Estimating the errors in the data and model are critical aspects of data assimilation. In this paper we present a reduced state space optimal interpolation scheme to assimilate satellite remotely sensed sea surface temperature into a coarse resolution general circulation model of the North Pacific. Using statistical tests on the principal components of a multidecadal model simulation and the misfits between model simulation and the remotely sensed data, we are able to show that the model and data have a small number of independent degrees of freedom (approximately 30--40), which is much less than the dimension of the model or data. Taking the difference between the model-data misfit and a fit to the model-data misfit using the principal components of the model, we are able to estimate the model representation error. The techniques presented in this paper can be adapted for other models and data sources.