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 Recent studies report an increase in vegetation greenness in mid-to-high northern latitudes. This increase is observed in leaf-out data in Europe and North America since the 1950s and in satellite data since the 1980s. Increased vegetation greenness is potentially a factor contributing to a land CO2 sink. Various causes for increased vegetation greenness are suggested, but their relative importance is uncertain. In the present study, the effect of climate and CO2 fertilization on increased vegetation greenness and the land CO2 sink are investigated. The study is organized as follows: (1) A model is used to simulate monthly global normalized difference vegetation index (NDVI) fields for 1901–2006. The model is derived from NDVI, precipitation, and temperature data for 1982–1999. The modeled fields, referred to as reconstructed vegetation index (RVI), are tested back in time on phenological data (1950s–1990s) and forward in time on Moderate Resolution Imaging Spectrometer (MODIS) data (2001–2006). The RVI represents the response of NDVI to variations in climate. (2) Residuals between RVI and NDVI are analyzed for associations with variations in downwelling solar radiation, nitrogen deposition, satellite-related artifacts, and CO2 fertilization. CO2 fertilization was the only factor that improved RVI modeling. (3) The effect of climate variations and CO2 fertilization on the land CO2 sink, as manifested in the RVI, is explored with the Carnegie Ames Stanford Assimilation (CASA) model. Climate (temperature and precipitation) and CO2 fertilization each explain approximately 40% of the observed global trend in NDVI for 1982–2006. For 1901–2006, estimated trends in NDVI related to CO2 fertilization are four to five times larger than climate-related trends. CASA simulations indicate that the CO2 fertilization effect on vegetation greenness contributes about 0.7 Pg C per year to the recent land CO2 sink. This is a conservative estimate and is likely larger. This effect of CO2 fertilization would be a large component of the land carbon sink. In the supporting information the RVI is used as a common standard to fuse MODIS and advanced very high resolution radiometer (AVHRR) NDVI data. This fusion compares well with SeaWiFS data.
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 A remarkable recent observation is the increase in vegetation greenness for large parts of the Northern Hemisphere. Evidence for this greening is supported by three independent types of observations: phenological records in Europe and North America which indicate that leaf-out of trees is about 2–4 weeks earlier for the 1990s compared to the 1950s [Menzel and Fabian, 1999; Schwartz and Reiter, 2000]; the advanced very high resolution radiometer (AVHRR) normalized difference vegetation index (NDVI) data for 1982–1999 shows increased greenness in temperate regions in the Northern Hemisphere [Myneni et al., 1997; Slayback et al., 2003]; and the atmospheric CO2 record shows longer seasonal cycles of larger amplitude, suggesting a longer growing season and larger uptake of CO2 by vegetation [Keeling et al., 1996]. Increases in vegetation greenness are attributed to increased temperatures during spring in midlatitudes [Keeling et al., 1996; Menzel and Fabian, 1999; Myneni et al., 1997], to variations in downwelling solar radiation in the tropics [Nemani et al., 2003], and to variations in the fraction of diffuse radiation [Lucht et al., 2002; Mercado et al., 2009]. Locally, increased vegetation is linked to increased precipitation, e.g., vegetation in the Sahel has partially recovered since the largest drought of the 20th century in 1984 [Tucker et al., 1991; Prince et al., 2007].
 Increased atmospheric CO2 concentrations may be a cause for increased vegetation greenness as well [Kohlmaier et al., 1989]. Laboratory experiments associate doubled ambient CO2 levels with increased crop yields, by over 30% in C3 plants and by 14% in C4 plants [Cure and Acock, 1986; Kimball et al., 1993]. The free air (chamberless) CO2 enrichment (FACE) experiments find a lower response of vegetation to increased atmospheric CO2 concentrations [Ainsworth et al., 2008; Leakey et al., 2009], although a direct comparison of the FACE experiments and laboratory experiments is hampered by differences in environmental factors such as drought, temperature and nutrient stress, and damage caused by pests. Lobell and Field  report evidence for CO2 fertilization from an analysis of a large sample of wheat and rice crop data for 1961–2002 from 20 countries. Their average estimate of CO2 fertilization is similar in magnitude to estimates from laboratory experiments and larger by a factor 2 compared to the FACE estimates. However, the spread around the estimates of Lobell and Field  is much larger than that around either the lab experiments or the FACE experiments.
 The present study explores causes for increased vegetation greenness and their implications for the land CO2 sink. Estimates of climate-related trends in vegetation greenness are obtained from a model that generates monthly 0.5∘ × 0.5∘ global NDVI look-alike records for 1901–2006 (section 3.1); the simulated NDVI is referred to as reconstructed vegetation index (RVI) [Los et al., 2006]. The RVI is tested for goodness of fit on AVHRR data and is tested back in time on historic records of leaf-out from North America and Eurasia and forward in time on global Moderate Resolution Imaging Spectrometer (MODIS) data (section 3.3). Differences between RVI and NDVI (model and observations) are analyzed for associations with increased atmospheric CO2 concentrations (section 3.2). Two alternative RVI scenarios, with and without CO2 fertilization, are compared in section 3.4. Other factors investigated to explain the difference between NDVI and RVI are variations in incoming shortwave radiation; changes in data collection from NOAA-7 to NOAA-9, nitrogen deposition, and correlations between increased atmospheric CO2 and increased land-surface temperatures (section 3.5). None of these factors significantly improved the RVI. Section 4 contains a discussion of the relative impact of various causes of trends in NDVI data; it also indicates the spatial distribution of CO2 fertilization and the effect of CO2 fertilization by biome (section 4.2). An analysis of the sensitivity of the land-surface carbon sink to increased greening as a result of CO2 fertilization is carried out with the Carnegie Ames Stanford Assimilation (CASA) model (Potter et al., 1993; Van der Werf et al., 2006; section 4.3).
 In the present study, the Fourier-adjusted, sensor and solar zenith angle corrected, interpolated and reconstructed (FASIR) Normalized Difference Vegetation Index (NDVI) version 4.1 data are used [Los et al., 2000, 2005]. The NDVI is calculated as (ρ2 − ρ1)/(ρ2 + ρ1), where ρ1 is the visible (red) reflectance measured by AVHRR channel 1 and ρ2 is the near-infrared reflectance measured by AVHRR channel 2. The NDVI is near-linearly related to the fraction of photosynthetically active solar radiation (largely visible light) absorbed by the green parts of the vegetation canopy (fAPAR; [Sellers, 1985]). The FASIR NDVI version 4.1 data are derived from the Pathfinder AVHRR Land (PAL) data for 1982–1999 [James and Kalluri, 1994]. Additional corrections were applied to adjust the 8 km PAL data for residual sensor degradation effects and sensor calibration differences [Los, 1998], bidirectional reflectance distribution function (BRDF) effects [Los et al., 2005], effects of volcanic aerosols [Los et al., 2000], short-term (≤2 months) cloud effects and atmospheric effects, and missing data. The corrected 8 km data were averaged to 0.5∘ × 0.5∘ resolution. The three largest sources of uncertainty remaining in the FASIR NDVI data are related to (1) residual BRDF effects; estimated at 0.03 NDVI (root-mean-square error; RMSE) for dense vegetation (NDVI > 0.4). The RMSE is 0.02 NDVI when only the interannual variation is considered [Los et al., 2005]; (2) residual effects of volcanic aerosols after the El Chichon (1982–1983) and Mount Pinatubo (1991–1993) eruptions (RMSE = 0.05 NDVI); and (3) missing data for September–December 1994 for which period a climatological average was used (RMSE = 0.05 NDVI); [Los et al., 2000]. For sparse vegetation (NDVI < 0.2), the error estimates are 2–10 times smaller. Other residual errors related to calibration, short-term variations in atmospheric aerosols, and residual cloud effects are 5–10 times smaller.
 The Moderate resolution imaging spectrometer (MODIS) NDVI data (MOD13C2 and MYD13C2 v5) were used for February 2000–December 2006 [Huete et al., 2002]. A maximum 3 × 3 spatial filter was used over data from broadleaf evergreen land-cover type. A weighted Fourier adjustment was applied to the data as described in [Sellers et al., 1996a; Los et al., 2000]. The 0.05∘ × 0.05∘ climate modeling grid then was spatially averaged to the 0.5∘ × 0.5∘ resolution of the other data sets.
 The 0.5∘ × 0.5∘ monthly Tyndall Centre Climate Research Unit (CRU) precipitation and temperature data version 3.0 [Mitchell et al., 2002] for 1901–2006 were used to model the seasonal and interannual variation in NDVI.
 The lilac leaf-out and bloom data for North America [Cayan et al., 2001; Schwartz and Reiter, 2000; Schwartz and Caprio, 2003], the oak leaf-out data for Germany from the German weather service, the Marsham oak leaf-out data for Norfolk, England [Sparks and Carey, 1995], and the bird cherry blossom data for Russia (http://www.biodat.ru/) were used to test NDVI simulations prior to 1982.
 Monthly atmospheric CO2 concentrations for 1958–2006 [Keeling et al., 1976; Thoning et al., 1989] are extended back in time with the annual CO2 records from the Law Dome DE08, DE08-2, and DSS ice cores [Etheridge et al., 2001]. The mean seasonal cycle for the first 4 years of the Mauna Loa record minus overall mean was added to the annual Law Dome ice core data to obtain monthly varying estimates of atmospheric CO2 concentrations for 1901–1957.
 The global MODIS International Geosphere Biosphere Projects (IGBP) majority land-cover classification at 0.05∘ × 0.05∘ (MCD12C1 v5, 2006, Loveland et al., 2001) is used to identify broadleaf evergreen land-cover for the FASIR adjustment of the MODIS data in this section; the International Satellite Land Surface Climatology Project (ISLSCP)-2 IGBP Simple Biosphere (SiB) land-cover data [Loveland et al., 2001] are used to analyze the 0.5∘ × 0.5∘ data in section 4.1. Global nitrogen deposition maps [Galloway et al., 2004; Dentener, 2006] for 1993 are obtained from the Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC) (http://daac.ornl.gov).
 Solar radiation fields are obtained from the National Centers for Environmental Prediction (NCEP)-Department of Energy (DOE) Atmospheric Model Intercomparison Project (AMIP)-II reanalysis [Kanamitsu et al., 2002]. The NCEP data were used since they cover the entire period for which Pathfinder AVHRR NDVI data are available (1982–1999).
3 Simulating and Testing the Reconstructed Vegetation Index (RVI)
 The RVI model is described in section 3.11. RVI is calculated from 0.5∘ × 0.5∘ monthly precipitation and temperature data for 1901–2006. In section 3.2, the RVI is further improved by incorporating a CO2 fertilization effect. In sections 3.3 and 3.4, the RVI is tested back in time on phenological data and forward in time on MODIS data. The RVI products with and without a CO2 fertilization effect are compared in section 3.4 as well. In section 3.5, it is explored if other factors improve the RVI; these are variations in downwelling solar radiation, nitrogen fertilization, satellite artifacts, and correlations between atmospheric CO2 concentrations and land-surface temperature.
 The RVI simulates monthly variations in the NDVI from monthly precipitation and temperature data and RVI estimates from previous time steps as well. The RVI is estimated in two stages: in the first stage, regression coefficients are estimated from NDVI, precipitation, and temperature data; in the second stage, the RVI is calculated.
3.1.1 Estimation of Coefficients
 Coefficients are estimated by month for time series in each 0.5∘ × 0.5∘ cell. The estimation uses the following equation [Los et al., 2006]:
Normalized difference vegetation index
Max. V of previous calendar year
Observed vegetation index for time t (–)
Anomaly of 10log(monthly precipitation (mm) +1)
Anomaly of monthly mean surface air temperature (°C)
Regression coefficient (mean NDVI1982–1999)
Regression coefficient for month t and lag i; constrained bt,j = bt − 12,j etc.
Time index in months
Lag index in months
 Anomalies (P,T) are relative to their respective monthly means of 1982–1999. As an example, the coefficients for all Mays in a time series are estimated from all monthly precipitation values for March until June, all monthly temperature values for March until May, all monthly NDVI values for March and April, and all maximum vegetation index values of the previous calendar years. Notice that precipitation of the next month can be an explanatory variable for vegetation greenness of the current month [Los et al., 2006]. For estimation of the coefficients, the boundary months at the start of the time series, January and February 1982, use the 1982–1999 November and December mean values for precipitation, temperature, and vegetation index as estimates for the preceding year. The boundary months at the end of the time series use the 1982–1999 mean for the first month of the year 1999. The memory term for the first year, Vy − 1, uses the average of the maximum annual NDVI values for 1982–1999. A least angle regression (LARS) technique [Efron et al., 2004] ranks estimated coefficients in order of the amount of variance explained. Coefficients are only incorporated in the regression if they decrease the Akaike Information Criterion (AIC); they are set to zero otherwise. The coefficients for selected variables are adjusted using a canonical correlation analysis to take into account the effect of errors in both the explanatory (precipitation, temperature, and NDVI) and response (NDVI) variables [Draper and Smith, 1998]. This adjustment increases the variance of the response variable (RVI), which would otherwise be underestimated.
3.1.2 Calculation of the RVI
 The monthly RVI was calculated for 1901–2006 from the CRU precipitation and temperature data [Mitchell et al., 2002] using estimated regression coefficients , , , , and and model estimates and in equation (1). Calculation starts with January 1901 for which estimate the RVI requires monthly RVI, temperature, and precipitation values for November and December of 1900 as well as a maximum RVI value for 1900. For these values, averages from 1982 to 1999 were used as substitutes. The RVI was first calculated for 1901–1920; the 1920 RVI estimates were then used as starting values to calculate the RVI for 1901–2006. This version of the RVI is referred to as the RVI control. The tests in sections 3.3 and 3.4 are applied to the RVI. A summary of the global distribution of the coefficient of correlations and RMSEs is shown in Table 1. The residual errors are similar in magnitude as the uncertainty in NDVI (section 2).
Table 1. Summaries of the Frequency Distributions of Global RVI Fitting Statistics (Coefficient of Correlation and Root-Mean-Square Error) for 1982–1999
3.2 CO2 Adjusted RVI
 From 1982 to 1999, the mean annual atmospheric CO2 concentrations at Mauna Loa increased from approximately 340 ppmv to 370 ppmv. There is evidence that increased atmospheric CO2 concentrations stimulate photosynthesis and increase the water-use efficiency of plants and that these effects may increase the leaf area index. Lobell and Field  obtained estimates of CO2 fertilization from an analysis of agricultural data for a period of approximately twice the length of the RVI training period and a 65% larger increase in atmospheric CO2. The approach in the present paper differs from Lobell and Field  in two ways. First, the variance explained by climate in interannual variations in crop yield was ignored by Lobell and Field  but is explicitly considered in the present analysis, and this likely improves estimates of CO2 fertilization [Lobell and Field, 2008]. Second, a CO2 fertilization factor is estimated directly from the residuals between model and observations rather than by using the first differences.
 An expression for the CO2 fertilization factor is given by Esser et al. :
 The equation above is shown to demonstrate the analogy with the regression-based estimation of a CO2 effect in NDVI data below; further details on equation (2) can be found elsewhere [Esser et al., 1994]. The magnitude of fsoil varies spatially, dependent on factors such as soil type, nutrient availability, and moisture retention capacity. Most values for fsoil are between 0.03 (Takyric Solonchak) and 2.8 (Gleyic Luvisol; see Esser et al. ).
 The detection of CO2 fertilization is based on a regression of the differences between RVI simulations and FASIR NDVI observations with fsoil = 1. This value is acceptable for regression analysis, since the correlation of for different values of fsoil is very high; for example, the correlation between with fsoil = 0.5 and fsoil = 4 for 1958–2008 exceeds 0.998. A regression-based approach does not allow to distinguish between different soil fertilization factors; neither does it lead to insights as to when CO2 fertilization may saturate. An equation to predict the effect of CO2 fertilization on net primary production (NPP) is as follows [Esser et al., 1994]:
with NPP the net primary production; ε the efficiency factor limited by T and moisture; fAPAR the fraction of photosynthetically active radiation (PAR) absorbed by green parts of the vegetation canopy; and IPAR the incoming photosynthetically active radiation. The fAPAR is closely linked to NDVI [Sellers et al., 1996a]. Analogous to this, the CO2 fertilization effect is estimated for each 0.5∘ × 0.5∘ by finding β0 and β1 using
 The simple ratio (SR) transformation of the NDVI and RVI is used, SR(x) = (1 + x)/(1 − x) with x = V or x = RVI, to avoid dividing by zero or a very small number in equation (4). Where the slope, β1, is significant at p < 0.1, the coefficients for are calculated; otherwise β0 = 1 and β1 = 0. Approximately 37,000 cells out of about 60,000 cells showed a significant correlation with (p < 0.1).
 The monthly time series of CO2 for 1901–2006 consisting of the merged Mauna Loa CO2 data and the Law Dome DE08, DE08-2, and DSS ice cores ( Etheridge et al., 2001; section 2) were used to adjust the global monthly RVI time series from 1901 to 2006 for the CO2 fertilization effect:
 The CO2 adjusted SR values can be transformed to NDVI values by using (x − 1)/(x + 1) with x the SR value. This CO2-adjusted RVI version is referred to as RVI.
3.3 Testing the RVI With Phenological Data
 Temporal variations in RVI control fields are compared with interannual variations in leaf-out and first day of bloom in five different data sets: the North America lilac leaf-out and lilac bloom data [Schwartz and Reiter, 2000; Schwartz and Caprio, 2003], the oak leaf-out data for Germany from the Deutscher Wetterdienst, the Marsham oak data [Sparks and Carey, 1995] from Norfolk (east England), and the Bird Cherry blossom data from Russia (http://www.biodat.ru/). For each phenological time series, the maximum correlation was calculated for the RVI control time series of the same location from a window of 1 month either side of the mean month indicated by the leaf-out data. Histograms of the correlations are shown in Figure 1. Negative correlations between day of leaf-out and vegetation greenness dominate (higher RVI values in spring correspond to an earlier leaf-out date). The correlation for the Marsham oak data [Sparks and Carey, 1995] from 1901 until 1958 and the April RVI is −0.78. Some correlations between the RVI and leaf-out date are positive (Figure 1); the correlations between spring temperature and leaf-out day was positive for these sites as well (not shown). The RVI 0.5∘ × 0.5∘ cells and site phenological data are observed at different spatial scales; however, both NDVI and temperature anomalies (closely linked to the RVI anomalies in temperate latitudes) have in general high spatial correlations at distances <60 km [Perry et al., 2002; Gunst, 1995], and this allows for a meaningful comparison.
3.4 Testing the RVI With Satellite Data
 Figure 2a shows the spatial distribution of the correlations between anomalies of the RVI and the fused AVHRR MODIS NDVI (supporting information). The mean r = 0.5 (excluding deserts and tropical forests); correlations are significant for most of the globe with the exception of deserts and tropical evergreen forests. These two land-cover types exhibit low seasonal and interannual variation in vegetation, and therefore low correlations are expected. Figure 2b shows a density scatter plot with, on the x axis, the correlations between the anomalies in RVI and FASIR NDVI and, on the y axis, the same correlations but for taking CO2 into account in both. The correlations for the latter are higher on average—the mean r = 0.55, the difference for the means of the two correlation distributions is small but statistically significant (p ≪ 0.01).
 Figures 2c and 2d show the same analysis for the correlations of the RVI anomalies with the MODIS data only; the MODIS period was not used to train the model; therefore, the correlation is an indication of the skill of the RVI. Correlations for the 2000–2006 are expected to be lower because (1) the interannual variation in climate and NDVI for this period is lower than for the 1982–1999 period (section 3.4) and (2) for 2001–2006 fewer observations are used to amalgamate the gridded precipitation and temperature data [Mitchell et al., 2002].
 The average global monthly RVI (control) for 1982–2006 and merged FASIR NDVI for 1982–2010 (supporting information) are shown in Figure 3a. The departures from the monthly means, the anomalies, are shown in Figure 3b. The anomalies in the global RVI have smaller variance than the anomalies in the FASIR NDVI; Figure 3b indicates larger negative values for the RVI anomalies for the earlier part of the record (1982–1990) and larger positive values for the later part (1991–1999). Part of this trend is caused by variations in climate (RVI control), and an additional trend is explained by CO2 fertilization (RVI).The difference in trend for 1982–2010 in the FASIR NDVI (supporting information) with and without CO2 fertilization is small (Figure 3b).
3.5 Testing for Other Factors
 Four additional factors that could explain the variance in residuals between NDVI and RVI are analyzed; these are as follows: variations in incoming solar radiation, nitrogen deposition, correlations between atmospheric CO2 concentrations and increased temperature, and potential artifacts in the NDVI related to the change of NOAA-7 to NOAA-9 in January 1985. The change from NOAA-7 to NOAA-9 coincides with the start of a large negative anomaly in the global mean NDVI Figure 3b and warrants closer scrutiny.
 The effect of radiation on vegetation greenness was estimated as follows. Monthly shortwave incoming radiation fields were linearly interpolated to 0.5∘ × 0.5∘ [Kanamitsu et al., 2002] and were used in equation (4) to obtain a radiation fertilization factor instead of a CO2 fertilization factor. The regression showed that, locally, variations in vegetation greenness can be explained by variations in incoming shortwave radiation (approximately 32,000 out of 60,000 cells showed a significant relationship at p < 0.1). However, radiation effects on NDVI were small and both positive and negative and canceled each other out when applied to the RVI. The change in the mean global RVI was between −0.0013 and −0.0034 for 1950–2006. The radiation adjustment was therefore ignored in further analysis.
 A second factor explored is the potential effect of nitrogen fertilization on NDVI. Global data on nitrogen deposition used in this study provide only snapshots for the 19th, 20th, and 21st centuries [Galloway et al., 2004; Dentener, 2006], and this poor temporal resolution prohibits a temporal comparison. It is possible however to compare the spatial distribution of the amount of N deposition with the estimated CO2 fertilization effect on NDVI. A correlation analysis between the log of N deposition versus the CO2 fertilization shows that, at the global scale, N deposition explains 4% of the variance in CO2 fertilization; the effect is statistically significant (p ≪ 0.01), but in a physical sense the effect is small and explains only a negligible proportion of the variance in the data. In Figure 4, trends between CO2 fertilization and N deposition are explored for the four biomes with the largest median CO2 fertilization effect. A variable span scatter plot smoother [Friedman, 1984] is applied to show the local relationship between CO2 fertilization and N deposition. Deciduous needleleaf shows an increase in CO2 fertilization with N deposition for values up to 200 mg N m−2 y−1; for agriculture, a consistently increasing relationship appears between CO2 fertilization and N deposition. The other two biomes show a small dependency of CO2 fertilization on N deposition. These results are similar to those by Nadelhoffer et al. , who found only a small effect of nitrogen deposition on the CO2 fertilization in temperate forests. Based on the analysis of limited data, N deposition appears to be a minor factor in explaining vegetation trends.
 A third potential problem is the correlation between land-surface temperatures and atmospheric CO2 concentrations. In the present paper, the RVI is calculated as a function of temperature and precipitation, and the CO2 fertilization is calculated from the differences between NDVI and RVI. This approach maximizes the variance explained by P and T and minimizes the variance explained by atmospheric CO2. The potential for a problem linked to correlations between CO2 and T is explored in Figure 5a; this figure shows low correlations for most vegetated areas and high correlations for bare areas. Similarly, Figure 5b shows near-zero correlations between annual surface temperature and the estimated effect of CO2 fertilization on NDVI but high (either positive or negative) correlations over bare areas. The variance in estimated CO2 fertilization effect over these areas is very small, however (section 4 and Figure 1).
 A fourth factor explored is related to a change in satellites. The low NDVI values during 1985–1986 (Figure 3b) could be spurious since they occur just after the switch from NOAA-7 to NOAA-9. The spatial distribution of 1985–1986 NDVI anomaly is therefore shown in Figure 6 with the anomalies in temperature, precipitation, and RVI. The largest negative NDVI anomalies occur in Australia, below and above the equator in Africa, and throughout Eurasia. These negative anomalies are largely reproduced in the RVI but are smaller in magnitude in Asia and parts of Africa (Figure 6b). A large negative anomaly is found in the temperature data throughout Eurasia and parts of North America similar to that in the NDVI data (Figure 6c), and below-normal rainfall is found in Australia (Figure 6d). Below-normal departures in precipitation are small in Africa but do to some extent appear in the RVI. These RVI anomalies are likely caused by a memory effect since the RVI allows low vegetation greenness values associated with drought (1984) to be carried over to the next year (equation (1); Los et al., 2006). The comparison with climate data indicates that the 1985–1986 NDVI is a genuine feature that is linked with low temperatures in midlatitudes to high latitudes and with low precipitation in Australia and to some extent in Africa.
4 Analysis of NDVI Trends and Implications for the Land CO2 Sink
 Causes for trends in the fused AVHRR MODIS NDVI data (supporting information) are analyzed in further detail: The effect of climate is discussed in section 4.1; the additional effect of CO2 fertilization is discussed in section 4.2, and the potential implications of CO2 fertilization for the land-surface carbon cycle are explored in section 4.3.
4.1 Trends in Annual Data
 Figure 7 shows the trends in global mean fused AVHRR MODIS NDVI for 1982–2010. Most areas show an increase in NDVI for this period; the exceptions are the Sahara which shows no change and areas in the western parts of North America, south of the Amazon (South America), in central Asia, and central Australia, which show a decrease. Positive trends in similar NDVI data were reported in other studies as well [Myneni et al., 1997; Tucker et al., 2001; Slayback et al., 2003; Nemani et al., 2003]; the large negative excursion in NDVI during the early part of the time series, 1985–1986, makes a very important contribution to these trends. Compared to the control, both positive and negative trends in the fused AVHRR MODIS NDVI + CO2 data (supporting information) are larger; the largest increases are found in western and central Europe and the highlands in eastern Africa. In some cases, e.g., where land-cover change occurs for example as a result of deforestation, the negative correlation between atmospheric CO2 correlation and NDVI is spurious.
 Figure 7c shows the trend in the RVI control for 1901–2006 and provides an estimate of the effect of climate (precipitation and temperature) on vegetation over the 20th century. Incorporating CO2 fertilization in the RVI leads to larger estimates of the trend for 1901–2006 (compare Figures 7c and 7d). The difference in the trend in Figures 7c and 7d provides an indication of the effect of CO2 fertilization only. For most of the land, except for the bare soil (largely desert), the CO2 fertilization is linked to a positive trend in vegetation.
 Figure 8 summarizes the increase in NDVI associated with variations in climate (Figure 2a) and CO2 fertilization (Figure 2b) as a function of biome type. The increase in NDVI associated with climate is calculated as the difference between the average monthly RVI for 1991–2000 and 1981–1990; the increase associated with CO2 fertilization uses the difference between RVI and RVI for the same periods. Average changes in trends are significantly different from 0 for all biomes. All biomes show an increase in average NDVI that is associated with variations in climate; this increase is small for tundra (class 10) and deserts (class 11). CO2 fertilization effect on NDVI is negative for tundra (class 10) and small for deserts (class 11), shrubs and ground cover (class 8), and needleleaf evergreen (class 4). The four cover types with the largest average increases are the broadleaf deciduous (2), mixed broad and needle leaf (3), grassland (7), and agriculture (12) classes.
4.2 CO2 Fertilization
 Figure 9a shows the time series of the mean global annual RVI with and without CO2 fertilization for 1901–2006. Similar to the spatial analysis, it is found that for 1901–2006, CO2 fertilization increases the trend 4 to 5 times compared to the RVI control. For 1982–2006, the robust trend in the RVI control (climate-related trend) is about 48% of the RVI + CO2 fertilization trend; and the trend in the RVI + CO2 fertilization is about 80% of the trend in the satellite data for the same period. The climate-associated trends appear larger in Figure 2 than in Figure 9; this is because estimates in the former figure are sensitive to the negative departure in NDVI during 1985–1986, whereas for Figure 9a robust regression was used, which is resistant to the effect of this large departure [Rousseeuw and Leroy, 1987]. As an aside, the difference in trend in the FASIR NDVI with and without CO2 fertilization is small (Figure 9a; supporting information).
4.3 Impact on Net Ecosystem Productivity (NEP)
 A sensitivity study is conducted with the Carnegie Ames Stanford Assimilation model (CASA; Potter et al., 1993) to investigate the effect of enhanced vegetation greenness associated with CO2 fertilization on net primary productivity (NPP) and net ecosystem productivity (NEP). An updated version of CASA [Van der Werf et al., 2006] is ported to the R environment [R Development Core Team, 2008]. CASA calculates NPP similar to equation (3) at a monthly time step. The efficiency factor ε depends on the monthly temperature and soil moisture; it decreases when monthly temperature and soil moisture move away from optimum conditions. CASA allocates the carbon taken up by plants to their stems, leaves, and roots. Dead plant material is allocated to various carbon pools with different rates of decomposition and turnover times.
 The net ecosystem productivity (NEP) is calculated as the difference between NPP and three respiration terms:
with RESP the heterotrophic respiration, HERB the consumption by herbivores, and FIRE the burning of biomass. The global, monthly RVI control and RVI + CO2 fertilization scenarios for 1901–2006 are used as inputs to CASA to estimate the sensitivity of NPP and NEP to variations in vegetation greenness. Other inputs are global monthly precipitation and temperature from the climate research unit for 1901–2006 [Mitchell et al., 2002] and monthly PAR fields averaged for 1983–1999 [Bishop et al., 1997]. In the present study, associated effects of global change such as changes in water-use efficiency, land-cover change, and radiation are not considered. The purpose is to isolate the effect of changes in vegetation greenness on NPP and NEP and to investigate the relative importance of climate variability and CO2 fertilization for the land CO2 sink. Prior to the simulations, CASA is spun up for each of the two scenarios as follows: hydrology and NPP are spun up for 5 years using mean observed fields for 1982–1998, and the carbon pools are spun up by repeating the first 10 years of RVI, precipitation, and temperature input (1901–1910) 350 times for a total spin-up of 3505 years. Transient simulations are carried out for 1901 to 2006 using the same values for turnover rates, decomposition rates, Q10, fire parameters soil parameters, vegetation class, and herbivore consumption parameters as in Van der Werf et al. . The heterotrophic respiration depends on temperature (using Q10 = 2) and soil moisture; the fire and herbivore calculations use average factors established for the 1990s [Van der Werf et al., 2006].
 The variations in annual NPP obtained by the two scenarios for 1901–2006 are shown in Figure 9. The variation in mean annual NDVI used as input to the CASA simulations is shown in Figure 9a. The NPP of the RVI with CO2 fertilization is about 4 Pg C y−1 lower during 1900–1920 than the RVI control (Figure 9b). The NEP (Figure 9c) is similar for the two scenarios from 1901 until the 1920s; from the 1930s onwards, the NEP calculations start to diverge. From the 1980s onwards, the sink in the RVI with CO2 fertilization scenario is about 0.5 Pg C y−1 higher. Both scenarios show depressed NEP values during the first half of the 1980s; the values are between −1 and 0 Pg C y−1 for the control and vary between 0 and 1 Pg C for the CO2 fertilization scenario. The average NEP values between 1960 and 2006 are about 0.15 Pg C y−1 for the control and about 0.7 Pg C y−1 for the CO2 fertilization scenario. The latter value is slightly less than half of the global annual land sink of 1–3 Pg per year averaged over the same period [Tans et al., 1990; Ciais et al., 1995; Le Quéré et al., 2009].
5 Discussion and Conclusions
 The RVI algorithm was developed in a previous study [Los et al., 2006] to simulate NDVI variations in Africa north of the equator for the 20th century. The same algorithm was applied to capture seasonal and interannual variations in the NDVI globally. Testing the RVI prior to 1982 is hampered by a paucity of data; comparisons with a limited number of data sets indicate that variations in the start of the growing season in phenological data were captured by the RVI in a majority of cases. A more thorough test of the RVI is carried out for the satellite era, 1982–2006. The RVI captured a significant proportion of the seasonal and interannual variation in the AVHRR data of 1982–1999 (Table 1), the period from which the regression coefficients were derived. A lower proportion of the interannual variance in the MODIS data was captured by the RVI (Figure 2). The lower interannual variation explained by the RVI in the MODIS data (median r 1982–2006 is 0.5 versus median r 2001–2006 is 0.2) is in large part linked to lower interannual variations in climate and vegetation for this period (Figure 3). The lower number of station data used to compile the CRU precipitation and temperature data is a likely contributing factor as well Mitchell et al. .
 Both climate (RVIcontrol) and CO2 fertilization (RVI) explain the trend in NDVI observations for 1982–2006. The two RVI scenarios indicate that for 1982–2006, about 40% of the trend can be attributed to climate and about 80% to CO2 fertilization and climate combined; about 20% of the trend in the observations is unexplained (Figure 9). Possible explanations for the residual trend of 20% is that some areas are not included in the calculation of the CO2 fertilization effect (equation (4)) because the variance explained in these areas is not significant and the trend can be underestimated as a result. A spurious “negative fertilization effect” is found in some areas, e.g., at the southern rim of the Amazon forest that is linked to land-cover change; this effect also adds to underestimation of the trend.
 Four alternative explanations for trends in the NDVI are explored: effects related to temporal variations in incoming solar radiation, effects related to spatial variations in nitrogen deposition, effects related to correlations between trends in land-surface temperature and atmospheric CO2 concentrations, and effects related to a change-over in sensors. These effects did explain at best only a small proportion of the trend in NDVI observations. Significant correlations between solar radiation and the residuals between NDVI and RVI occur for a large proportion of the land surface; however, the sign of the correlation varies from one location to the next, and the combined effects of variations in solar radiation on the NDVI do not contribute much to explaining variations in mean global NDVI. Variations in temperature are closely linked to variations in radiation; it is therefore plausible that most of the variations in the RVI linked to radiation are already captured by temperature variations. Nitrogen fertilization appears to be of some importance for agricultural areas, and this contributes to a statistically significant effect at the global scale as well (p ≪ 0.01). However, the amount of variance explained by N fertilization is small for both agricultural areas (4.2%) and the globe (3.9%); hence, as a physical factor, this effect does not contribute much to the explanation of trends in the NDVI-RVI residuals. There are possibly alternative explanations for the low amount of variance explained by nitrogen depositions such as inaccuracies in the N deposition fields. For example, large differences are found between N deposition fields by different authors [Van Drecht et al., 2005]. Moreover, data on nitrogen deposition were only available for 1993 [Galloway et al., 2004; Dentener, 2006] which prohibited the analysis of temporal variations. A change-over in satellites is an unlikely cause of variation in the NDVI data because a large negative anomaly in the NDVI data that occurred during the change-over from NOAA-7 to NOAA-9 can be attributed to a large climate anomaly, i.e., a large temperature anomaly in midlatitudes in the Northern Hemisphere and a negative precipitation anomaly in Australia and parts of Africa. Correlations between mean annual land-surface temperature and atmospheric CO2 concentrations are high over nonvegetated areas and low over vegetated areas. The spatial correlations of annual temperatures with NDVI variations linked to increased CO2 concentrations showed close to zero correlations over vegetated areas, indicating that the residuals in NDVI compared to the RVIcontrol cannot be attributed to increased temperatures. Moreover, the method used, i.e., first attributing NDVI variations to temperature and precipitation and attributing the residuals to atmospheric CO2 concentrations, will lead to conservative estimates of the effect of CO2 fertilization on NDVI. The CO2 fertilization is estimated from residuals that are similar in magnitude to the uncertainty in NDVI. However, for each cell, a significance test is applied, and a majority of vegetated regions shows a trend in the residuals that can be explained by increased atmospheric CO2 concentrations. In conclusion, of the various alternatives investigated, CO2 fertilization appears the most likely factor to explain variations in residuals between NDVI and RVI; its effect is likely underestimated in the present study.
 Analyzing a similar NDVI data set but for the 1980s, Thompson et al.  finds that CO2 fertilization is less important. This does not contradict the results of the present study, since the present analysis finds a large climate-related trend for the 1980s that can mask a smaller trend. In addition, Thompson et al.  study only nine years, and this may be too short to detect correlations with CO2 fertilization.
 The relationship between the trend in increased atmospheric CO2 concentrations and the trend in vegetation greenness is predominantly positive across the land surface (Figure 1). Over 1982–1999, the largest signal in atmospheric CO2 concentrations is a trend, the second largest signal the seasonal cycle, and the smallest signal the residual interannual variation. In the NDVI data over 1982–1999, the largest signal is the seasonal cycle, followed by the interannual variation, and the smallest signal is the trend. When both atmospheric CO2 concentrations and vegetation greenness data are detrended, a reversal of the positive relationship between atmospheric CO2 concentrations and vegetation greenness can occur. For example, the negative anomaly in NDVI and NEP in 1985–1986 (Figures 6 and 9) occurs at the same time as a positive deviation in detrended atmospheric CO2 concentrations [Keeling et al., 1995] and an increase of CO2 fluxes from the land surface [Bousquet et al., 2000].
 The CASA study assesses the effect of the greening of the RVI on NPP and NEP. This study has two purposes; it provides an estimate of the relative contribution of climate and of CO2 fertilization to the CO2 sink, and it provides a qualitative check on the magnitude of the CO2 fertilization estimates. The CASA study indicates that over the 20th century, the addition of CO2 fertilization increases NPP by about 6 Pg C; the increase in NEP is on average about 0.7 Pg C y−1 from the 1960s to the present. Only the change in the CO2 sink caused by CO2 fertilization, temperature, and precipitation was considered. The NEP associated with the effect of increased atmospheric on vegetation is likely larger because of limitations in the present analysis. These are the exclusion of areas that have positive trends that are not statistically significant and adoption of a method that favors estimation of trends associated with climate over trends caused by atmospheric CO2 rise. Other factors can contribute to a larger sink as well. For example, Sellers et al. [1996b] found that for doubled CO2, assimilation increases by about 10% as a result of increased water-use efficiency. If a comparable effect is assumed for an increase in atmospheric CO2 concentrations from below 300 to 390 ppmv, water-use efficiency could increase NPP by another 2 Pg over the 20th century and could increase NEP by 0.2–0.25 Pg C y−1. Estimates of the magnitude of increased CO2 land sink as a result of variations in diffuse and direct radiation associated with the variations in atmospheric aerosol concentrations are in the order of 0.25 Pg C y−1 but add only to the land sink for periods of 1 or 2 years after large volcanic eruptions (Lucht et al., 2002; Mercado et al., 2009). These effects are about 3 times smaller than the effect of climate and CO2 fertilization on NEP estimated in the present study.
 Uncertainties in the present analysis can be reduced if satellite vegetation products are improved and longer time series become available. Improvements in other data sets, e.g., in climate data for areas with low station density and in nitrogen deposition data, are likely to reduce uncertainties as well. It is concluded that a CO2 fertilization effect, in addition to changes in climate, is necessary to explain a large proportion of the observed trend in NDVI data; other factors investigated do not provide a satisfactory explanation.
 The author would like to thank the following persons and institutions for providing data and models: Dr P. Smith and Mr R. Rank of the Goddard DAAC for providing the PAL data; the Land Processes Distributed Active Archive Center (LP DAAC; lpdaac.usgs.gov) at the U.S. Geological Survey (USGS) Earth Resources Observation and Science (EROS) Center for providing the MODIS vegetation index data and the MODIS land-cover classification data; Dr T. Loveland and coworkers for making the 0.5 by 0.5 degree land-cover data available through the international satellite land surface climatology project (ISLSCP Initiative-2) on the Oak Ridge National Laboratory (ORNL) DAAC (daac.ornl.gov); the Deutscher Wetterdienst (German Meteorological Service) for providing the German oak phenology data; Drs. M. Schwartz and J. Caprio for providing the North American lilac phenology data through the NOAA NCDC Paleoclimatology Program; Dr T. Sparks (CEH) and Dr I. Robertson (Swansea University) for providing the Marsham oak data; Prof A. Andreevitch for providing the Russian Bird Cherry data (http://www.biodat.ru/); and Dr P. Tans at the NOAA ESRL for providing the Mauna Loa CO2 data. Global nitrogen depositions data for 1993 [Dentener, 2006] were obtained from the ORNL DAAC. Solar radiation fields were obtained from the NCEP-DOE AMIP-II reanalysis. Last but not least, five anonymous reviewers are thanked for their constructive comments to improve the present paper.