Selecting a global optimization method to estimate the oceanic particle cycling rate constants

The objective is to select an inverse method to estimate the parameters of a dynamical model of the oceanic particle cycling from in situ data. Estimating the parameters of a dynamical model is a nonlinear inverse problem, even in the case of linear dynamics. Generally, biogeochemical models are characterized by complex nonlinear dynamics and by a high sensitivity to their parameters. This makes the parameter estimation problem strongly nonlinear. We show that an approach based on a linearization around an a priori solution and on a gradient descent method is not appropriate given the complexity of the related cost functions and our poor a priori knowledge of the parameters. Global Optimization Algorithms (GOAs) appear as better candidates. We present a comparison of a deterministic (TRUST), and two stochastic (simulated annealing and genetic algorithm) GOAs. From an exact model integration, a synthetic data set is generated which mimics the space-time sampling of a reference campaign. Simulated optimizations of two to the eight model parameters are performed. The parameter realistic ranges of values are the only available a priori' information. The results and the behavior of the GOAs are analyzed in details. The three GOAs can recover at least two parameters. However, the gradient requirement of deterministic methods proves a serious drawback. Moreover, the complexity of the TRUST makes the estimation of more than two parameters hardly conceivable. The genetic algorithm quickly converges toward the eight parameter solution, whereas the simulated annealing is trapped by a local minimum. Generally, the genetic algorithm is less computationally expensive, swifter to converge, and has more robust procedural parameters than the simulated annealing.