Unsteady overland flow on flat surfaces induced by spatial permeability contrasts

Lateral redistribution of surface water in patchy arid ecosystems has been hypothesized to contribute to the maintenance of vegetation patches through the provision of a water subsidy from bare sites to vegetated sites. Such runon-runoff processes occur during Hortonian runoff events on topographically sloping ground. Surface flow redistribution may also occur on topographically flat ground if the presence of the vegetation patch creates a contrast in infiltration rate, leading to a free-surface gradient in ponded water. The precise dynamics and the eco-hydrologic role of this process has resisted complete theoretical treatment to date. Here the overland flow equations are modified to account for the presence of vegetation situated over a flat surface. The resulting model is solved numerically to determine whether this mechanism could influence the spatial partitioning of water in patchy arid ecosystems. Assumptions made about infiltration processes and overland flow in existing eco-hydrologic models of patchy and patterned arid ecosystems are evaluated in comparison to the solution of the ‘full’ coupled Saint-Venant equations with various infiltration models. The results indicate that the optimization of vegetation spatial patch scales with respect to water redistribution may be determined by the size of the infiltration redistribution length L over which the presence of an infiltration contrast perturbs baseline infiltration behavior.     

A model to couple overland flow and infiltration into macroporous vadose zone

Most vegetated land surfaces contain macropores that may have a significant effect on the rate of infiltration of water under ponded conditions on the ground surface. Owing to the small-scale variations of the land topography (microtopography), only portions of the land area may get ponded during the process of overland flow. As the macropores transmit water at much higher rates than the primary soil matrix, higher macropore activation in ponded areas produces larger effective infiltration rates into the soil. Therefore, overland flow and infiltration into the macroporous vadose zone are interrelated. Representing the microtopographic variation of the land surface by a simple sine wave function, a method was developed to relate the ponding area to the average ponding depth which was determined by overland flow. A numerical model coupling overland flow and infiltration into the macroporous vadose zone was developed. Overland flow was simulated using the St. Venant equations with the inertia terms neglected. A single macropore model was used to simulate the infiltration into the macroporous vadose zone. The interaction between overland flow and the infiltration into the macroporous vadose zone was analyzed for a hypothetical watershed. The sensitivity analysis revealed that the interaction of macropore flow and overland flow is significant. For the conditions tested, the macropore flow and the overland flow were found to be more sensitive to the macroporosity and less sensitive to the microtopographic surface variation.     

Integrated surface–groundwater flow modeling: A free-surface overland flow boundary condition in a parallel groundwater flow model

Interactions between surface and groundwater are a key component of the hydrologic budget on the watershed scale. Models that honor these interactions are commonly based on the conductance concept that presumes a distinct interface at the land surface, separating the surface from the subsurface domain. These types of models link the subsurface and surface domains via an exchange flux that depends upon the magnitude and direction of the hydraulic gradient across the interface and a proportionality constant (a measure of the hydraulic connectivity). Because experimental evidence of such a distinct interface is often lacking in field systems, there is a need for a more general coupled modeling approach.     

The generation and redistribution of overland flow on a massive oxic soil in a eucalypt woodland within the semi-arid tropics of North Australia

There is a dearth of knowledge on the runoff processes of eucalypt woodland communities in the semi-arid tropics of Australia. The work was undertaken on a 100 m transect of a 0·8 degree hillslope typical of the ‘smooth plainlands’ of central-north Queensland. This paper introduces a new experimental design for measuring overland flow in such areas by way of a cascade system of unbounded runoff plots which allow the inputs and outputs between troughs to be calculated. Most storms generate overland flow. Time to overland flow ranges between 1 and 18 min where rain intensities are above 10mm hr⁻¹ and when the average detention storage of 3·6 mm is exceeded. The bare soil surfaces within the scattered grass understory control the runoff generation process through the temporal variability of field saturated hydraulic conductivity. The study demonstrated that overland flow is mainly redistributed over the freely-draining oxic soil. Some areas export more overland flow than they gain from upslope (runoff), others gain more overland flow than they export (runon). Over the study period only 2 per cent of total rain is transferred out of this 100 m transect as overland flow due to the short duration of storms, the relatively high soil permeability, and the low slope angle. The remainder adds to the large soil water store or deep drainage. The variability of runoff–runon over these ‘smooth plainlands’ highlights how results from bounded plots would be misleading in such areas.     

Threshold relations for the transport of sediment by overland flow on desert hillslopes

Although the Shields relation was developed for rivers, it has been applied to sediment transport by overland flow. According to the Shields relation, where the critical boundary Reynolds number Re_*c exceeds 40, the critical Shields number F_*c is independent of both Re_*c and the ratio of the critical flow depth to particle diameter d_c/D. Analyses of data collected from runoff plots in southern Arizona reveal that F_*c is positively correlated with both Re_*c and d_c/D. Thus the Shields relation does not apply to overland flow on debris-covered desert hillslopes. Multiple regression analysis is employed to develop alternative threshold relations in which critical boundary shear stress τ_c is related to D and d_c/D (R² = 0.782) and to D and S_c (critical gradient) (R² = 0.625). The computed R² values derive in large part from the spurious correlations of d_c/D and S_c with τ_c. Nevertheless, the relations may be utilized to predict τ_c. In this regard, the latter relation is likely to prove more useful than the former because S_c is generally known, whereas d_c is not. An investigation of the functional relation between τ_c and D reveals that τ_c varies approximately with D² for overland flow on the desert hillslopes under study, whereas the Shields relation predicts a linear relation (i.e. a D exponent of 1). This result is consistent with Cheng's data which show that F_*c varies with (d_c/D)^?1 where 0.4 < d_c/D < 2 and may be explained in terms of increased energy dissipation both in separation zones downslope of particles and in distortion of the water surface as d_c/D decreases. Consequently, larger values of τ_c, and hence F_*c, are required to initiate the transport of particles of a given size D as d_c decreases.     

Hydraulics of interrill overland flow on rough,bare soil surfaces

A set of laboratory experiments on bare, rough soil surfaces was carried out to study the relationship between soil surface roughness and its hydraulic resistance. Existing models relating roughness coefficients to a measure of surface roughness did not predict the hydraulic resistance well for these surfaces. Therefore, a new model is developed to predict the hydraulic resistance of the surface, based on detailed surface roughness data. Roughness profiles perpendicular to the flow are used to calculate the wet cross‐sectional area and hydraulic radius given a certain water level. The algorithm of Savat is then applied to calculate the hydraulic resistance. The value for the equivalent roughness, which is used in the algorithm of Savat, could be predicted from the roughness profiles. Here, the tortuosity of the submerged part of the surface was used, which means that the calculated roughness depends on flow depth. The roughness increased with discharge, due to the fact that rougher parts of the surface became submerged at higher discharges. Therefore, a single measure of surface roughness (e.g. random roughness) is not sufficient to predict the hydraulic resistance. The proposed model allows the extension of the flow over the surface with increasing discharge to be taken into account, as well as the roughness within the submerged part of the surface. Therefore, the model is able to predict flow velocities reasonably well from discharge and roughness data only. Copyright © 2000 John Wiley & Sons, Ltd.     

A network theory approach for a better understanding of overland flow connectivity

Hydrological connectivity describes the physical coupling (linkages) of different elements within a landscape regarding (sub‐) surface flows. A firm understanding of hydrological connectivity is important for catchment management applications, for example, habitat and species protection, and for flood resistance and resilience improvement. Thinking about (geomorphological) systems as networks can lead to new insights, which has also been recognized within the scientific community, seeing the recent increase in the use of network (graph) theory within the geosciences. Network theory supports the analysis and understanding of complex systems by providing data structures for modelling objects and their linkages, and a versatile toolbox to quantitatively appraise network structure and properties. The objective of this study was to characterize and quantify overland flow connectivity dynamics on hillslopes in a humid sub‐Mediterranean environment by using a combination of high‐resolution digital‐terrain models, overland flow sensors and a network approach. Results showed that there are significant differences between overland flow connectivity on agricultural areas and semi‐natural shrubs areas. Significant positive correlations between connectivity and precipitation characteristics were found. Significant negative correlations between connectivity and soil moisture were found, most likely because of soil water repellency and/or soil surface crusting. The combination of structural networks and dynamic networks for determining potential connectivity and actual connectivity proved a powerful tool for analysing overland flow connectivity. Copyright © 2016 John Wiley & Sons, Ltd.     

A simple overland flow calculation method for distributed groundwater recharge models

A method to improve the calculation of overland flow in distributed groundwater recharge models is presented and applied to two sub‐catchments in the Thames Basin, UK. Recharge calculation studies tend to simulate the runoff flow component of river flow in a simplistic way, often as a fraction of rainfall over a particular period. The method outlined in this study intends to improve the calculation of groundwater recharge estimates in distributed recharge models but does not present an alternative to complex overland flow simulators. This method uses seasonally varying coefficients to calculate runoff for specified hydrogeological classes or runoff zones, which are used to model baseflow index variations across the basin. It employs a transfer function model to represent catchment storage. Monte Carlo simulation was applied to refine the runoff values. Decoupling the runoff zones between the two sub‐catchments produces a better match between the simulated and observed values; however, the difference between observed runoff and the simulated output indicates other factors, such as landuse and topographical characteristics that affect the generation of runoff flow, need to be taken into account when classifying runoff zones. British Geological Survey © NERC 2011. Hydrological Processes © 2011 John Wiley & Sons, Ltd.     

A generalized transformation approach for simulating steady-state variably-saturated subsurface flow

A numerical method is proposed to accurately and efficiently compute a direct steady-state solution of the nonlinear Richards equation. In the proposed method, the Kirchhoff integral transformation and a complementary transformation are applied to the governing equation in order to separate the nonlinear hyperbolic characteristic from the linear parabolic part. The separation allows the transformed governing equation to be applied to partially- to fully-saturated systems with arbitrary constitutive relations between primary (pressure head) and secondary variables (relative permeability). The transformed governing equation is then discretized with control volume finite difference/finite element approximations, followed by inverse transformation. The approach is compared to analytical and other numerical approaches for variably-saturated flow in 1-D and 3-D domains. The results clearly demonstrate that the approach is not only more computationally efficient but also more accurate than traditional numerical solutions. The approach is also applied to an example flow problem involving a regional-scale variably-saturated heterogeneous system, where the vadose zone is up to 1 km thick. The performance, stability, and effectiveness of the transform approach is exemplified for this complex heterogeneous example, which is typical of many problems encountered in the field. It is shown that computational performance can be enhanced by several orders of magnitude with the described integral transformation approach.     

Estimating time parameters of overland flow on impervious surfaces by the particle tracking method

Abstract

Travel time and time of concentration T_c are important time parameters in hydrological designs. Although T_c is the time for the runoff to travel to the outlet from the most remote part of the catchment, most researchers have used an indirect method such as hydrograph analysis to estimate T_c. A quasi two-dimensional diffusion wave model with particle tracking for overland flow was developed to determine the travel time, and validated for runoff discharges, velocities, and depths. Travel times for 85%, 95% and 100% of particles arrival at the outlet of impervious surfaces (i.e. T_t85, T_t95, and T_t100) were determined for 530 model runs. The correlations between these travel times and T_c estimated from hydrograph analysis showed a significant agreement between T_c and T_t85. All the travel times showed nonlinear relationships with the input variables (plot length, slope, roughness coefficient, and effective rainfall intensity) but showed linear relationships with each other.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi     

A numerical model for simulating Hortonian overland flow on tropical hillslopes with vegetation elements

This paper describes a two‐dimensional hydrodynamic model that characterizes surface runoff process resulting from a varying rainfall intensity event, on an infiltrating soil surface. The soil surface has spatially varied soil physical, hydraulic and microtopographic characteristics. Infiltration process is modelled with the Philip two‐term equation and the time before ponding approximated with the time compression algorithm. Vegetation is modelled as a dynamic component with the modified Gash model. The equation is solved with a modified second order Leapfrog explicit finite difference scheme with centred time and space derivatives. The model was validated with standard analytical solutions. Evaluation with results from field campaigns in the Volta Basin of West Africa during the 2002 rainfall season indicates good agreement, with r² values ranging from 0·89 to 0·96. The developed method will be useful in studying the dynamics of surface runoff generation under complex microtopographic conditions, spatially varying soil hydraulic characteristics and temporally dynamic rainfall intensity, as found in many tropical catchments. Copyright © 2007 John Wiley & Sons, Ltd.     

The effects of topographic depressions on multiscale overland flow connectivity: A high‐resolution spatiotemporal pattern analysis approach based on connectivity statistics

In watershed modelling, the traditional practice of arbitrarily filling topographic depressions in digital elevation models has raised concerns. Advanced high‐resolution remote sensing techniques, including airborne scanning laser altimetry, can identify naturally occurring depressions that impact overland flow. In this study, we used an ensemble physical and statistical modelling approach, including a 2D hydraulic model and two‐point connectivity statistics, to quantify the effects of depressions on high‐resolution overland flow patterns across spatial scales and their temporal variations in single storm events. Computations for both models were implemented using graphic processing unit‐accelerated computing. The changes in connectivity statistics for overland flow patterns between airborne scanning laser altimetry‐derived digital elevation models with (original) and without (filled) depressions were used to represent the shifts of overland flow response to depressions. The results show that depressions can either decrease or increase (to a lesser degree and shorter duration) the probability that any two points (grid locations) are hydraulically connected by overland flow pathways. We used macro‐connectivity states (Φ) as a watershed‐specific indicator to describe the spatiotemporal thresholds of connectivity variability caused by depressions. Four states of Φ are identified in a studied watershed, and each state represents different magnitudes of connectivity and connectivity changes (caused by depressions). The magnitude of connectivity variability corresponds to the states of Φ, which depend on the topological relationship between depressions, the rising/recession limb, and the total rainfall amount in a storm event. In addition, spatial distributions of connectivity variability correlate with the density of depression locations and their physical structures, which cause changes in streamflow discharge magnitude. Therefore, this study suggests that depressions are “nontrivial” in watershed modelling, and their impacts on overland flow should not be neglected. Connectivity statistics at different spatial scales and time points within a watershed provide new insights for characterizing the distributed and accumulated effects of depressions on overland flow.     

A new approach to rapid,desktop-level,environmental flow assessments for rivers in South Africa

Abstract

An approach is presented for desktop-level environmental flow requirement (EFR) determination that is aligned with the Habitat Flow–Stressor Response (HFSR) method which evolved in South Africa over recent years. The HFSR method integrates hydrological, hydraulic and ecological habitat data, involves ecological and hydraulic specialists and is data-intensive and time-consuming. The revised desktop method integrates hydrological information with estimates of channel hydraulic cross-sectional characteristics to generate habitat-type frequencies under changing flow conditions. This information is used with the expected natural habitat requirements to determine acceptable habitat availability under different levels of ecological protection, which is then used with the hydraulic data to define flow regime characteristics that meet the ecological objectives. The paper describes the model components, discusses the assumptions, data requirements and limitations and presents some example results. The revised desktop approach uses approaches that are aligned with the more complex methods and generates results that are similar.

Editor D. Koutsoyiannis; Guest editor M. Acreman

Citation Hughes, D.A., Desai, A.Y., Birkhead, A.L., and Louw, D., 2014. A new approach to rapid, desktop-level, environmental flow assessments for rivers in South Africa. Hydrological Sciences Journal, 59 (3–4), 673–687.     

An infiltration model based on flow variability in macropores: development, sensitivity analysis and applications

Simulating infiltration in soils containing macropores still provides unsatisfactory results, as existing models seem not to capture all relevant processes. Recent studies of macropore flow initiation in natural soils containing earthworm channels revealed a distinct flow rate variability in the macropores depending on the initiation process. When macropore flow was initiated at the soil surface, most of the macropores received very little water while a few macropores received a large proportion of the total inflow. In contrast, when macropore flow was initiated from a saturated or nearly saturated soil layer, macropore flow rate variation was much lower. The objective of this study was to develop, evaluate, and test a model, which combines macropore flow variability with several established approaches to model dual permeability soils. We then evaluate the INfiltration–INitiation–INteraction Model (IN³M) to explore the influence of macropore flow variability on infiltration behavior by performing a sensitivity analysis and applying IN³M to sprinkling and dye tracer experiments at three field sites with different macropore and soil matrix properties. The sensitivity analysis showed that the flow variability in macropores reduces interaction between the macropores and the surrounding soil matrix and thus increases bypass flow, especially for surface initiation of macropore flow and at higher rainfall intensities. The model application shows reasonable agreement between IN³M simulations and field data in terms of water balance, water content change, and dye patterns. The influence of macropore flow variability on the hydrological response of the soil was considerable and especially pronounced for soils where initiation occurs at the soil surface. In future, the model could be applied to explore other types of preferential flow and hence to get a generally better understanding of macropore flow.     

A new approach for phase transitions in miscible multi-phase flow in porous media

The tightly coupled, strongly nonlinear nature of non-isothermal multi-phase flow in porous media poses a tough challenge for numerical simulation. This trait is even more pronounced, if miscibility is also considered. A primary reason why inclusion of miscibility tends to be problematic are the difficulties stemming from phase transitions: on the one hand, phase transitions need to be included since the presence or absence of fluid phases has a major impact on the flow behavior; on the other hand, convergence of the nonlinear solver may be severely affected if they are not handled robustly.In this work, we present a mathematically sound approach to include phase transitions in the nonlinear system of equations: first, the transition conditions are formulated as a set of local inequality constraints, which are then directly integrated into the nonlinear solver using a nonlinear complementarity function. Under this scheme, Newton-Raphson solvers exhibit considerably more robust convergence behaviour compared to some previous approaches, which is then illustrated by several numerical examples.     

A smoothed particle hydrodynamics model for droplet and film flow on smooth and rough fracture surfaces

Flow on fracture surfaces has been identified by many authors as an important flow process in unsaturated fractured rock formations. Given the complexity of flow dynamics on such small scales, robust numerical methods have to be employed in order to capture the highly dynamic interfaces and flow intermittency. In this work we use a three-dimensional multiphase Smoothed Particle Hydrodynamics (SPH) model to simulate surface tension dominated flow on smooth fracture surfaces. We model droplet and film flow over a wide range of contact angles and Reynolds numbers encountered in such flows on rock surfaces. We validate our model via comparison with existing empirical and semi-analytical solutions for droplet flow. We use the SPH model to investigate the occurrence of adsorbed trailing films left behind droplets under various flow conditions and its importance for the flow dynamics when films and droplets coexist. It is shown that flow velocities are higher on prewetted surfaces covered by a thin film which is qualitatively attributed to the enhanced dynamic wetting and dewetting at the trailing and advancing contact lines. Finally, we demonstrate that the SPH model can be used to study flow on rough surfaces.     

A multi-model ensemble approach for the assessment of climatic and anthropogenic impacts on river flow change

ABSTRACT

Climate variability and human activities are considered to be the most likely reasons for negative trends in river inflow and the water level of some lakes and wetlands in the world. To quantify the uncertain impacts of climate variations and anthropogenic activities on Ajichay River flow in Iran, a multi-model ensemble approach based on the Bayesian model averaging (BMA) method is applied. Several statistical and simulation-based methods are used to distinguish the impacts of climatic and anthropogenic factors on river flow. The results show that almost all the methods identified human activities as the dominant impact on streamflow (about 73–85% of the change). The between-model and within-model uncertainty analyses using BMA showed that the 95% uncertainty intervals of the individual approaches have relatively large deviation ranges. The BMA mean prediction could reduce the range of between-model uncertainties to 14–27% for climate impacts and 74–80% for human impacts. This approach provides a way to better understand the contributions of climatic and anthropogenic impacts on river flow change.     

A new two-way nesting technique for ocean modeling based on the smoothed semi-prognostic method

A new two-way nesting technique is presented for a multiple nested-grid ocean modeling system. The new technique uses the smoothed semi-prognostic (SSP) method to exchange information between the different subcomponents of the nested-grid system. Four versions of the new nesting technique are described, together with conventional one-way nesting. The performance of the different nesting techniques is compared, using two independent nested-grid modeling systems, one for the Scotian Shelf of the northwest Atlantic Ocean and the other for the Meso-American Barrier Reef System of the northwestern Caribbean Sea. Nesting using the semi-prognostic method is shown to effectively prevent unrealistic drift of the inner model, while use of the SSP method avoids unnecessary damping of small scales on the inner model grid. Comparison of the annual-mean flow field with the near-surface currents determined by Fratantoni (in J Geophys Res 106:2977–2996, 2001) from observed trajectories of near-surface drifters demonstrates the overall superiority of the nesting technique based on the SSP method.     

A note on benchmarking of numerical models for density dependent flow in porous media

Verification of numerical models for density dependent flow in porous media (DDFPM) by the means of appropriate benchmark problems is a very important step in developing and using these models. Recently, Infinite Horizontal Box (IHB) problem was suggested as a possible benchmark problem for verification of DDFPM codes. IHB is based on Horton–Rogers–Lapwood (HRL) problem. Suitability of this problem for the benchmarking purpose has been investigated in this paper. It is shown that the wavelength of instabilities fails to be a proper criterion to be considered for this problem. However, the threshold of instability formation has been found to be appropriate for benchmarking purpose.     

A hybrid machine learning ensemble approach based on a Radial Basis Function neural network and Rotation Forest for landslide susceptibility modeling: A case study in the Himalayan area,India

In this paper, a hybrid machine learning ensemble approach namely the Rotation Forest based Radial Basis Function (RFRBF) neural network is proposed for spatial prediction of landslides in part of the Himalayan area (India). The proposed approach is an integration of the Radial Basis Function (RBF) neural network classifier and Rotation Forest ensemble, which are state-of-the art machine learning algorithms for classification problems. For this purpose, a spatial database of the study area was established that consists of 930 landslide locations and fifteen influencing parameters (slope angle, road density, curvature, land use, distance to road, plan curvature, lineament density, distance to lineaments, rainfall, distance to river, profile curvature, elevation, slope aspect, river density, and soil type). Using the database, training and validation datasets were generated for constructing and validating the model. Performance of the model was assessed using the Receiver Operating Characteristic (ROC) curve, area under the ROC curve (AUC), statistical analysis methods, and the Chi square test. In addition, Logistic Regression (LR), Multi-layer Perceptron Neural Networks (MLP Neural Nets), Naïve Bayes (NB), and the hybrid model of Rotation Forest and Decision Trees (RFDT) were selected for comparison. The results show that the proposed RFRBF model has the highest prediction capability in comparison to the other models (LR, MLP Neural Nets, NB, and RFDT); therefore, the proposed RFRBF model is promising and should be used as an alternative technique for landslide susceptibility modeling.