Estimation Of Hydrological Model Parameters Research Articles

Development of a stochastic hydrological modeling system for improving ensemble streamflow prediction

Streamflow prediction plays a crucial role in water resources systems planning and the mitigation of hydrological extremes such as floods and droughts. Since a variety of uncertainties exist in streamflow prediction, it is necessary to enhance our efforts to robustly address uncertainties and their interactions for improving the reliability of streamflow prediction. This paper presents a stochastic hydrological modeling system (SHMS) for improving daily streamflow prediction by explicitly addressing uncertainties in error and model parameters as well as in forcing data and model outputs. Specifically, the SHMS merges the strengths of the ensemble Kalman filter and the particle filter algorithms for improving the effectiveness and robustness of daily streamflow assimilation. Factorial analysis of variance and variance-based global sensitivity analysis are performed to reveal parameter interactions affecting predictive performance and temporal dynamics of parameter sensitivities, maximizing the accuracy of streamflow prediction. The SHMS has been applied to the Guadalupe River basin located in Texas of the United States to demonstrate feasibility and applicability. Our findings indicate that the SHMS improves upon the well-known ensemble Kalman filter for sequential estimation of hydrological model parameters through a more rapid and accurate convergence of model parameters in streamflow simulation. The SHMS also demonstrates a higher level of skill in streamflow prediction compared to the conditional vine copula model. The proposed SHMS can be applied straightforwardly to other river basins for probabilistic hydrological prediction.

Development of a hybrid regionalization model for estimation of hydrological model parameters for ungauged watersheds

Development of a hybrid regionalization model for estimation of hydrological model parameters for ungauged watersheds

Bayesian spectral likelihood for hydrological parameter inference

AbstractThis paper proposes a spectral domain likelihood function for the Bayesian estimation of hydrological model parameters from a time series of model residuals. The spectral domain error model is based on the power‐density spectrum (PDS) of the stochastic process assumed to describe residual errors. The Bayesian spectral domain likelihood (BSL) is mathematically equivalent to the corresponding Bayesian time domain likelihood (BTL) and yields the same inference when all residual error assumptions are satisfied (and all residual error parameters are inferred). However, the BSL likelihood function does not depend on the residual error distribution in the original time domain, which offers a theoretical advantage in terms of robustness for hydrological parameter inference. The theoretical properties of BSL are demonstrated and compared to BTL and a previously proposed spectral likelihood by Montanari and Toth (2007), using a set of synthetic case studies and a real case study based on the Leaf River catchment in the U.S. The empirical analyses confirm the theoretical properties of BSL when applied to heteroscedastic and autocorrelated error models (where heteroscedasticity is represented using the log‐transformation and autocorrelation is represented using an AR(1) process). Unlike MTL, the use of BSL did not introduce additional parametric uncertainty compared to BTL. Future work will explore the application of BSL to challenging modeling scenarios in arid catchments and “indirect” calibration with nonconcomitant input/output time series.

Towards a more representative parametrisation of hydrologic models via synthesizing the strengths of Particle Swarm Optimisation and Robust Parameter Estimation

Abstract. The development of methods for estimating the parameters of hydrologic models considering uncertainties has been of high interest in hydrologic research over the last years. In particular methods which understand the estimation of hydrologic model parameters as a geometric search of a set of robust performing parameter vectors by application of the concept of data depth found growing research interest. Bárdossy and Singh (2008) presented a first Robust Parameter Estimation Method (ROPE) and applied it for the calibration of a conceptual rainfall-runoff model with daily time step. The basic idea of this algorithm is to identify a set of model parameter vectors with high model performance called good parameters and subsequently generate a set of parameter vectors with high data depth with respect to the first set. Both steps are repeated iteratively until a stopping criterion is met. The results estimated in this case study show the high potential of the principle of data depth to be used for the estimation of hydrologic model parameters. In this paper we present some further developments that address the most important shortcomings of the original ROPE approach. We developed a stratified depth based sampling approach that improves the sampling from non-elliptic and multi-modal distributions. It provides a higher efficiency for the sampling of deep points in parameter spaces with higher dimensionality. Another modification addresses the problem of a too strong shrinking of the estimated set of robust parameter vectors that might lead to overfitting for model calibration with a small amount of calibration data. This contradicts the principle of robustness. Therefore, we suggest to split the available calibration data into two sets and use one set to control the overfitting. All modifications were implemented into a further developed ROPE approach that is called Advanced Robust Parameter Estimation (AROPE). However, in this approach the estimation of the good parameters is still based on an ineffective Monte Carlo approach. Therefore we developed another approach called ROPE with Particle Swarm Optimisation (ROPE-PSO) that substitutes the Monte Carlo approach with a more effective and efficient approach based on Particle Swarm Optimisation. Two case studies demonstrate the improvements of the developed algorithms when compared with the first ROPE approach and two other classical optimisation approaches calibrating a process oriented hydrologic model with hourly time step. The focus of both case studies is on modelling flood events in a small catchment characterised by extreme process dynamics. The calibration problem was repeated with higher dimensionality considering the uncertainty in the soil hydraulic parameters and another conceptual parameter of the soil module. We discuss the estimated results and propose further possibilities in order to apply ROPE as a well-founded parameter estimation and uncertainty analysis tool.

Using time‐lapse gravity for groundwater model calibration: An application to alluvial aquifer storage

The estimation of hydrological model parameters by calibration to field data is a critical step in the modeling process. However, calibration often fails because of parameter correlation. Here it is shown that time‐lapse gravity data can be combined with hydraulic head data in a coupled hydrogeophysical inversion to decrease parameter correlation in groundwater models. This is demonstrated for a model of riverbank infiltration where combined inversion successfully constrains hydraulic conductivity and specific yield in both an analytical and a numerical groundwater model. A sensitivity study shows that time‐lapse gravity data are especially useful to constrain specific yield. Furthermore, we demonstrate that evapotranspiration, and riverbed conductance are better constrained by coupled inversion to gravity and head data than to head data alone. When estimating the four parameters simultaneously, the six correlation coefficients were reduced from unity when only head data were employed to significantly lower values when gravity and head data were combined. Our analysis reveals that the estimated parameter values are not very sensitive to the choice of weighting between head and gravity data over a large interval of relative weights.

Calibration of a water and energy balance model: Recursive parameter estimation versus particle swarm optimization

It is well known that one of the major problems in the application of land surface models is the determination of the various model parameters. In most cases, only one or a limited number of variables are used to estimate these parameters. This study evaluates the use of two fundamentally different global optimization methods, multistart weight‐adaptive recursive parameter estimation (MWARPE) and particle swarm optimization (PSO), for the estimation of hydrologic model parameters on the basis of data for multiple variables. MWARPE iteratively uses the linear recursive filter equations in a Monte Carlo setting and therefore does not rely on the explicit minimization of an objective function. However, a major drawback of the MWARPE method is the high dimensionality, determined by the number of observations, of the matrix to be inverted. On the other hand, PSO is a stochastic optimization method based on the collective strength of a population of individuals with flocking or herding behavior, as observed in a wide number of biological systems. In situ observations of net radiation; latent, sensible, and ground heat fluxes; and the soil moisture profile are used to determine the parameters of a simplified water and energy balance model. Both optimization methods are analyzed in terms of model performance and computational efficiency. Comparable results, expressed in terms of the root mean square error values, were obtained for both methods. However, it was found that MWARPE tends to slightly overfit the data.

Robust estimation of hydrological model parameters

Abstract. The estimation of hydrological model parameters is a challenging task. With increasing capacity of computational power several complex optimization algorithms have emerged, but none of the algorithms gives a unique and very best parameter vector. The parameters of fitted hydrological models depend upon the input data. The quality of input data cannot be assured as there may be measurement errors for both input and state variables. In this study a methodology has been developed to find a set of robust parameter vectors for a hydrological model. To see the effect of observational error on parameters, stochastically generated synthetic measurement errors were applied to observed discharge and temperature data. With this modified data, the model was calibrated and the effect of measurement errors on parameters was analysed. It was found that the measurement errors have a significant effect on the best performing parameter vector. The erroneous data led to very different optimal parameter vectors. To overcome this problem and to find a set of robust parameter vectors, a geometrical approach based on Tukey's half space depth was used. The depth of the set of N randomly generated parameters was calculated with respect to the set with the best model performance (Nash-Sutclife efficiency was used for this study) for each parameter vector. Based on the depth of parameter vectors, one can find a set of robust parameter vectors. The results show that the parameters chosen according to the above criteria have low sensitivity and perform well when transfered to a different time period. The method is demonstrated on the upper Neckar catchment in Germany. The conceptual HBV model was used for this study.

Improvement of the PEST parameter estimation algorithm through Extended Kalman Filtering

During the last decades, a number of methods have been developed for the estimation of hydrologic model parameters. One frequently used and relatively simple algorithm is the parameter estimation (PEST) method. A close examination of this algorithm shows that it is very similar to the Extended Kalman Filter (EKF). The differences between the methods are caused by the derivation of the algorithms: the EKF is derived through a minimization of the square difference between the true and the estimated model state, while PEST has been derived through a minimization of an objective function related to, but not equal to, the root mean square error between the model results and the observations. The objective of this paper is to analyze the performance of these two algorithms. A synthetic-data experiment has been developed for this purpose. It has been found that under high observation errors and/or temporally sparse observations the EKF can lead to a stable parameter estimation, while it is possible that under the same circumstances PEST does not yield a solution. Also, the choice of the initial guess for the parameter values can be an important issue in the application of PEST, while this is not so important for the EKF. The application of the Marquardt algorithm can lead to stable parameter estimates in case the PEST algorithm fails (meaning that nonphysical parameter values were obtained which lead to a premature abortion of the model simulations), but numerically the EKF is still superior. In order to solve this problem, a simple alternative to the Marquardt algorithm has been developed, which leads to a quicker convergence. Application of both methods to a conceptual rainfall–runoff model with 10 parameters shows the robustness of the EKF for parameter calibration. The overall conclusion from this work is that generally PEST and the EKF will lead to similar results, but that under high observation errors, infrequent observations, and/or strongly erroneous initial parameter values, the PEST method can fail because of excessive parameter updates caused by the conceptual error in the objective function minimized by the calibration algorithm, while the EKF can still yield stable parameter estimates.