Gwo-Fong Lin

Finite-volume component-wise TVD schemes for 2D shallow water equations

Abstract Four finite-volume component-wise total variation diminishing (TVD) schemes are proposed for solving the two-dimensional shallow water equations. In the framework of the finite volume method, a proposed algorithm using the flux-splitting technique is established by modifying the MacCormack scheme to preserve second-order accuracy in both space and time. Based on this algorithm, four component-wise TVD schemes, including the Liou–Steffen splitting (LSS), van Leer splitting, Steger–Warming splitting and local Lax–Friedrichs splitting schemes, are developed. These schemes are verified through the simulations of the 1D dam-break, the oblique hydraulic jump, the partial dam-break and circular dam-break problems. It is demonstrated that the proposed schemes are accurate, efficient and robust to capture the discontinuous shock waves without any spurious oscillations in the complex flow domains with dry-bed situation, bottom slope or friction. The simulated results also show that the LSS scheme has the best numerical accuracy among the schemes tested.

Effective forecasting of hourly typhoon rainfall using support vector machines

[1] Typhoon rainfall is one of the most difficult elements of the hydrologic cycle to forecast because of the high variability in space and time and the complex physical process. To obtain more effective forecasts of hourly typhoon rainfall, novel models with better ability are desired. On the basis of support vector machines (SVMs), which are a novel kind of neural networks (NNs), effective hourly typhoon rainfall forecasting models are constructed. As compared with backpropagation networks (BPNs), which are the most frequently used conventional NNs, SVMs have three advantages: (1) SVMs have better generalization ability, (2) the architectures and the weights of the SVMs are guaranteed to be unique and globally optimal, and (3) SVM is trained much more rapidly. An application is conducted to clearly demonstrate these three advantages. The results indicate that the proposed SVM-based models are better performed, robust, and efficient than the existing BPN-based models. To further improve the long lead time forecasting, typhoon characteristics are added as key input to the proposed models. The comparison between SVM-based models with and without typhoon characteristics confirms the significant improvement in forecasting performance due to the addition of typhoon characteristics for long lead time forecasting. The proposed SVM-based models are recommended as an alternative to the existing models. The proposed modeling technique is also expected to be useful to support reservoir operation systems and flood, landslide, debris flow, and other disaster warning systems.

Hybrid Flux-Splitting Finite-Volume Scheme for the Shallow Water Flow Simulations with Source Terms

The extension of the hybrid flux-splitting finite-volume (HFF) scheme to the shallow water equations with source terms is presented. Based on the monotonic upstream schemes for conservation laws (MUSCL) method, the scheme is second-order-accurate both in space and time. An accurate and efficient surface gradient method (SGM), in conjunction with the HFF scheme, is adopted for the discretization of source terms, including the bed slopes and friction slopes. The resulting scheme has several desirable properties: ease of implementation, satisfaction of entropy condition, sharp shock resolution and preservation of well-balancing. The HFF scheme with SGM is verified through the simulations of steady transcritical flow over a hump and steady flow over an irregular bed. Besides, the effects of the limiter functions, the grid sizes and the Manning roughness coefficients on the simulated results are investigated for the steady transcritical flow problems. Using the laboratory measurements, the scheme is also applied to the dam-break flows: with an adverse slope, with a triangular hump, and with a constriction. Furthermore, the HFF scheme is employed in the simulation of typhoon flood flow with natural-irregular river topography to demonstrate the practical engineering application. The results show good agreements compared with the exact solutions, the experimental data and the field measurements.

High-resolution TVD schemes in finite volume method for hydraulic shock wave modeling

High-resolution total variation diminishing (TVD) schemes in the framework of the finite volume method are presented and evaluated for hydraulic shock wave modeling. Three approximate Riemann solvers, namely the FVS, Roe and Osher schemes, are extended to high-resolution TVD schemes based on the direct MUSCL-Hancock (DMH) slope limiter approach. The TVD schemes are then used to develop numerical models to compute water depth and velocity. The numerical models developed are then verified through simulations of the dam-break flows, the oblique hydraulic jump, and the shock-on-shock interaction. The numerical models with TVD schemes are capable of capturing discontinuous shock waves without any spurious oscillation. A comparison of numerical efficiency shows that the Osher-DMH scheme coupled with van Leer limiter performs the best among the proposed TVD schemes. Applications of the Osher-DMH scheme to flows of partial dam-break experiments have shown that the simulated water depths agree well with the measured data.

Parameter estimation for seasonal to subseasonal disaggregation

Abstract A model structure of staged disaggregation using the full Mejia and Rousselle model is considered and the parameter estimation problem for this model is addressed. A technique is developed to derive the corrected parameter estimation equations associated with the use of the Mejia and Rousselle model for a two-stage disaggregation scheme. The technique is based on making the parameter estimation equations mathematically consistent. Following this technique, it is found that corrected parameter estimation equations for the Mejia and Rousselle model are conditional on its key series (input) generation model. With parameters estimated from corrected parameter estimation equations coupled with the corrected moment estimates for the preservation of additivity, the modeling, in theory, can exactly preserve the important moments of interest and the additivity. The effects of using the corrected parameter estimation scheme are also verified by an example.

Determination of aquifer parameters using radial basis function network approach

Abstract In this paper, a radial basis function network (RBFN) approach to the determination of aquifer parameters is developed. The approach is based on the combination of an RBFN and the Theis or the Hantuch‐Jacob solution. The proposed RBFN approach has advantages over the existing back‐propagation network (BPN) approach. It avoids inappropriate setting of a trained range. It also determines the aquifer parameters more accurately and needs less training time. Testing the BPN and RBFN approaches by synthetic data also demonstrates these advantages. As to the comparison between the RBFN approach and the type‐curve graphical method, two applications to actual time‐drawdown data show that the RBFN approach determines the aquifer parameters more precisely for both nonleaky‐confined and leaky‐confined aquifers. The RBFN approach is recommended as an alternative to the type‐curve graphical method and the existing BPN approach.

An aggregation-disaggregation approach for hydrologic time series modelling

Abstract This paper describes the development and application of a new methodology to solve the failure of the disaggregation model. Based on the concept of aggregation, the parameters of the annual model are estimated from the parameters of the periodic model fitted to the seasonal series. Covariance estimates required in the parameter estimation procedure of the disaggregation model are calculated based on the derived annual model and the fitted periodic model. The covariance estimates are used in conjunction with the moment equations of the disaggregation model to produce the parameters for this model. The proposed methodology provides a linkage between the aggregation and disaggregation approaches for hydrologic time-series simulations. Using this methodology, the modelling in theory can preserve the additivity and many historical moments. The most significant advantage of this methodology over the existing remedies for the Mejia and Rousselle model is the preservation of over-year seasonal correlations.

Simulation of Hydraulic Shock Waves by Hybrid Flux-Splitting Schemes in Finite Volume Method

In the framework of the finite volume method, a robust and easily implemented hybrid flux-splitting finite-volume (HFF) scheme is proposed for simulating hydraulic shock waves in shallow water flows. The hybrid flux-splitting algorithm without Jacobian matrix operation is established by applying the advection upstream splitting method to estimate the cell-interface fluxes. The scheme is extended to be second-order accurate in space and time using the predictor-corrector approach with monotonic upstream scheme for conservation laws. The proposed HFF scheme and its second-order extension are verified through simulations of the 1D idealized dam-break problem, the 2D oblique hydraulic shock-wave problem, and the 2D dam-break experiments with channel contraction as well as wet/dry beds. Comparisons of the HFF and several well-known first-order upwind schemes are made to evaluate numerical performances. It is demonstrated that the HFF scheme captures the discontinuities accurately and produces no entropy-violating solutions. The HFF scheme and its second-order extension are proven to achieve the numerical benefits combining the efficiency of flux-vector splitting scheme and the accuracy of flux-difference splitting scheme for the simulation of hydraulic shock waves.

General stochastic instantaneous unit hydrograph

Abstract This paper describes a stochastic analysis of the Nash cascade of identical reservoirs in which the storage coefficient is treated as a random variable. Based on the theory of stochastic differential equations, a new stochastic expression for the instantaneous unit hydrograph is obtained and recommended as an alternative to the existing equation. It is found that the sample function of the proposed stochastic instantaneous unit hydrograph takes the same form as the corresponding deterministic solution (Nashs equation). Moments of the proposed stochastic instantaneous unit hydrograph are derived. An application to a watershed has shown that the proposed stochastic instantaneous unit hydrograph can preserve the statistical properties of the observed data. The effect of the random coefficient on the stochastic instantaneous unit hydrograph is also discussed.

Assessment of aggregated hydrologic time series modelling

Abstract The annual series aggregated from a seasonal series which is generated by a periodic AR(1) or ARMA(1,1) model is considered and the moments (variance and covariances) associated with the annual series are examined. It is found that the performance of the aggregated series in reproducing the historical moments depends on the type of periodic model and the number of seasons in a year. Only the annual series aggregated from a seasonal series which is generated by a two-season AR(1), two-season ARMA(1,1) or three-season ARMA(1,1) model can exactly preserve the historical variance, when the parameters of the periodic model are estimated using the method of moments.