Method and System for Wavelet Compression as an Observational Operator in Data Assimilation Systems for Sea Surface Temperature

A method of forecasting an ocean state via assimilation of ocean observations, the method comprising:

• receiving, by a processing device, data associated with a prior ocean state forecast;
• 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;
• converting, by the processing device, via the wavelet transform, the ocean observations to wavelet space observation data;
• filtering, by the processing device, the wavelet space observation data to generate filtered observation data;
• 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;
• 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;
• 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.