SEARCH

SEARCH BY CITATION

Keywords:

  • abrupt shift;
  • atmospheric CO2 growth rate;
  • carbon sinks;
  • change point detection;
  • net land uptake

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and Flux Estimates
  5. 3. Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Appendix A
  10. Appendix B
  11. Acknowledgments
  12. References
  13. Supporting Information

[1] A recent study of the net land carbon sink estimated using the Mauna Loa, Hawaii atmospheric CO2record, fossil fuel estimates, and a suite of ocean models suggests that the mean of the net land carbon uptake remained approximately constant for three decades and increased after 1988/1989. Due to the large variability in the net land uptake, it is not possible to determine the exact timing and nature of the increase robustly by visual inspection. Here, we develop a general methodology to objectively determine the nature and timing of the shift in the net land uptake based on the Schwarz Information Criterion. We confirm that it is likely that an abrupt shift in the mean net land carbon uptake occurred in 1988. After taking into account the variability in the net land uptake due to the influence of volcanic aerosols and the El Niño Southern Oscillation, we find that it is most likely that there is a remaining step increase at the same time (p-values of 0.01 and 0.04 for Mauna Loa and South Pole, respectively) of about 1 Pg C/yr. Thus, we conclude that neither the effect of volcanic eruptions nor the El Niño Southern Oscillation are the causes of the sudden increase of the land carbon sink. By also applying our methodology to the atmospheric growth rate of CO2, we demonstrate that it is likely that the atmospheric growth rate of CO2 exhibits a step decrease between two fitted lines in 1988–1989, which is most likely due to the shift in the net land uptake of carbon.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and Flux Estimates
  5. 3. Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Appendix A
  10. Appendix B
  11. Acknowledgments
  12. References
  13. Supporting Information

[2] Ocean and terrestrial sinks remove more than half of the anthropogenic CO2 emitted to the atmosphere, leaving less CO2 to accumulate in the atmosphere. Changes in the efficiency of these sinks could have a substantial impact on the rate of climate change [e.g., Raupach, 2011]. Thus, understanding of the temporal evolution of these sinks is important for the Earth's carbon cycle and climate system.

[3] Sarmiento et al. [2010] suggested that an abrupt shift in the net land carbon sink, estimated as the balance between the fossil fuel emissions, the growth rate of atmospheric CO2 at Mauna Loa and the ocean carbon uptake estimated from ocean models, occurred in the late 1980s (Figure 1). In their analysis, the land carbon uptake appears to have remained relatively constant (with a mean of 0.27 Pg C/yr) from 1960 to 1988 and to have increased after 1988 (to a mean of 1.15 Pg C/yr). However, they also pointed out that the nature of the increase is difficult to detect given the short period of observations (1960–2008), and the high variability and uncertainty in the observations.

image

Figure 1. Net land carbon uptake, its components and its covariate effects: (a) the ocean uptake estimated from four ocean models (LQ = Le Quéré et al. [2007], LO = Lovenduski et al. [2008], RO = Rodgers et al. [2008], and WE = Wetzel et al. [2005]) and the mean of the four net land uptake time series obtained with the four ocean uptake estimates, (b) the atmospheric growth rate at Mauna Loa and the fossil fuel emissions (dotted line), (c) the Multivariate ENSO Index, and (d) the stratospheric aerosol optical thickness. The references are presented in the data section.

Download figure to PowerPoint

[4] The large inter-annual variability in the land-atmosphere carbon uptake complicates both the detection and attribution of abrupt changes. For example,Sarmiento et al. [2010]visually identified a 1988/89 shift in the mean uptake. This identification, however, is ambiguous given the variability in the land uptake. Other classes of shifts (e.g., shifts in the mean and in the variance, a long-term linear trend or a shift in the long term linear trend) may or may not better explain the data, but these possibilities were not investigated bySarmiento et al. [2010]. Furthermore, it is well known that the variability of land uptake is strongly influenced by ENSO [Thoning et al., 1989; Keeling et al., 1995; Jones and Cox, 2005; Raupach et al., 2008; Le Quéré et al., 2009] and large volcanic eruptions [Jones and Cox, 2001; Sarmiento et al., 2010]. The extent to which a 1988/89 shift can be attributed to these factors, to long-term (or quasi-decadal) change in the solar irradiance reaching the Earth's surface [Sarmiento et al., 2010], or to other factors is not currently known.

[5] Given the importance of such a shift for the Earth's carbon cycle, we here conduct a more rigorous statistical analysis of the temporal shifts in the net land carbon uptake. In particular, we utilize objective change point detection in lieu of the visual method used by Sarmiento et al. [2010]. In a general sense, a change point can be viewed as a time instance at which the parameters of a statistical distribution or a statistical model change. Thus, most change point detection techniques identify the most likely time for a shift and determine whether or not this shift occurred by comparing a model with a shift (or a change point model) to a simpler model without a shift [e.g., Brown et al., 1975; Solow, 1987; Jandhyala and MacNeill, 1991; Lund et al., 2007]. An information criterion is then used to determine which model is more appropriate [Chen and Gupta, 1997, 1999, 2000]. This informational approach can also be useful to discriminate between several change point models with different types of changes (shift in the mean, shift in the parameters of a linear regression model, etc.), as it is generally used for model selection.

[6] In this study, we develop a general methodology based on the Schwarz Information Criterion (SIC) for model selection [Schwarz, 1978]. We use this criterion to detect the time of abrupt changes in time series and to discriminate between no-change, gradual change and abrupt change. We verify the conclusions ofSarmiento et al. [2010] by fitting several types of models (shift in the mean and shift in the parameters of a linear regression model) to the net land uptake estimated using the growth rate of atmospheric CO2 at Mauna Loa and South Pole from the Scripps Institution of Oceanography (SIO) observation network, the two longest atmospheric CO2 records available. Monte Carlo simulations are used to quantify the significance in our results. We repeat this analysis for all of the observing stations with publicly available atmospheric CO2 data starting no later than in 1980. We also investigate whether the shift in the net land uptake is related to the Mount Pinatubo eruption or to changes in ENSO variability by including these two covariate effects in the multiple linear regression models. Furthermore, we investigate if a similar shift is detected in the CO2 atmospheric growth rate to confirm the analysis performed on the net land uptake.

[7] The rest of this paper is organized as follows: section 2 presents the data used in this study. The methodology used to detect change points and to discriminate between several models and the Monte Carlo simulation scheme are described in section 3, and the results are presented in section 4. A discussion about the limitations of these results and the potential of application of this methodology to different problems is presented in section 5 and the conclusions are presented in section 6. The details of the change point detection and model selection technique and additional evidence for a shift in the net land uptake are presented in Appendices A and B.

2. Data and Flux Estimates

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and Flux Estimates
  5. 3. Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Appendix A
  10. Appendix B
  11. Acknowledgments
  12. References
  13. Supporting Information

2.1. Land and Ocean Uptake of Carbon

[8] Following Sarmiento et al. [2010], the net land uptake of CO2 is computed as the difference between the fossil fuel emissions, the atmospheric growth rate and the ocean uptake. The net land carbon sink, as opposed to the land carbon sink, does not require specification of land use emissions (Net land carbon sink = land carbon sink – land use emissions). The emissions from land use were not included because they are highly uncertain and are thought to have remained approximately constant from 1959 to 2006 [Canadell et al., 2007]. Several versions of the net land uptake were computed using the atmospheric CO2 growth rate at Mauna Loa and South Pole (described in section 2.2). Additional stations with shorter records were also used and are presented in Appendix B. The ocean uptake is estimated using four different ocean models to reflect its uncertainty: Le Quéré et al. [2007], Lovenduski et al. [2008], Rodgers et al. [2008] and Wetzel et al. [2005]. These ocean uptake estimates are presented in Figure 1a. We computed the net land uptake with these four ocean estimates and averaged it from 1960 to 2003 (the common period of observations and ocean model simulations) to perform our analyses (Figure 1a). The net land carbon sink and ocean uptake discussed in the paper are all in terms of carbon storage rather than flux. A comparison of our storage changes with air-to-sea or land to atmosphere fluxes should require adding the background natural fluxes due to weathering and related processes [Sarmiento and Sundquist, 1992].

2.2. Atmospheric Growth Rate and Fossil Fuel Emissions

[9] In this study, we primarily use the monthly CO2 concentration observations at Mauna Loa and the South Pole from the SIO network [Keeling et al., 2001] (available at http://scrippsco2.ucsd.edu/data/atmospheric_co2.html) because they are the two longest records available and the most commonly used to represent the global CO2concentrations. The annual atmospheric growth rate was computed annually as described on the NOAA-ESRL website (http://www.esrl.noaa.gov/gmd/ccgg/trends/#mlo_full):

  • display math

where agrt is the atmospheric growth rate in Pg C/year for year t and inline image is the mean CO2 concentration in ppm, for months November–February centered around January 1st of year t. The CO2concentration is corrected for the seasonal cycle, by subtracting a 4-harmonic fit with a linear gain factor from the data [Keeling et al., 2001]. The fossil fuel and cement emissions for 1958–2005 were obtained from Boden et al. [2009] (available at http://cdiac.ornl.gov/trends/emis/tre_glob.html). These estimates are based on the energy statistics from each country. Figure 1b presents the fossil fuel emissions and the atmospheric growth rate computed using the Mauna Loa observations from SIO.

2.3. Covariate Effects

[10] To first order, the net land uptake variability can be explained by ENSO and volcanic eruptions [Sarmiento et al., 2010]. In order to model these factors, the Multivariate ENSO Index was used as a proxy for the ENSO-related variability from the National Oceanic and Atmospheric Administration–Climate Diagnostics Center (NOAA-CDC) [Wolter and Timlin, 1993, 1998] (available at http://www.cdc.noaa.gov/people/klaus.wolter/MEI/table.html). Many other ENSO indices were considered in a preliminary analysis. However, most of them are based on sea surface temperatures and there is no clear consensus in the scientific community as to which of these indices is the best characterization of ENSO [Hanley et al., 2003]. The MEI was chosen because it combines the significant features of six observables over the tropical Pacific: sea level pressure, zonal and meridional components of the surface wind, sea surface temperature, surface air temperature and total cloudiness fraction. Bimonthly values are available and were related to monthly values as described on the NOAA-CDC website. To represent volcanic activity, we use the stratospheric aerosol optical thickness, a measure of the aerosols resulting from volcanic eruptions [Sato et al., 1993] (available at http://data.giss.nasa.gov/modelforce/strataer/). The covariate effects are presented in Figures 1c and 1d.

3. Methodology

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and Flux Estimates
  5. 3. Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Appendix A
  10. Appendix B
  11. Acknowledgments
  12. References
  13. Supporting Information

3.1. Change Point Detection

[11] The change point detection method used in this study can detect several types of changes and can be used to identify the most appropriate model from a range of candidates. The equations representing our candidate models are listed in Table 1 and illustrated in Figure 2. These models have been studied widely in the statistical and climate literature [e.g., Quandt, 1958; Brown et al., 1975; Worsley, 1979; Easterling and Peterson, 1995; Lund and Reeves, 2002; Chen and Gupta, 1999, 2000, 2001; Wang, 2003; Lund et al., 2007].

Table 1. List of Models Fitted in This Study
ModelDescriptionEquations
(i)Constant meanyt = μ + εt (t = 1,…,n) where yt represents the observations, μ is the mean, εt are the random errors, t is the time and n is the number of observations.
(ii)Shift in the mean inline image where μ1 and μ2 are the means before and after the shift at time p
(iii)Intercept and linear trendyt = λ + βt + εt (t = 1,…,n) where λ is the intercept, β the trend of the linear regression model,
(iv)Shift in the intercept and same linear trend inline image λ1 and λ2 are the intercept before and after the shift
(v)Shift in both the intercept and linear trend inline image β1 and β2 are the trend before and after the shift
(vi)Intercept and linear relation with ENSO and optical thicknessyt = λ + ηMEIt + τOTt + εt (t = 1,…,n) η and τ are the regression coefficients for the multivariate ENSO index,MEIt, and the optical thickness,OTt
(vii)Shift in the intercept and linear relation with ENSO and optical thickness inline image
 
image

Figure 2. Examples of synthetic series generated from models fitted in this study (i) a constant mean and standard deviation (μ = 0, σ = 10), (ii) a shift in the mean at time 25 (μ1 = 0, μ2 = 30, σ = 10), (iii) a linear trend (λ = 0, β = 0.2), (iv) a linear trend with a shift in the intercept at time 25 (λ1 = 0, λ2 = 20, β = 0.2) and (v) a shift in both the intercept and trend (λ1 = 0, λ2 = 20, β1 = 0.2, β2 = −0.4). The vertical line indicates the time of the shift and the dotted line indicates the model fit.

Download figure to PowerPoint

[12] To determine the position of the shift and to discriminate between these models, we use a methodology based on the informational approach proposed by Chen and Gupta [2000, 2001]. It consists of using the SIC which is based on the maximum likelihood function of a given model penalized by the number of parameters that are estimated in the model. In this study, we use the SIC to identify the position of the shift under a change point model formulation and to determine whether a model with or without a change point fits the data better. The model that minimizes the SIC can be considered as the most appropriate model [Chen and Gupta, 2000]. Here, the SIC is used as a measure for model selection among several models with different numbers of parameters. Because increasing the number of model parameters to be estimated may result in over fitting the data, SIC has a penalty term for the number of model parameters. The difference between the SIC and the Akaike Information Criterion (AIC) is the penalty term for the number of parameters to estimate, with a stronger penalty in the SIC. In the climate literature, the SIC has been used by Seidel and Lanzante [2004] to discriminate between several change point models to represent atmospheric temperature time series. In the present study, the SIC was used to search for the change point position in the models that include a change point, by calculating the SIC for each possible time for a change point. Then, the most likely position is the one that leads to the smallest SIC. The SIC was also used to discriminate between several models with different types of shifts or without a shift (the most likely model is the one which minimizes SIC). Further details on the statistical methodology are presented in Appendix A.

[13] Due to the large inter-annual variability in the estimated net land uptake, it is not clear from visual inspection alone whether the shift reported bySarmiento et al. [2010]takes the form of a shift in the mean state, a long-term linear trend, or some combination of the two (Figure 1a). Therefore, all the models listed in Table 1 were fitted to the net land uptake in order to objectively determine the nature of the shift. In a preliminary analysis, models with shift in the variance were also fitted, but did not seem likely for the net land uptake, as they led to higher SIC.

[14] By visual inspection, Figure 1b suggests that there was a linear trend in the atmospheric growth rate with a possible shift in the intercept or both the intercept and trend in the late 1980s. Thus, the models iii, iv, v (Table 1) are also fitted to the atmospheric growth rate. However, the ocean uptake and the fossil fuel emissions, analyzed in a preliminary analysis, did not exhibit a shift in the late 1980s. Thus, these results are not presented in this study.

3.2. Integrating Covariate Effects in the Change Point Model

[15] The variability in the net land uptake estimates comes primarily from the variability of the atmospheric CO2 growth rate. Variability in the ocean uptake (Figure 1a) and in the fossil fuel emissions (Figure 1b) is much smaller. A large part of the variability of the atmospheric CO2 growth rate can be explained by ENSO and volcanic eruptions [Conway et al., 1994; Keeling et al., 1995; Jones and Cox, 2005; Canadell et al., 2007; Raupach et al., 2008; Knorr, 2009]. In order to verify whether there are still change points after accounting for ENSO and the volcanic eruptions, we extended the change point multiple linear regression models to integrate these covariate effects. We assume that the relationship between the net land uptake and these covariates is linear. We then evaluate whether the temporal shifts and variability in the net land uptake can be explained in terms of a linear relationship to ENSO, volcanic eruptions, and random noise, or if there is a remaining abrupt shift in the residuals. An abrupt shift in the residuals would indicate that there is still a shift in the net land uptake that cannot be explained by linear covariate effects. This result can be expressed as a shift in the intercept of a multiple linear regression model, which is equivalent to a shift in the mean (model ii) after explaining a part of the variability coming from ENSO and volcanic eruptions. To represent ENSO, we use the MEI (described in section 2.3). The optical thickness was used to represent the volcanic eruptions in the model. We take the relationship between the dependent variable and the covariate effects to be constant in time. Although our analysis can be extended to search for a change point in the parameters representing the relation with the covariates, for the sake of simplicity we restrict the analysis to search for a shift in the intercept. If a shift in the relationship with the explanatory variables occurred, we expect that it would come out as a shift in the intercept. The models including covariate effects fitted to the net land uptake are presented in Table 1 (models vi and vii). Furthermore, a summary of all the regression models used in this work and their associated SIC is presented in Table A1 in Appendix A.

[16] We attempted several other generalizations of the model. For example, if the response of the dependent variable to these covariate effects is lagged [e.g., Lean and Rind, 2009], it is necessary to find the appropriate lags for the explanatory variables. For the present work, no lag in the explanatory variables led to a better correlation. Second, we also took the solar irradiance to be another candidate explanatory variable. However, after a preliminary analysis using the total solar irradiance reaching the Earth's surface record from Lean et al. [2005], it was found that the models including solar irradiance were less appropriate (according to the SIC) to represent the net land uptake. Thus, models including the solar irradiance as an explanatory variable are not presented in this work.

[17] Since the explanatory variables all have different units of measurement, one cannot compare their effects on the dependent variable. However, we computed standardized coefficients by also fitting the model to standardized land uptake, ENSO and optical thickness time series. We standardized the three time series by subtracting from them their respective mean and dividing them by their respective standard deviation. This ensures they all have a mean of zero, a variance of one, and that they are unit-free. Standardized coefficients are computed for all the models including ENSO and optical thickness to assess their effects on the net land uptake. These coefficients represent the change in terms of the standard deviation in the dependent variable that results from a change of one standard deviation in one of the explanatory variables.

[18] Finally, it must be noted that all these models rely on the assumption that the errors are normally distributed and independent. To validate this assumption, the residuals are usually analyzed. In this study, normality and independence tests were applied to the residuals in order to ensure that these assumptions are fulfilled.

3.3. Simulation Scheme

[19] In order to assess the skill of the technique and the significance of the model selected against a model with no shift, a Monte Carlo study was carried out. Using a Normal distribution random generator, we generated synthetic series with the same statistical properties (length, mean and variance) as those calculated in the net land uptake estimate. The first set of synthetic series we generated contains a shift in the mean net land uptake in 1988. In the second set of synthetic series we generate, there is no shift in the mean net land uptake.

3.3.1. Synthetic Series Mimicking a Shift in the Mean Net Land Uptake in 1988

[20] To represent series exhibiting a shift such as detected in the mean net land uptake, we generated series from two different distributions for the period 1960–1988 and 1989–2003 that have the same statistical properties observed in the net land uptake for these two respective periods. If there is a shift in the mean net land uptake after 1988, the model with a shift in the mean (model ii of Table 1) should be selected in a strong majority of the synthetic series that were generated. This simulation scheme seems appropriate since the net land uptake observations can be considered independent and normally distributed (Lilliefors and Wald-Wolfowitz test, 95% confidence level). A total number of 10,000 synthetic series for Mauna Loa and South Pole were generated. In a preliminary analysis, the number of synthetic series was found to be largely sufficient for the results to converge. In the remaining parts of the paper, we will denote the set of synthetic series generated from these two distributions as the set #1.

3.3.2. Synthetic Series Mimicking a Constant Mean Net Land Uptake

[21] It is well known that most change point detection techniques tend to detect more false shifts at the beginning or end of the time series [Wang et al., 2007]. In order to verify if the risk of false detection around 1988 is not higher than at other times, a second set (set #2) of synthetic series was randomly generated from a Normal distribution with a constant overall mean and variance based on the mean and variance of the net land uptake time series. Model i of Table 1, representing a constant mean, should be selected in this case. The different models listed in Table 1were applied to the two sets of synthetic series and the associated SIC were calculated. This is also the set of synthetic series that we used to determine the p-values and determine the significance of the model selected against a model with no-shift. A p-value measures the amount (in terms of probability) of sample evidence in favor of rejecting a null hypothesis. Specifically in this case, it is the probability of observing a difference between the models with a shift and models with no-shift at least as extreme as the observed value. Details on how the p-values in our model selection processes are computed are presented inAppendix A.

4. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and Flux Estimates
  5. 3. Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Appendix A
  10. Appendix B
  11. Acknowledgments
  12. References
  13. Supporting Information

4.1. Net Land Carbon Uptake

[22] Table 2presents the results of the change point analysis on the net land uptake computed using the mean of the four ocean models and the atmospheric growth rate at Mauna Loa and the South Pole. According to the SIC, the net land uptake computed with these stations remained constant for almost three decades and might have abruptly shifted after 1988 (with Mauna Loa data, p-value of 0.15) and after 1987 (with South Pole data, p-value of 0.35). The magnitude of the shift in the net land uptake calculated with Mauna Loa data is about 0.82 Pg C/yr and with South Pole data it is 0.70 Pg C/yr.Figure 3 presents the model selected for the two time series.

Table 2. Results of the Change Point Analysis on the Net Land Uptake at Mauna Loa and South Polea
StationPeriodModelTimeSICParameter Estimatesb
  • a

    The model number refers to the models listed in Table 1. The most likely model, its associated SIC, and time of shift are in bold. The p-value associated to the SIC difference between models i and ii is in parentheses. The p-values are the probabilities, under the hypothesis of a model with no-shift, of observing a difference between the models with a shift and models with no-shift at least as extreme as the observed difference. The smaller the p-value, the more significant the difference between the models is.

  • b

    The parameter estimates correspond to the model with the smallest SIC.

  • c

    Smallest SIC.

Mauna Loa (SIO)1960–2003i, ii, iii, iv, v-,1988, -, 1988, 1988137.55, 134.90c (0.15), 138.63, 138.15, 140.08μ1 = 0.28, μ2 = 1.10, μ1μ2 = −0.82, σ = 1.07
South Pole (SIO)1966–2003i, ii, iii, iv, v-,1987, -, 1987, 1988117.08, 116.10c (0.35), 118.80, 119.00, 122.36μ1 = 0.46, μ2 = 1.16, μ1μ2 = −0.70, σ = 1.04
image

Figure 3. Fit of the model selected to explain the net land uptake at Mauna Loa and South Pole. The dotted lines represent the most appropriate model fit and the vertical lines indicate the time of the shift.

Download figure to PowerPoint

[23] All models were also fitted to set #1 of the synthetic series and the associated SIC was computed for each time series. The results are presented in Figure 4. According to the SIC, the model with a shift in the mean only (model ii) is selected in a strong majority of cases for both Mauna Loa (78.2%) and South Pole (71.5%). Figure 4 also presents the most likely time for a shift when a shift in the mean was selected. The model with a shift in the mean occurring between 1986 and 1993 is found in a strong majority of cases for both Mauna Loa (60.5%) and South Pole (55.4%), with 1988 being the most likely year for the shift for both Mauna Loa (19.4%) and South Pole (15.4%). For all the other years of the time series (different than 1988), the shifts are identified with frequencies smaller than 10% (Figure 4). These detection rates are small because the power of detection of change point techniques is sensitive to the magnitude of the shift. In general, the power of change point techniques drops for magnitudes of about one standard deviation or less [e.g., Beaulieu et al., 2008]. Because the magnitude of the 1988 shift is smaller than the standard deviation of the time series (the standard deviation is about 1 for both Mauna Loa and South Pole, see Table 2), this shift is very hard to detect.

image

Figure 4. Results of the Monte Carlo study conducted on 5000 synthetic series generated with the same statistical properties (mean and variance) as the net land uptake at Mauna Loa and South Pole (set #1). (left) The frequency of model selected (constant mean (i), shift in the mean (ii), linear trend (iii), shift in the intercept (iv), shift in the intercept and trend (v)). (right) The most likely time for a shift, given the model with a shift in the mean (model ii) is selected.

Download figure to PowerPoint

[24] Figure 5 presents the results of the simulation study on synthetic series set #2, generated with the overall mean and variance in the net land uptake, and representing the case where no shift should be detected. Figure 5 shows that the risk of detecting a shift in the mean, when in reality there is not, is quite high (40%). However, it is also shown that the false alarms occur mostly near the beginning and end of the time series. The year 1988 lies in the region where the risk of false alarm is the smallest with a risk of about 1.8% (both Mauna Loa and South Pole).

image

Figure 5. Results of the Monte Carlo study conducted on 5000 synthetic series generated to represent the same statistical properties of the net land uptake at Mauna Loa and South Pole, if they would not exhibit any shift (set #2). (left) The frequency of model selected (constant mean (i), shift in the mean (ii), linear trend (iii), shift in the intercept (iv), shift in the intercept and trend (v)). (right) The most likely time for a shift, given the model with a shift in the mean (model ii) is selected.

Download figure to PowerPoint

[25] Additional evidence for this shift in the net land uptake was also investigated by repeating the analysis using CO2 concentrations at other stations. Out of 11 stations analyzed, 4 showed a change point in 1988 (Appendix B). However, these 11 stations are generally not considered to be as representative of global growth rates as Mauna Loa and South Pole. Furthermore, the length of the record at these stations is shorter than those at Mauna Loa and South Pole and so the power of detection is lower and the risk of false detection is higher. The analysis performed on the net land uptake calculated using the global growth rate from NOAA-ESRL also shows an abrupt shift in 1988.

4.2. Net Land Carbon Uptake With Covariate Effects

[26] The change point analysis was repeated including covariate effects with MEI and optical thickness in the model. The results of the fit to data are presented in Table 3. The analysis performed on the net land uptake shows that when accounting for a part of the variability using MEI and the optical thickness, it is likely that there is a remaining abrupt shift in the net land uptake, that is to say, that the intercept changes abruptly in 1988 (p-value of 0.01 for Mauna Loa and of 0.04 for the South Pole). The magnitude of this shift is 1.16 Pg C/yr (Mauna Loa) and 0.92 Pg C/yr (South Pole). The parameter estimates column inTable 3presents the coefficients obtained by fitting the regression model to the standardized (0-mean and unit variance) variables. This allows comparison of the relative importance of each independent variable under the same units. Generally, an increase of a unit in MEI will more strongly affect the net land uptake than an increase of a unit of optical thickness. For example, the coefficients of the standardized parameters are respectively −0.63 units and 0.36 units for Mauna Loa.Figure 6 presents the fit of the selected model.

Table 3. Results of the Change Point Analysis on the Net Land Uptake at Mauna Loa and South Pole with Explanatory Variablesa
StationPeriodModelTimeSICParameterParameter EstimatesbParameter Estimates in Standardized Units
  • a

    Explanatory variables are Multivariate ENSO Index and optical thickness. The model number refers to the models listed in Table 1. The most likely model, its associated SIC and time of shift are in bold. The p-value associated to the SIC difference between models vi and vii is in parenthesis. The p-values are the probabilities, under the hypothesis of a model with no-shift, of observing a difference between the models with a shift and models with no-shift at least as extreme as the observed difference. The smaller the p-value, the more significant the difference between the models is.

  • b

    The parameter estimates correspond to the model with the smallest SIC.

  • c

    Smallest SIC.

Mauna Loa (SIO)1960–2003vi, vii-,1988132.98, 118.67c (0.01)λ1−0.05−0.37
     λ21.110.72
     λ1λ2−1.16−1.09
     η−0.88−0.63
     τ15.840.36
South Pole (SIO)1966–2003vi, vii-,1988115.94, 109.65c (0.04)λ10.35−0.35
     λ21.270.53
     λ1λ2−0.92−0.88
     η−0.76−0.58
     τ9.530.22
image

Figure 6. Fit of the model selected to explain the net land uptake at Mauna Loa and South Pole with explanatory variables (Multivariate ENSO Index and Optical thickness). The dotted lines represent the most appropriate model fit and the vertical lines indicate the time of the shift.

Download figure to PowerPoint

[27] Models vi and vii were also fitted to the synthetic series set #1 and the results are presented in Figure 7. The model with a shift in the intercept (model vii) was selected in 88.4% (Mauna Loa) and 83.4% (South Pole) of the synthetic series. Figure 7 also presents the most likely time for a shift identified by model vii in all the synthetic series. Once again, the most likely time for a shift is 1988. The most likely time for a shift lies between 1986 and 1993 in 60.0% (Mauna Loa) and 55.1% (South Pole) of the synthetic series.

image

Figure 7. Results of the Monte Carlo study conducted on 5000 synthetic series generated with the same statistical properties (mean and variance) as the net land uptake at Mauna Loa and South Pole (set #1). (left) The frequency of the model selected (multiple linear regression model with covariates effects (vi), multiple linear regression model with covariate effects and a shift in the intercept (vii)). (right) The most likely time for a shift, given the model with a shift in the intercept (model vii) is selected.

Download figure to PowerPoint

4.3. Atmospheric Growth Rate

[28] Table 4 presents the results of the change point analysis of the annual growth rate of CO2. According to the SIC, there is a shift in the intercept in 1988. The magnitudes of the shift are 1.34 Pg C/yr and 1.09 Pg C/yr for Mauna Loa and South Pole data respectively. The long-term linear trends are both 0.09 Pg C/yr2. Figure 8 presents the fit of the model selected for each station.

Table 4. Results of the Change Point Analysis on the Annual Atmospheric Growth Rate of CO2 at Mauna Loa and South Polea
StationPeriodModelTimeSICParameter Estimatesb
  • a

    The model number refers to the models listed in Table 1. The most likely model, its associated SIC and time of shift are in bold.

  • b

    The parameter estimates correspond to the model with the smallest SIC.

  • c

    Smallest SIC.

Mauna Loa (SIO)1960–2008iii, iv, v-,1988, 1988147.72, 145.03,c 148.89λ1 = 1.22, λ2 = −0.12, λ1λ2 = 1.34, β = 0.09
South Pole (SIO)1966–2008iii, iv, v-,1988, 1988126.23, 125.98,c 129.72λ1 = 1.67, λ2 = 0.58, λ1λ2 = 1.09, β = 0.09
image

Figure 8. Fit of the model selected to explain the atmospheric CO2 growth rate at Mauna Loa and South Pole. The dotted lines represent the model selected (according to the SIC) and the vertical lines indicate the time of the shift.

Download figure to PowerPoint

5. Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and Flux Estimates
  5. 3. Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Appendix A
  10. Appendix B
  11. Acknowledgments
  12. References
  13. Supporting Information

5.1. Comparison With Previous Results

[29] The shift detected in the mean net land uptake is in agreement with the results of Sarmiento et al. [2010], in which a shift of about 0.88 Pg C/yr was detected at the same time in the net land uptake computed using Mauna Loa observations with a confidence level of 99%. In the present study, however, the confidence obtained through Monte Carlo simulations is not as large as in the Sarmiento et al. [2010] analysis because the statistical analysis applied is different. We estimate the time of the shift using change point detection and discriminate among several models, whereas Sarmiento et al. [2010]applied a t-test to test whether the mean changes after 1988. Furthermore, in the work bySarmiento et al. [2010], the decrease in the atmospheric growth rate was estimated to be approximately 0.53 Pg C/yr whereas we find a decrease of 1.34 Pg C/yr. The difference arises from the fact that Sarmiento et al. [2010] did not take into account the trend in the atmospheric CO2 growth rate, whereas both temporal trends and shifts were modeled through linear regression in the present study.

5.2. Ocean Models and Data Uncertainties

[30] If uncertainties in the ocean uptake are sufficiently large, they can bias our inferences concerning terrestrial carbon uptake. However, when we applied our change point detection method to the net land uptake estimated using each ocean model separately, we detected the same shift, at the same time, in all the net land uptake estimates using the four ocean models and the two series of CO2 atmospheric growth rate observations. We conclude that the detected shift is unaffected by uncertainty in ocean uptake, at least to the extent that the true ocean uptake is bracketed by the four models. Limitations common to all ocean models (e.g., coarse resolution, water formation, and inability to resolve eddies) were scrutinized by Sarmiento et al. [2010]. A comprehensive quantitative investigation of systematic uncertainties in forced ocean models is beyond the scope of this study, and left as a subject for future study. There is also data based information available about the ocean uptake [e.g., Takahashi et al., 2009]. However, there is not sufficient spatiotemporal coverage of these data during the period prior to the shift in order to reliably use them to determine whether the shift may occur in the ocean fluxes.

[31] Artificial shifts are often introduced in climate data time series due to changes in measurement procedures or instrumentation at observation stations [e.g., Peterson et al., 1998]. The growth rate time series is the time derivative of the atmospheric CO2 accumulation. The growth rate for a given year is expressed as the difference in concentration between the end of December and the start of January of that year. Thus, a mean shift in the CO2 concentrations due to change of measurement procedures or instrumentation in 1988 would affect only the growth rate in that year, as opposed to the growth rate of all the years after the change (from 1989 to 2008), as observed in the results of this study. Thus, the possibility that this shift was introduced by a change of measurement procedures or instrumentation is unlikely.

5.3. Change Point Technique

[32] The change point technique based on the informational approach used in this study is advantageous because it allows us to discriminate among several types of models (normal model, linear regression model, and multiple linear regression model) and to integrate several explanatory variables in the change point models. However, there is no significance level involved in this approach: the smaller the SIC value of a model is, among many possible models, the better the likelihood is for the data being described by that model. Thus, to quantify the power and risk of false detection associated to this technique, we performed Monte Carlo simulation on synthetic series reflecting the properties of the net land uptake computed using Mauna Loa and South Pole data.

[33] This approach could also be extended in order to search for other types of changes, such as changes in the relationship (linear or nonlinear relationship, given the form of the relationship is known) between the net land uptake of carbon and their respective explanatory variables. This approach would also be useful for applications to other time series of observations or model estimates of atmospheric or climatic variables, in which one needs to discriminate between several types of models. It can be easily adapted and generalized to other problems.

[34] Finally, the change point approach applied was designed to detect at most one change point. The hypothesis that there is at most one change point seems reasonable here since we were interested in characterizing the most dominant shift. For different applications, this change point technique could be extended for the detection of multiple change points following an approach similar to that used by Yao [1988] or Lu et al. [2010].

6. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and Flux Estimates
  5. 3. Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Appendix A
  10. Appendix B
  11. Acknowledgments
  12. References
  13. Supporting Information

[35] In this study, a change point analysis technique based on the SIC was applied to study shifts in the net land uptake of carbon. The atmospheric growth rate and the net land uptake were computed using CO2 concentrations observed at Mauna Loa and South Pole. These two stations are often used to represent the global CO2concentrations. Our analysis shows that it is likely that a sudden increase in the mean of the net land uptake occurred in 1988. It seems unlikely that this shift is a false alarm because the risk of false detection around 1988 is small (about 2%). Our best estimate for the magnitude of this shift is 1.2 Pg C/yr (Mauna Loa) and 0.9 Pg C/yr (South Pole). This estimate takes into account the variability in the net land uptake driven by ENSO and by volcanic eruptions. The shift we detect is highly significant (p-values of 0.01 and 0.04 for South Pole and Mauna Loa, respectively) of the synthetic series. We confirm the shift in the net land uptake by detecting a simultaneous shift in the CO2 atmospheric growth rate. According to the SIC, the CO2atmospheric growth rate exhibits a long-term linear trend that contains a sudden drop of about 1.3 Pg C/yr (Mauna Loa) and 1.1 Pg C/yr (South Pole) in 1988. We conclude that the most likely scenario is that a sudden increase in the land uptake occurred in 1988, leading to a corresponding decrease in the atmospheric CO2 growth rate.

[36] More analysis is necessary in order to understand what could have caused this shift. Several candidates that could explain this shift were pointed out by Sarmiento et al. [2010]: an underestimate of the pre-1988/89 fossil fuel emissions or an overestimate of the post-1988/89 fossil fuel emissions, a decrease in land use emissions (not supported by existing publications), plant growth stimulation by climate variability such as the Atlantic Multidecadal Oscillation or the Pacific Decadal Oscillation, and many others. Understanding what caused this shift in the net land uptake is very important in order to eventually be able to predict future major shifts in the sources and sinks of carbon.

[37] To our knowledge, change point methods have not been used before to detect shifts in the carbon cycle. The technique presented here can easily be used to detect other types of changes in a regression model or in the parameters of the underlying distribution such as a shift in the mean and/or in the variance. It could be extended to search for shifts in the relationship between carbon cycle variables and explanatory variables representing the natural climate variability, the hydrological cycle, external forcings, etc. The change point approach presented in this paper is presently being extended to integrate the autocorrelation structure in order to study shifts at smaller time scales. Future work should involve investigating shifts in the sources and sinks of atmospheric CO2 at monthly time scale.

Appendix A

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and Flux Estimates
  5. 3. Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Appendix A
  10. Appendix B
  11. Acknowledgments
  12. References
  13. Supporting Information

[38] In this appendix, we provide more details about the SIC formulation for the models fitted in this study. Details on how to obtain the SIC formulation for models iii-v are provided below. The SIC formulation can be obtained similarly for the other models and are summarized inTable A1.

Table A1. List of Models Fitted in This Study With the Associated SIC Formulation
ModelDescriptionEquations
(i)Constant meanyt = μ + εt (t = 1,…,n) SICi = n log(RSS) + n(1 + log(2π)) + (2 − n)log(n) inline image, where inline image is the sample mean
(ii)Shift in the mean inline image SICii(p) = n log(RSS) + n(1 + log(2π)) + (3 − n)log(n) inline image, where inline image and inline image are respectively the sample means before and after the shift
(iii)Intercept and linear trendyt = λ + βt + εt (t = 1,…,n) SICiii = n log(RSS) + n(1 + log(2π)) + (3 − n)log(n) inline image
(iv)Shift in the intercept and same linear trend inline image SICiv(p) = n log(RSS) + n(1 + log(2π)) + (4 − n)log(n) inline image
(v)Shift in both the intercept and linear trend inline image SICv(p) = n log(RSS) + n(1 + log(2π)) + (5 − n)log(n) inline image
(vi)Intercept and linear relation with ENSO and optical thicknessyt = λ + ηMEIt + τOTt + εt (t = 1,…,n) SICvi = n log(RSS) + n(1 + log(2π)) + (4 − n)log(n) inline image
(vii)Shift in the intercept and linear relation with ENSO and optical thickness inline image SICvii(p) = n log(RSS) + n(1 + log(2π)) + (5 − n)log(n) inline image

[39] The general formulation of the SIC to select between models j = 1,2,, m is given by:

  • display math

where SICj is the Schwarz Information Criterion for model j, L( inline image) is the maximum likelihood function for the estimated model j, kj is the number of parameters to be estimated for model j and n is the number of observations.

[40] In the regression model with no change point (model iii) and assuming the residuals are independent and normally distributed, the SIC can be expressed as:

  • display math
  • display math
  • display math

with inline image, inline image and inline image being the maximum likelihood estimates of the intercept λ, the linear trend β and the error variance σ2 in the regression model. The number 3 represents the number of parameters to estimate (intercept, trend and variance). By plugging equation (A4) and equation (A3) into equation (A2) and making some simplifications, we obtain:

  • display math

where inline image is the residual sum of squares of the model. Under the hypothesis that there is a shift in the intercept only (model iv), there is one additional parameter to estimate and the SIC becomes:

  • display math
  • display math
  • display math

where inline image and inline image are the maximum likelihood estimates of the intercept before (λ1) and after (λ2) the shift at time k in the regression model. Again, by plugging equation (A8) and equation (A7) into equation (A6) and doing simplifications, we get:

  • display math

where inline image. The SIC is evaluated for each possible time for a change point, from time 3 to n − 2, to ensure that there are at least as many observations as parameters to estimate on each side of the shift. Finally, under the hypothesis that there is a shift in both the intercept and trend (model v), the SIC is:

  • display math
  • display math
  • display math

where inline image and inline image are the maximum likelihood estimates of the trend before (β1) and after (β2) the shift at time k in the regression model. By plugging equation (A12) and equation (A11) into equation (A10) and simplifying, we get this expression:

  • display math

where RSS3 is the residual sum of squares of the model with a shift both in the intercept and trend and is given by inline image. The time of the most likely shift (p) is determined by SICv(p) = min{SICv(k), k = 2,…,n − 2}. Then, a model with a change after time p is selected if SICv(p) < SICiii or if SICiv(p) < SICiii. Otherwise, it seems more likely that there is no shift in the model. Similarly, the SIC can be computed for the different models with or without a change point that are presented in Table 1. The SIC formulation has to be modified according to the number of parameters to estimate and to the residual sum of squares of each respective model. Furthermore, the time for which the SIC is computed has to be modified to make sure there are at least as many observations as parameters to estimate on each side of the shift. The SIC equations for all the models used in this study are presented in Table A1.

[41] There is no significance level involved with the decision rule presented above. To assess significance, a critical value can be included in the decision rule. For example, when comparing model i and ii, model ii will be selected if SICii(p) + cα < SICi, with cα being the critical value at the α significance level. In this paper, we obtain the critical values and associated significance levels by Monte Carlo simulations. More specifically, we use the set of synthetic series mimicking a constant mean net land uptake presented in section 3.3.2. For each synthetic series, we fit models i and ii, compute the associate SIC values (SICi and SICii(p)) and their difference. These differences give an estimate of the distribution of cαunder a model with no-shift in the mean net land uptake. The value that is larger than 95% of the other values is the critical value associated to within a 5% significance level. The significance for a shift in the net land uptake observations can be obtained by comparing the difference between the SIC of a model with a shift and a model with no-shift to the critical value at a desired significance level (e.g., the common 5% level). If this difference is larger than the critical value for the 5% significance level approximated by Monte Carlo, the associated p-value is smaller than 0.05 and the hypothesis that there is no shift in the mean net land uptake can be rejected. In this context, the p-value represents the probability of observing a difference between the models with a shift and models with no-shift at least as extreme as the observed difference.

Appendix B

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and Flux Estimates
  5. 3. Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Appendix A
  10. Appendix B
  11. Acknowledgments
  12. References
  13. Supporting Information

[42] In this appendix, we look for additional evidence for a shift in the net land carbon uptake in 1988/1989 by analyzing the net land uptake of carbon computed using the atmospheric CO2 growth rate at several locations (Table B1). The longest publically available records of CO2concentration observations at several stations from SIO and NOAA-ESRL [Thoning et al., 1989] (available at http://www.esrl.noaa.gov/gmd/ccgg/trends/) are used. The analysis is performed at the annual time scale at stations for which there are enough observations to compute the growth rate since at least 1980. In order to avoid spurious change point detection, we only included data from stations with observations from 1980 to 2008 or longer and that do no have gaps of 12 consecutive months or more in the CO2record. If there are gaps of 12 months or longer at the beginning of the record, we leave out these years and use only the remaining part of the record for which there is no long gap. In addition, we analyzed the global time series calculated by NOAA-ESRL by combining their stations to produce a globally representative time series.

Table B1. Results of the Change Point Analysis on the Annual Net Land Uptake at Several Stationsa
StationPeriodModelTimeSICParameter Estimatesb
  • a

    The model number refers to the models listed in Table 1. The most likely model, its associated SIC and time of shift are in bold.

  • b

    The parameter estimates correspond to the model with the smallest SIC.

  • c

    Smallest SIC.

  • d

    The normality hypothesis is not respected (Lilliefors test, 95% confidence level).

La Jolla Pier (SIO)1970–2003i, ii, iii, iv, v-, 2001, -, 1988, 1998141.70,c 144.15, 145.21, 145.43, 147.95μ = 0.75, σ = 1.78
Point Barrow (SIO)1975–2003i, ii, iii, iv, v-, 1988, -,1988, 1988138.02, 140.00, 141.37, 137.72,c,d 141.02λ1 = 1.93, λ2 = 6.25, λ1λ2 = −4.33, β = −0.23
Christmas Island (SIO)1976–2003i, ii, iii, iv, v-, 1988, -, 1988, 197798.25,c 99.39, 101.35, 100.04, 103.11μ = 0.76, σ = 1.26
Key Biscane (NOAA-ESRL)1977–2003i, ii, iii, iv, v-, 1989, -, 1989, 1982107.50,c 108.18, 110.16, 109.97, 110.96μ = 0.61, σ = 1.60
Niwot Ridge (NOAA-ESRL)1977–2003i, ii, iii, iv, v-, 1988, -, 1988,1979100.61, 100.77, 103.32, 101.73, 99.93cλ1 = −3.98, λ2 = −0.16, β1 = 2.56, β2 = 0.05
Baring Head (SIO)1978–2003i, ii, iii, iv, v-, 1987, -, 1987, 198782.65,c,d 83.81, 85.85, 83.37, 86.12μ = 0.88, σ = 1.07
Palmer Station (NOAA-ESRL)1979–2003i, ii, iii. iv, v-, 1988, -,1988, 198874.94, 72.79, 77.44, 70.83,c 73.91λ1 = 0.85, λ2 = 2.92, λ1λ2 = −2.07, β = −0.10
Cape Kumukahi (SIO)1980–2003i, ii, iii, iv, v-, 1989, -, 1989, 198983.41,c 84.92, 86.47, 85.81, 88.95μ = 0.80, σ = 1.23
Cold Bay (NOAA-ESRL)1980–2003i, ii, iii, iv, v-, 2001, -, 1988, 198896.71,c 97.34, 99.75, 97.93, 101.11μ = 0.71, σ = 1.62
Mariana Islands (NOAA-ESRL)1980–2003i, ii, iii, iv, v-, 1988, -,1988, 198890.25, 90.88, 93.42, 87.30,c 90.17λ1 = 1.13, λ2 = 4.13, λ1λ2 = −2.99, β = −0.17
Global (NOAA-ESRL)1980–2003i, ii, iii, iv, v-, 1988, -,1988, 198884.55, 84.24, 87.45, 83.24,c 86.38λ1 = 0.82, λ2 = 3.22, λ1λ2 = −2.40, β = −0.12

[43] We found that it is likely that a shift occurred in 1988 in 4 stations out of 11. Most of these stations are not as representative for global growth rates as Mauna Loa or the South Pole. It should be noted that the analysis performed using the global growth rate from NOAA-ESRL also shows an abrupt shift in 1988.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and Flux Estimates
  5. 3. Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Appendix A
  10. Appendix B
  11. Acknowledgments
  12. References
  13. Supporting Information

[44] The authors would like to thank G. Stenchikov for helping with the optical thickness record; G. Marland for providing the fossil fuel emissions estimates; R. Keeling, S. Piper, and P. Tans for providing the CO2 concentration observations freely on the Internet; and K. Wolter for providing the Multivariate ENSO Index data freely on the Internet. The authors would also like to thank J. Lean for providing the solar irradiance data that was used in preliminary analyses. The authors would like to thank W. Buermann, M. Gloor, and J. Lanzante for useful comments on the manuscript. The authors would also like to thank I. Enting, an anonymous reviewer, the Associate Editor, and the Editor for making valuable comments that improved the quality of the paper. The authors acknowledge financial support from the Fonds Québécois de la Recherche sur la Nature et les technologies, the Carbon Mitigation Initiative with support from BP, the Cooperative Institute for Climate Science, and the New Zealand Research Foundation (contract C01X0703).

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and Flux Estimates
  5. 3. Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Appendix A
  10. Appendix B
  11. Acknowledgments
  12. References
  13. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and Flux Estimates
  5. 3. Methodology
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Appendix A
  10. Appendix B
  11. Acknowledgments
  12. References
  13. Supporting Information
FilenameFormatSizeDescription
gbc1830-sup-0001-t01.txtplain text document1KTab-delimited Table 1.
gbc1830-sup-0002-t02.txtplain text document1KTab-delimited Table 2.
gbc1830-sup-0003-t03.txtplain text document1KTab-delimited Table 3.
gbc1830-sup-0004-t04.txtplain text document1KTab-delimited Table 4.
gbc1830-sup-0005-taA01.txtplain text document2KTab-delimited Table A1.
gbc1830-sup-0006-taB01.txtplain text document2KTab-delimited Table B1.

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.