Scale‐Dependent Ocean Vertical Correlations in the California Current System

We present observation and model estimates of temperature and salinity depth‐depth cross‐correlations in two different horizontal scale regimes. Glider data from the 2021 S‐MODE pilot campaign were assimilated into an ocean simulation using a three dimensional variational algorithm. We map the glider time series into distance allowing a Fourier analysis of model errors in wavenumber space. Power spectra indicate model error variance is less than the observed variance at scales larger than approximately 250 km. Based on this result, a Gaussian filter partitions the glider and model data into larger and smaller scale series at each depth. The larger and smaller scale temperature and salinity cross‐correlations between depths are compared and contrasted. Glider and model cross‐correlations are found to be similar, implying that the model physics at scales not constrained by the observations are similar to the true world. Plain Language Summary Historical observations around the globe have enabled insight into the vertical variability of temperature and salinity within features having horizontal extent larger than about 200 km. The paper exploits a collection of high‐density data that provides the opportunity to observe vertical variability within structures at smaller scales. There are two applications. The first allows us to verify that numerical models, representing our theoretical understanding of the ocean, are consistent with observations. The second application is to improve regular ocean forecasts. As we seek to forecast smaller scale features through upcoming observing systems, we must be able to correct both the large‐ and small‐scale features and their underlying vertical variability. Key Points The assimilative nonlinear model has skill to 250 km using available observations Temperature and salinity vertical cross‐correlations have unique profiles in each corresponding horizontal regime Observation‐ and model‐based depth‐depth cross‐correlations are similar