The Three-dimensional Temperature Distribution and its Variation in Time 95 



coefficient is different for different wavelengths, water cannot be considered as a grey 

 radiator (Emden, 1913). It is, however, only for grey radiation that the final state of the 

 radiation equilibrium is an isothermal state, in which every layer absorbs just as much 

 energy as it gives off so that the temperature remains constant. For these reasons an 

 isothermal top layer (thin homogeneous layer of uniform density) thus cannot be in 

 iationalrad equilibrium with the solar radiation (direct and diffuse) (see Defant, 1936). 



{b) Thermal Conductivity 



If there exists a vertical temperature gradient in the water, then heat will be trans- 

 ferred from warmer to colder locations by the process of ordinary heat conduction. 

 There is a constant tendency towards equalization of temperature differences, and 

 this heat transport disappears only when there is a fully isothermal state. The question 

 of interest here is the speed of this process. From theoretical physics it can be shown 

 that the change of temperature with time for a temperature gradient ddjdz is given 

 by the differential equation 



dd _ _A_ 8^9 

 dt Cpp dz^ ' 



In case of a horizontal (along x-axis) movement (velocity u) in the water 



dd d'd' 8^9' 



where dd'fdt is the local change of temperature with time. For no horizontal motion 

 (u = 0) the equation for the thermal conductivity takes the form 



bd _ A d^d 



'Ft ^c^p d^' 



The solution of this equation (see, for example, Riemann-Weber, 1910) for different 

 boundary conditions provides the answer to important questions concerning the 

 temperature distribution in the sea. It is, for example, of interest to know how fast a 

 temperature change at the surface travels downwards within the water mass by thermal 

 conductivity. The numerical evaluation of the corresponding solution gives for 

 different depths the time required by the disturbance to reduce magnitude to half of 

 its surface value (half value-time). For a thermal conductivity 



a = Xlc^p = 1-309 Xl0-3cm2/sec 

 one obtains the following values (Table 40). Millions of years would be required 

 for a temperature change at the surface of the sea to reach the larger ocean 

 depths. These values show in the clearest possible way the unimportance of thermal 

 conductivity for oceanographic phenomena, since there are other processes which 

 give a much faster propagation of temperature changes down to the ocean interior. 



Table 40. Downward progression of a sudden temperature change in the sea by thermal 

 conductivity {time needed to reach the half value of the surface disturbance) 



Depth (m) | 1 j 10 I 50 100 500 1000 3000 9000 



Time (years) i 27 i 665 2660 66,500 i mill. I 2i mill, j 9 mill. 



