66 



METEOROLOGY— THEORY 



grailiciits. The eoetlicioiit of dill'iLsioii A' is ealeiilated 

 from the wind profile whieli is assumed to satisfy a 

 power law of the form U = Az"\ 



The difficulty arises because m is fixed once and 

 for all before "\ve solve the equation and thus the 

 tlieory cannot take account of changes in the tempei'a- 

 ture gradients of a diurnal character in so far as they 

 affect the liumidity distril)ution. At the same time we 

 believe that A' is very sensitive to the temperature 

 gradient. 



Further, values of in lunc been used which have no 

 meteorological support. The value in = 0.5, for ex- 

 ample, imi^lies a wind structure which is absurd if 

 extended up to 100 m and it certainly is invalid near 

 the ground. Chemical warfare technique measures in 

 directly by measuring R, the ratio of the wind at 3 m 

 to the wind at 1 m. Even in the very extreme condi- 

 tions which prevail over land no value of R exceeding 

 1.35 is observed. This makes in = 0.33. Over the sea, 

 even in a low layer, it is very unlikely that a value of 

 »;i differing significantly from ]■'■; would be found. 



The difficulty is that power laws apply only for very 

 limited ranges of height and can be extended only by 

 using a different power. Their only merit is that they 

 enable the equation of dift'usion to be solved; the 

 power law is not a law of nature. A complete solution 

 of the problem would involve a theory giving A' as 

 a function of temperature gradient. A start has been 

 made on this for the case of still air which is agitated 

 by thermal turbulence originating from heating on 

 its lowest level. The value of A' so calculated is small 

 compared with that for a light wind. It seems likely 

 that the effect of an inversion on E will also be small. 



To sum up, radar personnel should be warned that 

 the difl^usion theory is at present in a highly imsatis- 

 factory state ; any conclusions drawn from it should be 

 treated with the greatest reserve, and some calcula- 

 tions already published are based on assumptions 

 which have no meteorological foundations. 



6' PRELIMINARY RESULTS OF METEOR- 

 OLOGICAL MEASUREMENTS IN 

 MASSACHUSETTS BAY'' 



Tlie modification produced in land air when it 

 passes out over water is known to l)e particularly effec- 

 tive in producing nonstandard microwave propaga- 

 tion. The preliminary results of this study are covered 

 in the present report ; they are necessarily incomplete 

 and tentative. 



6-31 Modification of Air Plowing 



over Water 



To begin with, some basic considerations will be 

 l)resented. Figure 2 shows an airplane sounding in air 

 which is warm and dry relative to the underlying 

 water. Before leaving land the air was vertically 

 homogeneous : that is, potential temperature and 

 specific humidity were constant. This may be seen 

 by comparing the observed temperature and vapor 

 pressui'c with the Ijroken straight lines drawn for 



OCTOBER 19, O-K II4I-I203 C-231 



5 MILES NORTH OF PROVINCETOWN. MASS q FIRST ASCENT 



SURFACE WIND WEST 4B 



SECOND ASCENT 



■■By R. B. Montgomery, Radiation Laboratory, MIT. 



Figure 2. Typical airplane sounding, gi\'ing temper- 

 ature and water vapor variation with height. 



homogeneous air. The straight line of modified index 

 of refraction M is constructed for homogeneous air; 

 it is close to standard. The air is being modified by 

 loss of heat to the water and by evaporation. 



At the common l)oundary the temperatures of air 

 and water are identical. The vapor pressure also is 

 given by the water temperature; over sea water the 

 vapor pressure is 08 per cent of the saturation value 

 corresponding to the water temperature. It follows 

 that the modified index at the surface is determined 

 by the water temperature alone. 



Figure 2 illustrates in a striking manner the simi- 

 larity in shape of the three curves. The ratio of the 

 change from unmodified value at any height to the 

 change at the surface is the same for all three quan- 

 tities. 



Modification of air o\er water is due largely to 

 turbttlent mixing, wliich transports heat and water 

 vapor in exactly the same manner (the eddy dif- 

 fusivity is identical for l>otli). Next to the water 

 lioundary there is always a laminar layer, through 

 which heat is transported to the turbulent layer by 

 true conduction while the water vapor is transported 

 by true diffusion ; the coefficients for these two related 

 processes happen to be nearly the same, so heat and 

 water vapor arc transported vertically to nearly the 



