HydRun: A MATLAB toolbox for rainfall–runoff analysis

Understanding the nature of streamflow response to precipitation inputs is at the core of hydrological applications and water resource management. Indices such as the base flow index, recession constant, and response lag of a watershed retain an important place in hydrology as metrics to compare watersheds and understand the impact of human activity, geology, geomorphology, soils, and climate on precipitation–runoff relations. Extracting characteristics of the hyetograph–hydrograph relationship is often done manually, which is time consuming and may result in subjective and potentially inconsistent outcomes. Here, we present a MATLAB‐based toolbox, called HydRun, for rapid and flexible rainfall–runoff analysis. HydRun uses a series of flexible routines to extract base flow from the hydrograph and then computes commonly used time instants of the rainfall–runoff relationship. HydRun provides users the flexibility to decide thresholds and limits of analysis, but objectively computes hydrometric indices. The toolkit includes a graphical user interface and example files. In this paper, we apply HydRun to 4 watersheds, 3 in Scotland and 1 in Canada, to demonstrate the software functions and highlight important decisions the user must make in its application.     

Effects of the catchment runoff coefficient on the performance of TOPMODEL in rainfall–runoff modelling

Effects of the catchment runoff coefficient on the performance of TOPMODEL in simulating catchment rainfall–runoff relationships are investigated in this paper, with an aim to improve TOPMODEL's simulation efficiency in catchments with a low runoff coefficient. Application of TOPMODEL in the semi‐arid Yihe catchment, with an area of 2623 km² in the Yellow River basin of China, produced a Nash–Sutcliffe model efficiency of about 80%. To investigate how the catchment runoff coefficient affects the performance of TOPMODEL, the whole observed discharge series of the Yihe catchment is multiplied with a larger‐than‐unity scale factor to obtain an amplified discharge series. Then TOPMODEL is used to simulate the amplified discharge series given the original rainfall and evaporation data. For a set of different scale factors, TOPMODEL efficiency is plotted against the corresponding catchment runoff coefficient and it is found that the efficiency of TOPMODEL increases with the increasing catchment runoff coefficient before reaching a peak (e.g. about 90%); after the peak, however, the efficiency of TOPMODEL decreases with the increasing catchment runoff coefficient. Based on this finding, an approach called the discharge amplification method is proposed to enhance the simulation efficiency of TOPMODEL in rainfall–runoff modelling in catchments with a low runoff coefficient. Copyright © 2004 John Wiley & Sons, Ltd.     

The role of hydrograph indices in parameter estimation of rainfall–runoff models

A reliable prediction of hydrologic models, among other things, requires a set of plausible parameters that correspond with physiographic properties of the basin. This study proposes a parameter estimation approach, which is based on extracting, through hydrograph diagnoses, information in the form of indices that carry intrinsic properties of a basin. This concept is demonstrated by introducing two indices that describe the shape of a streamflow hydrograph in an integrated manner. Nineteen mid‐size (223–4790 km²) perennial headwater basins with a long record of streamflow data were selected to evaluate the ability of these indices to capture basin response characteristics. An examination of the utility of the proposed indices in parameter estimation is conducted for a five‐parameter hydrologic model using data from the Leaf River, located in Fort Collins, Mississippi. It is shown that constraining the parameter estimation by selecting only those parameters that result in model output which maintains the indices as found in the historical data can improve the reliability of model predictions. These improvements were manifested in (a) improvement of the prediction of low and high flow, (b) improvement of the overall total biases, and (c) maintenance of the hydrograph's shape for both long‐term and short‐term predictions. Copyright © 2005 John Wiley & Sons, Ltd.     

Error analysis for the evaluation of model performance: rainfall–runoff event time series data

This paper provides a procedure for evaluating model performance where model predictions and observations are given as time series data. The procedure focuses on the analysis of error time series by graphing them, summarizing them, and predicting their variability through available information (recalibration). We analysed two rainfall–runoff events from the R‐5 data set, and evaluated 12 distinct model simulation scenarios for these events, of which 10 were conducted with the quasi‐physically‐based rainfall–runoff model (QPBRRM) and two with the integrated hydrology model (InHM). The QPBRRM simulation scenarios differ in their representation of saturated hydraulic conductivity. Two InHM simulation scenarios differ with respect to the inclusion of the roads at R‐5. The two models, QPBRRM and InHM, differ strongly in the complexity and number of processes included. For all model simulations we found that errors could be predicted fairly well to very well, based on model output, or based on smooth functions of lagged rainfall data. The errors remaining after recalibration are much more alike in terms of variability than those without recalibration. In this paper, recalibration is not meant to fix models, but merely as a diagnostic tool that exhibits the magnitude and direction of model errors and indicates whether these model errors are related to model inputs such as rainfall. Copyright © 2004 John Wiley & Sons, Ltd.     

Effect of rainfall uncertainty on the performance of physically based rainfall–runoff models

This paper analyses the effect of rain data uncertainty on the performance of two hydrological models with different spatial structures: a semidistributed and a fully distributed model. The study is performed on a small catchment of 19.6 km² located in the north‐west of Spain, where the arrival of low pressure fronts from the Atlantic Ocean causes highly variable rainfall events. The rainfall fields in this catchment during a series of storm events are estimated using rainfall point measurements. The uncertainty of the estimated fields is quantified using a conditional simulation technique. Discharge and rain data, including the uncertainty of the estimated rainfall fields, are then used to calibrate and validate both hydrological models following the generalized likelihood uncertainty estimation (GLUE) methodology. In the storm events analysed, the two models show similar performance. In all cases, results show that the calibrated distribution of the input parameters narrows when the rain uncertainty is included in the analysis. Otherwise, when rain uncertainty is not considered, the calibration of the input parameters must account for all uncertainty in the rainfall–runoff transformation process. Also, in both models, the uncertainty of the predicted discharges increase in similar magnitude when the uncertainty of rainfall input increase.     

Comparison of genetic algorithms and shuffled complex evolution approach for calibrating distributed rainfall–runoff model

Three methods, Shuffled Complex Evolution (SCE), Simple Genetic Algorithm (SGA) and Micro‐Genetic Algorithm (µGA), are applied in parameter calibration of a grid‐based distributed rainfall–runoff model (GBDM) and compared by their performances. Ten and four historical storm events in the Yan‐Shui Creek catchment, Taiwan, provide the database for model calibration and verification, respectively. The study reveals that the SCE, SGA and µGA have close calibration results, and none of them are superior with respect to all the performance measures, i.e. the errors of time to peak, peak discharge and the total runoff volume, etc. The performances of the GBDM for the verification events are slightly worse than those in the calibration events, but still quite satisfactory. Among the three methods, the SCE seems to be more robust than the other two approaches because of the smallest influence of different initial random number seeds on calibrated model parameters, and has the best performance of verification with a relatively small number of calibration events. Copyright © 2009 John Wiley & Sons, Ltd.     

In situ measurements of soil saturated hydraulic conductivity: Assessment of reliability through rainfall–runoff experiments

The saturated hydraulic conductivity, K_s, is a soil property that has a key role in the partitioning of rainfall into surface runoff and infiltration. The commonly used instruments and methods for in situ measurements of K_s have frequently provided conflicting results. Comparison of K_s estimates obtained by three classical devices—namely, the double ring infiltrometer (DRI), the Guelph version of the constant‐head well permeameter (GUELPH‐CHP) and the CSIRO version of the tension permeameter (CSIRO‐TP) is presented. A distinguishing feature in this study is the use of steady deep flow rates, obtained from controlled rainfall–runoff experiments, as benchmark values of K_s at local and field‐plot scales, thereby enabling an assessment of these methods in reliably reproducing repeatable values and in their capability of determining plot‐scale variation of K_s. We find that the DRI grossly overestimates K_s, the GUELPH‐CHP gives conflicting estimates of K_s with substantial overestimation in laboratory experiments and underestimation at the plot scale, whereas the CSIRO‐TP yields average K_s values with significant errors of 24% in the plot scale experiment and 66% in laboratory experiments. Although the DRI would likely yield a better estimate of the nature of variability than the GUELPH‐CHP and CSIRO‐TP, a separate calibration may be warranted to correct for the overestimation of K_s values. The reasons for such discrepancies within and between the measurement methods are not yet fully understood and serve as motivation for future work to better characterize the uncertainty associated with individual measurements of K_s using these methods and the characterization of field scale variability from multiple local measurements.     

Real‐time recurrent learning neural network for stream‐flow forecasting

Various types of neural networks have been proposed in previous papers for applications in hydrological events. However, most of these applied neural networks are classified as static neural networks, which are based on batch processes that update action only after the whole training data set has been presented. The time variate characteristics in hydrological processes have not been modelled well. In this paper, we present an alternative approach using an artificial neural network, termed real‐time recurrent learning (RTRL) for stream‐flow forecasting. To define the properties of the RTRL algorithm, we first compare the predictive ability of RTRL with least‐square estimated autoregressive integrated moving average models on several synthetic time‐series. Our results demonstrate that the RTRL network has a learning capacity with high efficiency and is an adequate model for time‐series prediction. We also investigated the RTRL network by using the rainfall–runoff data of the Da‐Chia River in Taiwan. The results show that RTRL can be applied with high accuracy to the study of real‐time stream‐flow forecasting networks. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

Effectivity of dissolved SF6 tracer for clarification of rainfall–runoff processes in a forested headwater catchment

Understanding rainfall‐runoff processes is crucial for prevention and prediction of water‐related natural disasters. Sulfur hexafluoride (SF₆) is a potential tracer, but few researches have applied it for rainfall‐runoff process studies. We observed multiple tracers including SF₆ in spring water at 1‐ to 2‐hr intervals during rainstorm events to investigate the effectivity of SF₆ tracer in rainfall–runoff studies through the clarification of rainfall–runoff process. The target spring is a perennial spring in a forested headwater catchment with an area of 0.045 km² in Fukushima, Japan. The relationship between the SF₆ concentration in spring water and the spring discharge volume was negative trend; the SF₆ concentration in spring water becomes low as the spring discharge volume increases especially during rainstorms. The hydrograph separation using SF₆ and chloride ion tracers was applied for determining the contribution of principal sources on rainfall–runoff water. It suggested more than 60% contribution of bedrock groundwater at the rainfall peak and high percentage contribution continued even in the hydrograph recession phase. Based on observed low SF₆ concentration in groundwater after heavy rainfall, the replacement of groundwater near the spring with bedrock groundwater is indicated as a mechanism for water discharge with low SF₆ concentration during rainfall events. Consequently, rainstorm events play an important role as triggers in discharging water stored in the deeper subsurface area. In addition, SF₆ tracer is concluded as one of the strongest tracers for examining rainfall–runoff process studies. And, therefore, this study provided new insights into the dynamics of groundwater and its responses to rainfall in terms of SF₆ concentration variance in water in headwater regions.     

Modelling the rainfall–runoff process of the Mara River basin using the Soil and Water Assessment Tool

The delicate balance between human utilization and sustaining its pristine biodiversity in the Mara River basin (MRB) is being threatened because of the expansion of agriculture, deforestation, human settlement, erosion and sedimentation and extreme flow events. This study assessed the applicability of the Soil and Water Assessment Tool (SWAT) model for long‐term rainfall–runoff simulation in MRB. The possibilities of combining/extending gage rainfall data with satellite rainfall estimates were investigated. Monthly satellite rainfall estimates not only overestimated but also lacked the variability of observed rainfall to substitute gage rainfall in model simulation. Uncertainties related to the quality and availability of input data were addressed. Sensitivity and uncertainty analysis was reported for alternative model components and hydrologic parameters used in SWAT. Mean sensitivity indices of SWAT parameters in MRB varied with and without observed discharge data. The manual assessment of individual parameters indicated heterogeneous response among sub‐basins of MRB. SWAT was calibrated and validated with 10 years of discharge data at Bomet (Nyangores River), Mulot (Amala River) and Mara Mines (Mara River) stations. Model performance varied from satisfactory at Mara Mines to fair at Bomet and weak at Mulot. The (Nash–Sutcliff efficiency, coefficient of determination) results of calibration and validation at Mara Mines were (0.68, 0.69) and (0.43, 0.44), respectively. Two years of moving time window and flow frequency analysis showed that SWAT performance in MRB heavily relied on quality and abundance of discharge data. Given the 5.5% area contribution of Amala sub‐basin as well as uncertainty and scarcity of input data, SWAT has the potential to simulate the rainfall runoff process in the MRB. Copyright © 2012 John Wiley & Sons, Ltd.     

Counterpropagation fuzzy–neural network for streamflow reconstruction

This study combines neural networks and fuzzy arithmetic to present a counterpropagation fuzzy–neural network (CFNN) for streamflow reconstruction. The CFNN has a rule‐based control, a modified self‐organizing counterpropagation network, and a fuzzy control predictor. It can generate rules automatically by increasing the training data to improve the accuracy of streamflow reconstruction. The CFNN establishes the input and output relationship of a watershed without set‐up parameters. The parameters are estimated systematically by the approach converging to an optimal solution. One sequence of data generated by the Monte Carlo method is used to demonstrate the accuracy of the CFNN. The streamflow data of the Da‐chia River, in central Taiwan, is also used to evaluate the performances of the CFNN. The results indicate the reliability and accuracy of the CFNN for streamflow reconstruction. Copyright © 2001 John Wiley & Sons, Ltd.     

A simple rainfall–runoff model based on hydrological units applied to the Teba catchment (south‐east Spain)

A hydrological model (YWB, yearly water balance) has been developed to model the daily rainfall–runoff relationship of the 202 km² Teba river catchment, located in semi‐arid south‐eastern Spain. The period of available data (1976–1993) includes some very rainy years with intensive storms (responsible for flooding parts of the town of Malaga) and also some very dry years. The YWB model is in essence a simple tank model in which the catchment is subdivided into a limited number of meaningful hydrological units. Instead of generating per unit surface runoff resulting from infiltration excess, runoff has been made the result of storage excess. Actual evapotranspiration is obtained by means of curves, included in the software, representing the relationship between the ratio of actual to potential evapotranspiration as a function of soil moisture content for three soil texture classes. The total runoff generated is split between base flow and surface runoff according to a given baseflow index. The two components are routed separately and subsequently joined. A large number of sequential years can be processed, and the results of each year are summarized by a water balance table and a daily based rainfall runoff time series. An attempt has been made to restrict the amount of input data to the minimum. Interactive manual calibration is advocated in order to allow better incorporation of field evidence and the experience of the model user. Field observations allowed for an approximate calibration at the hydrological unit level. Copyright © 2001 John Wiley & Sons, Ltd.     

Assessing rainfall–runoff models for the management of Lake Verbano

Growing human pressure and potential change in precipitation pattern induced by climate change require a more efficient and sustainable use of water resources. Hydrological models can provide a fundamental contribution to this purpose, especially as increasing availability of meteorological data and forecast allows for more accurate runoff predictions. In this article, two models are presented for describing the flow formation process in a sub‐alpine catchment: a distributed parameter, physically based model, and a lumped parameter, empirical model. The scope is to compare the two modelling approaches and to assess the impact of hydrometeorological information, either observations or forecast, on water resources management. This is carried out by simulating the real‐time management of the regulated lake that drains the catchment, using the inflow predictions provided by the two models. Copyright © 2010 John Wiley & Sons, Ltd.     

A two‐step‐ahead recurrent neural network for stream‐flow forecasting

In many engineering problems, such as flood warning systems, accurate multistep‐ahead prediction is critically important. The main purpose of this study was to derive an algorithm for two‐step‐ahead forecasting based on a real‐time recurrent learning (RTRL) neural network that has been demonstrated as best suited for real‐time application in various problems. To evaluate the properties of the developed two‐step‐ahead RTRL algorithm, we first compared its predictive ability with least‐square estimated autoregressive moving average with exogenous inputs (ARMAX) models on several synthetic time‐series. Our results demonstrate that the developed two‐step‐ahead RTRL network has efficient ability to learn and has comparable accuracy for time‐series prediction as the refitted ARMAX models. We then investigated the two‐step‐ahead RTRL network by using the rainfall–runoff data of the Da‐Chia River in Taiwan. The results show that the developed algorithm can be successfully applied with high accuracy for two‐step‐ahead real‐time stream‐flow forecasting. Copyright © 2003 John Wiley & Sons, Ltd.     

Predicting catchment flow in a semi‐arid region via an artificial neural network technique

A model of rainfall–runoff relationships is an essential tool in the process of evaluation of water resources projects. In this paper, we applied an artificial neural network (ANN) based model for flow prediction using the data for a catchment in a semi‐arid region in Morocco. Use of this method for non‐linear modelling has been demonstrated in several scientific fields such as biology, geology, chemistry and physics. The performance of the developed neural network‐based model was compared against multiple linear regression‐based model using the same observed data. It was found that the neural network model consistently gives superior predictions. Based on the results of this study, artificial neural network modelling appears to be a promising technique for the prediction of flow for catchments in semi‐arid regions. Accordingly, the neural network method can be applied to various hydrological systems where other models may be inappropriate. Copyright © 2004 John Wiley & Sons, Ltd.     

Green‐Ampt Curve‐Number mixed procedure as an empirical tool for rainfall–runoff modelling in small and ungauged basins

The Soil Conservation Service Curve Number (SCS‐CN) method is a popular rainfall–runoff model that is widely used to estimate direct runoff from small and ungauged basins. The SCS‐CN is a simple and valuable approach to quantify the total streamflow volume generated by storm rainfall, but its use is not appropriate for estimating the sub‐daily incremental rainfall excess. To overcome this drawback, we propose to include the Green‐Ampt (GA) infiltration model into a mixed procedure, which is referred to as Curve Number for Green‐Ampt (CN4GA), aiming to distribute in time the information provided by the SCS‐CN method. For a given storm, the computed SCS‐CN total net rainfall amount is employed to calibrate the soil hydraulic conductivity parameter of the GA model. The proposed procedure is evaluated by analysing 100 rainfall–runoff events that were observed in four small catchments of varying size. CN4GA appears to provide encouraging results for predicting the net rainfall peak and duration values and has shown, at least for the test cases considered in this study, better agreement with the observed hydrographs than the classic SCS‐CN method. Copyright © 2012 John Wiley & Sons, Ltd.     

Probabilistic and ensemble simulation approaches for input uncertainty quantification of artificial neural network hydrological models

Artificial neural network (ANN) has been demonstrated to be a promising modelling tool for the improved prediction/forecasting of hydrological variables. However, the quantification of uncertainty in ANN is a major issue, as high uncertainty would hinder the reliable application of these models. While several sources have been ascribed, the quantification of input uncertainty in ANN has received little attention. The reason is that each measured input quantity is likely to vary uniquely, which prevents quantification of a reliable prediction uncertainty. In this paper, an optimization method, which integrates probabilistic and ensemble simulation approaches, is proposed for the quantification of input uncertainty of ANN models. The proposed approach is demonstrated through rainfall-runoff modelling for the Leaf River watershed, USA. The results suggest that ignoring explicit quantification of input uncertainty leads to under/over estimation of model prediction uncertainty. It also facilitates identification of appropriate model parameters for better characterizing the hydrological processes.     

Comparison of event‐specific rainfall–runoff responses and their controls in contrasting geographic areas

Numerous studies have examined the event‐specific hydrologic response of hillslopes and catchments to rainfall. Knowledge gaps, however, remain regarding the relative influence of different meteorological factors on hydrologic response, the predictability of hydrologic response from site characteristics, or even the best metrics to use to effectively capture the temporal variability of hydrologic response. This study aimed to address those knowledge gaps by focusing on 21 sites with contrasting climate, topography, geology, soil properties, and land cover. High‐frequency rainfall and discharge records were analysed, resulting in the delineation of over 1,600 rainfall–runoff events, which were described using a suite of hydrologic response metrics and meteorological factors. Univariate and multivariate statistical techniques were then applied to synthesize the information conveyed by the computed metrics and factors, notably measures of central tendency and variability, variation partitioning, partial correlations, and principal component analysis. Results showed that some response magnitude metrics generally reported in the literature (e.g., runoff ratio and area‐normalized peak discharge) did not vary significantly among sites. The temporal variability in site‐specific hydrologic response was often attributable to the joint influence of storage‐driven (e.g., total event rainfall and antecedent precipitation) and intensity‐driven (e.g., rainfall intensity and antecedent potential evapotranspiration) meteorological factors. Mean annual temperature and potential evapotranspiration at a given site appeared to be good predictors of hydrologic response timing (e.g., response lag and lag to peak). Response timing metrics, particularly those associated with response initiation, were also identified as the metrics most critical for capturing intrasite response variability. This study therefore contributes to the growing knowledge on event‐specific hydrologic response by highlighting the importance of response timing metrics and intensity‐driven meteorological factors, which are infrequently discussed in the literature. As few correlations were found between physiographic variables and response metrics, more data‐driven studies are recommended to further our understanding of landscape–hydrology interactions.     

Identification of physical processes inherent in artificial neural network rainfall runoff models

The emergence of artificial neural network (ANN) technology has provided many promising results in the field of hydrology and water resources simulation. However, one of the major criticisms of ANN hydrologic models is that they do not consider/explain the underlying physical processes in a watershed, resulting in them being labelled as black‐box models. This paper discusses a research study conducted in order to examine whether or not the physical processes in a watershed are inherent in a trained ANN rainfall‐runoff model. The investigation is based on analysing definite statistical measures of strength of relationship between the disintegrated hidden neuron responses of an ANN model and its input variables, as well as various deterministic components of a conceptual rainfall‐runoff model. The approach is illustrated by presenting a case study for the Kentucky River watershed. The results suggest that the distributed structure of the ANN is able to capture certain physical behaviour of the rainfall‐runoff process. The results demonstrate that the hidden neurons in the ANN rainfall‐runoff model approximate various components of the hydrologic system, such as infiltration, base flow, and delayed and quick surface flow, etc., and represent the rising limb and different portions of the falling limb of a flow hydrograph. Copyright © 2004 John Wiley & Sons, Ltd.