P. C. D. Milly

Global pattern of trends in streamflow and water availability in a changing climate

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 warming. 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.

Climate, soil water storage, and the average annual water balance

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 evapotranspiration), 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 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 within 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, 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 effects on the soil water balance.

Macroscale water fluxes 2. Water and energy supply control of their interannual variability

[1] Controls on interannual variations in water and energy balances of large river basins (10,000 km 2 and greater) are evaluated in the framework of the semiempirical relation E=P ¼½ 1 þð R=PÞ � n � � 1/n in which and E, P, and R are basin mean values of annual evaporation, precipitation, and surface net radiation, respectively, expressed as equivalent evaporative water flux, overbars denote long-term means, and n is a parameter. Precipitation is interpolated from gauges; evaporation is taken as the difference between precipitation and runoff, with the latter determined from basin discharge measurements and a simple storage-delay model; and radiation is based on a recent analysis in which 8 years of satellite observations were assimilated into radiative transfer models. Objective estimates of precipitation errors are considered; results suggest that past estimates of n may have been biased by systematic errors in estimates of precipitation. Under the assumption that the semiempirical relation applies also to annual values, long-term mean observations are sufficient to predict the sensitivity of annual runoff to fluctuations in precipitation or net radiation. Additionally, an apparent sensitivity of runoff to precipitation can be inferred from the observations by linear regression. This apparent sensitivity is generally in good agreement with the predicted sensitivity. In particular, the apparent sensitivity increases with decreasing basin R/P; however, slightly excessive apparent sensitivity (relative to the prediction) is found in humid basins of the middle latitudes. This finding suggests a negative correlation between precipitation and net radiation: the increase in runoff caused by a positive precipitation anomaly is amplified by an accompanying decrease in surface net radiation, possibly induced by increased cloud cover. The inferred sensitivity of radiation (water flux equivalent) to precipitation is on the order of � 0.1. Such a value is supported by independent direct analysis of annual precipitation and radiation data. The fraction of interannual variance in runoff explained by the annual precipitation anomaly (including any correlative influence of net radiation) varies systematically with climatic aridity, approaching unity in humid basins and falling to 40–80% in very arid basins. We conclude that the influence of seasonality of the precipitation anomaly on annual runoff is negligible under humid conditions, though it may be significant under arid conditions. INDEX TERMS: 1812 Hydrology: Drought; 1818 Hydrology: Evapotranspiration; 1854 Hydrology: Precipitation (3354); 1878 Hydrology: Water/energy interactions; 3359 Meteorology and Atmospheric Dynamics: Radiative processes; KEYWORDS: water balance, interannual variability, runoff, radiation

Estimated accuracies of regional water storage variations inferred from the Gravity Recovery and Climate Experiment (GRACE)

[1]xa0The 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.

Sensitivity of the global water cycle to the water-holding capacity of land

Abstract 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 ...

An analytic solution of the stochastic storage problem applicable to soil water

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 random variables. If the forcing (supply and demand) processes 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 functions of 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)/(eα(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 precipitation and potential evaporation.

Water and heat fluxes in desert soils: 2. Numerical simulations

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 of 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 36Cl (nonvolatile).

A minimalist probabilistic description of root zone soil water

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.

Macroscale water fluxes 1. Quantifying errors in the estimation of basin mean precipitation

[1]xa0Developments 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 the 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.

Relating low-flow characteristics to the base flow recession time constant at partial record stream gauges

[1]xa0Base flow recession information is helpful for regional estimation of low-flow characteristics. However, analyses that exploit such information generally require a continuous record of streamflow 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.