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The stochastic integral equation method (S.I.E.M.) is used to evaluate the relative performance of a set of both calibrated and uncalibrated rainfall-runoff models with respect to prediction errors. The S.I.E.M. is also used to estimate confidence (prediction) interval values of a runoff criterion variable, given a prescribed rainfall-runoff model, and a similarity measure used to condition the storms that are utilized for model calibration purposes.Because of the increasing attention given to the issue of uncertainty in rainfall-runoff modeling estimates, the S.I.E.M. provides a promising tool for the hydrologist to consider in both research and design. 相似文献
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Evaluating the effect of land development on sediment transport using a probability density function
T. V. Hromadka II R. J. Whitely 《Stochastic Environmental Research and Risk Assessment (SERRA)》1993,7(2):102-108
An important problem in sedimentation analysis is the development of a channel section that preserves, as best as possible, the current sedimentation regime even though the flood frequency tendencies have been altered due to land development within the catchment. In order to accomplish this task, a methodology is needed that estimates sediment transport capacity for various channel configurations. Such a procedure is described which allows the computation of the total sediment transport capacity for each of several T-year return frequency runoff hydrographs. This information is used to obtain an approximate probability distribution for the total sediment transport capacity, and the mean and standard deviation of this distribution are computed.Comparing the results for the catchment in its present state with a future developed state, using a selection of new channel parameters, indicates how to improve the channel to control changes in sedimentation due to development. The analysis procedure provides a basis for estimating a new channel configuration such that the new flow conditions retain, as best as possible, the existing condition sedimentation effects, and hence retain the natural sediment supply and transport trends even though runoff flow rates have changed due to land development within the catchment.The results of Wilson Creek are typical of the several sites examined, see Table 3 below. The T=2, T=5, T=25, and T=100 year values for total sediment transport capacity, in kilotons, are 6.9, 39.4, 61.3, and 96.7 with a mean of 17.1 and standard deviation of 19.3. After development with no change in the channel the respective values increase to: 17.9, 84.6, 128.1, and 258.0 with a mean of 39.1 and standard deviation of 44.3. A new channel can be constructed which will reduce these sediment transport capacity values, after development, to 5.2, 41.0, 62.0, and 124.8 with a mean of 17.4 and standard deviation of 22.0. 相似文献
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The Galerkin finite element method coupled with the Crank-Nicolson time advance procedure is often used as a numerical analog for unsaturated soil-moisture transport problems. The Crank-Nicolson procedure leads to numerical mass balance problems which results in instability. A new temporal and spatial integration procedure is proposed that exactly satisfies mass balance for the approximating function used. This is accomplished by fitting polynomials continuously throughout the time and space domain and integrating the governing differential equations. To reduce computational effort, the resulting higher order polynomials are reduced to quadratic and linear piece-wise continuous polynomial approximation functions analogous to the finite element approach. Results indicate a substantial improvement in accuracy over the combined Galerkin and Crank-Nicolson methods when comparing to simplified problems where analytical solutions are available. 相似文献
5.
The non-linear soil-moisture diffusivity model can be approximately linearized by using values of diffusivity assumed constant for small intervals of space and time. By a series expansion of the diffusivity function and integrating the resulting series of differential equations with respect to time, an improved numerical model is developed. Results from application of this new approach to a sharp wetting-front soil infiltration problem indicates that a 67% saving in numerical effort is achieved at comparable estimation accuracy levels when using the traditional finite timestep Crank-Nicolson approach. 相似文献
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T. V. Hromadka R. J. Whitley 《Stochastic Environmental Research and Risk Assessment (SERRA)》1988,2(3):213-239
The design storm approach, where the subject criterion variable is evaluated by using a synthetic storm pattern composed of identical return frequencies of storm pattern input, is shown to be an effective approximation to a considerably more complex probabilistic model. The single area unit hydrograph technique is shown to be an accurate mathematical model of a highly discretized catchment with linear routing for channel flow approximation, and effective rainfalls in subareas which are linear with respect to effective rainfall output for a selected “loss” function. The use of a simple “loss” function which directly equates to the distribution of rainfall depth-duration statistics (such as a constant fraction of rainfall, or a ?-index model) is shown to allow the pooling of data and thereby provide a higher level of statistical significance (in estimating T-year outputs for a hydrologic criterion variable) than use of an arbitrary “loss” function. The above design storm unit hydrograph approach is shown to provide the T-year estimate of a criterion variable when using rainfall data to estimate runoff. 相似文献
7.
The nodal domain integration method is applied to a one-dimensional advection—diffusion mathematical model without a source term. Comparison of the resulting numerical model to the well known Galerkin finite element, subdomain, and finite difference domain models indicates that a single numerical statement can be developed which includes the Galerkin finite element, subdomain, and finite difference models as special cases. 相似文献
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The nodal domain integration method is used to develop a numerical model of the linear diffusion equation. The nodal domain integration approach is shown to represent an infinity of finite element mass matrix lumping schemes including the Galerkin and subdomain integration versions of the weighted residual method and an integrated finite difference method. Neumann, Dirichlet and mixed boundary conditions are accommodated analogous to the Galerkin finite element method. In order to reduce the overall integrated approximation relative error, a mass matrix lumping formulation is developed which is based on the Crank-Nicolson time advancement approximation. The optimum mass lumping factors are found to be strongly related to the model timestep size. 相似文献
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T.V. Hromadka 《Advances in water resources》1984,7(2):76-80
The nodal domain integration method is applied to a two-dimensional advection-diffusion process in an anisotropic inhomogeneous medium. The domain is discretised into the union of irregular triangle finite elements with vertex-located nodal points and a linear trial function is used to approximate the governing flow equation's state variable in each element. Non-linear parameters are assumed quasi-constant for small durations in time in each element. The resulting numerical model represents the Galerkin and subdomain integration weighted residual methods and the integrated finite difference method as special cases. Both Dirichlet and Neumann boundary conditions are accommodated in a manner similar to the Galerkin finite element approach. 相似文献
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R. Whitley T. V. Hromadka II 《Stochastic Environmental Research and Risk Assessment (SERRA)》1997,11(1):51-63
A basic problem in hydrology is computing confidence levels for the value of the T-year flood when it is obtained from a Log
Pearson III distribution in terms of estimated mean, estimated standard deviation, and estimated skew. In an important paper
Chowdhury and Stedinger [1991] suggest a possible formula for approximate confidence levels, involving two functions previously
used by Stedinger [1983] and a third function, λ, for which asymptotic estimates are given. This formula is tested [Chowdhury
and Stedinger, 1991] by means of simulations, but these simulations assume a distribution for the sample skew which is not,
for a single site, the distribution which the sample skew is forced to have by the basic hypothesis which underlies all of
the analysis, namely that the maximum discharges have a Log Pearson III distribution. Here we test these approximate formulas
for the case of data from a single site by means of simulations in which the sample skew has the distribution which arises
when sampling from a Log Pearson III distribution. The formulas are found to be accurate for zero skew but increasingly inaccurate
for larger common values of skew. Work in progress indicates that a better choice of λ can improve the accuracy of the formula. 相似文献