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FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



and other processes. It is not obvious, however, 

 which one or combination of these factors de- 

 termines the temperature of the water at any 

 time or place. In order to gain an understanding 

 of the physical processes, then, or to assess their 

 relative importance, the problem must be formal- 

 ized in accordance with principles discussed by 

 Sverdrup et al. (1942). Here some of these 

 principles will be applied to the distribution 

 of the surface temperature, a variable of impor- 

 tance in any climatic study. 



I. HEAT (SALT) BUDGET 



On the basis of conservation of heat one can 

 say that, at any locality in the ocean, the net 

 heat exchange across the sea surface must be 

 balanced by the change in heat content of the 

 water column, heat diffused through the sides 

 of the column, and the lieat carried in or out of 

 the column by means of currents. Such an 

 expression can become complicated. However, 

 since this is a climatic study, interest lies in the 

 gross seasonal changes and, therefore, some 

 simplifying assumptions can be made for the 

 Hawaiian region (10°-30° N., 150° W.-180^). 



In this area the mixed surface layer is generally 

 well defined and since it has neutral stability one 

 can say that heat exchange across the sea surface 

 is unifonidy distributed throughout this layer. 

 Further, because of high stability in the ther- 

 mocline just below the mixed layer, and small 

 horizontal temperature gradients, vertical and 

 lateral diffusion are assumed negligibly small 

 compared to advection and heat exchange across 

 the sea surface. 



With these assumptions, a smiple heat budget 

 can be formulated in which the rate of change of 

 heat content of a column of water of unit cross 

 sectional area is balanced by the net heat exchange 

 across the sea surface and the heat transported 

 in and out by currents. This can be expressed 

 in vector notation by 



^)=/7-v(pc..3F) 



(1) 



hj.^cpejZjVp 



tj-zOcpe^ZaYj 



Here p is the density of the water and Cp its 

 specific heat; 6 is the temperature, z, the depth 

 of the column of water (depth of mixed surface 

 layer), and V, the horizontal velocity. H is the 

 net heat exchange across the sea surface and 

 V, the two-dimensional operator 



Similarly, the volume budget of the column of 

 water is expressed by 



dz 

 dt 



= -V-izV) 



(2) 



Equations (1) and (2) can be expanded as follows, 

 considering p and c^ constant: 



z ^^+d ~=— H-dzv-V-eV-vz-zV-ve (3) 



at ot pCp ' 



()Z TT 77 



(4) 



After multiplying equation (4) by d it can be 

 subtracted from (3), leaving 



z ^= — H—zV-ve 



C>t pCp 



(5) 



and then dividing by z, the temperature budget 

 for a unit mass of surface water becomes: 



— = v-ve 



ot pCp z 



(6) 



