A data-based regional scale autoregressive rainfall-runoff model: a study from the Odra River

This paper aims to compare the performances of multivariate autoregressive (MAR) techniques and univariate autoregressive (AR) methods applied to regional scale rainfall-runoff modelling. We focus on the case study from the upper and middle reaches of the Odra River with its main tributaries in SW Poland. The rivers drain both the mountains (the Sudetes) and the lowland (Nizina Śląska). The region is exposed to extreme hydrologic and meteorological events, especially rain-induced and snow-melt floods. For the analysis, four hydrologic and meteorological variables are chosen, i.e., discharge (17 locations), precipitation (7 locations), thickness of snow cover (7 locations) and groundwater level (1 location). The time period is November 1971–December 1981 and the temporal resolution of the time series is of 1 day. Both MAR and AR models of the same orders are fitted to various subsets of the data and subsequently forecasts of discharge are derived. In order to evaluate the predictions the stepwise procedure is applied to make the validation independent of the specific sample path of the stochastic process. It is shown that the model forecasts peak discharges even 2–4 days in advance in the case of both rain-induced and snow-melt peak flows. Furthermore, the accuracy of discharge predictions increases if one analyses the combined data on discharge, precipitation, snow cover, and groundwater level instead of the pure discharge multivariate time series. MAR-based discharge forecasts based on multivariate data on discharges are more accurate than AR-based univariate predictions for a year with a flood, however, this relation is reverse in the case of the free-of-flooding year. In contrast, independently of the occurrence of floods within a year, MAR-based discharge forecasts based on discharges, precipitation, snow cover, and groundwater level are more precise than AR-based predictions.     

Effects of streamflow isotope sampling strategies on the calibration of a tracer-aided rainfall-runoff model

Isotopes are increasingly used in rainfall-runoff models to constrain conceptualisations of internal catchment functioning and reduce model uncertainty. However, there is little guidance on how much tracer data is required to adequately do this, and different studies use data from different sampling strategies. Here, we used a 7-year time series of daily stable water isotope samples of precipitation and streamflow to derive a range of typical stream sampling regimes and investigate how this impacts calibration of a semi-distributed tracer-aided model in terms of flow, deuterium and flux age simulations. Over the 7 years weekly sampling facilitated an almost identical model performance as daily, and there were only slight deteriorations in performance for fortnightly sampling. Monthly sampling resulted in poorer deuterium simulations and greater uncertainty in the derived parameter sets ability to accurately represent catchment functioning, evidenced by unrealistic reductions in the volumes of water available for mixing in the saturation area causing simulated water age decreases. Reducing sampling effort and restricting data collection to 3 years caused reductions in the accuracy of deuterium simulation, though the deterioration did not occur if sampling continued for 5 years. Analysis was also undertaken to consider the effects of reduced sampling effort over the driest and wettest hydrological years to evaluate effects of more extreme conditions. This showed that the model was particularly sensitive to changes in sampling during dry conditions, when the catchment hydrological response is most non-linear. Across all dataset durations, sampling in relation to flow conditions, rather than time, revealed that samples collected at flows >Q50 could provide calibration results comparable to daily sampling. Targeting only extreme high flows resulted in poor deuterium and low flow simulations. This study suggests sufficient characterization of catchment functioning can be obtained through reduced sampling effort over longer timescales and the targeting of flows >Q50.     

Estimation for rainfall-runoff modeled as a partially observed Markov process

Abstract: Linear continuous time stochastic Nash cascade conceptual models for runoff are developed. The runoff is modeled as a simple system of linear stochastic differential equations driven by white Gaussian and marked point process noises. In the case of d reservoirs, the outputs of these reservoirs form a d dimensional vector Markov process, of which only the dth coordinate process is observed, usually at a discrete sample of time points. The dth coordinate process is not Markovian. Thus runoff is a partially observed Markov process if it is modeled using the stochastic Nash cascade model. We consider how to estimate the parameters in such models. In principle, maximum likelihood estimation for the complete process parameters can be carried out directly or through some form of the EM (estimation and maximization) algorithm or variation thereof, applied to the observed process data. In this research we consider a direct approximate likelihood approach and a filtering approach to an algorithm of EM type, as developed in Thompson and Kaseke (1994). These two methods are applied to some real life runoff data from a catchment in Wales, England. We also consider a special case of the martingale estimating function approach on the runoff model in the presence of rainfall. Finally, some simulations of the runoff process are given based on the estimated parameters.     

The applicability of a parsimonious model for local and regional prediction of runoff

Abstract

The Hydrological Recursive Model (HRM), a conceptual rainfall-runoff model, was applied for local and regional simulation of hourly discharges in the transnational Alzette River basin (Luxembourg-France-Belgium). The model was calibrated for a range of various sub-basins with a view to analysing its ability to reproduce the variability of basin responses during flood generation. The regionalization of the model parameters was obtained by fitting simultaneously the runoff series of calibration sub-basins after their spatial discretization in lithological contrasting isochronal zones. The runoff simulations of the model agreed well with the recorded runoff series. Significant correlations with some basin characteristics and, noticeably, the permeability of geological formations, could be found for two of the four free model parameters. The goodness of fit for runoff predictions using the derived regional parameter set was generally satisfactory, particularly for the statistical characteristics of streamflow. A more physically-based modelling approach, or at least an explicit treatment of quick surface runoff, is expected to give better results for high peak discharge.     

A comparative fuzzy logic approach to runoff coefficient and runoff estimation

In practice, rainfall–runoff relationships are achieved through a simply defined runoff coefficient concept that is widely used in many engineering hydrological designs in urban and rural areas. The simplicity of the method, with the sole requirement of runoff coefficient assessment, is the main attractiveness, in addition to its successful prediction of average runoff rates for a given rainfall record. Unfortunately, in the classical regression approach of the rainfall–runoff relationship, internal variabilities are not taken into consideration explicitly. The runoff coefficient is considered a constant value, and it is used without distinction of antecedent conditions for the calculation of runoff from the rainfall record. In this paper, various other uncertainty embedded versions of the runoff coefficient, and hence rainfall–runoff formulation, are presented in terms of statistics, probability, perturbation and, finally, fuzzy system modelling. It is concluded that the fuzzy logic approach yields the least relative error among the various alternative runoff calculation methods; therefore, it is recommended for use in future studies. The application of various alternatives is presented for two monthly rainfall‐runoff records around Istanbul, Turkey. Copyright © 2005 John Wiley & Sons, Ltd.     

Evidence of chaos in the rainfall-runoff process

Abstract

The transformation of rainfall into runoff is one of the most important processes in hydrology. In the past few decades, a wide variety of automated or computer-based approaches have been applied to model this process. However, many such approaches have an important limitation in that they treat the rainfall-runoff process as a realization of only a few parameters of linear relationships rather than the process as a whole. What is required, therefore, is an approach that can capture not only the overall appearance but also the intricate details of the nonlinear behaviour of the process. The purpose of this study is to investigate the possibility of understanding the dynamics of the rainfall-runoff process from a new perspective, as a chaotic process. The possible existence of chaotic behaviour in the rainfall-runoff process is studied by investigating the rainfall and runoff time series: (a) separately; and (b) jointly (using the runoff coefficient). Monthly rainfall and runoff observed over a period of 131 years (January 1807-December 1937) at the Göta River basin in the south of Sweden are analysed. The correlation dimension method is employed to identify the presence of chaos. The correlation dimensions obtained for the rainfall and runoff time series are 6.4 and 5.5, respectively. The finite dimensions obtained for the rainfall and runoff time series indicate the possible existence of chaos in these processes, implying that the joint rainfall-runoff process might also exhibit chaotic behaviour. The correlation dimension of about 7.8 obtained for the runoff coefficient also indicates the possible presence of chaos and supports the above results.     

Modelling groundwater level variations by learning from multiple models using fuzzy logic

Modelling time series of groundwater levels is investigated by three fuzzy logic (FL) models, Sugeno (SFL), Mamdani (MFL) and Larsen (LFL), using data from observation wells. One novelty in the study is the re-use of these three models as multiple models through the following strategies: (a) simple averaging, (b) weighted averaging and (c) committee machine techniques; these are implemented using artificial neural networks (ANN). These strategies provide some evidence that (i) multiple models improve on the performance of individual models and those using committee machines perform better than the other two options; and (ii) committee machine models produce defensible modelling results to develop management scenarios. The study investigates water table declines through management scenarios and shows that in this aquifer water use has higher impacts on water table variations than climatic variations. This provides evidence of the need for planned management in the study area.     

Conceptual fuzzy neural network model for water quality simulation

Artificial neural networks (ANNs) have been applied successfully in various fields. However, ANN models depend on large sets of historical data, and are of limited use when only vague and uncertain information is available, which leads to difficulties in defining the model architecture and a low reliability of results. A conceptual fuzzy neural network (CFNN) is proposed and applied in a water quality model to simulate the Barra Bonita reservoir system, located in the southeast region of Brazil. The CFNN model consists of a rationally‐defined architecture based on accumulated expert knowledge about variables and processes included in the model. A genetic algorithm is used as the training method for finding the parameters of fuzzy inference and the connection weights. The proposed model may handle the uncertainties related to the system itself, model parameterization, complexity of concepts involved and scarcity and inaccuracy of data. The CFNN showed greater robustness and reliability when dealing with systems for which data are considered to be vague, uncertain or incomplete. The CFNN model structure is easier to understand and to define than other ANN‐based models. Moreover, it can help to understand the basic behaviour of the system as a whole, being a successful example of cooperation between human and machine. Copyright © 2006 John Wiley & Sons, Ltd.     

Evaluation of rainfall-runoff performance using the stochastic integral equation method

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.     

Structural uncertainty assessment in a discharge simulation model

Abstract

A major goal in hydrological modelling is to identify and quantify different sources of uncertainty in the modelling process. This paper analyses the structural uncertainty in a streamflow modelling system by investigating a set of models with increasing model structure complexity. The models are applied to two basins: Kielstau in Germany and XitaoXi in China. The results show that the model structure is an important factor affecting model performance. For the Kielstau basin, influences from drainage and wetland are critical for the local runoff generation, while for the XitaoXi basin accurate distributions of precipitation and evapotranspiration are two of the determining factors for the success of the river flow simulations. The derived model uncertainty bounds exhibit appropriate coverage of observations. Both case studies indicate that simulation uncertainty for the low-flow period contributes more to the overall uncertainty than that for the peak-flow period, although the main hydrological features in these two basins differ greatly.

Citation Zhang, X. Y., Hörmann, G., Gao, J. F. & Fohrer, N. (2011) Structural uncertainty assessment in a discharge simulation model. Hydrol. Sci. J. 56(5), 854–869.     

River suspended sediment modelling using a fuzzy logic approach

Correct estimation of sediment volume carried by a river is very important for many water resources projects. Conventional sediment rating curves, however, are not able to provide sufficiently accurate results. In this paper, a fuzzy logic approach is proposed to estimate suspended sediment concentration from streamflow. This study provides forecasting benchmarks for sediment concentration prediction in the form of a numerical and graphical comparison between fuzzy and rating‐curve models. Benchmarking was based on a 5‐year period of continuous streamflow and sediment concentration data of Quebrada Blanca Station operated by the United States Geological Survey. The benchmark results showed that the fuzzy model was able to produce much better results than rating‐curve models. The fuzzy model proposed in the study is site specific and does not simulate the hysteresis effects. Copyright © 2006 John Wiley & Sons, Ltd.     

平原河网区降雨径流污染负荷测算——以太湖流域望虞河西岸为例

如何精细量化降雨径流污染负荷是流域尺度实现面源精准治污全过程控制的重要前提.本研究以水污染较为严重的望虞河西岸综合示范区为例,通过开展不同土地利用类型的降雨观测实验,修正SCS-CN模型中的初损率,并基于土地利用类型遥感解译和降雨径流污染物浓度测定,精细刻画降雨径流中总磷(TP)、总氮(TN)、氨氮(NH3-N)、化学...     

Hydrological time‐series modelling using an adaptive neuro‐fuzzy inference system

Accurate forecasting of hydrological time‐series is a quite important issue for a wise and sustainable use of water resources. In this study, an adaptive neuro‐fuzzy inference system (ANFIS) approach is used to construct a time‐series forecasting system. In particular, the applicability of an ANFIS to the forecasting of the time‐series is investigated. To illustrate the applicability and capability of an ANFIS, the River Great Menderes, located in western Turkey, is chosen as a case study area. The advantage of this method is that it uses the input–output data sets. A total of 5844 daily data sets collected from 1985 to 2000 are used for the time‐series forecasting. Models having various input structures were constructed and the best structure was investigated. In addition, four various training/testing data sets were built by cross‐validation methods and the best data set was obtained. The performance of the ANFIS models in training and testing sets was compared with observations and also evaluated. In order to get an accurate and reliable comparison, the best‐fit model structure was also trained and tested by artificial neural networks and traditional time‐series analysis techniques and the results compared. The results indicate that the ANFIS can be applied successfully and provide high accuracy and reliability for time‐series modelling. Copyright © 2007 John Wiley & Sons, Ltd.     

A fuzzy dynamic wave routing model

In this paper a fuzzy dynamic wave routing model (FDWRM) for unsteady flow simulation in open channels is presented. The continuity equation of the dynamic wave routing model is preserved in its original form while the momentum equation is replaced by a fuzzy rule based model which is developed on the principle that during unsteady flow the disturbances in the form of discontinuities in the gradient of the physical parameters will propagate along the characteristics with a velocity equal to that of velocity of the shallow water wave. The model gets rid off the assumptions associated with the momentum equation by replacing it with the fuzzy rule based model. It overcomes the necessity of calculating friction slope (S_f) in flow routing and hence the associated uncertainties are eliminated. The robustness of the fuzzy rule based model enables the FDWRM to march the solution even in regions where the aforementioned assumptions are violated. Also the model can be used for flow routing in curved channels. When the model is applied to hypothetical flood routing problems in a river it is observed that the results are comparable to those of an implicit numerical model (INM) which solves the dynamic wave equations using an implicit numerical scheme. The model is also applied to a real case of flow routing in a field canal. The results match well with the measured data and the model performs better than the INM. Copyright © 2007 John Wiley & Sons, Ltd.     

Advancing isotope-enabled hydrological modelling for ungauged calibration of data-scarce humid tropical catchments

Realistic projections of the future climate and how this translates to water availability is crucial for sustainable water resource management. However, data availability constrains the capacity to simulate streamflow and corresponding hydrological processes. Developing more robust hydrological models and methods that can circumvent the need for large amounts of hydro-climatic data is crucial to support water-related decisions, particularly in developing countries. In this study, we use natural isotope tracers in addition to hydro-climate data within a newly developed version of the spatially-distributed J2000iso as an isotope-enabled rainfall-runoff model simulating both water and stable isotope (δ²H) fluxes. We pilot the model for the humid tropical San Carlos catchment (2500 km²) in northeastern Costa Rica, which has limited time series, but spatially distributed data. The added benefit of simulating stable isotopes was assessed by comparing different amounts of observation data using three model calibration strategies (i) three streamflow gauges, (ii) three gauges with stream isotopes and (iii) isotopes only. The J2000iso achieved a streamflow Kling–Gupta efficiency (KGE) of 0.55–0.70 across all the models and gauges, but differences in hydrological process simulations emerged when including stable water isotopes in the rainfall-runoff calibration. Hydrological process simulation varied between the standard J2000 rainfall-runoff model with a high simulated surface runoff proportion of 37% as opposed to the isotope version with 84%–89% simulated baseflow or interflow. The model solutions that used only isotope data for calibration exhibited differences in simulated interflow, baseflow and model performance but captured bulk water balances with a reasonable match between the simulated and observed hydrographs. We conclude that J2000iso has shown the potential to support water balance modelling for ungauged catchments using stable isotope, satellite and global reanalysis data sets.     

Development of an automatic calibration scheme for the HBV hydrological model

An automatic calibration scheme for the HBV model (ACSH) was developed. The ACSH was based on the physical significance of the model parameters and structure. The inference of hydrologists in the manual calibration was adopted as the guideline. A slight modification of the model structure of the soil routine was suggested to avoid interdependence of the parameters. In total nine parameters, except the snow routine, Fc and MAXBAS, were calibrated automatically in two stages; first the soil moisture routine and then the others. There are six sets in two stages in total. Using the Powell method, the parameters in each step were calibrated simultaneously with carefully selected objective functions, and in particular a powerful objective function for the soil moisture routine. The steps were in a fixed order in the ACSH according to the model structure. The optimal values of the model parameters were stable, with the different initial values varying in considerable ranges. The automatic calibration gave the same model performance as the manual calibration when the ACSH was tested in two basins. The automatic calibration can thus be used as a reference or as an alternative solution of the model. © 1997 John Wiley & Sons, Ltd.     

Developing a hybrid multi‐model for peak flood forecasting

The present study aims to develop a hybrid multi‐model using the soft computing approach. The model is a combination of a fuzzy logic, artificial neural network (ANN) and genetic algorithm (GA). While neural networks are low‐level computational structures that perform well dealing with raw data, fuzzy logic deal with reasoning on a higher level by using linguistic information acquired from domain experts. However, fuzzy systems lack the ability to learn and cannot adjust themselves to a new environment. Moreover, experts occasionally make mistakes and thus some rules used in a system may be false. A network type structure of the present hybrid model is a multi‐layer feed‐forward network, the main part is a fuzzy system based on the first‐order Sugeno fuzzy model with a fuzzification and a defuzzification processes. The consequent parameters are determined by least square method. The back‐propagation is applied to adjust weights of network. Then, the antecedent parameters of the membership function are updated accordingly by the gradient descent method. The GA was applied to select the fuzzy rule. The hybrid multi‐model was used to forecast the flood level at Chiang Mai (under the big flood 2005) and the Koriyama flood (2003) in Japan. The forecasting results are evaluated using standard global goodness of fit statistic, efficient index (EI), the root mean square error (RMSE) and the peak flood error. Moreover, the results are compared to the results of a neuro‐genetic model (NGO) and ANFIS model using the same input and output variables. It was found that the hybrid multi‐model can be used successfully with an efficiency index (EI) more than 0·95 (for Chiang Mai flood up to 12 h ahead forecasting) and more than 0·90 (for Koriyama flood up to 8 h ahead forecasting). In general, all of three models can predict the water level with satisfactory results. However, the hybrid model gave the best flood peak estimation among the three models. Therefore, the use of fuzzy rule base, which is selected by GA in the hybrid multi‐model helps to improve the accuracy of flood peak. Copyright © 2009 John Wiley & Sons, Ltd.     

Effects of geological structures on rainfall-runoff responses in headwater catchments in a sedimentary rock mountain

Clarifying rainfall-runoff responses in mountainous areas is essential for disaster prediction as well as water resource management. Although runoff is considered to be significantly affected by topography, some previous studies have reported that geological structures also have significant effects on rainfall-runoff characteristics. Particularly in headwater catchments located in sedimentary rock mountains, dips and strikes may significantly affect rainwater discharge. In this study, the effects of geological structures on rainfall-runoff characteristics were investigated based on observed discharge hydrographs from 12 catchments, which lie radially from the summit of a sedimentary rock mountain. The results obtained were as follows: (1) Even though the topographic wetness index (TWI) distributions of the 12 catchments were similar, there were significant differences in their runoff characteristics; (2) Catchments with average flow direction oriented towards the strike direction (strike-oriented catchments) are characterized by large baseflows; (3) Catchments with average flow direction oriented towards the opposite dip direction (opposite dip-oriented catchments) are steep, and this results in quick storm runoff generation; (4) Catchments with average flow direction oriented toward the dip direction (dip-oriented catchments) are gentle, and this results in delayed storm runoff generation. It was presumed that in strike-oriented catchments, large quantities of groundwater flowing along the bedding planes owing to hydraulic anisotropy, exfiltrate and sustain the large amount of the observed baseflow, that is, in strike-oriented catchments, runoff is directly controlled by geological structures. Conversely, in opposite dip-oriented and dip-oriented catchments, runoff is indirectly controlled by geological structures, that is, geological structures affect slope gradients, which result in differences in storm runoff generation. Thus, this study clearly illustrates that geological structures significantly affect rainfall-runoff responses in headwater catchments located in sedimentary rock mountains.     

The influence of parametric uncertainty on the relationships between HBV model parameters and climatic characteristics

Abstract

An HBV rainfall–runoff model was applied to test the influence of climatic characteristics on model parameter values. The methodology consisted of the calibration and cross-validation of the HBV model on a series of 5-year periods for four selected catchments (Axe, Kamp, Wieprz and Wimmera). The model parameters were optimized using the SCEM-UA method which allowed for their uncertainty also to be assessed. Nine climatic indices were selected for the analysis of their influence on model parameters, and divided into water-related and temperature-related indices. This allowed the dependence of HBV model parameters on climate characteristics to be explored following their response to climate change conditioned on the catchment’s physical characteristics. The Pearson correlation coefficient and weighted Pearson correlation coefficient were used to test the dependence. Most parameters showed a statistically significant dependence on several climatic indices in all catchments. The study shows that the results of the correlation analysis with and without parametric uncertainty taken into account differ significantly.