APPLICATION OF FORECASTING TECHNIQUES AND CLIMATOLOGY 



125 



of S-sliaped M curves are not considered in tliis 

 method. Standard conditions can be presumed to 

 occur when the calculations indicate a duct width of 

 zero, which is the case when the M deficit is zero. Jf 

 the M deficit is negative, then the calculated duct 

 width will be negative, and substandard conditions are 

 to be inferred. A positive M deficit indicates duct 

 formation (simple surface trapping), and the calcula- 

 tions of the duct width given an estimate of the height 

 to which the duct extends. If this height is small, 

 conditions may be inferred to correspond to the tran- 

 sitional case. Once the duct width is calculated, a 

 complete picture of the distribution of M with height 

 can be approximated as indicated in Figure 15 by 

 assuming that standard conditions prevail above the 

 duct and that the M deficit (AM) is the difference 

 between the actual M value at the sea surface and 

 the M value that would exist at the sea surface if the 

 standard conditions were extended down to the surface. 



The method is not applicable to conditions over 

 land. 



In the case of air with a purely sea trajectory, it 

 turns out that the procedure is closely valid if, in 

 place of the air temperature and humidity measure- 

 ments made over land, these measurements are taken 

 in the air at a slight elevation above the sea surface, 

 for example, at bridge level on a large ship. 



In practical application results will be most reliable 

 when the assumptions listed under "General Proce- 

 dure" are satisfied. However, this does not mean 

 that the method is useless under other circumstances. 

 Figure 19, which is the crux of the method, is largely 

 empirical and is based on relationships which have 

 been observed to hold under varioiis meteorological 

 conditions. Consequently, reasonably accurate results 

 are not limited to only a few idealized situations. 



It should be mentioned also that use of the method 

 in a literal manner can be improved upon if the cal- 

 culated results are modified by the judgment of 

 someone trained or experienced in meteorology. Com- 

 plicating factors such as variations in the initial sta- 

 bility conditions, variability of the sea surface tem- 

 perature, effects of convergence, divergence, and sub- 

 sidence, and presence of fronts can best be taken into 

 account by one familiar with their effects. 



Qualitative Prediction of Eadae Eaxges 



The method described above gives a means of esti- 

 mating surface duct formation, whereas what is needed 

 is a knowledge of the effect of the duct on radio propa- 

 gation. It is impossible to make a blanket statement 



LIMITED TO OVER-WATER NO TRAVEL 

 TRAVEL 10-30 MILES LIMITATION 



30 



O 25 



o 



o 



I 20 



0. 



o 



Ui 

 UJ 



cn 



15 



10 



9 0-9 



TEMPERATURE EXCESS IN DEGREES F 



L 



_L 



I 



_L 



J 



5 0-5 



TEMPERATURE EXCESS IN DEGREES C 



Figure 19. Graphs showing the vakie of the ratio of 

 duct width d to the il/ deficit, AM for values of temper- 

 ature excess and wind speed at the 1,000-ft leveL 

 (Typical values are given in Table 2.) 



giving the exact range that will be obtained with any 

 particular duct width, since the range depends on the 

 power of the radio or radar set (also on the character 

 of the target, in the case of radar), as well as on the 

 factors listed in Section 8.3.2. However, some numer- 

 ical estimates of trapping effects can be made. 



Dependence on Duct Width, Frequency, and Eleva- 

 tion of Site. An approximate expression relating the 

 maximum wavelength that can be trapped by surface 

 ducts is given by 



Amax = 0.076(ZVAil/ — 0.036fZ, 



in which Amax is the maximum wavelength in centi- 

 meters, d is the duct width in feet, and A J/ is the M 

 deficit in M units. Table 2 is developed from this 

 formula and indicates, for given values of Ail/ and d, 



