All-Sky Satellite Radiance Data Assimilation: Methodology and Challenges - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 472

skewness for some instruments and channels that may be attributed to non-Gaussian
pdfs (e.g., Okamoto and Derber 2006 ; Errrico et al. 2007b ; Bauer et al. 2010 ), and
thus implies that data assimilation of all-sky satellite radiances may not perform
correctly in such cases. One should also be aware of ways to mitigate non-
Gaussianity in data assimilation (e.g., Simon and Bertino 2009 ; Bocquet et al. 2010 ).
One can distinguish several possible approaches to deal with non-Gaussian errors
of all-sky radiances: (1) neglect the problem, (2) apply Gaussian assumption, but
introduce bias correction, (3) apply change of variable to convert from non-Gaussian
to Gaussian framework, and (4) use non-Gaussian data assimilation framework.
The option (1) is the simplest, and thus the easiest. If one chooses to assimilate
only channels with approximately Gaussian observation errors, it may be still
possible to use the original Gaussian data assimilation framework. However, this
approach may leave important observation information not assimilated. It also
requires a good knowledge of the observation error statistics by channels, which
could take time to accumulate.
Option (2) is commonly used in operations (e.g., Harris and Kelly 2001 ; Dee
and Uppala 2009 ). Satellite bias is typically defined to include predictors, defined
to include satellite geometry (e.g., viewing angle) and atmospheric precursors (e.g.,
thickness, skin temperature, surface wind speed)
b.';x/ D X
i

' i r i .x/

(19.20)

where is regression coefficient. Parameters of such formed

regression are added as control variables to minimization thus creating an aug-
mented control variable and cost function. Although used with great success,
there are channels that are not well controlled using this technique. Also, current
operational practice includes mostly clear-sky, not all-sky radiance assimilation,
and so does the bias correction. This means that atmospheric precursors used for
clear-sky may not be adequate for cloudy conditions. Even if adequate atmospheric
precursors are found, it is clear that this approach requires a lot of experimenting and
fundamental knowledge of interactions between clouds and satellites. In addition,
the augmented control variable in minimization may be technically difficult to
implement, depending on the existing minimization setup. As suggested in several
papers (e.g., Errrico et al. 2007b ), if the actual observation error has skewed pdf
that resembles lognormal distribution, then one could pose the problem in terms of
logarithmic variable which would then be Gaussian. Although this is a feasible solu-
tion, it was shown to be non-unique (e.g., Fletcher and Zupanski 2008 ). The option
(4) may be the most complete since it addresses the true problem of having non-
Gaussian errors in data assimilation. It was shown that ensemble data assimilation
could be defined in terms of non-Gaussian errors within hybrid variational-ensemble
methodology (e.g., Fletcher and Zupanski 2006a ), or within particle filters (e.g., van
Leeuwen 2009 ). In either case, implementing new methodology is a slow process
and the ultimate decision about the approach for handling non-Gaussian errors
will depend on desired application and developmental time constraints. Addressing

r is predictor and '