Fitting dynamics to data

TLDR

Wind stress forcing is critical in oceanic models, yet wind stress observations are inadequate, so the formalism enables fitting an oceanic model to both oceanographic and meteorological data. The study presents a formalism for fitting dynamic forecast models to asynoptic data and examines whether such data can uniquely determine the model state. Because information propagates along wave characteristics, the data must be distributed to capture every flow feature, requiring satellite‑based widespread ocean coverage. Using a highly truncated wind‑driven equatorial ocean model, computational examples show that surface elevation and wind stress observations can recover the model state.

Abstract

A formalism is presented for fitting dynamic forecast models to asynoptic data. Because of the importance of wind stress forcing in oceanic models and of the inadequacies of wind stress observations, the formalism allows an oceanic model to be fit to both Oceanographic and meteorological data. Within the context of this formalism the important question of whether an asynoptic data set contains sufficient information to determine the model state completely and unambiguously is discussed. Because the information travels along wave characteristics, it is clear that for the data to be sufficient to determine the model state, they must be distributed so that every feature of the flow is seen at some time or another. Such widespread coverage of the oceans requires a data collection system that relies heavily on satellites. The formalism is illustrated using a highly truncated model of the wind‐driven equatorial ocean and computational examples demonstrate how surface elevation and wind stress observations might be used to recover the model state.