Further studies on the thermodynamic prediction of ocean temperatures

Abstract

A series solution for the conservation of thermal energy equation applied to the upper layer of the oceans is obtained. Given the initial values of the surface ocean temperature anomalies, the solution yields the values at a later time as functions of the scale, or size, of the initial anomalies themselves, as well as for the surface wind speed, the ocean current speed and the horizontal mixing coefficient. The solution is applied to determine the truncation error made when one approximates the time derivative of the temperature anomaly bye the finite-difference Euler approximation, and uses a forward time step. Given an upper limit for the truncation error, the permissible time step depends on the scale or size of the initial anomalies, the surface wind speed, the ocean currents and horizontal mixing are neglected, the solution is independent of the size of the anomalies, and a time step of 30 days appears to be justified. However, when these horizontal transport terms are included, a shorter time step must be used which depends on the above mentioned parameters.