Development of a variational data assimilation system for the diurnal cycle of sea surface temperature

Abstract

A variational data assimilation system based on an incremental 4D‐Var approach is proposed for use with a zero‐dimensional model of the diurnal cycle of sea surface temperature (SST). Traditional 4D‐Var, which seeks to find the initial state of a system, is not appropriate for diurnal SST which is a wind and heat flux driven system that has only a limited memory of its prior state. Instead the proposed assimilation system corrects both the initial SST and the heat and wind fluxes applied throughout the day. The assimilation system is tested using ensembles in a set of idealized twin experiments. In these tests controlling parameters are varied around reasonable “default” values with the quality of the analyses assessed against a known “truth”. Within our tests data assimilation is shown to improve diurnal SST under most circumstances. Analyzed heat fluxes are also sometimes improved, although the improvement is much less than that observed for diurnal SST. The system was not found to improve the wind stress. The only circumstances where diurnal SST was not found to be improved by the assimilation were where either observational errors were large (greater than 0.5 K in our tests), or biases in the observations were too big (less than −0.3 K or greater than 0.2 K). The non‐Gaussian behavior of the wind stress was found to have an impact on the assimilation in low‐wind conditions and under these conditions the best analyses were obtained by artificially inflating the observation error.