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.     

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.     

A systematic approach to the input determination for neural network rainfall–runoff models

Input determination has a great influence on the performance of artificial neural network (ANN) rainfall–runoff models. To improve the performance of ANN models, a systematic approach to the input determination for ANN models is proposed. In the proposed approach, the irrelevant inputs are removed. Then an adequate ANN model, which only includes highly relevant inputs, is constructed. Unlike the trial‐and‐error procedure, the proposed approach is more systematic and avoids unnecessary trials. To demonstrate the effectiveness of the proposed approach, an application to actual typhoon events is presented. The results show that the proposed ANN model, which is constructed by the proposed approach, has advantages over those obtained by the trial‐and‐error procedure. The proposed ANN model has a simpler architecture, needs less training time, and performs better. The proposed ANN model is recommended as an alternative to existing rainfall–runoff ANN models. Copyright © 2007 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.     

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.     

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.     

Correlation of the velocity parameter of three geomorphological instantaneous unit hydrograph models

Three geomorphological instantaneous unit hydrograph (GIUH) models are investigated. These GIUHs were derived as a function of watershed geomorphological characteristics. The geomorphological input parameters of the models were determined for 10 basins in Indiana, USA. The three GIUH models were used to simulate 187 observed runoff hydrographs of these basins. The non-measurable velocity parameters of the GIUH models were optimized and the relationships between them were investigated. The results of the investigation show that the velocity parameters of the three models are correlated. © 1998 John Wiley & Sons, Ltd.     

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.     

Assessment of rainfall‐runoff models based upon wavelet analysis

A basic hypothesis is proposed: given that wavelet‐based analysis has been used to interpret runoff time‐series, it may be extended to evaluation of rainfall‐runoff model results. Conventional objective functions make certain assumptions about the data series to which they are applied (e.g. uncorrelated error, homoscedasticity). The difficulty that objective functions have in distinguishing between different realizations of the same model, or different models of the same system, is that they may have contributed in part to the occurrence of model equifinality. Of particular concern is the fact that the error present in a rainfall‐runoff model may be time dependent, requiring some form of time localization in both identification of error and derivation of global objective functions. We explore the use of a complex Gaussian (order 2) wavelet to describe: (1) a measured hydrograph; (2) the same hydrograph with different simulated errors introduced; and (3) model predictions of the same hydrograph based upon a modified form of TOPMODEL. The analysis of results was based upon: (a) differences in wavelet power (the wavelet power error) between the measured hydrograph and both the simulated error and modelled hydrographs; and (b) the wavelet phase. Power difference and wavelet phase were used to develop two objective functions, RMSE(power) and RMS(phase), which were shown to distinguish between simulated errors and model predictions with similar values of the commonly adopted Nash‐Sutcliffe efficiency index. These objective functions suffer because they do not retain time, frequency or time‐frequency localization. Consideration of wavelet power spectra and time‐ and frequency‐integrated power spectra shows that the impacts of different types of simulated error can be seen through retention of some localization, especially in relation to when and the scale over which error was manifest. Theoretical objections to the use of wavelet analysis for this type of application are noted, especially in relation to the dependence of findings upon the wavelet chosen. However, it is argued that the benefits of localization and the qualitatively low sensitivity of wavelet power and phase to wavelet choice are sufficient to warrant further exploration of wavelet‐based approaches to rainfall‐runoff model evaluation. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Long‐term runoff forecasting by combining hydrological models and meteorological records

Reservoir operation is generally based on the inflows of the upstream catchment of the reservoir. If the arriving inflows can be forecasted, that can benefit reservoir operation and management. This study attempts to construct a long‐term inflow‐forecasting model by combining a continuous rainfall–runoff model with the long‐term weather outlook from the Central Weather Bureau of Taiwan. The analytical results demonstrate that the continuous rainfall–runoff model has good inflow simulation performance by using 10‐day meteorological and inflow records over a 33‐year period for model calibration and verification. The long‐term inflow forecasting during the dry season was further conducted by combining the continuous rainfall–runoff model and the long‐term weather outlook, which was found to have good performance. Copyright © 2005 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.     

Storm‐event rainfall–runoff modelling approach for ungauged sites in Taiwan

This work develops a top‐down modelling approach for storm‐event rainfall–runoff model calibration at unmeasured sites in Taiwan. Twenty‐six storm events occurring in seven sub‐catchments in the Kao‐Ping River provided the analytical data set. Regional formulas for three important features of a streamflow hydrograph, i.e. time to peak, peak flow, and total runoff volume, were developed via the characteristics of storm event and catchment using multivariate regression analysis. Validation of the regional formulas demonstrates that they reasonably predict the three features of a streamflow hydrograph at ungauged sites. All of the sub‐catchments in the study area were then adopted as ungauged areas, and the three streamflow hydrograph features were calculated by the regional formulas and substituted into the fuzzy multi‐objective function for rainfall–runoff model calibration. Calibration results show that the proposed approach can effectively simulate the streamflow hydrographs at the ungauged sites. The simulated hydrographs more closely resemble observed hydrographs than hydrographs synthesized using the Soil Conservation Service (SCS) dimensionless unit hydrograph method, a conventional method for hydrograph estimation at ungauged sites in Taiwan. Copyright © 2008 John Wiley & Sons, Ltd.     

Effects of differential hillslope‐scale water retention characteristics on rainfall–runoff response at the Landscape Evolution Observatory

Hillslopes turn precipitation into runoff and thus exert important controls on various Earth system processes. It remains difficult to collect reliable data necessary for understanding and modeling these Earth system processes in real catchments. To overcome this problem, controlled experiments are being conducted at the Landscape Evolution Observatory at Biosphere 2, The University of Arizona. Previous experiments have revealed differences in hydrological response between 2 landscapes within Landscape Evolution Observatory, even though both landscapes were designed to be identical. In an attempt to discover where the observed differences stem from, we use a fully 3‐dimensional hydrological model (CATchment HYdrology) to show the effect of soil water retention characteristics and saturated hydraulic conductivity on the hydrological response of these 2 hillslopes. We also show that soil water retention characteristics can be derived at hillslope scale from experimental observations of soil moisture and matric potential. It is found that differences in soil packing between the 2 landscapes may be responsible for the observed differences in hydrological response. This modeling study also suggests that soil water retention characteristics and saturated hydraulic conductivity have a profound effect on rainfall–runoff processes at hillslope scale and that parametrization of a single hillslope may be a promising step in modeling rainfall–runoff response in real catchments.     

Comparative analysis of a geomorphology‐based instantaneous unit hydrograph in small mountainous watersheds

A conceptual insytnataneous unit hydrograph (IUH) based on geomorphologival association of linear reservoirs (GR) previously developed by the authors has been compared with other IUH models: a distributed GR variation (GR(v)), the Nash IUH, the Chutha and Dooge IUH, and the Troutman and Karlinger IUH for the analysis of direct runoff hydrographs recorded in three experimental watershed of the north of Spain. The comparison was made through a calibration‐validation process in which a leave‐one‐out cross‐validation method was applied. The results indicate the satisfactory performance of all the models, with the advantage for the GR model of the dependence on only one parameter, which can be identified from the watershed and event characteristics. This property makes its use easier than that of other models. Copyright © 2011 John Wiley & Sons, Ltd.     

Conceptual rainfall–runoff model with a two‐parameter,infinite characteristic time transfer function

A two‐parameter transfer function with an infinite characteristic time is proposed for conceptual rainfall–runoff models. The large time behaviour of the unit response is an inverse power function of time. The infinite characteristic time allows long‐term memory effects to be accounted for. Such effects are observed in mountainous and karst catchments. The governing equation of the model is a fractional differential equation in the limit of long times. Although linear, the proposed transfer function yields discharge signals that can usually be obtained only using non‐linear models. The model is applied successfully to two catchments, the Dud Koshi mountainous catchment in the Himalayas and the Durzon karst catchment in France. It compares favourably to the linear, non‐linear single reservoir models and to the GR4J model. With a single reservoir and a single transfer function, the model is capable of reproducing hysteretic behaviours identified as typical of long‐term memory effects. Computational efficiency is enhanced by approximating the infinite characteristic time transfer function with a sum of simpler, exponential transfer functions. This amounts to partitioning the reservoir into several linear sub‐reservoirs, the output discharges of which are easy to compute. An efficient partitioning strategy is presented to facilitate the practical implementation of the model. Copyright © 2015 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.