Date of Award


Degree Type


Degree Name


Degree Program

Engineering and Applied Science - Physics



Major Professor

Leftwich, Kendal

Second Advisor

Ngodock, Hans

Third Advisor

Ioup, Juliette

Fourth Advisor

D'Addezio, Joseph

Fifth Advisor

Souopgui, Innocent

Sixth Advisor

Smith, Damon


The ocean remains severely under-observed, in part due to its sheer size. Containing nearly billion of water with most of the subsurface being invisible because water is extremely difficult to penetrate using electromagnetic radiation, as is typically used by satellite measuring instruments. For this reason, most observations of the ocean have very low spatial-temporal coverage to get a broad capture of the ocean’s features. However, recent “dense but patchy” data have increased the availability of high-resolution – low spatial coverage observations. These novel data sets have motivated research into multi-scale data assimilation methods. Here, we demonstrate a new assimilation approach utilizing the wavelet transform that is multi-scale by nature but only requires a single analysis step; the latter being a significant advancement over current multi-scale approaches that almost universally require at least two analysis steps. To produce a proof-of-concept, we utilize only sea surface temperature (SST), as that observational source has strong spatial coverage and is high-resolution. The current standard when assimilating SST is to first perform super observations. The super-observation approach reduces a dense field to weighted averaged points that are far enough away from each other such that their readings are statistically uncorrelated. The process typically reduces an SST field to less than 10% of the original size, leading to only large-scale corrections of the ocean model. Our advancement instead uses the wavelet transform as an “observational operator”. The wavelet transform allows the SST innovation to occur in wavelet space, and wavelet thresholding allows us to retain all the spatial information in the SST field, down to scales that are not well represented by the horizontal resolution of the ocean model. An Observing System Simulation Experiment (OSSE) was used to test the validity of using wavelets in data assimilation. We find that the wavelet-based assimilation produces less root mean square (RMS) error with respect to depth than the more traditional super-observation approach. Additionally, we evaluated the spatial scales constrained by each assimilation approach. We find that over a 31-day cycling experiment, the wavelet-based approach constrains 65.50 versus the super-observation, a 14% gain in assimilation skill for the wavelet method. By constraining roughly 10 km more wavelength in the assimilation, the wavelet-based approach will now allow the representation of ocean features in the 76-65km range, which were previously not present from using super-observations. We expect this is due explicitly to the fact that the wavelet transform allows the assimilation to consider many more spatial scales than is possible using the super-observation approach.


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