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Core data sets.

Normalized difference vegetation index. We obtained a time series of third-generation NDVI (NDVI3g) from the Global Inventory Modelling and Mapping Studies (GIMMS; ref. 24). This data set is gridded at 0.083° spatial resolution and was averaged from biweekly to annual time steps. The annual average for a given grid cell was determined only if >80% of biweekly values were available and was set to missing otherwise. Similarly, pixel trends were calculated only for pixels with annual time series >80% complete. Basin-specific NDVI values were obtained by averaging gridded data over basin areas.

Climatic variables. Monthly climatic fields (precipitation, minimum and maximum air temperature and shortwave radiation) were obtained from the ANUCLIM archive²⁵. The Australia-wide data are gridded at 0.05° spatial resolution and were produced by the ANUSPLIN software package^{25, 26} from meteorological station data using a thin-plate smoothing spline.

An annual time series of atmospheric CO₂ concentrations was obtained from National Oceanic and Atmospheric Administration Earth System Research Laboratory (NOAA ESRL; http://www.esrl.noaa.gov/gmd/ccgg/trends). The data report the mean annual CO₂ concentration measured at Mauna Loa observatory in parts per million. We ignored latitudinal differences in CO₂ concentration as these are small compared to the signal of interest.

Potential evapotranspiration (PET) was calculated using the Priestley–Taylor method as in ref. 27, using inputs of shortwave radiation and the mean of minimum and maximum air temperature from the ANUCLIM archive. The Priestley–Taylor method has been shown to be appropriate for estimating large-scale PET (refs 28,29) and has been adopted in other basin-scale studies^{14, 30, 31}.

Water-balance evapotranspiration. Water-balance evapotranspiration was calculated as the difference of observed annual precipitation and streamflow integrated over the river basin area. The water-balance method remains the most firmly observationally based estimator of ET, but assumes negligible changes in soil water storage at annual to decadal timescales (see Supplementary Section 1 for further discussion). Streamflow time series were acquired from a streamflow collation for unregulated catchments across Australia³². Gaps in the water-balance ET time series (accounting for <5% of monthly records) were filled using simulations from the Australian Water Availability Project³³, further detailed in Supplementary Section 1.

Study basins. The 190 study basins were chosen based on the completeness of streamflow records (>95%) and the extent of irrigated and farmed land (<5% of basin area). The basins were classified into wet, sub-humid, semi-arid and arid using the climatological aridity index A (A = PET/P, where PET =  annual mean potential ET and P =  annual mean precipitation) (see Supplementary Fig. 1 for basin locations and aridity classification). River basins with mean annual aridity index <1 were classified as wet, 1–2 as sub-humid, 2–5 as semi-arid and >5 as arid (adapted from UNEP (1997)³⁴). See Supplementary Section 1 for further details on basin selection and classification criteria.

Breakpoint regression.

Five-year running mean NDVI values were binned according to their corresponding precipitation values. Following ref. 6, the 95th percentile value was determined for each 20-mm-wide precipitation bin separately for each running mean. Breakpoint regression was applied to the 95th percentile values to calculate the first regression slope marking the maximum NDVI attainable for a given precipitation and the breakpoint where the vegetation–precipitation relationship plateaus and vegetation ceases to be water-limited. We then constructed time series of the slopes and breakpoints (Fig. 3) and determined linear trends for both variables. As running means were used to construct the time series, degrees of freedom were adjusted when determining the significance of trends. Farmlands, irrigated areas and wetlands were excluded from this analysis using the Dynamic Land Cover Dataset of Australia³⁵ (see Supplementary Section 1).

CO₂ sensitivity coefficients.

Estimation of observed CO₂ coefficients. Dimensionless CO₂ sensitivity coefficients were calculated from NDVI and ET corrected for precipitation and PET (a function of temperature and shortwave radiation). Precipitation and PET present the main climatic constraints on plant growth³⁶ and are the two first-order controls on ET (ref. 37). The effects of precipitation and PET were removed using linear regression: separately for each basin, annual ET (E) and NDVI were regressed against precipitation and PET and the annual corrected values were calculated as the sum of the regression residual and the 1982–2010 mean of the variable. The corrected annual variables were then log-transformed and regressed against log-transformed annual CO₂ concentrations (C_a) to derive the CO₂ sensitivity coefficients σ_ET = ∂lnE/∂lnC_a and σ_{NDV I} = ∂lnNDV I/∂lnC_a. The sensitivity coefficients represent the fractional change in the relevant variable per unit fractional change in CO₂, so that a change in ET (mm) due to CO₂ is well approximated by ΔE/E ≈ σ_E. ΔC_a/C_a for ΔE E and ΔC_a C_a (as in this study). ET and NDVI sensitivities to precipitation were calculated from uncorrected data using the same principles (further detailed in Supplementary Section 2).

Prediction of theoretical ET sensitivity to CO₂. The theoretical sensitivity of ET (E) to CO₂ concentration (C_a) for C₃ photosynthesis on a unit leaf area basis can be calculated by writing the CO₂ assimilation rate (A) and E in the form of diffusion equations:

and

where g_s is the stomatal conductance to CO₂, χ is the ratio of internal CO₂ concentration (C_i) to C_a, and D is the vapour pressure deficit. χ is a function of D and leaf temperature^{38, 39} and typically takes values from 0.4–0.5 in arid climates to 0.8–0.9 in wet climates. Substitution of g_s from equation (1) into equation (2) yields

Differentiating with respect to C_a, holding D and χ constant, gives:

where σ_A is the sensitivity of A to C_a:

Equation (4) implies that the sensitivity of E to C_a approaches −1 as the CO₂ fertilization effect on A saturates. However, so long as A is increasing with C_a, the sensitivity is smaller in magnitude than −1. The sensitivity of A to C_a can be calculated conservatively by invoking the coordination hypothesis (approximate equality of the carboxylation- and electron transport-limited rates of photosynthesis under field conditions: see, for example, ref. 40). With the further assumption that limitation by the maximum rate of electron transport (J_max) is not relevant in the field (because Rubisco limitation takes over at the highest light levels), we can express the assimilation rate as

where φ₀ is the intrinsic quantum efficiency of C₃ photosynthesis, I_abs is the absorbed photosynthetic photon flux density and Γ^∗ is the photorespiratory compensation point. Differentiating A with respect to C_a, holding χ constant, gives:

Evaluating equation (7) and then (4) at 25 °C, C_a = 370 ppm for illustration gives σ_E = −0.61 for χ = 0.8 and −0.38 for χ = 0.5.