# Robin Hogan and Jon Shonk Implementation of multiple regions in Edwards-Slingo.

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Robin Hogan and Jon Shonk Implementation of multiple regions in Edwards-Slingo

Shadows! Need separate regions even in clear skies? Downward short-wave flux (W m -2 )Upward short-wave flux (W m -2 ) Natural logarithm of IWC (g m -3 )

Anomalous horizontal transport Homogenization of clear-sky fluxes: –Reflected radiation has more chance to be absorbed -> 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

Two-stream scheme F 1.5 + F 1.5 - F 0.5 + F 0.5 - F 2.5 + F 2.5 - Consider a two- layer atmosphere Solve a tridiagonal matrix problem to obtain the fluxes Layer 1 reflection, transmission and emission: R 1, T 1, S 1 +, S 1 - Layer 2 reflection, transmission and emission: R 2, T 2, S 2 +, S 2 - TOA flux: S TOA - Surface emission and albedo: S s +, s

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

Two-regions: cloud and clear-sky a a b b Layer 1 Layer 2 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 Note that the overlap coefficients have been omitted in this example

New version a a b b Layer 1 Layer 2 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! R ab R ab is the reflection from region a to region b at the same level

Performance of new solver In calculating upwelling flux at half-level 1.5, downwelling flux sees albedo of whole atmosphere below, 1.5, which it reflects back into the same region –Much closer to the independent column approximation! 0.5 1.5

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