Estimation of subsurface vertical thermal structure from sea surface temperature

Based on a layered structure of temperature fields (mixed layer, thermocline, and lower layers), the parametric model transforms a vertical profile into several parameters: sea surface temperature (SST), mixed layer depth (MLD), thermocline bottom depth (TBD), thermocline temperature gradient (TTG), and deep layer gradient (DPG). These parameters vary on different timescales: SST and MLD on scales of minutes to hours, TBD and TTG on months to seasons, and DPG on an even longer timescale. If the long timescale parameters such as TBD, TTD, and DPG are known (or given by climatological values), the degree of freedom of a vertical profile fitted by the model reduces to one: SST. When SST is observed, one may invert MLD, and, in turn, the vertical temperature profile with the known long timescale parameters: TBD, TTG, and DPG. The U.S. NCEP Pacific Ocean Analysis Data Set for the northwest Pacific Ocean was used for the study, the latitude is 5N and the longitude is from 122E to 180E. The dataset excluding the test data is the training dataset. The training dataset (1993-2005) was processed into a dataset consisting of SST, MLD, TBD, TTG, and DPG using the parametric model. SST from the test dataset was used for the inversion based on the known information on TBD, TTG, and DPG. The inverted profiles of January 2006 agreed quite well with the corresponding observed profiles. The rms error is 0.780C, this is much better than the simple method of estimating subsurface temperature anomaly from SST anomaly by correlating the two in the training dataset.