Calibration Of Rainfall-runoff Models Research Articles

Addressing subjective decision-making inherent in GLUE-based multi-criteria rainfall–runoff model calibration

Summary GLUE is one of the most commonly used informal methodologies for uncertainty estimation in hydrological modelling. Despite the ease-of-use of GLUE, it involves a number of subjective decisions such as the strategy for identifying the behavioural solutions. This study evaluates the impact of behavioural solution identification strategies in GLUE on the quality of model output uncertainty. Moreover, two new strategies are developed to objectively identify behavioural solutions. The first strategy considers Pareto-based ranking of parameter sets, while the second one is based on ranking the parameter sets based on an aggregated criterion. The proposed strategies, as well as the traditional strategies in the literature, are evaluated with respect to reliability (coverage of observations by the envelope of model outcomes) and sharpness (width of the envelope of model outcomes) in different numerical experiments. These experiments include multi-criteria calibration and uncertainty estimation of three rainfall–runoff models with different number of parameters. To demonstrate the importance of behavioural solution identification strategy more appropriately, GLUE is also compared with two other informal multi-criteria calibration and uncertainty estimation methods (Pareto optimization and DDS-AU). The results show that the model output uncertainty varies with the behavioural solution identification strategy, and furthermore, a robust GLUE implementation would require considering multiple behavioural solution identification strategies and choosing the one that generates the desired balance between sharpness and reliability. The proposed objective strategies prove to be the best options in most of the case studies investigated in this research. Implementing such an approach for a high-dimensional calibration problem enables GLUE to generate robust results in comparison with Pareto optimization and DDS-AU.

Calibration of Conceptual Rainfall-Runoff Models Using Global Optimization

Parameter optimization for the conceptual rainfall-runoff (CRR) model has always been the difficult problem in hydrology since watershed hydrological model is high-dimensional and nonlinear with multimodal and nonconvex response surface and its parameters are obviously related and complementary. In the research presented here, the shuffled complex evolution (SCE-UA) global optimization method was used to calibrate the Xinanjiang (XAJ) model. We defined the ideal data and applied the method to observed data. Our results show that, in the case of ideal data, the data length did not affect the parameter optimization for the hydrological model. If the objective function was selected appropriately, the proposed method found the true parameter values. In the case of observed data, we applied the technique to different lengths of data (1, 2, and 3 years) and compared the results with ideal data. We found that errors in the data and model structure lead to significant uncertainties in the parameter optimization.

Calibration of Rainfall-Runoff Model in Urban Watersheds for Stormwater Management Assessment

AbstractPhysically based semidistributed rainfall-runoff models are an important tool for assessing decentralized green infrastructure alternatives in controlling combined sewer overflows (CSO). Few studies have analyzed reliable calibration methods of highly detailed rainfall-runoff models at the subcatchment level. This research presents calibration of the storm water management model version 5 (SWMM5) using high temporal resolution rainfall and flow data to perform a 10-month continuous simulation on a physically distributed urban catchment. Detailed analyses of parameters that physically represent the area in the SWMM5 model were done using remote sensing and geographical information systems techniques. Parallel computing and a multi-search driver were implemented along with a model-independent parameter estimation (PEST) method, to find global optima and accelerate the calibration process. PEST internal settings were tuned for the continuous SWMM5 estimation problem using one month of rainfall data. ...

Uncertainty-based multi-criteria calibration of rainfall-runoff models: a comparative study

This study compares formal Bayesian inference to the informal generalized likelihood uncertainty estimation (GLUE) approach for uncertainty-based calibration of rainfall-runoff models in a multi-criteria context. Bayesian inference is accomplished through Markov Chain Monte Carlo (MCMC) sampling based on an auto-regressive multi-criteria likelihood formulation. Non-converged MCMC sampling is also considered as an alternative method. These methods are compared along multiple comparative measures calculated over the calibration and validation periods of two case studies. Results demonstrate that there can be considerable differences in hydrograph prediction intervals generated by formal and informal strategies for uncertainty-based multi-criteria calibration. Also, the formal approach generates definitely preferable validation period results compared to GLUE (i.e., tighter prediction intervals that show higher reliability) considering identical computational budgets. Moreover, non-converged MCMC (based on the standard Gelman–Rubin metric) performance is reasonably consistent with those given by a formal and fully-converged Bayesian approach even though fully-converged results requires significantly larger number of samples (model evaluations) for the two case studies. Therefore, research to define alternative and more practical convergence criteria for MCMC applications to computationally intensive hydrologic models may be warranted.

Considering rating curve uncertainty in water level predictions

Abstract. Streamflow cannot be measured directly and is typically derived with a rating curve model. Unfortunately, this causes uncertainties in the streamflow data and also influences the calibration of rainfall-runoff models if they are conditioned on such data. However, it is currently unknown to what extent these uncertainties propagate to rainfall-runoff predictions. This study therefore presents a quantitative approach to rigorously consider the impact of the rating curve on the prediction uncertainty of water levels. The uncertainty analysis is performed within a formal Bayesian framework and the contributions of rating curve versus rainfall-runoff model parameters to the total predictive uncertainty are addressed. A major benefit of the approach is its independence from the applied rainfall-runoff model and rating curve. In addition, it only requires already existing hydrometric data. The approach was successfully demonstrated on a small catchment in Poland, where a dedicated monitoring campaign was performed in 2011. The results of our case study indicate that the uncertainty in calibration data derived by the rating curve method may be of the same relevance as rainfall-runoff model parameters themselves. A conceptual limitation of the approach presented is that it is limited to water level predictions. Nevertheless, regarding flood level predictions, the Bayesian framework seems very promising because it (i) enables the modeler to incorporate informal knowledge from easily accessible information and (ii) better assesses the individual error contributions. Especially the latter is important to improve the predictive capability of hydrological models.

On the choice of calibration periods and objective functions: A practical guide to model parameter identification

Despite the development of new measuring techniques, monitoring systems and advances in computer technology, rainfall-flow modelling is still a challenge. The reasons are multiple and fairly well known. They include the distributed, heterogeneous nature of the environmental variables affecting flow from the catchment. These are precipitation, evapotranspiration and in some seasons and catchments in Poland, snow melt also. This paper presents a review of work done on the calibration and validation of rainfall-runoff modelling, with a focus on the conceptual HBV model. We give a synthesis of the problems and propose a practical guide to the calibration and validation of rainfall-runoff models.

Using an informational entropy-based metric as a diagnostic of flow duration to drive model parameter identification

Calibration of rainfall-runoff models is made complicated by uncertainties in data, and by the arbitrary emphasis placed on various magnitudes of the model residuals by most traditional measures of fit. Current research highlights the importance of driving model identification by assimilating information from the data. In this paper, we evaluate the potential use of an entropybased measure as an objective function or as a model diagnostic in hydrological modelling, with particular interest in providing an appropriate quantitative measure of fit to the flow duration curve (FDC). The proposed Conditioned Entropy Difference (CED) metric is capable of characterising the information in the flow frequency distribution and thereby constrain the model calibration to respect this distributional information. Four years of hourly data from the 46.6 km2 Mahurangi catchment, NZ, are used to calibrate the 6-parameter Probability Distributed Moisture model. Results are analysed using three measures: the proposed entropy-based measure, the Nash-Sutcliffe (NSE), and the recently proposed Kling-Gupta efficiency (KGE). We also examine a conditioned entropy metric that trades-off and reweights different segments of the FDC to drive model calibration in a way that is based on modelling objectives. Overall, the entropy-based measure results in good performance in terms of NSE but poor performance in terms of KGE. This entropy measure is strongly sensitive to the shape of the flow distribution and is, from some viewpoints, the single best descriptor of the FDC. By conditioning entropy to respect multiple segments of the FDC, we can reweight entropy to respect those parts of the flow distribution of most interest to the modelling application. This approach constrains the behavioural parameter space so as to better identify parameters that represent both the “fast” and “slow” runoff processes. Use of this importance-weighted, conditioned entropy metric can constrain high flow predictions equally well as the NSE and KGE, while simultaneously providing wellconstrained low flow predictions that the NSE or KGE are unable to achieve.

Parameter calibration and uncertainty estimation of a simple rainfall-runoff model in two case studies

The simple rainfall-runoff conceptual KIDS (Kielstau Discharge Simulation) model using PCRaster is applied to simulate continuously daily discharge of the Kielstau and XitaoXi basins. This work focuses on parameter calibration procedure and, in particular, assessment of model prediction uncertainty. We employ a simplistic analysis routine SUFI-2, coupled with the implementation of a Monte Carlo based sampling strategy for the joint investigation of parameter calibration and uncertainty estimation. The scatter plots of model performance and parameter exhibit high equifinality of parameter sets in fitting observations, while their histogram distribution patterns imply that most parameters can be well defined. This study investigates parameter sensitivities and finds interesting local results: soil and groundwater parameters are more sensitive in Kielstau models than in XitaoXi models, and only the soil parameters ‘Sfk’ and ‘Kc’ are found strongly correlated. Finally, the uncertainty bounds are always thin and the global shape of the hydrograph is well approximated for both basins. As the validated uncertainty bounds also represent the desired coverage (P factor >50%) of the observations, and the calculated R factor values are in the targeted range (R factor < 1), it demonstrates the efficiency and suitability of this revised SUFI method for the two case studies.

A catchment classification scheme using local variance reduction method

Classification has been considered a fundamental step towards improved catchment hydrology science. This paper proposes a catchment classification scheme where the classification procedure is based on similarity interpreted as distances between catchments. If many sets of model parameters lead to similar model performance for two catchments, they are considered as similar catchments. Two procedures, namely multidimensional scaling (MDS) and local variance reduction (LVR), are undertaken to construct a configuration of n catchments’ characteristics in a Euclidean space using information about similar performance between the catchments. MDS is used to determine the appropriate dimension of the Euclidean space and LVR is used to obtain the transformation matrix and the coordinates in the transformed Euclidean space. This scheme avoids the idea of parametric regression-based regionalization approaches where a regression function is pre-defined between model parameters and catchment characteristics. The proposed scheme is tested with a research version of the HBV-IWS model on a total number of 27 catchments selected from the Rhine River Basin. The scheme can be extended to regional calibration of rainfall runoff models as well as regional drought or flood studies once similarity within catchments has been established.

Calibration of a rainfall–runoff model at regional scale by optimising river discharge statistics: Performance analysis for the average/low flow regime

Traditional procedures for rainfall–runoff model calibration are generally based on the fit of individual values of simulated and observed hydrographs. We use here an alternative option that is carried out by matching, in the optimisation process, a set of streamflow statistics. Such an approach has the significant advantage to enable also a straightforward regional calibration of model parameters, based on the regionalisation of the selected statistics. The minimisation of the set of objective functions is carried out by using the AMALGAM algorithm, leading to the identification of behavioural parameter sets. The procedure is applied to a set of river basins located in central Italy: the basins are treated alternatively as gauged and ungauged and, as a term of comparison, the results obtained with a traditional time-domain calibration are also presented. With respect to previous applications of analogous procedures, we investigate here the identification of the target statistics depending on the purposes of the application, and in particular when the focus is on the reproduction of the low-flows. The results show that a suitable choice of the statistics to be optimised leads to interesting results in real world case studies as far as the reproduction of the different flow regimes is concerned.

Towards improving river discharge estimation in ungauged basins: calibration of rainfall-runoff models based on satellite observations of river flow width at basin outlet

Abstract. Rainfall-runoff models are common tools for river discharge estimation in the field of hydrology. In ungauged basins, the dependence on observed river discharge data for calibration restricts applications of rainfall-runoff models. The strong correlation between quantities of river cross-sectional water surface width obtained from remote sensing and corresponding in situ gauged river discharge has been verified by many researchers. In this study, a calibration scheme of rainfall-runoff models based on satellite observations of river width at basin outlet is illustrated. One distinct advantage is that this calibration is independent of river discharge information. The at-a-station hydraulic geometry is implemented to facilitate shifting the calibration objective from river discharge to river width. The generalized likelihood uncertainty estimation (GLUE) is applied to model calibration and uncertainty analysis. The calibration scheme is demonstrated through a case study for simulating river discharge at Pakse in the Mekong Basin. The effectiveness of the calibration scheme and uncertainties associated with utilization of river width observations from space are examined from model input-state-output behaviour, capability of reproducing river discharge and posterior parameter distribution. The results indicate that the satellite observation of the river width is a competent surrogate of observed discharge for the calibration of rainfall-runoff model at Pakse and the proposed method has the potential for improving reliability of river discharge estimation in basins without any discharge gauging.

Map correlation method: Selection of a reference streamgage to estimate daily streamflow at ungaged catchments

Daily streamflow time series are critical to a very broad range of hydrologic problems. Whereas daily streamflow time series are readily obtained from gaged catchments, streamflow information is commonly needed at catchments for which no measured streamflow information exists. At ungaged catchments, methods to estimate daily streamflow time series typically require the use of a reference streamgage, which transfers properties of the streamflow time series at a reference streamgage to the ungaged catchment. Therefore, the selection of a reference streamgage is one of the central challenges associated with estimation of daily streamflow at ungaged basins. The reference streamgage is typically selected by choosing the nearest streamgage; however, this paper shows that selection of the nearest streamgage does not provide a consistent selection criterion. We introduce a new method, termed the map‐correlation method, which selects the reference streamgage whose daily streamflows are most correlated with an ungaged catchment. When applied to the estimation of daily streamflow at 28 streamgages across southern New England, daily streamflows estimated by a reference streamgage selected using the map‐correlation method generally provides improved estimates of daily streamflow time series over streamflows estimated by the selection and use of the nearest streamgage. The map correlation method could have potential for many other applications including identifying redundancy and uniqueness in a streamgage network, calibration of rainfall runoff models at ungaged sites, as well as for use in catchment classification.

Calibration of rainfall-runoff models in ungauged basins: A regional maximum likelihood approach

Parameter estimation for rainfall-runoff models in ungauged basins is a challenging task that is receiving significant attention by the scientific community. In fact, many practical applications suffer from problems induced by data scarcity, given that hydrological observations are often sparse or unavailable. This study focuses on regional calibration for a generic rainfall-runoff model. The maximum likelihood function in the spectral domain proposed by Whittle [40] is approximated in the time domain by maximising the fit of selected statistics of the river flow process, with the aim to propose a calibration procedure that can be applied at regional scale. Accordingly, the statistics above are related to the dominant climate and catchment characteristics, through regional regression relationships. The proposed technique is applied to the case study of 4 catchments located in central Italy, which are treated as ungauged and are located in a region where detailed hydrological, as well as geomorphologic and climatic information, is available. The results obtained with the regional calibration are compared with those provided by a classical least squares calibration in the time domain. The outcomes of the analysis confirm the potential of the proposed methodology and show that regional information can be very effective for setting up hydrological models.

Hydrological model performance and parameter estimation in the wavelet-domain

Abstract. This paper proposes a method for rainfall-runoff model calibration and performance analysis in the wavelet-domain by fitting the estimated wavelet-power spectrum (a representation of the time-varying frequency content of a time series) of a simulated discharge series to the one of the corresponding observed time series. As discussed in this paper, calibrating hydrological models so as to reproduce the time-varying frequency content of the observed signal can lead to different results than parameter estimation in the time-domain. Therefore, wavelet-domain parameter estimation has the potential to give new insights into model performance and to reveal model structural deficiencies. We apply the proposed method to synthetic case studies and a real-world discharge modeling case study and discuss how model diagnosis can benefit from an analysis in the wavelet-domain. The results show that for the real-world case study of precipitation – runoff modeling for a high alpine catchment, the calibrated discharge simulation captures the dynamics of the observed time series better than the results obtained through calibration in the time-domain. In addition, the wavelet-domain performance assessment of this case study highlights the frequencies that are not well reproduced by the model, which gives specific indications about how to improve the model structure.

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

AbstractThis 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.

The role of observation uncertainty in the calibration of hydrologic rainfall-runoff models

Abstract. Hydrologic rainfall-runoff models are usually calibrated with reference to a limited number of recorded flood events, for which rainfall and runoff measurements are available. In this framework, model's parameters consistency depends on the number of both events and hydrograph points used for calibration, and on measurements reliability. Recently, to make users aware of application limits, major attention has been devoted to the estimation of uncertainty in hydrologic modelling. Here a simple numerical experiment is proposed, that allows the analysis of uncertainty in hydrologic rainfall-runoff modelling associated to both quantity and quality of available data. A distributed rainfall-runoff model based on geomorphologic concepts has been used. The experiment involves the analysis of an ensemble of model runs, and its overall set up holds if the model is to be applied in different catchments and climates, or even if a different hydrologic model is used. With reference to a set of 100 synthetic rainfall events characterized by a given rainfall volume, the effect of uncertainty in parameters calibration is studied. An artificial truth – perfect observation – is created by using the model in a known configuration. An external source of uncertainty is introduced by assuming realistic, i.e. uncertain, discharge observations to calibrate the model. The range of parameters' values able to "reproduce" the observation is studied. Finally, the model uncertainty is evaluated and discussed. The experiment gives useful indications about the number of both events and data points needed for a careful and stable calibration of a specific model, applied in a given climate and catchment. Moreover, an insight on the expected and maximum error in flood peak discharge simulations is given: errors ranging up to 40% are to be expected if parameters are calibrated on insufficient data sets.

Comparison of neural network methods for infilling missing daily weather records

Summary Accurate estimate of missing daily precipitation data remains a difficult task particularly for large watersheds with coarse rain gauge network. Reliable and representative precipitation time series are essential for any rainfall–runoff model calibration as well as for setting-up any downscaling model for hydrologic impact study of climate change. This study investigates six different types of artificial neural networks namely the multilayer perceptron (MLP) network and its variations (the time-lagged feedforward network (TLFN)), the generalized radial basis function (RBF) network, the recurrent neural network (RNN) and its variations (the time delay recurrent neural network (TDRNN)), and the counterpropagation fuzzy-neural network (CFNN) along with different optimization methods for infilling missing daily total precipitation records and daily extreme temperature series. Daily precipitation and temperature records from 15 weather stations located within the Gatineau watershed in northeastern Canada, are used to evaluate the accuracy of the different models for infilling data gaps of daily precipitation and daily extreme temperatures. The experiment results suggest that the MLP, the TLFN and the CFNN can provide the most accurate estimates of the missing precipitation values. However, overall, the MLP appears the most effective at infilling missing daily precipitation values. Furthermore, the MLP also appears the most suitable for infilling missing daily maximum and minimum temperature values. The CFNN is similar to the MLP at infilling missing daily maximum temperature, however, it is less effective at estimating minimum temperature. The experiment results show that the dynamically driven networks (RNN and TDRNN) are the less suitable for infilling both the daily precipitation and the extreme temperature records, whereas the RBF appears fairly suitable only for estimating maximum and minimum temperature.

Integration and calibration of a conceptual rainfall-runoff model in the framework of a decision support system for river basin management

Abstract. Water balance models provide significant input to integrated models that are used to simulate river basin processes. However, one of the primary problems involves the coupling and simultaneous calibration of rainfall-runoff and groundwater models. This problem manifests itself through circular arguments - the hydrologic model is modified to calculate highly discretized groundwater recharge rates as input to the groundwater model which provides modeled base flow for the flood-routing module of the rainfall-runoff model. A possibility to overcome this problem using a modified version of the HBV Model is presented in this paper. Regionalisation and optimization methods lead to objective and efficient calibration despite large numbers of parameters. The representation of model parameters by transfer functions of catchment characteristics enables consistent parameter estimation. By establishing such relationships, models are calibrated for the parameters of the transfer functions instead of the model parameters themselves. Simulated annealing, using weighted Nash-Sutcliffe-coefficients of variable temporal aggregation, assists in efficient parameterisations. The simulations are compared to observed discharge and groundwater recharge modeled by the State Institute for Environmental Protection Baden-Württemberg using the model TRAIN-GWN.

Enhancing gradient-based parameter estimation with an evolutionary approach

Traditionally, the calibration of groundwater models has depended on gradient-based local optimization methods. These methods provide a reasonable degree of success only when the objective function is smooth, second-order differentiable, and satisfies the Lipschitz's condition. For complicated and highly nonlinear objective functions it is almost impractical to satisfy these conditions simultaneously. Research in the calibration of conceptual rainfall-runoff models, has shown that global optimization methods are more successful in locating the global optimum in the region of multiple local optima. In this study, a global optimization technique, known as shuffle complex evolution (SCE), is coupled to the gradient-based Lavenberg–Marquardt algorithm (GBLM). The resultant hybrid global optimization algorithm (SCEGB) is then deployed in parallel testing with SCE and GBLM to solve several inverse problems where parameters of a nonlinear numerical groundwater flow model are estimated. Using perfect (i.e. noise-free) observation data, it is shown SCEGB and SCE are successful at identifying the global optimum and predicting all model parameters; whereas, the commonly applied GBLM fails to identify the optimum. In subsequent inverse simulations using observation data corrupted with noise, SCEGB and SCE again outperform GBLM by consistently producing more accurate parameter estimates. Finally, in all simulations the hybrid SCEGB is seen to be equally effective as SCE but computationally more efficient.

Using genetic algorithm and TOPSIS for Xinanjiang model calibration with a single procedure

Genetic Algorithm (GA) is globally oriented in searching and thus useful in optimizing multiobjective problems, especially where the objective functions are ill-defined. Conceptual rainfall–runoff models that aim at predicting streamflow from the knowledge of precipitation over a catchment have become a basic tool for flood forecasting. The parameter calibration of a conceptual model usually involves the multiple criteria for judging the performances of observed data. However, it is often difficult to derive all objective functions for the parameter calibration problem of a conceptual model. Thus, a new method to the multiple criteria parameter calibration problem, which combines GA with TOPSIS (technique for order performance by similarity to ideal solution) for Xinanjiang model, is presented. This study is an immediate further development of authors' previous research (Cheng, C.T., Ou, C.P., Chau, K.W., 2002. Combining a fuzzy optimal model with a genetic algorithm to solve multi-objective rainfall–runoff model calibration. Journal of Hydrology, 268, 72–86), whose obvious disadvantages are to split the whole procedure into two parts and to become difficult to integrally grasp the best behaviors of model during the calibration procedure. The current method integrates the two parts of Xinanjiang rainfall–runoff model calibration together, simplifying the procedures of model calibration and validation and easily demonstrated the intrinsic phenomenon of observed data in integrity. Comparison of results with two-step procedure shows that the current methodology gives similar results to the previous method, is also feasible and robust, but simpler and easier to apply in practice.