Simulate Overland Flow Research Articles

Application of 1D model for overland flow simulations on 2D complex domains

High computational demand limits the applications of two-dimensional (2D) shallow water equation models for high resolution overland flow simulations, while one-dimensional (1D) models can achieve higher computing efficiency. This study applied a 1D hydrodynamic model to surrogate 2D models for overland flow simulations on complex 2D domains. With one dimension reduced, the surrogate model simulation would have acceptable accuracy with much higher computing efficiency. The surrogating is fulfilled through mimicking 2D models in mesh generations, so that the 1D channel network is generated in such a way that it geometrically covers the whole domain without overlapping and intersection, and hydrologically follows the steepest slopes. Several benchmark cases on 2D domains in both laboratory and field scales with complex geometry, where no 1D models have been ever applied, are used to compare the 1D and 2D model simulations. The comparisons demonstrate that the 1D model does have potentials to efficiently simulate overland flow on 2D complex domains with accuracy comparable to 2D models.

Generation of 1D channel networks for overland flow simulations on 2D complex domains

Conventionally two-dimensional (2D) models are used to simulate 2D overland flow with a non-overlapping 2D computational mesh. However, 2D models are not computationally efficient when applied to large domains. Due to their computing efficiency, one-dimensional (1D) models can be used to simulate 2D overland flows by replacing 2D computational meshes with 1D computational channel networks with topography described by closely-spaced transverse cross sections that fully cover the whole domain. Channel networks must enforce the basic physical laws of gravity-driven flows ensuring water flow paths converge and connect from high to low elevations. This manuscript presents a novel algorithm to generate channel networks following two principles, a geometric principle and a hydrologic principle. The geometric principle requires that the generated channel network covers the whole study domain without overlaps or intersections, while the hydrologic principle requires that the generated channel network follows the local steepest slope. Correspondingly, the proposed generation algorithm includes two main processes: (1) the extraction of channel network using a terrain slope-calculation-based delineation algorithm; and, (2) the generation of cross sections with varying channel widths determined by considering topographic complexity, the hydrological correctness, and computational requirements. The proposed cross section generation algorithm is described using several 2D geometrically complex domains at the laboratory scale, and is also applied to a natural watershed. An overflow simulation on a 2D domain with obliques walls using a 1D model demonstrated the effectiveness of the proposed generation algorithm for 1D channel networks of 1D model.

A novel Eulerian SPH shallow water model for 2D overland flow simulations

A 2D Eulerian meshless shallow water model based on smoothed particle hydrodynamics (SPH) is proposed to study overland flow. Rain on a dry bed to generate a runoff flow is one common hydraulic phenomenon. However, it is difficult for existing Lagrangian SPH shallow water models to present the flow because no computational particle exists on a dry bed. To overcome this difficulty, the Eulerian form of the 2D shallow water equations is used to describe flow behavior in the proposed model. An HLLC approximate Riemann solver is applied to calculate fluxes between two neighboring particles to smear out the instabilities caused by the discretization of the nonlinear convective term and the discontinuity of wet-dry beds. Additionally, we use a surface reconstruction method (SRM) to ensure that the proposed model has well-balanced and positivity-preserving properties. Bed friction and infiltration effects are also analytically considered. Eight case studies involving various overland flows with wet-dry transitions, rainfall, infiltration, bed friction and complex topography are adopted to test the proposed model capacity. The first-order convergence rate is obtained in the convergence analysis. Against the exact and measured results, in the analytical case studies, the relative root-mean-square errors of depth and velocity are approximately 0.02% to 0.3% and 1.3% to 1.7%, respectively. In the experimental case studies, the relative root-mean-square errors of depth and discharge (velocity) are approximately 3.8% and 1.2% to 6.1%, respectively. The good agreement demonstrates between the results shows the reliability of the proposed 2D Eulerian SPH shallow water model for real-world overland flows.

Assessing Integrated Hydrologic Model: From Benchmarking to Case Study in a Typical Arid and Semi-Arid Basin

Groundwater-surface water interactions play a crucial role in hydrologic cycles, especially in arid and semi-arid basins. There is a growing interest in developing integrated hydrologic models to describe groundwater-surface water interactions and the associated processes. In this study, an integrated process-based hydrologic model, ParFlow, was tested and utilized to quantify the hydrologic responses, such as changes in surface runoff and surface/subsurface storage. We progressively conducted a complexity-increasing series of benchmarking cases to assess the performance of ParFlow in simulating overland flow and integrated groundwater-surface water exchange. Meanwhile, the overall performance and the computational efficiency were quantitatively assessed using modified Taylor diagrams. Based on the benchmarking cases, two case studies in the Heihe River Basin were performed for further validation and to diagnose the hydrologic responses under disturbance, named the Bajajihu (BJH) and Dayekou (DYK) cases, respectively. Both cases were 2D transects configured with in-situ measurements in the mid- and downstream of the Heihe River Basin. In the BJH case, simulated soil moisture by ParFlow was shown to be comparable with in-situ observations in general, with Pearson’s correlation coefficient (R) > 0.93 and root mean square difference (RMSD) < 0.007. In the DYK case, seven scenarios driven by remote sensing and reanalysis data were utilized to study hydrological responses influenced by natural physical processes (i.e., precipitation) and groundwater exploitations (i.e., pumping) that are critical to surface and subsurface storage. Results show that subsurface storage is sensitive to groundwater exploitation before an obvious stationary point. Moreover, a correlation analysis was additionally provided demonstrating the impacts of different factors on subsurface storage timeseries. It was found that pumping influences subsurface storage remarkably, especially under short-term but large-volume pumping rates. The study is expected to provide a powerful tool and insightful guidance in understanding hydrological processes’ effects in arid and semi-arid basins.

Influence of Water Depth and Slope on Roughness—Experiments and Roughness Approach for Rain-on-Grid Modeling

Two-dimensional (2D) models have become a well-established tool for channel flow, as well as rain-induced overland flow simulations. In channel flow simulations, slopes are usually less than a few percent and water depths are over several meters, while overland flow simulations show steep slopes and flow of a few centimeters. Despite these discrepancies, modelers transfer roughness coefficients, validated for channel flow, to overland flow. One purpose of this study is to verify whether roughness values from the literature are also valid for overland flow simulations. Laboratory experiments with different degrees of bed roughness, various discharges and a range of experimental flume slopes were carried out. For a given discharge, water depth was measured, and bed roughness was derived. Experimental results reveal that roughness shows no clear dependence on slope but is strongly dependent on water depth for vegetated surfaces. To verify the influence of different roughness approaches, they were implemented in a 2D model. A comparison of different simulation results indicates differences in the hydrograph. Here, consideration of water depth-related roughness coefficients leads to retention and translation effects. With the results of this study, modelers may enhance the precision of the hydraulic component in overland flow simulations.

Impacts of grass planting density and components on overland flow hydraulics and soil loss

AbstractAlthough abundant studies have confirmed the positive effect of vegetation on runoff and soil erosion reduction, few studies have clarified the effects of planting density and its components (aboveground parts and roots) on slope runoff and soil erosion mechanisms. A series of field experimental plots were constructed on two slopes (3°, 6°), including a bare land plot as the control, three grassed plots with three grass (Agropyron cristatum) planting densities of 20 cm × 20 cm, 15 cm × 15 cm, and 10 cm × 10 cm, and a plot without aboveground parts, to examine runoff and soil erosion process under simulated overland flow of 4, 8, 12, and 16 L min−1. The runoff regime was transformed from supercritical‐turbulent flow to subcritical‐laminar flow with increasing planting density. Grass significantly reduced the runoff rate (RR), velocity (V), shear stress (τ), stream power (ω), and soil loss rate (SLR), with average reductions of 38.6%, 56.6%, 76.5%, 87.6%, and 61.9%, respectively. The aboveground parts contributed 74.1% and 75.1% of the total reduction in RR and V, respectively, while the grass roots contributed to 84.9%, 89.7%, 84.9%, and 69.7% of the reductions in Reynolds number, τ, ω, and SLR, respectively. RR, V, τ, ω, and SLR were significantly affected by slope, inflow discharge, root density, and the ratio of grass stem area to plot area. The runoff–sediment relationship changed from positively exponential function to linear and power functions with the planting density increased. Grass significantly weakened the sensitivity of soil erosion by reducing soil erodibility and improving critical hydrodynamic triggering soil erosion. This study improved the understanding of grass controlling soil and water loss, and the plants with well‐developed roots and planting space of 10–15 cm are preferred to provide a scientific reference for revegetation strategy.

Is forest location more important than forest fragmentation for flood regulation?

Native forest deforestation has been identified as one of the main land cover changes affecting flood risk specially during small and moderate storm events. In this regard, forest protection and reforestation are considered a nature-based solution (NbS) for flood regulation. However, there is a lack of knowledge about the effects of different deforestation spatial patterns over floods. Effects of land cover changes on floods in a humid tropical basin within the Ecuadorian Amazon are assessed distinguishing forest location and forest fragmentation. The hydrological distributed model TETIS was applied to simulate the hydrological response of a basin to extreme storms having return periods of 1, 10 and 100 years, considering five land cover scenarios. The model was calibrated and validated using nine storm samples collected at a gauge station during the years 2018 and 2020. The simulated overland flow in hillslopes and stormflows within the river channel were analyzed to i) assess the statistical differences among all land use scenarios with the Kruskal-Wallis test; ii) assess the statistical differences among pairs of both location and fragmentation scenarios through the post-hoc evaluation Dunn test; iii) assess the statistical differences in relation to the baseline. Obtained results indicate that stormflow is less sensitive than overland flow to land cover changes. Forest location have more influence than forest fragmentation over both, overland flow and storm flows. Deforestation of the upper basin represents the worst scenario for flood regulation, thus protection of existing forest, as well as reforestation of deforested areas located in the upper watersheds is a priority for flood risk mitigation and forest conservation. The results enhance our understanding of ecosystem services provided by tropical Andean foothills forests.

Temporal variation in soil detachment processes under litter incorporation effects in typical grassland on the Loess Plateau of China

Plant litter incorporation into soil is a widespread phenomenon in the natural environment. Accurate estimation of the soil detachment capacity (Dc) driven by overland flow under litter incorporation effects is crucial for improving soil erosion prediction. However, the effects of litter incorporation on soil detachment processes are often ignored, and the temporal variation of Dc under litter incorporation effects remains unclear for grassland in the Loess Plateau of China. In this study, two litter incorporation soil treatments (Bothriochloa ischaemum (L.) Keng. litter, and Artemisia sacrorum Ledeb. litter) and one bare soil treatment (control) were set. Flume tests with flow shear stress ranging from 5.66 to 22.11 Pa were conducted to simulate overland flow scouring and determine the temporal variation of Dc between May 2017 and October 2018 (nine times, a 524-day period). Furthermore, the key factors affecting Dc were identified. Our results showed that the temporal variation in Dc was consistent across the different soil treatments (two litter incorporation treatments and one bare soil control), showing a rapid decline and then fluctuating at a low level, with Dc ranging from 0.115 to 6.876 kg m−2 s−1. Incorporation of litter effectively reduced Dc, with the Dc of soil treatments incorporating litter being 15% to 29% lower than that of bare soil (2.110 kg m−2 s−1). Further analysis showed that the temporal variation in Dc was mainly affected by the development of a physical soil crust. Dc can be successfully estimated using a nonlinear equation incorporating flow shear stress and soil cohesion (R2 = 0.77, NSE = 0.65), which represent the erosive force and soil erosion resistance, respectively. Our study reveals the important role of plant litter in the soil detachment process and aids the understanding of soil erosion pathways. Further studies are needed to investigate the effects of a physical soil crust on the soil detachment process driven by overland flow.

Novel variable reconstruction and friction term discretisation schemes for hydrodynamic modelling of overland flow and surface water flooding

Due to the recent advances in computing and data acquisition technologies, numerical models solving the 2D shallow water equations (SWEs) are now widely used in predicting overland flow and surface water flooding process in natural catchments. In catchment-scale flood modelling, in addition to the calculation of convective terms that are usually achieved through solving local Riemann problems to capture transient flow dynamics, correct discretisation of source terms is also essential to handle complex domain topography and ensure accurate and stable numerical solutions. The external forces induced by gravity and bed friction create the key source terms that drive the change of momentum in the SWEs and affect the stability and accuracy of the adopted numerical scheme, especially for applications involving very shallow water depth (e.g. wet and dry fronts, overland flows). Herein, new schemes are introduced to reconstruct the face values of flow variables and a fully implicit algorithm is improved to discretise the stiff friction terms, in the context of developing a Godunov-type finite volume hydrodynamic model for accurate and stable simulation of overland flow and surface water flooding involving very shallow water depth. Five analytical test cases are considered to validate the resulting models and the numerical results are compared with those produed by two alternative numerical schemes. The performance of the models are further demonstrated by reproducing a flood event in the 2500 km2 Eden Catchment, UK.

Quantifying the Uncertainty Created by Non‐Transferable Model Calibrations Across Climate and Land Cover Scenarios: A Case Study With SWMM

AbstractPredictions of urban runoff are heavily reliant on semi‐distributed models, which simulate runoff at subcatchment scales. These models often use “effective” model parameters that average across the small‐scale heterogeneity. Here we quantify the error in model prediction that arises when the optimal calibrated value of effective parameters changes with model forcing. The uncertainty this produces, which we refer to as “calibration parameter transfer uncertainty,” can undermine the usefulness of important applications of urban hydrologic models, for example, to predict the hydrologic response to novel climate or development scenarios. Using the urban hydrologic model SWMM (“Stormwater Management Model”) as a case study, we quantify the transferability of two calibrated effective parameters: subcatchment “width” and “connected impervious area.” Through numerical experiments, we simulate overland flow across a highly simplified synthetic urban landscape subject to a range of scenarios (combinations of storm events, soil types, and impervious areas). For each scenario, we calibrate SWMM “width” and “connected impervious area” parameters to the outcomes of a distributed model. We find that the calibrated values of these parameters vary with soil, storm, and land cover forcing. This variation across forcing parameters can result in prediction errors up to a magnitude of 60% when a calibrated SWMM is used to predict runoff following changes in climate and land cover. Such calibration transfer uncertainty is largely unaccounted for in urban hydrologic modeling. These results point to a need for additional research to determine how to use urban hydrologic models to make robust predictions across future conditions.

Investigation of the drainage loss effects with a street view based drainage calculation method in hydrodynamic modelling of pluvial floods in urbanized area

Drainage loss effects are crucial for flash flood modelling induced by torrential rains in urbanized environment. This paper proposes a novel approach for incorporating drainage loss effects into two-dimensional hydrodynamic overland flow simulations with the open source databases offered by geographical information providers. Street inlet locations within the road network are determined using street view images based on feature points extracted throughout automatic navigation along the roads in the panoramas, where the runoff of the surface flood flow is determined by the drainage network's capacity. By implementing the proposed data acquisition and drainage loss calculation method into the 2D overflow model HiPIMS as an alternative to the often-unrealizable physically based method or to the overly simplistic rainfall reduction method, the flood modelling results are validated against field observations during severe flood events in an intensely urbanized area to demonstrate the feasibility and effectiveness of the newly proposed method. In comparison to other simulation scenarios without drainage loss effects or with those considered by the rainfall reduction method, the drainage loss effects induced by the newly proposed method are analyzed for both the spatially lumped and distributed urban flood patterns. While the drainage effects are more essential after the rainfall peak hours for the flood extent as spatially lumped results, the low-lying area with dense building complexes are found to benefit more from the drainage effects in a spatially distributed way. Variations of the speed and direction of flood flows caused by the drainage effects at inlets are observed to depend on the surrounding environment. Competitions between the drainage effects and the gravity effects induced by topographical features are revealed with street-level evaluations of the flood modeling results using high-resolution hydrodynamic modeling in conjunction with the proposed drainage calculation approach.

Interpreting the Manning Roughness Coefficient in Overland Flow Simulations with Coupled Hydrological-Hydraulic Distributed Models

There is still little experience on the effect of the Manning roughness coefficient in coupled hydrological-hydraulic distributed models based on the solution of the Shallow Water Equations (SWE), where the Manning coefficient affects not only channel flow on the basin hydrographic network but also rainfall-runoff processes on the hillslopes. In this kind of model, roughness takes the role of the concentration time in classic conceptual or aggregated modelling methods, as is the case of the unit hydrograph method. Three different approaches were used to adjust the Manning roughness coefficient in order to fit the results with other methodologies or field observations—by comparing the resulting time of concentration with classic formulas, by comparing the runoff hydrographs obtained with aggregated models, and by comparing the runoff water volumes with observations. A wide dispersion of the roughness coefficients was observed to be generally much higher than the common values used in open channel flow hydraulics.

Multi-Mode Surface Generalization Supports a Detailed Urban Flooding Simulation Model

With the aim of achieving high precision and high efficiency, recent research on hydraulic flood models has tended to focus on the algorithms for solving the shallow water equations of Saint-Venant. While development of the algorithms will help to improve the simulation precision and the solving of specific problems, the other influential factor in flood risk modeling is the precision and reasonable generalization of the data. This is even more important for increasing the model’s computational accuracy and efficiency but is frequently undervalued. Frequent rainstorm waterlogging is having a serious impact on China’s large cities. Early warning of waterlogging risk following a rainstorm forecast is an effective method for preventing or reducing potential losses. Concrete waterlogging information including locations, depth, and process is essential for early warnings. This paper focuses on the influence of data precision and reasonable generalization on an urban flooding model. A detailed hydraulic urban flooding model characterized by detailed data processing and component coupling can help to provide advance information. In Beijing city, road networks, overpasses, and buildings are so highly concentrated that rainstorms easily result in waterlogging in low-lying locations. Therefore, partial microrelief is the determinate factor in waterlogging simulation. This paper shows that multi-mode surface data generalization and detailed model coupling support a perfect simulation of a Beijing urban flooding model. The influence of buildings, roads, and overpasses on surface water flow was carefully considered based on the innovative aspect of a fine generalization of partial microrelief. One novelty is the simulation of the whole overland flow from the beginning of rainfall to mesh, not only from manhole overflow, because the waterlogging is caused mainly by initial surface water runoff rather than by manhole overflow. A second novelty is the use of a new kind of coupling mode based on physical mechanisms between surface and pipe models. Here, rain perforated strainers instead of manholes play a role as flow exchange points between pipe and surface. This coupling mode is much closer to the real world. Based on a detailed Beijing urban flooding model, a scenarios library of typical rainfall events and corresponding waterlogging results was constructed. Several years of practice have demonstrated that a rich library of scenarios can be used effectively for the quick identification and early warning of waterlogging risk for a forecast rainfall. Test results show that multi-mode surface generalization is effective in improving outcomes and useful for scientific decision making in controlling urban waterlogging.

Overland Flow Simulations in an Urban Catchment: A Straightforward Approach to Considering Culverts

AbstractExisting overland flow models tend to neglect culvert flow. The goal of the present study is to implement a straightforward and easily realizable representation of culvert flow into the ove...

An Augmented Reality Facility to Run Hybrid Physical-Numerical Flood Models

This article presents a novel installation for the development of hybrid physical-numerical flood models in an augmented reality environment. This installation extends the concept introduced by the well-known Augmented Reality-SandBox (AR-Sandbox) module, which presents a more educational, and less research-based and professional application. It consists of a physical scale topography built in a sandbox into which other elements (such as buildings, roads or dikes) can be incorporated. A scanner generates, in real time, a Digital Terrain Model (DTM) from the sandbox topography, which serves as a basis for the simulation of overland flow using professional hydraulic software (Iber+). The hydraulic and hydrological parameters (surface roughness, inlet discharges, boundary conditions) are entered with a simple Graphical User Interface (GUI) developed specifically for this project, as indeed was the entire system that allows the visualization of the simulation results. This allows us to obtain quantitative results of flood extension and magnitude, which are represented directly over the physical topography, yielding a realistic visual effect. This installation is conceived for both educational and professional uses. An example of its use is presented, through which its accuracy can be appreciated, and which also illustrates its potential.

Mechanism and role of seeded native grasses to immobilize nitrogen on harvested blanket peat forests for protection of water courses.

Forest harvesting activities on peatlands have long been associated with nutrient leaching and deterioration of downstream water quality. This study aims to assess the effect of grass seeding practice on harvested blanket peatlands to immobilize N and reduce its export to water courses. First, a plot-scale field experiment was conducted by seeding with two grass species (Holcus lanatus and Agrostis capillaris) to study the N uptake potential from a harvested area. Secondly, a simulated rainfall experiment was conducted to study the effect of these grasses on reducing N leaching from surface peat using laboratory flume approach. In the end, the role of seeded grasses in removing N from nutrient-rich throughflow water was assessed using simulated overland flow experiment. The results showed that the seeded grasses had the potential to uptake over 30 kg ha-1 of N in the first year after seeding on harvested peatlands, whereas it takes over 2.5 years to establish the same level of N uptake by natural re-vegetation (non-grassed). In the simulated rainfall experiment, the inorganic N (NH4+-N and NO3--N) leaching in surface runoff from grassed flumes was 72% lower (453 mg m-2) than non-grassed flumes (1643 mg m-2). In the simulated overland flow experiment, the N retention by grassed flumes was significantly higher (98%) as compared to non-grassed flumes (70%) in the simulated overland flow experiment. Comparatively higher concentrations of NH4+-N and NO3--N in soil porewaters of non-grassed flumes suggest that this N retention by non-grassed flumes is less sustainable and is likely to be leached in runoff in subsequent flow events. The results from all three experiments in this study suggest that seeded grasses are a major sink of N on harvested blanket peatland forests. Immobilization of N onsite using the grass seeding and mini-buffer practice could be an efficient and a feasible mean of reducing N export from harvested blanket peatland forests in order to protect the sensitive water courses. However, the sustainability of retention and immobilization of N by grasses needs to be studied further in long-term field-scale experiments on multiple peatland sites.

Assessing plot‐scale impacts of land use on overland flow generation in Central Panama

AbstractLand use in Panama has changed dramatically with ongoing deforestation and conversion to cropland and cattle pastures, potentially altering the soil properties that drive the hydrological processes of infiltration and overland flow. We compared plot‐scale overland flow generation between hillslopes in forested and actively cattle‐grazed watersheds in Central Panama. Soil physical and hydraulic properties, soil moisture and overland flow data were measured along hillslopes of each land‐use type. Soil characteristics and rainfall data were input into a simple, 1‐D representative model, HYDRUS‐1D, to simulate overland flow that we used to make inferences about overland flow response at forest and pasture sites. Runoff ratios (overland flow/rainfall) were generally higher at the pasture site, although no overall trends were observed between rainfall characteristics and runoff ratios across the two land uses at the plot scale. Saturated hydraulic conductivity (Ks) and bulk density were different between the forest and pasture sites (p < 10−4). Simulating overland flow in HYDRUS‐1D produced more outputs similar to the overland flow recorded at the pasture site than the forest site. Results from our study indicate that, at the plot scale, Hortonian overland flow is the main driver for overland flow generation at the pasture site during storms with high‐rainfall totals. We infer that the combination of a leaf litter layer and the activation of shallow preferential flow paths resulting in shallow saturation‐excess overland flow are likely the main drivers for plot scale overland flow generation at the forest site. Results from this study contribute to the broader understanding of the delivery of freshwater to streams, which will become increasingly important in the tropics considering freshwater resource scarcity and changing storm intensities.

Automatic triangular and triangular-prism mesh generation for overland and subsurface water flow simulations

In this paper, an automatic mesh generator is developed to simulate density-dependent water flow and transport problems in watershed systems. The two-dimensional (2D) triangular mesh is generated by global Delaunay triangulation, and the three-dimensional (3D) triangular-prism mesh is generated by vertical stretch. The implementation procedures of mesh generation are adjusted according to the interaction options of one-dimensional (1D) river, 2D overland, and 3D subsurface flows. An improved boundary point generation algorithm is proposed to maintain appropriate correspondence of points and edges according to the discrete patterns of river reaches and dead ends. Overlapped nodes are generated on zero-width river reaches and zero-width junctions without storage to construct the numerical models for 2D overland simulations. An additional triangular mesh generation method is proposed to create additional triangles for filling the empty water zones of finite-width river reaches, junctions with storage, finite-width ponds, lakes, and dead ends. The boundary loops bounding each water area are identified correctly, and the additional grids are created compatibly, aiming at the finite-depth and zero-depth patterns of storage zones. The computation equations of relevant parameters used for 3D stretch from triangles to triangular-prisms are built, and the 1D/2D/3D correspondence on river reaches, junctions, ponds, lakes, dead ends, and control structures is established. Finally, practical examples for discretizing real-world water areas are provided to demonstrate the robustness and effectiveness of our developed mesh generator by using the skewness as the mesh quality metric.

Simulation of overland flow considering the influence of topographic depressions

The simulation of overland flow, wherein runoff yield and concentration are influenced by topography, is fundamental to hydrological forecasting. Therefore, critically evaluating the characteristics of overland flow under the influence of topographic depressions—which are one of the most common microtopographic structures—is vital for improving current hydrological models. In this study, we developed a solution for the real-world application of overland flow simulations under the influence of depressions in hydrological models. A relative depression storage–outflow curve (RDOC) was proposed to investigate surface outflow processes. Experiments were conducted based on the variable-controlling approach using three rainfall return periods, four slopes, and four depression rates while ensuring a consistent initial soil moisture content. A homogenized RDOC was achieved based on shape analysis; it was parameterized by the outflow threshold and the reciprocal of the curve index of two outflow stages (B and D). A relative depression storage–outflow function (RDOF) was generated and a complete calculation procedure was applied within a hydrological model. Furthermore, we analyzed the hydrological responses to parameters of different hydrological factors to improve our understanding of the parameter determination of the RDOF.

Improving the Horton infiltration equation by considering soil moisture variation

Soil water infiltration simulation is a subject receiving great interest in hydrological cycle modelling. The traditional Horton equation is based on the curve of infiltration capacity-rainfall duration time. However, the infiltration process is directly affected by soil moisture content, rather than rainfall duration. The objective of this study was to determine a relationship between infiltration capacity and soil moisture content in order to improve the Horton infiltration equation. Artificial rainfall-infiltration experiments were used to determine a series of power functions. The improved equation was cross-validated with observations from 32 experiments of multiple rainfall intensities and antecedent soil moisture. The simulation performance and uncertainty of the improved equation were compared with those of the original Horton equation to verify its accuracy. The results showed that infiltration rate decreases nonlinearly as soil moisture increases, and finally approaches a stable infiltration rate when the soil is saturated. Overland flow simulations by the improved Horton equation closely matched the observations from all 32 experiments over a soil moisture range of 0.222–0.349 m3/m3. The simulation performance was rated as good for most of the experiments for both the calibration and validation data sets. Compared with the original Horton equation, the simulation performance of the improved equation clearly improved estimation of infiltration, particularly as quantified by the Nash-Sutcliffe efficiency coefficient (NSE) and the coefficient of determination (R2). The number of simulations with NSE values greater than 0.65 increased 11.59% and 2.50% for the calibration and validation data sets, respectively. The number of simulations with R2 values greater than 0.90 increased 31.14% and 22.50%, respectively. The uncertainty intervals of the improved Horton equation became a little greater than those of the original Horton equation. For all 32 experimental simulations, the average relative length of the uncertainty interval at the 95% confidence level increased from 40.52% with the original Horton equation to 49.17% with the improved Horton equation. The number of observations falling within the 95% confidence interval increased from 92.13% to 95.94% with the improved Horton equation. Most of the observations were accurately simulated using the improved Horton equation. The greatest improvements in simulating overland flow were seen for the experiments with low flow simulations. The study results provide insights into soil infiltration mechanisms, and also provide references to support improved infiltration simulation by considering soil moisture variation.