Implementation of the filter - Preliminary results of the twin experiments

Following Pham et al. (1997) , the computation of the EOFs is made through a simulation of the model itself. Thus, the model has been spun up for three years with the aim of reaching a statistically quasi-steady state. Next, two experiments were conducted: a twin experiment approach - a technique for validating data assimilation schemes, and sensitivity experiments to investigate the results sensitivity according to the number of retained EOFs.

For the twin experiments, pseudo-data, simulated by the model, were used to investigate the performance of the assimilation scheme on unobserved model variables indicating how the assimilation results converge toward the ‘truth' which is assumed to be provided by the model itself.

Following a two years simulation for the generation of a historical sequence , a reference experiment is performed by running the model for a half year to produce the reference data set and the reference states are retained to be compared later with the fields produced by the filter.

The assimilation experiments are performed on a three-day basis using surface chlorophyll pseudo-measurements calculated from the reference states. In these experiments, the filter starts from the mean state of the sample . The performance of the filter was assessed through the comparison of the relative root mean square RRMS error for each state variable, over the whole simulation domain. The definition of the RRMS can be found in Triantafyllou et al. (2003a) .

The performance (RRMS) of the assimilation runs is illustrated in Figure 1 compared with the RRMS of the free-run for phosphate, nitrate, diatoms, picoplankton, mesozooplankton and bacteria. It can be seen that the error is reduced and remains relatively low for all the variables.

Before accepting the rank of the correction base, evidence should be provided that this rank is not underestimated. Thus, the SFEK filter was run with 15 and 25 modes in the error covariance matrix and checked for any marked RRMS changes. One can see ( figure 1 ) that after 110 simulation days the error of all variables is reaching a saturation value. However, RRMS of picoplankton, mesozooplankton and bacteria shows small differences between 60 and 110 day in filter runs with 15 and 25 modes. The better performance of the filter with 25 modes might be attributed to the inconsistencies between the EOFs and the model, since during this period the model should exhibit a more non linear behaviour requiring a larger number of modes to catch the variability of the system.

If you wish to view some of the model results, click on the appropriate field:

Chlorophyll Misfits

• At 30m ( June 4 )
• At 80m ( June 4 )

Horizontal errors

• Chlorophyll RRMS (integration 0-20m and 20-120m )
• Phosphate RRMS (integration 0-20m and 20-120m )
• Bacteria RRMS (integration 0-20m and 20-120m )
• Detritus RRMS (integration 0-20m and 20-120m )

Vertical errors

• Chlorophyll RRMS at (a) Lon 025.5 E and (b) Lat 34.5 N
• Phosphate RRMS at (a) Lon 025.5 E and (b) Lat 34.5 N
• Bacteria RRMS at (a) Lon 025.5 E and (b) Lat 34.5 N
• Detritus RRMS at (a) Lon 025.5 E and (b) Lat 34.5 N