transmissivity¶

class
climlab.radiation.transmissivity.
Transmissivity
(absorptivity, reflectivity=None, axis=0)[source]¶ Bases:
object
Class for calculating and store transmissivity between levels, and computing radiative fluxes between levels.
Input: numpy array of absorptivities. It is assumed that the last dimension is vertical levels.
Attributes: (all stored as numpy arrays):
N: number of levels
absorptivity: level absorptivity (N)
transmissivity: level transmissivity (N)
Tup: transmissivity matrix for upwelling beam (N+1, N+1)
Tdown: transmissivity matrix for downwelling beam (N+1, N+1)
Example for N = 3 atmospheric layers:
tau is a vector of transmissivities
\[\tau = \left[ 1, \tau_0, \tau_1, \tau_2 \right]\]A is a matrix
\[\begin{split}A= \left[ \begin{array}{cccc} 1 & 1 & 1 & 1 \\ \tau_0 & 1 & 1 & 1 \\ \tau_0 & \tau_1 & 1 & 1 \\ \tau_0 & \tau_1 & \tau_2 & 1 \\ \end{array} \right]\end{split}\]We then take the cumulative product along columns, and finally take the lower triangle of the result to get
\[\begin{split}Tup= \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \\ \tau_0 & 1 & 0 & 0 \\ \tau_1 \tau_0 & \tau_1 & 1 & 0 \\ \tau_2 \tau_1 \tau_00 & \tau_2 \tau_1 & \tau_2 & 1 \\ \end{array} \right]\end{split}\]and Tdown = transpose(Tup)
Construct an emission vector for the downwelling beam:
Edown = [E0, E1, E2, fromspace]
Now we can get the downwelling beam by matrix multiplication:
D = Tdown * Edown
For the upwelling beam, we start by adding the reflected part at the surface to the surface emissions:
Eup = [emit_sfc + albedo_sfc*D[0], E0, E1, E2]
So that the upwelling flux is
U = Tup * Eup
The total flux, positive up is thus
F = U  D
The absorbed radiation at the surface is then F[0] The absorbed radiation in the atmosphere is the flux convergence:
diff(F)
Methods
flux_down
(fluxDownTop[, emission])Compute upwelling radiative flux at interfaces between layers.
flux_up
(fluxUpBottom[, emission])Compute downwelling radiative flux at interfaces between layers.
flux_reflected_up

flux_down
(fluxDownTop, emission=None)[source]¶ Compute upwelling radiative flux at interfaces between layers.
Inputs:
fluxUpBottom: flux up from bottom
emission: emission from atmospheric levels (N) defaults to zero if not given
 Returns:
vector of upwelling radiative flux between levels (N+1) element N is the flux up to space.

flux_up
(fluxUpBottom, emission=None)[source]¶ Compute downwelling radiative flux at interfaces between layers.
Inputs:
fluxDownTop: flux down at top
emission: emission from atmospheric levels (N) defaults to zero if not given
Returns:
vector of downwelling radiative flux between levels (N+1) element 0 is the flux down to the surface.