Comparison of Distributional Statistics of Aquarius and Argo Sea Surface Salinity Measurements
1. Introduction
In 2011, NASA launched a satellite mission to measure sea surface salinity (SSS) and to provide the global view of salinity variability needed for climate studies. The goal of the Aquarius mission is to understand “the interaction between ocean circulation, the water cycle, and climate by measuring salinity” (NASA 2012). Salinity affects the interaction between ocean circulation and the global water cycle, which in turn affects the regulation of the earth’s climate through the ocean’s capacity to store and transport heat and affects the onset of phenomena such as El Niño (Lagerloef et al. 2008). Characterizing salinity is vital to understanding the interaction between ocean circulation, the water cycle, and climate. Given a properly validated salinity product, Aquarius provides a spatially rich source of information about ocean salinity in a time frame that allows for the consideration of mesoscale regional events as well as global climate fluctuations.
The core of the Aquarius mission is the retrieval algorithm, the process by which satellite-measured microwave brightness temperatures are transformed into values of SSS. This complex algorithm has been well documented (Le Vine et al. 2007; Yueh and Chaubell 2012; PO.DAAC 2014) and is based on the dielectric model of Klein and Swift (1977). Some of the major issues with the retrieval algorithm have been radio frequency interference and the reflection of cosmic background radiation off a rough sea surface (Lagerloef et al. 2013; Meissner et al. 2014a). Validation, the comparison of retrieved values of SSS with values measured by in situ instrumentation, feeds back into the retrieval algorithm to update and improve the algorithm. Over the life of the mission, the retrieval algorithm has undergone a number of upgrades and improvements based on the results of validation studies.
One of the main goals behind the launch of Aquarius was the idea of using it as an ocean rain gauge (Lagerloef et al. 2008; Yu 2011), whereby changes in surface salinity would be used to infer changes in freshwater flux across the surface. As the mission has progressed, however, this goal has become more problematic as researchers have come to understand how important ocean dynamics are in determining the field of SSS (Yu 2014, 2010; Alory et al. 2012; Foltz and McPhaden 2008; Lee et al. 2012; Qu et al. 2011; Vinogradova and Ponte 2013; among others). There is not a direct relationship between freshwater flux and changes in SSS.
One of the most difficult aspects in the validation of Aquarius is the comparison of the satellite data to the existing in situ data, particularly Argo floats. Since the floats typically turn their sensors off at 3–5-m depth, and the satellite measures a near-surface (1–10 cm) value, the two measurements are not necessarily comparable. This is thought to result in Aquarius being biased low relative to Argo in regions with large rainfall like the intertropical convergence zone (ITCZ) and South Pacific convergence zone (SPCZ) (Tang et al. 2014a). Low-salinity events associated with rainfall are often confined to the near surface. In this context, near surface means the upper 1–2 m. Various authors have found that in the short term, the salinity impacts of rain events do not usually penetrate much farther than this (Henocq et al. 2010; Boutin et al. 2014, 2013; Santos-Garcia et al. 2014; Tang et al. 2013, 2014b; Asher et al. 2014b). Some progress is being made in this area, however, as we come to more effectively incorporate wind speed into the retrieval algorithm (Meissner et al. 2014a) and quantify the impact of rainfall on the float data (Drucker and Riser 2014).
As suggested by Drucker and Riser (2014), perhaps one possible way to return to the idea of the ocean rain gauge is to examine the differences between Argo and Aquarius when there is rainfall that freshens the surface. In this situation, it is important to know how the Aquarius instrument is performing for values of SSS that are low compared to the background value. In other words, we need to quantify the lower tail of the SSS distribution. Perhaps by understanding these differences, we can better use the Aquarius data to serve one of the original purposes of the mission. Thus, there is a need to examine not just the mean or median values of SSS from Aquarius, but the entire distribution to ensure that low SSS events in particular are being well measured.
Now that the basic product has approached a level of accuracy that makes it useful for science, a more nuanced view of the validity of the data is required, one that seeks to ensure the accuracy across the entire distribution of SSS. SSS tends to have a probability distribution that is skewed toward lower salinity values (Bingham et al. 2002) and often has an upper limit in a particular area, above which SSS is rarely observed. A plausible explanation of this has to do with rainfall, which adds freshwater to the surface ocean, making it stably stratified. Rain events freshen the water for time periods lasting from hours to days (Boutin et al. 2013; Henocq et al. 2010; Asher et al. 2014a). By contrast, the processes that make the surface ocean saltier, mainly evaporation, also make the water column unstable and overturn quickly (Hodges and Fratantoni 2014; Asher et al. 2014b; Yu 2010). Advection can also play a significant role in generating anomalies at both the upper and lower ends of the distribution (e.g., Busecke et al. 2014; Hasson et al. 2014).
The main dataset used to validate Aquarius is Argo floats (Argo 2000). Before the Argo era, it was barely possible to determine a mean, much less try to understand the variability or any extreme values over much of the ocean (Bingham et al. 2002). The new Aquarius dataset has given us the ability to characterize the probability of extreme values of SSS (OBPG 2014). What has not been done is the necessary step of comparing the probability distributions of the Argo and Aquarius datasets to determine whether they come from populations with similar characteristics.
Each salinity product has its advantages and limitations. We use an Aquarius, version 3.0 (V3.0), level 2 data product based on radiation input and deterministic relationships that provides complete global spatial coverage over 7 days. Argo is temporally complete on a 10-day scale but is spatially sparse globally. In addition, there are several sources of uncertainty in Aquarius measurements. The error budget for Aquarius measurements are briefly described in section 2b and further detailed in Lagerloef et al. (2008, 2013). Errors likely exhibit long correlation scales over time, and the error budget allocated for each source of error varies with latitude. There are additional considerations as a result of the retrieval algorithm, including processing biases resulting from contamination by other signals. To fully understand and characterize these processing errors and biases could involve characterization of the Aquarius signal under different versions of the Aquarius data processed in different ways [rain corrected versus not, combined active–passive (CAP) versus non-CAP, V4.0 versus V3.0, etc.]. This is beyond the scope of this manuscript, but it would be an important extension to the work presented here.
Argo floats and Aquarius measure different quantities. Argo measures bulk surface salinity (top 10 m), whereas Aquarius measures skin values (top 1–10 cm). The distinction between bulk and skin values of SSS is an active area of research (Henocq et al. 2010; Boutin et al. 2014; 2013; Santos-Garcia et al. 2014; Tang et al. 2013, 2014b). Most previous Aquarius validation analyses have treated these datasets as directly comparable (Lagerloef et al. 2013; Tang et al. 2014a; Abe and Ebuchi 2014). There are additional considerations due to the retrieval algorithm, including processing biases as a result of contamination by other signals. Fully understanding the difference between the two products is a matter of not only doing a direct point-by-point comparison but deconvolving that comparison from the very different sampling schemes, and the space and time scales inherent in the SSS field itself.
We consider sea surface salinity between 30°S and 30°N latitude from 25 August 2011 to 1 June 2014 to conduct an initial exploration of the physical validation of Aquarius measurements with Argo observations. Diagnostics are compared to calibrate the spatial and temporal agreement of Aquarius and the well-utilized in situ Argo float data. We also considered spatial characteristics and temporal agreement, as well as regional differences by ocean basin and hemisphere. Results are in general agreement with the Aquarius salinity validation analysis (Lagerloef et al. 2013) produced by the Aquarius Science Team based on the V2.0 data. However, we go beyond this by considering the entire probability distribution, especially the lower tails.
Section 2 describes the Aquarius and Argo data used in this paper. It is important to consider the distributional characteristics of salinity across time and space in order to facilitate a full understanding of the complex interactions across the hydrological cycle and global transport of freshwater. Section 3 considers a validation of the distributional characteristics of Aquarius measurements performed with Argo in situ observations, including a seasonal study by hemisphere and ocean basin by means of a comparison of Argo and Aquarius via observations matched across time and space. Section 4 details the temporal trends across eight regions defined within the 30°S and 30°N area of study in order to better describe the differences in seasonal and regional trends. Section 5 considers a comparison of Aquarius and Argo between a dry region and a rainy region. The Salinity Processes in the Upper Ocean Regional Study 1 and 2 (SPURS-1 and SPURS-2, respectively) regions are examined because of both their oceanic and meteorological properties, in order to begin to understand separating the effects of ocean dynamics from local meteorology, as well as because of their general scientific interest. Finally, section 6 provides a discussion of the findings and the important characteristics of salinity for which this paper offers a fuller description.
2. Data
This section details the sources and data processing techniques for the data utilized in this paper.
a. Aquarius data
The Aquarius data used in this paper are the level 2 swath-based data from version 3.0 (OBPG 2014). Files were downloaded from the PO.DAAC Aquarius data archive (http://podaac.jpl.nasa.gov). Data quality for Aquarius decreases rapidly poleward of the 30°S and 30°N latitudes, especially differences between ascending and descending passes (Lagerloef et al. 2013). Therefore, for this study we used only data between 30°S and 30°N, binned and averaged to 1/2° along-track intervals between those latitudes.
The satellite has a 7-day repeat track of 103 orbits or about 15 orbits per day (PO.DAAC 2014). Each orbit has three beams. The final dataset presented here consists of about 144 repeat cycles, each 1 week long, the first 33 months of available Aquarius data, spanning the time period from 25 August 2011 to 1 June 2014. The array generated had salinity values indexed by beam, orbit, ascending/descending state, and latitude/longitude. Each of the orbits defines a set of locations identified by beam number (three beams), repeat track, ascending/descending (two states), and latitude/longitude (120 bins, centered every 1/2° at 29.75°S–29.75°N). For clarity, we call each of these (3 × 144 × 2 × 120 = 103 680) points a node. Each node represents an SSS measurement with a footprint of about 100 km in diameter (PO.DAAC 2014).
The level 2 data were used rather than level 3 gridded data in order to avoid extraneous smoothing tying adjacent nodes to each other, and thus each node time series becomes an independent set of measurements. The initial quality control performed on the Aquarius salinity data for this paper was a gross range check, a check for land proximity, deletion of obviously erroneous values, and a check for valid orbital position. Data with a land fraction greater than 1/2% were removed to avoid spurious measurements due to land surface interaction. Measurements of salinity above 40 or below 20 psu were considered spurious for this analysis and were removed. This minimal truncation removed 85 of the total 3 681 718 available Aquarius measurements, less than 3/1000 of 1% of the total data.
b. Uncertainty sources in Aquarius measurements
There are several sources of uncertainty in Aquarius retrievals, including radiometer noise, antenna pointing error, surface roughness, ionospheric interference, galactic background reflection, and sea surface temperature uncertainty (Lagerloef et al. 2008). Using a triple-point analysis comparing satellite, in situ, and model values, Lagerloef et al. (2013) concluded that the 2.0 version of the Aquarius dataset has a global monthly root-mean-square (RMS) error of 0.3. Preliminary release version 2.7.1 has an RMS value between 0.22 and 0.3 (Tang et al. 2014a). Abe and Ebuchi (2014) compared the V3.0 standard, CAP, and Remote Sensing Systems (RSS) products with collocated Argo floats; they found RMS differences of 0.42, 0.51, and 0.41, respectively. The same calculation using the tropical moored buoy array yielded RMS differences of 0.35, 0.39 and 0.35, respectively.
As Lagerloef et al. (2013) indicate, many of the issues with regard to the quality of the Aquarius SSS product are exacerbated at higher latitudes and closer to coastal regions. We have taken care in this work to avoid such problems by confining the study to equatorward of 30° latitude and in areas away from the coast. Thus, we presume that the Aquarius accuracy for our study is better than the value of 0.3 quoted above, though we cannot say exactly what that value is. In addition, a source of uncertainty in Aquarius measurements includes the deterministic model input for the Hybrid Coordinate Ocean Model data product (PO.DAAC 2014) that is used as starting values in the algorithm for obtaining the Aquarius product.
The main continuing source of error is the reflection of cosmic background radiation from a nonsmooth ocean surface. This manifests itself in quasi-seasonal differences between ascending and descending passes, especially in the Southern Hemisphere. Ascending/descending path bias is much improved in version 3.0 over previous versions (Lagerloef et al. 2015). (Indeed much of the analyses detailed in this paper were performed separately on ascending and descending data with little difference found.) Thus, an ascending/descending path comparison is not a focus of the analyses considered in this paper. Other problems that are under active study are radio frequency interference (RFI) and antenna coupling issues that occur near the ITCZ. Again, however, this level of error is lower than for previous versions of the dataset. In particular, the radiometer calibrations are improving with time.
c. Argo data
We used Argo data (Argo 2000) spanning the time period 25 August 2011–1 June 2014. We used all available profiles in the 30°S–30°N range that had a data quality flag of good, taking the topmost salinity value above 10-m depth. Measurements of salinity above 40 or below 20 psu were considered spurious for this analysis and were removed. This truncation removed 417 of the 90 398 Argo measurements, less than one-half of 1% of the available measurements. SSS measurements from the Argo floats deployed during the SPURS mission in September of 2012 were removed for this validation analysis, so as not to bias overall SSS trends and comparisons with Aquarius. Twenty-four floats were deployed here, in the middle of the high salinity region of the subtropical North Atlantic, which sampled more frequently than other floats for some time. Thus, including the SPURS floats would increase the bias substantially. This masking removed 2381 Argo observations in the time period and region of study. An additional 785 observations were removed due to corresponding invalid pressure readings and/or possible individual float bias.
d. Matching observations
To determine the specific global agreement, Aquarius and Argo observations were matched on a 50-km footprint centered at the latitude and longitude by binned Aquarius measurement. Aquarius and Argo were then matched by calendar date to achieve maximum accuracy across possible mesoscale and microscale surface weather events. This results in N = 41 544 matches across the entire time period and region between 30°N and 30°S latitude.
3. Distributional characteristics
In this section we consider a global comparison as well as a seasonal study by hemisphere and ocean basin. We study the distributional characteristics, including mean and variance, as well as noncentral tendency comparisions across distributional quantiles.
a. Global comparison
We compare the relative agreement of the global distribution of salinity across the entire time period. The global means differ slightly across the two matched products, with the Aquarius global mean equal to 34.93 and the Argo global mean value of 35.10. Note that these are different but comparable to the median (0.50 quantile) values of 34.97 for Aquarius and 35.11 for Argo (Table 1). Additionally, 95% confidence intervals (CI) are calculated for the global means in which the standard deviations are calculated using a bootstrap method (Efron and Tibshirani 1986) to account for the high spatial and temporal dependency in the measurements for both products and the nonrandom sampling scheme inherent in the original data collection. A sensitivity analysis was run on the number of bootstrap replications with R = 1000 bootstrap iterations showing stable estimations. The standard deviations are 0.923 for Aquarius and 0.844 for Argo. This results in 95% confidence intervals for the global means of (34.877, 34.992) and (35.047, 35.151) for Aquarius and Argo, respectively. The confidence intervals for the mean global salinity products do not overlap, which indicates that the global means are significantly different across the two salinity products.
Global salinity quantiles: Argo and Aquarius. For example, the 0.10 quantile indicates the salinity for which 10% of observed values are less and 90% are greater.
To compare the spread of measurements across Aquarius and Argo, confidence intervals for the standard deviations of each product were calculated utilizing the chi-square distribution according to Sheskin (2011). The standard deviations exhibit different properties, with 95% confidence intervals of (0.8861, 0.9692) and (0.8102, 0.8862) for Aquarius and Argo, respectively, with the Argo product showing slightly less global variation. This could indicate lower accuracy of individual Aquarius measurements or could indicate a fundamental difference in the skin versus depth measurement sampling. There is slight overlap in confidence intervals for the global standard deviations, indicating no significant difference in global variation between Aquarius and Argo.
The empirical densities of the matched Argo and Aquarius observations are in relative agreement (Fig. 1); however, Argo shows more fluctuations in the upper tail of the distribution and Aquarius shows a longer, slightly heavier lower tail. To more fully explore the entire SSS distribution, particularly in the tails, we consider an empirical quantile analysis (Table 1). The overall global quantiles for Aquarius and Argo show the same relative trends across the distributions: that is, Aquarius captures a slightly heavier lower tail. This is possibly due to the surface-level measurements afforded by Aquarius, whereas the Argo measurements may have a depth effect. For instance, Aquarius has lower 0.01 and 0.05 quantile values (32.74 and 33.47, respectively) than Argo (33.18 and 33.86, respectively), which indicates that Aquarius has a higher probability of observing low values than Argo. This is also seen at the 0.10 and 0.25 quantile levels. There is also evidence that there is much less of a tendency for the upper tails to differ. This can be seen in the upper quantile levels, where Aquarius has a 0.99 quantile value of 37.43 compared to Argo’s corresponding value of 37.42.
Worldwide comparison of the pdfs for Argo and Aquarius.
Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0068.1
To formally test whether the quantile levels across Aquarius and Argo are statistically different, confidence intervals were constructed for the observed quantile-level point estimates. Under the same assumptions as utilized in the central limit theorem for means, the sampling distribution for quantile values follows a normal distribution (Woodruff 1952) with expected value 
The 95% confidence intervals (
The global quantile trends for the ascending and descending Aquarius tracks are in general agreement with each other and show the same pattern when compared to the Argo quantiles. The Aquarius ascending and descending paths are in general agreement with each other across averages and quantile levels. Thus, for the purposes of this analysis, a path comparison is not furthered considered.
The differences seen across the tails of the Aquarius and Argo distributions raises the question of an effect on measurements due to rain. There is literature building with regard to the rain effect on remotely sensed SSS versus in situ measurements, including Boutin et al. (2014). While not the focus of this manuscript, we briefly considered the relationship of rain with large differences (>5 psu) between Aquarius and Argo. Rain is measured in millimeters per day and is matched in time and space as described in section 2d. Figure 2 shows the locations where the absolute difference between Aquarius and Argo is greater than 5 psu (top) and the corresponding rain in millimeters per day (bottom). While there is not an absolute trend in the large differences between Aquarius and Argo measurements, smaller values are clustered around the equator at 0° longitude in the Atlantic. A cluster is seen in the northwest Pacific as well, with the highest values appear in the South Pacific. In the SSS plot, the lowest negative difference (Aquarius − Argo) in SSS (top right) corresponds to the highest rain amount (55 mm). Another high SSS difference in the Indian Ocean corresponds to a rain value of 29 mm. However, these large differences may have little to do with rainfall, being much more related to mesoscale stirring of the salinity field. This particular location would be subject to it because of the Amazon plume and tropical instability waves. Figure 7 in Boutin et al. (2014) shows a negative trend in the differences of SMOS–Argo with respect to rain. This is in agreement with Fig. 2 here, which shows that in general the high (positive) values of the differences are associated with less rain. It is important to note that a rain event may have occurred before a salinity measurement was taken, or vice versa. Measurements are matched within a day but not necessarily within a 24-h period. An empirical analysis of wind with respect to large SSS differences was also considered but no definitive relationship was seen. There was no apparent spatial relationship, and no changes in the magnitude of SSS difference with regard to the magnitude of the wind effect.
(top) Absolute SSS difference greater than 5 psu for Aquarius–Argo and (bottom) corresponding rain (mm day−1).
Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0068.1
b. Regional ocean basin comparison
The empirical distribution of salinity for the two matched products for the Atlantic, Indian, and Pacific Oceans (Fig. 3) shows relative agreement within ocean basins while also indicating Aquarius more smoothly captures the distribution of salinity. However, there are subtle but important differences in the salinity distributions across ocean basins, particularly in the tails, as showcased in Fig. 3. For instance, in the Indian Ocean basin (right), the Argo distribution indicates essentially zero probability below 33, whereas the Aquarius distribution shows positive probability. Figure 3 shows bimodal peaks in the Atlantic Ocean basin at approximately 36.2 and 37.5, which are not shown in the Aquarius distribution. The Pacific Ocean exhibits slightly less variability, as indicated by the higher peak and tighter spread exhibited in the Aquarius density. Note also that the peaks of the Argo probability distribution functions are lower than those of Aquarius for all basins.
Empirical probability distribution by ocean basin for Argo and Aquarius.
Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0068.1
The means and standard deviations of the distributions of salinity for Aquarius and Argo within an ocean basin are compared in Table 2. The Atlantic Ocean exhibits significantly higher average salinity than both the Indian and Pacific Oceans, indicated by the nonoverlapping 95% confidence intervals. This is consistent across both the Aquarius and Argo products. It is interesting to note that the variation in Aquarius measurements is significantly more than that of Argo in the Pacific Ocean. This is denoted by the nonoverlapping (bold) confidence intervals for σ when comparing a variation within a salinity measurement source and across an ocean basin.
Salinity mean (
The empirical quantile distributions indicate that Aquarius has a longer lower tail than Argo across all ocean basins (Table 3). The lower-tail effect in Aquarius is particularly pronounced in the Indian and Pacific Oceans, where at the 0.01 and 0.05 quantile levels, the SSS values for Aquarius are on the order of 0.5 less than those of Argo.
Argo and Aquarius quantiles by ocean basin for all observations and observations matched in space and time.
The 95% confidence intervals (
Examining the differences in SSS for Aquarius–Argo, 52.3% of the Atlantic differences are positive, with 48.3% of the Pacific differences positive and 38.1% in the Indian Ocean. For the large differences, 107 of the 110 absolute SSS differences greater than 5 psu are positive, including all 47 in the Atlantic.
c. Seasonal comparison by hemisphere
There is general agreement across seasons between Aquarius and Argo (Fig. 4), but the distributions exhibit some important distinctions. There are clear differences in seasonal patterns across the Northern and Southern Hemispheres across both Aquarius and Argo, such as a slightly lower mode of the salinity distribution and a longer upper tail in the Northern Hemisphere (Fig. 4. The higher and tighter peaks of the Argo distributions in spring and winter in both hemispheres (note the hemispheric seasonal definitions) may be due to the larger stratification of the upper ocean layer. A rain event is more likely to mix in during winter and spring as the stratification effect is lessened.
Empirical cumulative distributions: Argo vs Aquarius for the four seasons across the (top) Northern and (bottom) Southern Hemispheres.
Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0068.1
Aquarius and Argo exhibit different central tendencies across each hemisphere and season, with nonoverlapping 95% confidence intervals in all cases (Table 4). Note that the standard deviations were obtained using the bootstrap method to account for the highly correlated measurements, as explained in section 3a. For each season, the average salinity in the Northern Hemisphere is consistently lower than in the Southern Hemisphere. For both products, the difference is statistically significant, indicated by the nonoverlapping 95% confidence bounds across both hemispheres for mean salinity. Table 4 also shows that the variation in the Southern Hemisphere is lower than in the Northern Hemisphere for all four seasons. This is indicated by the significantly smaller values for the standard deviation—the 95% confidence intervals for σ are nonoverlapping across both hemispheres for both products. The standard deviations are typically larger for Aquarius for all seasons across both hemispheres with the exception of winter in the Southern Hemisphere. The significantly different standard deviations across Aquarius and Argo (indicated in bold) yield nonoverlapping 95% confidence intervals for σ for spring and summer in each hemisphere, again indicating that Aquarius and Argo capture SSS variability differently in the Southern Hemisphere in the winter and spring seasons.
Variables 
Examining the empirical quantile distribution in the Northern Hemisphere, Aquarius exhibits a longer tail (Table 5) with lower observed SSS at the lower quantile values, excepting the Northern winter season. The effect reverses in the Northern Hemisphere spring and summer in the upper half of the distribution in the higher quantiles, with Aquarius quantile values slightly higher than the corresponding Argo quantile values. This is illustrated in the cumulative distributions of Fig. 4. The same lower-tail relationship is seen in the Southern Hemisphere. The lower Aquarius quantile values are less than the corresponding Argo quantile values in the lower half of the distribution. This Southern Hemisphere trend continues in the upper half of the distribution, where the Aquarius quantile values are lower than the corresponding Argo quantile values.
Argo and Aquarius quantile by season and hemisphere for matched observations.
The 95% confidence intervals for the 0.01 quantile level of both Aquarius and Argo across all seasons and both hemispheres are constructed. For the single test at one quantile level, a significant difference is observed in the Northern Hemisphere for the fall and spring seasons. This trend is maintained in the more conservative multiple comparison test across the lower three quantile levels—0.01, 0.05, and 0.10—for the fall and spring seasons. In the Southern Hemisphere, only the winter season does not indicate a significant difference in quantile values at the 0.01 quantile levels for Aquarius and Argo. Considering the multiple comparison test, both fall and summer are significant across the 0.01, 0.05, and 0.10 quantile levels. Spring shows a significant difference for the 0.05 and 0.10 quantiles but not the lowest quantile level, 0.01. No significant difference was observed at the higher quantiles levels in the upper tails of the distributions.
4. Temporal and spatial behavior
Dependence, patterns over time, seasonal trends, and tail behavior are all indicative of salinity’s interaction with the global water cycle. They can also lead to important understandings about salinity’s relationship with surface-level meteorological factors and synoptic weather events. We examine how Aquarius and Argo compare across these characteristics.
Temporal trends
Certain regions are of specific interest because they exhibit interesting and possibly unique characteristics due to physical properties of the region. We divide the area of study into eight regions in order to consider a more focused comparison (Fig. 5).
Aquarius SSS for the week of 26 Aug 2011–2 Sep 2011 across the eight defined regions.
Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0068.1
Figure 6 compares the empirical probability densities of the Aquarius and Argo products across the eight defined ocean regions. The Argo empirical distribution tends to have higher and tighter peaks in both hemispheres, with Aquarius capturing the lower tail of SSS more completely in the Southern Hemisphere. This is particularly noticeable in the northwest Pacific and North Atlantic regions, and southwest Pacific and south Atlantic regions, respectively. The north Indian basin is an exception, probably because of its small extent and extreme seasonality (Rao and Sivakumar 2003).
Empirical densities: Argo vs Aquarius for the eight regions displayed in Fig. 5.
Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0068.1
Figure 7 displays the time series of vertical box plots of the distribution of salinity by date for the eight regions. The upper and lower bounds of the vertical boxes in the plots represent the first and third quartiles, respectively, of the salinity distribution at each date. Thus, the dark shaded areas represent the bulk of the distribution. Values beyond 1.5 times the interquartile range (IQR) are seen as dots above and mainly below these dark areas. The box plots for the Aquarius product (Fig. 7, right) capture more variability than the Argo version, especially in the Northern Hemisphere. There are seasonal changes in the distributional characteristics of SSS in the lower tails, while the upper parts of the distributions, as well as the medians, remain relatively constant for all basins (Fig. 7, right column). Each basin has its own distinct seasonality. In the North Pacific [northeast Pacific (NEP) and northwest Pacific (NWP)], the distributions get wider in the fall but are tighter and have more values in the tails in the spring. The south Indian basin is similar in pattern to the northwest Pacific. In the south Atlantic and southeast Pacific, there tends to be a lot of low-lying values in the winter and early spring. The north Indian basin shows a slight increase in the number of lower-tail values in the winter. In the North Atlantic, there is less seasonality exhibited, but there is an increase in the number of low SSS values in the summer. Note that the maxima and upper tails of the SSS distribution over time stay fairly consistent, whereas a seasonal trend can be seen in the lower tails (minima) around November–February of each year, with a few extremes in the summer and fall months in 2011 and 2012. However, the minima shows seasonal effects particularly in the North Pacific and southeast Pacific winter months, with smaller magnitude seen in winter and spring in the Atlantic.
Salinity distribution over time for the eight regions: (left) Argo and (right) Aquarius. Note that the psu scales (vertical axis) are different across spatial regions but are identical within regions to enable comparison between Aquarius and Argo. The upper and lower bounds of the vertical boxes in the plots represent the first and third quartiles, respectively, of the salinity distribution at each date. Values beyond 1.5 times the IQR are shown as dots.
Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0068.1
The box plot time series for the Argo product (Fig. 7, left column) largely displays little of the seasonality exhibited in Aquarius, with the exception of slight winter trends shown in the Pacific regions. In all regions, Aquarius captures more variability—especially in the Northern Hemisphere.
5. Comparing SPURS regions
Given the possible dependence of the SSS distribution on rainfall, we compare distributions in two regions associated with SSS field campaigns: the sites of SPURS-1 in the subtropical North Atlantic (15°–30°N, 30°–45°W; Lindstrom et al. 2015) and SPURS-2 in the tropical eastern Pacific (0°–10°N, 120°–130°W; Schmitt et al. 2015). These sites represent evaporation-dominated and rainfall-dominated areas, respectively. SPURS-1 was carried out in 2012/13 and SPURS-2 is anticipated to take place in 2016/17. The SPURS-1 region is one of high SSS, relatively low variability, weak seasonality, and stable forcing (Bingham et al. 2014; D’Addezio and Bingham 2014). The SPURS-2 region has lower SSS and very strong seasonality in both SSS (Bingham et al. 2012; Bingham et al. 2010) and rainfall (Waliser and Gauthier, 1993).
Table 6 compares the means and standard deviations for the two SPURS regions, calculated as in section 3a using a bootstrap sample of R = 200 to account for the smaller N. In both regions, Aquarius’s mean SSS is below that of Argo’s, although the difference is only significant in the SPURS-2 region. The increased trend in Aquarius’s variation over Argo previously observed is exhibited as well, and the standard deviations are significantly different across the SPURS-1 region.
Variables 
Figure 8 displays the times series of vertical box plots of the distribution of salinity by date for the SPURS regions. The results show Aquarius capturing more of the tails of the distribution, especially in the lower tails. Seasonal trends are more pronounced in the Aquarius box plots for both regions, particularly in the SPURS-2 regions where Aquarius captures more low-lying SSS values.
Salinity distribution over time for the SPURS regions: (left) Argo and (right) Aquarius. Note that the psu scales (vertical axis) are as in Fig. 7. The upper and lower bounds of the vertical boxes in the plots represent the first and third quartiles, respectively, of the salinity distribution at each date. Values beyond 1.5 times the IQR are shown as dots.
Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0068.1
The empirical cumulative distributions by season (Fig. 9; Table 7) indicate much stronger agreement between Argo and Aquarius in the SPURS-2 region than SPURS-1. In both regions the lower tail is fatter for the Aquarius data as we have found in previous sections, especially at the 0.10 quantile. However, in the SPURS-1 region, this difference extends well up to about the 0.75 quantile. In the SPURS-2 region, the distributions agree reasonably well at the center, with the exception of the summer. This result is different from what might be expected if the lower tails of the distributions are driven entirely by rainfall. This seems to suggest that Aquarius’s heavier lower tail is a result of not only very shallow surface rain puddles but also of the presence or absence of winds to mix those puddles rapidly down into the bulk mixed layer. The SPURS-1 region is not without rainfall, especially in the fall (D’Addezio and Bingham 2014), but the SPURS-2 region is much windier than SPURS-1.
Empirical cumulative distributions: (top) SPURS-1 and (bottom) SPURS-2 regions.
Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0068.1
SPURS regions by seasons.
6. Discussion
Throughout this paper it has consistently been seen that the probability distribution of Aquarius has longer, thicker tails and shorter central peaks than Argo (Figs. 1, 3, and 6). The longer tails are especially apparent in the lower portion of the distribution (Fig. 6). As stated above, this could be either due to the lower accuracy of Aquarius or the better ability of Aquarius to capture tail events. The second explanation seems more likely and plausible, however, as evidenced by the box plots of Fig. 7. This is a good sign for the future use of Aquarius data. While Argo can tell us about the mean SSS, Aquarius gives us much more information about the variability. As this variability is the result of events that may modify SSS, such as rainfall, evaporation, horizontal mixing, and upwelling, Aquarius can tell us where and when these processes are occurring: that is, Aquarius can actually begin to fulfill its mission as an ocean rain gauge (Lagerloef et al. 2008; Grunseich et al. 2013).
All of this assumes that Aquarius is accurately measuring values at the tails of the distribution. There are two retrieval issues that could cause an enhancement of lower-tail values: RFI and land contamination. We screened out land values higher than 0.5% so that should not be an issue. Also, we would not see the clear seasonality in Fig. 7 if low values were caused by land contamination. Though RFI is an issue, the lower values are present in both the SPURS-1 and SPURS-2 results. Both of these areas are far from known sources of RFI (Lagerloef et al. 2013). The Aquarius retrieval algorithm is also known to be sensitive to sea state and rain rate (Lagerloef et al. 2008). Tang et al. (2014b) in comparing the rain-corrected CAP version of the Aquarius data with the HYCOM model found there was little systematic difference between Aquarius and HYCOM as a function of rain rate or wind speed (see Fig. 4b in Tang et al. 2014b). We assume similar behavior from the non-CAP, rain-corrected version of Aquarius used in this paper. The results of this paper emphasize the need for an alternative validation dataset that measures the near-skin-surface SSS under calm conditions.
Assuming there are no issues with the retrieval algorithm, the clear result of this paper is that Aquarius captures tail variability in a way not previously seen. Another way of saying this is that tail variability is large and important enough to have an impact on the SSS field at the scale of the Aquarius footprint. Low-salinity events, regardless of their nature or how they originated, can affect the average SSS over a larger area. These events are not captured well by the Argo array. The most likely explanation is that such events are strongly confined to the near-surface, above the sampling depth of standard Argo floats (Asher et al. 2014b; Boutin et al. 2014; Tang et al. 2014b; Henocq et al. 2010). However, the relationship between rainfall and low-salinity outliers is not simple, as illustrated by the comparison between the SPURS-1 and -2 regions. To fulfill the Aquarius mission as an ocean rain gauge, we will need to use the lower tail of the SSS distribution, but with an understanding of the spatial scale of low-salinity events and how they may be related to wind and evaporation (Meissner et al. 2014b). Using the lower tail, we may be able to separate the effects of ocean dynamics from local meteorology.
A real understanding of the probability distribution of SSS, the space and time scales of its variations, and its connection to processes like surface forcing, ocean mixing, and stirring, and upwelling/downwelling, awaits future researchers. Characteristics such as those depicted in Figs. 8 and 9 are a beginning to that process. What seems most evident from the results of this paper, though, is that the key to this connection lies in the tails of the distribution, especially the lower tail. The low-probability events that the Aquarius satellite is able to capture shine a light on the events that define the hydrologic cycle and the global transport of freshwater that will play a crucial role in the future of a warming planet.
Acknowledgments
Elizabeth Mannshardt was supported as a postdoctoral research scholar through the National Science Foundation’s Collaborative Research: RNMS Statistical Methods for Atmospheric and Oceanic Sciences under Grant DMS-1107046. Frederick Bingham and Katarina Sucic were funded by NASA under Grants NNX09AU70G and NNX11AE83G. We thank two anonymous reviewers for their constructive comments, which helped improve the manuscript.
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