Operational Dust Prediction - Mineral Dust: A Key Player in the Earth System - page 254

for all the EnKF implementation schemes to reduce the spurious impact of distant
observations. The LETKF permits a flexible choice of observations to be assimilated
at each grid point. For example, the MRI/JMA system employs the covariance local-
isation with a Gaussian weighting function that depends on the physical distance
between the grid location and the observation. The limited ensemble size causes
both sampling errors at long distances and filter divergence. To compensate for the
error underestimation and avoid the filter divergence, it is necessary to increase the
ensemble spread every data assimilation cycle. This technique is called covariance
inflation. The MRI/JMA system utilises a multiplicative inflation method, in which
the ensemble spread is uniformly multiplied by a constant value larger than one;
it is common to tune this inflation factor empirically. Furthermore, adding random
perturbations to the initial state of each ensemble member is sometimes necessary to
maintain the diversity of the ensemble members and not to lose the error covariance
among the model variables. In the MRI/JMA system, random perturbations are
added to dust emission intensity. This type of flow-dependent background error
definition is very promising, and it has also been progressively adopted for standard
meteorological applications in variational systems through the so-called hybrid
approach (Buehner et al. 2010a , b ; Clayton et al. 2012 ), in which the assimilation
framework is variational, but the background errors of the day are defined through
ensemble methods. This approach should work well for dust initialisation, where
the errors on the dust prediction are both associated to emission uncertainties and
transport.
Observation Errors
The problem of defining appropriate errors for the observations when those are
retrieval products is very complex. Observation errors for these products are
comprised of measurements errors that depend on instrument calibration and
characteristics and a priori and representativeness errors that depend on the retrieval
assumptions regarding the parameters that are not directly observed but that affect
the retrieval output, such as the optical properties assumed for the aerosols, as well
as on the overall quality of the forward model used in the retrieval. Most satellite
data providers do not provide errors at the pixel level, but rather provide regression
parameters derived from comparison of the satellite products with ground-based
equivalent products like AERONET retrievals of AOD which are deemed to have
high accuracy. This type of regression-based error estimate does not faithfully
represent the accuracy of the retrieved product at the level of individual pixels,
which is what is needed in data assimilation. Often the developers end up assigning
their own errors to the observations to be able to fit the needs of their system.
For example, at ECMWF, the observation error covariance matrix is assumed to be
diagonal, to simplify the problem. The errors are also chosen ad hoc and prescribed
as fixed values over land and ocean for the assimilated observations (MODIS AOD
at 550 nm). This was decided after investigation revealed that biases were introduced
in the analysis due to the observation error assumptions when those were specified