362 REFRACTION AND REFRACTIVE INDEX MODELS 



Therefore, (8.37) becomes 



e.^ ^^-^Q (8-42) 



where g represents the "average" gradient on the ray path (i.e., g = dn/dh 

 at an intermediate point on the path). 



Since g depends upon the meteorological conditions along the path, 

 the basic problem is to determine g for a given target from the conditions 

 at and/or near the surface. 



8.4.5. Meteorological Parameters 



Measurement of the refractivity at the radar site will provide an esti- 

 mate of the gradient if a model of the refractive index structure is assumed. 

 In the exponential model, for example, 



n{h) = 1 + A^, exp (-c/i) X 10-« 

 where N ^ is the surface refractivity and c is a constant, then 



-77 = —cNs exp ( — c/i) X 10~^ 



For a target at a height, ht, the average gradient along the ray path is 



g = -^[1 - exp i-cht)] X 10-', (8.43) 



lit 



but since ht is not known, g must be approximated as a function of the 

 apparent height. 



Additional meteorological measurements at a sufficient height above 

 the surface to obtain values significantly different from the surface values 

 can be used to determine the initial gradient, 



^-1 '- = !'" (If) xi«'' («■«' 



where Nh is the refractivity at the height, H, of the above surface meas- 

 urements. The initial gradient provides a boundary condition for esti- 

 mating gf as a function of the apparent height. For convenience the initial 

 gradient of refractivity. Go = go X 10^ with H in kilometers, was used 

 as a prediction parameter. 



