Application of a land surface model for simulating rainfall streamflow hydrograph: 1. Model calibration

Different variants of parameters’ calibration of land surface model SWAP were examined with the aim to maximize the accuracy of reproducing rainfall runoff hydrograph. The optimization of parameter values was automated based on two different algorithms for the search of the global optimum of an objective function: a random search technique and a shuffled complex evolution method SCE-UA. In both cases, two objective functions, based on the mean systematic error and the Nash and Sutcliffe coefficient of efficiency, were used. The number of calibrated parameters varied from 10 to 15, and their values were within the reasonable range so as not to contradict the physical meaning and to ensure the best agreement between the simulated and observed daily river runoff. The streamflow hydrographs for some rivers in USA simulated with the use of different sets of optimized parameters were compared with observation data.     

Automatic calibration of HEC‐HMS using single‐objective and multi‐objective PSO algorithms

This study presents single‐objective and multi‐objective particle swarm optimization (PSO) algorithms for automatic calibration of Hydrologic Engineering Center‐ Hydrologic Modeling Systems rainfall‐runoff model of Tamar Sub‐basin of Gorganroud River Basin in north of Iran. Three flood events were used for calibration and one for verification. Four performance criteria (objective functions) were considered in multi‐objective calibration where different combinations of objective functions were examined. For comparison purposes, a fuzzy set‐based approach was used to determine the best compromise solutions from the Pareto fronts obtained by multi‐objective PSO. The candidate parameter sets determined from different single‐objective and multi‐objective calibration scenarios were tested against the fourth event in the verification stage, where the initial abstraction parameters were recalibrated. A step‐by‐step screening procedure was used in this stage while evaluating and comparing the candidate parameter sets, which resulted in a few promising sets that performed well with respect to at least three of four performance criteria. The promising sets were all from the multi‐objective calibration scenarios which revealed the outperformance of the multi‐objective calibration on the single‐objective one. However, the results indicated that an increase of the number of objective functions did not necessarily lead to a better performance as the results of bi‐objective function calibration with a proper combination of objective functions performed as satisfactorily as those of triple‐objective function calibration. This is important because handling multi‐objective optimization with an increased number of objective functions is challenging especially from a computational point of view. Copyright © 2012 John Wiley & Sons, Ltd.     

Simultaneous perturbation stochastic approximation for tidal models

The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decomposition-based calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.     

Incorporating spatial and temporal information for urban drainage model calibration: An approach using preference ordering genetic algorithm

In order to successfully calibrate an urban drainage model, multiple criteria should be considered, which raises the issue of adopting a method for comparing different parameter sets according to a set of objectives. Multi-objective genetic algorithms (MOGA) have proved effective in numerous such applications, where most of the techniques relying on the condition of Pareto efficiency to compare different solutions. However, as the number of criteria increases, the ratio of Pareto optimal to feasible solutions increases as well, worsening the efficiency of the genetic algorithm search. In this paper, firstly the drawbacks of single objective calibration approach are highlighted. Then, a new MOGA, the preference ordering genetic algorithm, is proposed, that alleviates the drawbacks of conventional Pareto-based methods. The efficacy of this algorithm is demonstrated on the calibration of a physically-based, distributed sewer network model, and the comparison is made with a known MOGA NSGA-II. The results are very encouraging because the obtained parameter sets closely resembled both calibration and validation events. The identifiability of 10 model parameters were analysed, showing significantly smaller ranges of optimal values for parameters related to impervious areas compared to those related to pervious areas, which is reasonable considering relatively low rainfall intensities. In addition to standard ways of presenting calibration results, “radar” plots were also used to present information on trade-off for eight objective functions for four rainfall-runoff events.     

A hybrid optimization approach for efficient calibration of computationally intensive hydrological models

ABSTRACT

The calibration of hydrological models is formulated as a blackbox optimization problem where the only information available is the objective function value. Distributed hydrological models are generally computationally intensive, and their calibration may require several hours or days which can be an issue for many operational contexts. Different optimization algorithms have been developed over the years and exhibit different strengths when applied to the calibration of computationally intensive hydrological models. This paper shows how the dynamically dimensioned search (DDS) and the mesh adaptive direct search (MADS) algorithms can be combined to significantly reduce the computational time of calibrating distributed hydrological models while ensuring robustness and stability regarding the final objective function values. Five transitional features are described to adequately merge both algorithms. The hybrid approach is applied to the distributed and computationally intensive HYDROTEL model on three different river basins located in Québec (Canada).     

Probabilistic calibration of a distributed hydrological model for flood forecasting

Abstract

The complexity of distributed hydrological models has led to improvements in calibration methodologies in recent years. There are various manual, automatic and hybrid methods of calibration. Most use a single objective function to calculate estimation errors. The use of multi-objective calibration improves results, since different aspects of the hydrograph may be considered simultaneously. However, the uncertainty of estimates from a hydrological model can only be taken into account by using a probabilistic approach. This paper presents a calibration method of probabilistic nature, based on the determination of probability functions that best characterize different parameters of the model. The method was applied to the Real-time Interactive Basin Simulator (RIBS) distributed hydrological model using the Manzanares River basin in Spain as a case study. The proposed method allows us to consider the uncertainty in the model estimates by obtaining the probability distributions of flows in the flood hydrograph.

Citation Mediero, L., Garrote, L. & Martín-Carrasco, F. J. (2011) Probabilistic calibration of a distributed hydrological model for flood forecasting. Hydrol. Sci. J. 56(7), 1129–1149.     

A multi-objective calibration approach using in-situ soil moisture data for improved hydrological simulation of the Prairies

ABSTRACT

Traditionally, hydrological models are only calibrated to reproduce streamflow regime without considering other hydrological state variables, such as soil moisture and evapotranspiration. Limited studies have been performed on constraining the model parameters, despite the fact that the presence of a large number of parameters may provide large degree of freedom, resulting in equifinality and poor model performance. In this study, a multi-objective optimization approach is adopted, and both streamflow and soil moisture data are calibrated simultaneously for an experimental study basin in the Saskatchewan Prairies in western Canada. The results of this study show that the multi-objective calibration improves model fidelity compared to the single objective calibration. Moreover, the study demonstrates that single objective calibration performed against only streamflow can fairly mimic the streamflow hydrograph but does not yield realistic estimation of other fluxes such as evapotranspiration and soil moisture (especially in deeper soil layers).     

Practical aspects of calibrating and selecting unit hydrograph-based models for continuous river flow simulation

Abstract

A continuous simulation rainfall-streamflow modelling approach that identifies unit hydrographs for total streamflow has been applied to an 11-year record from a national hydrometric monitoring network catchment in the UK. The model is of the parametrically parsimonious conceptual model (PPCM) type that can make efficient use of rainfall, streamflow and air temperature data readily available from established national and regional monitoring networks. A multiple split-sample model calibration and simulation analysis is presented that reveals some guiding principles for calibrating and applying PPCMs generally. The inadequacy of a one-dimensional objective function for calibrating best PPCMs is demonstrated. A two-dimensional objective function approach is superior but is shown to be unreliable in some cases, confirming the need for additional critical inspection of other model performance statistics, model parameters and time series plots as an integral part of the model calibration process. A strong tendency evident from the multiple split-sample analysis is that, for the catchment studied, models that fit relatively well in calibration mode perform relatively poorly in simulation mode.     

Selection of calibration objective fonctions in the context of rainfall-ronoff modelling in a Sudanese savannah area

Abstract

In the context of rainfall-runoff modelling carried out on the Sudanese savannah area in the northwest of the Ivory Coast, attempts are being made to reconstitute the flow at the outlets of catchments in 10 day time steps. By using algorithms with automatic fitting procedures for the parameters, it appeared necessary to make a choice concerning the calibration objective functions to be used. The paper presents the algorithms, data and objective functions that have been used. The results obtained from the calibrations made have been analysed. That analysis was done principally with the help of a comparative evaluation modulus which takes into account elements other than the value of the objective function alone and which enables the quality of the results to be picked out from a hydrological point of view. At the conclusion of the analysis, the objective function defined by Nash seems to stand out quite clearly in relation to the other formulae examined.     

Multiple criteria rainfall–runoff model calibration using a parallel genetic algorithm in a cluster of computers / Calage multi-critères en modélisation pluie–débit par un algorithme génétique parallèle mis en œuvre par une grappe d'ordinateurs

Abstract

Genetic algorithms are among of the global optimization schemes that have gained popularity as a means to calibrate rainfall–runoff models. However, a conceptual rainfall–runoff model usually includes 10 or more parameters and these are interdependent, which makes the optimization procedure very time-consuming. This may result in the premature termination of the optimization process which will prejudice the quality of the results. Therefore, the speed of optimization procedure is crucial in order to improve the calibration quality and efficiency. A hybrid method that combines a parallel genetic algorithm with a fuzzy optimal model in a cluster of computers is proposed. The method uses the fuzzy optimal model to evaluate multiple alternatives with multiple criteria where chromosomes are the alternatives, whilst the criteria are flood performance measures. In order to easily distinguish the performance of different alternatives and to address the problem of non-uniqueness of optimum, two fuzzy ratios are defined. The new approach has been tested and compared with results obtained by using a two-stage calibration procedure. The current single procedure produces similar results, but is simpler and automatic. Comparison of results between the serial and parallel genetic algorithms showed that the current methodology can significantly reduce the overall optimization time and simultaneously improve the solution quality.     

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.     

Improving the calibration strategy of the physically-based model WaSiM-ETH using critical events

Abstract

The use of a physically-based hydrological model for streamflow forecasting is limited by the complexity in the model structure and the data requirements for model calibration. The calibration of such models is a difficult task, and running a complex model for a single simulation can take up to several days, depending on the simulation period and model complexity. The information contained in a time series is not uniformly distributed. Therefore, if we can find the critical events that are important for identification of model parameters, we can facilitate the calibration process. The aim of this study is to test the applicability of the Identification of Critical Events (ICE) algorithm for physically-based models and to test whether ICE algorithm-based calibration depends on any optimization algorithm. The ICE algorithm, which uses the data depth function, was used herein to identify the critical events from a time series. Low depth in multivariate data is an unusual combination and this concept was used to identify the critical events on which the model was then calibrated. The concept is demonstrated by applying the physically-based hydrological model WaSiM-ETH on the Rems catchment, Germany. The model was calibrated on the whole available data, and on critical events selected by the ICE algorithm. In both calibration cases, three different optimization algorithms, shuffled complex evolution (SCE-UA), parameter estimation (PEST) and robust parameter estimation (ROPE), were used. It was found that, for all the optimization algorithms, calibration using only critical events gave very similar performance to that using the whole time series. Hence, the ICE algorithm-based calibration is suitable for physically-based models; it does not depend much on the kind of optimization algorithm. These findings may be useful for calibrating physically-based models on much fewer data.

Editor D. Koutsoyiannis; Associate editor A. Montanari

Citation Singh, S.K., Liang, J.Y., and Bárdossy, A., 2012. Improving calibration strategy of physically-based model WaSiM-ETH using critical events. Hydrological Sciences Journal, 57 (8), 1487–1505.     

Hydraulic Gradient Comparison Method to Estimate Aquifer Hydraulic Parameters Under Steady-State Conditions

The hydraulic gradient comparison method is an inverse method for estimation of aquifer hydraulic conductivity (or trans-missivity) and boundary conductance for a ground water flow model under steady-state conditions. This method, following formal optimization techniques, defines its objective function to minimize differences between interpreted (observed) and simulated hydraulic gradients, which results in minimization of differences between observed and simulated hydraulic heads. The key features of this method are that (1) the derived optimality conditions have an explicit form with a clear hydrology concept that is con-sistent with Darcy's law, and (2) the derived optimality conditions are spatially independent as they are a function of only local hydraulic conductivity and local hydraulic gradient. This second feature allows a multidimensional optimization problem to be solved by many one-dimensional optimization procedures simultaneously, which results in a substantial reduction in computation time. The results of the numerical performance testing on a heterogeneous hypothetical case confirm that minimizing gradient residuals in the entire model domain leads to minimizing head residuals. Application of the method in real-world projects requires rigorous conceptual model development, use of a global calibration target, and an iterative calibration proess. The conceptual model development includes interpretation of a potentiometric surface and estimation of other hydrologic parameters. This method has been applied to a wide range of real-world modeling projects, including the Rocky Mountain Arsenal and Rocky Flats sites in Colorado, which demonstrates that the method is efficient and practical.     

Development of conceptual semi-distributed hydrological models and estimation of their parameters with the aid of GIS

Abstract

Conceptual semi-distributed hydrological models are developed for a limited consideration of spatial heterogeneity of hydrological characteristics within a river basin. This heterogeneity can be described by area distribution functions of hydrological characteristics which can be estimated in a most effective way by a Geographical Information System (GIS). It is shown how the application of a GIS can support the development and the calibration of a conceptual hydrological model. GIS information is used to establish the criteria for sub-division of the river basin and for estimation of model structures (especially for further horizontal divisions of each basin into more homogeneous parts). That information is also used for estimation of basin characteristics and their differences between sub-basins as a support for parameter calibration by optimization. The methodology presented can be used for the development of a model structure on an objective basis and for model calibration which considers the physical explanation of model parameters. The proposed method was successfully applied to a river basin within the Mosel basin (Germany).     

Calibration of complex subsurface reaction models using a surrogate-model approach

Automatic calibration of complex subsurface reaction models involves numerous difficulties, including the existence of multiple plausible models, parameter non-uniqueness, and excessive computational burden. To overcome these difficulties, this study investigated a novel procedure for performing simultaneous calibration of multiple models (SCMM). By combining a hybrid global-plus-polishing search heuristic with a biased-but-random adaptive model evaluation step, the new SCMM method calibrates multiple models via efficient exploration of the multi-model calibration space. Central algorithm components are an adaptive assignment of model preference weights, mapping functions relating the uncertain parameters of the alternative models, and a shuffling step that efficiently exploits pseudo-optimal configurations of the alternative models. The SCMM approach was applied to two nitrate contamination problems involving batch reactions and one-dimensional reactive transport. For the chosen problems, the new method produced improved model fits (i.e. up to 35% reduction in objective function) at significantly reduced computational expense (i.e. 40–90% reduction in model evaluations), relative to previously established benchmarks. Although the method was effective for the test cases, SCMM relies on a relatively ad-hoc approach to assigning intermediate preference weights and parameter mapping functions. Despite these limitations, the results of the numerical experiments are empirically promising and the reasoning and structure of the approach provide a strong foundation for further development.     

Improvement and comparison of the rainfall–runoff methods in SWAT at the monsoonal watershed of Baocun,Eastern China

ABSTRACT

A new physics-based rainfall–runoff method of the Soil and Water Assessment Tool (SWAT) was developed, which integrates a water balance (WB) approach with the variable source area (WB-VSA). This approach was further compared with four methods—soil-water-dependent curve number (CN-Soil), evaporation-dependent curve number (CN-ET), Green and Ampt equation (G&A) and WB—in a monsoonal watershed, Eastern China. The regional sensitivity analysis shows that volumetric efficiency coefficient (VE) with river discharges is sensitive to the most parameters of all approaches. The results of model calibration against VE demonstrate that WB-VSA is the most accurate owing to its reflection of the spatial variation of runoff generation as affected by topography and soil properties. Other methods can also mimic baseflow well, but the G&A and CN-ET simulate floods much worse than the saturation excess runoff approaches (WB-VSA, WB and CN-Soil). Meanwhile, CN-Soil as an empirical method fails to simulate groundwater levels. By contrast, WB-VSA captures them best.

Editor M.C. Acreman; Associate editor S. Kanae     

Comparison of spectral and time domain calibration methods for precipitation‐discharge processes

Hydrological model parameter estimation is an important aspect in hydrologic modelling. Usually, parameters are estimated through an objective function minimization, quantifying the mismatch between the model results and the observations. The objective function choice has a large impact on the sensitivity analysis and calibration outcomes. In this study, it is assessed whether spectral objective functions can compete with an objective function in the time domain for optimization of the Soil and Water Assessment Tool (SWAT). Three empirical spectral objective functions were applied, based on matching (i) Fourier amplitude spectra, (ii) periodograms and (iii) Fourier series of simulated and observed discharge time series. It is shown that most sensitive parameters and their optimal values are distinct for different objective functions. The best results were found through calibration with an objective function based on the square difference between the simulated and observed discharge Fourier series coefficients. The potential strengths and weaknesses of using a spectral objective function as compared to utilising a time domain objective function are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Impact of the numbers of observations and calibration parameters on equifinality,model performance,and output and parameter uncertainty

The level of model complexity that can be effectively supported by available information has long been a subject of many studies in hydrologic modelling. In particular, distributed parameter models tend to be regarded as overparameterized because of numerous parameters used to describe spatially heterogeneous hydrologic processes. However, it is not clear how parameters and observations influence the degree of overparameterization, equifinality of parameter values, and uncertainty. This study investigated the impact of the numbers of observations and parameters on calibration quality including equifinality among calibrated parameter values, model performance, and output/parameter uncertainty using the Soil and Water Assessment Tool model. In the experiments, the number of observations was increased by expanding the calibration period or by including measurements made at inner points of a watershed. Similarly, additional calibration parameters were included in the order of their sensitivity. Then, unique sets of parameters were calibrated with the same objective function, optimization algorithm, and stopping criteria but different numbers of observations. The calibration quality was quantified with statistics calculated based on the ‘behavioural’ parameter sets, identified using 1% and 5% cut‐off thresholds in a generalized likelihood uncertainty estimation framework. The study demonstrated that equifinality, model performance, and output/parameter uncertainty were responsive to the numbers of observations and calibration parameters; however, the relationship between the numbers, equifinality, and uncertainty was not always conclusive. Model performance improved with increased numbers of calibration parameters and observations, and substantial equifinality did neither necessarily mean bad model performance nor large uncertainty in the model outputs and parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

The use of reduced finite element models in system identification

An a priori, analytical model in system identification of vibrating structures is improved by input and output measurements with least square fitting. The structure is modelled by the finite element method. Finite element models usually need a large number of degrees of freedom to simulate a small number of lower spectrum eigenfrequencies with accuracy. The large finite element model is reduced to a subspace of significant eigenfrequencies. The size of the subspace is chosen with regard to the frequency content of the measured data and the accuracy of the large analytical model. An identification method is formulated for the large analytical model. This procedure improves system parameters in the matrices of the large model by measured input and output data with a least square functional. The objective function is consistently reduced, so that the whole identification procedure can be performed in the small subspace. The proposed reduction method permits very large and accurate analytical models to be used, and it decreases the computational cost of the identification procedure significantly. The computational efficiency is demonstrated on an in situ experiment of a radar tower.     

Pilot-point based multi-objective calibration in a surface–subsurface distributed hydrological model

Abstract

In this study, a fully-coupled surface–subsurface, distributed, physics-based hydrological model was calibrated using the pilot-point method. A minimum variance field rule was included in the objective function to regularize the extensive calibration exercise that included 74 parameters (72 associated with pilot points and two spatially-invariant channel parameters). Because the overland and vadose zone systems are not in permanent hydrological connection, the information contained in the observation points may not be accessible by the pilot points at all times, rendering them insensitive to the observations and hindering the calibration process. An analysis of the spatial and temporal variability of parameter sensitivities was done to explore how the information contained in local observations spreads from the observation points to the pilot points, where parameter values are identified. The results show that the channel flow time series is valuable to identify the parameters at all pilot-point locations, indicating that the information in channel flow propagates to the entire basin. However, information in soil moisture measurements is of local extent and thus only valuable to identify the parameters at locations close to the observation point.

Editor D. Koutsoyiannis; Associate editor I. Nalbantis

Citation Maneta, M.P. and Wallender, W.W., 2013. Pilot-point based multi-objective calibration in a surface–subsurface distributed hydrological model. Hydrological Sciences Journal, 58 (2), 390–407.