Robin Hogan and Jon Shonk

1
Implementation of multiple regions in
Edwards-Slingo

• Robin Hogan and Jon Shonk

2
Shadows!
Natural logarithm of IWC (g m-3)

• Need separate regions even in clear skies?

Downward short-wave flux (W m-2)
Upward short-wave flux (W m-2)
3
Anomalous horizontal transport

• Homogenization of clear-sky fluxes
• Reflected radiation has more chance to be
  absorbed -gt TOA shortwave bias
• Effect is very small in the longwave
• This problem can be solved in a way that makes
  the code more efficient

Single cloud
4
Two-stream scheme
TOA flux STOA-
F0.5
F0.5-
Layer 1 reflection, transmission and emission
R1, T1, S1, S1-
F1.5
F1.5-

• Consider a two-layer atmosphere
• Solve a tridiagonal matrix problem to obtain the
  fluxes

Layer 2 reflection, transmission and emission
R2, T2, S2, S2-
F2.5
F2.5-
Surface emission and albedo Ss, as
5
Edwards-Slingo solution

• It is conceptually convenient to solve the system
  by
• Working up from the surface calculating the
  albedo ai and upward emission Gi of the whole
  atmosphere below half-level i.
• Then working down from TOA, calculating the
  upwelling and downwelling fluxes from ai and Gi.

6
Two-regions cloud and clear-sky
a
b

• With 2 regions (a b), matrix is denser
• Latest Edwards-Slingo only has approximate
  solvers SOLVER_MIX_DIRECT and SOLVER_TRIPLE for
  the 3-region version
• OK for upright convection but unacceptable errors
  introduced with realistic overlap

Layer 1
a
b
Layer 2
Note that the overlap coefficients have been
omitted in this example
7
New version
a
b

• But some elements represent unwanted anomalous
  horizontal photon transport
• Remove them and the problem can be solved
  exactly, and in closer agreement with ICA
• Enables triple (and quadruple, quintuple)
  regions to be implemented quite easily!

Layer 1
Rab
a
b
Layer 2
Rab is the reflection from region a to region b
at the same level
8
Performance of new solver

• In calculating upwelling flux at half-level 1.5,
  downwelling flux sees albedo of whole atmosphere
  below, a1.5, which it reflects back into the same
  region
• Much closer to the independent column
  approximation!

0.5
1.5
a1.5