HyPix: 1D physically based hydrological model with novel adaptive time-stepping management and smoothing dynamic criterion for controlling Newton–Raphson step

The newly developed open-source Hydrological Pixel model, HyPix, written in the fast and flexible Julia language, efficiently solves the mixed form of the Richardson–Richards’ equation (RRE). HyPix uses a cell-centred, finite-volume scheme for the spatial discretization, with an implicit Euler scheme for the temporal discretization, by using the weighted average inter-cell hydraulic conductivity. HyPix includes the following modules: (a) rainfall interception, (b) root water uptake with compensation algorithm and root growth, (c) soil evaporation, (d) ponding using a novel method for computing sorptivity, and (e) runoff. HyPix includes a wide range of top and boundary conditions (flux, pressure, free drainage). To control the Newton–Raphson iterations, HyPix incorporates a novel dynamic physical smoothing criterion, which improves not only the model performance but also its accuracy compared with using the traditional absolute convergence criterion. To control the time-step, the traditional physical time-step management based on changes in the soil water content was specifically designed to solve RRE based on soil water content. This work adapts the time-step management such that it is specifically designed to solve RRE based on soil water pressure without introducing further parameters. The novel time-step management also requires only one parameter and was found to be more efficient than the traditional time-step management. HyPix implements an option to solve the derivatives numerically, enabling the RRE to be modified and tested (e.g., the inter-cell hydraulic conductivity) by changing only a few lines of code. Numerically calculating derivatives was found to be as accurate as deriving the derivatives analytically, and only 10–25% slower.