Water Balance Backward: Estimation of Annual Watershed Precipitation and Its Long-Term Trend with the Help of the Calibration-Free Generalized Complementary Relationship of Evaporation

Abstract

Watershed-scale annual evapotranspiration (ET) is routinely estimated by a simplified water balance as the difference in catchment precipitation (P) and stream discharge (Q). With recent developments in ET estimation by the calibration-free generalized complementary relationship, the water balance equation is employed to estimate watershed/basin P at an annual scale as ET + Q on the United States (US) Geological Survey’s Hydrologic Unit Code (HUC) 2- and 6-level watersheds over the 1979–2015 period. On the HUC2 level, mean annual PRISM P was estimated with a correlation coefficient (R) of 0.99, relative bias (RB) of zero, root-mean-squared-error (RMSE) of 54 mm yr−1, ratio of standard deviations (RS) of 1.08, and Nash–Sutcliffe efficiency (NSE) of 0.98. On the HUC6 level, R, RS, and NSE hardly changed, RB remained zero, while RMSE increased to 90 mm yr−1. Even the long-term linear trend values were found to be fairly consistent between observed and estimated values with R = 0.97 (0.81), RMSE = 0.63 (1.63) mm yr−1, RS = 0.99 (1.05), NSE = 0.92 (0.59) on the HUC2 and HUC6 (in parentheses) levels. This calibration-free water-balance method demonstrates that annual watershed precipitation can be estimated with an acceptable accuracy from standard atmospheric/radiation and stream discharge data.

Keywords

• complementary relationship
• water balance
• precipitation estimation