Conditioning groundwater flow parameters with iterative ensemble smoothers: analysis and approaches in the continuous and the discrete cases

Abstract The purpose of this study was to improve the optimization model for predicting more parameters in more difficult conditions (more grid cell numbers and high time interval numbers) than other studies in groundwater flow modelling. Also, the model needs fewer observation numbers for estimating parameters than other studies. In the present study, an optimization model based on model calibration was developed to estimate simultaneously four groundwater flow parameters – hydraulic conductivity, transmissivity, storage coefficient and leakance. The modified clonal selection algorithm, a class of artificial immune systems, was used as a heuristic optimization method. In order to simulate the groundwater flow, MODFLOW was used in conjunction with the model in MATLAB. The input files for MODFLOW were obtained by GMS groundwater simulator. The model was applied to two different hypothetical groundwater systems (two- and three-dimensional) under transient conditions to evaluate its performance. The results showed that the model was feasible for groundwater flow modelling and it could determine the groundwater flow parameters successfully with less observations and more grid cell numbers than the other studies.

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Flexible iterative ensemble smoother for calibration of perfect and imperfect models

Computational Geosciences ◽

10.1007/s10596-020-10008-z ◽

2020 ◽

Author(s):

Muzammil Hussain Rammay ◽

Ahmed H. Elsheikh ◽

Yan Chen

Keyword(s):

Computational Cost ◽

Model Error ◽

Physical Models ◽

Model Parameters ◽

Model Errors ◽

Estimated Parameters ◽

Ensemble Smoother ◽

Ensemble Smoothers ◽

Iterative Ensemble Smoothers ◽

Iterative Ensemble Smoother

AbstractIterative ensemble smoothers have been widely used for calibrating simulators of various physical systems due to the relatively low computational cost and the parallel nature of the algorithm. However, iterative ensemble smoothers have been designed for perfect models under the main assumption that the specified physical models and subsequent discretized mathematical models have the capability to model the reality accurately. While significant efforts are usually made to ensure the accuracy of the mathematical model, it is widely known that the physical models are only an approximation of reality. These approximations commonly introduce some type of model error which is generally unknown and when the models are calibrated, the effects of the model errors could be smeared by adjusting the model parameters to match historical observations. This results in a bias estimated parameters and as a consequence might result in predictions with questionable quality. In this paper, we formulate a flexible iterative ensemble smoother, which can be used to calibrate imperfect models where model errors cannot be neglected. We base our method on the ensemble smoother with multiple data assimilation (ES-MDA) as it is one of the most widely used iterative ensemble smoothing techniques. In the proposed algorithm, the residual (data mismatch) is split into two parts. One part is used to derive the parameter update and the second part is used to represent the model error. The proposed method is quite general and relaxes many of the assumptions commonly introduced in the literature. We observe that the proposed algorithm has the capability to reduce the effect of model bias by capturing the unknown model errors, thus improving the quality of the estimated parameters and prediction capacity of imperfect physical models.

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