Satellite observations reveal a greening of the globe over recent decades. The role in this greening of the “CO2 fertilization” effect—the enhancement of photosynthesis due to rising CO2 levels—is yet to be established. The direct CO2 effect on vegetation should be most clearly expressed in warm, arid environments where water is the dominant limit to vegetation growth. Using gas exchange theory, we predict that the 14% increase in atmospheric CO2 (1982–2010) led to a 5 to 10% increase in green foliage cover in warm, arid environments. Satellite observations, analyzed to remove the effect of variations in precipitation, show that cover across these environments has increased by 11%. Our results confirm that the anticipated CO2 fertilization effect is occurring alongside ongoing anthropogenic perturbations to the carbon cycle and that the fertilization effect is now a significant land surface process.
 Carbon dioxide is a primary substrate of photosynthesis. Increases in atmospheric CO2 concentrations (Ca) are expected to lead to a CO2 fertilization effect where photosynthesis is enhanced with the rise in CO2 [Farquhar, 1997]. While a land-based carbon sink has been observed [Ballantyne et al., 2012; Canadell et al., 2007] and satellites reveal long-term, global greening trends [Beck et al., 2011; Fensholt et al., 2012; Nemani et al., 2003], it has proven difficult to isolate the direct biochemical role of Ca in these trends from variations in other key resources (such as light, water, nutrients [Field et al., 1992]) and from socioeconomic factors such as land use change [Houghton, 2003]. This complexity can be reduced by focusing on warm, arid environments, where water plays the dominant role in primary production and where foliage cover (F, the fraction of ground area covered by green foliage), plant water use, and photosynthesis are all tightly coupled. It is in these warm, arid environments where the CO2 fertilization effect on cover should be most clearly expressed. While widespread greening has been reported in these environments [Beck et al., 2011; Fensholt et al., 2012], the year-to-year variation in precipitation (P) at individual sites makes it very difficult to extract a clear fingerprint of the CO2 fertilization cover effect.
 Global satellite observations show that the relationship of F to P is generally curvilinear (Figure 1a) with a near-linear dependence of F on P under arid conditions (Figure 1b). At low P (i.e., < ~0.4 m a−1), there is a distinct upper edge that represents the maximum F (Fx) attainable for a given P (Figure 1b). The linearity of the Fx edge highlights the presence of a limit to F when water is the dominant limit to growth. The Fx relation has been previously investigated using the rain-use efficiency (RUE, the ratio of aboveground net primary productivity to P) framework [Huxman et al., 2004], and it was found that their upper limit (which is approximately synonymous with our Fx edge) was independent of vegetation and climate types [Huxman et al., 2004; Ponce Campos et al., 2013]. Leaf-scale gas exchange measurements show that transpiration and photosynthesis are directly coupled to Ca [Wong et al., 1979], and this leads us to hypothesize that Ca plays a key role in setting the Fx limit. If this is correct, then we expect that any rise in Ca will produce an increase in the Fx edge. Furthermore, we expect that a first-principles-based estimate of the effect of elevated Ca on cover (which we outline below) will provide an estimate of how much the Fx edge has increased, given the observed rise in Ca (Figure 1b). We test this hypothesis by comparing estimates of changes in Fx with historically observed changes in Fx deduced from satellite observations. This also provides a direct means of observing the CO2 fertilization cover effect under warm, arid conditions.
2 Predicting the CO2 Fertilization Cover Effect
 The water use efficiency of photosynthesis, Wp, is the ratio of the assimilation (Al) and transpiration (El) rates per unit of leaf area. It is defined as [Wong et al., 1979]
where Ca and Ci are the atmospheric and intercellular [CO2], respectively, and ν is the leaf-to-air water vapor pressure difference. The relative effect of a change in Ca on Wp is given by
 In leaves, Wong et al.  showed that Ci/Ca is reasonably conservative for a particular photosynthetic mode (C3 or C4) at a given ν. However, (1 − Ci/Ca) does increase slightly with increasing ν, and the effect has been modeled and observed by taking (1 − Ci/Ca) as being proportional to the square root of ν [Farquhar et al., 1993; Medlyn et al., 2011; Wong and Dunin, 1987]. With that, equation (2) becomes
 In warm, arid environments, the transpiration per unit ground area (Eg) is constrained by the available water supply (i.e., P) [Kerkhoff et al., 2004; Specht, 1972]. Such low-productivity environments typically have a small leaf area index (L, leaf area per unit ground area), and the following approximation is valid [Lu et al., 2003]:
 Our approach examines cover as a function of precipitation. Assuming constant water supply (i.e., constant Eg), we have
 Under warm, arid conditions, L is typically small and F and L vary near proportionally [Lu et al., 2003]. With that, we assume that dL/L and dF/F are approximately equal. For the warm, arid regions being considered, this gives
 Equation (6) provides a quantitative expression linking changes in F with changes in Ca, ν, and Al.
 Global satellite observations of F are available from 1982 (see below), and, for the 1982–2010 period, Ca increased by 14% [P. Tans and R. Keeling, 2012] (in using a single value of dCa/Ca, we are assuming that long-term changes in Ca occur uniformly across the globe). For the selected study area (see below), observations show that v increased by ~8% over the same period [Dee et al., 2011], (see supporting information Table S2). This leads to an estimated 10% rise in Wp across the analysis extent (that is, dCa/Ca − 1/2 ⋅ dv/v, or 0.14 − 0.08/2).
 If the change in Wp was shared evenly between dAl/Al and dF/F, it follows that F would have increased by 5%. Alternatively, in warm, arid regions, leaf area production might be so tightly linked to water availability that the change in Ca (and hence in Wp) might be predominantly expressed through El (and hence F), with little change in Al. In this scenario, dF/F would be around 10%. Thus, our a priori estimate of the CO2 fertilization effect on Fx in warm, arid regions over the last 30 years is for an increase of 5 to 10%.
3 Observing Changes in the Maximum Cover Edge
 To test our hypothesis that the Fx edge is set primarily by Ca, and therefore will increase with the Ca-driven rise in Wp, we quantified the global-scale changes in the Fx edge over the past 30 years using readily available satellite estimates of F [Tucker et al., 2005]. We did this by first restricting our analysis to warm, arid regions where water was the primary limit to vegetation growth. We set an analysis extent (Figure 2) to include only the following areas: (a) areas that were climatically water-limited [Nemani et al., 2003]; (b) areas that were free from irrigation and major surface water features [Siebert et al., 2002; United Nations Environment Programme, 2011]; and (c) areas with continuous P data coverage over the study period [Rudolf et al., 2010]. In order to minimize the impact of year-to-year “transient” effects (e.g., soil water storage change and the response lag of perennial foliage to changes in P), we performed analyses using sequential 3 year periods (yielding ten 3 year averages between 1982 and 2010, with the last period containing 2 years). Within the analysis extent, and for each 3 year average, we identified the location of the Fx edge by determining the 95th percentile of F for a given P (assessed in 0.02 m a−1 bin widths). We then defined the Fx edge as a linear regression fitted to the 95th percentile values that lay between 0.05 ≤ F ≤ 0.55. This gave 10 separate estimates of Fx. Finally, we tested whether the slope and intercept of the Fx regression had changed over time. Detailed descriptions of data and methods are presented in the supporting information.
 Our findings show that the Fx edge increased between 1982 and 2010 by ~11% (Figure 3a). The change was driven by an increase in the slope of the edge (Figure 3b) with little change in the offset (Figure 3c), consistent with our a priori expectation (Figure 1b). The cells that occur at the Fx edge were distributed across every continent (Figure 2). The ~11% increase observed from the satellite data is close to the upper value a priori estimate—an estimate made by assuming the change in Wp is expressed solely through El. This result provides strong support for our hypothesis that the Fx edge is, in large part at least, determined by Ca. By implication (and to the same degree that our hypothesis is correct), analyzing the changes in the Fx edge provides a means of directly observing the CO2 fertilization effect as it has historically occurred across the globe's warm, arid landscapes.
4 Assessing Alternative Mechanisms of the Rise in the Maximum Cover Edge
 Over the study period, average daily air temperature increased [Dee et al., 2011], leading to the question of what role, if any, this change may have had in the observed rise in the Fx edge. The impact of changes in air temperature on Wp are explicitly incorporated into our analysis via ν (equation (6)), where any temperature-based rise in ν will be accompanied by a decrease in Wp and F (and Al). Hence, higher air temperatures, via the effect on v, have, in our analysis, contributed to a lowering of the Fx edge rather than the observed rise in the edge.
Huxman et al.  showed that, regardless of vegetation or climate type, vegetation RUE converges (temporarily) toward a global maximum value (RUEx) under conditions of severe drought. The Fx edge is nearly synonymous with RUEx due to F being highly correlated with Aboveground Net Primary Productivity (ANPP) (but F was used here instead as it is much closer to being a direct observation of vegetation than is ANPP). One implication of this global convergence toward the Fx edge is that no individual geographic location lies constantly at the edge but continuously moves in P-F space in response to changes in local conditions. Another implication is that it is possible that an increase in the Fx edge could be caused by changes in the temporal characteristics of drought events and, in particular, by a gradual increase over the period in the severity of the onset of droughts. We tested for an increase in the severity of drought onset events (see supporting information). We found that the initial drop in P at the start of a drought event decreased over time such that the onset severity was smaller by 0.02 m a−1 at the end of the period than at the beginning. This trend of a reduction in drought onset severity is consistent with the 10% increase in P across the globe's warm, arid regions (supporting information Table S2) and with other recent analyses of drought [Sheffield et al., 2012; Sun et al., 2012] and rules out changes in drought conditions as a likely driver of the observed Fx trend.
 Across the study area and period, the 10% rise in P has been accompanied by a general greening—a rise in F of 14% (see supporting information Table S2). This P-induced greening cannot explain the rise in the Fx edge, however, for two reasons. First, our analysis technique removed the effects of variability in P; that is, changes in the Fx edge were determined for a constant P. Second, the edge represents the maximum F, rather than the average F, and both Huxman et al.  and Ponce Campos et al.  suggest that RUExdecreases with an increase in P.
 Another alternative mechanism that could potentially explain the observed change in the Fx edge is a change in disturbance regimes. Since an increase in disturbance generally reduces RUE [Herrmann et al., 2005; Prince et al., 2007; Seaquist et al., 2009], it seems plausible that a lessening of the frequency and/or severity of disturbances might lead to an increase in the Fx edge. We argue that this is unlikely for the following two reasons. First, if a location has been disturbed, such that F is lower than its usual “undisturbed” level, it would initially sit well below the Fx edge (i.e., have a depressed RUE). Regrowth of foliage postdisturbance would serve only to bring that location back up toward, and maybe onto, the Fx edge. Second, for disturbance recovery to raise the Fx edge, it would require that all locations across the analysis extent were initially in a synchronized postdisturbance recovery phase such that the Fx edge was suppressed globally at the start of the period. Only then would the gradual increase in postdisturbance cover be able to shift a global growth limit (i.e., the Fx edge). We are not aware of evidence to suggest that such a scenario has occurred.
 The increase in water use efficiency of photosynthesis with rising Ca has long been anticipated to lead to increased foliage cover in warm, arid environments [Berry and Roderick, 2002; Bond and Midgley, 2000; Farquhar, 1997; Higgins and Scheiter, 2012], and both satellite and ground observations from the world's rangelands reveal widespread changes toward more densely vegetated and woodier landscapes [Buitenwerf et al., 2012; Donohue et al., 2009; Knapp and Soule, 1996; Morgan et al., 2007; Scholes and Archer, 1997]. Our results suggest that Ca has played an important role in this greening trend and that, where water is the dominant limit to growth, cover has increased in direct proportion to the CO2-driven rise in Wp. This CO2 fertilization cover effect warrants consideration as an important land surface process.
 The results reported here for warm, arid regions do not simply translate to other environments where alternative resource limitations (e.g., light, nutrients, temperature) might dominate, although the underlying theory remains valid (equations ((1))–((3))). The remaining challenges are to develop a more general understanding of how the increase in Ca is shared between Al and El in environments that are not warm and arid and to develop capacity to quantify the multiple potential flow-on effects of fertilization in these environments, such as widespread changes in surface albedo, an increase in fire fuel loads for a given P, and possible reductions in stream flows due to enhanced rooting systems [Buitenwerf et al., 2012].
 Overall, our results confirm that the direct biochemical impact of the rapid increase in Ca over the last 30 years on terrestrial vegetation is an influential and observable land surface process.
 We thank A.P. O'Grady, J.G. Canadell, and P.B. Hairsine for comments on early versions of the manuscript. We are grateful to J.E. Pinzon and C.J. Tucker for providing the GIMMS 3g NDVI data set. R.J.D. and T.R.M. acknowledge the support of CSIRO's Sustainable Agriculture Flagship and Water for a Healthy Country Flagship. M.L.R acknowledges support from the Australian Research Council (CE11E0098, DP110105376). G.D.F. acknowledges support from the Australian Research Council (DP110105376) and Land & Water Australia.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.