A Multivariate Reduced-order Optimal Interpolation Method and its Application
295
(AC), Westem Mediterranean excluding AC, Ionian basin, Levantine basin. In
effect, at each model grid point, we solve a 4-EOF problem (ST has 4 columns), but
the background error variances in Di are zero except on the corresponding mask.
An hyperbolic tangent ramp in the background error variances provides a smooth
connection between regions.
In the present case where only one EOF is used at one given location, the EOFs
were not defined in the surface layer, since the Ekman layer variability is largely
decorrelated from the deeper variability and would require more EOFs. Therefore
the surface layer variables are not directly changed by the assimilation. However
they are influenced by the assimilation, e.g. through barotropic velocities.
Table 15.1 shows the percentages ofvariance explained by the various first EOFs
in model outputs, as well as the coefficients used to scale the variables (matrix ~ in
(15)). For one given variable, alIlevels were scaled with the same coefficient. The
modes shown in Fig. 15.1 are the colurnns of ~S'+. It can be seen from Fig. 15.1
that the dominant modes are surface-intensified and that the signs are pretty homogeneous across alI regions. Therefore our test case with only one basin-wide EOF
is certainly not widely erroneous. The fact that T and S are of opposite sign is
mostly the signature ofthe Modified Atlantic Water's important contribution to the
basin-wide variability. From Table 15.1, it can also be seen that in the model simulation the barotropic mode plays a specially important role in the Westem basin.
The Algerian Current area shows the largest variabilities in alI variables. In the
Eastem basin, the spectrum of eigenvalues is not as "red" as in the Westem basin
(more significant EOFs, more complex system), and the salinity variability
increases as one moves eastward.
Figs. 15.2 and 15.3 show assimilation results with reference to the free simulation. From Fig. 15.2, the assimilation does improve the capability ofthe model to
predict the temperature on the short term. In addition the regional EOFs do an even
better job at reduc ing the residual error, which is of the order of 0.35°C at 280m
(down from 0.55°C). It can be seen from Fig. 15.3 that the assimilation improves
the temperature (which is the assimilated variable) in most regions, but also the
salinity (not assimilated) in some regions such as the Levantine basin and the axis
of the Algerian Current. These results could very likely be improved by fine- tuning the regions and parameters.
15.3.3 Assimilation of altimeter data in 1993-97
We now illustrate the influence of altimeter data assimilation in the same GCM,
in a 5-year period simulation in 1993-97. For this purpose, we use TOPEXlPOSEIDON and ERS-1I2 along-track sea-level anomaly from CLS (G. Lamicol, pers.
comm, 1999). The processing includes long-wavelength error removal. The data
are not gridded prior to assimilating. The assimilation is carried out with one
model-derived trivariate basin-wide EOF as in Fig. 15.1a. As before, no assimilation goes on in surf ace layers (0-1 OOm) and at depth (below 85 Om) except for barotropic velocities. The average sea-level is not changed in the model. The
assimilation starts on Jan 1, 1993 and proceeds with a 7 -day cycle to Dec 31, 1997.
295
(AC), Westem Mediterranean excluding AC, Ionian basin, Levantine basin. In
effect, at each model grid point, we solve a 4-EOF problem (ST has 4 columns), but
the background error variances in Di are zero except on the corresponding mask.
An hyperbolic tangent ramp in the background error variances provides a smooth
connection between regions.
In the present case where only one EOF is used at one given location, the EOFs
were not defined in the surface layer, since the Ekman layer variability is largely
decorrelated from the deeper variability and would require more EOFs. Therefore
the surface layer variables are not directly changed by the assimilation. However
they are influenced by the assimilation, e.g. through barotropic velocities.
Table 15.1 shows the percentages ofvariance explained by the various first EOFs
in model outputs, as well as the coefficients used to scale the variables (matrix ~ in
(15)). For one given variable, alIlevels were scaled with the same coefficient. The
modes shown in Fig. 15.1 are the colurnns of ~S'+. It can be seen from Fig. 15.1
that the dominant modes are surface-intensified and that the signs are pretty homogeneous across alI regions. Therefore our test case with only one basin-wide EOF
is certainly not widely erroneous. The fact that T and S are of opposite sign is
mostly the signature ofthe Modified Atlantic Water's important contribution to the
basin-wide variability. From Table 15.1, it can also be seen that in the model simulation the barotropic mode plays a specially important role in the Westem basin.
The Algerian Current area shows the largest variabilities in alI variables. In the
Eastem basin, the spectrum of eigenvalues is not as "red" as in the Westem basin
(more significant EOFs, more complex system), and the salinity variability
increases as one moves eastward.
Figs. 15.2 and 15.3 show assimilation results with reference to the free simulation. From Fig. 15.2, the assimilation does improve the capability ofthe model to
predict the temperature on the short term. In addition the regional EOFs do an even
better job at reduc ing the residual error, which is of the order of 0.35°C at 280m
(down from 0.55°C). It can be seen from Fig. 15.3 that the assimilation improves
the temperature (which is the assimilated variable) in most regions, but also the
salinity (not assimilated) in some regions such as the Levantine basin and the axis
of the Algerian Current. These results could very likely be improved by fine- tuning the regions and parameters.
15.3.3 Assimilation of altimeter data in 1993-97
We now illustrate the influence of altimeter data assimilation in the same GCM,
in a 5-year period simulation in 1993-97. For this purpose, we use TOPEXlPOSEIDON and ERS-1I2 along-track sea-level anomaly from CLS (G. Lamicol, pers.
comm, 1999). The processing includes long-wavelength error removal. The data
are not gridded prior to assimilating. The assimilation is carried out with one
model-derived trivariate basin-wide EOF as in Fig. 15.1a. As before, no assimilation goes on in surf ace layers (0-1 OOm) and at depth (below 85 Om) except for barotropic velocities. The average sea-level is not changed in the model. The
assimilation starts on Jan 1, 1993 and proceeds with a 7 -day cycle to Dec 31, 1997.