2.1 δ13CPOC Measurements
 We compiled and analyzed two data sets of δ13CPOC. One consists of surface ocean, globally distributed δ13CPOC spanning 1962 to 2010. The other is a high temporal resolution data set from one location, the Ocean Flux Program (OFP) sediment traps (31°50′N; 64°10′W; 4500 m water depth) extending from 1978–2007.
 The global distribution of δ13CPOC was measured on cruises AMT18 (2008), AMT19 (2009) and Icechaser II (2010). 5–10 L of surface water (5 m) from either underway or Niskin bottles was filtered onto precombusted GF/F filters, rinsed with deionized water, and dried at 60°C for 12 hrs. δ13C of POC was measured according to [Hadas et al., 2001]. The 106 measured values of δ13CPOC from the Atlantic Ocean were supplemented with 419 measurements from the literature to create a globally distributed, temporal data set of 525 δ13CPOC values. It is assumed that the different methods in POC collection (Table S1, supporting information) did not introduce significant bias [Brodie et al., 2011; Goericke and Fry, 1994; Lorrain et al., 2003; McConnaughey and McRoy, 1979]. We also assumed that the effect of post-fixation fractionation due to organic matter degradation or differential carbon assimilation in higher trophic levels is small.
 For the OFP dataset, δ13CPOC was measured as an annual mean from a sediment trap at 3200 m between 1978 and 2007. Samples consisted of the fine fraction of the trap material (<125 µm for 1990–2007, <37 µm for 1978–1988), which comprises >80 % of the flux material. 1–3 mg of sample was decalcified using HCl and gentle drying. The dried samples were measured in tin capsules by CF-IRMS using a Europa 20-20 CF-IRMS interfaced to a Europa ANCA-SL elemental analyzer. Standards analyzed along with the POC gave standard deviation of ±0.2‰ for carbon.
2.2 Derivation of εp
 εp quantifies the difference in isotopic composition between fixed organic carbon and ambient CO2:
 It is, therefore, completely specified by the combination of δ13C of POC and δ13C of dissolved CO2. The latter is not measured directly, but derived from δ13C of dissolved inorganic carbon (DIC). To account for fractionation between the pools of CO2, HCO3− and CO32−, δ13C of CO2 is calculated from the isotopic mass balance as in Freeman and Hayes , using δ13C of DIC, the concentrations of the different inorganic carbon species and temperature-dependent equilibrium fractionation factors [Zhang et al., 1995]. In turn, the concentrations of individual carbon species are calculated from two parameters of the carbonate system ([CO2] or pCO2, alkalinity, total DIC), temperature and salinity.
 Values for temperature, salinity, and carbonate system parameters were taken from the original sources if available; climatological values [Antonov et al., 2010; Key et al., 2004; Locarnini et al., 2010; Quay et al., 2003; Takahashi et al., 2009] were substituted otherwise. δ13CDIC presents a greater challenge, as this variable is frequently unavailable, yet important for understanding the subtle temporal variation in δ13CPOC, as δ13CDIC itself changes in time [Bacastow et al., 1996]. During the recent AMT18 (2008), AMT19 (2009) and Icechaser II (2010) cruises, measurements of δ13CDIC were taken onboard: 30 mL seawater was filtered through 0.2 µm PES filter and poisoned with HgCl2 and δ13C of DIC was measured according to Hadas et al. . For samples reported in the literature without δ13CDIC, a basin-specific reconstruction of δ13C of DIC and its rate of change [Quay et al., 2003] was used to obtain a representative value. Quay et al.  characterize the variability in surface ocean δ13CDIC with a basin- and latitude-specific value representative for 1995, and rate of change. To estimate δ13CDIC for a single sample, we inferred the appropriate offset and rate of change, which were combined to estimate δ13CDIC at the sample time.
 As Table 1 shows, many inferred values of εp are based on one or more approximate (climatological) values for environmental variables. The uncertainties associated with these approximate values translate into uncertainties in the value of εp. This was accounted for by estimating standard deviations for each εp value from the uncertainty in input variables and the sample-specific sensitivity to each of those inputs (variances of inputs are multiplied with the square of the associated sensitivity, and then summed to arrive at the variance of εp). If we review the average uncertainty in approximate inputs and the associated mean sensitivity in εp (Table 1), we find that the reconstructed value of εp is particularly sensitive to errors in temperature and δ13C of DIC; uncertainties in salinity, alkalinity and pCO2 do not appreciably reduce confidence in the reconstructed value of εp.
Table 1. Use of Climatological Variables for Inference of εpa
|temperature||460/525||0.12‰/°C||[Locarnini et al., 2009; 2010]||1.25°C||0.14‰|
|salinity||352/525||0.003‰/PSU||[Antonov et al., 2010]||0.35 PSU||0.00‰|
|δ13C of DIC||83/525||0.99‰/‰||[Quay et al., 2003]||±0.21‰*||0.12‰|
|pCO2||238/525||0.0003‰/ppm||[Takahashi et al., 2009]||29 ppm||0.01‰|
|alkalinity||88/525||0.0000‰/mEq||[Key et al., 2004]||29 mEq||0.00‰|
 To obtain values for environmental variables corresponding to the OFP sediment trap samples, we took temperature, salinity, alkalinity, total DIC, and δ13CDIC from Keeling and Guenther,  collected from BATS between 1989–2002 and from Hydrostation “S” between 1982 and 1989. For the period following 2002, we obtained data from BATS (Nick Bates; personal communication).
2.3 Estimating the Change in εp
 Ideally, one would estimate the change in εp directly by comparing samples from different years, taken at the (approximate) same location and in the same season. However, as our data set is too sparse for this purpose, samples from different areas and seasons must be used to characterize εp in any given period. The consequence of this is that any long-term change in εp is likely to be obscured by natural variability. To solve this, we propose that part of the natural variability in εp may be explained by environmental variables, e.g., temperature. By formalizing the relationship between εp and environmental variables in a model, we can disentangle natural variability and long-term change.
 Given the plethora of factors that have been suggested to control εp, we do not invoke a mechanistic explanation for its natural variability. Instead, we describe its spatial pattern with a linear function of explanatory variables xi, which we will identify later and account for long-term change by allowing the regression coefficients βi to change at a constant rate:
 The long-term change in εp is then also given by a linear function of explanatory variables:
 This approach can be thought of as a continuous-time extension of extended Multiple Linear Regression (eMTL) [Friis et al., 2005], which models the spatial pattern in a target variable at two points in time with separate linear functions of environmental variables. In eMTL, the change in the target variable is given by the difference between the two linear equations. In our case, we have samples scattered over the world ocean over a period of five decades, rather than two comprehensive data sets at specific points in time. We therefore impose that the rate of change over the entire modeled period has a constant (linear) relationship with the explanatory variables and use a single linear equation to describe the global variability in εp.
 There are no a priori restrictions on the type of variables that could explain the variability in εp. An attractive choice may seem to be the concentration of CO2, which is often suggested to control εp [Rau et al., 1989]. However, the concentration of CO2 exhibits long-term change due to rising atmospheric CO2. While equation (2) does not prohibit a time-dependence of explanatory variables, using time-dependent variables has two drawbacks. First, a time-dependence causes spatial and temporal variability to become inextricably linked. This is most easily seen if we rederive the rate of change, dεp/dt, which then includes a dependence on ai. As a result, the estimated change in εp is sensitive to its spatial pattern and vice versa. Since εp exhibits pronounced spatial variability, but subtle temporal variability, a model based on time-dependent variables such as CO2 is likely to sacrifice temporal accuracy for a better representation of the spatial pattern. Experiments indicate that this problem indeed occurs when CO2 is used as the explanatory variable. The second problem with time-dependent explanatory variables is that they tend to increase the uncertainty in the estimated rate of change: If explanatory variables are time-dependent, the change in εp becomes a function of the change in explanatory variables. This change rarely is well-constrained. For these two reasons, we restrict ourselves to explanatory variables for which long-term temporal variability is thought to be small relative to their spatial variability.
 Several environmental variables exhibit little long-term change between 1962 and 2010 and could thus serve as explanatory variable. These variables include temperature, salinity, alkalinity, and nutrients. Although minor changes in these variables are known or suggested to have occurred (an estimated 0.3–0.5°C global increase in surface ocean temperature has been observed between 1960 and 2005 [Solomon et al., 2007]), these changes are small compared to their overall (spatial) variability. In view of the coverage of our data set, we select temperature, which is known for 88 % of samples (Table 1), as the primary explanatory variable. Temperature is known to correlate with numerous other environmental variables, including productivity and community composition. Notably, temperature has a well-defined relationship with the concentration of CO2 through the temperature-dependence of CO2 solubility [Weiss, 1974]. The commonly proposed dependence of εp on the concentration of CO2 should therefore be captured to some degree by a dependence on temperature as well. In addition to temperature, we have tested a range of secondary explanatory variables, including (climatological) salinity, nitrate, phosphate, silicate, alkalinity, apparent oxygen utilization, and temperature squared. The combination of temperature and nitrate was found to explain most of the observed variability in εp and is therefore used for the remainder of this work. Accordingly, the expected value of εp is given by a function of time t, temperature T and nitrate N:
 It should be noted that this model does not attempt to mechanistically explain the variability in εp in terms of temperature or nitrate; these variables were merely found to show the best correlation with εp, and accordingly produce the best constrained estimates of its rate of change.
 εp in the data set will display variability that is not captured by the model. We distinguish two sources of variability: errors in the reconstructed value of εp that arise from the use of approximate inputs (e.g., climatological variables, see Table 1) and residual errors (e.g., measurement error, variability not explained by temperature and nitrate). Accordingly, the variance of the difference between observed and modeled εp equals the sum of input-derived and residual variances. For the sake of simplicity, we assume that these differences are normally distributed and independent and that the residual variance is equal for all samples. Input-derived variances are estimated for each sample as described in the previous section.
 Given the model for εp and its variability, the coefficients describing spatial and temporal variation (a0, a1, a2, b0, b1 b2) can be estimated. First, a Restricted Maximum Likelihood (REML) procedure is used to estimate residual variance . This estimate is independent of the values of the model coefficients. With the variance for each sample known, model coefficients are given by their Weighted Least Squares (WLS) estimate. To minimize the influence of sampling bias (specifically, overrepresentation of the Southern hemisphere at high latitudes, and disproportional coverage of later years), a bootstrap-based resampling strategy is used [Efron and Tibshirani, 1998]. First, we separate low (0–30°), mid (30–60°) and high latitudes (60–90°). For each latitude range, we partition samples into four subsets by classifying according to hemisphere and time period (pre-1990, post-1990). From each of the four subsets, an equal number of samples is selected randomly with replacement. The selected number is equal to the size of the smallest subset. By combining selections from the three latitude ranges, a final set of 260 data points (out of the original 525) is obtained, which is then used to estimate model coefficients through REML and WLS. Estimated coefficients are combined with climatologies of temperature and nitrate [Garcia et al., 2010; Locarnini et al., 2009] to infer the annual mean distribution of εp in reference year 1990, as well as its time-independent rate of change b0 + b1T + b2N. Resampling, estimation and prediction is repeated 20,000 times to obtain robust estimates (the mean of results from all 20,000 trials) and confidence intervals (percentiles of trial results).