Abstract. Hydrological processes are irreversible and produce entropy. Hence, the framework of non-equilibrium thermodynamics is used here to describe them mathematically. This means flows of water are written as functions of gradients in the gravitational and chemical potential of water between two parts of the hydrological system. Such a framework facilitates a consistent thermodynamic representation of the hydrological processes in the model. Furthermore, it allows for the calculation of the entropy production associated with a flow of water, which is proportional to the product of gradient and flow. Thus, an entropy budget of the hydrological cycle at the land surface is quantified, illustrating the contribution of different processes to the overall entropy production. Moreover, the proposed Principle of Maximum Entropy Production (MEP) can be applied to the model. This means, unknown parameters can be determined by setting them to values which lead to a maximisation of the entropy production in the model. The model used in this study is parametrised according to MEP and evaluated by means of several observational datasets describing terrestrial fluxes of water and carbon. The model reproduces the data with good accuracy which is a promising result with regard to the application of MEP to hydrological processes at the land surface.