Proceedings - C-SRNWP Project

Figure 3: Vertical profiles of solar absorption (within 24 hours) for old scheme (red) and new scheme (blue).
1.2 Statistical approach for the computation of inter-layer gaseous exchange terms
The method for thermal radiation computations is based on the Net Exchanged Rate (NER)
formalism (Green, 1967). NER allows stratifying the N(N+1) /2 thermal exchange terms
between primary and secondary ones, where N is the number of discrete layers along the
vertical. For a more accurate computation, besides the primary ones treated exactly, the
secondary terms, although smaller, should not be neglected. To avoid of an unacceptable
increase of computation time an approximate treatment of these additional terms was
introduced. We can gain from the fact that the optical thickness under which layer is seen
from any part of the gas-only atmosphere is between two limits already computed, so we are
able to bracket the truth for additional terms between two computations (one with maximum
and one with minimum estimated optical thickness for the additional fluxes between layers).
The best possible estimate can be defined statistically, so a statistical parameterisation of the
local values of the weighting coefficient α between min (α =0) and max (α =1) has been
investigated. Stratifying a big amount of data, we found that α increases when the local gas
absorption potential increases, i.e. lower in the atmosphere as well as when there are strong
changes of the basic vertical temperature gradient, i.e. in inversions.
When such interpolation is applied to fluxes, the statistical fit works very well (see below the
dispersion diagram of fluxes between their exact and retrieved values).
Figure 4: The dispersion diagram thermal fluxes between exact and retrieved values for one example.
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