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.     

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.     

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).     

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).     

Regional models of flow-duration curves of perennial and intermittent streams and their use for calibrating the parameters of a rainfall–runoff model

Abstract

One of the main challenges faced by hydrologists and water engineers is the estimation of variables needed for water resources planning and management in ungauged river basins. To this end, techniques for transposing information, such as hydrological regional analyses, are widely employed. A method is presented for regionalizing flow-duration curves (FDCs) in perennial, intermittent and ephemeral rivers, based on the extended Burr XII probability distribution. This distribution shows great flexibility to fit data, with accurate reproduction of flow extremes. The performance analysis showed that, in general, the regional models are able to synthesize FDCs in ungauged basins, with a few possible drawbacks in the application of the method to intermittent and ephemeral rivers. In addition to the regional models, we summarize the experience of using synthetic FDCs for the indirect calibration of the Rio Grande rainfall–runoff model parameters in ungauged basins.

Editor D. Koutsoyiannis

Citation Costa, V., Fernandes, W., and Naghettini, M., 2013. Regional models of flow-duration curves of perennial and intermittent streams and their use for calibrating the parameters of a rainfall–runoff model. Hydrological Sciences Journal, 59 (2), 262–277.     

Incorporating uncertainty in hydrological predictions for gauged and ungauged basins in southern Africa

Abstract

The increasing demand for water in southern Africa necessitates adequate quantification of current freshwater resources. Watershed models are the standard tool used to generate continuous estimates of streamflow and other hydrological variables. However, the accuracy of the results is often not quantified, and model assessment is hindered by a scarcity of historical observations. Quantifying the uncertainty in hydrological estimates would increase the value and credibility of predictions. A model-independent framework aimed at achieving consistency in incorporating and analysing uncertainty within water resources estimation tools in gauged and ungauged basins is presented. Uncertainty estimation in ungauged basins is achieved via two strategies: a local approach for a priori model parameter estimation from physical catchment characteristics, and a regional approach to regionalize signatures of catchment behaviour that can be used to constrain model outputs. We compare these two sources of information in the data-scarce region of South Africa. The results show that both approaches are capable of uncertainty reduction, but that their relative values vary.

Editor D. Koutsoyiannis

Citation Kapangaziwiri, E., Hughes, D.A., and Wagener, T., 2012. Incorporating uncertainty in hydrological predictions for gauged and ungauged basins in southern Africa. Hydrological Sciences Journal, 57 (5), 1000–1019.     

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.     

Sensitivity of hydrological models to uncertainty in rainfall input

Abstract

Different approaches used in hydrological modelling are compared in terms of the way each one takes the rainfall data into account. We examine the errors associated with accounting for rainfall variability, whether in hydrological modelling (distributed vs lumped models) or in computing catchment rainfall, as well as the impact of each approach on the representativeness of the parameters it uses. The database consists of 1859 rainfall events, distributed on 500 basins, located in the southeast of France with areas ranging from 6.2 to 2851 km². The study uses as reference the hydrographs computed by a distributed hydrological model from radar rainfall. This allows us to compare and to test the effects of various simplifications to the process when taking rainfall information (complete rain field vs sampled rainfall) and rainfall–runoff modelling (lumped vs distributed) into account. The results appear to show that, in general, the sampling effect can lead to errors in discharge at the outlet that are as great as, or even greater than, those one would get with a fully lumped approach. We found that small catchments are more sensitive to the uncertainties in catchment rainfall input generated by sampling rainfall data as seen through a raingauge network. Conversely, the larger catchments are more sensitive to uncertainties generated when the spatial variability of rainfall events is not taken into account. These uncertainties can be compensated for relatively easily by recalibrating the parameters of the hydrological model, although such recalibrations cause the parameter in question to completely lose physical meaning.

Citation Arnaud, P., Lavabre, J., Fouchier, C., Diss, S. & Javelle, P. (2011) Sensitivity of hydrological models to uncertainty of rainfall input. Hydrol. Sci. J. 56(3), 397–410.     

Probabilistic flood forecasting for a mountainous headwater catchment using a nonparametric stochastic dynamic approach

Abstract

Hydrological models are commonly used to perform real-time runoff forecasting for flood warning. Their application requires catchment characteristics and precipitation series that are not always available. An alternative approach is nonparametric modelling based only on runoff series. However, the following questions arise: Can nonparametric models show reliable forecasting? Can they perform as reliably as hydrological models? We performed probabilistic forecasting one, two and three hours ahead for a runoff series, with the aim of ascribing a probability density function to predicted discharge using time series analysis based on stochastic dynamics theory. The derived dynamic terms were compared to a hydrological model, LARSIM. Our procedure was able to forecast within 95% confidence interval 1-, 2- and 3-h ahead discharge probability functions with about 1.40 m³/s of range and relative errors (%) in the range [–30; 30]. The LARSIM model and the best nonparametric approaches gave similar results, but the range of relative errors was larger for the nonparametric approaches.

Editor D. Koutsoyiannis; Associate editor K. Hamed

Citation Costa, A.C., Bronstert, A. and Kneis, D., 2012. Probabilistic flood forecasting for a mountainous headwater catchment using a nonparametric stochastic dynamic approach. Hydrological Sciences Journal, 57 (1), 10–25.     

Influence of landscape aggregation in modelling snow-cover ablation and snowmelt runoff in a sub-arctic mountainous environment

Abstract

Appropriate representation of landscape heterogeneity at small to medium scales is a central issue for hydrological modelling. Two main hydrological modelling approaches, deductive and inductive, are generally applied. Here, snow-cover ablation and basin snowmelt runoff are evaluated using a combined modelling approach that includes the incorporation of detailed process understanding along with information gained from observations of basin-wide streamflow phenomena. The study site is Granger Basin, a small sub-arctic basin in the mountains of the Yukon Territory, Canada. The analysis is based on the comparison between basin-aggregated and distributed landscape representations. Results show that the distributed model based on “hydrological response” landscape units best describes the observed magnitudes of both snow-cover ablation and basin runoff, whereas the aggregated approach fails to represent the differential snowmelt rates and to describe both runoff volumes and dynamics when discontinuous snowmelt events occur.     

On the value of isotope-enabled hydrological model calibration

ABSTRACT

Calibration of hydrological models is challenging in high-latitude regions where hydrometric data are minimal. Process-based models are needed to predict future changes in water supply, yet often with high amounts of uncertainty, in part, from poor calibrations. We demonstrate the utility of stable isotopes (¹⁸O, ²H) as data employed for improving the amount and type of information available for model calibration using the isoWATFLOOD^TM model. We show that additional information added to calibration does not hurt model performance and can improve simulation of water volume. Isotope-enabled calibration improves long-term validation over traditional flow-only calibrated models and offers additional feedback on internal flowpaths and hydrological storages that can be useful for informing internal water distribution and model parameterization. The inclusion of isotope data in model calibration reduces the number of realistic parameter combinations, resulting in more constrained model parameter ranges and improved long-term simulation of large-scale water balance.     

A) A. I. H. S. / A) A. I. H. S.

Abstract

A new method is presented to generate stationary multi-site hydrological time series. The proposed method can handle flexible time-step length, and it can be applied to both continuous and intermittent input series. The algorithm is a departure from standard decomposition models and the Box-Jenkins approach. It relies instead on the recent advances in statistical science that deal with generation of correlated random variables with arbitrary statistical distribution functions. The proposed method has been tested on 11 historic weekly input series, of which the first seven contain flow data and the last four have precipitation data. The article contains an extensive review of the results.

Editor D. Koutsoyiannis

Citation Ilich, N., 2014. An effective three-step algorithm for multi-site generation of stochastic weekly hydrological time series. Hydrological Sciences Journal, 59 (1), 85–98.     

The use of maximum entropy to increase the informational content of hydrological networks by additional gauges

ABSTRACT

The optimization and extension of existing gauging networks are a challenging task, which can be done under consideration of many different aspects. One possibility is to maximize the obtained information on regional hydrological characteristics by new gauges compared to existing ones. For this, information theory approaches are most suitable. Here, the principle of maximum entropy is applied to calculate the probability of non-similarity of catchments to determine locations of new gauges according to the catchment characteristics that are most relevant for the hydrological conditions. The realization in an interactive application, provided online, makes use easy for practitioners and scientists. Goodness-of-fit measures are applied to investigate the explanatory power of the model and the contribution of each characteristic to the model, which gives information on the most influential properties of the catchment. The relevance of the proposed approach is proven by comparing hydrological signatures between similar and non-similar catchment.     

BIBLIOGRAPHIE

Abstract

Time series modelling approaches are useful tools for simulating and forecasting hydrological variables and their change through time. Although linear time series models are common in hydrology, the nonlinear time series model, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, has rarely been used in hydrology and water resources engineering. The GARCH model considers the conditional variance remaining in the residuals of the linear time series models, such as an ARMA or an ARIMA model. In the present study, the advantages of a GARCH model against a linear ARIMA model are investigated using three classes of the GARCH approach, namely Power GARCH, Threshold GARCH and Exponential GARCH models. A daily streamflow time series of the Matapedia River, Quebec, Canada, is selected for this study. It is shown that the ARIMA (13,1,4) model is adequate for modelling streamflow time series of Matapedia River, but the Engle test shows the existence of heteroscedasticity in the residuals of the ARIMA model. Therefore, an ARIMA (13,1,4)-GARCH (3,1) error model is fitted to the data. The residuals of this model are examined for the existence of heteroscedasticity. The Engle test indicates that the GARCH model has considerably reduced the heteroscedasticity of the residuals. However, the Exponential GARCH model seems to completely remove the heteroscedasticity from the residuals. The multi-criteria evaluation for model performance also proves that the Exponential GARCH model is the best model among ARIMA and GARCH models. Therefore, the application of a GARCH model is strongly suggested for hydrological time series modelling as the conditional variance of the residuals of the linear models can be removed and the efficiency of the model will be improved.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Modarres, R. and Ouarda, T.B.M.J., 2013. Modelling heteroscedasticty of streamflow times series. Hydrological Sciences Journal, 58 (1), 1–11.     

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).     

Standardized uncertainty analysis for hydrometry: a review of relevant approaches and implementation examples

Abstract

The water-centric community has continuously made efforts to identify, assess and implement rigorous uncertainty analyses for routine hydrological measurements. This paper reviews some of the most relevant efforts and subsequently demonstrates that the Guide to the expression of uncertainty in measurement (GUM) is a good candidate for estimation of uncertainty intervals for hydrometry. The demonstration is made by implementing the GUM to typical hydrometric applications and comparing the analysis results with those obtained using the Monte Carlo method. The results show that hydrological measurements would benefit from the adoption of the GUM as the working standard, because of its soundness, the availability of software for practical implementation and potential for extending the GUM to hydrological/hydraulic numerical simulations.

Editor D. Koutsoyiannis

Citation Muste, M., Lee, K. and Bertrand-Krajewski, J.-L., 2012. Standardized uncertainty analysis for hydrometry: a review of relevant approaches and implementation examples. Hydrological Sciences Journal, 57 (4), 643–667.     

Analysis of recharge conceptualization in inverse groundwater modelling

ABSTRACT

This study presents a systematic illustration quantifying how misleading the calibration results of a groundwater simulation model can be when recharge rates are considered as the model parameters to be estimated by inverse modelling. Three approaches to recharge estimation are compared: autocalibration (Model 1), the empirical return coefficient method (Model 2), and distributed hydrological modelling using the Soil and Water Assessment Tool, SWAT (Model 3). The methodology was applied in the Dehloran Plain, western Iran, using the MODFLOW modular flow simulator and the PEST method for autocalibration. The results indicate that, although Model 1 performed the best in simulating water levels at observation wells in the calibration stage, it did not perform satisfactorily in real future scenarios. Model 3, with SWAT-based recharge rates, performed better than the other models in the validation stage. By not evaluating the model performance solely on calibration results, we demonstrate the relative significance of using more accurate recharge estimates when calibrating groundwater simulation models.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR M. Besbes     

Cold-regions Hydrological Indicators of Change (CHIC) for ecological flow needs assessment

Abstract

Ecological flow needs (EFN) frameworks incorporate a range of ecologically-relevant hydrological variables based on prior knowledge of river regime characteristics. However, when applied in cold regions, these approaches have largely ignored the influence of winter ice cover and the spring freshet on hydrological regimes: key components of river systems in cold regions with important direct effects on water quality, aquatic habitat and ecology. Here, we combine a review of the published literature on cold-regions hydrology and hydro-ecology with available hydrometric information for sites across Canada, a major cold-region country, to explore phenomena unique to these systems. We identify several ecologically-relevant hydrological measures (i.e. annual ice on/off dates, ice-cover duration, spring freshet initiation, peak water level during river ice break-up), pairing these with established metrics for incorporation into an enhanced suite of indicators specifically designed for cold regions. This paper presents the Cold-regions Hydrological Indicators of Change (CHIC), which can provide the basis for the assessment of EFN and climate change assessments in cold-region river ecosystems.

Editor Z.W. Kundzewicz; Guest editor M. Acreman

Citation Peters, D.L., Monk, W.A., and Baird, D.J., 2014. Cold-regions Hydrological Indicators of Change (CHIC) for ecological flow needs assessment. Hydrological Sciences Journal, 59 (3–4), 502–516.     

Spatial scale dependency issues in the application of the Modified Universal Soil Loss Equation (MUSLE)

ABSTRACT

The MUSLE is used within hydrological models to estimate sediment yields from catchments of various sizes, but the spatial scale dependency issues associated with estimating the MUSLE parameters have not been adequately addressed. In the absence of detailed observed data on both hydrological response and sediment yield, some analytical approaches and hypothetical examples are presented to identify the key issues. The results suggest that methods used to estimate both the erosivity and topographic factors are scale dependent, particularly if a lumped or semi-distributed modelling approach is used. The conclusion is that spatial scale dependencies will add to the uncertainties inherent in the use of the MUSLE if not carefully understood and appropriately addressed. One suggested approach is to apply the erosivity equation to a fixed (small) representative area and then scale up to the total catchment, an approach that recognizes the variability of averaged parameters across different spatial scales.     

The effective management of national hydrometric data: experiences from the United Kingdom

Abstract

Access to hydrometric information underpins many areas of effective water management. This paper explores the operational practices of one national hydrological information service, the UK National River Flow Archive, in collating, managing and providing access to river flow data. An information lifecycle approach to hydrometric data management is advocated, with the paper detailing current UK procedures in the areas of: monitoring network design and development; data sensing and recording; validation and archival; synthesis and analysis; and data dissemination. The methods and policies outlined herein are widely transferable to other hydrological data archives around the world.

Editor D. Koutsoyiannis

Citation Dixon, H., Hannaford, J., and Fry, M.J., 2013. The effective management of national hydrometric data: experiences from the United Kingdom. Hydrological Sciences Journal, 58 (7), 1383–1399.