JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS, VOL. 118, 3190–3201, doi:10.1002/jgrc.20200, 2013
Clarifying the link between surface salinity and freshwater fluxes on monthly to interannual time scales Nadya T. Vinogradova1 and Rui M. Ponte1 Received 2 January 2013; revised 11 April 2013; accepted 16 April 2013.; published 27 June 2013.
[1] Freshwater fluxes (F ) between the ocean and the atmosphere and land, comprised of evaporation, precipitation and terrestrial runoff, are an essential component of the Earth’s climate system. However, direct observations of F and its components are sparse and available estimates have substantial uncertainties. In this study we investigate if measurements of sea-surface salinity (S) can provide an alternative indirect method for estimating F . We examine the relationship between S, F and oceanic fluxes from surface advection and mixing processes, on time scales from months to years, using a consistent estimate of the ocean/atmosphere state obtained from model/data synthesis produced by the ECCO (Estimating Circulation and Climate of the Ocean) consortium. ECCO salinity averaged over the mixed layer is used as an estimate of S. Budget analysis shows that variability in S tendencies can be attributed to both F and oceanic fluxes, demonstrating the importance of the ocean’s role in evolution of S, for both local and global mean fields. Regression analysis of the 13 year long ECCO fields shows that there are only a few regions (e.g., subtropical gyres) where S can be used as a proxy for F using linear models, and only at monthly to annual time scales. Results are similar over a range of spatial scales from 100 to 2000 km. Findings are discussed in the context of the general sensitivities of S to atmospheric and oceanic processes and the potential of satellite salinity measurements to constrain estimates of F . Citation: Vinogradova, N. T., and R. M. Ponte (2013), Clarifying the link between surface salinity and freshwater fluxes on monthly to interannual time scales, J. Geophys. Res. Oceans, 118, 3190–3201, doi:10.1002/jgrc.20200.
1.
Introduction
[2] A key variable in understanding the global hydrological cycle is the amount of freshwater leaving or entering the ocean via the physical processes of evaporation (E), precipitation (P) and terrestrial runoff (R). The resulting ocean surface freshwater flux F ¼ E P R comprises 80% of the Earth’s total surface water flux (see, e.g., Durack et al. [2012] for a schematic summarizing relative contribution of each component) but is very difficult to measure directly and it is often estimated either from other ocean and atmospheric variables, including direct bulk-formula calculations of E [e.g., Jourdan et al., 1997; Sohn et al., 2004; Andersson et al., 2010] and atmospheric reanalysis products [e.g., Kalnay et al., 1996; Gibson et al., 1997; Schanze et al. 2010], or through ocean inverse calculations based on the divergence of ocean freshwater transports [e.g., Wijffels et al., 1992; Ganachaud and Wunsch, 2003; Stammer et al., 2004; Talley, 2008; Romanova et al., 2010]. 1 Atmospheric and Environmental Research Inc. (AER), Lexington, Massachusetts, USA.
Corresponding author: N. T. Vinogradova, Atmospheric and Environmental Research Inc. (AER), 131 Hartwell Ave., Lexington, MA 02421, USA. (
[email protected])
©2013. American Geophysical Union. All Rights Reserved. 2169-9275/13/10.1002/jgrc.20200
Despite continuous progress, including maturation of microwave measurements of precipitation and latent heat flux [e.g., Kummerow et al., 2000], uncertainties in water vapor transports remain large and the estimates of air-sea flux show significant deficiencies [e.g., Smith et al., 2001; Grist and Josey, 2003; Stammer et al., 2004; Beranger et al., 2006; Yu and Weller, 2007; Schanze et al., 2010]. [3] Because transport of freshwater in and out of the ocean can cause changes in ocean salinity, an increasing number of studies suggest that variations in salinity can provide an alternative approach to estimate F [e.g., Lagerloef et al., 2010; Hosoda et al., 2009; Helm et al., 2010; Bingham et al., 2012; Yu 2011; Durack et al. 2012]. The results of these studies show that depending on location, temporal and spatial scales, changes in salinity can be potentially used as ocean indicator of the water cycle, including its amplification due to human forcing of the climate system [Stott et al., 2008; Terray et al., 2012; Pierce et al., 2012; Durack et al., 2012]. For example, Yu [2011] shows that at seasonal time scales, a high level of covariance is expected between the satellite-derived estimates of E – P and the tendency in the mixed-layer climatological salinity in the Inter-Tropical Convergence Zone (ITCZ), South Pacific Convergence Zone (SPCZ) and the western North Pacific. Although an exact linkage between the mixed-layer salinity and F was not proposed, Yu [2011] concludes that the regions with E – P dominant regime provide an ‘‘opportunity for testing the ocean rain gauge
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concept’’. Another study by Bingham et al. [2012] uses harmonic analysis to infer annual cycle in F from in situ salinity measurements based on Argo, TAO (Tropical Atmosphere-Ocean) buoys, etc. The relationship is sought in a form of a simple balance between near-surface salinity and surface flux of freshwater, without explicit inclusion of the ocean fluxes due to advection, mixing and entrainment. Their results showed that seasonal cycles in near-surface salinity and F compare reasonably well, although with some differences in amplitude and shifts in phase. Helm et al. [2010] derived zonally averaged time mean freshwater fluxes by vertically integrating salinity changes, computed from full-depth World Ocean Circulation Experiment (WOCE) and Argo observations under the assumptions that first-order freshwater differences are due to E – P changes. Based on the qualitative agreement between the derived flux values and those obtained from coupled climate models that are used by the Intergovernmental Panel on Climate Change (IPCC), Helm et al. [2011] suggest a strong possibility of inferring the changes in the hydrological cycle (in that case, acceleration) from the observed salinity changes on large spatial (zonally averaged) and long (20þ years) temporal scales. [4] Durack et al. [2012] examines the link between the sea surface salinity and F at longer temporal scales. In their analysis, they demonstrate a strong link between the long-term (50 year) rates of change in basin-averaged seasurface salinity and E – P fluxes in simulations performed as part of the Coupled Model Intercomparison Project (Phase 3). In particular, both salinity-based and E – P multidecadal linear trends suggest an intensification of the global water cycle, supporting similar reports by Stott et al. [2008], Hosoda et al. [2009], Helm et al. [2011], Pierce et al. [2012], and Terray et al. [2012]. Specifically, these studies demonstrate that the detected changes in zonally averaged [Pierce et al., 2012], basin-averaged [Terray et al., 2012] and regional (e.g., Atlantic Ocean, Stott et al. [2008]) multidecadal (30–50 years) linear trends of the upper-ocean salinity are consistent with those expected from human effects on the climate and can improve our understanding of the response of the climate system to anthropogenic CO2 forcing. [5] Motivated by this previous work, in this study we investigate the link between sea-surface salinity (S) and F . One of the objectives is to assess how measurements of S can be used as a direct proxy for F on time scales from months to years. In particular, we are examining the possibility of a linear relationship between S and F . In case of linearity, one can infer the changes in freshwater content from salinity changes using a simple regression and a simple scaling of the salinity difference will be representative of the amount of freshwater added/subtracted into the ocean during the period of interest. The problem is particularly relevant in light of the two salinity remote sensing missions, namely Soil Moisture and Ocean Salinity (SMOS) launched on 9 November 2009 [Font et al., 2010] and Aquarius/SAC-D launched on 9 June 2011 [Lagerloef et al., 2008]. The spaceborn L-band microwave radiometers measure polarized brightness temperature, which can be related to salinity in the first centimeter of the ocean through the dielectric constant of sea water [Font et al., 2010]. The resulting salinity maps have near-global coverage and targeted accuracy of 0.2 practical salinity scale of 1978 (PSS-78) for both Aquar-
ius and SMOS monthly fields [Boutin et al., 2012] and can provide a useful tool in our understanding of the variability and change in the global hydrological cycle [Berger et al., 2002; Lagerloef et al., 2008, 2010]. [6] The relation between F and changes in S is quantified by the salt budget, which states that the salinity tendency (S 0 ) is governed by both F , comprised of E, P, and R, and oceanic fluxes (O) and can be written symbolically as: S 0 ¼ F þ O: 0
ð1Þ
[7] Any differences between S and F can be attributed to ocean processes, such as advection and mixing. Therefore, to understand the link between S 0 and F and to describe the nature of S 0 variations, it is useful to look at the salinity budget. Existing salinity budget studies are typically dedicated to the tropical oceans [e.g., Foltz et al., 2004; Cronin and McPhaden, 1998]. There are also a few that include high latitudes [e.g., Bingham et al., 2010; Ren and Riser, 2009; Ren et al., 2011], subtropics [e.g., Qu et al., 2011] and near-global studies [Bingham et al., 2012; Yu, 2011]. Most of the studies on budget analysis are typically done using an observational approach. And while many satellite-derived and in situ data sets are now available, they are still insufficient to resolve all processes governing the evolution of salinity (e.g., mixing, mixed-layer variations, etc.). Thus, the closure of salinity budget, a prerequisite to evaluate relative contribution of each term, is not guaranteed and can be difficult to achieve using observations alone. For example, Yu [2011] points out a large imbalance in the databased mixed-layer budget analysis, with the right-hand side of the equation explaining only 40% of seasonal variance of the mixed-layer salinity. [8] An alternative approach to examine salinity budget is based on the output of ocean general circulation models. Model-based estimates satisfy local and global budget closure exactly, provided careful consideration of model numerics and parameterizations [e.g., Campin et al., 2004; Kim et al., 2006]. Relatively few studies have used consistent formulation of the model-based salinity budget, particularly for the mixed-layer salinity. Those that have tend to focus on either a specific region and/or time scale [e.g., Qu et al. 2011]. Thus, a more comprehensive, global look at closed salinity budgets across a range of time scales is needed. Here salinity equation entailed in (1) is examined using an ocean state estimate produced by the ECCO (Estimating Circulation and Climate of the Ocean) consortium [Wunsch et al., 2007, 2009]. The ECCO solution combines oceanographic observations, along with suitable error estimates, with a general circulation model and attempts constrained estimation of the full four dimensional (time and space) oceanic state. The solution provides a dynamical description of the salinity variability, consistent with the known uncertainties in the data and the model physics. [9] The major strength of our method is that all our analyses are performed within a dynamically consistent framework, which provides closed budget estimates of S and respective atmospheric and oceanic fluxes, without introducing arbitrary sources or sinks of freshwater. The latter ensures accurate differentiation between regimes where O may play an important role in the evolution of S, and those where the changes in S are dominated by F . And in particular, it allows careful evaluation of the relationship
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between S and F and the potential of surface observations to constrain F and the global hydrological cycle.
2.
An Ocean State Estimate
[10] The ECCO solutions described in Wunsch et al. [2007, 2009] synthesize all the information available in the surface forcing fluxes, satellite and in situ ocean observations such as altimetric sea level fields, mean geoid from the Gravity Recovery and Climate Experiment (GRACE), satellite-based sea-surface temperature, scatterometer winds, hydrographic climatologies, etc., as well as the physical constraints, dynamics and conservation statements that are embedded in the equations of the MIT (Massachusetts Institute of Technology) general circulation model [Marshall et al., 1997; Adcroft et al., 2002]. The model is fit in a least-square sense to the entire data set involving more than 109 oceanic and meteorological observations [see, Wunsch et al., 2007, Table 1], each weighted according to estimated data and model errors. During optimization, air-sea fluxes (including F ) are adjusted to bring the model into consistency with all data within observational uncertainty. The result of ECCO optimization is an ocean state that is dynamically consistent with the model equations and all the forcing fields. [11] For the solution used here, adjustments are performed on the initial surface fluxes of momentum, heat and freshwater from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/ NCAR) reanalysis [Kalnay et al., 1996] over the globe during a 13 year period from 1992 to 2004. For detailed comparison between optimized and nonoptimized surface fluxes, as well as validation of ECCO fluxes against independent estimates in the context of a different ECCO solution, see Stammer et al. [2004]. Note that the runoff component of the flux (R) is included as a time-mean of the discharge rates and does not have a time-varying component, thus not resolving melting signatures. The solution used here (version 2 iteration 216 described in Wunsch et al. [2007]) is defined on a near-global (80 S–80 N) regular 1 1 grid with 23 vertical levels and does not include Arctic Ocean. The results are diagnosed as monthly averages. Appendix A and previous discussions by Wunsch and Heimbach [2006] and Wunsch et al. [2007, 2009] have more details on the optimization methods and solution characteristics. [12] As an estimate of surface salinity we use ECCO salinity fields averaged over the ocean’s mixed-layer. Thus, unless noted otherwise, in the rest of the paper S will refer to the mixed-layer salinity and S 0 to the mixed-layer salinity tendency. The depth of the mixed layer is diagnosed from the ECCO solution using a so-called ‘‘density criterion’’ that defines the base of the mixed layer as the depth at which the density is larger than that at the surface by 0.125 kg m3 [Kim et al., 2006]. As an alternative proxy for surface salinity, the output of the ECCO uppermost (10 m) model layer was also considered. However, the difference in salinity variations between the mixed-layer and 10 m averages is small, with 10 m salinity explaining about 98% of the variance of the mixed-layer salinity at annual, subannual and interannual time scales. Thus, the relationship between S 0 and F is not strongly dependent on whether one uses 10 m average or mixed-layer salinity. In contrast, oceanic fluxes
can be sensitive to the choice of layer, and to avoid the overly dominant role of vertical mixing and advection when using fixed-depth layer budgets [e.g., Alexander et al., 2000; Kim et al., 2006; Qu et al., 2011], we follow the practice of these and other previous studies and preference is given to mixed-layer budget analysis. [13] In any case, the relationship between the salinity averaged over the mixed layer or the top few meters, as typically estimated by models, and in the top centimeter, as measured from space, is not well documented, and is likely dependent on atmospheric and oceanic conditions (e.g., large rainfall), oceanic fluxes (e.g., strong mixing), definition of the mixed-layer, etc., as well as on location and temporal and spatial scales. Thus, while mixed-layer budgets provide an appropriate framework to describe surface processes, the derived relationship between mixed-layer salinity and F may be different from that based on salinity as would be measured from space. [14] ECCO estimates are routinely validated, with model/data misfits (as root-mean-square (RMS) and weighted RMS) available through web-based displays [Wunsch and Heimbach, 2007; see also http://www.eccogroup.org/). The solutions are close to the available data within a priori estimate of the data noise, including salinity data sets from Argo floats, WOCE and hydrographic climatologies. As an example, Figures 1a–1f compare time mean and standard deviation of S from ECCO solution with those based on Argo, as well with the estimates of surface (‘‘0 m’’) salinity from the World Ocean Atlas (WOA) 2005 products [Antonov et al., 2006]. The choice of not averaging WOA05 salinity over the mixed layer is deliberate and can be used as a crude measure of how well ECCO mixed-layer salinity approximates ‘‘surface’’ salinity. Climatological mean freshwater fluxes (Figure 1g) and its standard deviation (Figure 1h) are computed from monthly objectively analyzed fields provided by NOAA/NODC. The time mean and standard deviation of ECCO salinity fields (Figures 1a and 1b) and Argo fields (Figures 1c and 1d) correspond to a 10 year period 1995–2004. Notice, however, that there were only a few data points in the 1990s with Argo becoming active after 2002, as seen by the areas with no values plotted. [15] Large-scale mean patterns in S are reproduced quantitatively in the ECCO solution, including low-salinity tropical regions, high-salinity subtropical and trade wind regions, Arabian and Mediterranean Seas, and gradual decrease in S toward higher latitudes. Standard deviations in ECCO are also comparable with those in Argo and WOA05, including enhanced variability in the tropics, northern Indian Ocean, Indo-Pacific archipelago and regions affected by the outflows of major rivers. The most noticeable differences between the standard deviation of ECCO and WOA05 fields are found in the northern high latitudes, with ECCO displaying weaker variability compared to climatological values, most likely due to absence of the explicit sea-ice simulation in the ECCO configuration analyzed here. (We note that the most recent ECCO solutions now include active sea-ice calculations.) Nevertheless, global patterns in ECCO solution compare well with known S signatures [e.g., Boyer and Levitus, 2002 ; Stammer et al., 2004 ; Boyer et al., 2009 ; Romanova et al., 2010], including those displayed by Argo and WOA05 fields in Figure 1.
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Figure 1. Time mean and standard deviation of (g and h) freshwater flux and surface salinity estimated from (a and b) an optimized ECCO solution, (c and d) ARGO data, and (e and f) WOA05. Positive flux values indicate the loss of freshwater by the ocean. ARGO and ECCO salinity (referred to as S in the text) are based on salinity values averaged over the mixed-layer depth, which was estimated by the ECCO solution. WOA05 salinity is based on the objectively analyzed fields at the ‘‘surface’’ and is provided by NOAA/ NODC. [16] Figures 1g and 1h also show time mean and standard deviation in ECCO estimates of F . Positive values of F indicate net loss of freshwater by the ocean. As seen from
Figure 1e, loss of freshwater typically occurs over the eastern parts of all subtropical gyres, which roughly correspond to the regions of salinity maxima. Notice characteristic
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VINOGRADOVA AND PONTE: SURFACE SALINITY AND FRESHWATER FLUX
Figure 2. Local S budget as a function of time scale at subannual (12 months). The terms of the budget represent total salinity tendency (S 0 ), tendency due to freshwater flux E P R (F ), tendency due to sum of advective (A), diffusive (M) and entrainment (E) fluxes (O=A+M+E), salt fluxes, in terms of respective standard deviations at sub/interannual time scales and amplitude of the annual harmonic at the annual time scale. Units are PSS-78 mo1. asymmetry in freshwater loss between the hemispheres, with E dominating larger area in the Southern Hemisphere than in the Northern Hemisphere. The patterns in freshwater loss in the Atlantic, Pacific, and Indian Ocean show a lot of similarities, with extreme loss occurring around 20 N and 10 S in all oceans, except the South Indian Ocean where the maximum is slightly shifted toward 20 S. [17] Oceanic gain in freshwater (i.e., net precipitation) is found in the tropical convergence zones, several coastal regions, particularly near the outflows of major rivers, and in the Southern Ocean, particularly along the path of the Antarctic Circumpolar Current. Such areas are also characterized by low-salinity surface waters. Similar to S, ECCO F patterns display many of the large-scale features discussed in earlier studies [e.g., DaSilva et al., 1994a; Stammer et al., 2004]. More important for our study is dynamical consistency between S and F . The optimization ensures the ‘‘best’’ (optimal) correspondence between S and F without introducing any arbitrary sources or sinks of freshwater. The latter guarantees that the salinity budget closes exactly and ensures physically realistic relationship between S 0 and F .
3.
Salinity Budget
[18] The salinity in the mixed layer evolves according to the conservation equation (1), where oceanic term O includes the tendencies due to advective (A), mixing (M) and entrainment (E) fluxes of salt O ¼ A þ M þ E:
ð2Þ
[19] The definition of each term and details on budget formulation are provided in Appendix A. All terms in (1)
and (2) are computed at the model’s integration time step (1 hour) and diagnosed as monthly averages. Following formulation for entrainment developed by Kim et al. [2006], the salinity budget closes exactly within numerical accuracy of the solution. [20] Figures 2 and 3 examine variability of budget terms at subannual, annual and interannual time scales. Annual variability is analyzed using the amplitude of the mean annual cycle, which is computed by averaging fields corresponding to the months of January, February, etc. into a 12 month mean time series and then calculating its annual harmonic. Interannual and subannual variability is computed as the standard deviation of monthly series obtained by removing the annual cycle and then applying a low/highpass filter to remove anomalies at periods shorter/longer than 12 months. Comparing the variability in the various terms in (1) and (2) provides an assessment of their relative importance in the salinity budget. [21] Figure 2 shows that vast portions of the world ocean have weak variability, with standard deviations in S 0 , F and O being typically 12 months. Each row displays the values of linear fit (Figures 4a and 4d), correlation coefficient r between F and S 0 (Figures 4b and 4e) and the percentage of ECCO variance in F explained by the salinity-derived flux F S , (Figures 4c and 4f). Only values for which correlations are significant at 95% confidence level are shown. 3195
VINOGRADOVA AND PONTE: SURFACE SALINITY AND FRESHWATER FLUX
cies ‘‘explaining only about 40% of seasonal variances of the mixed-layer salinity over the global ocean’’ [Yu, 2011].
4. Deriving Freshwater Flux from Salinity Changes
Figure 5. Correlation coefficient between O and F at periods 12 months.
regions can be influenced by F induced by outflows of major rivers (e.g., Amazon, Congo, Ganges), as well as advection and mixing processes within regions of strong S gradients in western boundary currents. [24] The seasonal variability of the ECCO salinity budget is in general agreement with other model-based studies [e.g., Hasson et al., 2013]. For example, similar to ECCO solution, NEMO-based estimates in the tropical Pacific suggest a complicated balance between F and O tendencies, with ‘‘all terms being of analogous importance’’ [Hasson et al., 2013]. ECCO-based seasonal budget is also in qualitative agreement with the data-derived estimates by Yu [2011]. Figures 5 and 6 of Yu [2011] show the standard deviation of the seasonal tendencies derived from various satellite products. For direct comparison with the values of standard deviation, the values of the annualpamplitudes in ffiffiffi our Figures 2d and 2f should be divided by 2. The resulting tendencies S 0 in both ECCO (Figure 2d) and Yu’s estimates [Yu, 2011, Figure 6a] show large seasonal variability in the tropical oceans and along strong ocean currents, and weak variability in the subtropics and high latitudes. In the western boundary current regions, ECCO tends to show weaker seasonal variability and the features are less pronounced (e.g., Kuroshio extension, Gulf Stream). Seasonal changes in F based on ECCO (Figure 2e) and Yu’s [Yu, 2011, Figure 5f] estimates show similarities in major patterns and ranges, but also some differences in detail. For example, both estimates indicate large seasonal variability occurring in the tropical oceans and in the regions of strong ocean currents. However, ECCO shows a smaller magnitude of seasonal variability in F in the eastern Pacific warm pool and tropical north Atlantic, but slightly larger magnitudes in the Indian Ocean and Kuroshio Extension regions. Note that both Figure 2e and Yu’s Figure 5f are displaying seasonal variability of the ‘‘effective’’ forcing, which is obtained by scaling F by the mixed-layer depth (h) and average salinity ½S : F ½S =h. Uncertainties in h in both ECCO and data-derived estimates, as well as the uncertainties between the respective flux fields can contribute to the differences between the forcing tendencies [e.g., Chaudhuri et al., 2013]. Differences in other budget terms can be also attributed to substantial imbalances in databased budget formulation, with combined O and F tenden-
[25] Results in the previous section indicate that one should not expect a general one-to-one correspondence between S 0 and F , given the non-negligible effects of O in the S budget described by (1). Here we examine whether S 0 can still be used to diagnose F , even in the presence of O effects. [26] According to (1), the ability to express F in terms of S 0 will depend on how well O can be parameterized as a function of F . Such correlation can be expected, for example, in regions of strong influence of F on various O terms such as mixed-layer dynamics [e.g., Murtugudde and Busalaccchi, 1998] or intensity of surface currents [e.g., Han et al., 2001]. We consider the simple case of O being linearly dependent on F : O ¼ F þ "O ;
ð3Þ
where is linear fit parameter and "O is noise. Substituting O in (1) and defining ¼ 1=ð1 þ Þ yields : F ¼ S 0 þ " ¼ F S þ ";
ð4Þ
where " are residuals between the salinity-derived flux F S ¼ S 0 and the ‘‘true’’ flux F . Linear parameter in (4) can be determined by regressing F against S 0 at each grid point. To simplify the analysis, the offset is set to zero by removing the time mean from both series of F and S 0 . [27] Figure 4 displays the values of for the case of seasonal (monthly to annual) and longer (interannual) time scales. Also shown in Figure 4 are the correlation coefficient r between F and S 0 and the percentage of the ‘‘true’’ (ECCO) variance in F explained by the salinity-derived flux values F S , calculated as ¼
2 ðF Þ 2 ðF F S Þ 100%: 2 ðF Þ
ð5Þ
For the linear model to be adequate, we expect 6¼ 0, jrj 1 and 1, i.e., small residual variance compared to the true variability. [28] From Figure 4, the linear relation at interannual time scales is weak or nonexistent in most of the ocean, with F S explaining less than 30% of the variance of F almost everywhere. The lack of a strong linear relationship at these time scales reflects in part the generally weak correlation between F and S 0 (Figure 4) and indicates that the relatively strong variability in O, seen in Figure 2, is poorly correlated with F (not shown). At interannual time scales, it is plausible that important advection contributions to O (Figure 2) are primarily remotely driven and thus weakly correlated with local forcing including F . [29] At annual and shorter periods, a strong linear relationship between S 0 and F (r > 0:8, > 80%) is found in several regions away from the equator and coasts, including subtropical gyres in the South Pacific and North and South Atlantic (30 N and 30 S). The correspondence between
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Figure 6. (a) Global-mean budget of the mixed-layer salinity showing total changes in salinity averaged over the global ocean (S 0 ) and its tendency due to surface fluxes (F ) and ocean fluxes (O). (b) Tendencies in globalmean mixed-layer salinity due to advection (A), mixing (M), and the entrainment of salt (E). (c) Mean annual cycle of the global-average budget terms. (d) Salinity-derived values of F S inferred using linear model (black) and the observed (ECCO) values of the flux F (red) with the mean annual cycle removed.
O and F is also strong here (r 1 and > 80% in Figure 5), suggesting that F can be inferred from S 0 using linear model reasonably well. Notice, however, that the strong linear relationship is typically found in the areas of weak S 0 variations with monthly changes less than 0.2 PSS-78. As the targeted measurement error for monthly satellite retrievals is 0.2 PSS-78, poor signal-to-noise ratios can become a problem and inferring meaningful values of F from the data can be difficult in practice.
[30] As expected from the importance of O contributions at subannual scales, in the regions where S 0 and F are well correlated, values of are not necessarily equal to 1 (Figure 4a). Typically, 0 < < 1 (e.g., in the subtropical gyre regions), with a few regions with < 0 (e.g., off the west coast of Australia) and > 1 (e.g., off the coast of Chile, Gulf of Mexico, near Madagascar). The values of reflect positive or negative correlations between F and O through their dependence on . Results in Figure 5 indicate
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that over most regions F and O tend to be positively correlated, contributing together to either freshening or salinization at a given location, and thus yielding 0 < < 1. [31] Correlations between F and O presented in Figure 5 can be useful when examining the S 0 -F -relationship in the areas with large contribution of O. For example, in the subtropical gyres variability in O is comparable to or larger than that in F , as seen in Figure 2 [see also, Yu, 2011, Figure 9]. However, as long as O can be parameterized in terms of F as in (3), which seems to be the case at least for annual and shorter time scales, the importance of O does not preclude a meaningful linear regression between S 0 and F . Conversely, areas with F variability larger than O only suggest a possibility of linear relationship between S 0 and F , but does not guarantee it. For example, as seen in Figure 2, in some tropical ITCZ regions variability in F is larger than that in O [see also, Yu, 2011, Figures 9 and 7]. However, the relation between F and O is complex and a simple regression model like (4) is not found useful. [32] Results discussed so far are based on analyses done on the ECCO grid (1 1 ). Examining the relation between F and S 0 on larger spatial scales (2000 km) did not lead to substantially different results. The dependence on spatial scale was explored by meshing the globe with 20 20 boxes and computing volume-averaged values of the budget terms in (1) within each such region (not shown). On these larger scales, correlations between S 0 and F are weaker than those based on 1 1 boxes, with the variance explained by F S decreasing by up to 30%. As suggested by a reviewer, the sensitivity to spatial scales was also examined by looking at zonally integrated properties. Zonally averaged ECCO annual means of F were found similar to other published estimates of freshwater flux [e.g., Stammer et al., 2004; Lagerloef et al., 2010]. However, zonally averaged values of F are mostly balanced by those of O with S 0 emerging as a relatively small residual, which leads to a noisy relationship between F and S 0 when monthly to interannual scales are considered. Given recent evidence of strong correspondence between modeled basin-average multidecadal (50 year) trends in F and S 0 [e.g., Durack et al., 2012], this result suggests that the relationship between F and S 0 is very sensitive to the time scales considered. In particular, weak link between S 0 and F at relatively short time scales discussed here (monthly to interannual) can become stronger toward longer time scales (decadal and multidecadal).
5.
Analysis of Global Mean Fields
[33] Considering the importance of the net freshwater flux into (out of) the ocean and its crucial role in understanding the global hydrological cycle, we examine the relationship between globally averaged F , O and S 0 fields. Although estimates of F have been tried based on atmospheric reanalysis and altimetric and GRACE measurements [e.g., Chambers et al., 2004; Chen et al., 2005; Vinogradov et al., 2008], variability in F remains poorly known, particularly at periods other than annual. Depending on the relation between F , O, and S 0 , knowledge of S 0 may be useful to infer variability in F , in the context of the Earth’s total water budget.
[34] Figure 6a shows contribution of F , O and the resulting changes in S 0 . The time mean is removed from all series. Note, that global-mean S 0 here represents the net change of salt content in the mixed layer and does not include subsurface changes, allowing variations in mass of salt on time scales considered here. [35] Apart from the forcing surface fluxes, ocean fluxes greatly affect the evolution of S (Figure 6a). As seen from Figure 6b, variability in O can be induced by all ocean processes, with tendencies in A, M, and E having comparable magnitudes. The resulting total tendency S 0 in Figure 6a is characterized by a well-defined annual cycle, as well as semiannual changes of smaller amplitude. [36] The mean annual cycle in S 0 reflects an interplay between annual cycle in F , which has a maximum value of 0.008 PSS-78 mo1 in December, and annual changes in O of smaller amplitude (0.004 PSS-78 mo1) and almost out of phase with F (Figure 6c). For reference, annual cycle in S 0 corresponds to an annual cycle in global-mean S with amplitude 0.008 PSS-78 and a maximum in February. (Peak in S 0 in November, as seen in Figure 6c, corresponds to salinity peak in February because of a 3 month (90 ) lag between the variable and its time derivative). Notice that the annual amplitude in S (and S 0 ) are much smaller compared to local annual variability. For example, the amplitude of the annual harmonic of S near the mouths of major rivers, such as Amazon, Ganges, Brahmaputra, etc., can reach 8–10 PSS-78 [Boyer and Levitus, 2002]. [37] The amplitude and phase relations in Figure 6c reveal the nature of the global-mean annual cycle. On average, it takes the mixed layer about a month to adjust to the annual changes imposed by the surface forcing. Advective and mixing processes are, however, only able to partially compensate for the forcing effects, with O amplitudes about half of those in F . Apart from reducing the amplitude of S 0 relative to F , the lagged response of the mixed layer also introduces a phase shift between them, itself of approximately 1 month. (Note that our analysis is based on monthly average fields and that the actual phase shifts between the curves in Figure 6c could be somewhere within 1 month.) [38] To examine linearity, we regress S 0 against F and compare derived F S with F . The mean annual cycle is removed from both S 0 and F . From Figure 6d, the inferred flux F S tends to under-estimate the ‘‘true’’ variability and explains less than half of the F variance ( ¼ 43%). Timelagged regressions did not strengthen S 0 -F relationship, indicating that, unlike for the mean annual cycle, the relationship between O and F at other time scales is more complex. Thus, apart from the mean annual cycle, S measurements are not a good proxy for global-mean fluxes of F (and O) in the context of simple linear regression models used here.
6.
Conclusions
[39] Based on the analyses of a 13 year ECCO state estimate, changes in surface salinity reflect a complicated balance between atmospheric and oceanic processes across a range of time scales from months to years, with both F and O contributing to variability in S 0 . Depending on region, all components of O (mixing, advection, entrainment) can
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VINOGRADOVA AND PONTE: SURFACE SALINITY AND FRESHWATER FLUX
give rise to variability in S 0 , although advective fluxes are typically the largest (Figures 3a, 3d, and 3g). Given the non-negligible variability in O, a one-to-one correspondence between local S 0 and F cannot be expected on monthly to interannual time scales. Because of the general poor correlation between O and F , inferring F from S 0 values using simple linear regression models did not lead to much success : typically only a small part of the variability in F could be recovered at scales of 100 km and larger, except in a few small regions (e.g., subtropical South Pacific gyre) and only at annual and shorter time scales. [40] Variations in global-mean mixed-layer S fields are also greatly affected by ocean dynamics, with O being of equal importance as F . About half of the annual variations in F are balanced by O, although at a 1 month lag. Depending on the robustness of the lag estimates, the mean annual cycle in F can be inferred using global-mean S measurements reasonably well. At interannual time scales, there is no useful linear relationship between F and S 0 and F cannot be inferred from S 0 alone using linear model (4). [41] Our findings apply only to monthly to interannual time scales; the relationship between F and S 0 at shorter and longer time scales is not explored here and could be different. Previous studies suggest that considerable salinity variance can be contained at submonthly periods, related to short-lived changes in F such as intense precipitation events [e.g., Cronin and McPhaden, 1999; Delcroix et al., 2005; Vinogradova and Ponte, 2012]. If the time scales of ocean mixing and advection are long enough (e.g., lowwind and slow-current conditions), salinity fluctuations will reflect more directly the changes in F . In such cases, analysis of salinity estimates with higher temporal resolution will be valuable, including those derived from the Aquarius measurements. [42] Similarly due to the relatively short time period considered here (13 years), our conclusions do not apply to time scales longer than interannual, including decadal trends. As suggested by previous studies, the link between salinity variations and changes in F can become stronger, allowing one to use salinity as a direct proxy for F [Stott et al., 2008; Durack et al., 2012; Pierce et al., 2012; Terray et al., 2012]. One of the on-going ECCO efforts is to produce a multidecadal, dynamically consistent estimate of ocean state. Analysis of the relationship between S 0 and F using longer ECCO runs would be useful, especially in light of detected multidecadal salinity trends and their connection to anthropogenic forcing discussed in aforementioned studies. [43] Apart from issues of time scale, results are also likely dependent on the definition of the ‘‘surface’’ layer, i.e., whether one considers ‘‘subskin’’ or ‘‘mixed-layer’’ salinity. In this regard, it will be interesting to investigate the relation between satellite-derived salinity measurements and F . Very preliminary calculations (not shown) based on available Aquarius monthly salinity measurements (L3, v2.0) and time-integrated E – P estimates derived from NCEP reanalysis did not reveal any significant correlations, with inferred flux explaining
