Statistical Behavior of Monthly Load Estimators

Abstract

<abstract><title><italic>Abstract.</italic></title> Agricultural activities are important contributors to the pollution of water bodies. In this context, the establishment of relationships between changes in irrigation and agricultural practices and pollutant loads over long periods may help to diagnose the agriculture-related factors with higher influence on water quality. To this end, the first step is to generate robust, long-term pollutant load series with the available data. This article aims to ascertain the statistical performance of five mean monthly salt (MS) and nitrate (MN) load estimators based on the long-term records of the Surface Water Quality Control (SWQ) network of the Ebro Basin Authority (CHE) in Spain. The five loads estimates were compared with reference loads calculated with the more complete, daily frequency data of the irrigation return flows network (Recor-Ebro, or R-E) available at a sampling point on the Arba River at Tauste for the period April 2004 to September 2010. Three interpolation methods that make use of total dissolved solids (TDS_swq) and nitrate concentrations (NO_3swq) of samples taken once a month in the SWQ network were multiplied by flows at the sampling time (Q_swq), mean daily flow of the sampling day (Q_d), and mean monthly flow (Q_m). Two regression-based methods established the relationships between flow and TDS and between TDS and NO₃ concentration to estimate daily and monthly TDS and NO₃ concentrations, which were then multiplied by mean daily flow (Q_d) or mean monthly flow (Q_m), respectively, to estimate loads. Six statistical indexes were used to determine the fit of the five proposed methods to the reference load: the coefficient of determination (R²), mean bias (MB), root mean square error (RMSE), mean absolute error (MAE), Nash-Sutcliffe efficiency (NSE), and Nash-Sutcliffe efficiency modified (E1). Mean bias was not significant for the five MS and MN estimators (<7.5%), but the other statistical indexes showed different behavior for the MS and MN estimators. The RMSE and MAE were in general higher for the MS interpolation methods (RMSE ≈ 6,000 to 11,000 Mg per month; MAE ≈ 4,000 to 7,000 Mg per month) than for the regression-based methods (RMSE ≈ 5,000 Mg per month; MAE ≈ 4,000 Mg per month). The errors for the MN estimators were similar for the regression and interpolation methods when using the mean monthly flow or mean daily flow of the sample day (RMSE ≈ 30 Mg per month; MAE ≈ 20 Mg per month). The NSE and E1 for the three interpolation methods for MS were not satisfactory (NSE < 0.5; E1 < 0.3), while the interpolation methods for MN using daily or monthly average flow presented satisfactory NSE and E1 values (NSE > 0.5; E1 > 0.3), performing just as well as the regression methods. For the short period analyzed (six years), regression-based estimators presented the best reliability for the estimation of monthly salt and nitrate loads, along with interpolation methods that applied the mean daily flow (Q_d) or mean monthly flow (Q_m) for the estimation of monthly nitrate loads, provided that the data series were complete.