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A generic approach that allows extracting functional nonlinear dependencies and mappings between atmospheric or ocean state variables in a relatively simple form is presented. These dependencies and mappings between the 2-and 3D fields of the prognostic and diagnostic variables are implicitly contained in the highly nonlinear coupled partial differential equations of an atmospheric or ocean dynamical model. They also are implicitly contained in the numerical model output. An approach based on using neural network techniques is developed here to extract the inherent nonlinear relationship between the sea surface height anomaly and the other dependent variables of an ocean model. Specifically, numerically generated grid point fields from the real time ocean forecast system (RT-OFS) model of NCEP (National Centers for Environmental Prediction) are used for training and validating this relationship. The accuracy of the NN emulation is evaluated over the entire domain of the NCEP's RT-OFS. The differences in the accuracies of the technique in the coastal areas and in the deep water are discussed. Accurate determination of such relationships is an important first step to enhance the assimilation of the sea surface height measurements into an ocean model by propagating the signal to other dependent variables through the depth of the model.