THE ANNUAL TEMPERATURE CYCLE IN SHELF SEAS

A generalized theory is developed to describe the annual temperature c ycle in shelf seas. A sinusoidal approximation to the annual solar hea ting component, S, is assumed and the surface loss term is expressed a s a constant k times the air-sea temperature difference (T(a) - T(s)). In well-mixed seas, analytical solutions show that in shallow water t he sea temperature follows closely that of the ambient air temperature with limited separate effect of solar heating. Conversely in deep wat er, the sea surface temperature variations will be reduced relative to that of the ambient air. Providing such deep water remains mixed vert ically, the annual variation will be inversely proportional to depth a nd maximum temperatures will occur up to 3 months after the maximum of solar heating. Generally, the magnitude of the inter-annual variabili ty of sea surface temperatures will be less than corresponding variabi lity in either the effective solar heating, S, (reduced by cloud cover ) or the surface loss coefficient, k, (increased by stronger winds). T he annual-mean sea temperature will exceed the annual mean air tempera ture by the annual mean of S divided by k. The above results can be ex tended to partially-stratified waters so long as autumnal overturning does not occur. For such conditions, an analytical expression is deriv ed for the annual cycle of depth-varying temperatures for mixing assoc iated with a vertical eddy dispersion coefficient E (constant in depth and time). The time taken for solar heating to be equalized throughou t the water depth, D, is given by Tv = D2/E, for a tidal current ampli tude of 20 cm s-1, Tv ranges from 3.6 days for D = 50 m to 231 days fo r D = 400 m. To simulate the effect of gravitational instability that produces autumnal overturning, a numerical model is used that represen ts the effect of daily surface heat exchanges by a series expansion. R esults from this model are used to indicate the effects of stratificat ion over a range of values of both depth and Tv. Stratification will h ave a significant influence on the annual cycle and will be accompanie d by autumnal overturning for values of Tv > 40 days. Overall, stratif ication insulates the sea, (especially at greater depths) from atmosph eric influences (in more complex models where E is reduced by vertical density gradients this effect would be further enhanced). In combinat ion with autumnal overturning the effect is to lower both the variabil ity and mean of the temperature in deeper water. The above model is us ed to simulate the annual temperature cycle for an off-shore cross sec tion of constant slope (increasing in the example chosen from 25 to 25 0 m). The results indicate that horizontal gradients in temperature at the sea surface may be significantly smaller than those at lower dept hs. Sensitivity tests of the effects of both horizontal dispersion and advection showed that the ''localized-equilibrium'' for thermal excha nges assumed throughout the above analyses will be valid in many seas where bathymetry changes gradually. The dynamic response to the horizo ntal density gradients associated with these modelled cross-shore temp erature structures are calculated. These responses are generally small with (steady) currents much less than 1 cm s-1 and changes in elevati on less than 1 mm (except in fully enclosed seas where volume changes associated with thermal expansion cannot be balanced by oceanic exchan ges).