Diverging overland flow

This study investigates divering overland flow utilizing kinematic wave theory, which does not appear to have been dealt with previously. Explicit analytical solutions are derived in dimensionless form for space-time invariant rainfall. Analytical solutions do not seem to be tractable for time-varying rainfall. Depending upon the duration of rainfall, equilibrium and partial equilibrium cases are distinguished explicitly. The effect of divergence parameter on the hydrograph shape is shown. The adequacy of kinematic approximation for characterization of diverging overland flow is tested against laboratory watershed results. The diverging overland flow model is found to yield results which compare well with observations and with those of a plane model.     

Study on effect of surface roughness on overland flow from different geometric surfaces through numerical simulation

Effect of variability in surface roughness on overland flow from different geometric surfaces is investigated using numerical solution of diffusion wave equation. Three geometric surfaces rectangular plane, converging and diverging plane at slopes 1 to 3% are used. Overland flow is generated by applying rainfall at constant intensity of 10 mm/h for period 30 min and 100 min. Three scenarios of spatial roughness conditions viz. roughness increasing in downstream direction, roughness decreasing in downstream direction and roughness distributed at random are considered. Effect of variability of roughness on overland flow in terms of depth, velocity of flow and discharge along the distance from upstream to downstream for different geometric surfaces are discussed in detail. Results from the study indicate that roughness distribution has significant effect on peak, time to peak and overall shape of the overland flow hydrograph. The peak occurs earlier for the scenario when roughness increases in downstream direction as compared to scenario when roughness is decreasing in downstream for all three geometric surfaces due to very low friction factor and more velocity at the top of the domain. The converging plane attains equilibrium state early as compared to rectangular and diverging plane. Different set of random values result in different time to peak and shape of hydrograph for rectangular and diverging plane. However, in case of converging plane, the shape of computed hydrographs remains almost similar for different sets of random roughness values indicating stronger influence of converging geometry than effect due to variation of roughness sequence on computed runoff hydrograph. Hierarchically, the influence of geometry on overland flow is stronger than the influence of slope and the influence of slope is stronger than the influence of roughness. Copyright © 2013 John Wiley & Sons, Ltd.     

Velocities of shallow overland flow on semiarid hillslopes

A series of 188 rainfall plot simulations was conducted on grass, shrub, oak savanna, and juniper sites in Arizona and Nevada. A total of 897 flow velocity measurements were obtained on 3.6% to 39.6% slopes with values ranging from 0.007 m s^‐1 to 0.115 m s^‐1. The experimental data showed that shallow flow velocity on rangelands was related to discharge and ground litter cover and was largely independent of slope gradient or soil characteristics. A power model was proposed to express this relationship. These findings support the slope–velocity equilibrium hypothesis. Namely, eroding soil surfaces evolve such that steeper areas develop greater hydraulic roughness. As a result overland flow velocity becomes independent of the slope gradient over time. Our findings have implications for soil erosion modeling suggesting that hydraulic friction is a dynamic, slope and discharge dependent property. Copyright © 2018 John Wiley & Sons, Ltd.     

Modelling effects of spatial variability of saturated hydraulic conductivity on autocorrelated overland flow data: linear mixed model approach

The mixed linear model approach was introduced and applied in studying the effects of spatial variation of the saturated hydraulic conductivity (K _s ) on the variation of the overland flow. Analysis was carried out with 2,000 rainfall-runoff events, all generated through transformation of real, observed rainfall events and different spatially variable K _s fields in a small (12 ha) agricultural catchment. The parameters accounting for the variation in the generation method were the coefficient of variation (cv) and correlation length (L _x L _y ) of K _s both having two levels of values obtained from field measurements of other studies. The analysis showed that the combinations with both parameters having the smaller or bigger value during flow peaks only caused different response in the overland flow. However, the parameters were statistically significant only at the 10% level. Most of the flow variation was explained by the event dynamics. The mixed models were able to model the structure of the data efficiently with less restrictive assumptions than for example the analysis of variance, hence producing more reliable results. The method was able to take into account autocorrelation of the test series, correlation between the factors and unequal variances. The usefulness of the method was supported by the fact that the conclusions drawn by it were confirmed by simple, conventional methods of a previous study, added with statistical criteria and confidence levels for each calculation moment. The findings of the study can be utilized in practise for example when designing the field sampling experiments.     

Conjunctive surface-subsurface modeling of overland flow

In this paper, details of a conjunctive surface-subsurface numerical model for the simulation of overland flow are presented. In this model, the complete one-dimensional Saint-Venant equations for the surface flow are solved by a simple, explicit, essentially non-oscillating (ENO) scheme. The two-dimensional Richards equation in the mixed form for the subsurface flow is solved using an efficient strongly implicit finite-difference scheme. The explicit scheme for the surface flow component results in a simple method for connecting the surface and subsurface components. The model is verified using the experimental data and previous numerical results available in the literature. The proposed model is used to study the two-dimensionality effects due to non-homogeneous subsurface characteristics. Applicability of the model to handle complex subsurface conditions is demonstrated.     

Assessing the impact of the hydraulic properties of a crusted soil on overland flow modelling at the field scale

Soil surface crusts are widely reported to favour Hortonian runoff, but are not explicitly represented in most rainfall‐runoff models. The aim of this paper is to assess the impact of soil surface crusts on infiltration and runoff modelling at two spatial scales, i.e. the local scale and the plot scale. At the local scale, two separate single ring infiltration experiments are undertaken. The first is performed on the undisturbed soil, whereas the second is done after removal of the soil surface crust. The HYDRUS 2D two‐dimensional vertical infiltration model is then used in an inverse modelling approach, first to estimate the soil hydraulic properties of the crust and the subsoil, and then the effective hydraulic properties of the soil represented as a single uniform layer. The results show that the crust hydraulic conductivity is 10 times lower than that of the subsoil, thus illustrating the limiting role the crust has on infiltration. Moving up to the plot scale, a rainfall‐runoff model coupling the Richards equation to a transfer function is used to simulate Hortonian overland flow hydrographs. The previously calculated hydraulic properties are used, and a comparison is undertaken between a single‐layer and a double‐layer representation of the crusted soil. The results of the rainfall‐runoff model show that the soil hydraulic properties calculated at the local scale give acceptable results when used to model runoff at the plot scale directly, without any numerical calibration. Also, at the plot scale, no clear improvement of the results can be seen when using a double‐layer representation of the soil in comparison with a single homogeneous layer. This is due to the hydrological characteristics of Hortonian runoff, which is triggered by a rainfall intensity exceeding the saturated hydraulic conductivity of the soil surface. Consequently, the rainfall‐runoff model is more sensitive to rainfall than to the subsoil's hydrodynamic properties. Therefore, the use of a double‐layer soil model to represent runoff on a crusted soil does not seem necessary, as the increase of precision in the soil discretization is not justified by a better performance of the model. Copyright © 2005 John Wiley & Sons, Ltd.     

Do not only connect: a model of infiltration‐excess overland flow based on simulation

The paper focusses on connectivity in the context of infiltration‐excess overland flow and its integrated response as slope‐base overland flow hydrographs. Overland flow is simulated on a sloping surface with some minor topographic expression and spatially differing infiltration rates. In each cell of a 128 × 128 grid, water from upslope is combined with incident rainfall to generate local overland flow, which is stochastically routed downslope, partitioning the flow between downslope neighbours. Simulations show the evolution of connectivity during simple storms. As a first approximation, total storm runoff is similar everywhere, discharge increasing proportionally with drainage area. Moderate differences in plan topography appear to have only a second‐order impact on hydrograph form and runoff amount. Total storm response is expressed as total runoff, runoff coefficient or total volume infiltrated; each plotted against total storm rainfall, and allowing variations in average gradient, overland flow roughness, infiltration rate and storm duration. A one‐parameter algebraic expression is proposed that fits simulation results for total runoff, has appropriate asymptotic behaviour and responds rationally to the variables tested. Slope length is seen to influence connectivity, expressed as a scale distance that increases with storm magnitude and can be explicitly incorporated into the expression to indicate runoff response to simple events as a function of storm size, storm duration, slope length and gradient. The model has also been applied to a 10‐year rainfall record, using both hourly and daily time steps, and the implications explored for coarser scale models. Initial trails incorporating erosion continuously update topography and suggest that successive storms produce an initial increase in erosion as rilling develops, while runoff totals are only slightly modified. Other factors not yet considered include the dynamics of soil crusting and vegetation growth. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluating overland flow sediment transport capacity

An equation for evaluating the sediment transport capacity of overland flow is a necessary part of a physically based soil erosion model describing sediment detachment and transport as distributed processes. At first, for the hydraulic conditions of small-scale and large-scale roughness, the sediment transport capacity relationship used in the WEPP model is calibrated by Yalin and Govers' equation. The analysis shows that the transport coefficient K_t depends on the Shields parameter, Y, according to a semi-logarithmic (Yalin) or a linear (Govers) equation. The reliability of the semi-logarithmic equation is verified by Smart's, and Aziz and Scott's experimental data. Then the Low's formula, whose applicability is also proved by Smart's, and Aziz and Scott's data, is transformed as a stream power equation in which a stream power coefficient, K_SP, depending on Shields parameter, slope, sediment and water-specific weight, appears. A relationship between transport capacity and effective stream power is also proposed. Finally, the influence of rainfall on sediment transport capacity and the prediction of critical shear stress corresponding to overland flow are examined. © 1998 John Wiley & Sons, Ltd.     

Distributed dynamic modelling of interrill overland flow

A distributed, dynamic, process-based model for interrill overland flow that has previously been shown to predict accurately both total runoff and runoff hydraulics for a site on semi-arid shrubland is assessed in terms of (i) its portability, (ii) its sensitivity to the quality of data inputs, and (iii) its sensitivity to the size of cell used in the model. It is found that the model can be used at another site, but only after modifications to take account of the local controls of runoff routing. The model is portable, but not readily so. The model is sensitive to both the quality of data input and the size of cell. Data input cannot be reduced by use of stochastic distribution of model parameters without significant loss of accuracy in model predictions, particularly of runoff hydraulics. Larger cells produce poorer predictions of the runoff hydrograph. It is concluded that process-based modelling of interrill runoff may not be a realistic tool for predicting soil erosion, but is one that may be useful for identification of our present poor understanding of erosion processes. Such models help to define the research agenda for soil erosion studies. © 1997 John Wiley & Sons, Ltd.     

Sediment-transport competence of rain-impacted interrill overland flow

Laboratory experiments to determine the maximum size of sediment transported in shallow, rain-impacted flow were conducted in a recirculating flume 4·80 m long and 0·50 m wide. Rainfall intensities were varied between 51 and 138 mm h⁻¹, flow was introduced from a header tank into the flume at rates ranging from 0 to 0·64 l s⁻¹, and experiments were conducted on gradients between 3·5 and 10°. The following equation was developed: ML = (REFE)^1·6363 in which M is particle mass, L is distance moved in unit time (cm min⁻¹), RE is rainfall energy (J m⁻² s⁻¹) and FE is flow energy (J m⁻² s⁻¹). This equation can be used to predict sediment-transport competence of interrill overland flow. The equation is limited in its utility insofar as it has been developed using quartz grains and takes no account of variations in absorption of rain energy by natural ground surfaces. © 1998 John Wiley & Sons, Ltd.     

Partitioning resistance to overland flow on rough mobile beds

For overland flows transporting predominantly bed load over rough mobile beds without rainfall, resistance to flow f may be divided into four components: surface resistance f_s, form resistance f_f, wave resistance f_w, and bed‐mobility resistance f_m. In this study it is assumed that f = f_s + f_f + f_w + f_m, and an equation is developed for each component. The equations for f_s and f_f are borrowed from the literature, while those for f_w and f_m are developed from two series of flume experiments in which the beds are covered with various concentrations of large‐scale roughness elements. The first series consists of 65 experiments on fixed beds, while the second series contains 194 experiments on mobile beds. All experiments were performed on the same slope (S = 0·114) and with the same size of sediment (D = 0·00074 m). The equations for f_w and f_m are derived by a combination of dimensional analysis and regression analysis. The analyses reveal that the major controls of f_w and f_m are the Froude number F and the concentration of the roughness elements C_r. When the equations for f_w and f_m are summed, the C_r terms cancel out, leaving f_w+m = 0·63F^?2. An equation is developed that predicts total f, and the contributions of f_s, f_f, f_w and f_m to f are computed from the series 1 and 2 experiments. An analysis of the first series reveals that in clear‐water flows over fixed beds, f_w accounts for 52 per cent of f. A similar analysis of the second series indicates that in sediment‐laden flows over mobile beds f_w comprises 37 per cent and f_m 32 per cent of f, so that together f_w and f_m account for almost 70 per cent of f. Finally, regression analyses indicate that where F > 0·5, f_w and f_m each vary with F^?2 and f_w/f_m = 1·18. The equation developed here for predicting total f applies only to the range of hydraulic, sediment, and bed roughness conditions represented by the experimental data. With additional data from a broader range of conditions the same methodology as employed here could be used to develop a more general equation. Copyright © 2006 John Wiley & Sons, Ltd.     

The effect of bed mobility on resistance to overland flow

When sediment grains are transported as bed load in overland flow, there is a net transfer of momentum from the flow to the grains. When these grains collide with other grains, whether on the bed or in the flow, streamwise flow velocity decreases and resistance to flow increases. Resistance to flow generated in this manner is termed bed‐load transport resistance. Resistance to flow f over a plane bed may be partitioned into grain resistance f_g and bed‐load transport resistance f_bt. We use the symbols f_btf and f_btm to denote f_bt for flows over fixed beds and over mobile beds, respectively, and we compute the effect of bed mobility on flow resistance f_mob by subtracting f_btf from f_btm. The data for this study come from 54 flume experiments with fixed beds and 38 with mobile beds. On average f_mob is approximately equal to half of f_btm, which is about one‐quarter of f. Hence, f_mob is about one‐tenth of f. Predictive equations are developed for f_btf, f_btm and f_mob using dimensional analysis to identify the relevant independent variables and regression analysis to evaluate the coefficients associated with these variables. Values of f_mob are always positive which implies that mobile beds offer greater resistance to flow than do fixed beds. Evidently bed‐load grains colliding with mobile beds lose more momentum to the bed than do grains colliding with fixed beds. In other words, grain collisions with mobile beds are less elastic than those with fixed beds. Copyright © 2005 John Wiley & Sons, Ltd.     

Effect of saltating sediment on flow resistance and bed roughness in overland flow

The acceleration of saltating grains by overland flow causes momentum to be transferred from the flow to the grains, thereby increasing flow resistance and bed roughness. To assess the impact of saltating sediment on overland flow hydraulics, velocity profiles in transitional and turbulent flows on a fixed sand-covered bed were measured using hot-film anemometry. Five discharges were studied. At each discharge, three flows were measured: one free of sediment, one with a relatively low sediment load, and one with a relatively high sediment load. In these flows from 83 to 90 per cent of the sediment was travelling by saltation. As a result, in the sediment-laden flows the near-bed velocities were smaller and the velocity profiles steeper than those in the equivalent sediment-free flows. Sediment loads ranged up to 87·0 per cent of transport capacity and accounted for as much as 20·8 per cent of flow resistance (measured by the friction factor) and 89·7 per cent of bed roughness (measured by the ratio of the roughness length to median grain diameter). It is concluded that saltating sediment has a considerable impact on overland flow hydraulics, at least on fixed granular beds. Saltation is likely to have a relatively smaller effect on overland flow on natural hillslopes and agricultural fields where form and wave resistance dominate. Still, saltation is generally of greater significance in overland flow than in river flow, and for this reason its effect on overland flow hydraulics is deserving of further study. © 1998 John Wiley & Sons, Ltd.     

Transporting capacity of overland flow on plane and on irregular beds

In this paper the transporting capacity of thin flows, in the laminar and transitional flow regime, is studied. Experiments were carried out on irregular as well as on plane beds, using two totally different set-ups. The results of these two types of experiment were convergent. In both cases, sediment concentration was clearly related to grain shear velocity and unit stream power, expressed as the product of mean velocity and slope (Yang, 1973). The data agreed with those of Kramer and Meyer (1969). For a sandy bed, the unit stream power relationship was able to predict reasonably well the sediment concentrations measured on a mulched surface. For laminar and transitional flows, both the unit stream power and the shear velocity are related in the same way to slope and unit discharge. The unit stream power is a parameter which in particular can be very easily measured and might therefore become useful in obtaining a quick estimate of the transporting capacity of a thin flow. However, before a sediment transport equation for thin flows can be developed, more information is needed about the influence of the flow regime and grain size and density.     

Modelling plumes of overland flow from logging tracks

Most land‐based forestry systems use extensive networks of unsealed tracks to access the timber resource. These tracks are normally drained by constructing cross‐banks, or water bars, across the tracks immediately following logging. Cross‐banks serve three functions in controlling sediment movement within forestry compartments:

• 1. they define the specific catchment area of the snig track (also known as skid trails) so that the overland flow does not develop sufficient energy to cause gullies, and sheet and rill erosion is reduced;
• 2. they induce some sediment deposition as flow velocity reduces at the cross‐bank;
• 3. they redirect overland flow into the adjacent general harvesting area (GHA) so that further sediment deposition may take place.

This paper describes a simple model that predicts the third of these functions in which the rate of runoff from the track is combined with spatial attributes of the track and stream network. Predictions of the extent of the overland flow plumes and the volume of water delivered to streams is probabilistically presented for a range of rainfall‐event scenarios with rainfall intensity, time since logging and compartment layout as model inputs. Generic equations guiding the trade‐off between intercross‐bank length and flow path distance from cross‐bank outlet to the stream network needed for infiltration of track runoff are derived. Copyright © 2002 John Wiley & Sons, Ltd. Copyright © 2002 John Wiley & Sons, Ltd.     

Field studies of sediment transport by overland flow

Field studies on sandy soils of the Cottenham Series in mid-Bedfordshire show that the mean annual rate of sediment transport by overland flow on an 11° mid-slope is 98 g cm¹. The feasibility of using sediment transport equations to predict erosion by overland flow on a storm basis is examined by comparing the observed values of sediment yield with values predicted by four sediment transport equations and a regression equation which relates soil loss to runoff energy and rainfall energy. An expression combining Engelund's sediment transport capacity equation and the Manning equation for flow velocity, as modified by Savat for disturbed flow, best reflects field conditions. Although there is a significant correlation (r = 0.69; n 30) between the observed and predicted values using this expression, the coefficient of determination is too low for predictive purposes. Reasons for this are presented.     

Effects of sediment load on hydraulics of overland flow on steep slopes

Eroded sediment may have significant effects on the hydraulics of overland flow, but few studies have been performed to quantify these effects on steep slopes. This study investigated the potential effects of sediment load on Reynolds number, Froude number, flow depth, mean velocity, Darcy–Weisbach friction coefficient, shear stress, stream power, and unit stream power of overland flow in a sand‐glued hydraulic flume under a wide range of hydraulic conditions and sediment loads. Slope gradients were varied from 8·7 to 34·2%, unit flow rates from 0·66 to 5·26×10^?3 m² s^?1, and sediment loads from 0 to 6·95 kg m^?1 s^?1. Both Reynolds number (Re) and Froude number (Fr) decreased as sediment load increased, implying a decrease in flow turbulence. This inverse relationship should be considered in modeling soil erosion processes. Flow depth increased as sediment load increased with a mean value of 1·227 mm, caused by an increase in volume of sediment‐laden flow (contribution 62·4%) and a decrease in mean flow velocity (contribution 37·6%). The mean flow velocity decreased by up to 0·071 m s^?1 as sediment load increased. The Darcy–Weisbach friction coefficient (f) increased with sediment load, showing that the total energy consumption increased with sediment load. The effects of sediment load on f depended on flow discharge: as flow discharge increased, the influence of sediment load on f decreased due to increased flow depth and reduced relative roughness. Flow shear stress and stream power increased with sediment load, on average, by 80·5% and 60·2%, respectively; however, unit stream power decreased by an average of 11·1% as sediment load increased. Further studies are needed to extend and apply the insights obtained under these controlled conditions to real‐world overland flow conditions. Copyright © 2010 John Wiley & Sons, Ltd.     

Generalized conceptual modeling of dimensionless overland flow hydrographs

The rising and recession limbs of conceptual dimensionless overland flow hydrographs are calculated for specific values of the rating exponent in the range 1 ≤ m ≤ 3, including a linear reservoir (m = 1); 100% turbulent Chezy friction (m = 3/2); 100% turbulent Manning friction (m = 5/3); 67% turbulent Chezy (or 75% turbulent Manning) (m = 2); and 100% laminar flow (m = 3). These conceptual overland flow hydrographs show finite amounts of diffusion, increasing with decreasing rating exponent, unlike the kinematic wave hydrograph, which is nondiffusive.     

Predicting sediment transport by interrill overland flow on rough surfaces

Modelling soil erosion requires an equation for predicting the sediment transport capacity by interrill overland flow on rough surfaces. The conventional practice of partitioning total shear stress into grain and form shear stress and predicting transport capacity using grain shear stress lacks rigour and is prone to underestimation. This study therefore explores the possibility that inasmuch as surface roughness affects flow hydraulic variables which, in turn, determine transport capacity, there may be one or more hydraulic variables which capture the effect of surface roughness on transport capacity suffciently well for good predictions of transport capacity to be achieved from data on these variables alone. To investigate this possibility, regression analyses were performed on data from 1506 flume experiments in which discharge, slope, water temperature, rainfall intensity, and roughness size, shape and concentration were varied. The analyses reveal that 89·8 per cent of the variance in transport capacity can be accounted for by excess flow power and flow depth. Including roughness size and concentration in the regression improves that explained variance by only 3·5 per cent. Evidently, flow depth, when used in combination with excess flow power, largely captures the effect of surface roughness on transport capacity. This finding promises to simplify greatly the task of developing a general sediment equation for interrill overland flow on rough surfaces. Copyright © 1998 John Wiley & Sons, Ltd.