Abstract:

Insufficient model resolution is one source of model error in numerical
weather predictions. Methods for parameterizing this error in ensemble
data assimilations were explored here. Experiments were conducted with
a 2-layer primitive equation model, where the assumed true state was a
T127 forecast simulation. Ensemble data assimilations were performed
with the same model at T31 resolution, assimilating imperfect
observations drawn from the T127 forecast. By design, the magnitude of
errors due to model truncation was much larger than the error growth
due to initial condition uncertainty, making this a stringent test of
the ability of an ensemblebased data assimilation to deal with model
error. Two general methods, “covariance inflation” and “additive
error,” were considered for parameterizing the model error at the
resolved scales (T31 and larger) due to interaction with the unresolved
scales (T32 to T127). Covariance inflation expanded the background
forecast members’ deviations about the ensemble mean, while additive
error added specially structured noise to each ensemble member forecast
before the update step. The method of parameterizing this model error
had a substantial effect on the accuracy of the ensemble data
assimilation. Covariance inflation produced ensembles with analysis
errors that were no lower than the analysis errors from 3-dimensional
variational (3D-Var) assimilation, and for the method to avoid filter
divergence, the assimilations had to be periodically reseeded.
Covariance inflation uniformly expanded the model spread; however, the
actual growth of model errors depended on the dynamics, growing
proportionally more in the middle latitudes. The inappropriately
uniform inflation progressively degradated the capacity of the ensemble
to span the actual forecast error. The most accurate model error
parameterization was an additive model error parameterization, which
reduced the error difference between 3D-Var and a near-perfect
assimilation system by ∼ 40%. In the lowest-error simulations, additive
errors were parameterized using samples of model error from a time
series of differences between T63 and T31 forecasts. Scaled samples of
differences between model forecast states separated by 24 h were also
tested as additive error parameterizations, as well as scaled samples
of the T31 model state’s anomaly from the T31 model climatology. These
latter two methods produced analyses that were progressively less
accurate. The decrease in accuracy was likely due to their
inappropriately long spatial correlation length scales.

Thomas M. Hamill and
Jeffrey S. Whitaker