quasi-linear results are only part of the story. Once the mean flow is decelerated by two-fifths of its initial value in the fully nonlinear model, rapid wave breaking and irreversible mixing occur in the shear layer. But more slowly developing wave breaking also occurs for wave amplitudes that are too small to produce the two-fifths deceleration. Overturning of contours can be shown to occur in the quasi-linear slowly varying model once the mean flow has been decelerated by one-fifth of its initial value, and this appears to be the critical value for wave breaking to occur in the nonlinear integrations.

92. Held, Isaac, and Peter Phillipps, 1990: A barotropic model of the interaction between the Hadley cell and a Rossby wave. Journal of the Atmospheric Sciences, 47(7), 856-869.
    [ Abstract PDF ]

    A barotropic model is described that is designed to study the interaction of the Hadley cell with a Rossby wave forced in midlatitudes by a stationary "topographic" source. The Hadley cell is driven by a mass source/sink that is partly fixed, representing solar heating, and partly dependent on the layer thickness, representing infrared cooling. The response of the mean zonal and meridional winds to infinitesimal wave forcing is analyzed in detail; then the forcing is gradually increased to examine the departures from linearity.

93. Held, Isaac, and Mingfang Ting, 1990: Orographic versus thermal forcing of stationary waves: The importance of the mean low-level wind. Journal of the Atmospheric Sciences, 47(4), 495-500.
    [ Abstract PDF ]

    The amplitude of the linear, stationary response to low-level extratropical heating decreases as the magnitude of the low-level mean flow increases, while the amplitude of the orographically forced waves increases. As a result, linear theory predicts that the relative importance of thermal and orographic forcing for the extratropical stationary wave field is very sensitive to the magnitude of the zonal low-level winds. In the process of illustrating this sensitivity, we also show how the dependence of the orographic response on the low level winds can be distorted by a numerical sigma-coordinate model.

94. Ting, Mingfang, and Isaac Held, 1990: The stationary wave response to a tropical SST anomaly in an idealized GCM. Journal of the Atmospheric Sciences, 47(21), 2546-2566.
    [ Abstract PDF ]

    The upper tropospheric stationary wave response to a tropical sea surface temperature (SST) anomaly is examined with an idealized general circulation model (GCM) as well as steady linear and nonlinear models. The control climate of the GCM is zonally symmetric; this symmetric climate is then perturbed by a dipolar SST anomaly centered at the equator. Two experiments, with anomaly amplitudes differing by a fact of two, have been conducted. The response is very linear in the amplitude of the SST anomaly. A steady, baroclinic model linearized about a zonally symmetric basic state simulates the GCM's stationary wave reasonably well when it is forced by anomalous heating as well as anomalous transients. When decomposing the GCMs flow into parts forced separately by heating and transients, tropical transients are found to play a dissipative role to first approximation, reducing the amplitude of the response to heating by a factor of two. The effects of extratropical transients are relatively weak. A steady nonlinear model is also used to evaluate the importance of transients and confirms the diagnosis based on the linear model. Part of the tropical transients seems to be forced by tropical convection and part by midlatitude disturbances propagating into the tropics. The anomalous extratropical transients include a part related to a shift in the model's storm track and a part related to barotropic instability of the stationary wave, but the effects of both of these changes are relatively weak due to the absence of strong extratropical climatic zonal asymmetries in the model. The dissipative role of transients in this model is contrasted with the positive feedback found by Held, et al. (1989) in a GCM with realistic boundary conditions. The calculations in that paper are repeated, and the direct linear response to thermal forcing is found to be sensitive to the damping included in the model; but the positive feedback from the transients is robust to changes in the linear model. We speculate that a strong asymmetric storm track, with a well-defined barotropic decay region, is needed for the positive feedback to occur.

95. Feldstein, S B., and Isaac Held, 1989: Barotropic decay of baroclinic waves in a two-layer beta-plane model. Journal of the Atmospheric Sciences, 46(22), 3416-3430.
    [ Abstract PDF ]

    A two-layer quasi-geostrophic model is used to study the effects of a meridionally sheared zonal flow on the life cycle of a weakly unstable baroclinic wave. In most of the cases analyzed, the fluid is inviscid with the exception of scale-selective fourth-order horizontal diffusion. The initial zonal flow is identically zero in the lower layer. The character of the eddy life cycle in the limit of weak supercriticality is shown to depend on whether or not the meridional shear in the upper layer is strong enough to produce a critical latitude for the wave. If the shear is sufficiently weak, the wave undergoes periodic amplitude vacillation characterized by symmetric baroclinic growth and baroclinic decay. However, when the meridional shear is strong enough to allow for the existence of a critical layer, the flow undergoes an asymmetric life cycle which resembles that found by Simmons and Hoskins in a primitive equation model on the sphere: the wave grows baroclinically but decays barotropically toward a wave-free state. Throughout the barotropic decay stage, the wave is breaking and being absorbed either at or before the critical layer. As the supercriticality is increased, strong reflection begins to occur at the location of the wave breaking, resulting in irregular amplitude vacillaton. Consistent with critical layer theory, when a reflecting state is created the solution is sensitive to the inclusion of higher zonal harmonics of the fundamental wave. By relaxing the potential vorticity distribution back to an unstable state, periodic solutions are obtained in which each episode of growth and decay is similar to that found in these nearly inviscid solutions.

96. Held, Isaac, S W Lyons, and S Nigam, 1989: Transients and the extratropical response to El Niño. Journal of the Atmospheric Sciences, 46(1), 163-174.
    [ Abstract PDF ]

    A baroclinic stationary wave model linearized about a zonally symmetric flow is used to interpret the extratropical atmospheric response to El Niño produced by a general circulation model. When forced by the anomalous diabatic heating and tendency due to transients, the linear model provides a useful simulation of this response. The direct response to anomalous diabatic heating is found to be small in the extratropics; the dominant term is the response to the anomalous transients, particularly the anomalous upper tropospheric transients in the vorticity equation. These results are complementary to those obtained with a nonlinear barotropic model by Held and Kang, and indicate that the anomalous subtropical convergence which plays a key role in that study is itself primarily forced by the anomalous transients. One can distinguish between two distinct parts of the response of the transients to the tropical heating: the movement of the Pacific storm track associated with the anomalous extratropical wave train, and changes in the penetration of Rossby waves into the tropics resulting from the modified tropical winds.

97. Nakamura, N, and Isaac Held, 1989: Nonlinear equilibration of two-dimensional eady waves. Journal of the Atmospheric Sciences, 46(19), 3055-3064.
    [ Abstract PDF ]

    The initial-value problem for Eady's model is reexamined using a two-dimensional (x-z) primitive equation model. It is generally accepted that a finite amplitude instability of Eady's basic state will produce a frontal discontinuity in a finite time. When diffusion prevents the frontal discontinuity from forming, the wave amplitude eventually stops growing and begins to oscillate. We analyze this equilibration and suggest that it is a result of enhanced potential vorticity in the frontal region that is mixed into the interior from the boundaries. The dynamics of equilibration is crudely captured in a modified quasi-geostrophic model in which the zonal-mean static stability is allowed to vary. The magnitude of the meridional wind speed of the equlibrated wave is O(N0H), where N0 is the initial buoyancy frequency and H is the depth of the fluid. This is of the same order as the amplitude of the wave predicted by semigeostrophic theory at the point of frontal collapse. Scaling arguments are presented to determine the three-dimensional flows for which this equilibration mechanism should be important. It is argued that this mechanism is likely to be of some importance for shallow cyclones forming in regions of weak low-level static stability.

98. Cook, K H., and Isaac Held, 1988: Stationary waves of the ice age climate. Journal of Climate, 1(8), 807-819.
    [ Abstract PDF ]

    A linearized, steady state, primitive equation model is used to simulate the climatological zonal asymmetries (stationary eddies) in the wind and temperature fields of the 18000 YBP climate during winter. We compare these results with the eddies simulated in the ice age experiments of Broccoli and Manabe, who used CLIMAP boundary conditions and reduced atmospheric CO2 in an atmospheric general circulation model (GCM) coupled with a static mixed layer ocean model. The agreement between the models is good, indicating that the linear model can be used to evaluate the relative influences of orography, diabatic heating, and transient eddy heat and momentum transports in generating stationary waves. We find that the orographic forcing dominates in the ice age climate. The mechanical influence of the continental ice sheets on the atmosphere is responsible for most of the changes between the present day and ice age stationary eddies. This concept of the ice age climate is complicated by the sensitivity of the stationary eddies to the large increase in the magnitude of the zonal mean meridional temperature gradient simulated in the ice age GCM.

99. Lau, Ngar-Cheung, Isaac Held, and J D Neelin, 1988: The Madden-Julian Oscillation in an idealized general circulation model. Journal of the Atmospheric Sciences, 45(24), 3810-3832.
    [ Abstract PDF ]

    The structure of the intraseasonal oscillations in the tropics of an idealized general circulation model with a zonally symmetric climate is described. Space-time spectra show a peak in zonal winds and velocity potential at the equator in zonal wavenumbers 1 and 2, corresponding to eastward-propagating power at phase speeds of ~ 18 m s^-1. This speed is significantly greater than that of the observed oscillation but comparable to that obtained in similar models by Hayashi and Sumi and Swinbank et al. The corresponding eastward-propagating power in the precipitation spectrum is concentrated in wavenumbers 2-5. A composite procedure is used to describe the three-dimensional structure of the model's oscillation. The oscillation is characterized by circulation cells oriented along the equatorial zonal plane, with enhanced precipitation in the region of rising motion. Zonal wind changes tend to be positively correlated with geopotential height changes at the same level. Positive perturbations in the water vapor mixing ratio, evaporation, and lower tropospheric horizontal moisture convergence all exhibit distinct eastward displacements from the center of convection. Two different linear models are used to interpret the GCM results. The response to the GCM's composited diabatic heating field is first computed using a linear primitive equation model on the sphere. This linear model requires strong damping above the heated region, as well as near the surface, to produce a pattern in rough agreement with the GCM. A simple Kelvin wave-CISK model, in which the vertical structure of the heating is taken from the composite, is then shown to be capable of reproducing the phase speed simulated in the GCM.

100. Nigam, S, Isaac Held, and S W Lyons, 1988: Linear simulation of the stationary eddies in a GCM. Part II: The. Journal of the Atmospheric Sciences, 45(9), 1433-1452.
     [ Abstract PDF ]

     The validity of linear stationary wave theory in accounting for the zonal asymmetries of the winter-averaged tropospheric circulation obtained in a general circulation model (GCM) is ascertained. The steady linear primitive equation model used towards this end has the same vertical and zonal resolution as the spectral GCM, but is finite-differenced in the meridional direction. It is linearized about a zonally symmetric basic state and forced by topography and 3-dimensional diabatic heating and transient flux convergence fields, all of which are taken from the GCM. As in Part I (in which we studied a GCM with a flat lower boundary), we obtained the best correspondence between the GCM and the linear solutions when when strong Rayleigh friction is included in the linear model not only near the surface, but in the interior of the tropical troposphere as well. There is sufficient quantitative correspondence between the GCM and the linear solution to justify decomposing the linear simulation into parts forced by different processes, although in some regions, such as over North America, the simulation is unsatisfactory. Different fields give different impressions as to the relative importance of orography, heating, and transients. The eddy zonal vorticity field in the upper troposphere shows the orographic and thermal plus transient contributions to be nearly equal in amplitude, whereas the eddy meridional velocity field, dominated by shorter zonal scales, shows the orographic contribution to be decisively dominant. Although there is no systematic phase relationship between these two contributions, they are roughly in phase over the east Asian coast, where each of them is largest. They also contribute roughly equal amounts to the low level Siberian high. Other findings are that (i) the 300 mb extratropical response to tropical forcing reaches 50 gpm over Alaska (given our frictional parameterization), which is smaller than the response to local thermal forcing, (ii) the responses to sensible heating and lower tropospheric thermal transients are strongly anticorrelated, and (iii) the circulation in the vicinity of the Andes in the GCM is not attributable to direct mechanical forcing by the mountains.

101. Panetta, R L., and Isaac Held, 1988: Baroclinic eddy fluxes in a one-dimensional model of quasi-geostrophic turbulence. Journal of the Atmospheric Sciences, 45(22), 3354-3365.
     [ Abstract PDF ]

     Statistically steady states of a two-layer quasi-geostrophic model truncated to retain only the zonal mean flow and one nonzero zonal wavenumber, but with high meridional resolution, are described. The model is forced by imposing a time-mean unstable meridional temperature gradient, assuming that deviations from the time-mean are doubly periodic. A comparison is made with a more conventional channel model with the same zonal truncation, in which the flow is forced by radiative relaxation to an unstable temperature gradient. It is shown that the statistics of the channel model approach those of the doubly periodic model as the width of the unstable region in the former is increased. Implications for parameterization theories are discussed.

102. Held, Isaac, 1987: New conservation laws for linear quasi-geostrophic waves in shear. Journal of the Atmospheric Sciences, 44(16), 2349-2351.
     [ Abstract PDF ]

     There exists an infinite set of quadratic conserved quantities for linear quasi-geostrophic waves in horizontal and vertical shear, the first two members of the set corresponding to the pseudomomentum and pseudo-energy conservation laws that lead to the Rayleigh-Kuo (or Charney-Stern) and the Fjortoft stability criteria. This infinite hierarchy of conservation laws follows from the conservation of the pseudomomentum in each eigenmode of the shear flow.

103. Held, Isaac, and I-S Kang, 1987: Barotropic models of the extratropical response to El Niño. Journal of the Atmospheric Sciences, 44(23), 3576-3586.
     [ Abstract PDF ]

     A series of linear and nonlinear barotropic models are used to interpret the extratropical response to El Niño equatorial surface temperatures as simulated by an atmospheric general circulation model (GCM). The divergence, time-mean vorticity tendency due to transients, and the zonal mean flow are specified from the GCM, and the deviation of the streamfunction from its zonal mean flow are specified from the GCM, and the deviation of the streamfunction from its zonal mean at an upper-tropospheric level is predicted. Nonlinear steady-state model s suggest that the extratropical wave train is primarily forced from the central rather than the western Pacific and that subtropical divergence anomalies are of more importance than tropical anomalies. These nonlinear solutions can be reproduced with little loss in accuracy by linearizing about the zonally asymmetric climatological flow. If one linearizes about the zonally symmetric flow, the part of the solution forced from the western Pacific deteriorates significantly. The solution in the tropics and subtropics also deteriorates if advection of vorticity by the divergent flow is omitted. Forcing by transients plays a secondary role in generating the extratropical wave train in these barotropic models, but it is pointed out that the subtropical convergence that forces the bulk of this wave train could itself be closely related to anomalies in the transient forcing.

104. Held, Isaac, and Peter Phillipps, 1987: Linear and nonlinear barotropic decay on the sphere. Journal of the Atmospheric Sciences, 44(1), 200-207.
     [ Abstract PDF ]

     An example of the barotropic decay of wavelike midlatitude disturbance in the presence of a shear flow on the sphere is examined. The linear theory for the evolution of the disturbance is first described, with emphasis on the importance of the pseudomomentum spectrum for the resulting drag on the mean flow. After a brief discussion of the ways in which this linear theory can break down, a high-resolution nonlinear numerical model is used to examine the dependence of the mean-flow modification and the qualitative character of the decay on the amplitude of the initial disturbance.

105. Neelin, J D., and Isaac Held, 1987: Modeling tropical convergence based on the moist static energy budget. Monthly Weather Review, 115(1), 3-12.
     [ Abstract PDF ]

     The vertically integrated moist static energy equation provides a convenient starting point for the construction of simple models of the time-mean low level convergence in the tropics. A vertically integrated measure of the moist static stability, the "gross moist stability," proves to be of central importance. Minima in this quantity mark the positions of the tropical convergence zones. We argue that the positions of these minima are determined by the time-mean moisture field, which is, in turn, closely tied to the time-mean surface temperature.

106. Neelin, J D., Isaac Held, and K H Cook, 1987: Evaporation-wind feedback and low-frequency variability in the tropical atmosphere. Journal of the Atmospheric Sciences, 44(16), 2341-2348.
     [ Abstract PDF ]

     A mechanism by which feedback between zonal wind perturbations and evaporation can create unstable, low-frequency modes in a simple two-layer model of the tropical troposphere is presented. The modes resemble the 30-50 day oscillation. A series of general circulation model experiments designed to test the effect of suppressing this feedback on low-frequency variability in the model tropics is described. The results suggest that the evaporation-wind feedback can be important to the amplitude of the spectral peak corresponding to the 30-50 day oscillation in the model, but that the existence of the oscillation does not depend on it. The feedback is found to have a much more dramatic effect on low-frequency variability when sea surface temperatures are fixed than when the lower boundary is a zero heat capacity "swamp."

107. Panetta, R L., Isaac Held, and R T Pierrehumbert, 1987: External Rossby waves in the two-layer model. Journal of the Atmospheric Sciences, 44(20), 2924-2933.
     [ Abstract PDF ]

     In order to clarify the extent to which the two-layer model can successfully simulate the remote tropospheric response to localized stationary forcing, the structure of stationary Rossby waves in the two-layer model is compared with that in continuous models. One finds a close correspondence when the two-layer flow is supercritical in the sense of the Phillips' criterion, except for the possibility of upstream propagation in the two-layer model when the lower-layer wind is small. When the two-layer flow is subcritical, the stationary waves can be very seriously distorted. The manner in which neutral modes are spatially or temporally destabilized by damping in the two-layer model is contrasted with similar results for Charney's model.

108. Held, Isaac, R T Pierrehumbert, and R L Panetta, 1986: Dissipative destabilization of external Rossby waves. Journal of the Atmospheric Sciences, 43(4), 388-396.
     [ Abstract PDF ]

     External Rossby waves in vertical shear can be destabilized by thermal damping. They can also be destabilized by damping of potential vorticity if this damping is larger in the lower than in the upper troposphere. Results are described in detail for Charney's model. Implications for the effects of diabatic heating and mixing due to smaller scale transients on equivalent barotropic stationary or quasi-stationary long waves are discussed. It is pointed out that energy or potential enstrophy budgets may indicate that transients are damping the long waves while, in fact, their presence is destabilizing these waves.

109. Kang, I-S, and Isaac Held, 1986: Linear and nonlinear diagnostic models of stationary eddies in the upper troposphere during northern summer. Journal of the Atmospheric Sciences, 43(24), 3045-3057.
     [ Abstract PDF ]

     The upper tropospheric circulation during northern summer produced by a general circulation model (GCM) is studied using linear and nonlinear barotropic models and by analyzing a streamfunction budget. The model experiments and the budget calculations both show a simple Sverdrup balance to be a useful first approximation for the largest scales during this season. In this Sverdrup balance, the advection of planetary vorticity by the divergent component of the flow is found to be significant, particularly in the Southern Hemisphere tropics. Nonlinear barotropic models improve the simulation of regional structures. The correct position of the Tibetan high is explained by Sverdrup balance, but its amplitude and structure are reasonably well simulated only with the nonlinear models. With climatological forcing, the time-averaged solutions of the nonlinear model are insensitive to the strength of the damping included in the model. The difference between the GCM's climatology and the GCM's flow in a particular summer is more difficult to model because of the large contribution of anomalous transients to the maintenance of the flow. However, strongly damped models produce simulations that bear some resemblance to the anomalous flow, at least in the tropics. To estimate the potential importance of vertical transport of momentum during moist convection, a damping proportional to the precipitation rate in the GCM is added in the nonlinear model. The estimated damping time scale for the eddy streamfunction is ~ 5 days in the northern tropics, but the changes in the predicted stationary eddy streamfunction are modest.

110. Nigam, S, Isaac Held, and S W Lyons, 1986: Linear simulation of the stationary eddies in a general circulation model. Part I: The no-mountain model. Journal of the Atmospheric Sciences, 43(23), 2944-2961.
     [ Abstract PDF ]

     The quantitative validity of linear stationary wave theory is examined by comparing the results from a linear primitive equation model on the sphere with the stationary eddies produced by a general circulation model (GCM). The GCM simulated has a flat lower boundary, so that the stationary eddies can be thought of as forced by heating (sensible, latent and radiative) and time-averaged transient eddy flux convergences. Orographic forcing is examined in the second part of this study. The distribution of the diabatic heating and transient eddy flux convergences and the zonally symmetric basic state are taken directly from the GCM's climatology for Northern winter (DJF). Strong Rayleigh friction is included in the linear model wherever the zonal mean wind is amall, as well as near the surface. The linear model is found to simulate the stationary eddy pattern of the GCM with considerable skill in both midlatitudes and the tropics. Some deficiencies include the inaccurate simulation of the upper tropospheric geopotential over North America and distortion of the wind field near the low-level zero-wind line in the subtropics. Decomposition of the linear solution shows that 1) the extratropical upper tropospheric eddy pattern generated by tropical forcing is significant but smaller than that due to extratropical forcing, 2) the upper-level extratropical pattern deteriorates somewhat when forcing by transients is removed, while the low-level pattern deteriorates dramatically and 3) there is considerable compensation between the effects of low-level thermal transients and extratropical sensible heating, to the point that we argue that this decomposition is not physically meaningful. The sensitivity of the results to the Rayleigh friction formulation is discussed, as is the effect of replacing the transients with thermal damping.

111. Held, Isaac, 1985: Pseudomomentum and the orthogonality of modes in shear flows. Journal of the Atmospheric Sciences, 42(21), 2280-2288.
     [ Abstract PDF ]

     Linear modes on shear flows are not orthogonal in the sense of energy; if two modes are present, the eddy energy is not equal to the sum of the eddy energy in the separate modes. However, linear modes are othogonal in the sense of pseudomomentum (or pseudoenergy). Two applications of this result to planetary waves in horizontal and vertical shear are discussed. 1) The qualitative character of the evolution of a disturbance to a stable meridional shear flow, as described by the barotropic vorticity equation, depends critically on whether the disturbance projects primarily onto discrete modes or onto continuum modes that cascade enstrophy to small meridional scales. It is demonstrated that the pseudomomentum and pseudoenergy orthogonality relations provide a natural framework for examining the relative excitation of discrete and continuum modes. 2) Using a quasi-geostrophic potential vorticity equation, it is shown that pseudomomentum orthogonality provides a simple explanation for how quasi-stationary neutral external modes of large amplitude can be excited by a small initial disturbance.

112. Held, Isaac, and B J Hoskins, 1985: Large-scale eddies and the general circulation of the troposphere. Advances in Geophysics, 28A, 3-31.
113. Held, Isaac, R L Panetta, and R T Pierrehumbert, 1985: Stationary external Rossby waves in vertical shear. Journal of the Atmospheric Sciences, 42(9), 865-883.
     [ Abstract PDF ]

     The structure of stationary Rossby waves in the presence of a mean westerly zonal flow with vertical shear is examined. There is typically only one stationary vertical mode, the external mode, trapped within the troposphere. For more that one tropospheric mode to exist, we find that vertical shears must be smaller than those usually observed in extratropical latitudes. The vertical structure, horizontal wavenumber and group velocity of the external mode, and the projection onto this mode of topographic and thermal forcing are studied with continuous models (a linear shear profile as well as more realistic basic states), and a finite-differenced model with resolution and upper boundary condition similar to that used in GCMs. We point out that the rigid-lid upper boundary condition need not create artificial stationary resonances, as the artificial stationary vertical modes that are created are often horizontally evanescent. The results are presented in a form which allows one to design the equivalent barotropic model that captures the external mode's contribution to the stationary wave field. It is found, in particular, that the wind blowing over the topography in such a barotropic model should generally be larger than the surface wind but smaller than the wind at the equivalent barotropic level. Also, the group velocity of the stationary external mode in realistic vertical shear is found to be considerably greater than that of the stationary Rossby wave in the equivalent barotropic model.

114. Sardeshmukh, P D., and Isaac Held, 1984: The vorticity balance in the tropical upper troposphere of a general circulation model. Journal of the Atmospheric Sciences, 41(5), 768-778.
     [ Abstract PDF ]

     The time mean vorticity balance in the summertime tropical upper troposphere of an atmospheric general circulation model constructed at the Geophysical Fluid Dynamics Laboratory is examined, with particular emphasis on the detailed balance in the Tibetan anticyclone. The model produces a reasonable simulation of the large-scale features of the northern summer 200 mb flow in the tropics, without the inclusion of subgrid scale processes that strongly damp the upper tropospheric vorticity. the vorticity balance is essentially nonlinear and nearly inviscid. There is considerable cancellation between the stretching and horizontal advection of vorticity by the time mean flow in the vicinity of the Tibetan anticyclone, with much of the remainder balanced by vertical advection and twisting. Mixing by the resolved transients is not negligible in some regions, but considerably smaller than the horizontal advection overall and less well correlated with the stretching. Subgrid scale mixing (consisting only of a biharmonic horizontal diffusion) plays a negligible role in this vorticity budget. To relate this study to linear models of the stationary flow in the tropics, the steady state barotropic vorticity equation on the sphere is linearized about the GCM's July mean zonal flow at 200 mb and forced with the GCM's July mean vortex stretching. It is found that the strength of the Tibetan anticyclone can be reproduced only by including a very strong damping of vorticity in this linear model. The strong damping needed by other authors (e.g., Holton and Colton) in their linear diagnoses of the tropical upper tropospheric vorticity balance is therefore interpreted as possibly accounting for neglected nonlinearities, and not necessarily cumulus friction. Our conclusions are, however, potentially suspect, since the terms in our vorticity budget have considerable structure on the smallest scales that can be resolved by the GCM.

115. Held, Isaac, 1983: External Rossby waves and the barotropic response to stationary forcing In IAMAP-WMO Symposium on Maintenance of the Quasi-Stationary Components of the Flow in the Atmosphere and in Atmospheric Models, Geneva, Switzerland, World Meteorological Organization, 53-54.
116. Held, Isaac, 1983: Stationary and quasi-stationary eddies in the extratropical troposphere: theory In Large-scale Dynamical Processes in the Atmosphere, New York, NY, Academic Press, 127-168.
117. Held, Isaac, and D G Andrews, 1983: On the direction of the eddy momentum flux in baroclinic instability. Journal of the Atmospheric Sciences, 40(9), 2220-2231.
     [ Abstract PDF ]

     The direction of the vertically-integrated horizontal eddy flux momentum in linear baroclinically unstable modes is investigated in a number of cases where the basic flow contains horizontal, as well as vertical, shear. A general result is presented for slowly-growing modes on a flow with weak horizontal shear. Some special cases are described in which standard baroclinic instabilities of finite growth rate (for an internal jet, Eady's model, and a two-layer model) are perturbed by weak horizontal shear, and some computations for flows with large horizontal shear are also mentioned. A general rule emerging from these calculations is that for flows with horizontal jet structure of broader scale than the radius of deformation, the vertically-integrated momentum flux tends to be into the jet (or upgradient); while for jets narrower than the radius of deformation, momentum fluxes tend to be out of the jet (downgradient), even when the contribution of horizontal curvature to the basic state potential vorticity gradient is negligible. However, some exceptions to this general rule exist.

118. Nigam, S, and Isaac Held, 1983: The influence of critical latitude on topographically forced stationary waves in a barotropic model. Journal of the Atmospheric Sciences, 40(11), 2610-2622.
     [ Abstract PDF ]

     A nondivergent barotropic model on a sphere is used to study the effects of a critical latitude on stationary atmospheric waves forced by topography. Linear and "quasi-linear" calculations are performed with an idealized wavenumber 3 mountain and with realistic topography. Qusai-linear dynamics, where mean flow changes are due to momentum flux convergence, "form drag" and relaxation to a prescribed climatological mean flow, produces an S-shaped kink in the zonal mean absolute vorticity gradient near the critical latitude, resulting in enhanced reflection. The component of the quasi-linear solution resulting from enhanced reflection at the calculation with realistic topography and zonal flow, this reflected component is found to be dominated by a wave train emanating from the western tropical Pacific and propagating northward and then eastward across the Pacific Ocean and the North American continent. This wave train results from the reflection of the Himalayan wave train at the zero-wind latitude in the tropical winter troposphere. The vorticity gradients in the monthly mean statistics of Oort (1983) show structure near the critical latitude similar to that produced in our quasi-linear model, suggesting that some reflection of incident Rossby waves is likely in the atmosphere, at least in the western Pacific, and that the wind structure responsible for this reflection may be created in part by the stationary Rossby waves themselves.

119. Nigam, S, and Isaac Held, 1983: Linear and quasi-linear stationary waves: influence of a critical latitude In IAMAP-WMO Symposium on Maintenance of the Quasi-Stationary Components of the Flow in the Atmosphere and in Atmospheric Models, Geneva, Switzerland, World Meteorological Organization, 279-282.
120. Held, Isaac, 1982: On the height of the tropospause and the static stability of the troposphere. Journal of the Atmospheric Sciences, 39(2), 412-417.
     [ Abstract PDF ]

     Speculative arguments are presented that describe how radiative and dynamical constraints conspire to determine the height of the tropopause and the tropospheric static stability in midlatitudes and in the tropics. The arguments suggest an explanation for the observation that climatological isentropic slopes in midlatitudes are close to the critical slope required for baroclinic instability in a two-layer model.

121. Held, Isaac, 1982: Climate models and the astronomical theory of the ice ages. Icarus, 50(2-3), 449-461.
     [ Abstract PDF ]

     Attempts at determining the climatic response to perturbations in the Earth's orbital parameters are reviewed. The relationship between equilibrium and nonequilibrium responses and its implications for climatic sensitivity are discussed in the context of an empirical model due to Imbrie and Imbrie. Some counterintuitive features of the linear equilibrium response to the perihelion cycle in a simple energy balance model are then described in detail. The results of North and Coakley and of Pollard are examined as examples of results that are, respectively, discouraging and mildly encouraging for proponents of the astronomical theory of the ice ages. The attempt by Suarez and Held to address some of the deficiencies in the simplest energy balance models is reviewed, followed by a brief preview of some calculations of relevance to the ice age problem performed by Manabe and co-workers with an atmospheric general circulation model.

122. Held, Isaac, D I Linder, and M J Suarez, 1981: Albedo feedback, the meridional structure of the effective heat diffusivity, and climatic sensitivity: Results from dynamic and diffusive models. Journal of the Atmospheric Sciences, 38(9), 1911-1927.
     [ Abstract PDF ]

     The sensitivity of a two-level primitive equation atmospheric model to solar constant perturbations is examined in the presence of surface albedo feedback. The model is simplified to the point that a large number of numerical experiments can be performed and statistically steady states defined with relative ease. Exceptionally sensitive equilibrium states are found that are unrelated to the large and small ice-cap instabilities obtained in the simplest diffusive energy balance models. Similar results are produced in a two-level diffusive model closely patterned after the dynamic model, and in a more highly idealized one-level model, by choosing a diffusivity with pronounced meridional structure resembling that of the effective diffusivity of the dynamic model. Sensitive states occur in the diffusive models when the albedo gradient enters the region equatorward of 60 degrees in which the effective heat diffusivity of the atmosphere increases with increasing latitude.

123. Haidvogel, D B., and Isaac Held, 1980: Homogeneous quasi-geostrophic turbulence driven by a uniform temperature gradient. Journal of the Atmospheric Sciences, 37(12), 2644-2660.
     [ Abstract PDF ]

     Statistically steady states consistent with a horizontally uniform time-averaged temperature gradient in a two-layer quasi-geostrophic model on a beta-plane are found by numerically integrating the equations for deviations from this mean state in a doubly periodic domain. Based on the result that the flow statistics are not strongly dependent on the size of the domain, it is suggested that this homogeneous flow is physically realizable. Statistically steady states consistent with a horizontally uniform time-averaged temperature gradient in a two-layer quasi-geostrophic model on a beta-plane are found by numerically integrating the equations for deviations from this mean state in a doubly periodic domain. Based on the result that the flow statistics are not strongly dependent on the size of the domain, it is suggested that this homogeneous flow is physically realizable. The dependence of the eddy heat and potential vorticity fluxes and eddy energy level on various model parameters (the beta effect, surface drag, small-scale horizontal mixing) is described. Implications for eddy flux paramterization theories are discussed.

124. Held, Isaac, and A Y Hou, 1980: Nonlinear axially symmetric circulations in a nealy inviscid atmosphere. Journal of the Atmospheric Sciences, 37(3), 515-533.
     [ Abstract PDF ]

     The structure of certain axially symmetric circulations in a stably stratified, differentially heated, rotating Boussinesq fluid on a sphere is analyzed. A simple approximate theory [similar to that introduced by Schneider (1977)] is developed for the case in which the fluid is sufficiently inviscid that the poleward flow in the Hadley cell is nearly angular momentum conserving. The theory predicts the width of the Hadley cell, the total poleward heat flux, the latitude of the upper level jet in the zonal wind, and the distributions of surface easterlies and westerlies. Fundamental differences between such nearly inviscid circulations and the more commonly studied viscous axisymmetric flows are emphasized. The theory is checked against numerical solutions to the model equations.

125. Suarez, M J., and Isaac Held, 1979: The sensitivity of an energy balance climate model to variations in the orbital parameters. Journal of Geophysical Research, 84(C8), 4825-4836.
     [ Abstract PDF ]

     The responses of a zonally symmetric model of the global energy balance to perturbations in incident solar radiation are analyzed. The model is forced with seasonally varying insolation and incorporates in a simple way the positive feedback due to the high albedo of snow and sea ice. Meridional energy transport due to atmospheric motions is simulated with lateral diffusion of heat. Meridional energy transport by oceanic currents is ignored, as are possible variations in cloudiness. Emphasis is placed on the model's sensitivity to the latitudinal and seasonal redistribution of insolation produced by variations in the obliquity, the eccentricity, and the longitude of perihelion of the earth's orbit. It is found that when albedos are allowed to vary, increased seasonal variation of insolation leads to increased temperature in the northern hemisphere. In all cases considered, the latitudinal extent of perennial snow cover in the northern hemisphere is particularly sensitive to the perturbations, a response suggestive of the large fluctuations of continental glaciers during the Pleistocene. When the model is forced with the orbital variations of the past 150,000 years, its response is qualitatively similar to the geologic record of that period.

126. Held, Isaac, 1978: The tropospheric lapse rate and climatic sensitivity: Experiments with a two-level atmospheric model. Journal of the Atmospheric Sciences, 35(11), 2083-2098.
     [ Abstract PDF ]

     The sensitivity of both moist and dry versions of a two-level primitive equation atmospheric model to variations in the solar constant is analyzed. The models have fixed surface albedos, fixed cloudiness and a zero heat flux lower boundary condition, and are forced with annual mean solar fluxes. An attempt is made to understand the response of the static stability in these model atmospheres and the importance of these changes in stability for the climatic responses of other parts of the system. In the moist model, the static stability increases in low latitudes but decreases in high latitudes as the solar constant increases, resulting in considerable latitudinal structure in the sensitivity of surface temperatures and zonal winds. In the dry model the stability decreases at all latitudes as the solar constant increases. It is argues that this decrease in stability in the dry model, through its effect on ientropic slopes and the supercriticality of the flow, is responsible for the observed large increases in eddy energies and fluxes. Parameterization schemes for the eddy heat flux are critically examined in light ofthese results.

127. Held, Isaac, and M J Suarez, 1978: A two-level primitive equation atmospheric model designed for climatic sensitivity experiments. Journal of the Atmospheric Sciences, 35, 206-299.
     [ Abstract PDF ]

     A useful but as yet under-utilized tool for climatic studies is an atmospheric model in which the time evolution of large-scale eddies is resolved explicitly, but in a relatively simple dynamical framework. One such model is described in detail in this study- a two-level primitive equation model on a sphere with variable static stability, finite-differenced in the meridional direction but Fourier analyzed and then very severely truncated in the zonal direction. Two versions of the model -moist and dry- are developed, the maintenance of the model's static stability being markedly different in the two versions. Statistically steady states are obtained for a variety of spectral truncations for both versions of the model in order to determine the fewest zonal wavenumbers one can retain and still obtain a reasonable zonally averaged circulation. Including only one wave, of wavelength typical of strongly unstable waves in midlatitudes, results in a circulation with a subpolar jet as well as a subtropical jet in the zonal wind. The addition of a longer wave (i.e., the addition of wavenumber 3 to wavenumber 6) results in the destruction of the subpolar jet. No further dramatic changes in the zonally averaged flow occur as more waves are added to the system. Features of the model's dynamics which might limit its utility are emphasized, notably the dependence of the strength of the Hadley cell on the details of the convective adjustment scheme. We find, however, that the total energy transported by the Hadley cell is insensitive to such details. Climatic senstivity experiments with these models will be described in forthcoming papers.

128. Held, Isaac, 1975: Momentum transport by quasi-geostrophic eddies. Journal of the Atmospheric Sciences, 32(7), 1494-1497.
     [ Abstract PDF ]

     Some results due to Kuo concerning momentum fluxes in barotropic flows are generalized so as to apply to quasi-geostrophic flows on a beta-plane. It is shown that linear, amplifying waves on an arbitrary zonal flow cause a net transport of westerly momentum out of that part of the fluid in which Raleigh's stability criterion (as generalized by Charney and Stern, and by Pedlosky) is satisfied locally. Also, it is shown that if quasi-geostrophic eddies are introduced by some "external" agent into a region in which the zonal flow satisfies the stability criterion, then westerly momentum will flow into this region.

129. Held, Isaac, and M J Suarez, 1974: Simple albedo feedback models of the icecaps. Tellus, 26(6), 613-629.
     [ Abstract ]

     A series of simple models of the albedo feedback mechanism and its effect on the global climate are solved analytically. All of the models are similar to one considered by Budyko. The seasonal variation in incident solar radiation is ignored. Emphasis is placed on the parameter dependence of the models' sensitivity to changes in the solar constant. It is found in all cases that increasing the efficiency of the poleward transport of energy increases this sensitivity. It is also suggested that knowledge of the partitioning of the transport between the atmosphere and the oceans is of considerable importance for estimating sensitivity. The stability of equilibrium states is determined from the properties of small perturbations away from equilibrium. It is observed that relaxation times of perturbations can be increased considerably by the albedo feedback mechanism. The effect of variations in the obliquity of the planet's orbit on sensitivity and stability is also analyzed. The results indicate that albedo feedback may increase the significance of obliquity variations on Mars, as well as on the Earth.

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