Comparison of Langmuir and Freundlich adsorption equations within the SWAT-K model for assessing potassium environmental losses at basin scale

Potassium (K) is an important nutrient for agricultural crop growth. Adsorption of K in soil involves fertilizer optima for enhancing crop productivity and efficient nutrient management. Adsorption is often necessary to predict K transport and losses, such as solid/liquid distribution in soil, plant uptake, and transportation with water and suspended sediments. Based on the Soil and Water Assessment Tool (SWAT), the SWAT-K model has been developed to quantify daily K losses and budget at watershed scale. In this study, Langmuir and Freundlich adsorption equations were both applied and compared in the SWAT-K model to predict K adsorption in the soil and K losses in the volcanic Shibetsu River Watershed (672 km2, Hokkaido, Japan). Both the Langmuir and Freundlich adsorption equations well fitted the solid/liquid distribution of K in soil. The Freundlich and Langmuir equations showed similar performances to fit the measured data of K sorbed to soil (R2 = 0.91 for both cases) and Freundlich equation showed slightly better performances of dissolved K load in stream than Langmuir equation (Nash-Sutcliffe efficiency coefficient (ENS) = 0.66 and 0.60, respectively). Overall, Langmuir and Freundlich equations predicted similar K budgets, including soil K surplus with a difference of 1.2%. The uncertainty related to the choice of the adsorption equation is negligible. Hence, both Langmuir and Freundlich adsorption equations are recommended to predict the K adsorption in soil and in-stream K load when using the SWAT-K model in watershed similar to the study case. Their applicability deserve to be tested in other agricultural watersheds characterized by different soils.