Scientific Investigations Report 2007–5038
U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2007–5038
As a first step, data from the six active NWS stations in and near the study area (Bayview Model Basin, Coeur D’Alene 1E, Newport, Sandpoint Experiment Station, Priest River Experiment Station, and Spokane WSO Airport) were used to calculate mean monthly recharge using equations and methods described above: the Langbein, USDA, ESPAM, and single-coefficient FAO Penman-Monteith methods. Annual and monthly mean temperature and precipitation values used for the recharge calculations are for each station’s period of record through December 2005 (Western Regional Climate Center, 2006a, 2006b).
Apparent limitations of the mean monthly recharge calculations led to a second step in which daily recharge values for the six weather stations were calculated by using equations for the (dual-coefficient) FAO Penman-Monteith dual-crop evapotranspiration (ETcd) and deep percolation. Daily observations for temperature and precipitation for the period 1990-2005 were used for each station; however, wind speed for Spokane WSO Airport was applied to all stations (U.S. Department of Commerce, 2006).
Annual recharge values for each weather station and recharge method are shown in figure 2. These annual values were calculated by summing calculated mean monthly recharge values, except for the Langbein method, for which annual means were used in the calculations.
Annual recharge values calculated by the Langbein method are shown in table 4 and figure 2. Mean annual precipitation data were obtained from published annual means (Western Regional Climate Center, 2006a, 2006b) and mean annual potential evapotranspiration values for Bayview Model Basin, Coeur D’Alene 1E, and Sandpoint Experiment Station were taken from Allen and Brockaway (1983). For the remaining three stations—Priest River Experiment Station, Newport, and Spokane WSO Airport—Allen and Brockaway’s (1983) mean annual potential evapotranspiration value for Coeur D’Alene 1E was used.
The Langbein-method annual recharge for all six weather stations ranged from less than 1 percent to 11 percent of mean annual precipitation, yielding the lowest annual recharge values of the methods discussed in this report. The primary shortcoming of the Langbein method is that it can be applied only to annual time periods. For application to shorter periods, the annual values must be apportioned by some scheme, leading to further uncertainty. Furthermore, the previously stated assumption that basin yield is equal to basin recharge may not be valid: because the method was originally developed to determine runoff (as streamflow) from a basin, it does not account for subsurface underflow. Thus calculated recharge may be lower than actual recharge. In addition, basin yield does not equal recharge where there is significant surface-water runoff from lands within the study area. Finally, because independent mean annual potential evapotranspiration values were unavailable for three stations, the use of the Coeur D’Alene 1E estimate adds to the uncertainty.
The USDA-method mean monthly recharge was calculated using mean monthly crop growth stage coefficients (kc) for alfalfa from curve number 2 in U.S. Department of Agriculture (1970). Values for potential consumptive use (u) were calculated using equation 9; however, the minimum daily value was assumed to be 1 mm/d based on the maximum measured winter evapotranspiration at Kimberly, Idaho (Wright, 1993). Because this paper is concerned with recharge from precipitation, the net depth of applied irrigation water (D) was assumed to be 0.
Calculated mean monthly recharge ranged from 53 to 73 percent of mean monthly precipitation. Annual recharge ranged from 64 to 69 percent of mean annual precipitation (table 5). The method by which potential consumptive use (u) is selected—either potential evapotranspiration or from equation 9—affects calculated recharge, with equation 9 yielding a lower value of u, thus a higher recharge value. Furthermore, the USDA effective rainfall equation (equation 8) was derived empirically through the “analysis of 50 years of precipitation records” at 22 weather stations representing all climatic conditions in the conterminous United States (U.S. Department of Agriculture, 1970). Thus, it is difficult to evaluate how applicable the method is to the SVRP aquifer study area.
Mean monthly recharge calculations for the ESPAM method were made using thin-soil, thick-soil, and lava-rock parameters: transition precipitation (PT) was calculated as 2.07, 3.68, and 2.57 ft/mo, respectively. The lava-rock parameters yielded the highest recharge values; the thick-soil parameters the lowest (tables 6-8).
For thin-soil parameters, calculated monthly recharge ranged from 10 to 29 percent of monthly mean precipitation, and annual recharge ranged from 16 to 23 percent of mean annual precipitation (table 6). For thick-soil parameters, calculated monthly recharge ranged from 1 to 5 percent of monthly mean precipitation, and annual recharge ranged from 2 to 4 percent of mean annual precipitation (table 7). For lava-rock parameters, calculated monthly recharge ranged from 37 to 57 percent of monthly mean precipitation, and annual recharge ranged from 45 to 52 percent of mean annual precipitation (table 8).
For a given precipitation (P), paired slope parameter (K), and coefficient for curvature (N), recharge calculated by the ESPAM method will be equivalent to that calculated for the ESRP. It is difficult to evaluate the validity of this assumption: although the lowest values of mean annual precipitation on the ESRP are approximately one-half of those in the SVRP aquifer area, mean annual maximum temperatures at higher elevation stations on the ESRP are similar to those in the area of the SVRP aquifer. The range of March-October potential evapotranspiration values for the ESRP range from 46.5 to 57.4 in.; for the Bayview Model Basin, Sandpoint Experiment Station, and Coeur D’Alene 1E weather stations, the values are 39.1, 40.3, and 42.8 in., respectively (Allen and Brockaway, 1983).
The meteorological data needed for calculation of recharge using the single- or dual-coefficient FAO Penman-Monteith methods are available for only one station in the area—Spokane WSO Airport. Initially, to determine mean monthly recharge with the single-coefficient FAO Penman-Monteith method, the 15th day of each month was used to calculate the relevant radiation parameters for reference evapotranspiration (ETo) (except percentage of possible sunshine, for which the monthly mean was used). This value was then used with mean monthly meteorological data to obtain mean monthly recharge. Crop evapotranspiration (ETc), was calculated for grass pasture: development stages for grass pasture (Lini, Ldev, and Llate) and time-averaged crop coefficients for rotated grazing pasture (Kc ini, Kc dev, Kc late, and maximum crop height) were taken from tables 11 and 12, respectively, in Allen and others (1998). The grass-referenced ETc was converted to alfalfa-referenced ETc using the Kimberly, Idaho, conversion factor of 1.24 (Allen and others, 1998). Mean monthly recharge was then calculated by subtracting the mean monthly ETc from mean monthly precipitation. Mean monthly recharge values for both grass- and alfalfa-referenced calculations are shown in table 9.
For grass-referenced calculations, calculated mean monthly recharge ranged from 0 to 81 percent of mean monthly precipitation, and mean annual recharge was 21 percent of mean annual precipitation; for alfalfa- referenced calculations, calculated mean monthly recharge ranged from 0 to 85 percent of mean monthly precipitation, and mean annual recharge was 24 percent of mean annual precipitation (table 9). The most striking feature of these results from the single-coefficient FAO Penman-Monteith equations with mean monthly values is that calculated mean monthly recharge drops to zero during the eight warmest and driest months of the year (March-October). Such a result seems unlikely based on ground-water levels.
The relations of mean monthly precipitation at each weather station to mean monthly recharge values calculated by the USDA and ESPAM methods are shown in figure 3. For all stations, the lava-rock parameters yield the highest values of recharge and the thick-soil parameters the lowest among the ESPAM techniques. USDA recharge values are greater than any ESPAM values for all months. For the Spokane WSO Airport station, the single-coefficient FAO Penman-Monteith mean monthly recharge values are highest in the winter and lowest during the growing season.
As mentioned in the previous section, independent evidence does not support the calculated result of no recharge during the eight warmest and driest months of the year (March-September) and suggests that the single-coefficient FAO Penman-Monteith recharge using mean monthly data does not adequately represent changes in soil-moisture storage. A similar conclusion was reached by Kafri and Ben Asher (1978) in a southern Arizona study, in which they noted, “The conventional approach of calculating recharge by subtracting long-term averages of runoff and evapotranspiration from the total rainfall results in no apparent recharge. This result does not agree with observations of ground-water flows in the corresponding basins.”
Such anomalous results from calculations with monthly means may result from the assumption that there is always sufficient soil moisture to satisfy evapotranspiration. However, daily soil-moisture will occasionally be insufficient to meet crop evapotranspiration (ETc) demand, resulting in actual evapotranspiration being less than the calculated ETc value. Thus, recharge depends on the amount and timing of individual precipitation events to replenish soil moisture and exceed ETc, allowing deep percolation (assumed to be recharge) through the root zone.
In order to calculate a more realistic value of recharge, the dual-coefficient FAO Penman-Monteith dual-crop evapotranspiration (ETcd) and deep percolation calculations in equations 18 and 19 were applied to daily values from the Spokane WSO Airport for January 1990 through December 2005. Recorded “trace” values of precipitation were assigned a value of 0.01 in. for daily calculations (although actual trace amounts were between 0.00 and 0.01 in.). As above, crop evapotranspiration (ETc) was calculated for grass pasture: development stages and time-averaged crop coefficients were taken from tables 11 and 12, respectively, in Allen and others (1998). The key soil characteristics used were a maximum root depth of 0.8 m and an available water capacity (AWC) of 30 mm/m. The resultant monthly totals in table 10 show a temporal variability that is absent from the mean monthly values in table 9, and demonstrate that the daily amount and timing of precipitation dramatically affect calculated recharge. Daily values of precipitation and dual-coefficient FAO Penman-Monteith recharge for the Spokane station are shown in figure 4.
For a given month, there is little consistency between the amount of precipitation and recharge from year to year. The examination of daily values for such “anomalous” months as March 1993, when precipitation was near normal yet no recharge occurred, show a soil-moisture deficit early in the month that needed replenishment by daily precipitation later in the month before deep percolation could occur. Furthermore, significant precipitation on a given day can paradoxically result in calculated value of deep percolation for the following day being greater than precipitation as a result of soil-moisture storage.
Because the daily dual-coefficient FAO Penman-Monteith recharge better represents natural processes than do the mean monthly techniques discussed previously, daily calculations were made for the five remaining weather stations. Unfortunately, the required meteorological data for these stations is limited to maximum and minimum daily temperature and precipitation. To calculate recharge for these stations, two main assumptions were made: (1) wind-speed values for Spokane WSO Airport were used for all weather stations, and (2) dewpoint temperatures were assumed to equal the daily minimum temperature. As with Spokane WSO Airport, trace amounts of precipitation were assigned a value of 0.01 in. Missing precipitation values of six or fewer days were assumed to equal zero. Missing temperature values of six or fewer consecutive days were interpolated. For longer periods of missing data, values for a station were assumed to equal those at a station with similar mean values: (1) data from the Priest River Experiment Station were used for Newport from December 1995 through January 1996, and (2) data from Newport were used for Bayview Model Basin for February 1992, March-April 2004, and July 2005. Because the Coeur d’Alene 1E station was missing a substantial amount of data (January 1990 through October 1995, March 1996, March 1998, February 2004, April 2004, June 2005, and November 2005) deep percolation for these periods was not calculated. Monthly summaries for these five weather stations, 1990-2005, are shown in tables 11-15. Daily values of precipitation and dual-coefficient FAO Penman-Monteith recharge, 1990-2005, are shown in figures 5-9. The occasional days with large amounts of precipitation (and correspondingly high recharge) are very noticeable on these graphs. In areas with a thin unsaturated zone such events may be reflected in ground-water levels, however, for much of the area, processes in a thick unsaturated zone probably dampen these events into a fairly constant recharge rate.
The “Previous Work” section of this paper discusses earlier estimates of areal recharge and figure 10 shows a comparison between these monthly recharge rates and monthly recharge rates calculated in this study. The ranges of 1995-2005 monthly values of dual-coefficient FAO Penman-Monteith recharge are similar to those of the transient model of Bolke and Vaccaro (1988), though the ranges are larger than that of Buchanan (2000). If one considers the location and extent of these previous models and compares the Bolke and Vaccaro (1988) and the Golder Associates, Inc. (2004) recharge values to calculated recharge for Spokane WSO Airport, there is good agreement between the estimates. Similarly, if the recharge estimates from the three stations in the study area are compared to Buchanan’s (2000) estimates, they fall within his range.
Although beyond the scope of this report, these recharge estimates for individual points need to be applied to the study area as a whole. A number of techniques may be appropriate for this task.
Areal recharge commonly is the most uncertain component of water budgets and ground-water flow models and is therefore usually calculated as the residual of other components. Without a priori knowledge of probable values, choosing between values of areal recharge calculated by different methods is difficult. Thus, the larger context provided by water budgets and ground-water flow model calibration is crucial in determining reasonable values.
U.S.
Department of the Interior | U.S. Geological
Survey
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