Integrating hydrological, hydro-geological, soil-physical and hydrodynamic processes by means of particle based simulations
Final Report Abstract
The integration of hydrological processes and adjacent disciplines within hydrological models is of great interest for application-oriented tasks. The coupling of the relevant processes is challenging in terms of structural and content-related differences of the models. These include the spatial and temporal scale differences as well as the varying degrees of the process descriptions. The first result of the research project is a new classification scheme on the basis of hydraulic similarity which was obtained by applying a clustering algorithm to 100.000 simulated breakthrough curves. In order to meet the requirements of large-scale hydrological modelling, a new deterministic-stochastic model approach has been developed. The approach was based on a Lagrangian framework, in which the infiltrating water was first divided into discrete particles. The stochastic components and the deterministic motion equations were then coupled analytically. This new equation describes the probability of water in space and time by distribution parameters of the soil water velocities. In contrast to the classical van Genuchten parameters, the distribution parameters of the new model approach show a remarkably similar pattern to the previously determined hydraulic similarity clusters. The developed deterministic-stochastic model approach was combined with variance propagation in order to take into account the natural range of soil water characteristics within a soil type. For this purpose, the parameters of the model were estimated based on an objective function that covered both, the errors regarding the breakthrough curve of the Richards solution and the empirical variance of the hydrographs within a cluster. The model is mass conservative, stable, robust and provides good results on different temporal scales. The optimised deterministic-stochastic model was combined with a simple solute transport model in order to simulate solute transport through the soil. It could be shown that the model delivered plausible results and was able to include the natural bandwidth of possible breakthrough curves within a given soil type analytically. Furthermore, the deterministic-stochastic approach allows a stochastic view to the general advection-diffusion equation. It offers a mathematical distinction between molecular diffusion and hydrodynamic dispersion processes. In many hydrologic fields, such as transport modelling in rivers or in unsaturated or saturated soil zones, advection-diffusion processes play an important role. There has been an unsolved problem, which can be named as back diffusion in combined diffusion/dispersion models. Due to the relevance of the topic in general and the interesting findings, the focus of the original research proposal has partly shifted towards an innovative advection-diffusion-dispersion equation. The diffusion described by Einstein and Smoluchowski (Einstein-Smoluchowski equation) has been transformed into a time-dependent velocity equation by using the variance propagation law. It was proposed to include “time” as an essential component of the stochastic variance when adding two dispersion components (DDiff and DDisp). The flexibilization of the velocity dispersion can be interpreted as a link between the molecular Brownian motion and the macroscopic water motion. The new advection-diffusion-dispersion-equation was fitted to available experimental tracer data from a published study. The simulated concentration curves showed exceptionally good agreements to the observed data. In contrast to the classical parameterisation of the advection-diffusion-equation the characteristics of longitudinal dispersion processes were reproduced successfully.
Publications
- (2019): Classification of Hydrological Relevant Parameters by Soil Hydraulic Behaviour. In: Geosciences 9 (5), S. 206
Kreye, Phillip; Gelleszun, Marlene; Somasundaram, Manickam; Meon, Günter
(See online at https://doi.org/10.3390/geosciences9050206) - (2019): Innovative Methodik zur Klassifizierung bodenhydraulischer Eigenschaften anhand vorhandener Bodenparameter. In: Zehe, E., Hennrich, K., Ehret, U., Hassler, S., Nied, M., Scherer, U. (Hrsg.): Information und Organisation in der hydrologischen Forschung und Praxis. Forum für Hydrologie und Wasserbewirtschaftung, Heft 41.19 ISBN: 978-3-88721-821-8
Gelleszun, M., Kreye, P., Somasundaram, M., Meon, G.
- Multi scale smoothed particle hydrodynamics using particle agglomeration for simulating rainfall-runoff processes, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-18951, 2020
Somasundaram, M., Gelleszun, M., and Meon, G.
(See online at https://doi.org/10.5194/egusphere-egu2020-18951) - (2022): Deterministisch-stochastische Modellansätze als Grundlage hydrologischer Prozessbeschreibungen, Dissertationsschrift mit Disputation am 06.12.2021, Leichtweiß-Institut für Wasserbau, TU Braunschweig
Gelleszun, M.
(See online at https://dx.doi.org/10.24355/dbbs.084-202203010006-0)
