DIURNAL VARIATION OF THE GRADIENT OF MODIFIED M INDEX 



89 



6 <> DIURNAL VARIATION OF THE 

 GRADIENT OF MODIFIED M INDEX- 



The vertical gradient of modified refractive index 

 depends on tlie vapor pressure and temperature 

 gradients according to the formnhr'' 



dM 



dz 



_ 79 /■ 



4800- 0.14T\de 

 ~)jz 



T 



/9600e 

 (-Y- + P 



79 



JI2 



\dT / 1 , 79 dp\ 



Coefficients of vapor pressure and temperature gradi- 

 ents are about 4.5 and 1.5 respectively. The third term 

 gives a positive increase of 4 M units per 100 ft. In 

 this paper^^"^'' the diurnal variation of the vertical M 

 gradient will be inferred from the diurnal variation 

 of temperature and humidity gradients. 



*-*-^ Temperature Lapse Rates over Land 



On clear nights with light winds temperature in- 

 versions form in the lower atmosphere. The follow- 

 ing characteristics of these inversions are to be noted. 



1. The inversion begins as a shallow layer near the 

 ground before sunset, rises sharply after sunset and 

 then more gradually to a maximum height at about 

 sunrise. 



2. The temperature diiference between two fixed 

 levels in the first 100 ft of the ground is maximum 

 shortly before sunset and oscillates about a slightly 

 lower value the remainder of the night. (See Figure 

 10.) 



Observations at Leafield, England, and Potsdam, 

 German}', corroborate this. This phenomenon is prob- 

 ably due to the more favorable humidity gradient in 

 the early evening and to the heat of condensation re- 

 leased by dew formation in the later night hours. 



Superadiabatic lapse rates characterize the lower 

 atmosphere during clear days. The lapse rates in- 

 crease sharply from sunrise to 3 or 4 hours after, 

 gradually reach a maximum at about noon, and de- 

 crease sharply after the time of the maximum tem- 

 perature. 



'■*"^ Temperature Lapse Rates over the Sea 



The air over the sea has a greater diurnal range 

 than the sea itself. Over the Sunda Sea this range 

 has been observed to increase from 0.5 C at the sur- 



^By Raymond Waxier, Camp Evans Signal Laboratory. 



''Symbols have same meaning as in preceding section, 

 except that h is replaced by z. 



Figure 10. Mean temperature variation on clear .June 

 days at Leafield, England. 



face to 1.5 C at 500 m. The night lapse rates over the 

 ocean are therefore more unstable than the day lapse 

 rates. Observations of the Meteor expedition in equa- 

 torial regions revealed a mean inversion of 0.3 C in 

 the first 9 m during the early afternoon, whereas in 

 the early morning a mean lapse of 0.6 C was observed. 



6.6.3 Vertical Vapor Pressure Gradients 



At locations where a continuous supply of moisture 

 on the ground is available, vapor pressure gradients 

 follow evaporation processes and are maximum at the 

 time of the maximum temjjerature at about sunrise. 

 This diurnal course characterizes conditions over the 

 sea, cloudy days over the land, and winter or rainy 

 seasons over the continent. 



On clear days over the continent the vertical vapor 

 pressure gradient is minimum at about sunrise, 

 reaches a maximum in midmorning, and lowers to a 

 secondary minimum at the time of the maximum tem- 

 perature (in desert regions this is the princiisal maxi- 

 mum shortly after sunset). Evaporation and mixing 

 with drier air aloft govern this couise. At night the 

 soil absorbs moisture from the air causing a decrease 

 in vapor pressure gradient. 



The seasonal and diurnal variation of vapor pres- 

 sure gradient is illustrated in Figure 11. Maximum 

 vapor pressure gradients are noted during April, the 

 hottest time of year, and minimum in January. The 

 oceanic type is represented by the curve for July in 

 the rainy season. 



*•* * Vertical M Gradient 



Over the sea both temperature and humidity gradi- 

 ents aid in causing a maximum of trapping during the 

 day and a minimum during the night. The eflect, 

 however, is j)robably small. 



Over the continent, a minimum of trapping will 

 exist in midafternoon. Thereafter both temperature 



