An analytical model of the heat budget of the ship and sensor environment has therefore been developed. With certain assumptions the resulting equations can be solved for time-varying incoming solar radiation to give estimates of the difference between the ship environmental temperature and the ambient air temperature, and hence the error in ship measured air temperature. The analytical model contains constants relating to the thermal and physical properties of the ship and also the relative wind speed. These constants need to be empirically estimated using the ship air temperature data. Preliminary investigations used the VOS Special Observing Project for the North Atlantic (VSOP-NA) dataset of paired ship and Numerical Weather prediction (NWP) model air temperatures and showed that differences between ship and NWP model air temperature were well approximated by the heating model. The analysis shows that ships recruited by different countries can have very different heating characteristics, largely due to different exposure of the air temperature sensors. This implies that the empirical constants need to be derived separately for different countries where possible; this significantly reduces the residual heating error after correction.
The analytical model is then fitted using data from the Comprehensive Ocean Atmosphere Data Set (COADS) to extend the correction technique to the global ocean. The resulting corrections are verified by examining the correlation of air temperature and sea temperature anomalies and evaluating the decrease in the air temperature random errors.