Method and System for Wavelet Compression as an Observational Operator in Data …

Description (excerpt)

CROSS-REFERENCE This Application is a nonprovisional application of and claims the benefit of priority under 35 U.S.C. § 119 based on U.S. Provisional Patent Application No. 63/691,438 filed on Sep. 6, 2024. The Provisional Application and all references cited herein are hereby incorporated by reference into the present disclosure in their entirety. FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT The United States Government has ownership rights in this invention. Licensing inquiries may be directed to Office of Technology Transfer, US Naval Research Laboratory, Code 1004, Washington, DC 20375, USA; +1.202.767.7230; nrltechtran@us.navy.mil, referencing Navy Case #212239. TECHNICAL FIELD The present disclosure is related to, but not limited to, forecasting an ocean state via assimilation of ocean observations, and more specifically to transitioning the data assimilation system from physical space to wavelet space via a novel method. BACKGROUND 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. There exists a need for a solution whereby small-scale features are actively corrected in the model background. SUMMARY This summary is intended to introduce, in simplified form, a selection of concepts that are further described in the Detailed Description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter. Instead, it is merely presented as a brief overview of the subject matter described and claimed herein. Disclosed aspects provide a method of forecasting an ocean state via assimilation of ocean observations. The method may include receiving, by a processing device, data associated with a prior ocean state forecast, and converting, by the processing device, via a wavelet transform, the data associated with the prior ocean state forecast to wavelet space prior ocean state data, wherein the wavelet transform converts a signal from physical space to wavelet space. The method may include converting, by the processing device, via the wavelet transform, the ocean observations to wavelet space observation data, and filtering, by the processing device, the wavelet space observation data to generate filtered observation data. The method may include generating, by the processing device, a correction value based on a difference between the wavelet space prior ocean state data and the filtered observation data, the correction value being in wavelet space, and determining, by the processing device, a wavelet space increment value based on (i) the generated correction value, (ii) an error covariance associated with the prior ocean state forecast, and (iii) an error covariance associated with the ocean observations. The method may include converting, by the processing device, via an inverse of the wavelet transform, the wavelet space increment value to a physical space increment value, and generating, by the processing device, a current ocean state forecast based on (i) the converted physical space increment value and (ii) a background state associated with the prior ocean state forecast. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 , in accordance with one or more disclosed aspects: (a) Input SST image with average magnitude of 11. (b) Level one 2D wavelet transform of (a) where H1, V1, and D1 are respectively the level 1 horizontal, vertical, and diagonal detail coefficients with respectively average magnitude of 1.2×10{circumflex over ( )}(−2),4.0×10{circumflex over ( )}(−4), and 1.2×10{circumflex over ( )}(−2). A is the approximation coefficients with average magnitude of 22. (c) Level two 2D wavelet transform of (a) where H2, V2, and D2 correspond to the level 2 details, they have respective magnitude 4.7×10{circumflex over ( )}(−3),2.6×10{circumflex over ( )}(−4), and 2.8×10{circumflex over ( )}(−3). The first level details are the same as in (b). The approximation coefficients now have an average magnitude of 44. (d) The inverse wavelet transform of c with all the detail coefficients thresholded to 0. The average magnitude is still 11. FIG. 2 , in accordance with one or more disclosed aspects: (a) Raw innovation for the first day of assimilation. With low observational error this show cases the best-case of information retained from the observation. (b) Superobs increment on the model grid, without post-multiplication by B. This shows the sparsi