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Chapman's function

  1. Feb 20, 2006 #1
    According to Chapman theory the photon volume deposition rate for an incoming beam of solar radiation is given by
    [tex] q(h) = I_{t} \sigma n_{0} \exp\left(-\frac{h}{H} - \sigma n_{0} H \sec\chi \exp\frac{-h}{H}\right) [/tex]
    where It is the flux of incoming solar radiation, σ is the absorption cross-section, no is absorber density at the surface and H is its scale height. Prove that the deposition curve is displaced upwards by one scale height without changing shape if either σ or no are increased by a factor of e the natural log base. It is not sufficient to show that hmax increases by one scale height.

    well i tired multiplying sigma or n by e and i get this
    [tex] q(h) = I_{t} \sigma n_{0} \exp\left(1 -\frac{h}{H} - \sigma n_{0} H \sec\chi \exp(1 - \frac{-h}{H})\right) [/tex]

    the thing is i am not quite sure how one would show a displacement of H upward...
    are we aiming to get q(h) + H ? Is that the kind of dispacement that this quesiton requires?

    as always, help is greatly appreciated!
     
  2. jcsd
  3. Feb 22, 2006 #2
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