Tests with General Circulation Models

The four GCMs analysed all were fundamentally wind-driven from multi-layered numerically integrated primitive equations with different resolutions and handling of other boundary conditions. Carton's assimilating model (Carton et al., 2000a,b) extended from latitude with a spacing of in longitude and latitude spacing varying from at low to at high latitudes. Heat input was sun-driven constrained by seasonal climate values and modified in part by assimilated in-situ data from TOGA arrays in the tropical Atlantic and Pacific. (The TOGA arrays also supplied salinity data which also were used to modify seasonal climate values in these regions). In addition, sealevel variations were controlled by assimilated collinear altimetry during 1986-88 from Geosat and 1993-1996 from T/P. The data for this model extended from 1980 through 1996, with time samples every month.

Two non-assimilating models were also examined with time sampling every 3 days and resolution between latitude. The POCM  4B (Stammer et al., 1996) extended from 1987 through 1996, the Los Alamos National Laboratory LANL (Fu and Smith, 1996) from 1985 through 1996 and both these models also used Sun-driven heating of the upper layers constrained by seasonal climate data. We used 1x1 degree averages of the POCM 4B in our comparisons.

Figure 12

Average Sealevel Differences (Geosat-Ers1 Period) over a 5 year Gap, from three Global Circulation Models and Crossover Altimeter residuals to a 50x50 Geopotential Adjustment (see text for specifications).
The differences are averaged for April 1992 through December 1993, minus April 1987 through December 1988 in 2x3 bins.
a. Carton's Assimilating General Circulation Model, Rms deviation = 4.1 cm.
b. Los Alamos National Laboratory GCM, Rms deviation = 8.0 cm.
c. Parallel Ocean Circulation Model 4B, Rms deviation = 7.5 cm.
d. Pathfinder Altimeter (crossover) Residuals from a 50x50 Geopotential solution, Rms deviation = 4.5 cm.
Carton's model (which assimilates collinear altimetry in the Geosat and most of the Ers1 periods) altimetry has roughly the same power as the altimeter residuals but the struture differs considerably in most ocean regions. The other ocean models, unconstrained by any in situ data clearly shows excessive power compared to the altimetry.

The best overall picture of the interannual behaviour of these models is seen in Figure 12 for the 21 month average (April 1987 thru. December 1988) - (April 1992 thru. December 1993) over a 5 year gap compared to the average Geosat-Ers1 DSC residuals of the downweighted comprehensive solution. Note that the averages for the models are not over an integer number of years; thus the tendency of the non-assimilating models to drift away from constraining seasonal climatology appears here in an exaggerated way for both POCM 4B and the LANL model. Only the Carton model, which assimilates heat, salinity and altimeter heights, has about the correct power in these differences as judged by the altimeter results, though the details in the tropics only correspond fairly well. [We see better agreement of our crossover altimetry with Carton's model when we compare interannual changes with (integer) yearly averages].

To get a better appreciation of Carton's model against data it did not use we compared predictions from it against the same tide gauge differences used to test our crossover altimetry (Table 4). Since this model assess the heights at discrete locations and at better resolution in the tropics than the crossover altimetry it should show good agreement with most of these the tide-gauges, since it is also constrained by (collinear) Geosat and T/P altimetry. As Table 4 shows the agreement overall is about the same with the Carton model as with the residual crossover altimetry. As noted above, the inherent drift of the unassimilated POCM 4B makes for a poor comparison with the gauges in the 21 month averaged (5 year gap) Geosat-Ers1 time period (Table 4).

Finally, hoping to achieve better agreement with Carton globally than with the sparse tide-gauges, we tested our altimetry against the discrete locations of this model averaged across the gaps in the two periods (Geosat-Ers1 and Geosat-T/P). Unfortunately this global comparison was worse than with the gauges (Table 4) probably because, outside of the tropics, the resolution of the Carton model is poorer in latitude and does not resolve the strong eddy fields which we have found to have significant interannual expression (Klokocnik et al., 1999).

For example, using only the Carton model points within a narrow tropical band and for the 2 year averages in the Geosat-T/P time period (8 year gap), the comparison with our residual crossover altimetry is much better than with the global results (Table 4). The same comparison in the 21 month averaged Geosat-Ers1 time period is only marginally better in the tropics than globally, suggesting that the assimilation does not completely control the tendency of GCMs to drift over the long term outside of seasonal constraints. (For Carton's model, Figure 12 shows this drift to be more in phase than in amplitude with respect to the altimetry).

Though our DSC residuals from the geopotential seem to be a genuine averaged interannual signal over most of the oceans we still lack confirmation of this from an independent global data source. (Carton's model assimilates altimetry, albeit imperfectly). In the next section we compare independent collinear altimeter differences to the crossover residuals in the two periods (Geosat-Ers1 and Geosat-T/P).