Estimating Water Use in the United States A New Paradigm for the National Water-Use Information Program (2002) / Chapter Skim
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6. Regression Models of Water Use
6. Regression Models of Water Use
Pages 100-114
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From page 100... ...
National estimates focus primarily on measuring total water withdrawals, which include the annual extractions of both fresh water (with separate estimates for surface water and groundwater withdrawals) and saline water.
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From page 101... ...
These eight categories are nonoverlapping and sum up to total withdrawals. However, public supply withdrawals include water delivered by public water supply systems to some commercial, industrial, and thermoelectric uses, and detailed sectoral-use tables in Solley et al.
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From page 102... ...
For example, public supply withdrawals can be estimated using the following linear model: (6.3) where PSit represents public supply withdrawals within geographical area i during year t, Xj is a set of j explanatory variables (e.g., air temperature, precipitation, price of water, median household income, and others)
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From page 103... ...
The next section explores the structure of water demand in public supply sector water use and presents several statistical models that were fitted to the historical estimates of public supply withdrawals in the lower 48 states. STATE-LEVEL MODELS OF PUBLIC SUPPLY WITHDRAWALS Public supply water is water withdrawn by public or private water suppliers and delivered to users.
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From page 104... ...
Population served by public water supply systems was used to express the dependent variable as average public supply withdrawal per capita per day for each state and data year. If the per capita rate of withdrawal in each state can be predicted with sufficient accuracy, then total public supply withdrawals can be estimated by multiplying the per capita withdrawal by population served.
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From page 105... ...
The size and signs of the estimated regression coefficients fall within the ranges of expected values. These coefficients can be interpreted to mean that across the United States, from 1980 to 1995, the mean withdrawal was 183.7 TABLE 6.1 Linear Regression Model for State-Level Per-Capita Public Supply Withdrawals, 1980-1995 Dependent/Explanatory Variable Regression Coefficient l-Ratio F-value Probability Intercept (gpcd)
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From page 106... ...
Because a significant portion of public supply withdrawals is used to supply industrial and commercial uses, the gross state product variable captures the effects of the relative volume of nonresidential uses together with the effect of the ability to pay for water, which is typically captured by per capita or median household income variables in models of residential use. The binary indicator variable, which assumes the value of 1 for states with prior appropriation groundwater rights (generally western states)
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From page 107... ...
This can be done by substituting the corresponding values of price, per capita gross state product, total summer precipitation, and average temperature and adding four "intercept adjustors" one for state groundwater law system, one for state surface water law system, one indicator of an individual state (if present in the model) , and one state-specific trend (if present)
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From page 108... ...
-4.726 1.624 -2.91 0.0044 Gross state product per capita ($1,000) 2.430 0.352 6.91 <0.0001 Total precipitation during summer, inches -1.299 0.365 -3.55 0.0006 Average temperature during summer (deg.
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From page 109... ...
, generated by multiplying the estimated per capita value by population served. If the model predictions for individual states were to be used to prepare an estimate of the total national public supply withdrawals for 1995, then due to the compensating positive and negative
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From page 110... ...
Alabama 237.1 171.4 -27.7 Nebraska 221.4 272.9 23.3 Arizona 206.1 231.5 12.3 Nevada 324.8 339.8 4.6 Arkansas 190.8 171.3 -10.2 New Hampshire 140.0 154.5 10.4 California 184.5 246.4 33.5 New Jersey 149.5 168.8 12.9 Colorado 207.7 238.5 14.8 New Mexico 225.4 239.7 6.3 Connecticut 155.2 164.0 5.7 New York 185.1 188.6 1.9 Delaware 158.6 169.9 7.1 North Carolina 162.1 170.1 4.9 Florida 169.1 172.0 1.7 North Dakota 148.9 176.9 18.7 Georgia 195.5 177.2 -9.3 Ohio 153.1 174.8 14.2 Idaho 242.9 256.7 5.7 Oklahoma 193.8 210.5 8.6 Illinois 175.3 217.7 24.2 Oregon 234.8 213.0 -9.3 Indiana 156.1 169.2 8.4 Pennsylvania 170.8 204.0 19.5 Iowa 173.2 171.1 -1.2 Rhode Island 130.2 147.1 13.0 Kansas 159.1 157.8 -0.8 South Carolina 199.6 158.8 -20.4 Kentucky 147.8 163.5 10.6 South Dakota 146.7 158.6 8.1 Louisiana 165.8 175.8 6.0 Tennessee 175.9 166.4 -5.4 Maine 141.7 160.5 13.3 Texas 187.7 169.0 -9.9 Maryland 200.0 244.7 22.3 Utah 268.9 304.2 13.1 Massachusetts 130.0 160.5 23.5 Vermont 148.3 164.2 10.7 Michigan 188.4 183.8 -2.4 Virginia 158.5 155.0 -2.2 Minnesota 145.2 178.0 22.6 Washington 266.3 216.0 -18.9 Mississippi 151.8 158.1 4.1 West Virginia 133.7 149.2 11.6 Missouri 161.5 167.9 4.0 Wisconsin 168.6 195.4 15.9 Montana 222.1 253.6 14.2 Wyoming 260.6 250.7 -3.8 prediction errors among individual states, the prediction error in the national total would be +2.2 percent. STATE-LEVEL MODELS FOR THERMOELECTRIC WITHDRAWALS State-level data for public water supply withdrawals are more accurate than data for thermoelectric cooling withdrawals.
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From page 111... ...
>Ill Intercept 49.376 15.53 <0.0001 Percent generation capacity with cooling towers -0.362 -8.02 <0.0001 Percent utilization of existing capacity -0.423 -4.99 <0.0001 Percent generation from coal -0.096 -3.43 0.0009 Average size of generating units 0.174 6.34 <0.0001 Total heating degree-days 0.002 4.11 <0.0001 States w/ prior appropr. surface water law 3.962 -2.9 0.0047 NOTES: N = 91, R2 = 0.80; root MSE = 6.3 gal./kWh; mean APE = 17.6%.
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From page 112... ...
Although the regression model in Table 6.4 explains 80 percent of the variance in per kilowatt-hour thermoelectric water withdrawals, the mean absolute percentage error for in-sample predictions remains relatively high at 17.6 percent. As in the public supply sector, improved predictions of the thermoelectric withdrawals model could be obtained by introducing binary state indicator variables.
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From page 113... ...
· The predictive properties of the models can be improved through appropriately specified models and through the inclusion of both the standard explanatory variables and the indicator variables for individual states or counties to capture their "unique" water use characteristics as well as state-specific trends in usage rates over time. · The coefficients derived from regression models for adjustment of water use according to weather variations may be helpful in adjusting state-level water use estimates developed through statistical sampling or other means for departures from normal weather conditions in the year the estimates were made.
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From page 114... ...
Still, many challenges relating to data quality, inconsistent variable definitions, and statistical methodology need to be addressed, and they represent a fertile area for applied research as part of the NWUIP. As part of its research on estimation methods, the USGS should undertake a systematic investigation of water use models as it has done for estimation of river loads, urban nonpoint pollution discharges, and other hydrologic quantities.
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