R-Grunsky: an empirical method for globally predicting streamflow using precipitation and temperature data

In the early 1900s, engineer Carl E. Grunsky developed an empirical equation relating mean annual precipitation to mean annual runoff in the San Francisco Peninsula, California, United States of America (USA). Over a century later, this method, now referred to as the R-Grunsky, was reintroduced and generalized by incorporating a rainfall-streamflow coefficient (α) derived from mean annual temperature and precipitation. Previous studies have demonstrated its effectiveness in Mediterranean and Brazilian catchments. Here, we aim to expand the applicability of the R-Grunsky method by analyzing data from 14,894 catchments from the Caravan dataset, spanning Australia, Brazil, Chile, Great Britain, Europe, and the USA. We first developed a global relationship between α and the catchments' mean temperature and precipitation, subsequently fitting a multiple linear regression model to estimate α values for streamflow prediction using a simplified equation system. The R-Grunsky approach showed suitable results in mean annual streamflow estimation, with a Kling-Gupta Efficiency (KGE) of 0.47 and R² = 0.66 considering all studied catchments. The results align with those from previous studies of the method developed to Brazilian catchments. However, we noted that arid regions, primarily in Australia, central USA, northeastern Brazil, and northern Chile, exhibited lower KGE values, indicating reduced performance compared to wetter catchments, which requires further investigation. The R-Grunsky approach offers the advantage of requiring only precipitation and mean temperature data for streamflow predictions, making it particularly valuable for ungauged catchments. Consequently, it holds significant potential for diverse water resource projects and decision-making processes related to water security and management.