Parameters estimation of an aquatic biological system by the adjoint method

Simulation models are currently used to predict environment impacts. However, models must be adapted to the peculiarities of the given situation and one of these adaptations consists in the calibration of certain model parameters. The calibration is made by an optimization technique in which parameters must be adjusted to fit to the data coming from one sampling station. This paper presents an algorithm to estimate parameters for a dynamic system described by ordinary differential equations. Parameters are computed by the minimization of the objective function which evaluates the difference between states and observations. The minimization technique requires the gradient of the objective function. The methodology presented by Chavent is applied to evaluate the objective function derivatives. In this method, it is necessary to introduce auxiliary equations for adjoint variables; this increases the size of the differential equations system but the size of the adjoint equation does not depend on the number of parameters to be computed. This algorithm is used to identify biological parameters for plankton dynamics model. The model includes two ordinary differential equations and five unknown parameters. This method is compared with two standard methods, the sensitivity function method and the quasi-linearization method, and the investigation and the computer time are discussed for each method. The adjoint method is shown attractive when the number of states is lower than the number of unknown parameters.