Observation Influence Diagnostic of a Data Assimilation System - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 96

The estimate y 1 depends on y 1 ,x 1 and an additional term due to the second
observation. It is noticed that, with a diagonal R , the observational contribution
is generally devalued with respect to the background because a group of correlated
background values count more than the single observation [ ' !˙ 1;.2 ' 2 / ! 1

.
From the expression above we also see that the contribution from the second
observation is increasing with the correlation's absolute value, implying a larger
contribution due to the background x 2 and observation y 2 nearby observation y 1 .

4.4 Results

The diagonal elements of the influence matrix have been computed for the opera-
tional 4D-Var assimilation system at T159 spectral truncation 91 model levels for
October 2011. For the calculation details see Cardinalietal. ( 2004 ). The observation
departures ( y Hx b ) were calculated by comparing the observations with a 12-h
forecast integration at T511 resolution. The assimilated observations for each main
observation type are given in Table 4.1 . A large proportion ( 98 %) of the used data

is provided by satellite systems.

4.4.1 Trace diagnostic: Observation Influence and DFS

The global average Observation Influence ( OI )isdefinedas

tr . S /

OI D (4.32)

m

where . Con-

sequently, the average background global influence to the analysis at observation
points is equal to 0.82 (see 4.15 ). It is clear that in the ECMWF system the global
observation influence is quite low.
In Fig. 4.2 the OI for the all different observation types is plotted. In general, OI
of conventional observations (SYNOP, DRIBU, PROFILER, PILOT, DROP, TEMP,
Aircraft) is larger than the satellite one. The largest OI is provided by DRIBU
surface pressure observations because they are located over the oceans that are in
general very poor observed (less than continental areas). Moreover, DRIBU and
SYNOP observations are very high quality measurements and the observation error
variances is quite small, likely smaller than the background error variance (see 'toy
model' in Sect. 4.3.3 ). Similarly, the OI

m is the total number of observations. For October 2011 OI D 0:18

of the remaining conventional
data is due to their quite small observation error variance. In Sect. 4.3.3 it has been
proved that if R is diagonal the OI is bounded between (0,1) but from Fig. 4.2 ,we
can see that DRIBU OI is higher than 1. This is due to the approximation of the
numerical solution and, in particular, the use in the influence matrix calculation of

0:4 - 0:5