Our fusion method is based on estimating the local functions a(x) and b(x) of the linear approximation, Eq. (4.31), and then applying them to the SST template in order to construct the fused SSS map. As previously discussed, we have not in general access to those functions but to certain estimates, that we have calculated here by means of the expression in Eq. (4.33).
The estimates for the local slope and local intercept functions, ˆa(x) and ˆb(x), provide particular useful information about the structure of the ocean, as they convey information on the local functional dependence between SST and SSS. In Figure5.16we show an example of the monthly mean of both estimates for the month of June 2012.
Positive values of a(x) are found in areas where SSS increases as SST also increases; this situation, which is typically found in the subtropical gyres, is more intense in the Atlantic Ocean than in the Pacific Ocean. This relation varies during the year largely driven by the seasonal cycle of sea surface temperature. On the other hand, the local slope, a(x), is negative at those places where SST increases as SSS decreases. This is the situation which happens around the equatorial bands; see for instance the warm pool in Pacific Ocean, the footprint by
Figure 5.16: Top: Local slope estimation ˆa(x). Bottom: Local intercept estimation ˆb(x). Monthly mean of the estimations used in the derivation of the 9-day L4-2 maps as presented in Figure5.1for June 2012.
the Amazon, Congo and Niger plumes in the Equatorial Atlantic, and a vast area of exchange between the Pacific and the Indian Oceans. In those regions, although the SST is the highest in the globe, salinity is affected by major river discharges and rainfall that decrease salinity. The other observed negative structures, all in the Southern Ocean, should be taken with caution given the present limited capability of the instrument to provide an accurate SSS signal under strong winds and low SST.
The band of cool and fresh waters apparent all along the Equator with the strongest signal in the Pacific and Indian Oceans also corresponds to the highest values of the local intercept b(x). In this regions, a reverse correlation between SST and SSS confirms that exist a different dynamic adjustment between SST and SSS and are thus dominated by specific processes. The
Figure 5.17: Mean local regression coefficient of the estimation of local parameters used to produce the 9-day L4-2 maps as presented in Figure5.1for June 2012.
assumption of a local linear relation between SST and SSS is here less reliable, as the region has the lowest regression coefficients (Figure 5.17).
Local regression coefficients above 0.6 (in absolute value) are rare. The regression coefficients are not expected to be large due to present levels of noise in SMOS data. In the Equatorial Atlantic, Pacific and Indian Ocean, either additional variables should be taken in consideration to further improve the adequacy of our algorithm, or a more sophisticated relation between SSS and SST should be used. Interestingly enough, these regions are found around the Equator.
This implies first that geostrophic adjustment is not valid on those regions and thus the flow are less barotropic; and secondly, they are affected by higher influxes of fresh water (coming from the river plumes in the case of the Atlantic, and in the Pacific and Indian Oceans given by rain discharges). It is also worth highlighting that although the size of the regions and their position (especially in the Equatorial Atlantic) vary with time, they are almost permanent features along all the year.
A further step is here taken by using the monthly mean values of local regression coefficients as an alternative extrapolation ability of our fusion method. Now the L4 SSS (˜s) is computed by:
˜
s(x) = a(x) θ(x) + b(x) (5.1)
where a(x) and b(x) are monthly mean values of the estimates ˆa(x) and ˆb(x) in Eq. (4.33) presented in Chapter4.
Following Eq. 5.1, we produce 9-day L4-AB SSS maps using OSTIA SST as a template, and mean local regression coefficients. The mean values of the local regression coefficients are computed as monthly averages of the 9-day correlation coefficients from the generation of L4-2 SSS (section5.1) without any extrapolation. A sample map of the resulting L4-AB is presented
in Figure5.18for the first 9-day of June 2012 (compare to5.1bottom where the L4-2 is produced by extrapolation).
Figure 5.18: Map of surface salinity applying data fusion OSTIA SST using monthly mean linear coefficients 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 216188 213257 206580 129817 85970 113856 111463 73361 56254 7567 7448 6274 5129
∆S -0.03 -0.02 -0.02 0.01 -0.01 -0.07 -0.07 -0.06 -0.07 -0.12 -0.12 -0.09 -0.09 L4-AB
σ<∆S> 0.47 0.46 0.46 0.43 0.33 0.31 0.31 0.27 0.26 0.21 0.21 0.21 0.21
Table 5.11: Statistics between L4-2 SSS using mean a(x) and b(x) parameters vs Argo SSS measurements for the year 2012.
The results of buoy collocation differences by latitude bands, distance to coastal areas, depth of the Argo uppermost measurement and SST differences between Argo and ECMWF (following procedure used in previous sections) to quantitatively assess the new SSS L4 maps errors are presented in table5.11.
The number of total matchups are of the order of two-hundred thousand. At global scale the standard deviation of the SMOS minus Argo difference is reduced to 0.47 (it was 0.49 for L4-2 in section 5.1), and the bias is the same: -0.03. The bias is as before systematically negative probably due to a bias in the processing or to the fact that Argo measures salinity several meters below the surface.
Isolating the different contributions, we have once again taken data selected by latitudinal bands: the standard deviation of L4 SSS is reduced from 0.47 (global) to 0.46 (bounded by latitude 60), to 0.31 (bounded to latitude 30) and to 0.21 (in Zone 122). The biases are -0.03 (global), -0.02 (bounded by latitude 60), -0.07 (bounded to latitude 30) and to -0.12 (in Zone 122); the mean biases are reduced from -0.03 (global), -0.02 (bounded by latitude 60), -0.07
(bounded to latitude 30) and to -0.12 (in Zone 122). This implies an improvement in standard deviation and a slightly worse bias as compared to the validations both for L4-1 and L4-2 presented in section5.1.
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 less than 0.3◦C, L4AB SSS estimates have negative biases of -0.01, -0.07 and -0.09 at the 60◦, 30◦ latitude bands and Zone 122 respectively, and standard deviations of 0.33, 0.26 and 0.21 at the 60◦, 30◦ latitude bands and Zone 122 respectively. When restricting the validation to the regions without known associated issues, the errors are similar to the L4-2, and better than in the case of L4-1 presented in section 5.1. The use of monthly mean values of local regression coefficients allows a better global validation, particularly in most problematic areas as high latitudes and close to lands, but as this approach uses monthly mean local regression coefficient values and not the specific ones for the image produced, the quality degrades in locations where no extrapolation was needed or where the standard approach already provided an accurate SSS estimate.