The sustainability of human water use practices is a rapidly growing concern in the United States and around the world. To better characterize direct human interaction with hydrologic systems (stream basins and aquifers), we introduce the concept of the water use regime. Unlike scalar indicators of anthropogenic hydrologic stress in the literature, the water use regime is a two-dimensional, vector indicator that can be depicted on simple x-y plots of normalized human withdrawals (hout) versus normalized human return flows (hin). Four end-member regimes, natural-flow-dominated (undeveloped), human-flow-dominated (churned), withdrawal-dominated (depleted), and return-flow-dominated (surcharged), are defined in relation to limiting values of hout and hin. For illustration, the water use regimes of 19 diverse hydrologic systems are plotted and interpreted. Several of these systems, including the Yellow River Basin, China, and the California Central Valley Aquifer, are shown to approach particular end-member regimes. Spatial and temporal regime variations, both seasonal and long-term, are depicted. Practical issues of data availability and regime uncertainty are addressed in relation to the statistical properties of the ratio estimators hout and hin. The water use regime is shown to be a useful tool for comparative water resources assessment and for describing both historic and alternative future pathways of water resource development at a range of scales.
 Global concerns about the sustainability of human water use practices have grown markedly in recent years. Developments contributing to these concerns include (1) streamflow depletion and lake dessication at all scales, caused in part by human withdrawals (e.g., Yellow River, China; Colorado and Sacramento Rivers, United States; Aral Sea, central Asia; Lake Chad, central Africa); (2) regional-scale aquifer depletion due to groundwater withdrawals (e.g., High Plains, United States; North China Plain); and (3) in-stream flow needs for recreation, navigation, waste assimilation, and aquatic habitat [Poff et al., 1997; Richter et al., 2003; Alley and Leake, 2004]. At the global level, these concerns have prompted numerous recent assessments of human water use in relation to water availability, and the relative impacts of water use and climate change on the hydrologic cycle [Postel et al., 1996; Vörösmarty et al., 2000;Oki et al., 2001; Alcamo et al., 2003; Döll et al., 2003; Gleick, 2005; Oki and Kanae, 2006]. In the United States, studies of water availability and use historically focused on the arid West [Anderson and Woosley, 2005], although water use practices in the “water-rich” eastern United States have recently been shown to cause streamflow depletion and aquatic habitat degradation [Richter et al., 2003; Armstrong et al., 2004].
where SWout* is predevelopment outflow, obtained through simulation models [e.g., Alcamo et al., 2003], regional regression models [Vogel et al., 1999], or other means. For aquifers, natural water availability is typically equated with the predevelopment groundwater recharge from all sources.
 RWD is well suited for measuring one important type of anthropogenic stress: depletion of system storage and outflow caused by high rates of withdrawal in relation to renewable supply. However, certain globally important anthropogenic stresses cannot be adequately characterized by RWD, because this indicator ignores return flows and water imports. For example, about 10% of the world's 260 million hectares of irrigated agricultural land is affected by soil water logging and salinization, typically associated with high water tables caused by imports of surface water for irrigation in dry regions [Schoups et. al., 2005; Foley et al., 2005]. Contamination of streams and shallow aquifers by high rates of domestic, irrigation, and industrial return flow [Meybeck, 2003; Foster and Chilton, 2003] is another global phenomenon not addressed by RWD.
 A partial solution to this limitation is to specify net demand (Hout − Hin) in the numerator of (1), yielding the relative net demand (RND) or “consumptive use in relation to renewable renewable supply” [U.S. Geological Survey, 1984] (expressed here for a stream basin):
where Hin is total return flows plus imports of water and wastewater to the basin. Negative values of RND indicate return flows (plus imports) in excess of withdrawals; hence RND can be used to characterize return-flow-dominated and withdrawal-dominated systems. Note, however, that RND fails to characterize the intensity of water use. Both highly developed and relatively undeveloped systems can have similar RND values, if the net human demand (Hout − Hin) is similar for both systems. The essential limitation of RWD and RND is that they are both one-dimensional, scalar indicators of human-induced hydrologic stress. A fully two-dimensional or vector approach, allowing for independent variation of both withdrawals and return flows relative to total system flows, is needed to adequately characterize the nature and degree of human interaction with hydrologic systems.
 Humans interact with hydrologic systems both directly and indirectly. For the purposes of this paper, “direct” interactions are limited to withdrawals and return flows. Indirect interactions, which nevertheless can have profound effects, include (1) anthropogenic land cover change [Foley et al., 2005]; (2) dam construction for flood control and hydropower generation [Vörösmarty and Sahagian, 2000]; and (3) anthropogenic climate change [Vörösmarty et al., 2000]. Conversely, some interactions between human water infrastructure and hydrologic systems are direct but unintentional. Examples include infiltration of groundwater into wastewater collection systems, conveyance losses from water distribution networks to the subsurface or the atmosphere, and evaporative losses from surface reservoirs [Weiss et al., 2002]. For simplicity, only intentional withdrawals and return flows are considered in this paper.
 The purpose of this paper is to describe and apply a quantitative understanding of human water use, the water use regime, that accommodates the two-dimensional character of direct human interaction with terrestrial hydrologic systems. An approach is developed for characterizing the full range of anthropogenic flow stress upon hydrologic systems, in addition to certain “syndromes” of water quality degradation caused by return flows [Meybeck, 2003]. The approach is designed for hydrologists who conduct comparative water resource assessments at local, regional, or global scales [Falkenmark and Chapman, 1989; National Research Council (NRC), 2002], and who seek to define sustainable pathways of water resource development that maximize the productivity of water use while accounting for spatial and temporal variation in water availability [Loucks and Gladwell, 1999; Molden and Sakthivadivel, 1999; Falkenmark and Rockström, 2004; Rogers et al., 2006].
2. Defining the Water Use Regime
2.1. Terrestrial Water Balance
 The water use regime is defined with respect to the water balance of an explicitly bounded hydrologic system (stream basin or aquifer; Figures 1a and 1b). It is useful to consider stream basins and aquifers separately because of their contrasting boundary conditions. A stream basin control volume is considered to include the land surface, its vegetation, streams and other surface water bodies, and both the unsaturated and saturated zones of the subsurface; it can be either a “headwater” or “downstream” basin (Figure 1a). An aquifer control volume is restricted to the saturated portion of the subsurface (Figure 1b), and may range in scale from an individual model cell to an entire aquifer.
 In the case of a stream basin control volume, the total water balance can be expressed:
where P is precipitation; (GWin + SWin) is groundwater and surface water inflows; ET is evapotranspiration; (GWout + SWout) is groundwater and surface water outflows; Hin is total return flow to the control volume from all sources, equivalent to the sum of (1) locally generated return flows from local withdrawals, (2) locally generated return flows from imported withdrawals, and (3) return flows imported from other basins through wastewater infrastructure; Hout is withdrawals from the control volume; and ΔS/Δt is the rate of change in control volume storage (surface and subsurface), all averaged over the period of interest. Constant water density is assumed. We then subtract ET from both sides of equation (3) to obtain the net water flux through the basin control volume, since only the net basin flux is directly available for human use:
where Rp is aquifer recharge from precipitation; Rgw and Rsw are aquifer recharge from adjacent groundwater and surface water systems, respectively; Det is groundwater ET; Dgw and Dsw are aquifer discharge to adjacent groundwater and surface water systems; Hin is total return flow to the aquifer; Hout is aquifer withdrawals; and ΔS/Δt is the rate of change in aquifer storage. All units are length3/time (L3/T) averaged over the period of interest. All flow terms are positive, except ΔS/Δt, which can be positive, negative or zero during the period of interest. All terms in (4) and (5) except P are considered to be potentially affected by human-induced flow stress during the period of interest. In this paper, all water balance components under predevelopment conditions are denoted with an asterisk (e.g., SWout*).
 Normalized forms of (4) and (5) are obtained by dividing each term in the water balance by the respective net system flux, and expressing the resulting terms in lower case letters [cf. Lent et al., 1997]. For example, the normalized Hin and Hout components are defined as:
where NetFluxbasin = (SWout + GWout) + Hout, and NetFluxaquifer = (Dgw + Dsw) + Hout.
2.2. Water Use Regime
 The water use regime of a hydrologic system is defined as the set of system withdrawals, uses, and return flows during a period of interest. This paper focuses upon withdrawals and return flows, the two aspects of the water use regime that entail direct interaction with the hydrologic system, and their relative magnitude with respect to overall flow through the system. These relative magnitudes can be used to construct a water use regime plot, an x-y plot of hout versus hin (Figure 2). The plot domain defines the possible universe of direct flow interaction between humans and a hydrologic system. The domain is bounded by four end-member regimes (Figure 2): (1) natural-flow-dominated (or undeveloped, where hout = hin = 0), (2) withdrawal-dominated (depleted; hout = 1; hin = 0), (3) return-flow-dominated (surcharged; hout = 0; hin = 1), and (4) human-flow-dominated (churned; hout = hin = 1). Regimes characterized by net, human-induced depletion of system outflow and (or) storage plot in the lower right half of this domain (hout > hin); net accretion regimes plot in the upper left half (hin > hout).
 A pair of descriptive regime indicators, the human water balance (HWB) and the water use intensity (WUI), may be derived from hout and hin as follows:
HWB ranges from −1 to +1, and corresponds to the distance of a regime point to the right (−) or the left (+) of the line of equality (hin = hout) on the regime plot. The magnitude and sign of HWB indicate the degree and character, respectively, of direct human alteration of the system water balance (net accretion or depletion of system outflows and storage by humans). WUI varies from 0 to +1, and indicates the relative magnitude of human versus natural flows through a system.
 For illustration, the water use regimes of 19 hydrologic systems representing a range of climatic zones, stress conditions, and spatial/temporal scales are plotted and briefly discussed. Hydrologic budgets for the 7 stream basins and 12 aquifers were obtained from the published literature (Tables 1–3). The stream basin budgets were estimated or simulated using methods described in the references; all of the aquifer budgets were obtained from published simulation models.
Table 1. Hydrologic Systems Selected for Water Use Regime Analysis
 The South Platte River Basin was the most intensively developed of the seven stream basins considered, as measured by water use intensity (WUI = 0.76; Table 2 and Figure 3a). This water use regime reflects large irrigation withdrawals, substantial water imports from the Colorado River Basin, and low water availability (P − ET) over most of the basin area. By contrast, the Muskegeon River Basin in west central Michigan had a low-intensity regime (WUI = 0.03), with high water availability, low population density, and low total withdrawals and returns. Wisahickon Creek Basin, west of Philadelphia, Pennsylvania, had a somewhat higher water use intensity (WUI = 0.18), a slightly negative human water balance, and an overall water use regime typical of urbanized basins in the humid northeastern United States.
 In the remaining basins, human inflows and outflows were significantly out of balance under the various conditions considered. The largest of these systems is the Yellow River Basin, which drains a 865,000 km2 semiarid, agricultural region in northern China. The human water balance was strongly negative (HWB = −0.73) during the period studied (1998–2000); the basin approached the withdrawal-dominated, or depleted, end-member regime (Figure 3a). In August 1993, the Upper Ipswich River Basin, Massachusetts, also had a very high normalized withdrawal coupled with low water availability. However, this moderately urbanized basin had higher rates of return flow (hin = 0.37) than the Yellow River, and therefore displayed a mixed regime between the depleted and and churned end-members. Although the Upper Ipswich Basin is considered one of the most flow-stressed basins in the northeastern United States [Zarriello and Ries, 2000], only during the summer does it display a regime comparable to the average annual regime of the Yellow River Basin, which covers an area ∼7500 times larger.
 The Sacramento River Basin in California, like the Yellow River Basin, is a globally important agricultural region with high withdrawal rates per unit basin area (240 mm/yr), mostly for irrigation and urban uses. However, because average water availability (418 mm/yr) was over 6 times greater in the Sacramento Basin than in the Yellow Basin, (Table 2), hout was smaller (Figure 3a), and the water use regime was more balanced (HWB = −0.37). The moderately urbanized Upper Assabet Main stem River Basin in east central Massachusetts, simulated for average September conditions during 1997–2001, was the only stream basin considered with a positive human water balance during the period of interest (HWB = +0.31). This regime reflects imports of treated municipal wastewater to the main stem river in excess of local withdrawals, combined with low summer baseflows.
3.2. Water Use Regimes: Aquifers
 The selected aquifers showed an equally wide diversity of water use regimes (Figure 3b). The California Central Valley Aquifer most closely approximates a churned regime, in which withdrawals and return flows dominated the overall water balance (WUI = 0.87). By contrast, a group of aquifers from the humid northeastern and north central United States (Cape Cod, Upper Charles, and La Crosse County) could be considered natural-flow-dominated (WUI = 0.05 to 0.08). The Floridan and Long Island Aquifers displayed more developed regimes (WUI = 0.15 and 0.25, respectively), while the Northeast Antelope Valley Aquifer in the Mojave Desert, California, approached a purely withdrawal-dominated or depleted regime, where essentially all outflows from the system were captured for human use (HWB = −0.83;). By contrast, the Eastern Snake River Plain Aquifer, Idaho, had a positive human water balance (HWB = +0.45). In this case, infiltration of surface irrigation water imported to the aquifer from adjacent mountain areas substantially exceeded local withdrawals.
 The remaining aquifers displayed mixed regimes involving two developed end-members. For example, the 75,000 km2 Southern High Plains Aquifer was pumped at very high rates during the period of interest relative to natural recharge from precipitation (Hout = 115 mm/yr; Rp ≈ 3 mm/yr). However, unlike some other heavily pumped aquifers, (e.g., the Northeast Antelope Valley), the Southern High Plains Aquifer derived significant inflow from irrigation return flow as well as from storage depletion, placing it midway between the depleted and churned end-members. The Irwin Aquifer, California, had a contrasting type of mixed regime—midway between the surcharged and churned end-members. In this case, large wastewater imports were balanced by both withdrawals and accretion of storage.
3.3. Spatial Variation in Water Use Regime
 Water use regimes and their derived indicators (HWB and WUI) may be mapped at any spatial scale for which required data or model output are available. Regimes for stream basins may be spatially discretized by subbasin (Figure 4), or by model cell if a gridded model is used. Subbasins in the the Assabet River Basin, for example, showed significant variation in human water balance and water use intensity (Figures 4a and 4b). A series of main stem subbasins, extending from the southwestern headwaters to the confluence with the Sudbury River in the northeast (Figure 4), all had moderately positive HWB values (+0.15 to +0.31). This reflects net import of wastewater from adjacent tributary subbasins, which, in turn, were relatively depleted due to net wastewater export (HWB values of −0.02 to −0.26). Water use intensity is greatest in the main stem subbasins, where WUI ranges from 0.15 to 0.34.
3.4. Long-Term Temporal Change: Water Resources Development Pathway
 The position vector connecting the origin of a regime plot (hout = hin = 0) to a regime point depicts the average water resources development pathway of a hydrologic system over its history. The actual pathway to a particular regime can be expected to be circuitous, due to historical changes in withdrawals, return flows, and climatic conditions. The Mississippi River Alluvial Aquifer of northeast Arkansas, as simulated by Reed , serves to illustrate the pathway concept (Figure 5). Significant withdrawals from the aquifer for agricultural irrigation began in the early 1900s, and averaged 27 m3/s from 1918 to 1957. By 1998, withdrawals had increased to 207 m3/s, due mainly to the rapid expansion of irrigated rice agriculture. Until 1972, return flows were simulated to be relatively small; most of the withdrawal demand was met by increased recharge from, and decreased discharge to, adjacent streams and adjacent aquifer units, accompanied by modest depletion of aquifer storage. After 1972, return flows were estimated to be a significant fraction of the total budget. The development pathway shifted upward from the hout axis, and proceeded toward a relatively high-intensity regime by 1998 (WUI = 0.63).
3.5. Short-Term Temporal Change: Effects of Seasonality
 The Upper Charles River Aquifer had a highly seasonal pattern of simulated natural recharge, natural discharge, and human withdrawal [Eggleston, 2003], similar to the pattern previously documented in a New England glacial valley aquifer by Barlow and Dickerman . Although precipitation was evenly distributed throughout the year, natural recharge from precipitation (Rp) occurred mainly from October to May, when ET from the unsaturated zone is low. Net withdrawals (Hout − Hin), by contrast, were greatest from June to September, when Rp is very low due to high unsaturated zone ET. Consequently, summer withdrawal demands were met largely by depletion of aquifer storage. The net result was an essentially balanced annual regime (Figure 6), with peak water use intensity in September (WUI = 0.16), and a slightly negative human water balance in the summer months (HWB = −0.01 to −0.04).
4. Data Availability, Model Simulation, and Regime Uncertainty
4.1. Data Availability and the Role of Simulation Models
 Only three types of data are required to specify the water use regime of a hydrologic system: (1) net system outflow under stressed conditions (SWout + GWout for stream basins or Dsw + Dgw for aquifers); (2) withdrawals (Hout); and (3) return flows from local sources plus imports to the system (Hin); see (3) through (9). The most widely available data type, by far, is net basin outflow. In the United States, the U.S. Geological Survey presently operates about 7300 continuous record stream gages in a wide variety of basins where SWout may be quantified at hourly to decadal timescales, depending upon the period of record (see http://water.usgs.gov/nsip/). In many basins, GWout is either very small relative to SWout or close in magnitude to GWin. In such cases, SWout approximates net basin outflow. In many aquifer systems, Dgw is either small relative to Dsw, or close in magnitude to Rgw. In such cases, stream baseflow (Dsw) approximates net aquifer outflow. Baseflow may be estimated from streamgage records using a variety of manual and automated hydrograph separation methods [Rutledge, 1998].
 In areas of the world with sparse streamflow data, or in areas with substantial regional groundwater recharge or discharge, the GWout and GWin (or Dgw and Rgw) terms cannot be neglected and simulation models may be required to estimate SWout. At global and continental scales, however, gridded, steady state, meteorologically driven water balance models of the global land surface have recently been developed to estimate SWout*, both with and without calibration to streamflow data [Vörösmarty et al., 2000, 2005; Oki et al., 2001; Alcamo et al., 2003; Döll et al., 2003].
 The remaining two data types required, withdrawals and return flows, are less widely available than streamflow data in most regions. In the United States, the U.S. Geological Survey compiles withdrawal (Hout) estimates at 5-year intervals for thermoelectric, irrigation, public supply, self-supplied industrial, self-supplied domestic, and other water use sectors, aggregated most recently at State, County, and principal aquifer levels [Hutson et al., 2004; Maupin and Barber, 2005] (see http://water.usgs.gov/watuse/). The U.S. Department of Agriculture (USDA) also assesses U.S. irrigation withdrawals at 5-year intervals [USDA, 2004], and the States collect a wide range of aggregated and site-specific water use data [NRC, 2002]. Recently, global water resources assessments have used georeferenced population and irrigated area data to estimate withdrawal rates, by major sector, for use in gridded models [e.g., Alcamo et al., 2003]. Periodic, worldwide estimates of withdrawals are also available by country [Gleick, 2005].
 Throughout the world, return flows (Hin) are generally less well characterized than withdrawals. In most developed countries, programs such as the U.S. National Pollutant Discharge Elimination System (NPDES) program http://cfpub.epa.gov/npdes/ track large return flows from municipal and industrial water use sectors. However, nonpoint and unregulated point returns from these and other sectors are usually poorly known, and are typically estimated using empirical consumptive use coefficients. Coefficient errors [Solley et al., 1998] are generally unknown but potentially large. Recently, improved estimates of irrigation return flow have been obtained using georeferenced withdrawal data in concert with models that simulate irrigation requirements as a function of climate and crop type [Döll and Siebert, 2002; Schoups et al., 2005].
4.2. Water Use Regime Uncertainty
 All water resources assessment approaches are subject to uncertainty, due to measurement error, sampling error, and model error in cases where models are used. Although a comprehensive uncertainty analysis of water use regimes is a topic for future research, we briefly describe one approach for estimating likelihood intervals for estimated values of the ratio estimators hin and hout, where hin = Hin/(SWout + Hout) and hout = Hout/(SWout + Hout). Vogel and Wilson  and others have found that a normal distribution provides a good approximation to the probability density function (pdf) of annual streamflows (SWout) for most temperate regions, whereas a Gamma or Pearson type III distribution is needed in regions of greater hydrologic variability. In this initial study, we begin by assuming a normal pdf for estimates of Hout and Hin, as well as SWout. Since Geary , numerous investigators have studied the statistical properties of the ratio of two normal random variables. The pdf of R = X/Y is given by Öksoy and Aroian . In our case, X = Hout and Y = SWout + Hout; and they are considered to be bivariate normal variables (see Appendix A).
Figure 7 shows a set of hypothetical 90% confidence intervals around the previously plotted (hout, hin) positions of Figure 3a, based on this analysis. These intervals were calculated using hypothetical coefficients of variation of 0.05, 0.1, and 0.15 for SWout, Hout, and Hin respectively. The relative magnitude of these Cv values reflects one possible set of assumptions concerning these variables, namely, the suspected low, moderate, and high degree of uncertainty concerning SWout, Hout, and Hin. Note that hin and hout are least sensitive to error when near 0 or 1, and most sensitive to error toward the middle of the regime plot. The exact location of the zone of maximum error sensitivity will depend upon the relative magnitude of the respective Cv values. Improvements in water use regime uncertainty analysis should result from (1) further exploration of the statistical properties of Hin, Hout, and SWout (or Dsw in the case of aquifer systems), (2) better characterization of Hout and Hin variability and error (because error for SWout is already well characterized), and (3) extensions which treat R as the ratio of two Gamma or Pearson type III variables [Loaiciga and Leipnik, 2005].
 The study leads to the following conclusions.
 1. Human water use may be characterized as a two-dimensional process, entailing both withdrawals from and return flows to hydrologic systems. The water use regime framework provides a more complete representation of this process than commonly used one-dimensional indicators. The framework specifies four end-member regimes: natural-flow-dominated (undeveloped), human-flow-dominated (churned), withdrawal-dominated (depleted), and return-flow-dominated (surcharged). Regime plots can be used for comparative analysis of developed hydrologic systems, and for interpreting their seasonal dynamics and long-term historical development.
 2. Regional-scale hydrologic systems can be highly impacted by human water use, even when the effects are spatially and temporally averaged. The 52,000 km2 California Central Valley Aquifer and the 63,000 km2 South Platte River Basin, for example, both displayed average water use regimes approaching the churned end-member. The 865,000 km2 Yellow River Basin, China, approached the depleted end-member on an annual basis. Typically, highly impacted regional systems have low water availability (P − ET) combined with large consumptive losses (Hout − Hin) from irrigation, although consumptive losses and return flows were found to vary widely.
 3. Characterization of water use regimes is limited by data availability and uncertainty. In particular, human return flows (Hin) are often poorly estimated or not adequately differentiated from natural inflows to a system. Improved procedures for site-specific estimation of withdrawals, return flows, and their variability are a high-priority research need. Although subject to additional forms of uncertainty, gridded water balance models at the basin, continental, and global scales [Alcamo et al., 2003; Vörösmarty et al., 2005], as well as groundwater flow models (Table 1 sources) are useful tools for future mapping of water use regimes.
Appendix A:: Probability Density Function of the Ratio of Two Normal Variables
 In this initial study we focus on the statistical properties of hout, however, the exact same approach may be applied to hin. In the case of hout = Hout/(SWout + Hout) = X/Y the mean of X and Y, μx and μy, are given by μx = and μy = + and their variances σx2 and σy2, are given by σx2 = and σy2 = + Here we assume, initially, that Hout and SWout are independent, in which case it can also be shown that the correlation of X and Y, is equal to ρ = 1/. Interestingly, even though Hout and SWout are assumed to be independent and thus uncorrelated, the numerator X and denominator Y in R = X/Y are correlated. One can easily show that the correlation between Hout and Hout + SWout increases as their ratio, hout, increases and as the coefficient of variation (Cv) of Hout increases, relative to the Cv of SWout.
ϕ (z) and Φ(z) are the pdf and cdf of a standard normal random variable z and r = x/y is a realization of the random variable R = X/Y. A number of investigators have introduced approximations to the pdf of R, however, Öksoy and Aroian  show that such approximations can lead to gross errors. Interestingly, all moments of R are undefined yet its median is equal to μx/μy. The distribution of R is rarely symmetric and can even exhibit bimodal behavior. One may compute the likely interval of values for the ratio R using
with fR(r) given in (A1) and α = 0.10 to obtain a 90% likelihood interval [Rlower, Rupper].
 This work was supported by the U.S. Geological Survey's National Assessment of Water Availability and Use. We thank William Alley, Paul Barlow, Stephen Garabedian, Matthew Cooke, Sandra Postel, Ximing Cai, and three anonymous reviewers for their comments and Richard Hooper and Robert Lent for helpful discussions.