Operational Dust Prediction - Mineral Dust: A Key Player in the Earth System - page 253

A10.3 Definitions of Background and Observational Errors

Since the relative weight between the background and the observations is decided
by the error statistics prescribed for both, in areas that are data-limited such
as the deserts, the aerosol analysis is severely under-constrained relative to the
observations and relies almost entirely on the background. Also, the background
matrix is responsible for the redistribution of the aerosol information from the
observations to the model fields. This is again especially true for dust due to the
already-mentioned paucity of observations over bright surfaces.

Background Error Covariance Matrices

The aerosol background error covariance matrix used for aerosol analyses at
ECMWF was derived using the Parrish and Derber method (also known as NMC
method; Parrish and Derber 1992 ) as detailed by Benedetti and Fisher ( 2007 ). This
method was long used for the definition of the background error statistics for the
meteorological variables and is based on the assumption that the forecast differences
between the 48 h and the 24 h forecasts are a good statistical proxy to estimate the
model background errors. The advantage in using the model to define the errors
is the grid-point availability of the statistics over a long period. This leads to a
satisfactory background error covariance matrix without the need to prescribe the
vertical and horizontal correlation length as shown in Kahnert ( 2008 ). However, a
shortcoming of this method consists in the static definition of the background error
covariance matrix, which can lead to suboptimal analysis in the case of unusual
situations such as intense storms. This is addressed by the ensemble methods with
flow-dependent error estimates which suit the specific situation (“errors of the day”).
For the FNMOC/NRL NAAPS global model, background error covariances were
estimated in a number of methods, all converging to the same number for the error
covariance length (250 km, the same as is commonly assumed for water vapour).
This length was determined from experiments from the MODIS data set. As a
check, error covariances were also estimated from a 3-month simulation from the
20-member NAAPS ensemble driven purely from the NOGAPS meteorological
ensemble.

Flow-Dependent Background Error Covariance Matrix

“Errors of the day” can be estimated in the context of the ensemble methods, where
at each analysis time, a series of forecasts is run starting from perturbed conditions,
and these forecasts provide an estimate of the model errors. However, the EnKF
tends to be easily influenced by sampling errors at long distances because the
available ensemble size is too small to estimate the background error covariance
of the atmospheric system. Therefore, a covariance localisation must be applied