Analyses of selected statistical methods for estimating groundwater withdrawal

Abstract

A procedure for estimating groundwater withdrawal ideally should (1) maintain an acceptable level of accuracy and (2) significantly reduce data collection. Two procedures that were investigated, random sampling and regression analysis, meet these objectives. Random sampling theory allows the calculation of sample size for any combination of accuracy limit and probability level, once the population type and parameters have been determined. Groundwater withdrawals in the Arkansas River valley in southeastern Colorado exhibit an approximately log normal distribution with a standard deviation of 1.25. Gross annual withdrawal can be estimated within 15% at the 0.90 probability level from a sample of 225 wells (about one‐fourth the number presently monitored). Random samples of actual data show errors that agree closely with errors predicted by sampling theory. Annual withdrawal can be related to certain independent variables using regression techniques. The independent variables used in this study were (1) annual precipitation, (2) total annual canal diversion, (3) annual electrical energy used by pumps, and (4) change in groundwater storage during the irrigation season. The standard errors of estimate of the four regressions, which used four or five data points each, ranged from 8900 ac ft/yr for the relation between annual withdrawal and change in groundwater storage during the irrigation season to 17,700 ac ft/yr for the relation between annual withdrawal and precipitation. The mean annual groundwater withdrawal was 122,000 acre‐feet.