REPORTS ON MEETINGS

Abstract

This paper examines the efficiency of various methods of calibrating a rainfall-runoff model. The model used is a 12 parameter version of the Boughton model which has been developed for large tropical basins. Attempts were made to improve the efficiency of calibration in three areas: selection of the best nonlinear programming algorithms; reduction of the number of objective functions required for calibration; and simplification of the model structure. The best algorithms were found to be those of Powell, Rosenbrock, and the simplex method of Nelder and Mead. The Davidon method did not perform well. The number of objective function evaluations can be reduced by performing a sensitivity analysis on the model and selecting a small group of parameters which are not interdependent and which the objective function is sensitive to. This may yield a substantial reduction in the computer time required to calibrate the model. Simplification of the model structure can also yield substantial savings, especially where it removes calculations which are redundant and reduces the number of model parameters.     

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).     

Estimation of unconfined aquifer parameters by genetic algorithms

Abstract

Unconfined aquifer parameters, viz. transmissivity, storage coefficient, specific yield and delay index from a pumping test are estimated using the genetic algorithm optimization (GA) technique. The parameter estimation problem is formulated as a least-squares optimization, in which the parameters are optimized by minimizing the deviations between the field-observed and the model-predicted time–drawdown data. Boulton's convolution integral for the determination of drawdown is coupled with the GA optimization technique. The bias induced by three different objective functions: (a) the sum of squares of absolute deviations between the observed and computed drawdown; (b) the sum of squares of normalized deviations with respect to the observed drawdown; and (c) the sum of squares of normalized deviations with respect to the computed drawdown, is statistically analysed. It is observed that, when the time–drawdown data contain no errors, the objective functions do not induce any bias in the parameter estimates and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the case considered, defining the objective function as the sum of the squares of absolute deviations between the observed and simulated drawdowns resulted in the best possible estimates. A comparison of the GA technique with the curve-matching procedure and a conventional optimization technique, such as the sequential unconstrained minimization technique (SUMT), is made in estimating the aquifer parameters from a reported field pumping test in an unconfined aquifer. For the case considered, the GA technique performed better than the other two techniques in parameter estimation, with the sum-of-squares errors obtained from the GA about one fourth of those obtained by the curve matching procedure, and about half of those obtained by SUMT.

Citation Rajesh, M., Kashyap, D. & Hari Prasad, K. S. (2010) Estimation of unconfined aquifer parameters by genetic algorithms. Hydrol. Sci. J. 55(3), 403–413.     

Which objective function to calibrate rainfall–runoff models for low-flow index simulations?

Much has been written on the subject of objective functions to calibrate rainfall–runoff models. Many studies focus on the best choice for low-flow simulations or different multi-objective purposes. Only a few studies, however, investigate objective functions to optimize the simulations of low-flow indices that are important for water management. Here, we test different objective functions, from single objective functions with different discharge transformations or using low-flow indices, to combinations of single objective functions, and we evaluate their robustness and sensitivity to the rainfall–runoff model. We find that the Kling and Gupta efficiency (KGE) applied to a transformation of discharge is inadequate to fulfil all assessment criteria, whereas the mean of the KGE applied to the discharge and the KGE applied to the inverse of the discharge is sufficient. The robustness depends on the climate variability rather than the objective function and the results are insensitive to the model.

EDITOR A. Castellarin; ASSOCIATE EDITOR C. Perrin     

Development of operating rules for a complex multi-reservoir system by coupling genetic algorithms and network optimization

Abstract

An alternative procedure for assessment of reservoir Operation Rules (ORs) under drought situations is proposed. The definition of ORs for multi-reservoir water resources systems (WRSs) is a topic that has been widely studied by means of optimization and simulation techniques. A traditional approach is to link optimization methods with simulation models. Thus the objective here is to obtain drought ORs for a real and complex WRS: the Júcar River basin in Spain, in which one of the main issues is the resource allocation among agricultural demands in periods of drought. To deal with this problem, a method based on the combined use of genetic algorithms (GA) and network flow optimization (NFO) is presented. The GA used was PIKAIA, which has previously been used in other water resources related fields. This algorithm was linked to the SIMGES simulation model, a part of the AQUATOOL decision support system (DSS). Several tests were developed for defining the parameters of the GA. The optimization of various ORs was analysed with the objective of minimizing short-term and long-term water deficits. The results show that simple ORs produce similar results to more sophisticated ones. The usefulness of this approach in the assessment of ORs for complex multi-reservoir systems is demonstrated.

Citation Lerma, N., Paredes-Arquiola, J., Andreu, J., and Solera, A., 2013. Development of operating rules for a complex multi-reservoir system by coupling genetic algorithms and network optimization. Hydrological Sciences Journal, 58 (4), 797–812.     

Reservoir attenuation of floods from ungauged basins

Abstract

In a typical reservoir routing problem, the givens are the inflow hydrograph and reservoir characteristic functions. Flood attenuation investigations can be easily accomplished using a hydrological or hydraulic routing of the inflow hydrograph to obtain the reservoir outflow hydrograph, unless the inflow hydrograph is unavailable. Although attempts for runoff simulation have been made in ungauged basins, there is only a limited degree of success in special cases. Those approaches are, in general, not suitable for basins with a reservoir. The objective of this study is to propose a procedure for flood attenuation estimation in ungauged reservoir basins. In this study, a kinematic-wave based geomorphic IUH model was adopted. The reservoir inflow hydrograph was generated through convolution integration using the rainfall excess and basin geomorphic information. Consequently, a fourth-order Runge-Kutta method was used to route the inflow hydrograph to obtain the reservoir outflow hydrograph without the aid of recorded flow data. Flood attenuation was estimated through the analysis of the inflow and outflow hydrographs of the reservoir. An ungauged reservoir basin in southern Taiwan is presented as an example to show the applicability of the proposed analytical procedure. The analytical results provide valuable information for downstream flood control work for different return periods.     

Analysis of objective functions used in urban runoff models

The objective functions used in parameter estimation in urban runoff models are compared by using a method proposed by Diskin and Simon¹ and the urban runoff model ILLUDAS. Two sets of objective functions, the first one used by Diskin and Simon in their study and a second one which includes other objective functions are used. Rainfall-runoff data from urban watersheds in the US are used in the study. The results indicate that the least squares criterion is the best among those studied.     

A benchmark comparison of numerical methods for infinite Prandtl number thermal convection in two-dimensional Cartesian geometry

Abstract

A comparison is made between seven different numerical methods for calculating two-dimensional thermal convection in an infinite Prandtl number fluid. Among the seven methods are finite difference and finite element techniques that have been used to model thermal convection in the Earth's mantle. We evaluate the performance of each method using a suite of four benchmark problems, ranging from steady-state convection to intrinsically time-dependent convection with recurring thermal boundary layer instabilities. These results can be used to determine the accuracy of other computational methods, and to assist in the development of new ones.     

A Modified Neural Network for Improving River Flow Prediction/Un Réseau de Neurones Modifié pour Améliorer la Prévision de L'Écoulement Fluvial

Abstract

Artificial neural network (ANN) models provide huge potential for simulating nonlinear behaviour of hydrological systems. However, the potential of ANN is yet to be fully exploited due to the problems associated with improving the model generalization performance. Generalization refers to the ability of a neural network to correctly process input data that have not been used for calibrating the neural network model. In the hydrological context, better generalization performance implies higher precision of forecasting. The primary objectives of this study are to explore new measures for improving the generalization performance of an ANN-based rainfall–runoff model, and to evaluate the applicability of the new measures. A modified neural network model (entitled goal programming (GP) neural network) for modelling the rainfall–runoff process has been developed, in which three enhancements are made as compared to the widely-used backpropagation (BP) network. The three enhancements are (a) explicit integration of hydrological prior knowledge into the neural network learning; (b) incorporation of a modified training objective function; and (c) reduction of network sensitivity to input errors. Seven watersheds across a range of climatic conditions and watershed areas in China were selected for examining the alternative networks. The results demonstrate that the GP consistently outperformed the BP both in the calibration and verification periods and three proposed measures yielded improvement of performance.     

Identification of trends in Malaysian monthly runoff under the scaling hypothesis

Abstract

Statistical tests have been widely used for several decades to identify and test the significance of trends in runoff and other hydrological data. The Mann-Kendall (M-K) trend test is commonly used in trend analysis. The M-K test was originally proposed for random data. Several variations of the M-K test, as well as pre-processing of data for use with it, have been developed and used. The M-K test under the scaling hypothesis has been developed recently. The basic objective of the research presented in this paper is to investigate the trends in Malaysian monthly runoff data. Identification of trends in runoff data is useful for planning water resources projects. Existence of statistically significant trends would also lead to identification of possible effects of climate change. Monthly runoff data for Malaysian rivers from the past three decades are analysed, in both five-year segments and entire data sequences. The five-year segments are analysed to investigate the variability in trends from one segment to another in three steps: (1) the M-K tests are conducted under random and correlation assumptions; (2) the Hurst scaling parameter is estimated and tested for significance; and (3) the M-K test under the scaling hypothesis is conducted. Thus the tests cover both correlation and scaling. The results show that the number of significant segments in Malaysian runoff data would be the same as those found under the assumption that the river flow sequences are random. The results are also the same for entire sequences. Thus, monthly Malaysian runoff data do not have statistically significant trends. Hence there are no indications of climate change in Malaysian runoff data.

Citation Rao, A. R., Azli, M. & Pae, L. J. (2011) Identification of trends in Malaysian monthly runoff under the scaling hypothesis. Hydrol. Sci. J. 56(6), 917–929.     

Identifiability analysis: towards constrained equifinality and reduced uncertainty in a conceptual model

Abstract

Different sets of parameters and conceptualizations of a basin can give equally good results in terms of predefined objective functions. Therefore, a need exists to tackle equifinality and quantify the uncertainty bands of a model. In this paper we use the concepts of equifinality, identifiability and uncertainty to propose a simple method aimed at constraining the equifinal parameters and reducing the uncertainty bands of model outputs, and obtaining physically possible and reasonable models. Additionally, the uncertainty of equifinal solutions is quantified to estimate the amount by which output uncertainty can be reduced by knowing how to discard most of the equifinal solutions of a model. As a study case, a conceptual model of the Chillán basin in Chile is carried out. From the study it is concluded that using identifiability analysis makes it possible to constrain equifinal solutions with reduced uncertainty and realistic models, resulting in a framework that can be recommended to practitioners, especially due to the simplicity of the method.     

Identification of rainfall–runoff models for operational applications / Identification de modèles pluie–débit pour des applications opérationnelles

Abstract

The problem of selecting appropriate objective functions for the identification of a lumped conceptual rainfall–runoff model is investigated, focusing on the value of the model in an operational setting. A probability-distributed soil moisture model is coupled with a linear parallel routing scheme, and conditioned on rainfall–runoff observations from three catchments in the southeast of England. Using an abstraction control problem, which requires accurate simulation of the intermediate flow range, it is shown that using the traditional RMSE fit criterion, produces operationally sub-optimal predictions. This is true in the identification period, when applied to a testing period, and to proxy catchment data. Using a second case study of the Leaf River in Mississippi (USA), where the focus changes to predicting flood peaks over a specified threshold, also suggests that the relevant flood threshold should govern the objective function choice. It is concluded that, due to limitations in the structure of the employed model, it would be counter-productive to try to achieve a good all-round representation of the rainfall–runoff processes, and that a more empirical approach to identification may be preferred for specific forecasting problems. This leaves us with the question of how far hydrological realism should be sacrificed in favour of purpose-driven objective functions.     

The Navier–Stokes-α equations revisited

The Navier–Stokes-α equation is a regularised form of the Euler equation that has been employed in representing the sub-grid scales in large-eddy simulations. Determined efforts have been made to place it on a secure deductive foundation. This requires two steps to be completed. The first is fundamental and consists of establishing from the equations governing the fluid flow, a relationship between two velocities called by Holm (Chaos, 2002a, 12, 518) the “filtered” and “unfiltered” velocities. The second consists of the relation between these two velocities. Until now, the preferred route to the first objective has been variational, by varying the action using Hamilton's principle. Soward and Roberts (J. Fluid Mech., 2008, 604, 297) followed that variational route and established the existence of an important but unwelcome term omitted by Holm in his derivation. It is shown here that the Soward and Roberts result may be derived from Euler's equation by a direct approach with considerably greater efficiency. Holm achieved the second objective by making a “Taylor hypothesis”, which we use here to evaluate the unwelcome term missing from his analysis of the first step. The resulting model equations differ from those of Holm's α model, and the attractive mean Kelvin's circulation theorem that follows from his α equations is no longer valid. For that reason, we call the term omitted by Holm unwelcome.     

Availability and performance of sediment detachment and transport functions for overland flow conditions

Abstract

Soil erosion is a global environmental problem. To quantify water erosion rates at the field, hillslope or catchment scale, several spatially-distributed soil erosion models have been developed. The accuracy of those models depends largely on the sediment detachment and transport functions used, many of which were developed from empirical research. In this paper, the physical basis of the available sediment detachment and transport functions is reviewed, and their application boundaries determined. Well-known and widely-used sediment detachment and transport functions are discussed on the basis of composite force predictors, i.e. shear stress, stream power, unit stream power and effective stream power, and their suitability is elucidated based on information in the literature. It was found that only a few sediment detachment functions are available, and those have been poorly tested. Most erosion models ignore direct calculation of sediment detachment, but use the sediment transport capacity deficit approach to estimate detachment rate. Many more sediment transport functions are available that also tested better for overland flow conditions. However, our tests did not result in a single function that appeared to perform best under a range of experimental conditions. The unit stream power-based functions developed by Govers seem to be the most promising ones for water erosion modelling. It is therefore recommended to evaluate the performance of existing sediment transport functions with more detailed field and laboratory datasets.

Editor Z.W. Kundzewicz     

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.     

A physically based distribution function for low flow

Abstract

An attempt is made to incorporate the physical mechanism in a distribution function of low flow in terms of baseflow recession. The derived distribution function contains four parameters of which two are determined from a traditional recession analysis of low flow periods. The other two are derived from a statistical analysis of the maximum length of “dry weather” periods when precipitation is less than an assumed threshold value. The distribution function with the same parameters can be applied to calculate mean low flow for different durations. It is applied and tested for summer low flow in southern and western Norway.     

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.     

Optimization of groundwater abstraction from a coastal aquifer

ABSTRACT

An analytical mathematical model, based on Jacobian elliptic functions, has been used to identify feasible wellfield locations and pumping rates for large-scale abstraction from an unconfined coastal aquifer. The choice of optimum feasible wellfield strategy has been made using a simple economic model which calculates the cost of the pipelines required to transport the abstracted groundwater to a large coastal city which forms the demand centre. Results indicate that the cheapest wellfield design would be a single large wellfield. However, because of the need to maintain at least a minimum supply in the city until a new surface water source is developed, a better solution may well be to develop two smaller wellfields pumping a greater total abstraction.     

Equilibrium of magnetic fields with arbitrary interweaving of the lines of force i. discontinuities in the torsion

Abstract

This paper considers the static force-free equilibrium V×B=αB of a magnetic field in which all of the lines of force connect without knotting between parallel planes. The field is formed by continuous deformation from an initial uniform field, and is conveniently described in terms of the scalar function ψ, which is effectively the stream function for the incompressible wrapping and interweaving of the lines of force, and the scalar function θ, which describes the local compression and expansion. Equilibrium requires satisfaction of two independent equations (the third equation defines α), which cannot be accomplished without the full freedom of both functions ψ and θ. It is shown by integration along the characteristics of the equilibrium equations that, when ψ is predetermined by an arbitrary winding pattern, there appear discontinuities in α. Discontinuities in α have discontinuities in the field (i.e. current sheets) associated with them.

We expect such discontinuities to be produced in the magnetic fields extending outward from the convecting surfaces of the cooler stars.     

Analyses of suspended sediment loads in Slovenian rivers

ABSTRACT

Suspended solids are present in every river, but high quantities can worsen the ecological conditions of streams; therefore, effective monitoring and analysis of this hydrological variable are necessary. Frequency, seasonality, inter-correlation, extreme events, trends and lag analyses were carried out for peaks of suspended sediment concentration (SSC) and discharge (Q) data from Slovenian streams using officially monitored data from 1955 to 2006 that were made available by the Slovenian Environment Agency. In total more than 500 station-years of daily Q and SSC data were used. No uniform (positive or negative) trend was found in the SSC series; however, all the statistically significant trends were decreasing. No generalization is possible for the best fit distribution function. A seasonality analysis showed that most of the SSC peaks occurred in the summer (short-term intense convective precipitation produced by thunderstorms) and in the autumn (prolonged frontal precipitation). Correlations between Q and SSC values were generally relatively small (Pearson correlation coefficient values from 0.05 to 0.59), which means that the often applied Q–SSC curves should be used with caution when estimating annual suspended sediment loads. On average, flood peak Q occurred after the corresponding SSC peak (clockwise-positive hysteresis loops), but the average lag time was rather small (less than 1 day).

Editor M.C. Acreman; Associate editor Y. Gyasi-Agyei