Sea Surface Salinity Short Term Variability in the Tropics

Using data from the Global Tropical Moored Buoy Array we study the validation process for satellite measurement of sea surface salinity (SSS). We compute short-term variability (STV) of SSS, variability on time scales of 2-17 days. It is a proxy for subfootprint variability over a 100 km footprint as seen by a satellite measuring SSS. We also compute representation 10 error, which is meant to mimic the SSS satellite validation process where footprint averages are compared to pointwise in situ values. We present maps of these quantities over the tropical array. We also look at seasonality in the variability of SSS and find which months have maximum and minimum amounts. STV is driven at least partly by rainfall. Moorings exhibit larger STV during rainy periods than non-rainy ones. The same computations are also done using output from a high-resolution global ocean model to see how it might be used to study the validation process. The model gives good estimates of STV, in 15 line with the moorings, though tending to have smaller values. Plain text summary. Satellite measurements of sea surface salinity (SSS) are compared with measurements in the ocean to verify the quality of the satellite data. SSS satellites measure average values over a footprint with size ~100 km, whereas ocean values are usually taken at a single point in space and time. Using SSS data from a network of buoys across the global tropics 20 we estimate the size of the mismatch between satellite and in place measurements to better understand the error structure of the satellite.


GTMBA SSS
The GTMBA is a vast network of buoys stretching across the global tropics ( Figure 1). It was originally set up in the mid-1980's to measure El Niño-related variability of the tropical Pacific (McPhaden et al., 1998;McPhaden et al., 2010) and has 95 since been expanded to the Atlantic (Foltz et al., 2009) and Indian (McPhaden et al., 2009) basins. The moorings have sensors that measure SSS at ~1 m depth with a Sea-Bird SBE-37 microcat instrument (Freitag et al., 2018). GTMBA SSS measurements are reported hourly. No quality control was carried out beyond that done by the agencies operating the array. Bao et al., (2019) identified a small number of moorings with suspicious drifts in their SSS records. We examined the same records and did not judge them to be problematic. As the analysis done here uses short bursts of data to study variability, 100 usually on time scales of ~7 days or less, absolute accuracy of the sensor is not crucial. SSS in the tropics tends to be quite spiky, with many low outliers, (e.g. Bingham et al. (2021a), their Figure 2) Overly stringent quality control could eliminate many valid data points and alter the statistics of the record.
Many of the GTMBA moorings also recorded precipitation using an R.M. Young: 50203 self-siphoning rain gauge (Freitag et 105 al., 2018). The available records are at one-minute intervals, from which we computed hourly averages.

OSCAR currents
Ideally, in order to determine SFV, we would have a spatially distributed set of ocean measurements taken simultaneously like those from SPURS-1 and 2 (Bingham, 2019;Bingham & Li, 2020). Instead, we have intensively sampled time series of SSS 110 measurements (Section 2.1) at a set of discrete locations. Our assumption is that one can substitute for the other. To tie space and time together, we use the OSCAR dataset, which is an estimate of surface current derived from satellite altimetry, sea surface temperature and surface vector winds (Bonjean & Lagerloef, 2002). The values of surface current come on a 1/3° grid at 5-day intervals (ESR, 2009). We computed average speed (not average velocity) over the 1992-2020 time period at each mooring location (Figure 1). This average speed was then turned into a short-term ensemble time period by dividing100 km 115 by the average speed. The time periods varied from 2 to 17 days, with a median value of 5 days. The main assumption is that within the short-term ensemble time period, the mooring samples about a 100 km area of ocean at the given average speed, and that this 100 km sample gives an estimate of the SFV.

MITgcm 120
We will use the MITgcm with a latitude-longitude polar cap grid, the "LLC-4320" (Su et al., 2018). The nominal horizontal resolution is 2.3 km (1/48°) near the equator. The very high resolution of the model should help to make the statistics as close as possible to the real ocean. Su et al. (2018) successfully used this same model to simulate the global submesoscale variability.
The model output was available for the 1 November 2011 to 31 October 2012 time period. The model is free-running, i.e. no 125 ocean data assimilation, and forced with 6-hour atmospheric fields from the ECMWF (European Centre for Medium-range Weather Forecasting) 0.14° atmospheric operational model analysis. For this reason, it is not expected that there would be detailed agreement between model and mooring data, but the statistics of each should be similar. We obtained the SSS field from the model and extracted time series for each of the locations of the GTMBA moorings. We carried out many of the same analyses with model SSS data as we did with the real mooring data -see below -with the exception of computing the seasonal 130 cycle. Only one year of output is not enough to get a robust estimate of the seasonal variability.
In addition, at all the mooring sites, we computed once daily values of SFV from the model grid surrounding each site. SFV is computed as a gaussian weighted standard deviation using a 50 km decay scale, i.e., a 100 km footprint. The method is the same as that of Bingham et al. (2021b). 135

Short-term variability
To compute STV from the SSS data, each record was divided into weekly evaluation times. At each of these times, we isolated an ensemble of SSS measurements surrounding it in the time interval given by the ensemble time period computed from the 140 OSCAR data. The STV was computed as the standard deviation of SSS within the ensemble time period. Figure 2 shows an example of a mooring SSS record. The weekly evaluation times are indicated by red symbols. The ensemble time periods surround each of these, shown by the red lines. The STV, or standard deviation, is computed over each of the times shown by the red lines. This then forms a time series of STV.

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To mimic the process of validating satellite measurements, we also computed a mean SSS within each ensemble time period (red symbols and lines in Figure 2). The mean over this interval is an approximation of the footprint mean that Aquarius would have seen in one L2 sample. For illustration, we show the SSS record for one ensemble time period (~7 days) for one mooring in Figure 3a. The mean is also shown (red symbol in Figure 3a), and the STV (red lines in Figure 3a). The STV in Figure 3a makes up part of the distribution for the entire record at this location shown in Figure 3b (red line). The median value of STV 150 for this record (green line in Figure 3b) is reported for each mooring ( Figure 4). As stated above, the validation process for satellite L2 measurements might compare them with a single in situ measurement. To get a sense of this, we choose a random value from the ensemble to simulate a float popping up into the satellite footprint or nearby in space or time (blue symbol in Figure 3a), and compare it with the ensemble mean. This forms a time series of differences, summarized as a histogram in Figure 3c, over the length of the record from which we can compute the RMS (green lines in Figure 3c). This RMS is what we 155 will call the "RE", a single number from each mooring. The root mean square difference (RMSD) between the "float" value and the satellite value is what is commonly reported in validation studies (e.g. Kao et al., 2018b). In this case there is no satellite retrieval error, so the RMSD between averaged and individual values we compute is due only to RE. The mean difference (instantaneous value -short-term mean) for each mooring is also computed (e.g. blue line in Figure 3c) and reported below as the bias. 160 The GTMBA mooring time series have many gaps and missing data. The STV and RE were computed within each ensemble time period only if there were 10 or more hourly values of measured SSS.

Results 165
The median STV at each mooring (Figures 4 and 5a) mainly ranges from 0.02 to 0.15, with most between 0.02 and 0.08. In the Pacific, the values are smallest along the equator and to the south. Larger values are found along 8°N (0.06-0.11), along 95°W in the eastern basin (0.08-0.11) at the edge of the eastern Pacific fresh pool (Alory et al., 2012), and in the western basin (0.04-0.10). The Atlantic basin has some larger values, especially one of 0.3 close to the coast of Africa near the outlet of the 170 Congo river. In the Indian basin, large values are seen in the Bay of Bengal (0.06-0.15). This is likely due to the large input of freshwater from rivers (Akhil et al., 2020). Of all the moorings, the median value of STV is 0.05, though the distribution of values ( Figure 5a) shows a wide range.
The RE (Figures 5b and 6) is generally larger than the STV. The difference is especially notable in the southwest Indian basin. 175 Most values of STV lie between 0.04 and 0.14 ( Figure 5b). This difference between RE and STV may be due to the presence of outlier values in the distribution of SSS (Bingham et al., 2002;Bingham 2019). If the distribution of SSS were close to normal, these two quantities would be about the same. This is illustrated in Figure 3c. The green bars, which represent the RMS difference between random samples and short-term mean, are larger than one would expect from looking at the distribution shown due to the presence of a large outlier that is not pictured in the histogram. This large value of RMS 180 difference, ~0.12, the green bar in Figure 3c, is larger than the median STV for this mooring, which is about 0.03.
Though one might have expected it due to low outlier values, there is almost no bias error detected. The distribution of median bias error is centred closely around zero, with most values less than 0.005 ( Figure 3c). There is no sign of tendency for the bias to be positive or negative. For brevity we do not show maps of bias error.

7
The STV computed from mooring data has been shown to be highly seasonal by Bingham (2019) for the two SPURS regions.
To understand the degree of seasonality in the variability, we have computed the average STV in each month for the entire record at each mooring location. We display the month where STV is maximum, and the ratio of maximum STV to the minimum STV (Figure 7). The amount of seasonality does depend on location. In the Pacific, it is strong in the eastern basin, 190 and along the northern portion of the GTMBA, but much weaker elsewhere. The seasonality is notably weak in the western Pacific, in contrast to the strong STV there (Figure 4a). The Atlantic basin displays stronger seasonality than the other two basins, especially at the western and eastern sides. The Indian basin has relatively weak seasonality in the eastern part of the basin, but stronger in the southwest. The Bay of Bengal moorings show very little in contrast to their RE (Figure 6b).

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The timing of maximum STV varies substantially from one part of the tropical ocean to another (Figure 7) and is very much dependent on local conditions. STV is maximum in January-February in the eastern Pacific as the eastern Pacific fresh pool extends to the west (Melnichenko et al., 2019). It is maximum in August-September under the ITCZ, mixed along the equator, River plume, which reaches maximum extent in boreal spring (Chao et al., 2015). In the southwestern Indian ocean, the seasonality is large, but the timing is varied from Jan-Feb to April-May. In the Bay of Bengal, STV is maximum is inconsistent, with two moorings giving maximum STV in September-October and another one in January. We suspect that STV variability in the BoB is closely related to river outflow (Akhil et al., 2014). much smaller in the model than in the mooring data, possibly due to the model's use of climatological river outflow (Feng et al., 2021;Fekete et al., 2002). A similar set of maps for the RE was created for the model output, but not included here for brevity. We do include histograms of STV, RE and bias (Figure 9) for comparison with the mooring data ( Figure 5). The distributions from the model are again similar to those from the moorings, but somewhat smaller. Table 1 gives median values of the distributions of STV and RE, showing larger values for the observed data. A direct comparison of STV from the 215 moorings vs. the model indicates that the mooring STV is larger in most cases (Figure 10), but the two have a close relationship.
In only about 10% of the mooring locations is the model STV greater than the mooring STV.
STV may be mainly caused by rainfall, by internal variability in the mesoscale or submesoscale SSS field of the ocean, or by the motion of large-scale fronts (Drushka et al., 2019). It is difficult to measure these effects separately to disentangle them.

8
One problem with measuring the impact of rainfall on STV is that it has a strange distribution, hourly values being mostly zero even during rainy periods (e.g. Bingham et al., 2002;their Figure 11). Many of the GTMBA moorings, 88 out of 123, have precipitation measurements. To measure the impact of rainfall on STV, we used those records to determine the maximum rain rate over each ensemble period. We then found the STV during periods when the maximum rain rate was greater than 1 mm / hr, and when it was less than 1 mm / hr. For almost every mooring (78 out of 88) the STV during rainy periods was greater 225 than for non-rainy periods. A typical example of this is presented in Figure 11. Because of the way rainfall is distributed, it does not make sense to compute correlations between maximum rain rate and STV, which can be easily seen in Figure 11. So we report the apparent connection here in this simple way, concluding that STV is indeed at least partly driven by rainfall.
A non-result that is important to report here is the lack of temporal aliasing. One might expect, within the ensemble time 230 periods we used, that the difference between the short-term mean (e.g. red symbol in Figure 3a) and the random samples we took (e.g. blue symbol in Figure 3a) would increase with the difference in time between the samples and the mean times. We plotted this for each mooring and uniformly found there to be no relationship between the two. The ensemble time periods we used were too short for there to be changes in the statistics of the SSS field.

4 Discussion
We have computed values for STV and RE that can be factored into error budgets of satellite SSS. The values in Table 1 are typical, but there is a large range (Figures 4-6). If anything is clear from the analysis done here, it is that STV and RE depend on both time and space. In many areas studied here, especially the equatorial Pacific, STV is small and would be negligible compared to other sources of error in L2 satellite estimates. In other areas, such as the Bay of Bengal, western North Atlantic, 240 and eastern and western Pacific, STV is important and could play a larger or even dominant role in the error budget.
As stated in Section 2, the STV is used here as a proxy for SFV over a 100 km footprint. That is, it is the variability over a 100 km spatial scale surrounding each mooring. This use depends on the assumptions that the velocity field we used derived from OSCAR is generally representative of that experienced by the mooring. This is needed to make the jump from our estimate of 245 STV to that of SFV. More subtly, the region sampled is that parallel to the flow at the mooring. The scheme we have used does not sample across the flow field. Thus, we have assumed that the spatial variability across the direction of flow is similar to that along the direction of flow. Without simultaneous sampling in a spatial region surrounding the moorings (e.g. Bingham, 2019;Reverdin et al., 2015) it is impossible to know how much variation is being missed. We were able to compute SFV at each mooring location from the MITgcm for comparison to STV from the model (Figure 12). This result shows that STV and ½ of the true SFV. Thus, the values given in Table 1 as estimates of STV might be multiplied by two to get estimates of SFV at the mooring locations.
The main purpose of this work is to understand subfootprint variability and representation error and its impact on satellite 255 measurement of SSS. This type of analysis is a good test for the MITgcm, and could be used for other models. The fact that STV is lower in the model than for the moorings suggests that either the model resolution is not quite good enough to match the statistics of the real ocean, or (more likely) that the forcing fields used, especially the rainfall, are too coarse compared to the real forcing. It is clear that rainfall occurs on a scale that is smaller than what the typical ocean model is exposed to (Bingham & Li, 2020;Thompson et al., 2019). The atmosphere continually adds small scale variance to the ocean in the form 260 of freshwater forcing. It would be interesting to see how the scale of the input freshwater forcing variance affects the behavior of forced models like the one we used. Table 1 can be thought of as an estimate of "snapshot error" (Bingham, 2019) due to representation. This is the error in each L2 estimate captured by a SSS satellite as it passes overhead due to variability within the satellite footprint. 265

The numbers in
Most estimates of SSS error are computed at L3 (e.g. Qin et al., 2020;Olmedo et al., 2020). Production of L3 values entails combining numerous individual L2 snapshots into a gridded product on a quasi-weekly or monthly basis using some form of optimal interpolation (Melnichenko et al., 2014(Melnichenko et al., , 2016 or bin-averaging (Vergely and Boutin, 2017). Thus, the numbers in Table 1 and Figure 4 are a worst case, errors that can be averaged out in the process of moving from L2 to L3 -assuming they are random. In a sense this is a hopeful sign. The numbers in Table 1 are much smaller than total errors associated with satellite 270 retrieval including surface roughness, galactic reflection, etc. (Olmedo et al., 2020;Meissner et al., 2018). However, a more granular analysis, like that of Figure 6, suggests that it may not be that simple. There are times and places where REs may be significant, the eastern Pacific, Bay of Bengal and river plume regions for example. These are all regions where higher SSS open ocean waters interact intermittently with much lower SSS coastal or river plume water. Thus, it may make sense, when computing RMS errors for satellite retrievals, to leave these areas out of the analysis, or to somehow account for the larger 275 amounts of RE that may be present in the L2 measurements there.
There is a remarkable similarity between the STV in Figure 3  Convergence zone, some areas of the central and western South Indian Ocean, the Bay of Bengal and a couple of the moorings in the western tropical North Atlantic. Most of these areas have small amplitude in seasonal precipitation compared to the rest of the tropics (see Bingham et al. (2012), their Figure 11e). Thus, regions with large (small) seasonal variability are also ones with large (small) STV. As STV appears to be somewhat driven by rainfall (Figure 11), this makes sense. Many tropical regions, like the northern hemisphere ITCZ, with heavy rainfall are also ones with strong seasonality in rainfall as well. 285 The vague nature of the relationship between rainfall and STV is highlighted in Figure 11 and similar single-mooring analyses that we do not show. The original concept for satellite SSS is that it could be used as a rain gauge (Lagerloef et al., 2008). This may be more complicated than originally thought, at least for the short-term relationship. Work is ongoing into the use of SSS as a rain gauge (Supply et al., 2018), i.e. a way to estimate precipitation over the ocean. Doing this with mooring precipitation 290 and SSS data will require a much more sophisticated approach than we have attempted here. At the very least, perhaps SSS can be used to detect whether rain is happening or not.

Code availability
Code used in this publication is available from the author on request. 295

Data Availability
Data used in this publication were obtained as follows: •