The annual temperature cycle in shelf seas

Abstract

A generalized theory is developed to describe the annual temperature cycle in shelf seas. A sinusoidal approximation to the annual solar heating component, S, is assumed and the surface loss term is expressed as a constant k times the air-sea temperature difference ( T a − T s ). In well-mixed seas, analytical solutions show that in shallow water the sea temperature follows closely that of the ambient air temperature with limited separate effect of solar heating. Conversely in deep water, the sea surface temperature variations will be reduced relative to that of the ambient air. Providing such deep water remains mixed vertically, the annual variation will be inversely proportional to depth and maximum temperatures will occur up to 3 months after the maximum of solar heating. Generally, the magnitude of the inter-annual variability of sea surface temperatures will be less than corresponding variability in either the effective solar heating, S, (reduced by cloud cover) or the surface loss coefficient, k, (increased by stronger winds). The annual-mean sea temperature will exceed the annual mean air temperature by the annual mean of S divided by k. The above results can be extended to partially-stratified waters so long as autumnal overturning does not occur. For such conditions, an analytical expression is derived for the annual cycle of depth-varying temperatures for mixing associated with a vertical eddy dispersion coefficient E (constant in depth and time). The time taken for solar heating to be equalized throughout the water depth, D, is given by Tv = D 2/E , for a tidal current amplitude of 20 cm s −1. Tv ranges from 3.6 days for D = 50m to231days forD = 400m. To simulate the effect of gravitational instability that produces autumnal overturning, a numerical model is used that represents the effect of daily surface heat exchanges by a series expansion. Results from this model are used to indicate the effects of stratification over a range of values of both depth and Tv. Stratification will have a significant influence on the annual cycle and will be accompanied by autumnal overturning for values of Tv > 40days. Overall, stratification insulates the sea, (especially at greater depths) from atmospheric influences (in more complex models where E is reduced by vertical density gradients this effect would be further enhanced). In combination with autumnal overturning the effect is to lower both the variability and mean of the temperature in deeper water. The above model is used to simulate the annual temperature cycle for an off-shore cross section of constant slope (increasing in the example chosen from 25 to 250 m). The results indicate that horizontal gradients in temperature at the sea surface may be significantly smaller than those at lower depths. Sensitivity tests of the effects of both horizontal dispersion and advection showed that the “localized-equilibrium” for thermal exchanges assumed throughout the above analyses will be valid in many seas where bathymetry changes gradually. The dynamic response to the horizontal density gradients associated with these modelled cross-shore temperature structures are calculated. These responses are generally small with (steady) currents much less than 1 cm s −1 and changes in elevation less than 1 mm (except in fully enclosed seas where volume changes associated with thermal expansion cannot be balanced by oceanic exchanges).