Bibliography - P C D Milly

1. Milly, P C., J Betancourt, M Falkenmark, R M Hirsch, Z W Kundzewicz, D Lettenmaier, and Ronald J Stouffer, 2008: Stationarity is dead: Whither water management? Science, 319(5863), 573-574.
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2. Eng, K, and P C D Milly, 2007: Relating low-flow characteristics to the base flow recession time constant at partial record stream gauges. Water Resources Research, 43, W01201, doi:10.1029/2006WR005293.
   [ Abstract PDF ]

   Base flow recession information is helpful for regional estimation of low-flow characteristics. However, analyses that exploit such information generally require a continuous record of streamf low at the estimation site to characterize base flow recession. Here we propose a simple method for characterizing base flow recession at low-flow partial record stream gauges (i.e., sites with very few streamflow measurements under low-streamflow conditions), and we use that characterization as the basis for a practical new approach to low-flow regression. In a case study the introduction of a base flow recession time constant, estimated from a single pair of strategically timed streamflow measurements, approximately halves the root-mean-square estimation error relative to that of a conventional drainage area regression. Additional streamflow measurements can be used to reduce the error further.

3. Eng, K, P C D Milly, and G D Tasker, November 2007: Flood regionalization: A hybrid geographic and predictor-variable region-of-influence regression method. Journal of Hydrologic Engineering, 12(6), 585-591.
   [ Abstract ]

   To facilitate estimation of streamflow characteristics at an ungauged site, hydrologists often define a region of influence containing gauged sites hydrologically similar to the estimation site. This region can be defined either in geographic space or in the space of the variables that are used to predict streamflow (predictor variables). These approaches are complementary, and a combination of the two may be superior to either. Here we propose a hybrid region-of-influence (HRoI) regression method that combines the two approaches. The new method was applied with streamflow records from 1,091 gauges in the southeastern United States to estimate the 50-year peak flow (Q50). The HRoI approach yielded lower root-mean-square estimation errors and produced fewer extreme errors than either the predictor-variable or geographic region-of-influence approaches. It is concluded, for Q50 in the study region, that similarity with respect to the basin characteristics considered (area, slope, and annual precipitation) is important, but incomplete, and that the consideration of geographic proximity of stations provides a useful surrogate for characteristics that are not included in the analysis. http://dx.doi.org/10.1061/(ASCE)1084-0699(2007)12:6(585)

4. Findell, Kirsten L., Elena Shevliakova, P C D Milly, and Ronald J Stouffer, July 2007: Modeled impact of anthropogenic land cover change on climate. Journal of Climate, 20(14), doi:10.1175/JCLI4185.1.
   [ Abstract ]

   Equilibrium experiments with the Geophysical Fluid Dynamics Laboratory’s climate model are used to investigate the impact of anthropogenic land cover change on climate. Regions of altered land cover include large portions of Europe, India, eastern China, and the eastern United States. Smaller areas of change are present in various tropical regions. This study focuses on the impacts of biophysical changes associated with the land cover change (albedo, root and stomatal properties, roughness length), which is almost exclusively a conversion from forest to grassland in the model; the effects of irrigation or other water management practices and the effects of atmospheric carbon dioxide changes associated with land cover conversion are not included in these experiments. The model suggests that observed land cover changes have little or no impact on globally averaged climatic variables (e.g., 2-m air temperature is 0.008 K warmer in a simulation with 1990 land cover compared to a simulation with potential natural vegetation cover). Differences in the annual mean climatic fields analyzed did not exhibit global field significance. Within some of the regions of land cover change, however, there are relatively large changes of many surface climatic variables. These changes are highly significant locally in the annual mean and in most months of the year in eastern Europe and northern India. They can be explained mainly as direct and indirect consequences of model-prescribed increases in surface albedo, decreases in rooting depth, and changes of stomatal control that accompany deforestation.

5. 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

6. Findell, Kirsten L., Thomas R Knutson, and P C D Milly, 2006: Weak simulated extratropical responses to complete tropical deforestation. Journal of Climate, 19(12), 2835-2850.
   [ Abstract PDF ]

   The Geophysical Fluid Dynamics Laboratory atmosphere–land model version 2 (AM2/LM2) coupled to a 50-m-thick slab ocean model has been used to investigate remote responses to tropical deforestation. Magnitudes and significance of differences between a control run and a deforested run are assessed through comparisons of 50-yr time series, accounting for autocorrelation and field significance. Complete conversion of the broadleaf evergreen forests of South America, central Africa, and the islands of Oceania to grasslands leads to highly significant local responses. In addition, a broad but mild warming is seen throughout the tropical troposphere (<0.2°C between 700 and 150 mb), significant in northern spring and summer. However, the simulation results show very little statistically significant response beyond the Tropics. There are no significant differences in any hydroclimatic variables (e.g., precipitation, soil moisture, evaporation) in either the northern or the southern extratropics. Small but statistically significant local differences in some geopotential height and wind fields are present in the southeastern Pacific Ocean. Use of the same statistical tests on two 50-yr segments of the control run show that the small but significant extratropical differences between the deforested run and the control run are similar in magnitude and area to the differences between nonoverlapping segments of the control run. These simulations suggest that extratropical responses to complete tropical deforestation are unlikely to be distinguishable from natural climate variability.

7. Swenson, S C., and P C D Milly, 2006: Climate model biases in seasonality of continental water storage revealed by satellite gravimetry. Water Resources Research, 42, W03201, doi:10.1029/2005WR004628.
   [ Abstract ]

   Satellite gravimetric observations of monthly changes in continental water storage are compared with outputs from five climate models. All models qualitatively reproduce the global pattern of annual storage amplitude, and the seasonal cycle of global average storage is reproduced well, consistent with earlier studies. However, global average agreements mask systematic model biases in low latitudes. Seasonal extrema of low-latitude, hemispheric storage generally occur too early in the models, and model-specific errors in amplitude of the low-latitude annual variations are substantial. These errors are potentially explicable in terms of neglected or suboptimally parameterized water stores in the land models and precipitation biases in the climate models.

8. Eng, K, G D Tasker, and P C D Milly, 2005: An analysis of region-of-influence methods for flood regionalization in the Gulf-Atlantic rolling plains. Journal of the American Water Resources Association, 41(1), 135-143.
   [ Abstract ]

   Region-of-influence (RoI) approaches for estimating streamflow characteristics at ungaged sites were applied and evaluated in a case study of the 50-year peak discharge in the Gulf-Atlantic Rolling Plains of the southeastern United States. Linear regression against basin characteristics was performed for each ungaged site considered based on data from a region of influence containing the closest gages in predictor variable (PRoI) or geographic (GRoI) space. Augmentation of this count based cutoff by a distance based cutoff also was considered. Prediction errors were evaluated for an independent (split-sampled) dataset. For the dataset and metrics considered here: (1) for either PRoI or GRoI, optimal results were found when the simpler count based cutoff, rather than the distance augmented cutoff, was used; (2) GRoI produced lower error than PRoI when applied indiscriminately over the entire study region; (3) PRoI performance improved considerably when RoI was restricted to predefined geographic subregions.

9. Milly, P C., March 2005: Trends in the water budget of the Mississippi River basin, 1949-1997 In U.S. Geological Survey Fact Sheet 2005-3020, 1-2.
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10. Milly, P C., Krista A Dunne, and A V Vecchia, 2005: Global pattern of trends in streamflow and water availability in a changing climate. Nature, 438(7066), doi:10.1038/nature04312.
    [ Abstract ]

    Water availability on the continents is important for human health, economic activity, ecosystem function and geophysical processes. Because the saturation vapour pressure of water in air is highly sensitive to temperature, perturbations in the global water cycle are expected to accompany climate warming6. Regional patterns of warming-induced changes in surface hydroclimate are complex and less certain than those in temperature, however, with both regional increases and decreases expected in precipitation and runoff. Here we show that an ensemble of 12 climate models exhibits qualitative and statistically significant skill in simulating observed regional patterns of twentieth-century multidecadal changes in streamflow. These models project 10–40% increases in runoff in eastern equatorial Africa, the La Plata basin and high-latitude North America and Eurasia, and 10–30% decreases in runoff in southern Africa, southern Europe, the Middle East and mid-latitude western North America by the year 2050. Such changes in sustainable water availability would have considerable regional-scale consequences for economies as well as ecosystems.

11. Potter, N J., L Zhang, P C D Milly, T A McMahon, and A J Jakeman, 2005: Effects of rainfall seasonality and soil moisture capacity on mean annual water balance for Australian catchments.. Water Resources Research, 41, W06007, doi:10.1029/2004WR003697.
    [ Abstract ]

    An important factor controlling catchment-scale water balance is the seasonal variation of climate. The aim of this study is to investigate the effect of the seasonal distributions of water and energy, and their interactions with the soil moisture store, on mean annual water balance in Australia at catchment scales using a stochastic model of soil moisture balance with seasonally varying forcing. The rainfall regime at 262 catchments around Australia was modeled as a Poisson process with the mean storm arrival rate and the mean storm depth varying throughout the year as cosine curves with annual periods. The soil moisture dynamics were represented by use of a single, finite water store having infinite infiltration capacity, and the potential evapotranspiration rate was modeled as an annual cosine curve. The mean annual water budget was calculated numerically using a Monte Carlo simulation. The model predicted that for a given level of climatic aridity the ratio of mean annual evapotranspiration to rainfall was larger where the potential evapotranspiration and rainfall were in phase, that is, in summer-dominant rainfall catchments, than where they were out of phase. The observed mean annual evapotranspiration ratios have opposite results. As a result, estimates of mean annual evapotranspiration from the model compared poorly with observational data. Because the inclusion of seasonally varying forcing alone was not sufficient to explain variability in the mean annual water balance, other catchment properties may play a role. Further analysis showed that the water balance was highly sensitive to the catchment-scale soil moisture capacity. Calibrations of this parameter indicated that infiltration-excess runoff might be an important process, especially for the summer-dominant rainfall catchments; most similar studies have shown that modeling of infiltration-excess runoff is not required at the mean annual timescale.

12. Cazenave, A, P C D Milly, H Douville, J Beaveniste, P Kosuth, and D Lettenmaier, 2004: Space techniques used to measure change in terrestrial waters. EOS, 85(6), 59.
    [ Abstract ]

    Terrestrial waters—including snowpack, glaciers, water in aquifers and other geological formations, water in the plant root zone, rivers, lakes, man-made reservoirs, wetlands, and inundated areas—represent less than a mere 1% of the total amount of water on Earth. However, they have a crucial impact on terrestrial life and human needs and play a major role in climate variability. Land waters are continuously exchanged with the atmosphere and oceans in vertical and horizontal mass fluxes through evaporation, transpiration, and surface and subsurface runoff. Although it is now recognized that improved description of the terrestrial branch of the global water cycle is of major importance for climate research and for inventory and management of water resources, the global distribution and spatial-temporal variations of terrestrial waters are still poorly known because routine in situ observations are not available globally. So far, global estimates of spatial-temporal change of land water stored in soils and in the snowpack essentially rely on hydrological models, either coupled with atmosphere/ocean global circulation models and/or forced by observations.

13. Manabe, Syukuro, P C D Milly, and Richard T Wetherald, 2004: Simulated long-term changes in river discharge and soil moisture due to global warming. Hydrological Sciences, 49(4), 625-642.
    [ Abstract PDF ]

    By use of a coupled ocean-atmosphere-land model, this study explores the changes of water availability, as measured by river discharge and soil moisture, that could occur by the middle of the 21st century in response to combined increases of greenhouse gases and sulphate aerosols based upon the "IS92a" scenario. In addition, it presents the simulated change in water availability that might be realized in a few centuries in response to a quadrupling of CO2 concentration in the atmosphere. Averaging the results over extended periods, the radiatively forced changes, which are very similar between the two sets of experiments, were successfully extracted. The analysis indicates that the discharges from Arctic rivers such as the Mackenzie and Ob' increase by up to 20% (of the pre-Industrial Period level) by the middle of the 21st century and by up to 40% or more in a few centuries. In the tropics, the discharges from the Amazonas and Ganga-Brahmaputra rivers increase substantially. However, the percentage changes in runoff from other tropical and many mid-latitude rivers are smaller, with both positive and negative signs. For soil moisture, the results of this study indicate reductions during much of the year in many semiarid regions of the world, such as the southwestern region of North America., the northeastern region of China, the Mediterranean coast of Europe, and the grasslands of Australia and Africa. As a percentage, the reduction is particularly large during the dry season. From middle to high latitudes of the Northern Hemisphere, soil moisture decreases in summer but increases in winter.

14. Manabe, Syukuro, Richard T Wetherald, P C D Milly, Thomas L Delworth, and Ronald J Stouffer, 2004: Century-scale change in water availability: CO2-quadrupling experiment. Climatic Change, 64(1-2), 59-76.
    [ Abstract PDF ]

    It has been suggested that, unless a major effort is made, the atmospheric concentration of carbon dioxide may rise above four times the pre-industrial level in a few centuries. Here we use a coupled atmosphere-ocean-land model to explore the response of the global water cycle to such a large increase in carbon dioxide, focusing on river discharge and soil moisture. Our results suggest that water is going to be more plentiful in those regions of the world that are already `water-rich'. However, water stresses will increase significantly in regions and seasons that are already relatively dry. This could pose a very challenging problem for water-resource management around the world. For soil moisture, our results indicate reductions during much of the year in many semi-arid regions of the world, such as the southwestern region of North America, the northeastern region of China, the Mediterranean coast of Europe, and the grasslands of Australia and Africa. In some of these regions, soil moisture values are reduced by almost a factor of two during the dry season. The drying in semi-arid regions is likely to induce the outward expansion of deserts to the surrounding regions. Over extensive regions of both the Eurasian and North American continents in high and middle latitudes, soil moisture decreases in summer but increases in winter, in contrast to the situation in semi-arid regions. For river discharge, our results indicate an average increase of ~ 15% during the next few centuries. The discharges from Arctic rivers such as the Mackenzie and Ob' increase by much larger fractions. In the tropics, the discharges from the Amazonas and Ganga-Brahmaputra also increase considerably. However, the percentage changes in runoff from other tropical and many mid-latitude rivers are smaller.

15. Milly, P C., 2004: Groundwater Fluxes Across Interfaces, Washington, D.C.: The National Academy Press, 85 pp.
    [ Abstract ]

    Atmosphere, surface and subsurface portions of the hydrological system are three dynamically linked water reservoirs having distinctly different time and space scales. Many challenges remain in understanding and measuring the dynamic interchange among these reservoirs, especially for interchanges with the subsurface. Most subsurface storage of water is in the groundwater reservoir, with a small amount of water stored as soil moisture in the overlying unsaturated zone. Fluxes to and from the groundwater zone are called, respectively, recharge and discharge. Natural groundwater recharge has several origins. The most important of these are the flux of water across the water table from precipitation that percolates through the unsaturated zone, and the influx of water from a bounding or overlying surface water body including rivers, lakes, wetlands and the ocean. Natural groundwater discharge is the efflux of water from the groundwate reservoir to surface water, or to the land surface itself where, for example, it may return to the atmosphere through evaporation and transpiration.

16. Milly, P C., A Cazenave, and M C Gennero, 2003: Contribution of climate-driven change in continental water storage to recent sea-level rise. Proceedings of the National Academy of Sciences, 100(23), 13158-13161.
    [ Abstract PDF ]

    Using a global model of continental water balance, forced by interannual variations in precipitation and near-surface atmospheric temperature for the period 1981-1998, we estimate the sea level changes associated with climate-driven changes in storage of water as snowpack, soil water, and ground water; storage in ice sheets and large lakes is not considered. The 1981-1998 trend is estimated to be 0.12 mm/yr. and substantial interannual fluctuations are inferred; for 1993-1998, the trend is 0.25 mm/yr. At the decadal time scale, the terrestrial contribution to eustatic (i.e., induced by mass exchange) sea-level rise is significantly smaller than the estimated steric (i.e., induced by density changes) trend for the same period, but is not negligibly small. In the model the sea-level rise is driven mainly by a downtrend in continental precipitation during the study period, which we believe was generated by natural variability in the climate system.

17. Swenson, S C., J Wahr, and P C D Milly, 2003: Estimated accuracies of regional water storage variations inferred from the Gravity Recovery and Climate Experiment (GRACE). Water Resources Research, 39(8), 1223, doi:10.1029/2002WR001808.
    [ Abstract ]

    The satellite Gravity Recovery and Climate Experiment (GRACE) provides data describing monthly changes in the geoid, which are closely related to changes in vertically integrated terrestrial water storage. Unlike conventional point or gridded hydrologic measurements, such as those from rain gauges, stream gauges, rain radars, and radiometric satellite images, GRACE data are sets of Stokes coefficients in a truncated spherical harmonic expansion of the geoid. Swenson and Wahr [2002] describe techniques for constructing spatial averaging kernels, with which the average change in vertically integrated water storage within a given region can be extracted from a set of Stokes coefficients. This study extends that work by applying averaging kernels to a realistic synthetic GRACE gravity signal derived in part from a large-scale hydrologic model. By comparing the water storage estimates inferred from the synthetic GRACE data with the water storage estimates predicted by the same hydrologic model, we are able to assess the accuracy of the GRACE estimates and to compare the performance of different averaging kernels. We focus specifically on recovering monthly water storage variations within North American river basins. We conclude that GRACE will be capable of estimating monthly changes in water storage to accuracies of better than 1 cm of water thickness for regions having areas of 4.0 . 10⁵ km² or larger. Accuracies are better for larger regions. The water storage signal of the Mississippi river basin (area = 3.9 . 10⁶ km²), for example, can be obtained to better than 5 mm. For regional- to global-scale water balance analyses, this result indicates that GRACE will provide a useful, direct measure of seasonal water storage for river-basin water balance analyses; such data are without precedent in hydrologic analysis.

18. Milly, P C., and Krista A Dunne, 2002: Macroscale water fluxes 1. Quantifying errors in the estimation of basin mean precipitation. Water Resources Research, 38(10), doi:10.1029/2001/WR000759.
    [ Abstract PDF ]

    Developments in analysis and modeling of continental water and energy balances are hindered by the limited availability and quality of observational data. The lack of information on error characteristics of basin water supply is an especially serious limitation. Here we describe the development and testing of methods for quantifying several errors in basin mean precipitation, both in the long-term mean and in the monthly and annual anomalies. To quantify errors in long-term mean, two error indices are developed and tested with positive results. The first provides an estimate of the variance of the spatial sampling error of long-term basin mean precipitation obtained from a gauge network, in the absence of orographic effects; this estimate is obtained by use only of the gauge records. The second gives a simple estimate of the basin mean orographic bias as a function of the topographic structure of the basin and the locations of gauges therein. Neither index requires restrictive statistical assumptions (such as spatial homogeneity) about the precipitation process. Adjustments of precipitation for gauge bias and estimates of the adjustment errors are made by applying results of a previous study. Additionally, standard correlation-based methods are applied for the quantification of spatial sampling errors in the estimation of monthly and annual values of basin mean precipitation. These methods also perform well, as indicated by network subsampling tests in densely gauged basins. The methods are developed and applied with data for 175 large (median area of 51,000 km2 ) river basins of the world for which contemporaneous, continuous (missing fewer than 2% of data values), long-term (median record length of 54 years) river discharge records are also available. Spatial coverage of the resulting river basin data set is greatest in the middle latitudes, though many basins are located in the tropics and the high latitudes, and the data set spans the major climatic and vegetation zones of the world. This new data set can be applied in diagnostic and theoretical studies of water balance of large basins and in the evaluation of performance of global models of land water balance.

19. Milly, P C., and Krista A Dunne, 2002: Macroscale water fluxes 2. Water and energy supply control of their interannual variability. Water Resources Research, 38(10), doi:10.1029/2001/WR000760.
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20. Milly, P C., and A B Shmakin, 2002: Global modeling of land water and energy balances. Part I: The land dynamics (LaD) model. Journal of Hydrometeorology, 3(3), 283-299.
    [ Abstract PDF ]

    A simple model of large-scale land (continental) water and energy balances is presented. The model is an extension of an earlier scheme with a record of successful application in climate modeling. The most important changes from the original model include 1) introduction of non-water-stressed stomatal control of transpiration, in order to correct a tendency toward excessive evaporation; 2) conversion from globally constant parameters (with the exception of vegetation-dependent snow-free surface albedo) to more complete vegetation and soil dependence of all parameters, in order to provide more realistic representation of geographic variations in water and energy balances and to enable model-based investigations of land-cover change; 3) introduction of soil sensible heat storage and transport, in order to move toward realistic diurnal-cycle modeling; 4) a groundwater (saturated-zone) storage reservoir, in order to provide more realistic temporal variability of runoff; and 5) a rudimentary runoff-routing scheme for delivery of runoff to the ocean, in order to provide realistic freshwater forcing of the ocean general circulation model component of a global climate model. The new model is tested with forcing from the International Satellite Land Surface Climatology Project Initiative I global dataset and a recently produced observation-based water-balance dataset for major river basins of the world. Model performance is evaluated by comparing computed and observed runoff ratios from many major river basins of the world. Special attention is given to distinguishing between two components of the apparent runoff ratio error: the part due to intrinsic model error and the part due to errors in the assumed precipitation forcing. The pattern of discrepancies between modeled and observed runoff ratios is consistent with results from a companion study of precipitation estimation errors. The new model is tuned by adjustment of a globally constant scale factor for non-water-stressed stomatal resistance. After tuning, significant overestimation of runoff is found in environments where an overall arid climate includes a brief but intense wet season. It is shown that this error may be explained by the neglect of upward soil water diffusion from below the root zone during the dry season. With the exception of such basins, and in the absence of precipitation errors, it is estimated that annual runoff ratios simulated by the model would have a root-mean-square error of about 0.05. The new model matches observations better than its predecessor, which has a negative runoff bias and greater scatter.

21. Milly, P C., and A B Shmakin, 2002: Global modeling of land water and energy balances. Part II: Land-characteristic contributions to spatial variability. Journal of Hydrometeorology, 3(3), 301-310.
    [ Abstract PDF ]

    The withholding of information on global variations in these parameters leads to a significant degradation of the capability of the model to simulate the annual runoff ratio. An additional set of optimization experiments, in which the parameters are examined individually, reveals that the stomatal resistance is, by far, the parameter among these three whose spatial variations add the most predictive power to the model in stand-alone mode. Further single-parameter experiments with surface roughness length, available water capacity, thermal conductivity, and thermal diffusivity show very little sensitivity to estimated global variations in these parameters. Finally, it is found that even the constant-parameter model performance exceeds that of the Budyko and generalized Turc–Pike water-balance equations, suggesting that the model benefits also from information on the geographic variability of the temporal structure of forcing.

22. Milly, P C., and Richard T Wetherald, 2002: Macroscale water fluxes 3. Effects of land processes on variability of monthly river discharge. Water Resources Research, 38(11), 1235, doi:10.1029/2001WR000761.
    [ Abstract PDF ]

    A salient characteristic of river discharge is its temporal variability. The time series of flow at a point on a river can be viewed as the superposition of a smooth seasonal cycle and an irregular, random variation. Viewing the random component in the spectral domain facilitates both its characterization and an interpretation of its major physical controls from a global perspective. The power spectral density functions of monthly flow anomalies of many large rivers worldwide are typified by a "red noise" process: the density is higher at low frequencies (e.g., <1y–1 ) than at high frequencies, indicating disproportionate (relative to uncorrelated "white noise") contribution of low frequencies to variability of monthly flow. For many high-latitude and arid-region rivers, however, the power is relatively evenly distributed across the frequency spectrum. The power spectrum of monthly flow can be interpreted as the product of the power spectrum of monthly basin total precipitation (which is typically white or slightly red) and several filters that have physical significance. The filters are associated with (1) the conversion of total precipitation (sum of rainfall and snowfall) to effective rainfall (liquid flux to the ground surface from above), (2) the conversion of effective rainfall to soil water excess (runoff), and (3) the conversion of soil water excess to river discharge. Inferences about the roles of each filter can be made through an analysis of observations, complemented by information from a global model of the ocean-atmosphere-land system. The first filter causes a snowmelt-related amplification of high-frequency variability in those basins that receive substantial snowfall. The second filter causes a relatively constant reduction in variability across all frequencies and can be predicted well by means of a semiempirical water balance relation. The third filter, associated with groundwater and surface water storage in the river basin, causes a strong reduction in high-frequency variability of many basins. The strength of this reduction can be quantified by an average residence time of water in storage, which is typically on the order of 20–50 days. The residence time is demonstrably influenced by freezing conditions in the basin, fractional cover of the basin by lakes, and runoff ratio (ratio of mean runoff to mean precipitation). Large lake areas enhance storage and can greatly increase total residence times (100 to several hundred days). Freezing conditions appear to cause bypassing of subsurface storage, thus reducing residence times (0–30 days). Small runoff ratios tend to be associated with arid regions, where the water table is deep, and consequently, most of the runoff is produced by processes that bypass the saturated zone, leading to relatively small residence times for such basins (0–40 days).

23. Milly, P C., Richard T Wetherald, Krista A Dunne, and Thomas L Delworth, 2002: Increasing risk of great floods in a changing climate. Nature, 415(6871), 514-517.
    [ Abstract PDF ]

    Radiative effects of anthropogenic changes in atmospheric composition are expected to cause climate changes, in particular an intensification of the global water cycle with a consequent increase in flood risk. But the detection of anthropogenically forced changes in flooding is difficult because of the substantial natural variability; the dependence of streamflow trends on flow regime further complicates the issue. Here we investigate the changes in risk of great floods- that is, floods with discharges exceeding 100-year levels from basins larger than 200,000 km2- using both streamflow measurements and numerical simulations of the anthropogenic climate change associated with greenhouse gases and direct radiative effects of sulphate aerosols. We find that the frequency of great floods increased substantially during the twentieth century. The recent emergence of a statistically significant positive trend in risk of great floods is consistent with results from the climate model, and the model suggests that the trend will continue.

24. Schlosser, C A., and P C D Milly, 2002: A model-based investigation of soil moisture predictability and associated climate predictability. Journal of Hydrometeorology, 3(4), 483-501.
    [ Abstract PDF ]

    Soil moisture predictability and the associated predictability of continental climate are explored as an initial-value problem, using a coupled land–atmosphere model with prescribed ocean surface temperatures. Ensemble simulations are designed to assess the extent to which initial soil moisture fields explain variance of future predictands (soil moisture, near-surface air temperature, and precipitation). For soil moisture, the decrease of explained variance with lead time can be characterized as a first-order decay process, and a predictability timescale is introduced as the lead time at which this decay reaches e–1. The predictability timescale ranges from about 2 weeks or less (in midlatitudes during summer, and in the Tropics and subtropics) to 2–6 months (in mid- to high latitudes for simulations that start in late fall and early winter). The predictability timescale of the modeled soil moisture is directly related to the soil moisture's autocorrelation timescale. The degree of translation of soil moisture predictability to predictability of any atmospheric variable can be characterized by the ratio of the fraction of explained variance of the atmospheric variable to the fraction of explained soil moisture variance. By this measure, regions with the highest associated predictability of 30-day-mean near-surface air temperature (ratio greater than 0.5) are, generally speaking, coincident with regions and seasons of the smallest soil moisture predictability timescales. High associated temperature predictability is found where strong variability of soil moisture stress on evapotranspiration and abundant net radiation at the continental surface coincide. The associated predictability of 30-day-mean precipitation, in contrast, is very low.

25. Shmakin, A B., P C D Milly, and Krista A Dunne, 2002: Global modeling of land water and energy balances. Part III: Interannual variability. Journal of Hydrometeorology, 3(3), 311-321.
    [ Abstract PDF ]

    The Land Dynamics (LaD) model is tested by comparison with observations of interannual variations in discharge from 44 large river basins for which relatively accurate time series of monthly precipitation (a primary model input) have recently been computed. When results are pooled across all basins, the model explains 67% of the interannual variance of annual runoff ratio anomalies (i.e., anomalies of annual discharge volume, normalized by long-term mean precipitation volume). The new estimates of basin precipitation appear to offer an improvement over those from a state-of-the-art analysis of global precipitation (the Climate Prediction Center Merged Analysis of Precipitation, CMAP), judging from comparisons of parallel model runs and of analyses of precipitation-discharge correlations. When the new precipitation estimates are used, the performance of the LaD model is comparable to, but not significantly better than, that of a simple, semiempirical water-balance relation that uses only annual totals of surface net radiation and precipitation. This implies that the LaD simulations of interannual runoff variability do not benefit substantially from information on geographical variability of land parameters or seasonal structure of interannual variability of precipitation. The aforementioned analyses necessitated the development of a method for downscaling of long-term monthly precipitation data to the relatively short timescales necessary for running the model. The method merges the long-term data with a reference dataset of 1-yr duration, having high temporal resolution. The success of the method, for the model and data considered here, was demonstrated in a series of model-model comparisons and in the comparisons of modeled and observed interannual variations of basin discharge.

26. Cubasch, U, G A Meehl, G J Boer, Ronald J Stouffer, M R Dix, A Noda, C A Senior, S C B Raper, K S Yap, A Abe-Ouchi, S Brinkop, M Claussen, M Collins, J Evans, I Fischer-Bruns, J C Fyfe, A Ganopolski, J M Gregory, Z-Z Hu, F Joos, Thomas R Knutson, R Knutti, C Landsea, L Mearns, P C D Milly, J F B Mitchell, T Nozawa, H Paeth, J Räisänen, R Sausen, S Smith, T F Stocker, A Timmermann, U Ulbrich, A J Weaver, J Wegner, P Whetton, T M L Wigley, Michael Winton, and F Zwiers, 2001: Projections of future climate change 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, 526-582.
27. Koster, R D., P A Dirmeyer, P C D Milly, and G Russell, 2001: Comparing GCM-generated land surface water budgets using a simple common framework In Land Surface Hydrology, Meteorology, and Climate: Observations and Modeling, Water Science and Application, Vol. 3, Washington, DC, American Geophysical Union, 95-105.
    [ Abstract ]

    Multi-decade simulations with four atmospheric general circulation models (GCMs) are analyzed to determine the extent to which the precipitation and net radiation forcing simulated by each model determines the simulated annual surface water budget in a given region. The success of two simple climatological relations in characterizing the mean and interannual variability of each GCM's surface water budget implies that the forcing does indeed impose a primary control. Intermodel differences in the forcing are found to be strongly related to intermodel differences in the normalized surface fluxes (i.e., the mean and variability of the annual evaporation and runoff normalized by annual precipitation), with the forcing differences explaining roughly half the variance in the normalized flux differences. The results imply that to understand the annual evaporation and runoff fluxes simulated by a GCM in a given region, a study of the forcing and its relationship to both the large-scale circulation and the land surface itself is at least as relevant as a focused analysis of the evaporation and runoff parameterizations used by the land surface scheme.

28. Milly, P C., 2001: A minimalist probabilistic description of root zone soil water. Water Resources Research, 37(3), 457-463.
    [ Abstract PDF ]

    The probabilistic response of depth-integrated soil water to given climatic forcing can be described readily using an existing supply-demand-storage model. An apparently complex interaction of numerous soil, climate, and plant controls can be reduced to a relatively simple expression for the equilibrium probability density function of soil water as a function of only two dimensionless parameters. These are the index of dryness (ratio of mean potential evaporation to mean precipitation) and a dimensionless storage capacity (active root zone soil water capacity divided by mean storm depth). The first parameter is mainly controlled by climate, with surface albedo playing a subsidiary role in determining net radiation. The second is a composite of soil (through moisture retention characteristics), vegetation (through rooting characteristics), and climate (mean storm depth). This minimalist analysis captures many essential features of a more general probabilistic analysis, but with a considerable reduction in complexity and consequent elucidation of the critical controls on soil water variability. In particular, it is shown that (1) the dependence of mean soil water on the index of dryness approaches a step function in the limit of large soil water capacity; (2) soil water variance is usually maximized when the index of dryness equals 1, and the width of the peak varies inversely with dimensionless storage capacity; (3) soil water has a uniform probability density function when the index of dryness is 1 and the dimensionless storage capacity is large; and (4) the soil water probability density function is bimodal if and only if the index of dryness is <1, but this bimodality is pronounced only for artificially small values of the dimensionless storage capacity.

29. Milly, P C., and Krista A Dunne, 2001: Trends in evaporation and surface cooling in the Mississippi River basin. Geophysical Research Letters, 28(7), 1219-1222.
    [ Abstract PDF ]

    A synthesis of available data for the Mississippi River basin (area 3x106 km2) reveals an upward trend in evaporation during recent decades, driven primarily by increases in precipitation and secondarily by human water use. A cloud-related decrease in surface net radiation appears to have accompanied the precipitation trend. Resultant evaporative and radiative cooling of the land and lower atmosphere quantitatively explains downward trends in observed pan evaporation. These cooling tendencies also reconcile the observed regional atmospheric cooling with the anticipated regional "greenhouse warming." If recent high levels of precipitation (which correlate with the North Atlantic Oscillation) are mainly caused by an internal climatic fluctuation, an eventual return to normal precipitation could reveal heretofore-unrealized warming in the basin. If, instead, they are caused by some unidentified forcing that will continue to grow in the future, then continued intensification of water cycling and suppression of warming in the basin could result.

30. Van Dam, T, J Wahr, P C D Milly, A B Shmakin, G Blewitt, D Lavallée, and V E Larson, 2001: Crustal displacements due to continental water loading. Geophysical Research Letters, 28(4), 651-654.
    [ Abstract PDF ]

    The effects of long-wavelength (> 100 km), seasonal variability in continental water storage on vertical crustal motions are assessed. The modeled vertical displacements ()r_M ) have root-mean-square (RMS) values for 1994-1998 as large as 8 mm, with ranges up to 30 mm, and are predominantly annual in character. Regional strains are on the order ot 20 nanostrain for tilt and 5 nanostrain for horizontal deformation. We compare )r_M with observed Global Positioning System (GPS) heights ()r_o ) (which include adjustments to remove estimated effects of atmospheric pressure and annual tidal and non-tidal ocean loading) for 147 globally distributed sites. When the )r_o time series are adjusted by )r_M , their variances are reduced, on average, by an amount equal to the variance of the )r_M . Of the )r_o time series exhibiting a strong annual signal, more than half are found to have an annual harmonic that is in phase and of comparable amplitude with the annual harmonic in the )r_M . The )r_M time series exhibit long-period variations that could be mistaken for secular tectonic trends or post-glacial rebound when observed over a time span of a few years.

31. Milly, P C., 1999: Comment on "Antiphasing between rainfall in Africa's Rift Valley and North America's Great Basin". Quaternary Research, 51(1), 104-107.
    [ PDF ]
32. Milly, P C., 1999: Factors determining the partitioning of precipitation into evaporation and runoff In Global Energy and Water Cycles, Cambridge, UK, Cambridge University Press, 247-253.
33. Milly, P C., and Krista A Dunne, 1998: Non-detectability of 20th-Century trends in river discharge from large basins: Observational and model-based results In Ninth Symposium on Global Change Studies and Namias Symposium on the Status and Prospects for Climate Prediction, Boston, MA, American Meteorological Society, 162-163.
34. Chen, T H., and P C D Milly, et al., 1997: Cabauw experimental results from the Project for Intercomparison of Land-Surface Parameterization Schemes. Journal of Climate, 10(6), 1194-1215.
    [ Abstract PDF ]

    In the Project for Intercomparison of Land-Surface Parameterization Schemes phase 2a experiment, meteorological data for the year 1987 from Cabauw, the Netherlands, were used as inputs to 23 land-surface flux schemes designed for use in climate and weather models. Schemes were evaluated by comparing their outputs with long-term measurements of surface sensible heat fluxes into the atmosphere and the ground, and of upward longwave radiation and total net radiative fluxes, and also comparing them with latent heat fluxes derived from a surface energy balance. Tuning of schemes by use of the observed flux data was not permitted. On an annual basis, the predicted surface radiative temperature exhibits a range of 2 K across schemes, consistent with the range of about 10 W m^-2 in predicted surface net radiation. Most modeled values of monthly net radiation differ from the observations by less than the estimated maximum monthly observational error (± 10 W m^-2). However, modeled radiative surface temperature appears to have a systematic positive bias in most schemes; this might be explained by an error in assumed emissivity and by models' neglect of canopy thermal heterogeneity. Annual means of sensible and latent heat fluxes, into which net radiation is partitioned, have ranges across schemes of 30 W m^-2 and 25 W m^-2, respectively. Annual totals of evapotranspiration and runoff, into which the precipitation is partitioned, both have ranges of 315 mm. These ranges in annual heat and water fluxes were approximately halved upon exclusion of the three schemes that have no stomatal resistance under non-water-stressed conditions. Many schemes tend to underestimate latent heat flux and overestimate sensible heat flux in summer, with a reverse tendency in winter. For six schemes, root-mean-square deviations of predictions from monthly observations are less than the estimated upper bounds on observation errors (5 W m^-2 for sensible heat flux and 10 W m^-2 for intent heat flux). Actual runoff at the site is believed to be dominated by vertical drainage to groundwater, but several schemes produced significant amounts of runoff as overland flow or interflow. There is a range across schemes of 184 mm (40% of total pore volume) in the simulated annual mean root-zone soil moisture. Unfortunately, no measurements of soil moisture were available for model evaluation. A theoretical analysis suggested that differences in boundary conditions used in various schemes are not sufficient to explain the large variance in soil moisture. However, many of the extreme values of soil moisture could be explained in terms of the particulars of experimental setup or excessive evapotranspiration.

35. Koster, R D., and P C D Milly, 1997: The interplay between transpiration and runoff formulations in land surface schemes used with atmospheric models. Journal of Climate, 10(7), 1578-1591.
    [ Abstract PDF ]

    The Project for Intercomparison of Land-surface Parameterizaion Schemes (PILPS) has shown that different land surface models (LSMs) driven by the same meteorological forcing can produce markedly different surface energy and water budgets, even when certain aspects of the LSMs (vegetation cover, albedo, turbulent drag coefficient, and snowcover) are carefully controlled. To help explain these differences, the authors devised a monthly water balance model that successfully reproduces the annual and seasonal water balances of the different PILPS schemes. Analysis of this model leads to the identification of two quantities that characterize an LSM's formulation of soil water balance dynamics: 1) the efficiency of the soil's evaporation sink integrated over the active soil moisture range, and 2) the fraction of this range over which runoff is generated. Regardless of the LSM's complexity, the combination of these two derived parameters with rates of interception loss, potential evaporation, and precipitation provides a reasonable estimate for the LSM's simulated annual water balance. The two derived parameters shed light on how evaporation and runoff formulations interact in an LSM, and the analysis as a whole underscores the need for compatibility in these formulations.

36. Milly, P C., 1997: Sensitivity of greenhouse summer dryness to changes in plant rooting characteristics. Geophysical Research Letters, 24(3), 269-271.
    [ Abstract PDF ]

    A possible consequence of increased concentrations of greenhouse gases in Earth's atmosphere is "summer dryness," a decrease of summer plant-available soil water in middle latitudes, caused by increased availability of energy to drive evapotranspiration. Results from a numerical climate model indicate that summer dryness and related changes of land-surface water balances are highly sensitive to possible concomitant changes of plant-available water-holding capacity of soil, which depends on plant rooting depth and density. The model suggests that a 14% decrease of the soil volume whose water is accessible to plant roots would generate the same summer dryness, by one measure, as an equilibrium doubling of atmospheric carbon dioxide. Conversely, a 14% increase of that soil volume would be sufficient to offset the summer dryness associated with carbon-dioxide doubling. Global and regional changes in rooting depth and density may result from (1) plant and plant-community responses to greenhouse warming, to carbon-dioxide fertilization, and to associated changes in the water balance and (2) anthropogenic deforestation and desertification. Given their apparently critical role, heretofore ignored, in global hydroclimatic change, such changes of rooting charactistics should be carefully evaluated using ecosystem observations, theory, and models.

37. Milly, P C., 1994: Climate, interseasonal storage of soil water, and the annual water balance. Advances in Water Resources, 17, 19-24.
    [ Abstract ]

    The effects of annual totals and seasonal variations of precipitation and potential evaporation on the annual water balance are explored. It is assumed that the only other factor of significance to annual water balance is a simple process of water storage, and that the relevant storage capacity is the plant-available water-holding capacity of the soil. Under the assumption that precipitation and potential evaporation vary sinusoidally through the year, it is possible to derive an analytic solution of the storage problem, and this yields an expression for the fraction of precipitation that evaporates (and the fraction that runs off) as a function of three dimensionless numbers: the ratio of annual potential evaporation to annual precipitation (index of dryness); an index of the seasonality of the difference between precipitation and potential evaporation; and the ratio of plant-available water-holding capacity to annual precipitation. The solution is applied to the area of the United States east of 105 degrees W, using published information on precipitation, potential evaporation, and plant-available water-holding capacity as inputs, and using an independent analysis of observed river runoff for model evaluation. The model generates an areal mean annual runoff of only 187 mm, which is about 30% less than the observed runoff (263 mm). The discrepancy is suggestive of the importance of runoff-generating mechamisms neglected in the model. These include intraseasonal variability (storminess) of precipitation, spatial variability of storage capacity, and finite infiltration capacity of land.

38. Milly, P C., 1994: Climate, soil water storage, and the average annual water balance. Water Resources Research, 30(7), 2143-2156.
    [ Abstract PDF ]

    This paper describes the development and testing of the hypothesis that the long-term water balance is determined only by the local interaction of fluctuating water supply (precipitation) and demand (potential evaporation), mediated by water storage in the soil. Adoption of this hypothesis, together with idealized representations of relevant input variabilities in time and space, yields a simple model of the water balance of a finite area having a uniform climate. The partitioning of average annual precipitation into evapotranspiration and runoff depends on on seven dimensionless numbers: the ratio of average annual potential evapotranspiration to average annual precipitation (index of dryness); the ratio of the spatial average plant-available water-holding capacity of the soil to the annual average precipitation amount; the mean number of precipitation events per year; the shape parameter of the gamma distribution describing spatial variability of storage capacity; and simple measures of the seasonality of mean precipitation intensity, storm arrival rate, and potential evapotranspiration. The hypothesis is tested in an application of the model to the United States east of the Rocky Mountains, with no calibration. Study area averages of runoff and evapotranspiration, based on observations, are 263 mm and 728 mm, respectively; the model yields corresponding estimates of 250 mm and 741 mm, respectively, and explains 88% of the geographical variance of observed runoff wihin the study region. The differences between modeled and observed runoff can be explained by uncertainties in the model inputs and in the observed runoff. In the humid (index of dryness <1) parts of the study area, the dominant factor producing runoff is the excess of annual precipitation over annual potential evapotranspiration, but runoff caused by variability of supply and demand over time is also significant; in the arid (index of dryness >1) parts, all of the runoff is caused by variability of forcing over time. Contributions to model runoff attributable to small-scale spatial variability of storage capacity are insignificant throughout the study area. The consistency of the model with observational data is supportive of the supply-demand-storage hypothesis, which neglects infiltration excess runoff and other finite-permeability effect on the soil water balance.

39. Milly, P C., and Krista A Dunne, 1994: Sensitivity of the global water cycle to the water-holding capacity of land. Journal of Climate, 7(4), 506-526.
    [ Abstract PDF ]

    The sensitivity of the global water cycle to the water-holding capacity of the plant-root zone of continental soils is estimated by simulations using a mathematical model of the general circulation of the atmosphere, with prescribed ocean surface temperatures and prescribed cloud. With an increase of the globally constant storage capacity, evaporation from the continents rises and runoff falls, because a high storage capacity enhances the ability of the soil to store water from periods of excess for later evaporation during periods of shortage. In addition to this direct effect, atmospheric feedbacks associated with the resulting higher precipitation and lower potential evaporation drive further changes in evaporation and runoff. Most of the changes in evaporation and runoff occur in the tropics and in the northern middle- latitude rain belts. Global evaporation from land increases by about 7 cm for each doubling of storage capacity in the range from less than 1 cm to almost 60 cm. Sensitivity is negligiblefor capacity above 60 cm. In the tropics and in the extratropics, the increased continental evaporation is split, in approximately equal parts, between increased continental precipitation and decreased convergence of atmospheric water vapor from ocean to land. In the tropics, this partitioning is strongly affected by induced circulation changes, which are themselves forced by changes in latent heating. The increased availability of water at the continental surface leads to an intensification of the Hadley circulation and a weakening of the monsoonal circulations. In the northern middle and high latitudes, the increased continental evaporation moistens the atmosphere. This change in humidity of the atmosphere is greater above the continents than above the oceans, and the resulting reduction in the sea-land humidity gradient causes a decreased onshore transport of water vapor by transient eddies. Results established here may have implications for certain problems in global hydrology and climate dynamics, including the effects of water resource development on global precipitation, climatic control of plant rooting characteristics, climatic effects of tropical deforestation, and climate-model errors induced by errors in land-surface hydrologic parameterizations.

40. Scanlon, B R., and P C D Milly, 1994: Water and heat fluxes in desert soils 2. Numerical simulations. Water Resources Research, 30(3), 721-733.
    [ Abstract PDF ]

    Transient one-dimensional fluxes of soil water (liquid and vapor) and heat in response to 1 year of atmospheric forcing were simulated numerically for a site in the Chihuahuan Desert of Texas. The model was initialized and evaluated using the monitoring data presented in a companion paper (Scanlon, this issue). Soil hydraulic and thermal properties were estimated a priori from a combination of laboratory measurements, models, and other published information. In the first simulation, the main drying curves were used to describe soil water retention, and hysteresis was ignored. Remarkable consistency was found between computed and measured water potentials and temperatures. Attenuation and phase shift of the seasonal cycle of water potentials below the shallow subsurface active zone (0.0- to 0.3-m depth) were similar to those temperatures, suggesting that water potential fluctuations were driven primarily by temperature changes. Water fluxes in the upper 0.3 m of soil were dominated by downward and upward liquid fluxes that resulted from infiltration of rain and subsequent evaporation from the surface. Upward flux was vapor dominated only in the top several millimeters of the soil during periods of evaporation. Below a depth of 0.3 m, water fluxes varied slowly and were dominated by downward thermal vapor flux that decreased with depth, causing a net accumulation of water. In a second simulation, nonhysteretic water retention was instead described by the estimated main wetting curves; the resulting differences in fluxes were attributed to lower initial water contents (given fixed initial water potential) and unsaturated hydraulic conductivities that were lower than they were in the first simulation. Below a depth of 0.3 m, the thermal vapor fluxes dominated and were similar to those in the first simulation. Two other simulations were performed, differing from the first only in the prescription of different (wetter) initial water potentials. These three simulations yielded identical solutions in the upper 0.2 m of soil after infiltration of summer rain; however, the various initial water potentials were preserved throughout the year at depths greater than 0.2 m. Comparison of all four simulations showed that the predominantly upward liquid fluxes below a depth of 0.2 m were very sensitive to the differences in water retention functions and initial water potentials among simulations, because these factors strongly affected hydraulic conductivities . Comparison of numerical modeling results with chemical tracer data showed that values of downward vapor flux below the surface evaporation zone were of the same order of magnitude as those previously estimated by analysis of depth distributions of bomb 3H (volatile) and bomb ³⁶C1 (nonvolatile).

41. Milly, P C., 1993: An analytic solution of the stochastic storage problem applicable to soil water. Water Resources Research, 29(11), 3755-3758.
    [ Abstract ]

    The accumulation of soil water during rainfall events and the subsequent depletion of soil water by evaporation between storms can be described, to first order, by simple accounting models. When the alternating supplies (precipitation) and demands (potential evaporation) are viewed as random variables, it follows that soil water storage, evaporation, and runoff are also ramdom variables. If the forcing (supply and demand) are stationary for a sufficiently long period of time, an asymptotic regime should eventually be reached where the probability distribution functions of storage, evaporation, and runoff are stationary and uniquely determined by the distribution functionsof the forcing. Under the assumptions that the potential evaporation rate is constant, storm arrivals are Poisson-distributed, rainfall is instantaneous, and storm depth follows an exponential distribution, it is possible to derive the asymptotic distributions of storage, evaporation, and runoff analytically for a simple balance model. A particular result is that the fraction of rainfall converted to runoff is given by (1 - R^-1)/(e^a(1-R-1) - R^-1), in which R is the ratio of mean potential evaporation to mean rainfall and a is the ratio of soil water-holding capacity to mean storm depth. The problem considered here is analogous to the well-known problem of storage in a reservoir behind a dam, for which the present work offers a new solution for reservoirs of finite capacity. A simple application of the results of this analysis suggests that random, intraseasonal fluctuations of precipitation cannot by themselves explain the observed dependence of the annual water balance on annual totals of of precipitation and potential evaporation.

42. Milly, P C., 1993: Sensitivity of the global water cycle to the water-holding capacity of soils In Exchange Processes at the Land Surface for a Range of Space and Time Scales, IAHS Publication No. 212, Yokohama, Japan, IAHS, 495-501.
    [ Abstract ]

    A numerical experiment using an atmospheric general circulation model was employed to estimate the sensitivity of the global water cycle to the water-holding capacity of soils. An increase of the globally constant capacity from 4 cm to 60 cm yielded an increase (24 cm) of evaporation from land, a decrease (-11 cm) of runoff, and an increase (13 cm) of precipitation onto land. Decreased runoff was balanced by decreased water-vapor flux convergence over the continents. In the tropics, the induced weakening of the monsoonal circulations was the major factor in this net export of water vapor to the oceans; in the middle latitudes, moistening of continental air masses, with resultant reduction in onshore vapor transport by transient eddies, was the dominant mechanism.

43. Milly, P C., 1992: Land surface processes and climate variability. EOS, 73(15), 163.
44. Milly, P C., 1992: Potential evaporation and soil moisture in general circulation models. Journal of Climate, 5(3), 209-226.
    [ Abstract PDF ]

    The parameterization of continental evaporation in many atmospheric general circulation models (GCMs) used for simulation of climate is demonstrably inconsistent with the empirical work upon which the parameterization is based. In the turbulent transfer relation for potential evaporation, the climate models employ the modeled actual temperature to evaluate the saturated surface humidity, whereas the consistent temperature is the one reflecting cooling by the hypothetical potential evaporation. A simple theoretical analysis and some direct computations, all ignoring atmospheric feedbacks, indicate that whenever the soil moisture is limited, GCM-based climate models produce rates of potential evaporation that exceed, by a factor of two or more, the rates that would be yielded by use of the consistent temperature. Further approximate analyses and supporting numerical simulations indicate that the expected value of dry-season soil moisture has a short memory relative to the annual cycle and that dry-season evaporation is therefore nearly equal to dry-season precipitation. When potential evaporation is overestimated, it follows that the soil moisture is artificially reduced by a similar factor, and actual evaporation may or may not be overestimated, depending on other details of the hydrologic parameterization. These arguments, advanced on theoretical grounds, explain the substantial, systematic differences between GCM-generated and observation-based estimates of potential evaporation in the assessment of the effects of climatic change on continental hydrology and water resources. They also provide a partial explanation of the excessively low values of summer soil moisture in GCMs and raise questions concerning the results of studies of soil-moisture changes induced by an increase of greenhouse gases. Nevertheless, an approximate state was qualitatively preserved in those studies.

45. Blain, C A., and P C D Milly, 1991: Development and application of a hillslope hydrologic model. Advances in Water Resources, 14(4), 168-174.
    [ Abstract ]

    vertically integrated two-dimensional lateral flow model of soil moisture has been developed. Derivation of the governing equation is based on a physical interpretation of hillslope processes. The lateral subsurface-flow model permits variability of precipitation and evapotranspiration, and allows arbitrary specification of soil-moisture retention properties. Variable slope, soil thickness, and saturation are all accomodated. The numerical solution method, a Crank-Nicolson, finite-difference, upstream-weighted scheme, is simple and robust. A small catchment in northeastern Kansas is the subject of an application of the lateral subsurface-flow model. Calibration of the model using observed discharge provides estimates of the active porosity (0.1 cm³/cm³) and of the saturated horizontal hydraulic condictivity (40 cm/hr). The latter figure is at least an order of magnitude greater than the vertical hydraulic conductivity associated with the silty clay loam soil matrix. The large value of hydraulic condictivity derived from the calibration is suggestive of macropore-dominated hillslope drainage. The corresponding value of active porosity agrees well with a published average value of the difference between total porosity and field capacity for a silty clay loam.

46. Milly, P C., 1991: A refinement of the combination equations for evaporation. Surveys in Geophysics, 12, 145-154.
    [ Abstract PDF ]

    Most combination equations for evaporation rely on a linear expansion of the saturation vapor-pressure curve around the air temperature. Because the temperature at the surface may differ from this temperature by several degrees, and because the saturation vapor-pressure curve is nonlinear, this approximation leads to a certain degree of error in those evaporation equations. It is possible, however, to introduce higher-order polynomial approximations for the saturation vapor-pressure curve and to derive a family of explicit equations for evaporation, having any desired degree of accuracy. Under the linear approximation, the new family of equations for evaporation reduces, in particular cases, to the combination equations of H. L. Penman (Natural evaporation from open water, bare soil and grass. Proc, R. Soc. London, Ser. A, 193, 120-145, 1948) and of subsequent workers. Comparison of the linear and quadratic approximations leads to a simple approximate expression for the error associated with the linear case. Equations based on the conventional linear approximation consistently underestimate evaporation, sometimes by a substantial amount.

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