Sustainable soil and water resources: modelling soil erosion and its impact on the environment

With the projected increase in world population to 9 billion by 2050, along with per capita income growth, the demand for land and water resources is going to increase significantly. Conversion of land to intensive agriculture has led to dramatic decreases in plant, animal and insect biodiversity, with approximately 40% of the world’s land surface now covered by croplands and pastures. Intensive agricultural practices cause erosion and lead to transport of soil particles and associated sorbed chemical (fertilizers, pesticides and herbicides) contaminants, which are responsible for significant degradation in the quality of both surface and subsurface water bodies. Soil erosion is an outcome of complex interactions between precipitation, physical transport, topography and conservation management strategies; and there have been many physically based mathematical models developed over the past 20 years that attempt to make predictions of erosion rates as a function of these interactions. These have been applied across scales corresponding to the laboratory, plot, hillslope and watershed with varying degrees of success. Two particular characteristic features of erosion data from both the laboratory and field scale that almost all these models have yet to reproduce reliably are hysteresis in the water discharge versus sediment discharge relationship, and the size distributions of transported sediment. We show that the model of Hairsine and Rose is able to produce the known common types of hysteresis curves, these being clockwise, counter-clockwise, figure 8 (both flow orientations), and that these forms are in keeping with measured data in the literature. Numerical simulations demonstrate that such curves are a consequence of (i) the soil’s sediment size distribution and (ii) the existence and evolution of a deposited layer of non-cohesive sediment on top of original un-eroded cohesive soil. It is shown that the initial state of this layer prior to a rainfall event plays a significant role in determining which type of hysteresis loop evolves. An application to published experimental data for flow-driven erosion down a rill is then considered. Excellent agreement between measured and suspended sediment concentrations was found throughout the hysteretic cycle.

Parameter Changes from Upscaling of a Local Scale, Process-Based Erosion Model

David Andrew Barry, Seifeddine Jomaa

Soil erosion affects agricultural productivity, the natural environment and infrastructure security. Soil loss and its associated impacts are important environmental problems. Consequently, model-based predictions of erosion are beneficial for a variety of applications. Process-based erosion models are used to forecast sediment transport concentration as it varies temporally and spatially. Of these, the one-dimensional Hairsine-Rose model describes multiple particle size classes, rainfall detachment, flow-driven entrainment and deposition. This model has been evaluated for different experiments, and has been shown to reliably explain experimental data in a consistent manner. It is common on both the hillslope and laboratory scales to apply one-dimensional erosion models even though the overland flow and sediment transport is two-dimensional. One-dimensional parameter determinations, which are based typically on outflow data, implicitly average the two-dimensional flow. Here we compare experimentally and numerically this averaging process for the Hairsine-Rose model. For this purpose, laboratory experiments were performed using different configurations of the 2 m × 6 m EPFL erosion flume. The flume was divided into 4 smaller flumes, with widths of 1 m, 0.5 m, and 2 × 0.25 m, but otherwise identical. A series of experiments was to provide data sets for analysis by the Hairsine-Rose model. After running the experiments, the amount of the eroded sediment in each subplot was assessed by comparing the temporal variation of eroded mass to evaluate the effect of, and sensitivity to, transverse width on erosion dynamics. The surface elevation changes due to erosion were examined to provide further understanding of the erosion data. A high resolution laser scanner provided details of the soil surface in the form of digital terrain maps before and after the experiment. This method presents a promising way for identification of spatial distribution pattern of eroded soil. In addition, we ran simulations using a fully two dimensional implementation of the Hairsine-Rose model for erosive flows with varying topography with spatially dependent flow and erosion input parameters to produce both outflow hydrographs and suspended sediment graphs. The data were integrated transversely and, as for the experimental data, the one-dimensional Hairsine-Rose model was used to fit the integrated data and so provide parameter estimates to compare with the two-dimensional input values.

2009

Numerical modeling of cohesive sediment transport and bed morphology in estuaries

Célestin Leupi

Two major lines of investigation have been pursued in this thesis: (1) More efficient, robust and realistic numerical techniques are designed for the simulation of complex turbulent fluid flows; (2) A new algorithm and its analysis is performed in the context of multiphasic fluid flow, for a cohesive fine-grained sediment (fluid mud) transport in estuaries. Estuaries exist between marine and freshwater system where waters of different physical, chemical and biological composition meet, combine and disperse primarily due to tidal influences. In the present thesis, the behavior of cohesive sediment in estuaries is reviewed based on the existing literature. Basic theories and recent developments are introduced to describe the formation of fluid mud from a very dilute suspension and its motion down a natural river bed with complex bathymetry. The present work contributes to the numerical simulation of complex turbulent multiphasic fluid flows encountered in estuarine channels, with the aim of the better understanding of the underlying physical processes as well as predicting realistically the cohesive sediment transport and bed morphology in such a zone. The model is based on the mass preserving method by using the so-called Raviart-Thomas finite element on the unstructured mesh in the horizontal plane. In the vertical, the computational domain is divided into number of layers at predefined heights and the method uses a conventional conforming P1 finite element scheme, with the advantage that the lowermost and uppermost layers variable height allow a faithful representation of the time-varying bed and free surface, respectively. Concerning the modeling of turbulence, the research effort focuses on the turbulence two-equation k - ε closure for the vertical parameterization of eddy viscosity. More precisely, a robust up-to-date algorithm is used for this issue. The new methodology is developed with the aim to account for more general relevant effects in the closure. The proposed model offers the capability to cope with the stiffness problem introduced by the large difference between the solid phase flow time scale and the hydrodynamic one, by using a sub-cycling strategy, whereas the splitting scheme is adopted with the aim of stability and the positivity of the relevant turbulent variables. The flexibility of the model and its performance are evaluated on several free-surface flow configurations with increasing complexity : homogeneous unsteady non-uniform flows in plane open channel flows, U-shaped (193°) curved open channel flow. Concerning the cohesive sediment transport, most of the existing models in the literature assume the analogous transport characteristics with that of the coarse sediment and adopt the relevant developed sediment transport for the latter to treat the former. Moreover, these existing models do not account for the consolidation of the mud-bed. The present research effort focused on a novel methodology based on the realistic empirical relationships, which accounts for the mutually exclusive processes for re-suspension and/or erosion and deposition of fine sediment, whereas only a limited range of bed shear stresses is allowed for simultaneous erosion and deposition to occur. Hence, on this basis, the new model investigated the bed morphology evolution by taking into account of the fluidization and/or consolidation of the fluid mud, which was handled by modeling the bed in three layers: (i) the mud-bed layer, (ii) the partially consolidated bed and (iii) the fully consolidated bed. The prediction of deposition/re-suspension using these two different methods lead to a non negligible difference in the results. Therefore, investigation of the true mechanism of erosion/deposition processes for cohesive sediments and their implementation in the numerical model is very important. This suggests that a realistic prediction must account for the fresh mud-bed re-suspension once deposited, as well as the consolidation and/or fluidization of the mud-bed deposits. Finally, the capability and improvements of the model are demonstrated, and its predicting performance is successfully evaluated by applying it to the simulation of the Po River Estuary (PRE) in Italy, which is the main source of river water discharge into the Northern Adriatic Sea. The analysis showed that the consolidation/fluidization process at the bed may have important influence on the prediction of bed morphology evolution. The three-layer approach used in this thesis is a first attempt to model these processes in detail within a numerical model.

EPFL2005

Statistical and physical characterization of rainfall-driven overland flow morphologies

Mohsen Cheraghi

Environmental transport processes are highly coupled with the shape of landscapes. Modern catchment analysis with high-resolution data and huge computational powers demand more detailed within-cell metrics for surface evolution modeling. This dissertation involves experiments and numerical simulations of rainfall-driven sediment transport at laboratory scales of which areas were less than the common computational cell sizes at catchment scales. The objective was a stochastic and physical study of unchanneled overland flow morphologies. In the first step, a detailed laboratory study was conducted to highlight the effects of morphological changes on hysteretic sediment transport under a time-varying rainfall. A rainfall pattern composed of seven sequential stepwise varying rainfall intensities was applied to a 5-m×2-m soil erosion flume. Clockwise hysteresis loops in the sediment concentration versus discharge curves were measured for the total eroded soil and the finer particle sizes. However, for larger particle sizes, hysteresis effects decreased and suspended concentrations tended to vary linearly with discharge. Overall, it is found that hysteresis varies amongst particle sizes and that the predictions of the HR model are consistent with hysteretic behavior of different sediment size classes. After demonstrating the role of morphological changes (generation of a shield layer on the topsoil) on erosion patterns, overland flow morphologies were statistically characterized. To do so, the catchment-scale network analyses were applied on the micro-roughnesses of unchanneled surfaces at the laboratory scale (2-m×1-m flume). The scaling relation between the drainage area and stream length (Hack¿s law), along with exceedance probabilities of drainage area, discharge, and upstream flow network length, is well known for catchment-scale channelized fluvial regions. It was found that the relationships for the overland flow network were the same as those found for large-scale catchments and for laboratory experiments with observable channels. In addition, the scaling laws were temporally invariant, even though the network dynamically changed over the course of the experiment. In the next step, we tested the applicability of a physically-based catchment scale landscape evolution model (LEM) at laboratory scale and in absence of rills. We modeled the overland flow as a network that preserves the water flux for each cell in the discretized domain. This network represented the surface flow and determined the evolution direction. The spectral analysis confirmed that the model predictions capture the main characteristics of the measured morphology. However, the model could not reproduce the experimental scaling relation as the micro-roughnesses of the surface were not produced by the model. In order to modify the LEM, it was solved as a stochastic partial differential equation. The results showed that an extra term for roughness was necessary to simulate more details of the morphology. Furthermore, a new deterministic approach (diffusion coefficient as a step function of curvature) was proposed and tested to improve the model predictions in the statistical sense.\ Besides the scientific contributions, useful modeling, optimization and data analysis tools (C++ and Python codes) were provided for future geomorphological studies.

EPFL2019