Proceedings with Extended Abstracts (single PDF file) - Radio ...

⎡7800 ∂q⎤(3)⎢ 15500q⎥M = M ⎢ + −T ∂zD1⎥⎢ T ∂ lnθ⎥⎢⎣∂z⎥⎦It can be seen that the dry approximation is valid when the second and third terms in thesquare brackets of Equation 3 are significantly less than 1; this is typically assumed to be thecase above the first few kilometres of the atmosphere. This assumption will be examined ingreater detail shortly. For the time being the humidity contributions will be ignored entirely.It will be recognised that the p/T term in Equation 2 is proportional to density, which can beapproximated as ρ 0 exp(-z/ H ) where ρ 0 (hPa) is the pressure at mean sea level and H (m) isthe mean scale height across the considered altitude range. For the data considered in presentinvestigation, the value of H, which is given by RT/g, where R is the gas constant for dry air,is typically around 8 km at an altitude of 1 km and decreases to around 6 km at thetropopause level; it remains approximately constant at this value between the tropopause andan altitude of 15.7 km. A mean value of 6.71 km is calculated over all data points. Assumingρ 0 = 1000 hPa, the observed and assumed values of density are typically within 10% of eachother at all altitudes within the range 1.0 - 15.7 km.Combining the expectation that P ∝ M 2 /z 2 (Gage et al., 1981) with Equation 2, andsubstituting for Equation 1, gives:P ∝2[ exp( −z/ H ) ω ]z22Bwhich can be rearranged in order to define a radar factor r B 2 :r2 = z exp( z / H km P(5)B km km)where the altitude above mean sea level, z km , and the mean scale height, H km , are both givenin units of kilometres, such that the following linear relationship is expected:3. Resultsω y(6)2 2B= g0rB+Figure 1(left panel) shows the relationship between radar-derived values of r 2B andradiosonde-derived values of ω 2 B . The plot area is divided into a 100 by 100 grid, withdivisions of 0.1×10 -4 rad 2 s -2 along the y-axis and 0.1×10 3 arbitrary r 2 B units along the x-axis;the grey scale represents the number of data points falling within each cell. There is clearly ahigh degree of correlation between the two sets of values and two distinct clusters of datapoints can be seen; those with small values of ω 2B and of r 2 B , which correspond totropospheric measurements, and those with larger values of both, which correspond to lowerstratospheric measurements. There is, nevertheless, considerable scatter around theseclusters.Much of this scatter, for the tropospheric measurements, can be accounted for by the fact thatthe humidity contributions to M have been ignored in the retrieval model. The values of r B2are, in fact, overestimated by a factor |M/M D |, i.e. by the modulus of the square bracket in0(4)43