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Article

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

1
Department of Water Resources and Hydraulic Engineering, Budapest University of Technology and Economics, 1111 Budapest, Hungary
2
Conservation and Survey Division, School of Natural Resources, University of Nebraska—Lincoln, Lincoln, NE 68588, USA
Water 2020, 12(6), 1775; https://doi.org/10.3390/w12061775
Received: 15 May 2020 / Revised: 1 June 2020 / Accepted: 18 June 2020 / Published: 22 June 2020
(This article belongs to the Special Issue Hydrological Modeling in Water Cycle Processes)
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. View Full-Text
Keywords: complementary relationship; water balance; precipitation estimation complementary relationship; water balance; precipitation estimation
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MDPI and ACS Style

Szilagyi, J. 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. Water 2020, 12, 1775. https://doi.org/10.3390/w12061775

AMA Style

Szilagyi J. 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. Water. 2020; 12(6):1775. https://doi.org/10.3390/w12061775

Chicago/Turabian Style

Szilagyi, Jozsef. 2020. "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" Water 12, no. 6: 1775. https://doi.org/10.3390/w12061775

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