Streamflow prediction in ungauged catchments by using the Grunsky method

Establish a reliable rainfall-runoff relation capable of predicting runoff in ungauged basins is a matter of interest across the world for a long time and has been taking importance during the past decades. Regionalization approaches, hydrological models and machine learning techniques have been used to estimate runoff. However, returning some simplicity to the predictions might be necessary for practical uses. In this paper, we re-introduce C. E. Grunsky approach, developed in the early 1900s to predict runoff from values of precipitation on a two-equations system. Here, we analyze the Grunsky generalized method applied for 716 Brazilian catchments, on an interannual and monthly scales. First, we established the best method to find the rainfall-runoff relation coefficient for each catchment. Then, we evaluate the performance of the method on a local scale, i.e., catchment by catchment. Lastly, we analyze the method of regionalization, by grouping the catchments into six hydrologically similar classes. For local scale, the Kling-Gupta Efficiency (KGE) values range from 0.87 to 0.93 on the interannual scale and is greater than 0.50 on the monthly scale. For the regionalized approach, KGE varies from 0.60 to 0.84 on an interannual scale. We also found suitable KGE values on a monthly scale, with more than 22% of catchments with KGE greater than 0.50, being the best performances in the Non-seasonal and Extremely-wet groups, and the worst performance in the Dry group. Our findings indicate that Grunsky approach is suitable to predict streamflow for Brazilian catchments on interannual and monthly scales. This simple and easy-to-use equation presents a reliable alternative to more complex methods to compute runoff by only using rainfall data.