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In this chapter, the application of a DLRNN is demonstrated to simulate rainfall-runoff processes and recognize the transition of UHs in hydrology. Although most neural networks are black-box models that lack physical meanings of weights, the DLRNN developed in this chapter connects its weights with UHs that reveal the physical concepts from the network based on the special structure of RNNs. Without trial and error method, the structure and the weights of DLRNN can be quickly determined through a modified form of system identification that combines indirect system identification with the subspace algorithm. Then, the DLRNN learning algorithm based on the interchange of the roles of the network state variables and the weight matrix is derived for on-line training. In this chapter, the DLRNN introduced can not only simulate rainfall-runoff processes, but also recognize the transition of UHs. Owing to the feedback connections, DLRNN performs rainfall-runoff simulations as dynamic systems, and the advantage of DLRNN's dynamic feature has been proven after the comparison between DLRNN and FNN. The investigation of the connections between weights and physical meanings is an extension of neural networks applied in hydrological field due to the linearization of the RNN. Based on the linearization, weights of DLRNN are treated as Markov parameters to realize the transition of UHs. Through on-line learning, DLRNN modifies the weights to capture the relation between rainfall and runoff every time step, and the transition of rainfall-runoff processes can be emerged based on the changes of UHs. Furthermore, a modified system identification that combines indirect system identification with subspace algorithm is described to calibrate the DLRNN. This method determines the quantity of neurons in hidden layer and the weights of the network. It overcomes the drawback of costing time by traditional trial and error search for optimum structure of DLRNN. Additionally, the different forms of DLRNN have also been discussed herein. The results show that the performances of DLRNNs in different forms are close. Hence, the transformation of canonical form can be ignored in the flowchart of simulation via DLRNN. Finally, four criteria have been applied to evaluate the performance of rainfall-runoff simulation via DLRNN. The results show that the performance is satisfactory and DLRNN is competent to simulate dynamic systems, like rainfall-runoff processes.

Characterizing the dynamic relationship between rainfall and runoff is a highly interesting modeling problem in hydrology. This study develops a deterministic linearized recurrent neural network (denoted as DLRNN) that deals with the system’s nonlinearity by recalibration at each time interval, and relates the weights of DLRNN to unit hydrographs in order to describe the transition of the rainfall–runoff processes. Case studies of 38 events, from 1966 to 1997, are implemented in the Wu-Tu watershed of Taiwan, where the runoff path-lines are short and steep. A comparison between the DLRNN and a feed-forward neural network demonstrates the advantage of DLRNN as a dynamic system model. It is concluded that DLRNN shows superiority in the performance of rainfall–runoff simulations and the ability to recognize transitions in hydrological processes.

This work develops a preliminary method for coding random self-similar patterns as a series of numbers and investigates the corresponding algorithm to calculate the topological distance between starting point and the link in the generated fractal pattern from the code series. With reference to the wide range of stochastic property in natural patterns, a process for generating fractal patterns with various generating probabilities of the pattern links denoted as separately random self-similar generation or separately random fractal is proposed. To assess the adaptability of the process, the coding method is applied to the generation of a random self-similar river network and the corresponding algorithm for calculating topological distance of the links is used to determine the width function of the pattern. The width function-based geomorphologic instantaneous unit hydrograph (WF-GIUH) model is then applied to estimate the runoff of the Po-bridge watershed in northern Taiwan. The results show that the separately random self-similar generating algorithm can be implemented successfully to calculate hydrologic responses.

Many novel techniques for reconstructing rainfall-runoff processes require hydrometeorologic and geomorphologic information for modelling. However, certain information is not always measurable. In this paper, we employ a special recurrent neural network to reconstruct the rainfall-runoff process by using collected rainfall data. In addition, we propose an indirect system identification to overcome the drawback of a traditional, time-consuming trial-and-error search. The indirect system identification is an efficient method to recognize the structure of a recurrent neural network. The unit hydrograph can be derived directly from the weights of the network due to a state-space form embedded in the recurrent neural network. This improves the link between the weights of the network and the physical concepts that most neural networks fail to connect. The case studies of 41 events from 1966 to 1997 have been implemented in Taiwan's Wu-Tu watershed, where the runoff path-lines are short and steep. Two recurrent neural networks and one state-space model are utilized to simulate the rainfall-runoff processes for comparison. The results are validated by four criteria: coefficient of efficiency; peak discharge error; time to peak arrival error; total discharge volume error. The resulting data from the recurrent neural network reveal that the neural network proposed herein is appropriate for hydrological systems. Copyright © 2005 John Wiley & Sons, Ltd.

Rainfall-runoff processes are dynamic systems that are better described by a dynamic model. In this paper, a specific dynamic neural network, called state space neural network (SSNN), is modified to perform short term rainfall-runoff forecasts. The lead time is extended to 3 h. To improve the link between the weights of the network and physical concepts that most neural networks lack for, a method of the unit hydrograph representation is proposed to reproduce the unit hydrographs based on the weights of the network. Hence, a transition of rainfall-runoff systems can be observed via the changes of the unit hydrograph hour by hour. Furthermore, a new learning method developed from the interchange of the roles of the network states and the weight matrix is applied to train the SSNN and helps the network to evolve into a time-variant model while forecasting the rainfall-runoff process. A study case has been implemented in Taiwan's Wu-Tu watershed, where the runoff path-lines are short and steep. Forty-seven events from 1966 to 1997 are forecasted via the SSNN, and the results are validated via four criteria. The convergence of the new learning algorithm is shown during the model training process. Performance of the SSNN for short term rainfall-runoff forecasting reveals that the specific dynamic recurrent neural network is appropriate for hydrological forecasts.

This study develops a model using the grey analytic hierarchy process to analyze hazard potential of typhoon damage. The main component of the model is the grey analytic hierarchy process involving the analytic hierarchy process and grey relational analysis. First, the model is employed to determine the hazard potential indices. Each region in the project area is then divided into various classes using the two breaking points method to classify appropriately the hazard potential indices. The map of classified hazard potential in the project area can enable decision makers to establish a strategy for preventing flood disaster.

This paper presents the application of a multimodel method using a wavelet-based Kalman filter (WKF) bank to simultaneously estimate decomposed state variables and unknown parameters for real-time flood forecasting. Applying the Haar wavelet transform alters the state vector and input vector of the state space. In this way, an overall detail plus approximation describes each new state vector and input vector, which allows the WKF to simultaneously estimate and decompose state variables. The wavelet-based multimodel Kalman filter (WMKF) is a multimodel Kalman filter (MKF), in which the Kalman filter has been substituted for a WKF. The WMKF then obtains M estimated state vectors. Next, the M state-estimates, each of which is weighted by its possibility that is also determined on-line, are combined to form an optimal estimate. Validations conducted for the Wu-Tu watershed, a small watershed in Taiwan, have demonstrated that the method is effective because of the decomposition of wavelet transform, the adaptation of the time-varying Kalman filter and the characteristics of the multimodel method. Validation results also reveal that the resulting method enhances the accuracy of the runoff prediction of the rainfall–runoff process in the Wu-Tu watershed. Copyright © 2004 John Wiley & Sons, Ltd.

This study applies the discrete wavelet transform (DWT) to decompose the unit hydrograph, thereby generating parsimonious reparameterizations of the unit hydrograph. A model compression method is then employed to significantly compress the unit hydrograph requiring that fewer coefficients be estimated. Moreover, a wavelet-based linearly constrained least mean squares (WLCLMS) algorithm is also used to estimate on-line the wavelet coefficients of the unit hydrograph. The updated wavelet coefficients of the unit hydrograph, convoluted with effective rainfall input in the wavelet domain, allow for accurate prediction of one-step-ahead runoff in the time domain. The proposed approach allows the unit hydrographs to vary in time and accurately predicts runoff from a basin in Taiwan, thus making it highly promising for flood forecasting.

An approach to apply the fractal concept to estimate hydrologic response is proposed in this paper by matching suitable self-similar networks (SSNs) to a specific watershed, and modeling the runoff with a width-function based geomorphologic instantaneous unit hydrograph (WF-GIUH). In order to work out the identification between a specific basin and SSNs that are generated by an interior generator cooperating with an exterior generator, a generalized width function is derived. Subsequently, cumulative width functions on the basis of the derived function, as well as the informational entropies are used as criteria to decide the best patterns of the two cooperating generators for the specific watershed. The WF-GIUH model is then applied to calculate the runoff of this watershed as an outcome of the estimation. To assess the adaptability of the estimation model, San-Hsia watershed of Northern Taiwan is selected as a study area, where the analytical results of the outflow estimation indicate that the fractal algorithm has been implemented successfully for the calculation of hydrologic responses.

This study focuses mainly on observing urban development in Taiwan's Wu-Tu watershed from the perspective of urban hydrological theory. An approach is proposed for developing a method for incorporating available meteorological data to define the degree of change in a runoff hydrograph for urbanizing basins. The mean rainfall was estimated using the Kriging method. For calibration, two methods of calculating the effective rainfall (the Φ-index method and the non-linear-programming (NLP) method) were used as model inputs, and the optimal global parameters of the linear reservoir model were then obtained from the shuffled complex evolution (SCE) algorithm. Twenty-six (1966–1991) and eight (1994–1997) rainfall–runoff events were used for calibration and verification, respectively. The NLP method yielded better results than the Φ-index method, especially for multipeak rainfall–runoff events. The regression equation determined the relationship between the parameters of the model and impervious areas. A comparison based on the results of the instantaneous unit hydrograph of the study area revealed that three decades of urbanization had increased the peak flow by 27%, and the time to peak was decreased by 4 h. The study simply describes the results of the impact of imperviousness on hydrological modelling. Copyright © 2002 John Wiley & Sons, Ltd.

The main purpose of this paper is to introduce a semi-distributed parallel surface rainfall-runoff conceptual model. In this paper, a general solution of the instantaneous unit hydrograph (IUH) has been derived successfully for N linearly connected reservoirs, each having a different storage constant. The solution is a function of geomorphologic parameters, meteorologic factors and roughness coefficients. The model also takes into account the hydrologic response which is influenced by outflow downstream of a reservoir. For calibration, the shuffled complex evolution (SCE) algorithm is used to search for the global optimal parameters of the model. Because of the parallel structure, the mean roughness parameter of the channel becomes a “conceptual” parameter without a real physical meaning. To evaluate the adaptability of the model adopted, three watersheds around the city of Taipei in Taiwan were chosen to test the effectiveness of the model. The study provides an appropriate rainfall-runoff model for planning flood mitigation in Taiwan. Copyright © 1999 John Wiley & Sons, Ltd.

The main purpose of the colored noise effect in parameter estimation for a linear model is to make the estimators tend to the true values as closely as possible. The differential hydrological grey model with dual series is adopted in this study. The least squares estimation of model parameters with the colored noise effect is applied to improve the parameter identification. By using the shuffled complex evolution (SCE) algorithm, the parameter derived from the least squares estimation with the colored noise effect is optimized. Then, the degree of the colored noise effect affecting the parameter estimation of a linear model is investigated. The applicability of the proposed procedure to two watersheds in Taiwan is verified and the simulated results with and without the colored noise effect are compared. From the theoretical investigation and discussion, the superiority of the parameter estimation with the colored noise effect is proved. That colored noise effect plays an important role not only in parameter estimation, but also in simulation of the rainfall-runoff process, is also verified

A preliminary method for coding random self-similar river networks and the corresponding distance calculations are proposed in a companion paper. The coding method is applied to generate random self-similar river networks, and the corresponding algorithm for calculating the geometric distances of the links is employed to determine the width function of the river networks, and thus evaluates the adaptability of the process. The width function-based geomorphological instantaneous unit hydrograph (WF-GIUH) model is then applied to estimate the runoff of the Po-bridge watershed in northern Taiwan. The results imply that the separately random self-similar generating algorithm can be used to simulate river networks during the rainfall–runoff process. It can also help analyse the variations of the river network when rainfall locations change and study the influence on hydrological responses (IUH) when the shape of river network changes.

This study proposes a preliminary method for coding random self-similar river networks as a series of numbers, and investigates the corresponding algorithm that calculates the geometric distances from the code series. The coding method, generating random self-similar patterns with various probabilities of particular pattern links, and transferring the pattern into numerical code series, is proposed, based on the wide range of stochastic characteristics of natural patterns. The heredity of self-similarity and the connecting relationships inside the generated pattern are discussed. Finally, the algorithm to calculate the geometric distances of the generated pattern are developed.