Weighting Functions
The outgoing radiance or upward radiance, Ru, for channel i from an atmospheric column is given by
Riu = Bi(T(p)) · (
u(p)/
ln p) d ln p
The weighting function is defined as
W(p)
u(p)/
ln p
and the contribution function is the integrand of the outgoing radiance calculation
C(p) Bi(T(p)) ·
(
u(p)/
ln p)
and can be normalized as
C(p) Bi(T(p))/Riu ·
(
u(p)/
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) (
Bi(T(p))/
T) ·
(
u(p)/
ln p)