CERFACS CERFACS Scientific Activity Report Jan. 2010 – Dec. 2011

DATA ASSIMILATION
2.3 Calibrating observation- and background-error variances using
assimilation statistics (T. Pangaud, A. Weaver)
The difficulty in defining background- and observation-error statistics means that they are likely to be
incorrectly specified in a practical data assimilation system. [1] discuss how the innovations and analysis
increments generated by a data assimilation system can be used to diagnose a posteriori the covariances of
observation error and the covariances of background error in observation space. Here we have attempted
to use these diagnostics, known as the Desroziers method, to calibrate the variances of background and
observation error. Innovations and increments were collected from a 5-year assimilation experiment from
January 1, 2004 to December 31, 2008 with a pre-operational version of NEMOVAR [3] and used to
diagnose the temperature and salinity observation- and background-error variances (σo 2 and σb 2 ) on a regular
5 ◦ ×5 ◦ global grid. The method produces largest σ o and σ b in boundary current regions where the variability
is dominated by mesoscale eddies which are unresolved in the global (ORCA1) configuration considered.
The parameterized σ o and σ b that were specified in NEMOVAR do not capture this important source of
error.
The assimilation experiment was then repeated using the diagnosed (tuned) σ o and σ b in place of the
parameterized ones. The left panel in Figure 2.1 shows the globally averaged vertical profiles of the specified
σ b (solid curves) and diagnosed σ b (dashed curves) for salinity, before tuning (red curves) and after tuning
(blue curves). Before tuning, the specified σ b is largely overestimated compared to the diagnosed values,
especially in the upper 250m. After tuning, there is greater consistency between the specified and diagnosed
σ b as one might expect. The right panel in Figure 2.1 shows the impact of using the tuned variances on the
globally averaged root-mean-square of the innovations. The rms errors are systematically reduced below
100 metres, while in the upper 100 metres the impact is neutral. These results illustrate that, as well as
being a useful diagnostic, the Desroziers method can be an effective tool for objectively tuning covariance
parameters.
FIG. 2.1: Left panel : vertical profiles of the 2004-2008, globally averaged specified (solid curves) and
diagnosed (dashed curves) standard deviations of background salinity error before tuning (red curves) and
after tuning (blue curves). Right panel : globally averaged root-mean-square salinity errors (backgroundminus-observations)
before and after tuning of the background-error standard deviations (red and blue
curves, respectively). The horizontal axis is in psu ; the vertical axis is depth in metres.
CERFACS ACTIVITY REPORT 75