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)