Mathematical properties of the kinematic cascade

Kibler, David F.; Woolhiser, David A.

doi:10.1016/0022-1694(72)90123-0

Cited by 37 publications

(14 citation statements)

References 5 publications

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“…Conversely, as the rainfall rate decreases, tp(X) will increase until, at some rainfall rate rcrit , ponding will not occur at x = L. For lower rainfall rates the runoff/run-on phenomenon will always occur. In the characteristic solution the run-on front must be represented by a kinematic shock [Smith, 1972], and a shock-following scheme [Kibler and Woolhiser, 1972] must be included in the program.…”

Section: Hydrographs For Cases 4 5 and 6 Insupporting

confidence: 51%

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Effects of Spatial Variability of Saturated Hydraulic Conductivity on Hortonian Overland Flow

Woolhiser¹,

Smith²,

Giráldez³

1996

Water Resources Research

155

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Many field investigations have documented the existence of significant spatial variability of the saturated hydraulic conductivity Ks in typical catchments, and several modeling studies have examined the effects of this variability on Hortonian surface runoff. However, these modeling studies had limitations, and some could not deal adequately with possible runoff/run-on phenomena where areas of low saturated hydraulic conductivities K s are upstream of areas of higher K s . The kinematic wave equations with interactive Smith-Parlange infiltration are solved by a finite-difference scheme on a characteristic computational net. It is shown that runoff hydrographs are strongly affected by trends in hydraulic conductivity, particularly for small runoff events. The results also show that Smith and Hebbert [1979] mislabeled outflow hydrographs, resulting in incorrect conclusions about the effects of linear trends in K s. A simple technique is introduced to account for flow concentration in rills and the resulting reduced effective wetted areas subject to infiltration after rainfall ceases. It is shown that this mechanism has a major impact on runoff peaks, volumes, and time to peak for cases where Ks increases downslope.

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Section: Hydrographs For Cases 4 5 and 6 Insupporting

confidence: 51%

“…Note that the characteristics converge and cross for the K s increasing case, indicating the formation of a kinematic shock [c.f. Kibler and Woolhiser, 1972]. Because we have not included a shock-following scheme in the computer program, multiple values of depth occur in the shock zone.…”

Section: Mathematical Modelmentioning

confidence: 99%

Effects of Spatial Variability of Saturated Hydraulic Conductivity on Hortonian Overland Flow

Woolhiser¹,

Smith²,

Giráldez³

1996

Water Resources Research

155

View full text Add to dashboard Cite

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“…This facility was utilized in earlier studies by Woolhiser (1969), Smith and Woolhiser (1971a,b), Woolhiser et al (1971), Kibler and Woolhiser (1972), Rovey (1974), Singh (1974Singh ( , 1975a and Lane (1975). Singh (1974Singh ( , 1975aSingh ( ,b,c, 1976a studied the applicability of the kinematic wave theory on the above large experimental facility.…”

Section: Laboratory Investigationsmentioning

confidence: 96%

Kinematic wave modelling in water resources: a historical perspective

Singh

2001

Hydrological Processes

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Abstract:The history of the kinematic wave theory and its applications in water resources are traced. It is shown that the theory has found its niche in water resources and its applications are so widespread that they may well constitute what may be termed 'kinematic wave hydrology'. Few theories have been applied in hydrology and water resources as extensively as the kinematic wave theory. This theory, however, is not without limitations and when it is applied they must be so recognized.

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“…During infiltration calculated using equation (18), in the case of falling slugs using equation (19), or in the case of groundwater fronts using equation (21), higher velocities in bins to the right can result in an imbalanced profile as shown in Figure 2a. Smith [1983] called these shock fronts, and are analogous to kinematic shocks in kinematic wave flow theory [Kibler and Woolhiser 1972]. We posit that these shocks are dissipated by capillary relaxation [Moebius et al, 2012], which involves movement of water at the pore scale from regions of lower capillarity to regions of higher capillarity.…”

Section: Capillary Relaxationmentioning

confidence: 99%

A new general 1‐D vadose zone flow solution method

Ogden

Lai

Steinke

et al. 2015

Water Resources Research

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We have developed an alternative to the one-dimensional partial differential equation (PDE) attributed to Richards (1931) that describes unsaturated porous media flow in homogeneous soil layers. Our solution is a set of three ordinary differential equations (ODEs) derived from unsaturated flux and mass conservation principles. We used a hodograph transformation, the Method of Lines, and a finite water-content discretization to produce ODEs that accurately simulate infiltration, falling slugs, and groundwater table dynamic effects on vadose zone fluxes. This formulation, which we refer to as ''finite water-content'', simulates sharp fronts and is guaranteed to conserve mass using a finite-volume solution. Our ODE solution method is explicitly integrable, does not require iterations and therefore has no convergence limits and is computationally efficient. The method accepts boundary fluxes including arbitrary precipitation, bare soil evaporation, and evapotranspiration. The method can simulate heterogeneous soils using layers. Results are presented in terms of fluxes and water content profiles. Comparing our method against analytical solutions, laboratory data, and the Hydrus-1D solver, we find that predictive performance of our finite water-content ODE method is comparable to or in some cases exceeds that of the solution of Richards' equation, with or without a shallow water table. The presented ODE method is transformative in that it offers accuracy comparable to the Richards (1931) PDE numerical solution, without the numerical complexity, in a form that is robust, continuous, and suitable for use in large watershed and land-atmosphere simulation models, including regional-scale models of coupled climate and hydrology.

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Mathematical properties of the kinematic cascade

Cited by 37 publications

References 5 publications

Effects of Spatial Variability of Saturated Hydraulic Conductivity on Hortonian Overland Flow

Effects of Spatial Variability of Saturated Hydraulic Conductivity on Hortonian Overland Flow

Kinematic wave modelling in water resources: a historical perspective

A new general 1‐D vadose zone flow solution method

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