Can Gauss‐Newton Algorithms Outperform Stochastic Optimization Algorithms When Calibrating a Highly Parameterized Hydrological Model? A Case Study Using SWAT

Abstract The calibration of highly parameterized hydrological models is a major computational challenge, especially for models with long run times. This challenge motivates the reconsideration of gradient‐based algorithms often overlooked for their perceived lack of robustness. Our study evaluates two Gauss‐Newton algorithms, robust Gauss‐Newton (RGN), and Levenberg‐Marquardt (PEST), and two stochastic algorithms, Shuffled Complex Evolution (SCE), and Dynamically Dimensioned Search (DDS), on a 38‐parameter SWAT model calibration problem. Algorithm performance is comprehensively assessed using trajectory plots from 100 invocations and by analyzing the distribution of estimated optima at fixed budgets of 200, 500, 1,000, 2,000, 3,000, and 5,000 objective function evaluations (model runs). Empirical results indicate that: (a) Gauss‐Newton algorithms are more likely than stochastic algorithms to locate good solutions for the budgets considered in this work, and more likely to locate satisfactory solutions when budget is tight (200–500 model runs) and (b) RGN shows the fastest initial convergence amongst the algorithms under consideration and has the highest chance of finding satisfactory solutions when the budget is tight. The results indicate that Gauss‐Newton algorithms offer an attractive choice for the calibration of highly parameterized hydrological models.