Wavelet Data Assimilation for High-Resolution Sea Surface Temperature
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Solution Overview
Problem
Current ocean data assimilation methods discard high-resolution information from observations, leading to inefficient model updates and inaccurate forecasts due to the use of superobservations, which reduce the data to large-scale corrections.
Innovation Solution
A novel method utilizing the wavelet transform to convert observations and model background into wavelet space, allowing for filtering and correction of small-scale features directly at each model grid point, eliminating the need for superobservations and retaining high-resolution information.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If superobservations are used to reduce data to large-scale corrections, then computational efficiency is improved, but small-scale feature accuracy deteriorates
Solution Approach 1:
The patent segments the observation data processing by applying wavelet transform to decompose the data into different scale components. This allows the system to process and correct small-scale features separately from large-scale features, maintaining small-scale accuracy while preserving computational efficiency through targeted processing of specific scale components rather than processing all data at full resolution.
2Device complexity
If dense observations are thinned before assimilation, then error covariance assumptions are simplified, but model skill at small scales deteriorates
Solution Approach 1:
The patent extracts and isolates small-scale features from the observation data using wavelet transform before assimilation. By separating small-scale components and processing them through the data assimilation system, the method enables the model to correct small-scale features without requiring complex error covariance assumptions for the entire dense observation field, thus maintaining model skill while simplifying the error covariance structure.
3Device complexity
If high-resolution observation information is discarded, then data processing complexity is reduced, but forecast accuracy deteriorates
Solution Approach 1:
The patent transforms the observation data from physical space to wavelet space, adding a scale dimension to the data representation. This dimensional transformation allows the system to selectively process different scale components, retaining high-resolution small-scale information where it is most needed for forecast accuracy while reducing processing complexity by not uniformly processing all data at full resolution across the entire domain.
Data Source
AI summary
A method includes converting, via a wavelet transform, (i) data associated with a prior ocean state forecast to wavelet space prior ocean state data and (ii) ocean observations to wavelet space observation data, and then filtering the wavelet space observation data. The method includes generating a correction value based on a difference between the wavelet space prior ocean state data and the filtered observation data, and determining 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 includes converting, via an inverse of the wavelet transform, the wavelet space increment value to a physical space increment value, and generating 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.