A Robust Gauss-Newton Algorithm for the Optimization of Hydrological Models: Benchmarking Against Industry-Standard Algorithms

Abstract

Optimization of model parameters is a ubiquitous task in hydrological and environmental modeling. Currently, the environmental modeling community tends to favor evolutionary techniques over classical Newton-type methods, in the light of the geometrically problematic features of objective functions, such as multiple optima and general nonsmoothness. The companion paper (Qin et al., 2018, https://doi.org/10.1029/2017WR022488) introduced the robust Gauss-Newton (RGN) algorithm, an enhanced version of the standard Gauss-Newton algorithm that employs several heuristics to enhance its explorative abilities and perform robustly even for problematic objective functions. This paper focuses on benchmarking the RGN algorithm against three optimization algorithms generally accepted as “best practice” in the hydrological community, namely, the Levenberg-Marquardt algorithm, the shuffled complex evolution (SCE) search (with 2 and 10 complexes), and the dynamically dimensioned search (DDS). The empirical case studies include four conceptual hydrological models and three catchments. Empirical results indicate that, on average, RGN is 2–3 times more efficient than SCE (2 complexes) by achieving comparable robustness at a lower cost, 7–9 times more efficient than SCE (10 complexes) by trading off some speed to more than compensate for a somewhat lower robustness, 5–7 times more efficient than Levenberg-Marquardt by achieving higher robustness at a moderate additional cost, and 12–26 times more efficient than DDS in terms of robustness-per-fixed-cost. A detailed analysis of performance in terms of reliability and cost is provided. Overall, the RGN algorithm is an attractive option for the calibration of hydrological models, and we recommend further investigation of its benefits for broader types of optimization problems.