Lawrence R. Dicksee

As a depth-integrated quantity dependent upon the density structure of the water column, altimeter ADT estimations reveal the presence of mesoscale structures and allow for the retrieval of surface currents using geostrophic balance (Tandeo et al., 2014). Theoretically, the upper ocean turbulence for horizontal scales between 50 km to few hundred kilometers is still consistent

Figure 5.12: Map AVHRR SST (^◦C ) (top) and (bottom) associated singularity exponents for the first nine days of June 2012.

with the geostrophic turbulence theory. Under this assumption, the upper ocean dynamics can be inferred from pressure variations, driven by sea level high and in a second order, surface density horizontal variations which are dominated by SST and SSS variations (Isern-Fontanet et al.,2006;LaCasce and Mahadevan,2006).

The temporal evolution of ADT is significantly different from that of SST or SSS, as ADT is an active scalar driving the circulation and so it is not simply passively advected by the flow;

in particular, its evolution is highly non-linear. For instance, the ADT response to changes in large-scale winds can be described as long first baroclinic mode Rossby waves whose evolution depends on the meridional advection of the background potential vorticity gradient. This term is important at large spatial scales. Nevertheless, horizontal advection is the dominant process

Figure 5.13: L4-1-AVHRR SSS (top) and L4-2-AVHRR SSS (bottom) for the first nine days of June 2012.

in the creation of localized strong gradients in ADT at the mesoscale. On a given passive or non-passive scalar such that horizontal advection is the only term inducing sharp transitions that is, introducing singular structure in the scalar, it follows that the singularity exponents derived from that scalar will be related to streamlines (Isern-Fontanet et al.,2007;Turiel et al., 2009), independent of the particular scalar of choice. The regions of the largest gradients in the ADT are associated with mesoscale fields where the Rossby number is large (we define the Rossby number as U/fL where U is the velocity scale, L is the length scale, and f is the Coriolis parameter). As advection becomes important at large Rossby numbers, we expect that the singularity fields of ADT will be similar to those of other scalar fields.

Using AVISO MADT as template (a sample map with the correspondent singularity expo-nents is presented in Figure5.14), the data fusion is applied both to the original L3 SSS (section

Figure 5.14: Map AVISO MADT (m)(top) and (bottom) associated singularity exponents for the first nine days of June 2012.

3.2.1) resulting in L4-1-MADT SSS, and to the L3 SSS coming from an alternative filtering of L2 data (section 3.5.1) resulting in L4-2-MADT SSS. A sample map of both L4-MADT products is presented in Figure 5.15. The validation of the resulting 9-day L4-MADT SSS products calculated every three days is made using close-to-surface data from Argo profilers following the same procedure as in previous sections (see tables 5.9and 5.10).

The number of total matchups are of the order of two-hundred thirty thousand. Both L4-1-MADT and L4-2-MADT have similar statistics than L4-1-AVHRR and L4-2-AVHRR (see tables 5.7 and 5.8 for comparison). At global scale the standard deviation of the SMOS minus Argo differences is slightly increased to 0.50 for L4-2-MADT SSS (it was 0.49 when using AVHRR SSS as a template); however the bias is reduced to -0.01 (it was -0.03). When

Figure 5.15: Map L4-1-MADT SSS (top) and L4-2-MADT SSS (bottom) for the first nine days of June 2012.

Latitude Global 60S-60N 30S-30N Zone 122

Maximum depth >10 m >10 m >10 m

Coast distance 1000 km 1000 km 1000 km

ECMWF-Argo SST <0.3 ºC <0.3 ºC <0.3 ºC

n 237999 233464 225342 131841 87420 126813 124041 75582 57854 7682 7564 6276 5114

∆S -0.11 -0.10 -0.09 -0.02 -0.05 -0.15 -0.15 -0.13 -0.14 -0.18 -0.18 -0.14 -0.14 L4-1-MADT

σ<∆S> 0.53 0.50 0.50 0.45 0.35 0.36 0.36 0.28 0.28 0.21 0.21 0.20 0.20

Table 5.9: Statistics of 9-day L4-1-MADT vs Argo SSS measurements for the year 2012.

data are selected by latitudinal bands and distance to coast, the global error reduces from 0.50 (global) (it was 0.49), to 0.49 (bounded by latitude 60; it was 0.47), to 0.37 (bounded to latitude 30; it was 0.35) and to 0.22 (in Zone 122 it was the same 0.22). The biases are -0.01 (global;

it was -0.03), 0.00 (bounded by latitude 60; it was -0.02), -0.07 (bounded to latitude 30; it was

Latitude Global 60S-60N 30S-30N Zone 122

Maximum depth >10 m >10 m >10 m

Coast distance 1000 km 1000 km 1000 km

ECMWF-Argo SST <0.3 ºC <0.3 ºC <0.3 ºC

n 229146 225474 217858 130655 86633 121618 119047 74553 57142 7672 7554 6269 5107

∆S -0.01 -0.00 0.00 0.02 -0.00 -0.07 -0.07 -0.08 -0.08 -0.16 -0.15 -0.12 -0.12 L4-2-MADT

σ_<∆S> 0.50 0.49 0.49 0.45 0.35 0.37 0.37 0.28 0.28 0.22 0.22 0.21 0.21

Table 5.10: Statistics of 9-day L4-2-MADT vs Argo SSS measurements for the year 2012.

-0.06) and to -0.16 (in Zone 122; it was -0.13). The bias is not reduced for this product when the matchups are restricted to narrower latitudinal bands.

When the data is requested to be more than 1000 km from the coast, the upper Argo measurement in the first 10 m below the ocean surface and points with differences between reference and in situ SST lower than 0.3^◦C, L4-2-MADT SSS estimates have biases of 0.00, -0.08 and -0.12 at the 60^◦, 30^◦ latitude bands and Zone 122 respectively; and standard deviations of 0.35, 0.28 and 0.23 at the 60^◦, 30^◦ latitude bands and Zone 122 respectively. Compared to the results when OSTIA SST or AVHRR SST were used as a template at the global and 60^◦, 30^◦ latitude band, standard deviation are slightly worse, but the bias of L4-MADT are slightly better. In 30^◦ latitude bands and Zone 122, L4-MADT SSS estimates are similar or do not improve the results.

Although resulting maps qualitatively differ, it is not clear which template give better results when validating with Argo measurements at a global scale, although using SST templates give slightly better results than using absolute dynamic topography. In next chapter we will analyze the effect of using different templates in the specific case of Western boundary currents, where the high mesoscale activity will give us more insight in the relation between SSS and the different variables used as template in the data fusion.