Maps accompanying the paper:

Cuthbert, M.O., Gleeson, T., Moosdorf, N., Befus, K.M., Schneider, A., Hartmann, J., Lehner, B., (2019).
Global patterns and dynamics of climate–groundwater interactions. Nature Climate Change, 9, 137–141.
DOI:10.1038/s41558-018-0386-4
https://www.nature.com/articles/s41558-018-0386-4

PLEASE ACKNOWLEDGE WITH A CITATION IF YOU USE THESE DATA, thank you!

Three maps are part of the supplementary material: 
1) Log_GRT_a.tif
2) LOG_WTR_NL_01.tif
3) LOG_WTR_L_01.tif

Here, the contents and development of each map is described.

All maps are in Eckert IV equal area projection, with a grid cell (i.e. pixel) size of 1000 m. Each grid contains 33843 times 15011 cells with an extent of:
top left: 8366114.8807, -16921201.8457
bottom right: 16921798.1543, -6644885.1193
All geographical transformations and calculations were done using the software ESRI ArcGIS 10. All rasters were projected from their original projections and transformed to the named grid parameters using ArcGIS functionality.

Contents of - and calculations leading to - each map:
1) Log_GRT_a.tif
This map contains the logarithm (all LOG are with base of 10) of the groundwater response time in years. It is calculated following equation 14 of Cuthbert et al., 2019:
LOG(GRT) = LOG((L^2*S)/beta*T)

2) LOG_WTR_NL_01.tif
Thes map contains the logarithm of the nonlinear water table ratio, following equation 8 of Cuthbert et al. 2019:
LOG(WTR_NL) = LOG(sqrt(b^2+((R*L^2)/4*K)-b)/d)

3) LOG_WTR_L_01.tif
This map contains the logarithm of the linearly water table ratio, following equation 9 of Cuthbert et al., 2019:
LOG(WTR_L) = LOG((R*L^2)/(8*T*d))



The parameters used are (in alphabetical order):

b: saturated thickness of the aquifer [L]
b was set to 100 m, following Gleeson et al. (2011).

H: saturated thickness of the aquifer [L]
This parameter is set to 100 m, following Gleeson et al. (2011)

beta: constant [dimensionless]
The value of beta, pi^2, was chosen in order to be consistent with mathematically equivalent uses of ‘time constants’, in other branches of science such as for defining thermal or electrical response times.

d: maximum terrain rise between rivers [L]
d is based on the range of elevations in the 250m GMTED2010 dataset (Danielson & Gesch, 2011). Zonal statistics of the range of elevations for each watershed in the global HYDROSHEDS database (Lehner et al., 2008) was calculated and used for this purpose. To avoid mathematical problems, for zero values of d, 1 was added.

K: hydraulic conductivity [L*T^-1]
This parameter was derived from the global permeability map of the GLHYMPS dataset (Gleeson et al., 2014). It was transformed to match the grid projection and parameters used here and the values were changed to meters per year. The original GLHYMPS permeability information [L^2] was converted to hydraulic conductivity [L*T^-1] by assuming standard temperature and pressure (1 * 10^7 multiplication factor) and then converted to units of m/y.

L = distance between two perennial streams [L]
L was calculated using a globally consistent river network provided by the HydroSHEDS database (Lehner et al., 2008), which was derived from the 90 m digital elevation model of the Shuttle Radar Topography Mission (SRTM). We extracted the global river network from the HydroSHEDS drainage direction grid at 500 m pixel resolution by defining streams as all pixels that exceed a long-term average natural discharge threshold of 0.1 cubic meters per second , resulting in a total global river length of 29.4 million kilometers. Estimates of long-term (1971-2000) discharge averages have been derived through a geospatial downscaling procedure (Lehner & Grill, 2013) from the 0.5º resolution runoff and discharge layers of the global WaterGAP model (version 2.2, 2014). 

R: groundwater recharge [L*T^-1]
This parameter was derived from Döll & Fiedler (2008). 
For WTR estimates, regions where contemporary groundwater recharge was estimated as < 5 mm/y were excluded from the analysis due to the increasingly large relative uncertainties in recharge below this range, and the resulting unrealistic sensitivity of the resulting WTR estimates.
To avoid mathematical problems, for zero values R, 0.00001 was added.

S: Specific yield [dimensionless]
Assuming unconfined aquifers, S was set to the porosity provided in the GLHYMPS dataset (Gleeson et al., 2014).

T: transmissivity [L^2*T^-1], T = K*H 
K and H are described above.



References:

Cuthbert, M.O., Gleeson, T., Moosdorf, N., Befus, K.M., Schneider, A., Hartmann, J., Lehner, B., (2019). Global patterns and dynamics of climate–groundwater interactions. Nature Climate Change. http://dx.doi.org/10.1038/s41558-018-0386-4

Danielson, J. J. & Gesch, D. B., (2011). Global multi-resolution terrain elevation data 2010 (GMTED2010). Report No. 2331-1258, US Geological Survey.

Döll, P., Fiedler, K., 2008. Global-scale modeling of groundwater recharge. Hydrology and Earth System Sciences, 12(3): 863-885.

Gleeson, T., Smith, L., Moosdorf, N., Hartmann, J., Dürr, H.H., Manning, A.H., van Beek, L.P.H., Jellinek, A.M., 2011. Mapping permeability over the surface of the Earth. Geophysical Research Letters, 38(2): L02401.

Gleeson, T., Moosdorf, N., Hartmann, J., van Beek, L.P.H., 2014. A glimpse beneath earth's surface: GLobal HYdrogeology MaPS (GLHYMPS) of permeability and porosity. Geophysical Research Letters, 41(11): 3891-3898.

Lehner, B., Verdin, K., Jarvis, A., 2008. New global hydrography derived from spaceborne elevation data. EOS Transactions, 89(10): 93-94.

Lehner, B., Grill, G., 2013. Global river hydrography and network routing: baseline data and new approaches to study the world's large river systems. Hydrological Processes, 27(15): 2171-2186.