Using recurrent neural networks to reconstruct rainfall‐runoff processes

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.     

Prediction of sediment yield by coupling Kalman filter with instantaneous unit sediment graph

An instantaneous unit sediment graph (IUSG) model in conjunction with Kalman filter was investigated for prediction of sediment yield from an upland watershed in Northwestern Mississippi. The state vector of the watershed sediment yield system was constituted by the IUSG and then the sediment yield was estimated by the IUSG model using Kalman filter. The initial values of the state vector were assumed as the average of the IUSG values and the initial sediment yield estimated from the average IUSG. The IUSG model using Kalman filter with a recursive algorithm accurately predicted sediment yield from watershed W‐5, Mississippi. The filter allowed the IUSG to vary in time, increased the accuracy of the IUSG model, and reduced physical uncertainty of the sediment yield process in the watershed. Copyright © 1999 John Wiley & Sons, Ltd.     

Application of the Kalman filter to the Nash model

The Nash model was used for application of the Kalman filter. The state vector of the rainfall–runoff system was constituted by the IUH (instantaneous unit hydrograph) estimated by the Nash model and the runoff estimated by the Nash model using the Kalman filter. The initial values of the state vector were assumed as the average of 10% of the IUH peak values and the initial runoff estimated from the average IUH. The Nash model using the Kalman filter with a recursive algorithm accurately predicted runoff from a basin in Korea. The filter allowed the IUH to vary in time, increased the accuracy of the Nash model and reduced physical uncertainty of the rainfall–runoff process in the river basin. © 1998 John Wiley & Sons, Ltd.     

Two‐dimensional continuous simulation of spatiotemporally varied hydrological processes using the time‐area method

Distributed, continuous hydrologic models promote better understanding of hydrology and enable integrated hydrologic analyses by providing a more detailed picture of water transport processes across the varying landscape. However, such models are not widely used in routine modelling practices, due in part to the extensive data input requirements, computational demands, and complexity of routing algorithms. We developed a two‐dimensional continuous hydrologic model, HYSTAR, using a time‐area method within a grid‐based spatial data model with the goal of providing an alternative way to simulate spatiotemporally varied watershed‐scale hydrologic processes. The model calculates the direct runoff hydrograph by coupling a time‐area routing scheme with a dynamic rainfall excess sub‐model implemented here using a modified curve number method with an hourly time step, explicitly considering downstream ‘reinfiltration’ of routed surface runoff. Soil moisture content is determined at each time interval based on a water balance equation, and overland and channel runoff is routed on time‐area maps, representing spatial variation in hydraulic characteristics for each time interval in a storm event. Simulating runoff hydrographs does not depend on unit hydrograph theory or on solution of the Saint Venant equation, yet retains the simplicity of a unit hydrograph approach and the capability of explicitly simulating two‐dimensional flow routing. The model provided acceptable performance in predicting daily and monthly runoff for a 6‐year period for a watershed in Virginia (USA) using readily available geographic information about the watershed landscape. Spatial and temporal variability in simulated effective runoff depth and time area maps dynamically show the areas of the watershed contributing to the direct runoff hydrograph at the outlet over time, consistent with the variable source area overland flow generation mechanism. The model offers a way to simulate watershed processes and runoff hydrographs using the time‐area method, providing a simple, efficient, and sound framework that explicitly represents mechanisms of spatially and temporally varied hydrologic processes. Copyright © 2015 John Wiley & Sons, Ltd.     

A kinematic‐wave‐based distributed watershed model using FEM,GIS and remotely sensed data

For the appropriate management of water resources in a watershed, it is essential to calculate the time distribution of runoff for the given rainfall event. In this paper, a kinematic‐wave‐based distributed watershed model using finite element method (FEM), geographical information systems (GIS) and remote‐sensing‐based approach is presented for the runoff simulation of small watersheds. The kinematic wave equations are solved using FEM for overland and channel flow to generate runoff at the outlet of the watershed concerned. The interception loss is calculated by an empirical model based on leaf area index (LAI). The Green‐Ampt Mein Larson (GAML) model is used for the estimation of infiltration. Remotely sensed data has been used to extract land use (LU)/land cover (LC). GIS have been used to prepare finite element grid and input files such as Manning's roughness and slope. The developed overland flow model has been checked with an analytical solution for a hypothetical watershed. The model has been applied to a gauged watershed and an ungauged watershed. From the results, it is seen that the model is able to simulate the hydrographs reasonably well. A sensitivity analysis of the model is carried out with the calibrated infiltration parameters, overland flow Manning's roughness, channel flow Manning's roughness, time step and grid size. The present model is useful in predicting the hydrograph in small, ungauged watersheds. Copyright © 2007 John Wiley & Sons, Ltd.     

Multi‐scale assimilation of root zone soil water predictions

When hydrology model parameters are determined, a traditional data assimilation method (such as Kalman filter) and a hydrology model can estimate the root zone soil water with uncertain state variables (such as initial soil water content). The simulated result can be quite good. However, when a key soil hydraulic property, such as the saturated hydraulic conductivity, is overestimated or underestimated, the traditional soil water assimilation process will produce a persistent bias in its predictions. In this paper, we present and demonstrate a new multi‐scale assimilation method by combining the direct insertion assimilation method, particle swarm optimisation (PSO) algorithm and Richards equation. We study the possibility of estimating root zone soil water with a multi‐scale assimilation method by using observed in situ data from the Wudaogou experiment station, Huaihe River Basin, China. The results indicate there is a persistent bias between simulated and observed values when the direct insertion assimilation surface soil water content is used to estimate root zone soil water contents. Using a multi‐scale assimilation method (PSO algorithm and direct insertion assimilation) and an assumed bottom boundary condition, the results show some obvious improvement, but the root mean square error is still relatively large. When the bottom boundary condition is similar to the actual situation, the multi‐scale assimilation method can well represent the root zone soil water content. The results indicate that the method is useful in estimating root zone soil water when available soil water data are limited to the surface layer and the initial soil water content even when the soil hydraulic conductivities are uncertain. Copyright © 2011 John Wiley & Sons, Ltd.     

A self‐organization algorithm for real‐time flood forecast

The group method of data handling (GMDH) algorithm presented by A. C. Ivakhnenko and colleagues is an heuristic self‐organization method. It establishes the input–output relationship of a complex system using a multilayered perception‐type structure that is similar to a feed‐forward multilayer neural network. This study provides a step towards understanding and evaluating a role for GMDH in the investigation of the complex rainfall–runoff processes in a heterogeneous watershed in Taiwan. Two versions of the revised GMDH model are implemented: a stepwise regression procedure and a recursive formula. Eleven typhoon events in the Shen‐cei Creek watershed, Taiwan, are used to build the model and verify its usefulness. The prediction results of the revised GMDH models and the instantaneous unit hydrograph (IUH) model are compared. Based on the criteria of forecasting precision and the rate and time of peak error, a much better performance is obtained with the revised GMDH models. Copyright © 1999 John Wiley & Sons, Ltd.     

An approach for evaluating the hydrological effects of urbanization and its application

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.     

Modelling the hydrologic effects of dynamic land‐use change using a distributed hydrologic model and a spatial land‐use allocation model

This study develops a novel approach for modelling and examining the impacts of time–space land‐use changes on hydrological components. The approach uses an empirical land‐use change allocation model (CLUE‐s) and a distributed hydrological model (DHSVM) to examine various land‐use change scenarios in the Wu‐Tu watershed in northern Taiwan. The study also uses a generalized likelihood uncertainty estimation approach to quantify the parameter uncertainty of the distributed hydrological model. The results indicate that various land‐use policies—such as no change, dynamic change and simultaneous change—have different levels of impact on simulating the spatial distributions of hydrological components in the watershed study. Peak flow rates under simultaneous and dynamic land‐use changes are 5·71% and 2·77%, respectively, greater than the rate under the no land‐use change scenario. Using dynamic land‐use changes to assess the effect of land‐use changes on hydrological components is more practical and feasible than using simultaneous land‐use change and no land‐use change scenarios. Furthermore, land‐use change is a spatial dynamic process that can lead to significant changes in the distributions of ground water and soil moisture. The spatial distributions of land‐use changes influence hydrological processes, such as the ground water level of whole areas, particularly in the downstream watershed. Copyright © 2010 John Wiley & Sons, Ltd.     

Response analysis of rainfall–runoff processes using wavelet transform: a case study of the alpine meadow belt

Rainfall–runoff processes appear to be highly nonlinear in Bayinbluk watersheds of the northwestern China. In this study, the time‐scale wavelet transform has been used for the analysis of this nonstationary system. The Haar and Morlet wavelet transform were used to analyse the rainfall–runoff conversion relationship. Wavelet power spectrum and change point methods are also employed to analyse rainfall rates and runoffs measured at daily to half‐hourly sampling rate. The four experimental sites (Luoto, Haer, Kuce and Shengl) are located in the Tianshan Mountains (Xinjiang province, China). Correlation analysis and wavelet transform are first applied to runoff process in different underlying surfaces. Wavelet analyses of rainfall rates and runoffs also give meaningful information on the temporal variability of the rainfall–runoff relationship. Change point and wavelet power spectrum analysis provide simple interpretation of energy distribution between different scales. The results indicate that wavelet transform is a good method for analysing the nonlinear relationship of temporal–spatial responses between rainfall and runoff. This method allowed quantification of the processes affecting runoff and provided an insight into their implications in surface water management. Copyright © 2011 John Wiley & Sons, Ltd.     

Snow water equivalent prediction using Bayesian data assimilation methods

Using the U.S. National Weather Service’s SNOW-17 model, this study compares common sequential data assimilation methods, the ensemble Kalman filter (EnKF), the ensemble square root filter (EnSRF), and four variants of the particle filter (PF), to predict seasonal snow water equivalent (SWE) within a small watershed near Lake Tahoe, California. In addition to SWE estimation, the various data assimilation methods are used to estimate five of the most sensitive parameters of SNOW-17 by allowing them to evolve with the dynamical system. Unlike Kalman filters, particle filters do not require Gaussian assumptions for the posterior distribution of the state variables. However, the likelihood function used to scale particle weights is often assumed to be Gaussian. This study evaluates the use of an empirical cumulative distribution function (ECDF) based on the Kaplan–Meier survival probability method to compute particle weights. These weights are then used in different particle filter resampling schemes. Detailed analyses are conducted for synthetic and real data assimilation and an assessment of the procedures is made. The results suggest that the particle filter, especially the empirical likelihood variant, is superior to the ensemble Kalman filter based methods for predicting model states, as well as model parameters.     

Analysis of earthquake ground motions using an improved Hilbert–Huang transform

Some limitations of the Hilbert–Huang transform (HHT) for nonlinear and nonstationary signal processing are remarked. As an enhancement to the HHT, a time varying vector autoregressive moving average (VARMA) model based method is proposed to calculate the instantaneous frequencies of the intrinsic mode functions (IMFs) obtained from the empirical mode decomposition (EMD) of a signal. By representing the IMFs as time varying VARMA model and using the Kalman filter to estimate the time varying model parameters, the instantaneous frequencies are calculated according to the time varying parameters, then the instantaneous frequencies and the envelopes derived from the cubic spline interpolation of the maxima of IMFs are used to yield the Hilbert spectrum. The analysis of the length of day dataset and the ground motion record El Centro (1940, N–S) shows that the proposed method offers advantages in frequency resolution, and produces more physically meaningful and readable Hilbert spectrum than the original HHT method, short-time Fourier transform (STFT) and wavelet transform (WT). The analysis of the seismic response of a building during the 1994 Northridge earthquake shows that the proposed method is a powerful tool for structural damage detection, which is expected as the promising area for future research.     

Lumped surface and sub‐surface runoff for erosion modeling within a small hilly watershed in northern Vietnam

Developing models to predict on‐site soil erosion and off‐site sediment transport at the agricultural watershed scale represent an on‐going challenge in research today. This study attempts to simulate the daily discharge and sediment loss using a distributed model that combines surface and sub‐surface runoffs in a small hilly watershed (< 1 km²). The semi‐quantitative model, Predict and Localize Erosion and Runoff (PLER), integrates the Manning–Strickler equation to simulate runoff and the Griffith University Erosion System Template equation to simulate soil detachment, sediment storage and soil loss based on a map resolution of 30 m × 30 m and over a daily time interval. By using a basic input data set and only two calibration coefficients based, respectively, on water velocity and soil detachment, the PLER model is easily applicable to different agricultural scenarios. The results indicate appropriate model performance and a high correlation between measured and predicted data with both Nash–Sutcliffe efficiency (Ef) and correlation coefficient (r²) having values > 0.9. With the simple input data needs, PLER model is a useful tool for daily runoff and soil erosion modeling in small hilly watersheds in humid tropical areas. Copyright © 2013 John Wiley & Sons, Ltd.     

Plot and small‐watershed scale runoff from two reclaimed surface‐mined watersheds in Alberta

Infiltration excess overland flow has been identified as the dominant flow pathway in recently reclaimed surface mined watersheds as a result of compaction and sorting during the reclamation procedure. Therefore, there could be a fairly direct relationship between runoff generated from the hillslopes to that measured at the watershed outlet. A 3‐year study was initiated in 1993 to determine how well surface runoff at a watershed scale could be predicted from 1‐m² runoff frames placed on hillslopes in two reclaimed surface‐mined watersheds in central Alberta. Runoff from the hillslope frames suggests outlet discharge should be high from the 3\4‐ha Sandy Subsoil Watershed and much less for the 9\8‐ha West Watershed, but the opposite occurred. Most of the hillslope runoff from the Sandy Subsoil Watershed infiltrated once it reached the channel and depression storage played an insignificant role in determining runoff. In contrast, most of the runoff from the West Watershed originated from rain falling directly on the saturated channel (depression storage) or near‐channel saturated areas, rather than the hillslopes. Neither watershed runoff magnitude nor timing could be predicted from the same parameters for hillslope runoff frames for either reclaimed watershed. Copyright © 2000 John Wiley & Sons, Ltd.     

On-line estimation of unit hydrographs using the wavelet-based LMS algorithm / Estimation en ligne des hydrogrammes unitaires grâce à l'algorithme des moindres carrés moyens à base d'ondelettes

Abstract

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.     

Obtaining refined first‐order predictive models of linear structural systems

This study presents an effective method for identifying predictive models and the underlying modal parameters of linear structural systems using only measured output and excitation time histories obtained from dynamic testing. The system under examination is modelled as a first‐order multi‐input multi‐output time‐invariant system, and the structural model is realized using the Eigensystem Realization Algorithm together with the Observer/Kalman filter IDentification algorithm. The identified state‐space model is further refined using a non‐linear optimization technique based on sequential quadratic programming. The numerical examples show that the developed methodology performs very well even in the presence of inadequate instrumentation and measurement noise, and that the methodology is highly capable of creating realistic predictive models of structural systems, as well as estimating their underlying modal parameters. Copyright © 2002 John Wiley & Sons, Ltd.     

Development of a support‐vector‐machine‐based model for daily pan evaporation estimation

Evaporation estimation is an important issue in water resources management. In this article, a four‐season model with optimal input combination is proposed to estimate the daily evaporation. First, the model based on support vector machine (SVM) coupled with an input determination process is used to determine the optimal combination of input variables. Second, a comparison of the SVM‐based model with the model based on back‐propagation network (BPN) is made to demonstrate the superiority of the SVM‐based model. In addition, season data are used to construct the SVM‐based four‐season model to further improve the daily evaporation estimation. An application is conducted to demonstrate the performance of the proposed model. Results show that the SVM‐based model can select the optimal input combination with physical mechanism. The SVM‐based model is more appropriate than the BPN‐based model because of its higher accuracy, robustness and efficiency. Moreover, the improvement due to the use of the four‐season model increases from 3.22% to 15.30% for RMSE and from 4.84% to 91.16% for CE, respectively. In conclusion, the SVM‐based model coupled with the proposed input determination process should be used to select input variables. The proposed four‐season SVM‐based model with optimal input combination is recommended as an alternative to the existing models. The proposed modelling technique is expected to be useful to improve the daily evaporation estimation. Copyright © 2012 John Wiley & Sons, Ltd.     

Geospatially based distributed rainfall‐runoff modelling for simulation of internal and outlet responses in a semi‐forested lower Himalayan watershed

This study presents a Geographic Information System (GIS)‐based distributed rainfall‐runoff model for simulating surface flows in small to large watersheds during isolated storm events. The model takes into account the amount of interception storage to be filled using a modified Merriam ( 1960 ) approach before estimating infiltration by the Smith and Parlange ( 1978 ) method. The mechanics of overland and channel flow are modelled by the kinematic wave approximation of the Saint Venant equations which are then numerically solved by the weighted four‐point implicit finite difference method. In this modelling the watershed was discretized into overland planes and channels using the algorithms proposed by Garbrecht and Martz ( 1999 ). The model code was first validated by comparing the model output with an analytical solution for a hypothetical plane. Then the model was tested in a medium‐sized semi‐forested watershed of Pathri Rao located in the Shivalik ranges of the Garhwal Himalayas, India. Initially, a local sensitivity analysis was performed to identify the parameters to which the model outputs like runoff volume, peak flow and time to peak flow are sensitive. Before going for model validation, calibration was performed using the Ordered‐Physics‐based Parameter Adjustment (OPPA) method. The proposed Physically Based Distributed (PBD) model was then evaluated both at the watershed outlet as well as at the internal gauging station, making this study a first of its kind in Indian watersheds. The results of performance evaluation indicate that the model has simulated the runoff hydrographs reasonably well within the watershed as well as at the watershed outlet with the same set of calibrated parameters. The model also simulates, realistically, the temporal variation of the spatial distribution of runoff over the watershed and the same has been illustrated graphically. Copyright © 2011 John Wiley & Sons, Ltd.     

Daily streamflow modelling and assessment based on the curve‐number technique

A cell‐based long‐term hydrological model (CELTHYM) that can be integrated with a geographical information system (GIS) was developed to predict continuous stream flow from small agricultural watersheds. The CELTHYM uses a cell‐by‐cell soil moisture balance approach. For surface runoff estimation, the curve number technique considering soil moisture on a daily basis was used, and release rate was used to estimate baseflow. Evapotranspiration was computed using the FAO modified Penman equation that considered land‐use‐based crop coefficients, soil moisture and the influence of topography on radiation. A rice paddy field water budget model was also adapted for the specific application of the model to East Asia. Model sensitivity analysis was conducted to obtain operational information about the model calibration parameters. The CELTHYM was calibrated and verified with measured runoff data from the WS#1 and WS#3 watersheds of the Seoul National University, Department of Agricultural Engineering, in Hwaseong County, Kyounggi Province, South Korea. The WS#1 watershed is comprised of about 35·4% rice paddy fields and 42·3% forest, whereas the WS#3 watershed is about 85·0% forest and 11·5% rice paddy fields. The CELTHYM was calibrated for the parameter release rate, K, and soil moisture storage coefficient, STC, and results were compared with the measured runoff data for 1986. The validation results for WS#1 considering all daily stream flow were poor with R², E² and RMSE having values of 0·40, ?6·63 and 9·69 (mm), respectively, but validation results for days without rainfall were statistically significant (R² = 0·66). Results for WS#3 showed good agreement with observed data for all days, and R², E² and RMSE were 0·92, 0·91 and 2·23 (mm), respectively, suggesting potential for CELTHYM application to other watersheds. The direct runoff and water balance components for watershed WS#1 with significant areas of paddy fields did not perform well, suggesting that additional study of these components is needed. Copyright © 2002 John Wiley & Sons, Ltd.     

Fuzzy computing based rainfall–runoff model for real time flood forecasting

This paper analyses the skills of fuzzy computing based rainfall–runoff model in real time flood forecasting. The potential of fuzzy computing has been demonstrated by developing a model for forecasting the river flow of Narmada basin in India. This work has demonstrated that fuzzy models can take advantage of their capability to simulate the unknown relationships between a set of relevant hydrological data such as rainfall and river flow. Many combinations of input variables were presented to the model with varying structures as a sensitivity study to verify the conclusions about the coherence between precipitation, upstream runoff and total watershed runoff. The most appropriate set of input variables was determined, and the study suggests that the river flow of Narmada behaves more like an autoregressive process. As the precipitation is weighted only a little by the model, the last time‐steps of measured runoff are dominating the forecast. Thus a forecast based on expected rainfall becomes very inaccurate. Although good results for one‐step‐ahead forecasts are received, the accuracy deteriorates as the lead time increases. Using the one‐step‐ahead forecast model recursively to predict flows at higher lead time, however, produces better results as opposed to different independent fuzzy models to forecast flows at various lead times. Copyright © 2004 John Wiley & Sons, Ltd.