Global relationships of total alkalinity with salinity and temperature in surface waters of the world's oceans



[1] A simple function of sea surface salinity (SSS) and temperature (SST) in the form AT = a + b (SSS − 35) + c (SSS − 35)2 + d (SST − 20) + e (SST − 20)2 fits surface total alkalinity (AT) data for each of five oceanographic regimes within an area-weighted uncertainty of ±8.1 μmol kg−1 (1σ). Globally coherent surface AT data (n = 5,692) used to derive regional correlations of AT with SSS and SST were collected during the global carbon survey in the 1990s. Such region-specific AT algorithms presented herein enable the estimation of the global distribution of surface AT when observations of SSS and SST are available.

1. Introduction

[2] Total alkalinity (AT) variability in the surface ocean is controlled mainly by freshwater addition (precipitation and sea-ice melting) or removal (evaporation and sea-ice formation) which also acts to change salinity [Brewer et al., 1986; Millero et al., 1998a]. In the (Sub)tropical oceans (i.e., 30°N−30°S), surface AT variations associated with water balance-induced changes in salinity account for more than ∼80% of total variability in AT [Millero et al., 1998a]. At higher latitudes (i.e., north of ∼30°N or south of ∼30°S), a progressive increase in the convective mixing of deep waters rich in AT during seasonal cooling is an important additional factor that acts to increase surface AT concentrations. The greater the intensity of seasonal convective mixing; the higher the AT associated with the dissolution of CaCO3 and the lower the water temperature. In this case, AT is negatively correlated with sea surface temperature. Coccolithophorid blooms during seasonal warming are key biological factors that decrease surface AT in a measurable way [Balch et al., 2005]. The formation and destruction of organic matter also impact surface AT, but only in a minor way, except in biologically productive waters [Kim et al., 2006]. Such decrease in AT due to marine biota generally occurs in tandem with sea surface temperature increase. Overall, variations in both sea surface salinity (SSS) and temperature (SST) can be good proxies for surface AT variations.

[3] Identifying the controls on surface AT is becoming increasingly important for understanding the effects of ocean acidification resulting from the addition of anthropogenic CO2 into surface waters [Feely et al., 2004]. However, determining the global distribution of surface AT is problematic because in many parts of the ocean AT data are severely limited compared to the SSS and SST data sets, which are several orders of magnitude larger. In this case, empirical algorithms that relate surface AT to SSS and SST are particularly useful in constructing the global distribution of AT when combined with the global fields of SSS and SST. Such empirical AT algorithms can aid in predicting the CO2 flux across the air-sea interface in a numerical ocean model because surface pCO2 could be calculated from the values of AT and total inorganic carbon (CT) for the model's surface box. In such a model, AT and CT are transported between the ocean boxes. Alternatively, surface pCO2 and AT data are used to calculate the surface CT. The surface AT algorithms can also be used to study other aspects of the marine carbonate system. For example, the annual cycle of AT in the global ocean derived from the surface AT algorithms along with hydrographic parameters can be extended to estimate the annual export production of biogenic CaCO3 by integrating the seasonal decrease in the mixed-layer inventory of AT, once it is corrected for salinity effects [Lee, 2001].

[4] The first set of global relationships of salinity-normalized AT with SST [Millero et al., 1998a] was derived using subsets (n = 1,740) of historical AT data as well as those collected during the global carbon survey of the 1990s. Since the global AT relationships first became available, a significant number of new AT measurements have been added to the global data set. Here, we use surface AT measurements (n = 5,692) from the Global Ocean Data Analysis Project v1.1 data set [Key et al., 2004] which have been carefully quality controlled to determine the relationships of AT with SSS and SST for different ocean regimes. The functional form of the model used in our analysis of surface AT results is also distinct from that used by Millero et al. [1998a]. In the previous analysis, the equations that relate salinity-normalized AT to SST probably include erroneous trends [Friis et al., 2003]. Therefore, for each ocean regime we relate AT results to both SSS and SST.

2. Methods

2.1. Optimal Polynomial Model for Fitting AT Data

[5] An optimal functional form for fitting AT data for each ocean regime was chosen on the basis of results obtained from analysis of AT data using the 10-fold cross validation method, which tests which polynomial form (first, second, or third order) gives a better fit [Stone, 1974; Breiman, 1996]. For each ocean regime, we randomly divided the AT data set into 10 subsets. The first step of the 10-fold cross validation analysis was to remove 1 subset from the 10 data sets. Then we derived a regression model without this subset, predicted the output values for this subset using the derived regression model, and computed the residuals. This calculation routine was repeated for each subset and the squares of the resulting residuals were summed. This cross-validation analysis applied for polynomial models of first, second, and third order. We found that a second-order polynomial model yielded the lowest value of the sum of the squares of the residuals; hence we chose a second-order model as the optimal regression model for fitting AT data for each ocean regime.

[6] We also tested whether the cross-correlation term between the two predictor variables (SSS and SST) should be included in the selected functional form. In all regimes, lower tolerance values (i.e., <0.2), calculated from 1 − r2 for the regression of the interaction term on SSS and SST, indicate a high correlation between the two predictor variables and their interactions. Therefore, the interaction term was not included in the polynomial model that was used for generating AT algorithms. However, for the North Pacific, the model including the interaction term between SST and longitude significantly reduced systematic errors.

2.2. Global Surface AT Data Used to Derive AT Algorithms

[7] Global surveys of marine inorganic carbon parameter distributions were conducted from 1990 to 1998 as part of the Joint Global Ocean Flux Study, the Ocean Atmosphere Carbon Exchange Study, and the World Ocean Circulation Experiment. The final AT data set is internally consistent to ±5 μmol kg−1 [Key et al., 2004]. Detailed descriptions of measurement techniques and calibration procedures for AT data are provided elsewhere [Millero et al., 1998b; Key et al., 2004]. Subsets (n = 5,692) of the final AT data collected from waters of less than 20 m depth in the (Sub)tropics (i.e., 30°N−30°S) and 30 m depth at latitudes poleward of ∼30° were used in deriving region-specific correlations of surface AT with SSS and SST.

[8] Monthly mean global AT fields on 1° latitude × 1° longitude grid cells were estimated from five regional AT relationships presented in Table 1, along with monthly mean SSS and SST fields from the World Ocean Atlas 2001 [Conkright et al., 2002].

Table 1. Regional Representations of Surface Total Alkalinity (AT) in the World's Oceansa
ZoneOceanApproximate RegionbAT, μmol kg−1σcNd
  • a

    For predicting AT from SSS and SST values in a given zone, the primary criterion for choosing an appropriate AT algorithms is the SST. That is, when the temperature of a water sample in the zone of interest is out of the range of the applicable equation, the equation for an adjacent zone sharing a common boundary should be used instead.

  • b

    Geographic boundaries between the South Pacific−South Atlantic, between the South Atlantic−South Indian, and between the South Indian−South Pacific, are 70°W, 20°E, and 120°E, respectively.

  • c

    Root mean square deviation = {(Δ)2/(N − 1)}0.5, where Δ is the difference between measured AT values and those calculated from the equations.

  • d

    The number of data points used for fitting.

  • e

    Arabian Sea and Bay of Bengal are included.

1(Sub)tropicse30°S–30°N (Atlantic, Indian, and Pacific Oceans excluding Zone 2), SST > 20°C, 31 < SSS < 382305 + 58.66 (SSS − 35) + 2.32 (SSS − 35)2 − 1.41 (SST − 20) + 0.040 (SST − 20)28.62756
2Equatorial upwelling Pacific75°W–110°W → 20°N–20°S and 110°W–140°W → 10°N–10°S, SST > 18°C, 31 < SSS < 36.52294 + 64.88 (SSS − 35) + 0.39 (SSS − 35)2 − 4.52 (SST − 29) − 0.232 (SST − 29)27.5644
3North Atlantic30°N–80°N, 0°C < SST < 20°C, 31 < SSS < 372305 + 53.97 (SSS − 35) + 2.74 (SSS − 35)2 − 1.16 (SST − 20) − 0.040 (SST − 20)26.4326
4North Pacificnorth of 30°N, SST < 20°C, 31 < SSS < 352305 + 53.23 (SSS − 35) + 1.85 (SSS − 35)2 − 14.72 (SST − 20) − 0.158 (SST − 20)2 + 0.062 (SST − 20) (LONG)8.7258
5Southern Ocean30°S–70°S, SST < 20°C, 33 < SSS < 362305 + 52.48 (SSS − 35) + 2.85 (SSS − 35)2 − 0.49 (SST − 20) + 0.086 (SST − 20)28.41708

3. Results and Discussion

3.1. Parameterization of Alkalinity in Surface Oceans

[9] Our analysis indicates that the distribution of surface AT can be derived by dividing the global ocean into five regimes with corresponding equations relating AT to SSS and SST (Table 1 and Figure 1). Since the derived equations given in Table 1 are expressed as functions of SSS and SST, the geographic boundaries of the regimes where the equations apply are dynamic, depending on seasonal variations in SST. For each ocean regime, surface AT results are fitted to a second-order polynomial in SSS and SST and are also forced to satisfy equations for adjacent regime(s) which share boundaries with the regime of interest. The use of this functional form of equation is to ensure a smooth transition in AT between adjacent regimes, and thus to minimize errors in AT predictions at their mutual boundaries.

Figure 1.

Monthly mean values of surface AT (μmol kg−1) for August for the world's ocean, as estimated from the regional AT algorithms given in Table 1 applied to monthly mean sea surface salinity (SSS) and temperature (SST) fields (1° latitude × 1° longitude) from the World OceanAtlas 2001 [Conkright et al., 2002]. White lines represent the approximate boundaries for the five different regions with unique relationships of AT with SSS and SST and the numerical numbers represent the five regions listed in Table 1. Crosses denote locations of sampling stations.

[10] In the (Sub)tropical oceans (Zone 1), except for the equatorial upwelling Pacific, waters with a temperature of 20°C and salinity of 35 have AT values of about 2305 μmol kg−1 for the entire (Sub)tropics. Thus, at SST = 20°C and SSS = 35, AT values in these warm waters are forced to an intercept of 2305 μmol kg−1 for the (Sub)tropics (see the first equation in Table 1). In the equatorial upwelling Pacific (Zone 2), waters have generally higher AT values than those observed at the same salinity in similar latitude bands of the Atlantic and Indian Oceans. Thus, a separate equation is derived for this region to account for the effect of upwelling waters on the AT trend. To make a smooth transition to values of AT in the (Sub)tropics, the equation for this region is forced to an intercept of 2294 μmol kg−1 at SST = 29°C and SSS = 35. This intercept is similar to a mean AT value for waters generally found at the boundary between the equatorial upwelling Pacific and the (Sub)tropics.

[11] In higher latitude oceans (poleward of 30°), regionally contrasting sets of coefficients are derived for equations of the same functional form for the North Atlantic (Zone 3), North Pacific (Zone 4), and Southern Ocean (Zone 5). In the North Pacific, the AT values in the northwestern Pacific are significantly higher than those observed at the same salinity in the northeastern Pacific. Such contrasting trends of AT in the North Pacific can be attributed to the east-west differences in the intensity of convective mixing. The greater the intensity of seasonal convective mixing; the higher the AT. Therefore, the variable “longitude” is added to the equation to account for east-west AT differences in the North Pacific (see the fourth equation in Table 1). The equations for the three zones at higher latitudes are all forced to the same intercept of 2305 μmol kg−1 at SST = 20°C and SSS = 35 to ensure a smooth transition to values of AT in the (Sub)tropics.

[12] The effect of seasonal differences in AT data on the derived AT relationships was also addressed by comparing AT values predicted from the relationships in Table 1 with AT measurements which are not included in the data set. The mean difference of −1.2 ± 7.8 μmol kg−1 (1σ) indicates that the derived AT relationships can be used to predict seasonal extrapolation of surface AT. Some differences are found locally (Figure 2b), but these are still close to uncertainties of our AT relationships (see the fifth column in Table 1). The effect of seasonality on the AT relationships can be more thoroughly evaluated when time-series measurements become available in high latitude regions in which seasonal variations in both salinity and convective mixing lead to contrasting changes in surface AT values, either in terms of magnitude or sign.

Figure 2.

Comparison of the estimated AT values from the regional AT algorithms given in Table 1 with measurements which are (a) used or (b) not used when deriving the AT algorithms. The measurements which are not used when deriving the AT algorithms given Table 1 include data from the three major ocean basins: I8N/I8S (January 1995, along ∼80°E), I03I04 (2003, along ∼20°S), P06 (2003, along ∼30°S), P15S/SR05 (2001, along ∼170°E), P17N (2001, 135°W−160°W and 30°N−55°N), A10 (2003, along ∼30°S), A16N/A16S (2003/2005, along ∼20°W), and A22 (2003, along ∼65°W).

[13] For predicting AT from SSS and SST values in a given zone, the primary criterion for choosing an appropriate AT algorithm is the SST. That is, when the temperature of a water sample in the zone of interest is out of the range of the applicable equation, the equation for an adjacent zone sharing a common boundary should be used instead. For example, for waters with SST < 20°C, which are commonly found in the northern (Sub)tropical Atlantic (Zone 1) during the winter season, the equation that applies to the North Atlantic (Zone 3) should be used to predict AT.

3.2. Global Distribution of Alkalinity in the Surface Ocean

[14] The global distribution of surface AT for August calculated using the derived AT algorithms of Table 1 applied to climatological SSS and SST fields [Conkright et al., 2002] is shown in Figure 1. The surface AT field shows broad maxima in the central gyres centered at about 25° north and south of the Equator, similar to the pattern for salinity. Such strong salinity-dependent trends in surface AT result from the fact that the concentrations of the key chemical species (i.e., HCO3, CO32−, and B(OH)4) that contribute to AT proportionally increase with increasing salinity, and thus the ratio of AT to salinity is approximately constant throughout the (Sub)tropics.

[15] Poleward of the (Sub)tropics, the annual excess precipitation over evaporation increases, and thus salinity decreases, with latitude. As a result, the values of AT generally decrease with increasing latitude (Figure 1). Seasonal changes in the intensity of the convective mixing here are additional key factors that act to change surface AT in a measurable way. During seasonal cooling, the intensive vertical mixing brings deep waters rich in CaCO3-driven AT to the surface, and thus increases surface AT. During seasonal warming, however, the shoaling of the mixed layer makes the contribution of AT-rich deep waters to the change in surface AT minimal.

[16] The magnitude of seasonal AT variability (Figure 3), computed by differencing the maximum and minimum monthly mean AT values in each 1° latitude × 1° longitude grid cell, is directly proportional to the seasonal variations in salinity. Seasonal AT variations are generally larger in the (Sub)tropics than in the higher-latitude oceans. In particular, larger amplitudes of seasonal variability are observed in areas where freshwater inputs through rivers (e.g., near the Amazon River and the Bay of Bengal) and the melting of ice (e.g., near sea-ice edges) are significant, or where tropical upwelling occurs.

Figure 3.

Distribution of the seasonal amplitude (maximum AT-MAX – minimum AT-MIN) of surface AT predicted from the regional AT relationships given in Table 1, applied to monthly mean sea surface salinity and temperature fields (1° latitude × 1° longitude) from the World Ocean Atlas 2001 [Conkright et al., 2002].

[17] Comparison of the surface AT values for August calculated using the five equations (Table 1) applied to climatological SSS and SST fields with the corresponding values estimated using the algorithms previously reported by Millero et al. [1998a] reveals that the degree of discordance between the two sets of estimates varies regionally (Figure 4). The greatest differences are found in the North Pacific and the North Atlantic and, to a lesser extent, in the Southern Ocean. Non-negligible differences also are observed in the subtropical gyres of the South Pacific and South Indian Oceans. In the (Sub)tropics, Millero et al. [1998a] forced the single equation to two different intercepts for SST at 20°C; one for the northern and southern (Sub)tropical Pacific and another for the rest of (Sub)tropics. However, our analysis indicates that, regardless of basins, only a single intercept of the AT equation is needed at SSS = 35 and SST = 20°C for the entire (Sub)tropics.

Figure 4.

Differences (μmol kg−1) in values of surface AT for August determined from the regional AT algorithms listed in Table 1, versus those calculated from previously reported AT algorithms [Millero et al., 1998a].

[18] Finally, since the five regional AT algorithms given in Table 1 were derived from the most comprehensive surface AT data available using the laboratory-calibrated measurement protocol, we propose that this new set of AT equations should be used for the prediction of surface AT over large oceanic areas where SSS and SST values are known.


[19] We thank all individuals who contributed to the global alkalinity data set, including the chief scientists. This work was financially supported by the National Research Laboratory Program of the Korea Science and Engineering Foundation. Partial support was provided by the AEBRC at the POSTECH, the Korea Aerospace Research Institute, the MOEHRD (KRF-2005-070-C00143), the Korea Science and Engineering Foundation (R01-2002-000-00549-0, 2004), and NOAA's Office of Climate Observation; PMEL contribution 2938.