Chapter 6 

 METEOROLOGY— THEORY" 



61 MODIFICATION OF WARM AIR BY 

 A COLD WATER SURFACE" 



"■^■'^ History 



Two OF THE COMMOXEST TYPES of M curves which 

 prodiTce nonstandard propagation are the S-shaped 

 curve and the simple trapping curve where M decreases 

 from the surface to "300 ft, say. The S-shaped curve 

 occurs in regions of subsidence, for example, in the 

 extensive subtropical anticyclones. The forecasting 

 of this phenomenon will not be presented in this dis- 

 cussion which is confined to the simple trapping case. 



During 1943 the question arose regarding the 

 feasibility of forecasting the change in the temperature 

 and vapor pressure distribution as warm air flows over 

 a cold water surface. Through practice, considerable 

 success had already been obtained in forecasting the 

 M curve a few miles offshore in Boston Harbor. How- 

 ever, it was suggested that a general method be de- 

 vised whereby the M curve could be predicted for 

 greater distances from the shoreline and for different 

 regions of the world. In order to solve this forecast 

 problem the Boston Harbor soundings were investi- 

 gated in the light of turbulence theory. 



Two factors had to be kept in mind, namely : 



1. The Boston Harbor soundings of temperature 

 and vapor pressui-e were scant. A more serious diffi- 

 culty was the total absence of data at distances in 

 excess of 15 miles from the land. 



2. Since forecasting techniques were the primary 

 aim it was necessary to find a solution which was 

 suitable for field use. 



^■^■^ Diffusion Equation 



The differential equation for turbulent mass ex- 

 change may be written 



dT 



dt 



ff K, the coefficient of eddy diffusion, is assumed con 

 stant, then 



'^'-'^ _e( '\ 1 



To - T^ \^J4Kt/ ' 



dz\ dz/ 



(1) 



(2) 



where E = error function, that is, 



T' = temperature at a level z over the ocean, 

 T = initial temperature at z over the land, 



Tg ~ initial air temperature over laud at z = 0, 



Tj„ — water temperature, 

 t = time. 

 Values of K were then computed from the observa- 

 tional data by evaluating the ratio {T'—T)/{Tg—T,,) 

 for different evaluations and different times. These 

 values were averaged for each level and the results 

 shown in Table 1 were obtained. After plotting K 



''See also Parts II and III of Chapter 17, Volume 1, Com- 

 mittee on Propagation. 



''By J. M. Austin, Meteorology Department, MIT. 



against elevation, the approximate linear variation 

 of K was extrapolated to give values of E for eleva- 

 tions up to 700 ft. This level of 700 ft lies well within 

 the limit of 250 m which was indicated by Mildner^ 

 to be the level where K reaches its maximum. 



These values of K were then used to construct Table 

 2, which gives {T'-T)/{T-T,,) for all levels in 

 terms of the time that the air has been over the water. 

 The same values of K were obtained from the analysis 

 of vapor pressure changes; hence the same table can 

 be used to evaluate the ratio {e'—e)/{eg — «,„). From 

 this table it is a simple matter to reconstruct the M 

 curve at any distance over the ocean, provided the 

 initial state of the air is known. An example of the 

 changes in the M curve are given in Figure 1. 



*'^'^ Discussion of Procedure 



Summarizing the favorable aspects of this study, 

 it can be stated that: 



1. The values of K were almost identical for vapor 

 pressure and temperature changes. This suggests that 

 the data were reliable. 



2. The values of K agreed with those of Giblett^ 

 for wind variations from the surface to 150 ft. 



3. This extrapolation method, that is, the error 

 function extrapolation, gives reasonable values after 



63 



