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A global runoff flux of 37,288 km3 per year was obtained from a previous compilation of discharge measurements3, and has been independently reproduced within 1,300 km3 per year (36,055 km3 per year) using satellite measurements4. The larger uncertainty reported by Coenders-Gerrits et al.1 (± 5,100) is obtained using a higher runoff value from a schematic in a review5, which also included direct groundwater discharge to oceans, making this number 10% higher than it should be. Because the uncertainty estimate recommended by Coenders-Gerrits et al.1 also includes water fluxes not included in our runoff parameter, we stand by the original values used, which seem to us to be the best approximation of this uncertainty3,4.

Global interception, derived from satellite measurements6,7 (7,500 km3 per year, as used in our paper2), global climate model outputs8 (11,900 km3 per year, shown in figure 6b of ref. 4) and stand-level measurements9 (median value of 17.9% of precipitation, or 19,700 km3 per year), all fall into a range from 7,500 km3 per year to 19,700 km3 per year. We note that the high end-member applied by ref. 1 is derived from stand-level measurements and was not intended to be used to estimate a global interception flux. Its use in this manner1 introduces bias towards regions where interception is expected to be important, because interception measurements are not often reported in areas free of canopy cover.

The Comment1 also suggests that the uncertainties we applied to the deuterium excess (d = δ2H – 8δ18O) of transpired moisture (dT ) and evaporate (dE ) were understated2. First, Coenders-Gerrits et al.1 propose a deuterium excess uncertainty of ±19‰ for transpired moisture, quoting the individual uncertainties in our paper in the δ18O and δ2H models. This uncertainty is too large because they do not recognize that δ18O and δ2H values covary10, resulting in a well-constrained range of deuterium excess values for groundwater tapped by plant roots. The uncertainty we applied2 for dT (±3‰) is validated by a database of stable oxygen and hydrogen isotope values for shallow and deep groundwater across the continental USA (the Water Quality Portal, http://www.waterqualitydata.us). Samples from depths of <4.6 m—the global average rooting depth11—show a deuterium excess of 7.8 ± 4.1‰ (n = 1,021; 25th to 75th percentile range of data set), found to be nearly identical in deuterium excess to that of samples collected from depths greater than 4.6 m: d = 7.9 ± 3.1‰ (n = 24,309). These ranges are consistent with our estimate2 of dT of 8 ±3‰. Coenders-Gerrits et al.1 suggest that the deuterium excess value ascribed to evaporating moisture should be higher than ±30‰. Our uncertainty of ±30‰ was derived from the range of deuterium excess calculations for 73 lakes used in our study. We used percentile ranges so that the high sensitivity (and associated high uncertainty) would be carried through to our final, global scale calculation of transpiration and evaporation fluxes.

Finally, Coenders-Gerrits et al.1 suggest that we neglect uncertainty in water-use efficiency (WUE), despite our use of the standard error of regression that resulted in a global WUE of 3.4 ± 0.9 mmol CO2 per mol H2O (ref. 2). CO2 fertilization does indeed affect WUE12, as we acknowledged2, and continued research into WUE will allow us to monitor and map these changes as atmospheric CO2 increases. We strongly disagree with Coenders-Gerrits et al.1 that gross primary production models “fail at the regional and local scale,” given the success of the FLUXNET project in constraining this vital component of the carbon cycle (123 ± 8 Gt of C per year reported13). Finally, WUE has in fact been measured at scales that are larger than the leaf level (see Supplementary Infomation refs 105, 114, 116 and 118 in ref. 2).

We do not agree with the magnitude of the increase in uncertainty in ref. 1, nor with the unidirectional changes to input parameters that produce lower transpiration fluxes. However, we agree with the final point of the Comment1: that further method development and the use of stable O and H isotopes in hydrology can help to reduce uncertainty in terrestrial evaporation and transpiration.