A spatially explicit hydrological model was applied to the Great Basin in the western United States to predict runoff magnitude and lake distributions under modern and late Pleistocene conditions. The model iteratively routes runoff through depression to find a steady state solution and was calibrated with mean annual precipitation, pan evaporation, temperature, and stream runoff data. The predicted lake distribution provides a close match to present-day lakes. For the late Pleistocene, the sizes of lakes Bonneville and Lahontan are well predicted by linear combinations of 0.2°–5.8°C decreases in temperature and corresponding increases in precipitation from 2.0 to 1.0 times modern values. This corresponds to runoff depths ranging from 1.7 to 4.1 times the present values and yearly evaporation from 0.4 to 1 times modern values. To reproduce Lake Manly, however, combinations of temperature decreases up to 9°C or precipitation up to 2.8 times the present values were required.
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 In most terrestrial fluvial networks, storage and evaporative loss of water in lakes and reservoirs has negligible impact on water budgets and flow routing, and where such water bodies do occur, such as along the Colorado River, evaporative losses in reservoirs can be individually calculated. In some landscapes, however, such as the U.S. Great Basin Region, climate changes cause large variation in the number and size of lakes as well as in the connectivity and magnitude of interbasin flows. Conversely, changes in lake level in enclosed basins preserved over geologic time provide information on the local climate change [Benson and Paillet, 1989; Godsey et al., 2005; Menking et al., 2003]. Such lakes receive water from streams, overflow from adjacent basin lakes, and groundwater flow, and they rise and fall in response to changes in these inputs [Benson and Paillet, 1989]. Thus, the water budget and lake distributions respond to dynamic interactions between the flow of water from precipitation through the drainage basin and evaporative losses within intermediate and terminal lakes. Here we present a spatially explicit flow routing model that incorporates local topography in the form of a Digital Elevation Model (DEM). Similar to the surface water area model (SWAM) proposed by Coe , this model uses DEMs to determine flow direction and balances runoff generated from precipitation and lacustrine evaporation to estimate the lake distributions. As a test of the model we have used a simple regression-based estimation of the water balance to predict lake extent within the Great Basin region under both modern conditions and conditions characteristic of the pluvial late Pleistocene epoch.
 The objectives of this study are to (1) test the validity of the newly developed, spatially explicit flow routing model using high-resolution elevation data, (2) evaluate previously published estimates of late Pleistocene climatic conditions in Great Basin area, and (3) determine what ranges of climatic conditions best fit the known distribution of lakes in the Great Basin during the Last Glacial Maximum (LGM). This model is not coupled with an atmospheric model to estimate present or Pleistocene climate and resulting lake distributions [e.g., Clement, 2005; Coe, 1998; Giorgi et al., 1994; Hostetler and Giorgi, 1993]. Rather, this exploratory study focuses on testing of the flow routing model and determining what changes in climatic factors relative to the present conditions were required to create the Pleistocene megalakes based on a simple balance between precipitation and evaporation.
2. Model Description
 The present hydrologic model is based upon yearly balances of runoff from precipitation and evaporation from lakes. Because large lakes require multiyear changes in this balance to effect appreciable changes in lake levels, we do not include event-based flow routing. Also, we do not model groundwater flow contributions to the water cycle to keep the model simple. We consider the effects of this omission in the discussion. The hydrologic balance for a given enclosed basin is expressed by a standard water balance equation [e.g., Horton, 1943; Benson and Thompson, 1987]:
where VO is the yearly volumetric rate of overflow from the basin, VI is the inflow rate from adjacent basins, AT and AL are, respectively, the total basin and lake area, P is the average precipitation rate, RB is the fraction of precipitation that contributes to runoff, and E is the evaporation rate. Hence, any changes in precipitation, evaporation, or runoff would cause variations in lake volume and surface area and, possibly, integration or fragmentation of larger basins depending upon whether smaller contributing basins overflow. In the model P, E, and RB are spatially variable, but the lake area, AL, is determined by the basin-wide balancing of equation (1).
 Each basin has a maximum lake area (ALM), which is determined by the topography, and any ponding beyond this point would result in an overflow into an adjacent basin. If the calculated AL (using equation (1) under the assumption of no overflow to nearby basins) is greater than ALM, then there is an overflow; thus, VO is calculated as the excess volume by substituting ALM for AL. An iterative approach is used since overflow from one basin could serve as an inflow into another basin, requiring recalculation of its water balance using equation (1). The iterative procedure continues until there is no change in VI for any basin. Additional complications arise since two or more overflowing basins may mutually drain, and filling of a downstream basin may submerge the outlet for an upstream basin. In such occurrences the basins are combined into a new subbasin for subsequent iterations. Model convergence to a steady state condition is speeded by recalculating the hydrological balance only for subbasins experiencing changes in VI during the previous iteration. Calculation of discharges and lake distributions for the grid of 1142 × 1203 cells utilized for the Great Basin study requires about 15 min of computation time on a typical microcomputer.
 Because the model is spatially explicit, both runoff and evaporation need to be estimated for each grid cell. Prediction of runoff is based upon modern yearly runoff at gauging stations within the Great Basin as correlated with estimates of mean annual temperature and precipitation. Evaporation estimates utilize correlations of measured evaporation rates with mean annual temperature and elevation. The following sections describe the exploratory model parameterization for the Great Basin of the western United States.
3. Application to the Great Basin
 The Great Basin of the western United States is an ideal location to study variations in local climate because it contains enclosed basins featuring perennial and ephemeral lakes, playas, and salt pans. The Great Basin consists of most of Nevada, western Utah, and portions of California, Idaho, Oregon, and Wyoming (outlined in Figures 1 and 2). At present it supports an extremely dry, desert environment in valley bottoms. However, about 40 lakes, some reaching the size of present-day Great Lakes, episodically occupied the Great Basin. The most recent occurrence of such lakes was during the Last Glacial Maximum (LGM) from 20 ka to 10 ka [Hostetler et al., 1994; Madsen et al., 2001; Snyder and Langbein, 1962]. The Great Basin has been strongly shaped by fluvial and lacustrine erosion, and multiple paleolacustrine deposits and shorelines indicate that the climate has fluctuated greatly during the late Pleistocene [Benson et al., 1990; Oviatt et al., 1992; Smith and Street-Perrott, 1983].
 Climatic conditions and lake levels in the Great Basin during the late Pleistocene have been studied extensively. However, spatially explicit modeling of runoff and lake distribution for either modern or the LGM period has not been well established. Previous studies either focus on only one lake or lake system or they cover the entire Great Basin at coarse spatial resolution. In addition, it is often assumed that the Pleistocene conditions can be described as a “region-wide” change in climatic conditions relative to modern values. However, Pleistocene precipitation, temperature, evaporation, and runoff may have had somewhat different functional variation with latitude, longitude, and elevation relative to modern conditions. Examples might include changes in storm tracks due to shifting of the jet stream and suppression of evaporation by greater cloud cover during pluvial episodes [e.g., Hostetler and Benson, 1990; Orme, 2008], as well as changes in the spatial pattern of evapotranspiration due to vegetation changes [e.g., Madsen et al., 2001; Minckley et al., 2007]. Systematic mismatches between model-predicted and mapped late Pleistocene lakes may be informative of spatial differences in such climatic factors within the Great Basin. As a result, this spatially explicit, high-resolution model that simulates lake distribution throughout the Great Basin represents a useful extension of previous work. Such modeling allows for a more definitive test of possible variations in runoff and evaporation during pluvial conditions that cannot be captured by spatially uniform changes in temperature and precipitation [Knight et al., 2001].
 Three lake systems in the Great Basin that are commonly used as indicators of the climatic conditions during the LGM are Lake Bonneville, Lake Lahontan, and Owens Lake. This study refers to these three lake systems for the purpose of estimating paleoenvironments, but much of the study focuses on the three terminal lakes: Lake Bonneville, Lake Lahontan, and Lake Manly (Figure 2).
 Lake Bonneville and Lake Lahontan are the two largest pluvial lakes that occupied the northern Great Basin (Figure 2a). Lake Bonneville is the predecessor of the Great Salt Lake and covered as much as 51,000 km2 when it had reached its highstand elevation of 1552 m [Lemons et al., 1996]. When Lake Bonneville was at this highstand elevation, it started to overflow into the Snake River through Red Rock Pass in Idaho. This stabilized the lake surface level at the 1552 m shoreline until a catastrophic outflow event occurred around 14.5–13.5 ka, which caused the lake surface elevation to lower to 1440 m [Godsey et al., 2005; Oviatt, 1997]. The lake surface elevation continued to decline below the outlet level to form the Great Salt Lake, and it has been maintained close to its current level of around 1280 m since ca. 8 ka [Oviatt et al., 2003].
 The Lahontan basin is located in the western Great Basin. It is currently occupied by Pyramid Lake, Honey Lake, Walker Lake, and Winnemucca Lake along with several salt flats (e.g., Carson Sink and Humboldt Sink), all of which were parts of pluvial Lake Lahontan. Lake Lahontan reached its most recent highstand elevation of 1330 m around 13.8 ka, at which point it covered an area of 22,300 km2 [Adams and Wesnousky, 1999; Benson and Thompson, 1987; Benson et al., 1995].
 Lake Manly in Death Valley was the largest of a chain of five lakes in the Owens Lake system that was fed by the Owens, the Amargosa and the Mojave Rivers (Figure 2b). The lacustrine history of Pleistocene lakes in the southern portion of the Great Basin is not as well constrained as that of the northern Great Basin due to poorly developed shorelines with few absolute age determinations. During OIS 2 Panamint Valley was the terminal basin of the Owens River system, being fed by overflow from Searles Lake, with overflows occurring between 24 ka to at least 15.5 ka [Jayko et al., 2008]. Although overflow of the Owens river system into Death Valley occurred during the mid-Pleistocene, overflow appears not to have occurred during OIS2 [Anderson and Wells, 2003; Phillips, 2008], and the main sources of flow into Lake Manly were the Mojave and Amargosa river systems [Anderson and Wells, 2003; Enzel et al., 2003; Reheis and Redwine, 2008; Wells et al., 2003]. The surface elevation and area of Lake Manly during the LGM were between 46 and 61 m above sea level and approximately 1600 km2, respectively [Ku et al., 1998; Li et al., 1997], but these high OIS 2 lake levels apparently date to about 26–24 ka [Caskey et al., 2006]. Flows into Lake Manly from the Mojave River system appear to have been most significant after 18 ka subsequent to breaching of Lake Manix through Afton Canyon and erosional lowering of the outlet of Silver Lake [Anderson and Wells, 2003; Enzel et al., 2003; Reheis and Redwine, 2008; Tchakerian and Lancaster, 2002; Wells et al., 2003]. Death Valley has not supported a perennial lake since the desiccation of Lake Manly around 10 ka [Lowenstein et al., 1998].
4. Data and Methods
4.1. Data Acquisition and Analysis
 Many of the data used for this study were obtained electronically, including the digital elevation models (DEMs). All available DEMs are produced by methods that introduce spurious depressions within the landscape [Soille et al., 2003], and because the model balances evaporation from water within depressions and runoff, these false depressions would result in overestimation of evaporation. In a landscape with true depressions, such as considered here, care must be taken to distinguish between real and false depressions.
 Our approach was to use 1 × 1 km grid cells generalized from ∼30 m high resolution DEMs obtained from the National Elevation Data set (NED, http://seamless.usgs.gov). For our 1-km2 grid, we utilized the minimum elevation from all NED DEM cells within our coarser grid for flow routing, and the average elevation within the NED cells for estimating precipitation and MAT. To reduce residual false depressions, we replaced each 1 km2 cell with a third-order polynomial fit for that cell and the surrounding 24 cells. Finally, all of depressions smaller than 5 grid cells were infilled, because they are more likely the products of generalization of topography rather than the actual depressions. We have not included bathymetry of modern lakes in our DEM. This has little effect on estimated lake areas and elevation but leads to underprediction of lake depth and volume, particularly for modern climatic conditions. The 1 × 1 km grid used in this study provides greater spatial resolution than the 5 × 5 km grid used in the Clement  lake model.
 Because Lake Bonneville overflowed its basin around 14.5–13.5 Ka and eroded its outlet from about 1552 m to 1440 m, we raised the level of the Bonneville basin sill to its preoverflow level of 1552 m to test the ability of the model to predict basin-full conditions. Other Pleistocene lakes such as Manix, Mojave, and Tecopa experienced similar outlet lowering or draining during the LGM interval [e.g., Enzel et al., 2003], but we have not attempted to replicate the detailed drainage network evolution during this time period. As suggested by Enzel et al.  the highstand of Lake Manly during the LGM probably occurred after significant lowering of the outlet of these contributing lakes.
 Mean annual precipitation data was obtained from the National Resources Conservation Services (NRCS, http://www.ncgc.nrcs.usda.gov/products/datasets/climate/data/precipitation-state) in grid format. These grid data were created by the PRISM project group from Oregon State University based on precipitation data collected from January 1961 through December 1990 [Daly et al., 1994]. Precipitation data grids are available for each state, and after combining grids for all of the states within the Great Basin, this was also reduced from 30 arc second resolution to the 1 km resolution.
 The mean annual temperature data along with the deviation from the historical average and pan evaporation rate were provided by the National Climatic Data Center (NCDC, http://www7.ncdc.noaa.gov/IPS/CDPubs?action=getstate) and the Western Regional Climate Center (WRCC, http://wrcc.dri.edu/htmlfiles/westevap.final.html), respectively. There were 24 stations within the Great Basin that had records of mean annual pan evaporation rate and also had MAT recorded at the same location. The Period of record used to calculate the mean annual pan evaporation rates varied from station to station. For each station, pan evaporation rate and elevation of the station were recorded. The actual lake evaporation is lower than the pan evaporation rate; hence we reduce lake evaporation rates as discussed below. The mean annual temperature data were available for 309 stations within the Great Basin, and the MAT, latitude, longitude, and elevation of the station were recorded.
 Another data set obtained for this study was mean annual discharge volume from U.S. Geological Survey (USGS, http://waterdata.usgs.gov/nwis/sw). There were 375 stations that had at least 10 years of recorded data within the Great Basin region, of which 124 stations were discarded due to the location of the gauging stations. Because this region is constantly water limited, many of the stream flows are regulated by dams, reservoirs, and diversions, thus any stations located immediately downstream of such features were discarded. Additionally, 86 stations were excluded because the location of the gauging station could not be matched on our DEM. Such circumstances were determined by comparing the contributing drainage basin area defined by our model and those measured by USGS. When the ratio of the predicted to the measured drainage area was greater than 2 or less than 0.5, the gauging station was eliminated. This could occur, for example, when station is located on a small tributary and was not captured when the DEM was generalized. The average mean annual surface runoff depths for the remaining 165 stations were calculated using the discharge measurements and dividing them by the contributing basin area as measured by the USGS.
 Aside from these climate and hydrological data, a map of current lakes in the Great Basin (revised by Gary Raines, 1996, gb_wb: DDS 41, U.S. Geological Survey, Denver) and a map of late Pleistocene lakes at their maximum extent (M. D. Mifflin and M. M. Wheat, 1996, pluvial: DDS 41, U. S. Geological Survey) were obtained from the W. M. Keck Earth Sciences and Mining Research Information Center (http://keck.library.unr.edu/data/gbgeosci/gbgdb.htm). This file was converted from its original ESRI ArcGIS shapefile format to a grid cell format (zero for no lake, one for a lake) to compare model results to the actual lake distributions.
4.2. Estimation of Runoff and Evaporation
 Producing a hydrological model requires spatially explicit estimates of runoff and evaporation, which we express as functions of precipitation, temperature, latitude, and elevation.
4.2.1. Mean Annual Evaporation Rate
 Evaporation is an important component of the hydrologic cycle [Brutsaert, 2005] and has a great influence on lake-level fluctuations in the Great Basin since it is a primary process for lakes to lose water [Hostetler and Bartlein, 1990]. However, evaporation rate is hard to estimate owing to the difficulty of accurately measuring its controlling parameters like wind speed, atmospheric moisture content, and cloud cover [Shevenell, 1999].
 There are many methods proposed for estimating evaporation [Brutsaert, 1982; Hargreaves and Allen, 2003; Winter et al., 1995; Wu, 1997]. While many of them require various climatic parameters, not all parameters are easily obtainable [Shevenell, 1999; Wu, 1997]. Weather stations are widely scattered within the Great Basin region, especially in Nevada, and only few of them have records over sufficient periods of time to obtain reliable average values. A simpler method for estimating evaporation rate was desirable to compensate for paucity of data for the Great Basin region.
 The mean annual temperature can be estimated using the following expression obtained through a multiple regression analysis between the MAT, latitude (lat., in decimal degree), and elevation:
It should be noted that elevation used to calculate MAT and evaporation is the average elevation of the lake surface, which fluctuates with changes in lake level. This allows evaporation rate to change in accord with lake level since increase in lake level would cause evaporation rates to decrease.
4.2.2. Mean Annual Runoff
 Surface runoff is sensitive to variations in precipitation inputs, evapotranspiration, and topography [Mifflin and Wheat, 1979; Haddeland et al., 2002]. Our aim for choosing methods for estimating climatic and hydrologic parameters was to keep the relationship as generalized and simple as possible. While a number of methods are used for runoff estimation [U.S. Soil Conservation Service, 1986; Ferguson, 1996; Knight et al., 2001], many of them were developed mainly for agricultural and city planning purposes and are more appropriate for estimating runoff for small localized areas where specific soil types and land covers are well characterized and somewhat uniform. The Great Basin is too large of a region to apply area-specific methods.
Schumm  suggested that mean annual runoff can be expressed as a function of precipitation and temperature. His graph of mean annual precipitation against mean annual runoff for different MAT values for the entire United States clearly showed a strong relationship between runoff, MAT, and precipitation. This method can be regarded (at least under present-day conditions) to include implicitly the effects of soil and land cover types, since gauging stations measure discharges responding to local influences of soils and land cover [Schumm, 1965].
 Following the methodology of Schumm , mean annual runoff (R, in meters per year) was expressed as a function of annual precipitation (P, in meters per year) and MAT (T, in °C). We utilized an expression that permits runoff depth to approach but never exceed precipitation depth as precipitation increases. However, using discharge data from a gauging station to estimate the surface runoff for every grid cell within its contributing area upstream of the station may lead to a biased estimation. Therefore, in deriving the runoff expression we utilized precipitation and MAT that were averaged over all cells within each contributing drainage basin and runoff measured at the gauging station. Nonlinear regression was conducted using the statistical analysis package, SPSS, which resulted in the following equation for runoff:
This relationship exhibits the type of functional relationship expected for precipitation-runoff relationships [e.g., Budyko, 1974; Milly, 1994] in that the evapotranspiration ratio, (P − R)/P, approaches unity for low precipitation and high MAT (high dryness) and approaches direct proportionality to precipitation for high precipitation and low MAT (low dryness).
 Because equation (4) was estimated using basin-averaged values of precipitation and runoff, we compared the gauging station runoff to the estimated runoff at the ganging stations using our model employing equation (4) and using the spatially distributed values of precipitation and estimated MAT to estimate local runoff, which was then routed downstream. The predicted and observed runoff are directly proportional, indicating that the effects of the nonlinearity of equation (4) are minor.
5. Application to Modern and Pleistocene Conditions
 The model was first validated by applying it to the present-day Great Basin. Most past studies have expressed paleoclimate conditions in terms of a regional decrease in MAT and a proportional change in yearly precipitation (a “multiplicative” model). In addition, however, we investigate scenarios in which the change in precipitation is hypothesized to be an areally uniform addition to yearly precipitation depth (an “additive” model). The distinction is that the greatest absolute increase of precipitation occurs in the highlands with the multiplicative model, whereas desert regions receive the greatest proportional increase in precipitation with the additive model.
Equation (2) shows that any changes in MAT would also change evaporation rate in our model. For our simulations, changes in evaporation rate are assumed to occur only as a result of changes in MAT and lake surface elevation. Nevertheless, evaporation rate change due to increased cloud cover could always be included by further reducing the evaporation rate independent of temperature change. Also, because we are extrapolating from the modern-day data, evaporation rate could become negative when MAT is lowered by a large amount. In such cases, evaporation was defined to equal zero. Equation (2) clearly becomes inappropriate for estimating evaporation for large decreases in MAT, so we have limited our simulations to temperature decreases less than 6.0°C when optimizing the conditions for Lake Lahontan and 9.5°C for a deep Lake Manly.
6.1. Present-Day Great Basin
 Several simulations were conducted using evaporation rates expressed as different fractions of the pan evaporation rate given by equation (2). The actual lake evaporation is known to be about 70% of the pan evaporation rate [Kohler et al., 1955]. However, most of the stations within this region recorded pan evaporation only during the summer months, which caused mean annual pan evaporation to be lower than the actual. This was compensated for by increasing the proportion of pan evaporation; the estimated lake distribution matched the observed lake distributions best when evaporation rate was set to be 90% of the pan evaporation rate (Table 2).
Table 2. Comparison of the Actual and Simulated Lake Surface Area and Lake Level Under Present-Day Conditions for Endorheic Lakes in the Great Basina
 The lake distribution map created by our model was overlaid on top of the map of current lakes to visually assess the results (Figure 1). Using our DEM, the grid-based precipitation map, and estimation of runoff and evaporation from equations (2)–(4), the flow routing model was able to approximately reproduce the modern spatial distributions and sizes of most lakes. Results for lakes in endorheic basins were compared quantitatively (Table 2). Most of the basins lacked lakes as anticipated, and the larger lakes such as the Great Salt Lake, Pyramid Lake, and Mono Lake matched closely to the present-day lake sizes. On the other hand, some of the lakes were clearly overestimated. Owens Lake and Sevier Lake are examples of such lakes since currently they are both dry lakes but our model predicted them as ephemeral lakes. This can be attributed to the fact that this region is constantly water limited, thus rivers feeding into these lakes are often diverted, regulated, or dammed for agricultural and industrial purposes [Grayson, 1993]. This would cause the streamflow and water ponding not reflective of the natural climatic controls. Owens Lake was much deeper and larger before 1912 when the flow was diverted to provide water to Los Angeles and for agricultural irrigation [Smith and Street-Perrott, 1983]. Harney Lake and Malheur Lake in southern Oregon are other examples where the model results were overestimated. However, Harney Lake can overflow and merge with Malheur Lake during the wet years, creating one large lake similar to the size of simulated lake.
 In summary, our model reproduced lake surface elevations within the observed modern range of elevations for four of the nine endorheic lakes in Table 2, an additional three were reproduced within ten meters of observed levels, and the remaining two were within 20 and 30 m. Predicted lake areas showed greater variability, with over- or underestimation by up to 369%.
 Our simulated lake levels and areas are compared in Table 2 with results from prior modeling by Clement . The predictions from our simple regression-based estimation of runoff and evaporation have similar patterns and magnitudes of discrepancies to the more elaborate but lower-resolution model of Clement , which utilizes local climate modeling and monthly balancing of precipitation, evaporation, and subdivided estimates of runoff from snowmelt, base flow saturation-overland flow, and Hortonian overland flow.
 In the hydrologic model, each enclosed basin must have at least a small lake in order to satisfy the water balance of equation (1). In actuality within the Great Basin, many of the enclosed depressions support only flat-floored ephemeral playa lakes. The model contains a provision for identifying those lakes which are likely to be ephemeral. The average lake depth, D, is calculated for each enclosed basin lake. If the ratio of D to the estimated yearly evaporation depth, E, were less than a specified value, then the lake is considered to be ephemeral. In Figures 1, 2a and 2b we use a conservative critical D/E ratio value of 0.5 to identify probable ephemeral lakes. We have not applied this criterion to modern perennial lakes and reservoirs because our DEM is not corrected for lake bathymetry.
6.2. Last Glacial Maximum Great Basin
 Using both multiplicative and additive approaches our model resulted in lake distributions that were consistent with the mapped late Pleistocene paleoshorelines for changes in precipitation and MAT within previous paleoclimate estimates. We estimate the climatic conditions leading to the late OIS2 highstand of Lake Lahontan as well as conditions for Lake Bonneville to have overflowed into the Snake River. Owing to the overflow, the latter provides a minimum estimate of requisite climate change. Because of the uncertainty about the height and timing of Lake Manly, we estimate requirements for both a shallow, possibly ephemeral lake with a maximum depth of about 5 m, and a deeper lake reaching about a maximum depth of 135 m.
 Observed and resultant lake surface elevations and surface areas simulated under optimal conditions for lakes Lahontan and Manly are summarized in Table 3. With the multiplicative precipitation model, the maximum extent of late Pleistocene lakes at the northern half and southern half of the Great Basin could not be simultaneously produced by the same regional change in MAT and proportional change of precipitation (Figures 2a and 2b). A deep (135 m deep) Lake Manly in the southern region could not be created whenever conditions were set to fit the two large northern lakes, lakes Bonneville and Lahontan (Figure 2a). Conversely, when conditions were set to fit for a deep Lake Manly, Lake Lahontan and other northern lakes (except for the overflowing Lake Bonneville) were overestimated (Figure 2b).
Table 3. Comparison of Observed and Simulated Lake Surface Levels and Surface Areas for the Last Glacial Maximuma
Lakes are grouped into those in the Lake Bonneville, Lahontan, and Manly regions, respectively. For the multiplicative method, simulated lakes in the Lahontan and Bonneville groups are optimized to match the size of Lake Lahontan (50% increase in precipitation and 3.1°C decrease in MAT), and lakes in the Manly region reflect optimization for the size of Lake Manly (50% increase in precipitation and 7.6°C decrease in MAT). Simulated lake surface areas for Lake Manly region under the condition optimized for Lahontan are shown in parentheses for comparison with the additive lake surface areas, and levels for the additive method are results from a condition optimized for Lake Lahontan (0.3 m increase in precipitation and 0.8°C decrease in MAT). Ranges in surface area created using different optimal conditions for Lake Lahontan are included in parentheses for lakes Bonneville and Manly.
 The additive precipitation model, on the other hand, comes closer to simultaneously simulating the size of Lake Lahontan and a deep Lake Manly (Table 3, Figure 3). While many of the additive simulations resulted in similar lake extent and distributions as multiplicative method (Table 3), additive method can create close to full depth (∼80%) Lake Manly when 0.36 m of precipitation was added without changing the MAT (Figure 4). The additive method has smaller north and south regional difference when lakes are created mainly due to increase in precipitation.
 Although neither the additive or multiplicative precipitation models can simultaneously create a deep lake Manly for conditions optimized for Lake Lahontan, a shallow (∼5 m deep) lake Manly is created by both models.
 In both cases, it can be inferred that slightly greater changes were required for the Lake Bonneville than the Lake Lahontan. For instance, 50% increase in precipitation and 3.1°C decrease in temperature is one of the optimal conditions for the Lake Lahontan for multiplicative method. Under this condition, Lake Bonneville surface level is at 1508.9 m. In order to raise Bonneville lake level to its 1552 m outlet level, either the MAT must be lowered by an additional −0.4°C or precipitation must be increased by an additional 8% relative to the Lahontan-optimized climate. As for the additive method, additional 0.05 m of precipitation is required to raise the surface lake level from 1522 m to 1552 m when MAT is lowered by 3.1°C. Moreover, the additive method can create full size lakes Bonneville and Lahontan simultaneously when MAT is lowered by −5°C. The differences in optimal climate conditions between the two lakes are very small, and this illustrates that the model is doing well given the strong sensitivity of the model results to small differences in MAT or precipitation. At least part of the added moisture required to create an overflowing Lake Bonneville relative to a full size Lake Lahontan may have come from lake-atmosphere interactions such that moisture evaporated from Lake Bonneville may have been recycled as precipitation in the mountains to the east, a situation not occurring for Lake Lahontan [Hostetler et al., 1994].
 Additionally, under the climatic conditions optimized for Lake Lahontan, paleolakes between lakes Bonneville and Lahontan are generally underestimated for both the additive and multiplicative precipitation scenarios (Figures 2a and 3). This could be due either to underestimated runoff in the mid Great Basin or overestimated evaporation relative to lakes Bonneville and Lahontan. Because the underestimated lakes are at similar elevations and latitudes to the major lakes, underestimation of runoff is more likely than overestimation of evaporation. Lake Lahontan and Lake Bonneville derive most of their drainage from the high mountains along the western and eastern margins of the Great Basin, respectively. This suggests that variation of precipitation and runoff with elevation were less under LGM conditions than at present. All of the above suggests that the assumption of region-wide, uniform changes in temperature and precipitation leads to systematic regional biases in prediction. Gradients in precipitation and/or temperature with latitude and with elevation appear not to have been as strong during the LGM as under the modern climate.
 When examining the simulation results for the southern end of the Great Basin, neither of the models were able to produce Lake Manix and other lakes along the Mojave River upstream of Lake Manly (Figures 2b and 3). Lake Manix was incised at the Afton Canyon, which caused the topography to change [Enzel et al., 2003; Meek, 1989; Reheis and Redwine, 2005]. Other lakes share similar histories. Therefore Lake Manix and other lakes fed by Mojave River could not be replicated by using a modern DEM. We did not restore the original lake level like we did for Lake Bonneville, because lakes along the Mojave Rivers are not major lakes like Lake Bonneville. Also, Lake Manly probably reached its maximum LGM depth after the lowering of the outlet levels of upstream lakes such as Lake Manix [Anderson and Wells, 2003; Enzel et al., 2003; Phillips, 2008].
 We estimated conditions necessary to produce the observed Pleistocene lakes expressed in two ways: (1) combinations of changes in average runoff and evaporation and (2) combinations of changes in precipitation and MAT. The former is less model-dependent, since unlike the second method, it does not strongly depend upon the particular assumed relationship between precipitation, MAT and runoff. Because we have run the model to fit the observed size of particular Pleistocene lakes, the adequacy of the simulations is evaluated by the reasonableness of the predicted changes in climate conditions and the ability of the model to replicate the lake surface elevation and surface area of lakes other than the one for which the simulation is optimized. Of particular interest is the degree to which our simple postulation of proportional or additive changes in precipitation and temperature fails to match mapped LGM lake distributions and the resulting implications for the LGM paleoclimate.
 To investigate the spatial variations in estimated climate, we defined three regions, Bonneville, Lahontan, and Manly for which we estimated the regional changes in precipitation, MAT, evaporation, and surface runoff necessary to produce the LGM lakes defining the three regions (Figure 5). In making regional estimates, we utilized only points within the Great Basin (white areas in Figure 5). Values of MAT and precipitation (and corresponding evaporation rates and runoff) for those simulations providing the best match to the sizes of lakes Bonneville, Lahontan, and Manly for both additive and multiplicative precipitation changes were summarized and expressed as functional relationships. Figure 6 shows the average values of nonlake surface runoff (R: in m a−1) and lake-surface evaporation rate (E, in meters per year) producing observed LGM lakes, which can be expressed as linear functions for the regions draining to the lakes: Lahontan
The simulations indicate that in order to have lakes approximately equal to those of the LGM, surface runoff must be increased by factor of 1.7–7.5 for evaporation rates in the range of 0.6–2.0 m a−1 (inset in Figure 6). This result is reasonable since Smith and Street-Perrott  estimated that the flow in the Owens system during the LGM was at least 3.5 times greater than that of the present-day. When compared to the conditions required for each lake, it can be inferred that a greater relative changes in runoff and/or evaporation were required to create a deep Lake Manly than to produce Lake Lahontan (inset in Figure 6). For the additive precipitation simulations the equivalent regression equations become Lahontan
Similarly, the range of combinations of changes in precipitation and MAT that can recreate the mapped LGM paleoshorelines for multiplicative method are shown in Figure 7. This graph also shows that climate required to reproduce mapped lakes differed between the northern (Lahontan) and the southern (Manly) Great Basin regions. The parametric values producing the observed late Pleistocene lakes are within the range of previously proposed conditions, though specific combinations may be different than previously proposed (cf. Table 1 and Figure 7). For instance, some studies have suggested about 13°C decrease in MAT along with the precipitation increase by factor of 1.2 as required conditions to form Lake Lahontan [Thompson et al., 1999], while our model required only 4.7°C decrease in MAT for same precipitation increase. Specific equations for multiplicative precipitation are (subscript M refers to modern values) Lahontan
Equivalent equations for the additive precipitation model are Lahontan
Overall, both multiplicative and additive precipitation simulations produced similar results. Both models showed regional climate difference between the northern and southern Great Basin and underestimated lake Bonneville and lakes between Bonneville and Lahontan when conditions were optimized for Lake Lahontan. One positive feature of the additive precipitation simulations is that a deep lake Manly is produced without overflow from the Owens River system through Searles Lake, which seems not have occurred during OIS2 [Anderson and Wells, 2003; Phillips, 2008]. By contrast, simulations producing a deep Lake Manly using multiplicative increases in precipitation result in the major source of water being overflow of Searles Lake.
 This subregional climate difference could be seen in plant macrofossil assemblages from packrat middens as well [Spaulding and Graumlich, 1986]. While area north of 36 °N supported more cold-tolerant desert vegetations, areas south of 36 °N supported vegetation that requires low temperature and abundant precipitation [Spaulding and Graumlich, 1986]. One possible explanation for this difference may be that the polar jet stream had greater effects to the southern Great Basin than to the northern Great Basin. The difference in the effect of jet stream between the two regions could be attributed to the topography of the western United States [Spaulding and Graumlich, 1986]. Located at the western border of the Great Basin are the two north-south trending mountain ranges, the Sierra Nevada and Cascades, which block the greater part of the winds coming in from the Pacific Ocean and cause most of the moisture to precipitate to the west of the mountain range [Antevs, 1952; Mock, 1996]. Currently, when the wind from the west encounters the Sierra Nevada and the Cascade mountain ranges, it detours south around the Sierra Nevada flowing inland through the Mojave Desert [Bryson and Hare, 1974]. Around 20 to 18 ka, the polar jet had shifted south of Sierra Nevada [Kutzbach and Wright, 1985], and flowed directly inland through Mojave Desert region into the Great Basin [Benson et al., 1990, 1995]. Precipitation is most closely associated with the jet stream today and its maxima tend to be oriented along or just north of the jet stream [Riehl et al., 1954]. Therefore, when the jet stream was located over the Mojave region, Lake Manly could have experienced the full impact of the polar front.
 Another possible source of water contributing to the southern Great Basin is groundwater inflow (J. Quade, personal communication, 2006). Death Valley receives groundwater flow primarily from Spring Mountain near Las Vegas, Nevada [D'Agnese et al., 1997; Hunt, 1975; Li et al., 1997; Plume, 1996; Prudic et al., 1995], and the core sample from Death Valley includes deposits with high concentration of Ca-rich minerals, indicating that groundwater inflow had often played an important role over its history [Anderson and Wells, 2003; Li et al., 1997]. Currently groundwater inflow is not considered in our model and some of the excess water (relative to the amount needed for Lake Lahontan) that is needed to create the Lake Manly maximum might be attributable to such flow. A significant contribution of groundwater flow can change the location and size of predicted lakes in two ways. The first is through interbasin flow transfer. In addition, if a significant proportion of precipitation flows underground, it would have the effect of increasing apparent runoff due to the greater evapotranspiration losses of surface flows.
7. Discussion: Model Successes and Limitations
 The accuracy of the model simulations is constrained by limitations in the input data and the simplified model structure. The precipitation, temperature, runoff, and evaporation data is based upon interpolation and extrapolation of records that are sparse, particularly in the central Great Basin, desert lowlands, and high elevations. Intra and interbasin diversions of water for irrigation and water supply are widespread in the Great Basin. We have attempted to eliminate use of runoff data from strongly affected streams, such as those below reservoirs, but few gauged streams in the region are totally natural. Finally, we compare simulated lakes with the historical range of lake levels to avoid most of the problems introduced by modern water diversions, but our late 20th century climatic data may not be representative of conditions producing the early historic lake levels.
 Simulation of Pleistocene lakes involves additional limitations beyond those of modeling of modern lakes. The exact lake levels and relative timing of highstands in many of the lakes (particularly Lake Manly) are uncertain. In addition, outlets were eroded by overflows (we have compensated for this for Lake Bonneville but not the others, such as Lake Mojave, Lake Manix, etc.). Tectonic deformation and drainage captures have affected flow paths during this time. Finally, given the limited goals of the project and inevitable uncertainties regarding past climate, we have limited our climatic change scenarios to areally uniform changes in temperature, evaporation, runoff, and rainfall. Given these uncertainties, the model provides approximate reproduction of late Pleistocene lake distributions for reasonable changes in the controlling variables.
 Estimation of runoff and evaporation in the present study is also limited by the use of basin-wide regression equations for estimating mean annual temperature, lake evaporation, and runoff. Although these equations account for 86%, 77%, and 67%, respectively, of the variance of the data used for estimation, they are limited in accuracy both by the limitations of the data set and by the assumption of a single equations valid for the entire region. For modern conditions the equations generally predict reasonable values of runoff relative to precipitation. Figure 8a shows a plot of simulated runoff against precipitation under present conditions with a sample of 10,378 of 529,299 Great Basin grid cells. 8.4% of cells have predicted runoff greater than 25% of precipitation and only 0.5% have greater than 50% runoff. On the other hand, for uniform changes of MAT or annual precipitation producing the LGM Lake Lahontan, 4.9% have greater than 50% runoff, and 30.8% percent have greater than 25% runoff (Figure 8b). A similar situation occurs for simulations of LGM Lake Manly; for the region draining to this lake, 6.7% exceed 50% runoff, and 33.9% exceed 25% runoff. Our formulation for runoff (equation (4)) assures that runoff can never exceed precipitation.
 Despite these data and estimating equation limitations, the model was able to successfully route flow through channels and create lakes at their appropriate terminal locations for both present-day and late Pleistocene simulations. In case of present-day simulation, most of the major lakes in endorheic basins resulted in lake area and level close to the ranges of historical record. In general, there are more lakes predicted by our model than those actually mapped. A small lake is predicted in each enclosed basin to balance runoff and evaporation. In the modern Great Basin, most small basin host ephemeral playa lakes, which are not always mapped. Our model does not explicitly treat short-term variations in ephemeral lakes but rather represents them as very small lakes of constant size.
 The present model calculates only steady state response of lake distribution to forcing climate. Hostetler and Benson  estimate that attainment of steady state lake size during increase in relative runoff/evaporation ratio may require up to 1400 years, whereas Clement  suggests about 300 years. In any case, lakes probably did not fully respond to the often rapid climate changes occurring during the LGM, leading to potential bias in estimates of requisite hydrologic conditions forming the observed LGM lakes.
 Another reason why lakes could be over or underestimated is because of the DEM we created. We have reduced the resolution of the DEM to 1 km2 pixel using the lowest elevation and the third-order polynomial fit. These procedures reduced the number of false depressions, but in a few cases it can route channels incorrectly. In locations where the topography is relatively flat, slight differences in elevation in a small localized area can determine the course of a river. When generalizing the topography, these small differences may not be captured. Initially in our study Walker Lake was significantly underestimated. When the results were carefully examined, we noticed that the lake was not receiving any flow from the west as seen today, and the river was diverted northward, flowing into another terminal lake. The DEM was adjusted to correct this misrouting.
 Overall, our simple parameterized model was able to approximately replicate the extent and spatial distributions of Pleistocene lakes based upon areally uniform changes in mean annual precipitation and MAT. The sizes of lakes Bonneville and Lahontan were well predicted by linear combinations of decrease in MAT from −0.2 to −5.8°C and corresponding proportional changes in mean annual precipitation from 2.0 to 1.0 times modern values (Figure 4). To produce a deep Lake Manly, however, combinations of MAT decrease up to −9.3°C or precipitation increase up to 2.8 times modern values are required. Possible explanations for this latitudinal difference in estimated climate include groundwater contributions to Lake Manly that we had not included or spatially nonuniform climate and vegetation change in consequence to the positioning of the jet stream.
 The estimated changes in mean annual precipitation and MAT (or alternatively runoff and evaporation) are within previous estimates. Moreover, our model was able to replicate pluvial lakes with smaller magnitude changes than has been proposed by some previous studies. For example, to reproduce Lake Manly with a 2.5-fold increase in precipitation we require only a −1.8°C decrease in MAT rather than the −8°C estimated by Thompson et al.  for Yucca Mountain, NV from packrat middens.
 We also simulated the late Pleistocene lake distributions using an additive method where the change in precipitation is represented a uniform addition to yearly precipitation. Our additive model does a better job than the multiplicative one for the southern Great Basin in that Lake Manly can be replicated without an input from Owens River. For the same range of MAT change, Lake Lahontan can be created with precipitation addition of 0.05–0.3 m. For the additive model, it is easier to simultaneously create Lake Lahontan and a deep Lake Manly when temperature changes are small and precipitation increases are large.
 The simulations of Great Basin lakes under both modern and late Pleistocene conditions demonstrates the ability of the model to work over a broad range of balances between precipitation and runoff and to model both sparse and abundant, large lakes in complex topography. The flow routing model has potential applications beyond the present use for the Great Basin region. Howard  incorporated the flow routing algorithm in a landscape evolution model to investigate how differences in relative magnitudes of runoff and lake evaporation affected erosion and sedimentation patterns in cratered landscapes on the planet Mars featuring numerous enclosed basins. The model also could be applied to modeling hillslope runoff through incorporating flow detention and infiltration in depressions.
 This study was supported by the NASA Planetary Geology and Geophysics Program. We are indebted to comments on an earlier draft by Saxon Sharpe of the Desert Research Institute and Robert Webb and Christopher Magirl of the U.S. Geological Survey. We would also like to acknowledge all of the reviewers for their useful comments, including the suggestion of the additive precipitation model.