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Ozone Profile Reconstruction

In some cases, e.g. for radiative transfer procedure in numerical models of the atmosphere, one can need simple method of reconstruction of ozone profile from total ozone value only. The empirical formula of Lacis and Hansen (1974) can be used for such a purpose written in a form

where u(h) represents the integrated amount of ozone from the top of atmosphere, h is the height above mean sea level and A, B, C are the parameters of the profile. The meaning of the parameter A can be found immediately

,

thus A represents total ozone amount in atmospheric column. Differentiating the formula with respect to h yields

,

which means actually well known ozone profile, with unit transformation by Claude et al. (1986)

for partial pressure of ozone, or, for mass mixing ratio

where p₀, T₀ are standard pressure and temperature on sea level height, R, R_N are gas constant of air and universal gas constant, respectively, N AvogadroÎs number and m mass unit. T represents the temperature on the level of h.

Differentiating the formula again with respect to h yields

,

where searching extreme (maximum) of ozone profile

,

thus parameter B represents the height of ozone partial pressure maximum. Differentiating the formula again with respect to h yields

,

where searching for further points of inflections we have

, i.e. .

It means that parameter C is in relation to the depth of the main ozone partial pressure maximum.

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