We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating). The migrating cells perform nonlinear diffusion and two types of taxis in response to non-diffusing cues: away from proliferating cells and up the gradient of surrounding tissue. Transitions between the two cell subpopulations are influenced by subcellular (receptor binding) dynamics, thus conferring the setting a multiscale character.We prove global existence of weak solutions to a simplified model version and perform numerical simulations for the full setting under several phenotype switching and motility scenarios. We also compare (via simulations) this model with the corresponding haptotaxis-chemotaxis one featuring indirect chemorepellent production and provide a discussion about possible model extensions and mathematical challenges.

The Shivalik foothills of northwestern India are very prone to soil erosion by water due to undulating slopes, highly erodible soils and high intensity rainstorm events during monsoon season. Physically based soil erosion modeling is seen as viable method for planning of measurements to reduce damages done by soil erosion. Nevertheless, parametrization of such models is a major challenge for large inaccessible areas. Several methods do exist for the estimation of the input parameters skin factor, surface roughness and resistance to erosion for the physically based soil erosion model EROSION-3D. Four rainfall experiments, each including dry and wet run, were conducted on different land use conditions on a research farm of the Regional Research Station Ballowal Saunkhri to test estimation methods. Modeling parameters were determined from these experiments. Parameter estimation by two methods for experimental conditions produced values in close range to experimentally determined values for resistance to erosion and surface roughness. Therefore, existing estimation methods are considered to be applicable for the conditions of the Shivalik mountains, except for skin factor. A first modeling with EROSION-3D using preliminary data of a small example catchment shows uncertainties resulting from range of determined and estimated soil parameters.

<p>Measurement of runoff events induced by natural rainfall or rainfall simulators of various construction and dimensions is a common method for obtaining data needed for run-off and soil erosion models calibration. As every simulator is different so are the methods for data collection, recording, processing and utilization. Mining the data from different sources for comparison or a common purpose can be quite exhausting as all the teams and workers use different software, workflows and structures for storing the data. The database presented is an attempt to provide a robust structure for storing experimental data together with its metadata, relationships between data sets and other information about the data collection and preprocessing. The desired state is where any record is back-trackable to the original source field record regardless if it was written by hand on paper or registred by digital logger.</p><p>The relational database is built in MySQL and provides a comprehensive structure for storing and retrieving the data and metadata. The access to the database is differentiated into multiple levels with different rights. A public web user interface allows low-level access to the data that can be viewed as tables and charts. Private web interface provides logged-in users the rights to add, delete and alter data. The web interface incorporates basic search, order and filter capabilities on the data. High level access by direct querying the DB is available for trusted users who are familiar with MySQL language and so are capable of creating their own complex queries. The direct access to the database is possible via any programing language with appropriate libraries. Querying the DB directly by code comes especially handy when preparing extensive datasheets for statistical evaluation or model calibration runs.</p><p>The database follows the “FAIR Guiding Principles for scientific data management and stewardship”.</p><p>So far the database was successfully tested on the data from the three institutions of the authors' affiliation . Further development and tuning of the DB to enable incorporation of wider range of data structures is desired and any suggestions are welcome. If you are dealing with measurements related to rainfall-runoff processes and are interested in making your data accessible, please bring a typical dataset or an overview of recorded parameters to this PICO.</p><p> </p><p>The research has been supported by the research project QK1810341 of Czech National Agricultural Research Agency and the European Social Fund in the Free State of Saxony (Förderbaustein: Promotionen)</p>

To investigate relevant processes as well as to predict the possible impact of soil erosion, many soil erosion modelling tools have been developed. The most productive development of process-based models took place at the end of the 20th century. Since then, the methods available to observe and measure soil erosion features as well as methods to inter- and extrapolate such data have undergone rapid development, e.g., photogrammetry, light detection and ranging (LiDAR) and sediment tracing are now readily available methods, which can be applied by a broader community with lower effort. This review takes 13 process-based soil erosion models and different assessment techniques into account. It shows where and how such methods were already implemented in soil erosion modelling approaches. Several areas were found in which the models miss the capability to fully implement the information, which can be drawn from the now-available observation and data preparation methods. So far, most process-based models are not capable of implementing cross-scale erosional processes and can only in parts profit from the available resolution on a temporal and spatial scale. We conclude that the models’ process description, adaptability to scale, parameterization, and calibration need further development. The main challenge is to enhance the models, so they are able to simulate soil erosion processes as complex as they need to be. Thanks to the progress made in data acquisition techniques, achieving this aim is closer than ever, if models are able to reap the benefit.