A new interpretation of kinematic stormflow generation

The paper reviews a number of possible fast and slow hydrological flow mechanisms to account for rapid runoff generation within a catchment. A new interpretation of the kinematic wave process is proposed which develops some of these concepts to explain rapid subsurface flow from a watershed. Evidence for the process is provided by the results from a laboratory soil core experiment and an investigation of the hydrology of a Dartmoor hillslope. A tension response was monitored in the soil core in which pressure waves were propagated downwards and expelled water from the base. The transmission of the wave down the core was considerably faster than the movement of a chloride tracer. The concept of this kinematic wave process and associated water flux was then extended to the Dartmoor watershed. Raindrops reaching the wet soil surface caused pressure waves to travel laterally downslope. During large rainstorms, the hillslope became hydrologically highly connected and the pressure waves forced existing water from seepage faces into the saturated area adjacent to the stream, contributing substantially to the stream discharge. A kinematic contributing area was defined, as determined by both rainfall–runoff ratios and geostatistical analyses of hillslope soil moisture contents, which extended over at least 65% of the catchment area. This kinematic wave theory is consistent with results of translatory flow and macropore flow models, and stable isotope field studies of ‘old/new’ water. Copyright © 2002 John Wiley & Sons, Ltd.     

Accuracy of the kinematic wave and diffusion wave approximations for time-independent flows with infiltration included

Errors in the kinematic wave and diffusion wave approximation for time-independent (or steady-state) cases of channel flow with infiltration were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors of less than 1·4% for KF²₀≥7·5, and up to 14% for KF²₀≤0·75 for the upstream boundary condition of zero discharge and finite depth, where K is the kinematic wave number and F₀ is the Froude number. The kinematic wave approximation was reasonably accurate except at the channel boundaries and for small values of KF²₀ (≤1). The accuracy of these approximations was significantly influenced by the downstream boundary, both in terms of the magnitude of the error and the segment of the channel reach for which these approximations would be applicable. © 1998 John Wiley & Sons, Ltd.     

The role of overland flow and subsurface flow on the spatial distribution of soil moisture in the topsoil

Many investigations show relationships between topographical factors and the spatial distribution of soil moisture in catchments. However, few quantitative analyses have been carried out to elucidate the role of different hydrological processes in the spatial distribution of topsoil moisture in catchments. A spatially distributed rainfall—runoff model was used to investigate contributions of subsurface matric flow, macropore flow and surface runoff to the spatial distribution of soil moisture in a cultivated catchment. The model results show that lateral subsurface flow in the soil matrix or in macropores has a minor effect on the spatial distribution of soil moisture. Only when a perched groundwater table is maintained long enough, which is only possible if the subsurface is completely impermeable, may a spatial distribution in moisture content occur along the slope. Surface runoff, producing accumulations of soil moisture in flat flow paths of agricultural origin (field boundaries), was demonstrated to cause significant spatial variations in soil moisture within a short period after rainfall (<2 days). When significant amounts of surface runoff are produced, wetter moisture conditions will be generated at locations with larger upstream contributing areas. Copyright © 2001 John Wiley & Sons, Ltd.     

On the controls of preferential flow in soils of different hillslope position and lithological origin

Soils derived from different lithologies and their controls on preferential flow remain underexplored in forested landscapes. In the same lithology, the propensity for preferential flow occurrence at different hillslope positions also remains largely elusive. By utilizing a soil moisture response time method, we compared preferential flow occurrence between a shale site (Shale Hills, silt loam soils) and a sandstone site (Garner Run, sandy loam soils) at four hillslope positions: ridge-top, North- and South-facing mid-slopes and toe slope, for over 2 years. The catchments are neighbouring and covered by temperate forest. For the four hillslope positions, Shale Hills had higher preferential flow frequencies compared to Garner Run. Between these two catchments, the South-facing mid-slope sites showed the highest contrasts in preferential flow frequency (33.5% of events at Shale Hills vs. 8.8% at Garner Run) while the ridge-top sites showed the lowest contrasts (18.7 vs. 13.2%). Additionally, over the unfrozen period, for seven out of eight monitoring sites, drier antecedent conditions tended to be more favourable for preferential flows to occur, with significant (p < .01) relationships at two sites. Except for the South-facing mid-slope sites, both Shale Hills and Garner Run had two preferential flow pathways. The characteristic preferential flow pathways at Shale Hills were the B_w and C horizons, and for Garner Run, preferential flow moved from the E/AE horizon to the B_w horizon. This study shows that shale-derived soils tended to have higher preferential flow occurrence than sandstone soils, but hillslope positions exhibit different levels of contrasts. More effort should be paid to study the impact of lithology on preferential flows in the context of land surface modelling and biogeochemical reactions to improve ecosystem services of headwater catchments.     

Accuracy of kinematic wave and diffusion wave for spatial‐varying rainfall excess over a plane

The kinematic‐wave and diffusive‐wave approximations were investigated for unsteady overland flow resulting from spatially varying rainfall excess. Three types of boundary conditions were adopted: zero flow at the upstream end, and critical flow and zero depth‐gradient at the downstream end. Errors were derived by comparing the dimensionless profiles of the flow depth over the plane with those computed from the dynamic‐wave solution. It was found that the mean errors for both the approximations were independent of the type of rainfall excess distribution for KF₀² > 5, where K is the kinematic‐wave number and F₀ is the Froude number. Therefore, the regions (KF₀², F₀) where the kinematic‐wave and diffusive‐wave solutions would be fairly accurate and for any distribution of spatially varying rainfall, were characterized. The kinematic‐wave approximation was reasonably accurate, with a mean error of less than 5% and for the critical depth at the downstream end, for KF₀² ≥ 20 with F₀ ≤ 1; if the rainfall excess was concentrated in a portion of the plane, the field where the kinematic‐wave solution was found accurate, it was more limited and characterized for KF₀² > 35 with F₀ ≤ 1. The diffusive‐wave solution was in good agreement with the dynamic‐wave solution with a mean error of less than 5%, in the flow depth, for KF₀² ≥ 15 with F₀ ≤ 1; for rainfall excess concentrated in a portion of the plane, the accuracy of the diffusion wave solution was in a region more restricted and defined for KF₀² ≥ 30 with F₀ ≤ 1. For zero‐depth gradient at the downstream end, the accuracy field of the kinematic‐wave was found to be greater and characterized for KF₀² > 10 with F₀ ≤ 1; for rainfall excess concentrated in a portion of the plane, the region was smaller and defined for KF₀² > 15 with F₀ ≤ 1. The diffusive‐wave solution was found accurate in the region defined for KF₀² > 7·5, whereas for rainfall excess concentrated in a portion of the plane, the field of accuracy was for KF₀² > 12·5 with F₀ ≤ 1. The lower limits of the regions, defined on KF₀², can be considered generally valid for both approximations, but for F₀ < 1 smaller lower limits were also characterized. Finally, the accuracy of these approximations was influenced significantly by the downstream boundary condition. Copyright © 2002 John Wiley & Sons, Ltd.     

Accuracy of kinematic wave and diffusion wave approximations for time-independent flows

Errors in the kinematic wave and diffusion wave approximations for time-independent (or steady-state) cases of channel flow were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors in the range 1–2% for values of KF (? 7.5), where K is the kinematic wave number and F₀ is the Froude number. Even for small values of KF (e.g. KF²₀ = 0.75), the errors were typically less than 15%. The accuracy of the diffusion wave approximation was greatly influenced by the downstream boundary condition. The error of the kinematic wave approximation was found to be less than 13% in the region 0.1 ? x ? 0.95 for KF = 7.5 and was greater than 30% for smaller values of KF (? 0.75). This error increased with strong downstream boundary control.     

Numerical simulation of an unsaturated flow equation

A numerical model for an unsaturated flow problem by using the finite element method is established in order to simulate liquid moisture flow In an unsaturated zone with homogeneous soil and deep subsurface water, and with different initial and boundary conditions. For infiltration or evaporation problems, a traditional method usually yields oscillatory non-physics profiles. However, nonoscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method. Moreover, the kind of boundary condition is handled very well. Project supported by the National Key Project of Fundamental Research ”Climate Dynamics and Climate Prediction Theory“ and China Postdoctoral Science Foundation.     

Scale invariance and self‐similarity in kinematic wave overland flow in space and time

Fractals are famous for their self‐similar nature at different spatial scales. Similar to fractals, solutions of scale invariant processes are self‐similar at different space–time scales. This unique property of scale‐invariant processes can be utilized to translate the solution of the processes at a much larger or smaller space–time scale (domain) based on the solution calculated on the original space–time scale. This study investigates scale invariance conditions of kinematic wave overland flow process in one‐parameter Lie group of point transformations framework. Scaling (stretching) transformation is one of the one‐parameter Lie group of point transformations and it has a unique importance among the other transformations, as it leads to the scale invariance or scale dependence of a process. Scale invariance of a process yields a self‐similar solution at different space–time scales. However, the conditions for the process to be scale invariant usually dictate various relationships between the scaling coefficients of the dependent and independent variables of the process. Therefore, the scale invariance of a process does not assure a self‐similar solution at any arbitrary space and time scale. The kinematic wave overland flow process is modelled mathematically as initial‐boundary value problem. The conditions to be satisfied by the system of governing equations as well as the initial and boundary conditions of the kinematic wave overland flow process are established in order for the process to be scale invariant. Also, self‐similarity of the solution of the kinematic wave overland flow under the established invariance conditions is demonstrated by various numerical example problems. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimation of field irrigation water demand based on lumped kinematic wave model considering soil moisture balance

An estimation model of farm field irrigation water demand is developed. The model is based on the lumped kinematic wave model considering soil water balance. The lumped model approach reduces the computational load in rainfall-runoff analysis and allows application to large river basins. Evapotranspiration is estimated on hourly basis by the improvement of FAO’s method. Not only water volume necessary for farm field irrigation but also the number of the water charge and its interval can be estimated by the combined use of the lumped runoff model and the hourly evapotranspiration model.     

Errors of kinematic wave and diffusion wave approximations for time‐independent flows with infiltration and momentum exchange included

Error equations for kinematic wave and diffusion wave approximations were derived for time‐independent flows on infiltrating planes and channels under one upstream boundary and two downstream boundary conditions: zero flow at the upstream boundary, and critical flow depth and zero depth gradient at the downstream boundary. These equations specify error in the flow hydrograph as a function of space. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors below 2% for values of KF (e.g. KF ≥ 7·5), where K is the kinematic wave number and F is the Froude number. Even for small values of KF (e.g. KF = 2·5), the errors were typically less than 3%. The accuracy of the diffusive approximation was greatly influenced by the downstream boundary condition. For critical flow depth downstream boundary condition, the error of the kinematic wave approximation was found to be less than 10% for KF ≥ 7·5 and greater than 20% for smaller values of KF. This error increased with strong downstream boundary control. The analytical solution of the diffusion wave approximation is adequate only for small values of K. Copyright © 2005 John Wiley & Sons, Ltd.     

A constitutive model for water flow in unsaturated fractured rocks

A conceptual model for describing effective saturation in fractured hard rock is presented. The fracture network and the rock matrix are considered as an equivalent continuum medium where each fracture is conceptualized as a porous medium of granular structure and the rock matrix is assumed to be impermeable. The proposed model is based on the representation of a rough‐walled fracture by an equivalent porous medium, which is described using classical constitutive models. A simple closed‐form equation for the effective saturation is obtained when the van Genuchten model is used to describe saturation inside fractures and fractal laws are assumed for both aperture and number of fractures. The relative hydraulic conductivity for the fractured rock is predicted from a simple relation derived by Liu and Bodvarsson. The proposed constitutive model contains three independent parameters, which may be obtained by fitting the proposed effective saturation curve to experimental data. Two of the model parameters have physical meaning and can be identified with the reciprocal of the air entry pressure values in the fractures of minimum and maximum apertures. Effective saturation and relative hydraulic conductivity curves match fairly well the simulated constitutive relations obtained by Liu and Bodvarsson. Copyright © 2008 John Wiley & Sons, Ltd.     

Stochastic analysis of bounded unsaturated flow in heterogeneous aquifers: Spectral/perturbation approach

This paper describes a stochastic analysis of steady state flow in a bounded, partially saturated heterogeneous porous medium subject to distributed infiltration. The presence of boundary conditions leads to non-uniformity in the mean unsaturated flow, which in turn causes non-stationarity in the statistics of velocity fields. Motivated by this, our aim is to investigate the impact of boundary conditions on the behavior of field-scale unsaturated flow. Within the framework of spectral theory based on Fourier–Stieltjes representations for the perturbed quantities, the general expressions for the pressure head variance, variance of log unsaturated hydraulic conductivity and variance of the specific discharge are presented in the wave number domain. Closed-form expressions are developed for the simplified case of statistical isotropy of the log hydraulic conductivity field with a constant soil pore-size distribution parameter. These expressions allow us to investigate the impact of the boundary conditions, namely the vertical infiltration from the soil surface and a prescribed pressure head at a certain depth below the soil surface. It is found that the boundary conditions are critical in predicting uncertainty in bounded unsaturated flow. Our analytical expression for the pressure head variance in a one-dimensional, heterogeneous flow domain, developed using a nonstationary spectral representation approach [Li S-G, McLaughlin D. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour Res 1991;27(7):1589–605; Li S-G, McLaughlin D. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour Res 1995; 31(3):541–51], is precisely equivalent to the published result of Lu et al. [Lu Z, Zhang D. Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via Kirchhoff transformation. Adv Water Resour 2004;27:775–84].     

Accuracy of kinematic wave and diffusion wave approximations for space-independent flows on infiltrating surfaces with lateral inflow neglected in the momentum equation

Error equations for the kinematic wave and diffusion wave approximations with lateral inflow neglected in the momentum equation are derived under simplified conditions for space-independent flows. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions are parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel-bed slope, lateral inflow, infiltration and channel roughness when the initial condition is non-vanishing; it reflects the effect of bed slope, channel roughness and acceleration due to gravity when the initial condition is vanishing. The error equations are found to be the Riccati equation. The structure of the error equations in the case when the momentum equation neglects lateral inflow is different from that when the lateral inflow is included.     

Differences in gravity‐dominated unsaturated flow during autumn rains and snowmelt

Five tracer experiments have been performed in a coarse‐textured soil near the new main airport at Gardermoen, Norway. In two lysimeter walls, 30 and 40 measuring points form the basis for spatial moment calculations. Although experiments were performed under different meteorological conditions (autumn and snowmelt) and at two different sites, the ratios of centres of vertical mass over cumulative infiltration were of the same order of magnitude, indicating a gravity‐dominated flow. Two‐dimensional transport simulations with SUTRA (Voss, 1984), with a priori estimated input parameters and random fields of soil hydraulic properties revealed a relatively good agreement with the experimental results. Three possible sources of heterogeneity affecting the vertical displacement of solute during snowmelt were identified: variability of soil physical properties, soil surface elevations and variability of ground frost during the melting period. To obtain accurate predictions, soil heterogeneity was the most important factor to characterize for the coarse‐textured soil under consideration. Copyright © 1999 John Wiley & Sons, Ltd.     

Unified macroscopic model for unsaturated water flow in soils of bimodal porosity

Abstract

Natural soils very often contain micro- and macropores, having different hydraulic properties. At the macroscopic scale, the unsaturated flow in such soils can be described with various models, depending on the hydraulic diffusivity ratio of the components and the connectivity of the most conductive component. Three macroscopic models recently derived by the homogenization method are discussed. The limit passages between the models are studied. A unified model suitable for the entire range of the hydraulic diffusivity ratio is proposed. A numerical example shows the application of the model to macroscopically one-dimensional infiltration in a porous medium containing inclusions. A parametric study for varying conductivity (diffusivity) ratio is performed.     

Coupling the Xinanjiang model to a kinematic flow model based on digital drainage networks for flood forecasting

The Xinanjiang model, which is a conceptual rainfall‐runoff model and has been successfully and widely applied in humid and semi‐humid regions in China, is coupled by the physically based kinematic wave method based on a digital drainage network. The kinematic wave Xinanjiang model (KWXAJ) uses topography and land use data to simulate runoff and overland flow routing. For the modelling, the catchment is subdivided into numerous hillslopes and consists of a raster grid of flow vectors that define the water flow directions. The Xinanjiang model simulates the runoff yield in each grid cell, and the kinematic wave approach is then applied to a ranked raster network. The grid‐based rainfall‐runoff model was applied to simulate basin‐scale water discharge from an 805‐km² catchment of the Huaihe River, China. Rainfall and discharge records were available for the years 1984, 1985, 1987, 1998 and 1999. Eight flood events were used to calibrate the model's parameters and three other flood events were used to validate the grid‐based rainfall‐runoff model. A Manning's roughness via a linear flood depth relationship was suggested in this paper for improving flood forecasting. The calibration and validation results show that this model works well. A sensitivity analysis was further performed to evaluate the variation of topography (hillslopes) and land use parameters on catchment discharge. Copyright © 2009 John Wiley & Sons, Ltd.     

Estimating macropore and matrix flow using the hydrograph separation procedure in an experimental forest plot

This study was conducted to estimate macropore space, macropore flow and matrix flow in an experimental forest plot in the Ouachita Mountains of Arkansas. Lateral soil water fluxes and soil capillary potentials were observed in the isolated plot during applied rainfall experiments. Rainfalls were applied 17 times during the period 17 July to 10 October 1991. The subsurface hydrograph separation technique was used to estimate macropore space, macropore flux and matrix flux. The boundary between macropore and matrix flow was statistically determined by covariance analysis. The maximum estimated lateral macropore space was approximately 0.006 (cm³ cm^?3). The maximum estimated lateral macropore and matrix flow were 0.042 and 0.00066 cm s^?1, respectively. This report also emphasizes the need for further research on the hydrograph separation procedure for estimating macropores and macropore flow.     

A sensor array system for profiling moisture in unsaturated rock and soil

As the scope of hydrologic investigations extend deeper into the subsurface profile, and increasingly include fractured rock, there is a growing need for techniques that can accurately monitor saturation changes at a high spatial and temporal resolution in this environment. We have developed a technique, the Electrical Resistance Sensor Array System (ERSAS), to track moisture dynamics in vadose zone regions that include both fractured rock and soil. The performance of ERSAS was compared with the time domain reflectometry (TDR) technique under controlled and field conditions. We found that ERSAS was effective in determining patterns of saturation changes along vertical soil/rock profiles. Because of the small size of individual sensors, it was able to resolve travel times associated with a wetting front and peak saturation better than TDR. In addition, ERSAS is significantly cheaper than the TDR system, and the sensor arrays are relatively easier to install in the subsurface profile. Published in 2011 by John Wiley & Sons, Ltd.     

Lateral water flux in the unsaturated zone: A mechanism for the formation of spatial soil heterogeneity in a headwater catchment

Measurements of soil water potential and water table fluctuations suggest that morphologically distinct soils in a headwater catchment at the Hubbard Brook Experimental Forest in New Hampshire formed as a result of variations in saturated and unsaturated hydrologic fluxes in the mineral soil. Previous work showed that each group of these soils had distinct water table fluctuations in response to precipitation; however, observed variations in soil morphology also occurred above the maximum height of observed saturation. Variations in unsaturated fluxes have been hypothesized to explain differences in soil horizon thickness and presence/absence of specific horizons but have not been explicitly investigated. We examined tensiometer and shallow groundwater well records to identify differences in unsaturated water fluxes among podzols that show distinct morphological and chemical differences. The lack of vertical hydraulic gradients at the study sites suggests that lateral unsaturated flow occurs in several of the soil units. We propose that the variations in soil horizon thickness and presence/absence observed at the site are due in part to slope‐parallel water flux in the unsaturated portion of the solum. In addition, unsaturated flow may be involved in the translocation of spodic material that primes those areas to contribute water with distinct chemistry to the stream network and represents a potential source/sink of organometallic compounds in the landscape.