Data assimilation for nonlinear ocean models can be extremely complicated. A typical marine ecosystem model consists of equations that are both nonlinear and coupled to each other, and the data assimilation problem is therefore nontrivial. While several papers describe data assimilation techniques for estimating the model parameters in marine ecosystem models, this paper discusses a different approach. We let the model parameters have fixed values and instead allow for an unknown error term in each of the model equations. Thus, the model is included as a weak constraint in a variational formulation. To be more specific, unknown error terms are assumed for the model, the initial conditions and the data, and a weak constraint cost function containing weighted squares of the unknown error terms is to be minimized. For this purpose, we use very simple iterative gradient descent schemes, where each iterate is based on the gradient of the cost function. An ordinary gradient steepest descent scheme is compared to a more elaborate conjugate gradient scheme denoted by the Fletcher and Reeves method. Several data assimilation experiments are performed in which the data are generated from an “exact” forward model integration (twin experiments). To make the experiments more realistic, normally distributed noise is added to the measurements. Properties like the sensitivity with respect to data density and length of the assimilation interval are investigated. Also, a twin experiment with measurements of only the phytoplankton component is performed. Remotely sensed ocean colour data represent the major part of currently available observations and data sets of this type may be used to measure the phytoplankton compartment. Thus, showing that it is possible to obtain good results also for the other ecosystem components when only phytoplankton is measured seems to be of vital importance for creating a marine biochemical data assimilation system.