Sea Surface Salinity Seasonal Variability in the Tropics from Satellites, in situ compilations and Mooring Observations

Satellite observations of sea surface salinity (SSS) have been validated in a number of instances using different forms of in situ data, including Argo floats, moorings and gridded in situ products. Since one of the most energetic timescales of variability of SSS is the seasonal, it is important to know if satellites and in situ gridded products are observing the seasonal variability correctly. In this study we validate the seasonal SSS from satellite and in situ products using observations from moorings in the global tropical moored buoy array. We utilize 6 different satellite products, and two different in situ gridded products. For each product we have computed seasonal harmonics, including amplitude, phase and fraction of variance (R2). These quantities are mapped for each product and for the moorings. We also do comparisons of amplitude, phase and R2 between moorings and all the satellite and in situ products. Taking the mooring observations as ground truth, we find general good agreement between them and the satellite and in situ products, with near zero bias in phase and amplitude and small root mean square differences. Tables are presented with these quantities for each product quantifying the degree of agreement.

variations in the tropics, especially north of the equator in the Pacific and Atlantic basins [17, 18, 22, 45 27, 28] where the ITCZ is present and as a result of strong river discharge into the tropical Atlantic.

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The global tropical moored buoy array (GTMBA) is a vast network of moorings stretching across all the ocean basins ( Figure 1). It was set up starting in the 1980's to measure variations related to El https://www.pmel.noaa.gov/gtmba/ and [29] for a history of the program in the three different basins, 50 and www.tpos2020.org for a discussion on the future of the Pacific portion of the array.) These 51 moorings measure quantities such as wind, precipitation, humidity, currents, sea surface 52 temperature, subsurface temperature, and, most importantly for the current study, SSS. The high 53 quality standards, long record duration (some over 20 years - Figure 1)     Record Length (Years)  (Tables S5-S7).

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. A1 (A2) is the amplitude of the (semi)annual harmonic. " ( # ) is the phase of the (semi) annual 149 harmonic. t is the time. S0 is the mean value of salinity at each location. e is a residual to be minimized in the least squares sense by determination of A1, A2, " and # . . (2) The f-statistic was then calculated from R 2 using the equation Where n is the number of observations (non-null data points in the time series at that location) and k is 155 the number of independent variables, two in the case of looking at the annual and semiannual 156 harmonics individually. Then the cumulative F-distribution function was used on the given f-statistic, 157 n, and k, and fits with values greater than 0.95 were considered significant. The significance was 158 calculated as if all the data points were independent observations. In addition to filtering by 159 significance, we only considered locations where we had at least one year total of data points for a given 160 data set.

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In comparing the amplitudes, phases and R 2 values between mooring and products, we used the 162 entirety of each dataset, including possibly non-overlapping periods. This was done because: 1) the 163 computed amplitudes and phases seemed stable as described below, 2) we wanted to increase the 164 significance of the computed fits, and 3) many of the moorings were sampled sporadically (e.g. Figure   165 2a) making determination of overlapping periods computationally cumbersome.

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As an illustration of the method, we show the mooring data, harmonic fit, SIO data and its fit at    Phase (months)  (Table S2) and semi-annual (Table S5) 209 harmonics.    Phase (months) Figure 5. As in Figure 3, but for the SMAP RSS data.

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The similarity of the mooring and SMAP RSS results is striking, and is repeated for most of the 241 other datasets we analyzed (Tables S3 and S4

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In a couple of cases we can compare two products whose underlying measurement is the same.

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There are two different L3 SMAP products and two L3 SMOS products (Figure 8)

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With the first harmonic amplitudes, we find that most satellite and in situ products compare 288 well with the moorings (Figure 9 and Table 2 Table 2 shows the median of the difference between R 2 values for the mooring and that of the 299 various products. In other words, for each dot in Figure 9, one can subtract the mooring value from 300 the comparison product value, to obtain the degree to which those dots depart from the one-to-one 301 line. One can then compute the median of those differences, to get the numbers displayed in Table 2. 302 Table 3 shows the median over the dots for, say, the moorings or SMAP RSS. These values show 303 which products tend to have large or small values of R 2 .

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An example set of R 2 comparisons are shown ( Figure 10; Table 3 (Table 3). The moorings, one assumes as they are sampled hourly, capture all or almost all 309 of the temporal variance in nature. The in situ datasets (EN4 and SIO) are averaged monthly and over 310 a 1°X1° area, so any variance with smaller time and space scales is not present in those datasets. Thus, 311 one would expect R 2 in the annual harmonic would be larger for these than for the moorings, which 312 it is (Figure 10c; Table 3). For Aquarius, the issue is the same. It has a footprint similar in size to the 313 in situ products' grids, generating an average over about a 100 km area. Thus, it does not sample 314 most of the variability at less than 100 km in size. As much of ocean SSS variance is at sizes less than 315 50 km [44], the Aquarius dataset cannot resolve it, and therefore, the annual harmonic constitutes a 316 larger fraction of the variance than for the moorings (Figure 10d; Table 3). As we have seen, the SMOS 317 BEC data underestimate the size of the annual harmonic, and so the fraction of variance captured in 318 that dataset is less than for the moorings (Figure 10a; Table 3). Finally, the SMAP RSS product ( Figure  10b; Table 3) has a smaller footprint than Aquarius, and more frequent sampling than SIO. The 320 fraction of variance depicted in that dataset is comparable to that of the moorings. The datasets not 321 plotted in Figure 10, SMOS CATDS, SMAP JPL, EN4 and CCI, all show similar patterns as SMAP RSS

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( Table 2).  give a reasonable value for the amplitude. Amplitude median differences are as high as 0.06 (Table   350 2, column 4), with some within the uncertainty range of zero.

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It's difficult to track what exactly might be causing differences in products quantified in Table 2 352 given the variety of different processing algorithms, hardware configurations, antenna patterns,

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ancillary input data, etc. detailed in the references shown in Table 1

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This effect is quite visible in Figure 2d. This could potentially lead to the mooring data having larger 381 seasonal amplitudes than the other two types of data as low outliers during rainy seasons influence in terms of variability [21], it is important to make sure these products themselves are validated. We have done some of that here for a limited geographical extent and a very limited time scale -i.e. annual.
and Figure 10). Given the fact that in situ products are mostly generated from sparse Argo data, it's 392 expected that the seasonal time scale would be more heavily represented than anything shorter. Our 393 results show however, that if validation is done using gridded products, important parts of the 394 temporal spectrum of variability are missing. Do the satellite products get the balance correct 395 between seasonal and shorter-term variability? Our results from Table 3 and Figure 10 show that this 396 varies from one product to another.

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As the moorings are a directly-measured, in situ dataset, the value of R 2 presented in Table 3 398