Wavelet ocean data assimilation

Due to necessary assumptions of observational errors with an exigency for appropriate and timely inversion in the assimilation, dense observations are thinned and/or altered before being assimilated into ocean models. Historically, this process did not significantly restrict model skill because most of the observation types had a quite coarse horizontal distribution. However, recent advances in observation resolution demand new assimilation approaches, whereby small-scale features are actively corrected in the model background. A novel method is introduced that applies multiscale data assimilation utilizing the wavelet transform. Unlike other currently employed ocean multiscale techniques, this method is performed in a single analysis step. Utilizing the wavelet transform allows for observational information to be retained at all its original grid points, compared to the averaging and removal in traditional techniques, such as super observations. This comes from the unique space and frequency relation available to the wavelet transform, which instead filters the potentially correlated small-scale observation errors at each model grid point. Several six-month identical twin data assimilation experiments were used to validate the method. Results indicate comparable to substantial improvements over super observations. On average, the sea surface temperature RMSE was 39% lower for the wavelet method over the six-months compared to super observations. The wavelet method was also able to constrain horizontal scales in assimilation 29 km and above compared to 60 km and above for the super observations.