Inverse problem

Singular value decomposition

Mathematics

Algorithm

Statistics

Mathematical optimization

Mathematical analysis

Calibration

Tikhonov regularization

Artificial intelligence

Regularization (linguistics)

Computer science

Applied mathematics

Artificial neural network

Levenberg–Marquardt algorithm

Applied Sciences

Various models were developed in the past to simulate different hydrological processes. However, discrepancies between simulated and observed values are still significant and pose a challenge to many researchers. Models contain many parameters that cannot be directly measured. The values of most of these parameters are determined in the calibration process conditioning the efficiency of such models. This paper introduces the use of the enhanced Gauss–Levenberg–Marquardt (GLM) procedure in combination with the singular value decomposition (SVD) and Tikhonov regularization to improve the process of hydrological model calibration. The procedure is tested on a freely available hydrological model using a synthetic dataset. Based on several efficiency measures, the GLM procedure, in combination with SVD and Tikhonov regularization, was found to provide efficient model history matching and almost perfect parameter calibration. Moreover, by comparing the results of the proposed procedure with the results of global evolutionary calibration procedures, it was found that the only calibration using the combined GLM procedure gave a perfect fit in low flows. Last but not least, the noise in the calculation results with the combined GLM method was practically the same in either the calibration or validation procedure, suggesting that only computational noise remained in the results.

Efficient Calibration of a Conceptual Hydrological Model Based on the Enhanced Gauss–Levenberg–Marquardt Procedure