Abstract
3 min read[1] Ahlbeck [2002] raises an important issue: Is the increase in the atmospheric concentration of CO2 [Keeling and Whorf, 2001] partially responsible for the increase in the normalized difference vegetation index (NDVI), which we report in the work of Zhou et al. [2001]? To demonstrate its effect, Ahlbeck [2002] adds the atmospheric concentration of CO2 (hereinafter referred to as CO2) to equation (11) in the Zhou et al. [2001] article. Ahlbeck [2002] finds that CO2 is correlated with NDVI and concludes that "fertilizing due to increased atmospheric carbon dioxide concentration also may increase greenness." As described below, this conclusion, and the results on which it is based, is a statistical artifact. When the regression equation is specified correctly, we find that there is no relation between the NDVI and the atmospheric concentration of CO2. [4] Why does the presence of a time trend eliminate the statistical significance of CO2? The answer can be seen in the work of Ahlbeck [2002, Figure 1]. The atmospheric concentration of CO2 rises steadily over the sample period, 1982–1999. As such, CO2 "looks like" a time trend. As such, the two variables in equation (2) are highly correlated. The resulting colinearity causes ordinary least squares to overstate the size of the standard errors associated with β1 and β3. Under these conditions, the regression coefficients appear to be statistically insignificant. [6] If CO2 affects NDVI (and not some other variable that "looks like" a time trend), movements in CO2 which are faster or slower than the linear time trend will have explanatory power about NDVI beyond the explanatory power of the linear time trend; that is, if CO2 does affect NDVI, NDVI should rise faster than predicted by the linear time trend in years when CO2 increases faster than the time trend. Similarly, NDVI should increase slower than predicted by the linear time trend in years when CO2 increases slower than the time trend. [8] When equation (4) is estimated from data for North America and Eurasia, the estimate for β3 is not statistically different from zero. This result indicates that movements in CO2, faster or slower than a time trend have no explanatory power about NDVI beyond a time trend. This implies that the result found by Ahlbeck [2002] is caused by the similarity between CO2 and a time trend during the sample period, and not the effect of CO2 on NDVI. [10] We recognize that the interpretation of the statistical results described above is limited by the small sample size of the North American and Eurasian data sets. These limits can be alleviated by combining the two data sets and using F tests to evaluate whether the coefficients estimated from the North American data set are equal to those estimated from the Eurasian data set [Hsiao, 1986]. These F tests indicate that we cannot reject restrictions that equalize the coefficients other than the intercepts for equations (1), (2), (4), and (5). Under these conditions, the equations can be estimated from the combined data set using a fixed effects estimator. This allows us to estimate results that have more than twice the degrees of freedom than those estimated from the individual data sets. These results confirm those described above (Table 1). [11] Together, these results indicate that there is no evidence that increases in the atmospheric concentration of CO2 are responsible for the increases in NDVI described by Zhou et al. [2001]. Although CO2 correlates with NDVI, the relation described by Ahlbeck [2002] is a coincidence based on the similarity between CO2 and a linear time trend. The mechanism that lays behind the linear increase in NDVI is uncertain but could include forest regrowth following the effects of human disturbance and/or the decay of the increase in aerosol optical depth associated with the volcanic eruption of El Chichon at the start of the sample period (L. Zhou et al., manuscript in preparation, 2001).
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