Bibliography - Shaoqing Zhang

1. Chang, You-Soon, Shaoqing Zhang, Anthony Rosati, Thomas L Delworth, and William F Stern, February 2013: An assessment of oceanic variability for 1960–2010 from the GFDL ensemble coupled data assimilation. Climate Dynamics, 40(3-4), DOI:10.1007/s00382-012-1412-2.
   [ Abstract ]

   The Geophysical Fluid Dynamics Laboratory has developed an ensemble coupled data assimilation (ECDA) system based on the fully coupled climate model, CM2.1, in order to provide reanalyzed coupled initial conditions that are balanced with the climate prediction model. Here, we conduct a comprehensive assessment for the oceanic variability from the latest version of the ECDA analyzed for 51 years, 1960–2010. Meridional oceanic heat transport, net ocean surface heat flux, wind stress, sea surface height, top 300 m heat content, tropical temperature, salinity and currents are compared with various in situ observations and reanalyses by employing similar configurations with the assessment of the NCEP’s climate forecast system reanalysis (Xue et al. in Clim Dyn 37(11):2511–2539, 2011). Results show that the ECDA agrees well with observations in both climatology and variability for 51 years. For the simulation of the Tropical Atlantic Ocean and global salinity variability, the ECDA shows a good performance compared to existing reanalyses. The ECDA also shows no significant drift in the deep ocean temperature and salinity. While systematic model biases are mostly corrected with the coupled data assimilation, some biases (e.g., strong trade winds, weak westerly winds and warm SST in the southern oceans, subsurface temperature and salinity biases along the equatorial western Pacific boundary, overestimating the mixed layer depth around the subpolar Atlantic and high-latitude southern oceans in the winter seasons) are not completely eliminated. Mean biases such as strong South Equatorial Current, weak Equatorial Under Current, and weak Atlantic overturning transport are generated during the assimilation procedure, but their variabilities are well simulated. In terms of climate variability, the ECDA provides good simulations of the dominant oceanic signals associated with El Nino and Southern Oscillation, Indian Ocean Dipole, Pacific Decadal Oscillation, and Atlantic Meridional Overturning Circulation during the whole analyzed period, 1960–2010.

2. Vecchi, Gabriel A., Rym Msadek, Whit G Anderson, You-Soon Chang, Thomas L Delworth, Keith W Dixon, Rich Gudgel, Anthony Rosati, William F Stern, G Villarini, Andrew T Wittenberg, Xiaosong Yang, Fanrong Zeng, Rong Zhang, and Shaoqing Zhang, in press: Multi-year Predictions of North Atlantic Hurricane Frequency: Promise and limitations. Journal of Climate. DOI:10.1175/JCLI-D-12-00464.1. 2/13.
   [ Abstract ]

   Retrospective predictions of multi-year North Atlantic hurricane frequency are explored, by applying a hybrid statistical-dynamical forecast system to initialized and non-initialized multi-year forecasts of tropical Atlantic and tropical mean sea surface temperatures (SSTs) from two global climate model forecast systems. By accounting for impacts of initialization and radiative forcing, retrospective predictions of five-year mean and nine-year mean tropical Atlantic hurricane frequency show significant correlation relative to a null hypothesis of zero correlation. The retrospective correlations are increased in a two-model average forecast and by using a lagged-ensemble approach, with the two-model ensemble decadal forecasts hurricane frequency over 1961-2011 yielding correlation coefficients that approach 0.9. These encouraging retrospective multi-year hurricane predictions, however, should be interpreted with care: although initialized forecasts have higher nominal skill than uninitialized ones, the relatively short record and large autocorrelation of the time series limits our confidence in distinguishing between the skill due to external forcing and that added by initialization. The nominal increase in correlation in the initialized forecasts relative to the uninitialized experiments is due to improved representation of the multi-year tropical Atlantic SST anomalies. The skill in the initialized forecasts comes in large part from the persistence of a mid-1990s shift by the initialized forecasts, rather than from predicting its evolution. Predicting shifts like that observed in 1994-1995 remains a critical issue for the success of multi-year forecasts of Atlantic hurricane frequency. The retrospective forecasts highlight the possibility that changes in observing system impact forecast performance.

3. Yang, Xiaosong, Anthony Rosati, Shaoqing Zhang, Thomas L Delworth, Rich Gudgel, Rong Zhang, Gabriel A Vecchi, Whit G Anderson, You-Soon Chang, T DelSole, Keith W Dixon, Rym Msadek, William F Stern, Andrew T Wittenberg, and Fanrong Zeng, January 2013: A predictable AMO-like pattern in GFDL's fully-coupled ensemble initialization and decadal forecasting system. Journal of Climate, 26(2), DOI:10.1175/JCLI-D-12-00231.1.
   [ Abstract ]

   The decadal predictability of sea surface temperature (SST) and 2m air temperature (T2m) in Geophysical Fluid Dynamics Laboratory (GFDL)'s decadal hindcasts, which are part of the Fifth Coupled Model Intercomparison Project experiments, has been investigated using an average predictability time (APT) analysis. Comparison of retrospective forecasts initialized using the GFDL's Ensemble Coupled Data Assimilation system with uninitialized historical forcing simulations using the same model, allows identification of internal multidecadal pattern (IMP) for SST and T2m. The IMP of SST is characterized by an inter-hemisphere dipole, with warm anomalies centered in the North Atlantic subpolar gyre region and North Pacific subpolar gyre region, and cold anomalies centered in the Antarctic Circumpolar Current region. The IMP of T2m is characterized by a general bi-polar seesaw, with warm anomalies centered in Greenland, and cold anomalies centered in Antarctica. The retrospective prediction skill of the initialized system, verified against independent observations, indicates that the IMP of SST may be predictable up to 4 (10) year lead time at 95% (90%) significance level, and the IMP of T2m may be predictable up to 2 (10) years at 95% (90%) significance level. The initialization of multidecadal variations of northward oceanic heat transport in the North Atlantic significantly improves the predictive skill of the IMP. The dominant roles of oceanic internal dynamics in decadal prediction are further elucidated by fixed-forcing experiments, in which radiative forcing is returned to 1961 values. These results point towards the possibility of meaningful decadal climate outlooks using dynamical coupled models, if they are appropriately initialized from a sustained climate observing system.

4. Wu, X, Shaoqing Zhang, Z Liu, Anthony Rosati, and Thomas L Delworth, in press: A study of impact of the geographic dependence of observing system on parameter estimation with an intermediate coupled model. Climate Dynamics. DOI:10.1007/s00382-012-1385-1. 4/12.
   [ Abstract ]

   Observational information has a strong geographic dependence that may directly influence the quality of parameter estimation in a coupled climate system. Using an intermediate atmosphere-ocean-land coupled model, the impact of geographic dependent observing system on parameter estimation is explored within a ‘‘twin’’ experiment framework. The ‘‘observations’’ produced by a ‘‘truth’’ model are assimilated into an assimilation model in which the most sensitive model parameter has a different geographic structure from the ‘‘truth’’, for retrieving the ‘‘truth’’ geographic structure of the parameter. To examine the influence of data-sparse areas on parameter estimation, the twin experiment is also performed with an observing system in which the observations in some area are removed. Results show that traditional single-valued parameter estimation (SPE) attains a global mean of the ‘‘truth’’, while geographic dependent parameter optimization (GPO) can retrieve the ‘‘truth’’ structure of the parameter and therefore significantly improves estimated states and model predictability. This is especially true when an observing system with data-void areas is applied, where the error of state estimate is reduced by 31 % and the corresponding forecast skill is doubled by GPO compared with SPE.

5. Wu, X, Shaoqing Zhang, Z Liu, Anthony Rosati, Thomas L Delworth, and Y Liu, December 2012: Impact of Geographic Dependent Parameter Optimization on Climate Estimation and Prediction: Simulation with an Intermediate Coupled Model. Monthly Weather Review, 140(12), DOI:10.1175/MWR-D-11-00298.1.
   [ Abstract ]

   Due to the geographic dependence of model sensitivities and observing systems, allowing optimized parameter values to vary geographically may significantly enhance the signal in parameter estimation. Using an intermediate atmosphere-ocean-land coupled model, the impact of geographic dependence of model sensitivities on parameter optimization is explored within a twin experiment framework. The coupled model consists of a 1-layer global barotropic atmosphere model, a 1.5-layer baroclinic ocean including a slab mixed layer with simulated upwelling by a streamfunction equation and a simple land model. The assimilation model is biased by erroneously setting the values of all model parameters. Four most sensitive parameters identified by sensitivity studies are used to perform traditional single-value parameter estimation and new geographic dependent parameter optimization. Results show that the new parameter optimization significantly improves the quality of state estimates compared to the traditional scheme, with reductions of root mean square errors as 41%, 23%, 62% and 59% for the atmospheric streamfunction, the oceanic streamfunction, sea surface temperature and land surface temperature respectively. Consistently, the new parameter optimization greatly improves the model predictability due to the improvement of initial conditions and the enhancement of observational signals in optimized parameters. These results suggest that the proposed geographic dependent parameter optimization scheme may provide a new perspective when a coupled general circulation model is used for climate estimation and prediction.

6. Zhang, Shaoqing, Z Liu, Anthony Rosati, and Thomas L Delworth, January 2012: A study of enhancive parameter correction with coupled data assimilation for climate estimation and prediction using a simple coupled model. Tellus A, 64, 10963, DOI:10.3402/tellusa.v64i0.10963.
   [ Abstract ]

   Uncertainties in physical parameters of coupled models are an important source of model bias and adversely impact initialisation for climate prediction. Data assimilation using error covariances derived from model dynamics to extract observational information provides a promising approach to optimise parameter values so as to reduce such bias. However, effective parameter estimation in a coupled model is usually difficult because the error covariance between a parameter and the model state tends to be noisy due to multiple sources of model uncertainties. Using a simple coupled model consisting of the 3-variable Lorenz model and a slowly varying slab ‘ocean’, this study first investigated how to enhance the signal-to-noise ratio in covariances between model states and parameters, and then designed a data assimilation scheme for enhancive parameter correction (DAEPC). In DAEPC, parameter estimation is facilitated after state estimation reaches a ‘quasiequilibrium’ where the uncertainty of coupled model states is sufficiently constrained by observations so that the covariance between a parameter and the model state is signal dominant. The observation-updated parameters are applied to improving the next cycle of state estimation and the refined covariance of parameter and model state further improves parameter correction. Performing dynamically adaptive state and parameter estimations with speedy convergence, DAEPC provides a systematic way to estimate the whole array of coupled model parameters using observations, and produces more accurate state estimates. Forecast experiments show that the DAEPC initialisation with observation-estimated parameters greatly improves the model predictability - while valid ‘atmospheric’ forecasts are extended two times longer, the ‘oceanic’ predictability is almost tripled. The simple model results here provide some insights for improving climate estimation and prediction with a coupled general circulation model.

7. Zhang, Shaoqing, Michael Winton, Anthony Rosati, Thomas L Delworth, and B Huang, in press: Impact of Enthalpy-Based Ensemble Filtering Sea-Ice Data Assimilation on Decadal Predictions: Simulation with a Conceptual Pycnocline Prediction Model. Journal of Climate. DOI:10.1175/JCLI-D-11-00714.1. 10/12.
   [ Abstract ]

   The non-Gaussian probability distribution of sea-ice concentration makes difficulties for directly assimilating sea-ice observations into a climate model. Because of the strong impact of the atmospheric and oceanic forcing on the sea-ice state, any direct assimilation adjustment on sea-ice states is easily overridden by model physics.A new approach implements sea-ice data assimilation in enthalpy space where a sea-ice model represents a nonlinear function that transforms a positive-definite space into the sea-ice concentration subspace.Results from observation-assimilation experiments using a conceptual pycnocline prediction model that characterizes the influences of sea-ice on the decadal variability of the climate system show that the new scheme efficiently assimilates “sea-ice observations” into the model – while improving “sea-ice” variability itself, it consistently improves the estimates of all “climate” components.The resulted coupled initialization that is physically consistent among all coupled components significantly improves decadal-scale predictability of the coupled model.

8. Chang, You-Soon, Anthony Rosati, and Shaoqing Zhang, February 2011: A construction of pseudo salinity profiles for the global ocean: Method and evaluation. Journal of Geophysical Research, 116, C02002, DOI:10.1029/2010JC006386.
   [ Abstract ]

   This study demonstrates a reconstruction of salinity profiles for the global ocean for the period 1993-2008. All available T-S profiles from the GTSPP and Argo data are divided in two subsets; one half used for producing the vertical coupled T-S EOF modes and the other for the verification. We employ a weighted least square method that minimizes the misfits between the predetermined EOF structures and independent observed temperature and altimetry data. Verification shows that the South Indian and North Atlantic Oceans maintain good correlations to 900 m depth between the observed and reconstructed salinity with altimetry data. Meanwhile, the Pacific and Antarctic Oceans below 500 m show significant negative correlations, which is associated with the relationship between steric height and salinity variability in these basins. In order to guarantee general agreements with observations for all ocean depths, we calculate a regional correlation index considering the impact of altimetry data and employ it for our final products. Except for the surface ocean, the pseudo salinity profiles show general improvements compared to the existing climatology and the reanalysis outputs from the GFDL’s ensemble coupled data assimilation system. Near the surface layer, reanalysis outputs show a relatively high performance due to the coupling between the atmosphere and ocean. Assimilation system produces reliable surface flux variability not accounted for the construction of the global pseudo salinity profiles. These results encourage the application of the global pseudo salinity profiles into an assimilation system for the 20th century when the observed salinity data are sparse.

9. Chang, You-Soon, Shaoqing Zhang, and Anthony Rosati, July 2011: Improvement of salinity representation in an ensemble coupled data assimilation system using pseudo salinity profiles. Geophysical Research Letters, 38, L13609, DOI:10.1029/2011GL048064.
   [ Abstract ]

   The scarcity of salinity observations prior to the Argo period makes it tremendously difficult to estimate ocean states. By using the so-called pseudo salinity profiles constructed from temperature and altimetry information, here we show the improvement of salinity representation estimated by the ensemble coupled data assimilation system of the Geophysical Fluid Dynamics Laboratory. The comparisons with climatology and independent observations show that the pseudo salinity data considerably improve the assimilation skill for the pre-Argo period (1993- 2001). For the Argo period (2002-2007), there is little degradation of the assimilation skill using pseudo salinity instead of Argo observations. This result ensures the robustness of the new assimilation fields with pseudo salinity for the pre-Argo period when salinity observations are sparse. We also suggest that the interannual variability of the existing reanalysis products could suffer from erroneously-estimated discontinuities due to the non-stationary nature of the salinity observing system.

10. Mahajan, S, Rong Zhang, Thomas L Delworth, Shaoqing Zhang, Anthony Rosati, and You-Soon Chang, September 2011: Predicting Atlantic meridional overturning circulation (AMOC) variations using subsurface and surface fingerprints. Deep-Sea Research, Part II, 58(17-18), DOI:10.1016/j.dsr2.2010.10.067.
    [ Abstract ]

    Recent studies have suggested that the leading modes of North Atlantic subsurface temperature (T_sub) and sea surface height (SSH) anomalies are induced by Atlantic meridional overturning circulation (AMOC) variations and can be used as fingerprints of AMOC variability. Based on these fingerprints of the AMOC in the GFDL CM2.1 coupled climate model, a linear statistical predictive model of observed fingerprints of AMOC variability is developed in this study. The statistical model predicts a weakening of AMOC strength in a few years after its peak around 2005. Here, we show that in the GFDL coupled climate model assimilated with observed subsurface temperature data, including recent Argo network data (2003–2008), the leading mode of the North Atlantic T_sub anomalies is similar to that found with the objectively analyzed T_sub data and highly correlated with the leading mode of altimetry SSH anomalies for the period 1993–2008. A statistical auto-regressive (AR) model is fit to the time-series of the leading mode of objectively analyzed detrended North Atlantic T_sub anomalies (1955–2003) and is applied to assimilated T_sub and altimetry SSH anomalies to make predictions. A similar statistical AR model, fit to the time-series of the leading mode of modeled T_sub anomalies from the 1000-year GFDL CM2.1 control simulation, is applied to predict modeled T_sub, SSH, and AMOC anomalies. The two AR models show comparable skills in predicting observed T_sub and modeled T_sub, SSH and AMOC variations.

11. Zhang, Shaoqing, January 2011: Impact of observation-optimized model parameters on decadal predictions: Simulation with a simple pycnocline prediction model. Geophysical Research Letters, 38, L02702, DOI:10.1029/2010GL046133.
    [ Abstract ]

    A skillful decadal prediction that foretells varying regional climate conditions over seasonal-interannual to multidecadal time scales is of societal significance. However, predictions initialized from the climate observing system tend to drift away from observed states towards the imperfect model climate due to model biases arising from imperfect model equations, numeric schemes and physical parameterizations, as well as the errors in the values of model parameters. Here I show how to mitigate the model bias through optimizing model parameters using observations so as to constrain the model drift in climate predictions with a simple decadal prediction model. Results show that the coupled state-parameter optimization with observations greatly enhances the predictability of the coupled model. While valid “atmospheric” forecasts are extended by more than 5 times, the decadal predictability of the “deep ocean” is almost doubled. The coherence of optimized model parameters and states is critical to improve the long time scale predictions.

12. Zhang, Shaoqing, December 2011: A study of impacts of coupled model initial shocks and state-parameter optimization on climate predictions using a simple pycnocline prediction model. Journal of Climate, 24(23), DOI:10.1175/JCLI-D-10-05003.1.
    [ Abstract ]

    A skillful decadal prediction that foretells varying regional climate conditions over seasonal-interannual to multidecadal time scales is of societal significance. However, predictions initialized from the climate observing system tend to drift away from observed states towards the imperfect model climate due to model biases arising from imperfect model equations, numeric schemes and physical parameterizations, as well as the errors in the values of model parameters. Here a simple coupled model that simulates the fundamental features of the real climate system and a “twin” experiment framework are designed to study the impact of initialization and parameter optimization on decadal predictions. One model simulation is treated as “truth” and sampled to produce “observations” that are assimilated into other simulations to produce “observation”-estimated states and parameters. The degree to which the model forecasts based on different estimates recover the truth is an assessment of the impact of coupled initial shocks and parameter optimization on climate predictions of interests. The results show that the coupled model initialization through coupled data assimilation in which all coupled model components are coherently adjusted by observations minimizes the initial coupling shocks that reduce the forecast errors on seasonal-interannual time scales. Model parameter optimization with observations effectively mitigates the model bias, thus constraining the model drift in long time scale predictions. The coupled model state-parameter optimization greatly enhances the model predictability. While valid “atmospheric” forecasts are extended 5 times, the decadal predictability of the “deep ocean” is almost doubled. The coherence of optimized model parameters and states is critical to improve the long time scale predictions.

13. Zhang, Shaoqing, Anthony Rosati, and Thomas L Delworth, October 2010: The adequacy of observing systems in monitoring AMOC and North Atlantic climate. Journal of Climate, 23(19), DOI:10.1175/2010JCLI3677.1.
    [ Abstract ]

    The Atlantic Meridional Overturning Circulation (AMOC) has an important influence on climate, and yet we lack adequate observations of this circulation. Here we assess the adequacy of past and current widely deployed routine observing systems for monitoring the AMOC and associated North Atlantic climate. To do so we draw on two independent simulations of the 20th century using an IPCC AR4 coupled climate model. We treat one simulation as “truth” and sample it according to the observing system we are evaluating. We then assimilate these synthetic “observations” into the second simulation within a fully-coupled system that instantaneously exchanges information among all coupled components and produces a nearly balanced and coherent estimate for global climate states including the North Atlantic climate system. The degree to which the assimilation recovers the “truth” is an assessment of the adequacy of the observing system being evaluated. As the coupled system responds to the constraint of the atmosphere or ocean, the assessment of the recovery for climate quantities such as Labrador Sea Water (LSW) and the North Atlantic Oscillation increases our understanding for the factors that determine AMOC variability. For example, we found the low-frequency sea-surface forcings provided by the atmospheric and sea-surface temperature observations can excite a LSW variation that governs the long time scale variability of the AMOC. When we use the most complete modern observing system consisting of atmospheric winds and temperature, along with Argo ocean temperature and salinity down to 2000 meters, a skill estimate of AMOC reconstruction is 90% (out of 100% maximum). Similarly encouraging results hold for other quantities, such as LSW. The past XBT observing system, in which deep ocean temperature and salinity were not available, has a lesser ability to recover the “truth” AMOC (the skill is reduced to 52%). While these results raise concerns about our ability to properly characterize past variations of the AMOC, they also hold promise for future monitoring of the AMOC and for initializing prediction models.

14. Zhang, Shaoqing, and Anthony Rosati, October 2010: An inflated ensemble filter for ocean sata assimilation with a biased coupled GCM. Monthly Weather Review, 138(10), DOI:10.1175/2010MWR3326.1.
    [ Abstract ]

    A “biased twin” experiment using two coupled general circulation models (CGCMs) that are biased with respect to each other is used to study the impact of deep ocean bias on ensemble ocean data assimilation. The “observations” drawn from one CGCM based on the Argo network are assimilated into the other. Traditional ensemble filtering can successfully recover the upper-ocean temperature and salinity of the target model but it usually fails to converge in the deep ocean where the model bias is large compared to the ocean’s intrinsic variability. The inconsistency between the well-constrained upper ocean and poorly constrained deep ocean generates spurious assimilation currents. An adaptively inflated ensemble filter is designed to enhance the consistency of upper- and deep-ocean adjustments, based on “climatological” standard deviations being adaptively updated by observations. The new algorithm reduces deep-ocean errors greatly, in particular, reducing current errors up to 70% and vertical motion errors up to 50%. Specifically, the tropical circulation is greatly improved with a better representation of the undercurrent, upwelling, and Western Boundary Current systems. The structure of the subtropical gyre is also substantially improved. Consequently, the new algorithm leads to better estimates of important global hydrographic features such as global overturning and pycnocline depth. Based on these improved estimates, decadal trends of basin-scale heat content and salinity as well as the seasonal–interannual variability of the tropical ocean are constructed coherently. Interestingly, the Indian Ocean (especially the north Indian Ocean), which is associated with stronger atmospheric feedbacks, is the most sensitive basin to the covariance formulation used in the assimilation. Also, while reconstruction of the local thermohaline structure plays a leading-order role in estimating the decadal trend of the Atlantic meridional overturning circulation (AMOC), more accurate estimates of the AMOC variability require coupled assimilation to produce coherently improved external forcings as well as internal heat and salt transport.

15. Chang, You-Soon, Anthony Rosati, Shaoqing Zhang, and Matthew J Harrison, February 2009: Objective analysis of monthly temperature and salinity for the world ocean in the 21st century: Comparison with World Ocean Atlas and application to assimilation validation. Journal of Geophysical Research, 114, C02014, DOI:10.1029/2008JC004970.
    [ Abstract ]

    A new World Ocean atlas of monthly temperature and salinity, based on individual profiles for 2003–2007 (WOA21c), is constructed and compared with the World Ocean Atlas 2001 (WOA01), the World Ocean Atlas 2005 (WOA05), and the data assimilation analysis from the Coupled Data Assimilation (CDA) system developed by the Geophysical Fluid Dynamics Laboratory (GFDL). First, we established a global data management system for quality control (QC) of oceanic observed data both in real time and delayed mode. Delayed mode QC of Argo floats identified about 8.5% (3%) of the total floats (profiles) up to December 2007 as having a significant salinity offset of more than 0.05. Second, all QCed data were gridded at 1° by 1° horizontal resolution and 23 standard depth levels using six spatial scales (large and small longitudinal, latitudinal, and cross-isobath) and a temporal scale. Analyzed mean temperature in WOA21c is warm with respect to WOA01 and WOA05, while salinity difference is less evident. Consistent differences among WOA01, WOA05, and WOA21c are found both in the fully and subsampled data set, which indicates a large impact of recent observations on the existing climatologies. Root mean square temperature and salinity differences and offsets of the GFDL's CDA results significantly decrease in the order of WOA01, WOA05, and WOA21c in most oceans and depths as well. This result suggests that the WOA21c is of use for the collocated assessment approach especially for high-performance assimilation models on the global scale.

16. Zhang, Shaoqing, Anthony Rosati, and Matthew J Harrison, December 2009: Detection of multidecadal oceanic variability by ocean data assimilation in the context of a “perfect” coupled model. Journal of Geophysical Research, 114, C12018, DOI:10.1029/2008JC005261.
    [ Abstract ]

    The impact of oceanic observing systems, external radiative forcings due to greenhouse gas and natural aerosol (GHGNA), and oceanic initial conditions on long time variability of oceanic heat content and salinity is assessed by the assimilation of oceanic “observations” in the context of a “perfect” Intergovernmental Panel on Climate Change Fourth Assessment Report model. According to times and locations at which observations are available, the 20th century expendable bathythermograph (XBT) temperature and 21st century Argo temperature and salinity observations are drawn from a model simulation (set as the “truth”) with historical GHGNA radiative forcings. These model observations are assimilated into another coupled model simulation based on temporally varying or fixed year GHGNA values and different oceanic initial conditions. The degree to which the assimilation recovers the truth variability of oceanic heat content and salinity is an assessment of the impact of each factor on the detection of the oceanic “climate.” Results show that both the 20th century XBT and 21st century Argo observations adequately capture the basin-scale variability of heat content. The Argo salinity observations appear to be necessary to reproduce the North Atlantic thermohaline structure and variability. The addition of historical radiative forcings does not make a significant contribution to the detection skill. The initial conditions spun up by historical GHGNA produce better detection skill than the initial conditions spun up by preindustrial fixed year GHGNA due to reduced assimilation shocks. While the 20th century XBT temperature observations alone capture some basic features of salinity variations of the tropical ocean due to the strong T-S relationship from tropical air-sea interactions, the Argo salinity observations are important for global state estimation, particularly in high latitudes where haline effects on ocean density are greater.

17. Zhang, Shaoqing, Matthew J Harrison, Anthony Rosati, and Andrew T Wittenberg, 2007: System Design and Evaluation of Coupled Ensemble Data Assimilation for Global Oceanic Climate Studies. Monthly Weather Review, 135(10), DOI:10.1175/MWR3466.1.
    [ Abstract ]

    A fully coupled data assimilation (CDA) system, consisting of an ensemble filter applied to the Geophysical Fluid Dynamics Laboratory’s global fully coupled climate model (CM2), has been developed to facilitate the detection and prediction of seasonal-to-multidecadal climate variability and climate trends. The assimilation provides a self-consistent, temporally continuous estimate of the coupled model state and its uncertainty, in the form of discrete ensemble members, which can be used directly to initialize probabilistic climate forecasts. Here, the CDA is evaluated using a series of perfect model experiments, in which a particular twentieth-century simulation—with temporally varying greenhouse gas and natural aerosol radiative forcings—serves as a “truth” from which observations are drawn, according to the actual ocean observing network for the twentieth century. These observations are then assimilated into a coupled model ensemble that is subjected only to preindustrial forcings. By examining how well this analysis ensemble reproduces the “truth,” the skill of the analysis system in recovering anthropogenically forced trends and natural climate variability is assessed, given the historical observing network. The assimilation successfully reconstructs the twentieth-century ocean heat content variability and trends in most locations. The experiments highlight the importance of maintaining key physical relationships among model fields, which are associated with water masses in the ocean and geostrophy in the atmosphere. For example, when only oceanic temperatures are assimilated, the ocean analysis is greatly improved by incorporating the temperature–salinity covariance provided by the analysis ensemble. Interestingly, wind observations are more helpful than atmospheric temperature observations for constructing the structure of the tropical atmosphere; the opposite holds for the extratropical atmosphere. The experiments indicate that the Atlantic meridional overturning circulation is difficult to constrain using the twentieth-century observational network, but there is hope that additional observations—including those from the newly deployed Argo profiles—may lessen this problem in the twenty-first century. The challenges for data assimilation of model systematic biases and evolving observing systems are discussed.

18. Anderson, Jeffrey L., Bruce Wyman, Shaoqing Zhang, and T Hoar, 2005: Assimilation of surface pressure observations using an ensemble filter in an idealized global atmospheric prediction system. Journal of the Atmospheric Sciences, 62(8), DOI:10.1175/JAS3510.1.
    [ Abstract ]

    An ensemble filter data assimilation system is tested in a perfect model setting using a low resolution Held-Suarez configuration of an atmospheric GCM. The assimilation system is able to reconstruct details of the model's state at all levels when only observations of surface pressure (PS) are available. The impacts of varying the spatial density and temporal frequency of PS observations are examined. The error of the ensemble mean assimilation prior estimate appears to saturate at some point as the number of PS observations available once every 24 h is increased. However, increasing the frequency with which PS observations are available from a fixed network of 1800 randomly located stations results in an apparently unbounded decrease in the assimilation's prior error for both PS and all other model state variables. The error reduces smoothly as a function of observation frequency except for a band with observation periods around 4 h. Assimilated states are found to display enhanced amplitude high-frequency gravity wave oscillations when observations are taken once every few hours, and this adversely impacts the assimilation quality. Assimilations of only surface temperature and only surface wind components are also examined. The results indicate that, in a perfect model context, ensemble filters are able to extract surprising amounts of information from observations of only a small portion of a model's spatial domain. This suggests that most of the remaining challenges for ensemble filter assimilation are confined to problems such as model error, observation representativeness error, and unknown instrument error characteristics that are outside the scope of perfect model experiments. While it is dangerous to extrapolate from these simple experiments to operational atmospheric assimilation, the resulrts also suggest that exploring the frequency with which observations are used for assimilation may lead to significant enhancements to assimilated state estimates.

19. Zhang, Shaoqing, Matthew J Harrison, Andrew T Wittenberg, Anthony Rosati, Jeffrey L Anderson, and Ventakramani Balaji, 2005: Initialization of an ENSO Forecast System using a parallelized ensemble filter. Monthly Weather Review, 133(11), DOI:10.1175/MWR3024.1.
    [ Abstract ]

    As a first step toward coupled ocean–atmosphere data assimilation, a parallelized ensemble filter is implemented in a new stochastic hybrid coupled model. The model consists of a global version of the GFDL Modular Ocean Model Version 4 (MOM4), coupled to a statistical atmosphere based on a regression of National Centers for Environmental Prediction (NCEP) reanalysis surface wind stress, heat, and water flux anomalies onto analyzed tropical Pacific SST anomalies from 1979 to 2002. The residual part of the NCEP fluxes not captured by the regression is then treated as stochastic forcing, with different ensemble members feeling the residual fluxes from different years. The model provides a convenient test bed for coupled data assimilation, as well as a prototype for representing uncertainties in the surface forcing. A parallel ensemble adjustment Kalman filter (EAKF) has been designed and implemented in the hybrid model, using a local least squares framework. Comparison experiments demonstrate that the massively parallel processing EAKF (MPPEAKF) produces assimilation results with essentially the same quality as a global sequential analysis. Observed subsurface temperature profiles from expendable bathythermographs (XBTs), Tropical Atmosphere Ocean (TAO) buoys, and Argo floats, along with analyzed SSTs from NCEP, are assimilated into the hybrid model over 1980-2002 using the MPPEAKF. The filtered ensemble of SSTs, ocean heat contents, and thermal structures converge well to the observations, in spite of the imposed stochastic forcings. Several facets of the EAKF algorithm used here have been designed to facilitate comparison to a traditional three-dimensional variational data assimilation (3DVAR) algorithm, for instance, the use of a univariate filter in which observations of temperature only directly impact temperature state variables. Despite these choices that may limit the power of the EAKF, the MPPEAKF solution appears to improve upon an earlier 3DVAR solution, producing a smoother, more physically reasonable analysis that better fits the observational data and produces, to some degree, a self-consistent estimate of analysis uncertainties. Hybrid model ENSO forecasts initialized from the MPPEAKF ensemble mean also appear to outperform those initialized from the 3DVAR analysis. This improvement stems from the EAKF's utilization of anisotropic background error covariances that may vary in time.

20. Zhang, Shaoqing, Jeffrey L Anderson, Anthony Rosati, Matthew J Harrison, S P Khare, and Andrew T Wittenberg, 2004: Multiple time level adjustment for data assimilation. Tellus A, 56A(1), 2-15.
    [ Abstract PDF ]

    Time-stepping schemes in ocean-atmosphere models can involve multiple time levels. Traditional data assimilation implementation considers only the adjustment of the current state using observations available, i.e. the one time level adjustment. However, one time level adjustment introduces an inconsistency between the adjusted and unadjusted states into the model time integration, which can produce extra assimilation errors. For time-dependent assimilation approaches such as ensemble-based filtering algorithms, the persistent introduction of this inconsistency can give rise to computational instability and requires extra time filtering to maintain the assimilation. A multiple time level adjustment assimilation scheme is thus proposed, in which the states at times t and t- 1, t- 2, ... , if applicable, are adjusted using observations at time t. Given a leap frog time-stepping scheme, a low-order (Lorenz-63) model and a simple atmospheric (global barotropic) model are used to demonstrate the impact of the two time level adjustment on assimilation results in a perfect model framework with observing/assimilation simulation experiments. The assimilation algorithms include an ensemble-based filter (the ensemble adjustment Kalman filter, EAKF) and a strong constraint four-dimensional variational (4D-Var) assimilation method. Results show that the two time level adjustment always reduces the assimilation errors for both filtering and variational algorithms due to the consistency of the adjusted states at times t and t- 1 that are used to produce the future state in the leap frog time-stepping. The magnitude of the error reduction made by the two time level adjustment varies according to the availability of observations, the nonlinearity of the assimilation model and the strength of the time filter used in the model. Generally the sparser the observations in time, the larger the error reduction. In particular, for the EAKF when the model uses a weak time filter and for the 4D-Var method when the model is strongly nonlinear, two time level adjustment can significantly improve the performance of these assimilation algorithms.

21. Zhang, Shaoqing, and Jeffrey L Anderson, 2003: Impact of spatially and temporally varying estimates of error covariance on assimilation in a simple atmospheric model. Tellus A, 55A(2), 126-147.
    [ Abstract PDF ]

    The background error covariance (correlation) between model state variables is of central importance for implementing data assimilation and understanding model dynamics. Traditional approaches for estimating the background error covariance involve many heuristic approximations, and often the estimated covariance is flow-independent, i.e., only reflecting statistics of the climatological background. This study examines temporally and spatially varying estimates of error covariance in a spectral barotropic model using a Monte Carlo approach, an implementation of an ensemble square root filter called the ensemble adjustment Kalman filter (EAKF). The EAKF is designed to maintain as much information about the distribution of the prior state variables as possible, and results show that this method can produce reasonable estimates of error correlation structure with an affordable sample (ensemble) size. The impact of using temporally and spatially varying estimates of error covariance in the EAKF is examined by using the time and spatial mean error covariances derived from the EAKF in an ensemble optimal interpolation (OI) assimilation scheme. Three key results are: (1) for the same ensemble size, an ensemble filter such as the EAKF produces better assimilations since its flow-dependent error covariance estimates are able to reflect more about the synoptic-scale wave structure in the simulated flows; (2) an ensemble OI scheme can also produce reasonably good assimilation results if the time-invariate covariance matrix is chosen appropriately; (3) when using the EAKF to estimate the error covariance matrix for improving traditional assimilation algorithms such as variational analysis and OI, a relatively small ensemble size may be used to estimate correlation structure although larger ensembles produce progressively better results.

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