# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Dip and Temperature Gradient**

**From:**Marcel Tschudin

**Date:**2013 Apr 23, 18:23 +0300

From Paul’s derivation of dip as a function of difference in air refractivity one can also determine the temperature gradient corresponding to a certain dip. The astronomical refraction values which are generally used compare well or may even have been calculated with the standard temperature gradient in the troposphere of -6.5 K/km. This may not apply for the dip, i.e. for the temperature gradient between height of eye, H, and sea level which is generally calculated with the empirical(?) formula DIPapp[moa]=1.76*sqrt(H[m]) One may therefore ask which temperature gradient the dip resulting from this formula corresponds to. The following calculation assumes that the height of eye is also 10 m (as in Paul’s examples) and that according to the above equation the dip is DIPapp = 5.57 moa Using the above result and Paul’s equation: DIPapp[moa] = 1.926 * sqrt(dn′ + H) one obtains dn’ = -1.648 and further, by assuming for the earth the same radius of curvature as in Paul’s example with dn = dn’ / 6371000 also dn = -2.587e-7 = ((refractive index at eye) - (refractive index at sea)) At this point it is assumed that the observer has (nautical) standard conditions, i.e. T=283.15 K and P=1010 hPa and that the refractivity of air (using the online calculator which Paul proposed) is correspondingly (n-1)=2.81622e-4 Knowing that the refractivity of air is inversely proportional to the temperature allows calculating the temperature difference, dT, between height of eye and sea level as dT = dn/(n-1) * T = -0.260 K resulting finally in a temperature gradient, TG, between eye and sea level of: TG=-0.0260 K/m This means that the dip formula comprises a temperature gradient between height of eye and sea level which corresponds (surprisingly exact) to four times the standard temperature gradient in the troposphere. Marcel