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

Abstract

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. The well-established hydrological model HYDRUS was used to validate HyPix without the sink term. The HyPix results show good agreement to HYDRUS, validating the algorithms implemented in HyPix. Even for challenging conditions, HyPix can provide accurate and reliable results using the recommended standard options. Moreover, the algorithm developed in HyPix is more efficient than the one used in HYDRUS, particularly for coarse texture soils. The recommended options were also tested by running HyPix with sink term using field data.