Geoscience Reference
In-Depth Information
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Fig. 3.7 Plots of select joint PDFs for observations of precipitation rate, liquid water path, and ice
water path (PLI; row 1 ), PLI plus observations of outgoing long and shortwave radiation (PLIOO;
row 2 ), PLIOO with reduced error on the radiative fluxes ( row 3 ), and PLIOO with reduced
error on the radiative fluxes and the constraint that the graupel fall speed coefficient exceed the
snowfall speed coefficient (ag
as). White solid and dashed curves correspond to the 68 and 95 %
probability contours, respectively; red solid lines indicate the position of the parameter truth value;
and red dashed lines indicate the truth value for the situation in which snow and graupel parameters
are interchanged (Adapted from Posselt and Vukicevic ( 2010 ), Fig. 12)
>
Close inspection of the posterior PDFs in Fig. 3.7 i-l indicates that nonuniqueness
in the relationship between snow and graupel may be the underlying cause of
multiple modes in the solution. If snow and graupel are essentially interchangeable
in the code, then identical solutions will be obtained if snow parameters are set to
graupel truth values and vice versa. This possibility was eliminated by applying the
constraint that graupel fall faster than snow; note that this is easily tested in the
MCMC framework by adding another criterion to the Metropolis update that rejects
 
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