Published online 21 June 2006
Published in Vadose Zone J 5:850-855 (2006)
DOI: 10.2136/vzj2005.0109
© 2006 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
NOTES
Can Basin-Scale Recharge Be Estimated Reasonably with Water-Balance Models?
Abigail E. Fausta,b,
Ty P. A. Ferréb,*,
Marcel G. Schaapc and
Andrew C. Hinnellb
a USGS, 520 N. Park Ave., Suite 221, Tucson, AZ 85719
b Dep. of Hydrology and Water Resources, Univ. of Arizona, P.O. Box 210011, Tucson, AZ 85721
c George E. Brown, Jr., Salinity Lab., 450 W. Big Springs Rd., Riverside, CA 92507
* Corresponding author (ty{at}hwr.arizona.edu)
Received 9 September 2005.
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ABSTRACT
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We examine in-place recharge as an example of the complex, basin-scale hydrologic processes that are being represented with simplified numerical models. The rate and distribution of recharge depend on local meteorological conditions and hydrogeologic properties. The pattern of recharge is defined predominantly by the distribution of net precipitation (precipitation less evapotranspiration), but different pedotransfer functions (PTFs) predict different fractions of precipitation that become in-place recharge at a given location. At any single location, these differences can often be explained on the basis of the PTF characteristics, but because of the complex averaging that occurs across a basin, the combined effects of meteorological variation and soil textural variation on the basin-wide recharge rates cannot be predicted on the basis of the characteristics of different PTFs. In fact, we show that the same basin-scale numerical model, using identical inputs and modeling options, can produce almost an order of magnitude variation in predicted basin total recharge depending on the choice of PTF. This suggests that sensitivity analyses should be performed on the choice of constitutive relationship (e.g., PTF) when assessing the predictive capability of basin-scale hydrologic models.
Abbreviations: BCM, Basin Characterization Model • PET, potential evapotranspiration • P-PET, partitioning of net precipitation • PTF, pedotransfer function • STATSGO, State Soil Geographic database
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INTRODUCTION
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ACCURATE estimates of recharge rates and areal distributions of recharge within basins are useful for water resources management and aquifer protection planning. Unfortunately, there are no readily available methods to measure basin-scale recharge directly, let alone the distribution of recharge throughout a basin. Currently, basin-scale water-balance models are seen as the best available tool for estimating recharge (or potential recharge) in the absence of direct measurements (e.g., Ragab et al., 1997; Disse, 1999; Flint et al., 2000, 2002, 2004; Walker et al., 2002). These models account for net water flux and changes in water storage; they do not include complete physical descriptions of water movement. Generally, these models partition water among potential recharge, runoff, and storage on the basis of readily available meteorological and soils data. As a result, they require many correlative relationships to infer hydrologic properties. While the simplified approach of water-balance models limits their use for some hydrologic applications, the flexibility of their application over a range of temporal and spatial scales makes them well suited to basin-scale recharge estimation (Scanlon et al., 2002). However, because of the large number of correlative relationships that underlie these models and the complexity of the processes being represented, it is not clear how accurately these models describe the quantity and patterns of recharge.
Given the almost complete lack of direct measurements of recharge distribution at the basin scale, it is currently unreasonable to expect to validate recharge predictions produced by basin-scale water-balance models or even to identify optimal correlative relationships to use with these models. To further complicate efforts to validate these models, many of these models (e.g., the Basin Characterization Model, BCM; Flint et al., 2004) predict infiltration past the root zone (potential recharge) rather than actual recharge as flux across the water table. Despite this limitation, some insight into the quality of the predictions of basin-scale water-balance models can be gained by examining the dependence of the predictions of the quantity and pattern of recharge on any one of these underlying relationships.
In this study, we use the BCM to predict potential recharge rates and patterns within the Rillito Creek Basin near Tucson, AZ. Specifically, we examine the effect of the choice of PTF used to relate readily available soil textural data to soil hydraulic properties on these predictions. All of our simulations make use of identical input data and model parameters; only the choice of PTF varies among the analyses.
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MATERIALS AND METHODS
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The Rillito Creek Basin in Tucson, AZ (Fig. 1) was selected for this study because of the availability of meteorological and soils data. The study area is delineated by the drainage basin of Rillito Creek, which coincides with Hydrologic Unit 15050302 (Seaber et al., 1987). The drainage basin is bounded by the Santa Catalina Mountains to the north, the Rincon and Whetstone Mountains to the east, and the Santa Rita Mountains to the south and west. The study area has a semiarid climate that is characterized by mild winters and hot summers, and has distinct winter and summer precipitation peaks. Approximately 700 mm yr–1 of precipitation falls in the mountains, and approximately 300 mm yr–1 falls in the valley (National Oceanic and Atmospheric Administration, 2002).
We chose the Basin Characterization Model (Flint et al., 2004) to estimate the monthly average potential recharge, Rp, throughout the study area. Long-term average monthly estimates of precipitation and air temperatures were derived from existing meteorological data (National Climatic Data Center, 2000) and were spatially distributed using a gradient-plus-inverse-distance-squared method (Nalder and Wein, 1998). Following the approach of Flint et al. (2004), potential evapotranspiration (PET) was estimated by using a solar radiation model (Flint and Childs, 1987) that has been modified to calculate net radiation and to use the Priestley-Taylor evapotranspiration equation (Priestley and Taylor, 1972). The soil depth was estimated from the State Soil Geographic (STATSGO) database (USDA-NRCS, 1994) and surface geology maps (Hevesi et al., 2003). A maximum depth for calculation of Rp was set equal to the 6-m rooting depth of creosote (Flint et al., 2004). The hydraulic conductivity of the bedrock was set sufficiently high so it would not limit Rp. While this does not necessarily represent the field conditions throughout the basin, it helps to separate the effects of the soil hydraulic properties and bedrock permeability on the rates and patterns of Rp. The land surface elevation was determined using a 30-m digital elevation model. The version of the BCM available at the time of this analysis did not model runoff routing; runoff is removed from the system without the possibility of infiltrating in streams. For this reason, it is important to note that we present estimated in-place potential recharge values for comparison only. They should not be used as quantitative estimates of recharge rates in the Rillito Creek Basin.
Many different PTFs are available in the literature (see reviews by Rawls et al., 1991 and Wösten et al., 2001). We examined the 16 PTFs evaluated by Schaap et al. (2004) on the Natural Resources Conservation Service database (Soil Survey Staff, 1995). Ten of these PTFs could be used with the data available in the STATSGO database to estimate soil properties for the Rillito Creek Basin; the remaining PTFs lacked required data (e.g., organic content). For ease of comparison, we retain the PTF numbering of Schaap et al. (2004). The required input data for each of the 10 PTFs examined are listed in Table 1. The types of PTFs examined range from simple lookup tables that give hydraulic parameters according to textural class, to linear or nonlinear regression equations, and neural networks. The first three PTFs were derived from the original Rosetta model by Schaap et al. (2001). Model 1 estimates van Genuchten (1980) retention parameters on the basis of textural class averages; retention parameters thus have discrete changes across textural class boundaries for this model. Model 2 is a neural network PTF that uses the actual sand, silt, and clay percentages and provides continuously varying retention parameters. Model 3 uses the same input as Model 2 but also includes bulk density into its set of predictors. Models 6, 7, and 8 use the same input as Models 1, 2, and 3, respectively, but have their estimated parameters modified to reduce systematic errors (Schaap et al., 2004). Model 11 is a PTF by Rawls and Brakensiek (1985) that uses bulk density and sand and clay percentages to estimate Brooks–Corey (1964) retention parameters. Model 12 is the same PTF but with the Brooks–Corey parameters converted to van Genuchten parameters (Rawls and Brakensiek, 1985). Models 13 and 14 were presented by Cosby et al. (1984) and estimate parameters in the Campbell (1974) retention equation. Model 13 estimates the Campbell parameters using univariate expressions of sand or clay percentages. Model 14 expresses the Campbell parameters in bivariate expressions with sand, silt, or clay percentages. For the purposes of this study, the estimated Campbell parameters were converted to Brooks–Corey parameters.
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Table 1. Key characteristics of pedo-transfer functions used in this study. Pedotransfer functions are described in detail in Schaap et al. (2004), and their numbering system is retained.
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The BCM requires porosity, field capacity, and wilting point values. These values were determined from the STATSGO data using each of the 10 PTFs examined. Within STATSGO, each spatially defined area (map unit) is divided into as many as 21 components. The percentage of the total map unit area occupied by each component is given. Each component is divided into as many as six horizontal layers. The thickness, particle-size distribution, and bulk density of each layer are given. We determined the porosity, field capacity, and wilting point of each layer using the PTFs listed in Table 1. We then computed the depth-weighted average of these properties for each component. Subsequently, we computed the area-weighted average of the component properties for each map unit.
The retention function used to determine the porosity, field capacity, and wilting point is listed for each PTF in Table 1. The porosity was defined as the water content at full saturation. Field capacity was defined as the volumetric water content at a pressure of –10 kPa (Hillel, 1998). The wilting point was set equal to the wilting point of creosote, –6000 kPa, following Flint et al. (2004).
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RESULTS
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The Rillito Creek Basin shows concentrated in-place potential recharge in mountainous regions (Fig. 2). This is due to the locally high precipitation, low PET, and thin soils (Fig. 3). The basin floor sees very low recharge rates. Most of the potential in-place recharge occurs in the Santa Catalina Mountains, which bound the northern boundary of the study area. Potential recharge also occurs in the Santa Rita Mountains to the south and west, and in the Whetstone and Rincon Mountains to the east. Depending on the choice of PTF, the areal extent of nonzero in-place Rp ranges from 180 to 380 km2 (44 000 to 94 000 acres), which represents from 4.6 to 9.6% of the study area. Depending on the PTF used, basin-wide in-place Rp estimates range from 2.2 x 106 to 14.6 x 106 m3 yr–1 (1800–11 800 acre-ft yr–1) (Fig. 4).
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Fig. 2. Annual potential recharge estimates for (A) Pedotransfer function PTF12 and (B) PTF 8. PTF 12 results in the least amount of basin total recharge of all the PTFs used in the study, and PTF 8 results in the greatest amount of basin total recharge.
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Fig. 3. Distribution of (A) soil depth (B) average annual precipitation, and (C) average annual precipitation less potential evaporation in the Rillito Creek study area from the Basin Characterization Model. Part C is the sum of monthly values, after adjusting for negative values.
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Fig. 4. Basin total recharge estimates and the percentage of the precipitation less potential evapotranspiration (P-PET) that becomes potential recharge in the Rillito Creek study area for each pedotransfer function.
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DISCUSSION
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The similarities in the patterns of recharge demonstrate the controlling influence of local meteorological conditions on the patterns of recharge, but the widely varying predictions of basin total recharge demonstrate a strong dependence on the choice of PTF. Within the BCM, the difference between the porosity and the field capacity predicted by the PTFs controls the partitioning of net precipitation (P-PET) into potential recharge, runoff, and change in storage. There is a direct, linear dependence of the fraction of net precipitation that became potential recharge on P-PET for five map units (Fig. 5). This suggests that, at least at the local scale, the porosity and field capacity predicted by each PTF will control the recharge rate. However, owing to the averaging that occurs over the basin, this does not necessarily mean that this (or any other) single characteristic of the PTF controls the recharge prediction. For example, the basin-wide average difference between porosity and field capacity does not show good correlation with the fraction of P-PET that the PTF predicts will become in-place potential recharge (Fig. 6). To retain the dependence of the basin-wide recharge rate on the difference between porosity and field capacity would require that this property be averaged in a way that accounts for (i.e., weights by) spatial variations in net precipitation. This is exactly what the BCM does. Therefore, this suggests that, unless there is very little variation in soil type across the basin, there is no a priori way to determine the likely effect of choice of PTF on the predicted basin-wide recharge.
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Fig. 5. Positive linear relation between the normalized recharge summed for a map unit and the difference of porosity and field capacity of the same map unit.
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CONCLUSIONS
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Basin-scale recharge is a complex process that is controlled by the interaction of local meteorological conditions and hydrogeologic properties. This complexity can lead to unexpected dependence of predicted basin total recharge on seemingly minor choices underlying modeling efforts. For the conditions studied here, there is little dependence of the predicted pattern of recharge on choice of PTF because this spatial pattern is largely controlled by the local meteorological conditions. However, we show that a single model, using identical inputs and modeling options, can produce almost an order of magnitude variation in predicted basin total recharge depending on the choice of PTF used to convert soil physical properties to soil hydraulic properties. Furthermore, because of the complex averaging that occurs, the combined effects of meteorological variation and soil textural variation cannot be predicted on the basis of simple characteristics of the PTFs. This is true even if there is a clear relationship between the PTF property and the fraction of net precipitation that becomes recharge at the local scale. Rather, the most efficient way to determine the uncertainty that is added to predictions on the basis of the choice of correlative relationships selected (or other model options) is to conduct separate modeling analyses using a range of values for each uncertain correlative relationship. This would clearly complicate the application of basin-scale models, but it is necessary to provide a measure of the confidence that should be placed in the model predictions.
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ACKNOWLEDGMENTS
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The authors thank Dr. Alan Flint and Joan Blainey, both of the U.S. Geological Survey, for providing assistance with the Basin Characterization Model and climate modeling. The Ground-Water Resources Program of the U.S. Geological Survey and SAHRA, a National Science Foundation Research Center, provided funding for this study. M.G. Schaap was also supported, in part, by grant NSF-EAR0440024.
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ABSTRACT
INTRODUCTION
s), field capacity (