Skewness of the Prior Through Position Errors and Its Impact on Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 161

the location of the observation. We note in passing that we have also compared the
structure of the true posterior covariance matrices ( 7.15 ) against those covariance
matrices determined from ( 7.22 and 7.28 ). The result is that the covariance's are also
similarly in error when compared to the structure of the true posterior covariance
matrix (not shown). Because a covariance between two variables may be positive
or negative, the error in ( 7.22 and 7.28 ) when compared to ( 7.15 ) may be wrong
in both the magnitude as well as the sign of that covariance. Hence, to produce
an ensemble consistent with the “errors of the day” requires the consideration
of the posterior error covariance matrix as a function of the innovation ( 7.15 ).
Unfortunately, traditional ensemble generation schemes make use of the expected
posterior error variance ( 7.14 ), which does not properly account for information
from the innovation.

7.4.2 Hurricane Katia (2011)

In this section we will illustrate that the idealized results found in the previous
section can be found in a real ensemble DA experiment with a tropical cyclone. We
utilize a prior distribution from an 80-member ensemble for Hurricane Katia (2011)
generated with the Coupled Ocean/Atmosphere Mesoscale Prediction System for
Tropical Cyclones (COAMPS

-TC; Doyle et al. 2012 ) ensemble data assimilation
system. The COAMPS-TC system is a limited area model designed specifically
for the simulation and prediction of tropical cyclones. It is comprised of a suite
of packages and parameterizations that represent physical processes unique to
the tropical environment. COAMPS-TC uses three horizontally nested domains
with the horizontal resolution decreasing from 45 km on the outer basin-scale
domain to 5-km on the inner vortex-scale domain. All calculations below are
done on the 5-km inner vortex-scale domain. In order for COAMPS-TC to remain
computationally efficient, the inner two domains are designed to track the location
of the storm. The system utilizes the Data Assimilation Research Testbed (DART;
Anderson et al. ( 2009 ) developed at the National Center for Atmospheric Research
to assimilate observations with a square-root version of the EnKF as well as adaptive
prior inflation.
The results presented in this section are based upon a prior distribution for
Hurricane Katia valid on 12 UTC, 2 September 2011. The ensemble was initialized
00 UTC, 30 August by interpolating the Global Forecasting System ensemble
( Hamill et al. 2011 ) to the three COAMPS-TC nested domains. The COAMPS-TC
ensemble was then cycled by using DART to assimilate observations of radiosondes,
cloud-track winds, surface observations, and aircraft data every 6-h until 12 UTC,
2 September. The fact that Katia developed away from land in the central Atlantic
Ocean makes it an ideal case to test the various filter algorithms because any
skewness will be a direct result of phase and intensity variability and not interactions
with land.
This ensemble will be used in precisely the same way as in the previous section
to compare the levels of approximation resulting from DA with linear and quadratic

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