Weighting Functions

The outgoing radiance or upward radiance, Ru, for channel i from an atmospheric column is given by

Riu = integ Bi(T(p)) · (partial taunuu(p)/partial ln p) d ln p

The weighting function is defined as

W(p) ident partial taunuu(p)/partial ln p

and the contribution function is the integrand of the outgoing radiance calculation

C(p) ident Bi(T(p)) · (partial taunuu(p)/partial ln p)

and can be normalized as

C(p) ident Bi(T(p))/Riu · (partial taunuu(p)/partial ln p)

the information content will require derivative w.r.t. temperature of the radiation transfer equation and, therefore, the Kernel function represents the best estimate of the sounding level for temperature retrievals.

K(p) ident (partial Bi(T(p))/partial T) · (partial taunuu(p)/partial ln p)