Ensemble Adaptive Data Assimilation Techniques Applied to Land-Falling North American Cyclones - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 550

an initial-time perturbation spread spatially and into other variables through the
background error covariance relationships of the ensemble (similar to ( 23.4 )). Since
observational information is spread in a similar manner within the EnKF analysis
procedure, and since the temporal evolution of perturbations can be represented
with adjoint sensitivity, Ancell and Hakim ( 2007a ) exploit the relationship between
ensemble and adjoint sensitivity to derive an expression for the reduction in the
variance of R due to a single observation within an EnKF:

2

Variance R D . D i @ R =@ y i / =. D i O i / (23.6)

where D i represents the variance of a single anlaysis variable, y i is the

ensemble sensitivity with respect to the same analysis variable, and O i represents the
observation error variance associated with a targeted observation. This calculation
can be quickly made with respect to each observable analysis variable to reveal
the estimated variance reduction from a single additional, hypothetical observation
anywhere on the model domain. An advantage of these ensemble-based methods is
that they rely not on actual observation values, but on observation error variance
which exists prior to hypothetical observations being taken. They also allow
the estimation of forecast variance reduction of additional targeted observations
conditioned on the simultaneous assimilation of the initial targeted data. Ancell
and Hakim ( 2007a ) also derive an ensemble version of the observation impact
developed in Langland and Baker ( 2004 ) without the use of an adjoint model.
Liu and Kalnay ( 2008 ) discuss yet another ensemble-based observation impact
technique that requires no adjoint model.
In summary, adaptive data assimilation techniques have evolved from those that
consider only dynamical error growth to those that consider all aspects of the
data assimilation system used to assimilate routine and targeted observations. In
turn, modern adaptive data assimilation methods provide estimates of the impacts
from assimilated or additional hypothetical observations with regard to a specific
assimilation system such as 3DVAR or an EnKF. It should be noted that nearly all
observation impact/targeting techniques are based on the assumption that error evo-
lution is linear over the duration of the forecast, an assumption that doesn't always
hold. Furthermore, both modern data assimilation systems and forecasting models
are not perfect, and present another source of error for observation impact and
targeting schemes. Langland ( 2005 ) provides an excellent review of the potential
impacts these issues cause, and discusses the performance of different adaptive data
assimilation methods during a variety of recent field programs. As computational
resources are constantly improving, investigating adaptive assimilation techniques
at very high resolution (grid spacing of a few kilometers) is now becoming possible.
In turn, a major research focus in the coming years will likely be on the application
of adaptive data assimilation systems at different scales.

@ R =@