The study was conducted in the Ti Tree basin, a 5500 km2 basin located approximately 200 km north of Alice Springs (NT) and 180 km north of the Tropic of Capricorn (22.28∘ S, 1933.25∘ E, 549 m a.s.l.). Climate is characterized as tropical and arid with hot summers and warm winters. The nearest Bureau of Meteorology station (Territory Grape Farm; Met Station 015643; within 25 km of all study sites) recorded mean and median annual precipitation of 319.9 and 29 mm, respectively (1987–May 2016; http://www.bom.gov.au/, last access: April 2018). Of the annual median rainfall, 72 % falls during the summer months (December–February) and 86 % falls during the monsoon season (November–April). Mean minimum and maximum monthly temperatures range from 5 and 22.6 ∘C in July to 22 and 37.5 ∘C in January.

The soil is a “red kandosol” (74 : 11 : 15, sand : silt : clay; Eamus et al., 2013), typical of large portions of semi-arid Australia, and has a high potential for drainage (Morton et al., 2011; Schmidt et al., 2010). Patches of hard siliceous soil are often observed and are likely surface expressions of the underlying hardpan (Cleverly et al., 2013), a common formation in the top 1–1.5 m in this type of soil (Cleverly et al., 2013, 2016a, b; Morton et al., 2011). The major potable source of water for this region is a large underground reservoir, recharged mainly by seepage from creek/river channels and their flood-out zones, “mountain” front recharge, and occasional very heavy rainfall events (NRETAS, 2009; Calf et al., 1991). The Ti Tree basin has a natural gradient in DTGW. The depth of the water table below ground level is shallow (<2m) in the northern part and groundwater is lost through evapotranspiration (Shanafield et al., 2015), whereas DTGW reaches 60 m in the southern and western parts of the basin and 20–40 m in the eastern region (NRETA, 2007).

All study sites were characterized as being in one of three distinct vegetation types (Nolan et al., 2017; Cleverly et al., 2016a): (1) riparian, predominantly consisting of Eucalyptus camaldulensis var. obtusa, which line the banks of the ephemeral streams in the Ti Tree basin (Woodforde River and Allungra Creek); (2) low mixed woodland (A. aneura F. Muell. ex Benth., A. aptaneura Maslin & J. E. Reid, A. kempeana F. Muell.) with an understorey of shrubs, herbs, and C3 and C4 grasses; (3) tall, open Corymbia savanna with extensive Spinifex grass (Triodia spp.), sparse Corymbia opaca (D. J. Carr & S. G. M.Carr) K. D. Hill & L. A. S. Johnson trees, and occasional Acacia spp. trees. The Woodforde River and Allungra Creek are ephemeral streams that flow only after large extensive rainfall events. Nonetheless, perched aquifers beneath their riparian corridors are recharged by large storms (Villeneuve et al., 2015), providing long-term access to groundwater near ephemeral streams. Allungra Creek and its flood-out zone represent zones of local recharge (NRETAS, 2009). Overbank flooding and sheet flow occur in flood-outs where the Woodforde River and Allungra Creek enter the basin and split into a network of smaller channels (NRETA, 2007), resulting in an estimated 1.8 ML (megaliters) of groundwater recharge per year (NRETAS, 2009).

Four sampling plots (see the map in the Supplement) were established for determination of foliar Δ13C and of δ18O and δ2H values for xylem water and groundwater from a nearby bore. DTGW in each of the four plots was 4.4, 8.3, 8.8, and 13.9 m, respectively. One of the four plots was located on the banks of the Woodforde River (plot 1, DTGW = 4.4 m). E. camaldulensis is the dominant tree species in plot 1, and C. opaca is also present. In the second plot, A. aneura is the dominant species (plot 2, DTGW = 8.3 m). C. opaca is the dominant tree species in the two remaining plots (plot 3, DTGW = 8.8 m; plot 4, 13.9 m).

Δ13C of E. camaldulensis, C. opaca, and A. aneura were examined along three additional transects to investigate the influence of topography and of distance from a creek on WUEi. The three transects were established perpendicularly to the banks of Allungra Creek, which is in an area of known groundwater recharge at the base of the hills that bound the southern extent of the basin (NRETAS, 2009). One of the three transects was located near a permanent water hole near the flood-out and the bottom of Allungra Creek. Transects two and three were 1–2 km upstream of the water hole. Transects extended from the creek bank within 1 m of the creek up to a maximum of 1800 m from the creek (vertical, that is, elevational, distance from the creek bed ranged from 0 to 4 m), across which vegetation graded from riparian forest to Corymbia open savanna, with occasional Acacia spp. trees interspersed throughout.

In addition to the four plots and three transects, “spot sampling” for foliar Δ13C alone was performed at three sites to extend the examination of variation in WUEi to 20, 36, and 49.5 m DTGW for A. aneura or 20 and 36 m for C. opaca. Finally, continental sampling of foliar Δ13C of multiple dominant tree species was undertaken at seven sites distributed across Australia (Table S1 in the Supplement; Karan et al., 2016; Rumman et al., 2017) in order to allow comparison of foliar Δ13C of our three Ti Tree species with a continental-scale regression of Δ13C with rainfall. A summary of the isotopes analysed for each species and for each groundwater sampling undertaken, for each site, is given in Table 1.

Sampling was undertaken in April 2014 (end of the wet season) and September 2013 (end of the dry season). Three mature, healthy leaves on each of three branches from two or three replicate trees were sampled for Δ13C in all plots, transects, and spot sampling sites. In addition, terminal branches of the trees in the four plots were collected for deuterium and δ18O analyses of xylem water. Bore water samples were also collected in the four plots and the three spot sampling sites using groundwater samples were also collected from the bores located at each site using a HydraSleeve no-purge groundwater sampler (Cordry, 2003). Sampling along the three transects occurred at three or four points along each transect. The three trees of each of the dominant species at each location were located within 50 m of the bore. Leaves for leaf-vein analysis (see below) were collected during September 2013.

Climate conditions preceding and during the sampling periods were obtained from two eddy-covariance towers (Fluxnet sites AU-ASM and AU-TTE; Cleverly et al., 2016a; Cleverly, 2011, 2013). AU-ASM is located to the west of the Ti Tree at the spot sampling site where DTGW is 49.5 m. AU-TTE is located near the eastern edge of the Ti Tree in plot 3 where DTGW is 8.8 m.

Branch xylem water was extracted by cryogenic vacuum distillation (whereby samples are subject to a vacuum and water vapour is frozen using liquid nitrogen, as described in Ingraham and Shadel, 1992; West et al., 2006). Water from each branch sample was extracted for a minimum of 60–75 min (West et al., 2006). δ2H and δ18O analyses of branch water and groundwater were performed using a Picarro L2120-i Analyser for Isotopic H2O. Five laboratory standards were calibrated against IAEA VSMOW2 – SLAP2 scale (Vienna Standard Mean Ocean Water 2, VSMOW2: δ18O =0 ‰ and δ2H =0 ‰; Standard Light Antarctic Precipitation 2, SLAP2: δ18O =-55.5 ‰ and δ2H =-427.5 ‰) and Greenland Ice Sheet Precipitation (GISP, δ18O =-24.8 ‰ and δ2H =-189.5,‰) as quality control references (IAEA, 2009). The standard deviation of the residuals between the VSMOW2 – SLAP2 value of the internal standards and the calculated values based on best linear fits was ca. 0.2 ‰ for δ18O and ca. 1.0 ‰ for δ2H.

Leaf samples stored in paper bags were completely dried in an oven at 60 ∘C for 5 days. After drying, each leaf sample was finely ground to powder with a Retsch MM300 bead grinding mill (Verder Group, Netherlands) until homogeneous. Between 1 and 2 mg of ground material was sub-sampled in 3.5 mm × 5 mm tin capsules for analysis of the stable carbon isotope ratio (δ13C), generating three representative independent values per tree. All δ13C analyses were performed in a Picarro G2121-i Analyser (Picarro, Santa Clara, CA, USA) for isotopic CO2. Atropine and acetanilide were used as laboratory standard references. Results were normalized with the international standards sucrose (IAEA-CH-6, δ13CVPDB=-10.45 ‰), cellulose (IAEA-CH-3, δ13CVPDB=-24.72 ‰) and graphite (USGS24, δ13CVPDB=-16.05 ‰). The standard deviation of the residuals between IAEA standards and calculated values of δ13C based on best linear fit was ca. 0.5 ‰.

WUEi was determined from 13C discrimination (Δ13C), which is calculated from the bulk-leaf carbon isotope ratio (δ13C), using the following equations (Werner et al., 2012): Δ13C‰=Ra-RpRp=δ13Ca-δ13Cp1+δ13Cp1000,WUEi=ca(b-Δ13C)1.6(b-a).

A small sub-section (approximately 1 cm2) of all leaves sampled for 13C were used for LVD analysis, providing three leaf sub-sections per tree (nine samples per species). Due to the small size of A. aneura phyllodes, several phyllodes were combined and ground for 13C analysis and one whole phyllode was used for LVD analysis. Each leaf section was cleared and stained following the approach described in Gardner (1975). A 5 % (w/v) NaOH solution was used as the principal clearing agent. Leaf sections were immersed in the NaOH solution and placed in an oven at 40 ∘C overnight (Gardner, 1975). Phyllodes of Acacia proved difficult to clear effectively and were kept in the oven longer than overnight to aid clearing. Once cleared, the partially translucent leaf sections were stained with a 1 % (w/v) safranin solution. Most leaf sections were stained for up to 3 min and then soaked with a 95 % (w/v) ethanol solution until the vein network was sufficiently stained and the majority of colour was removed from the lamina. After staining, the cuticle was removed to aid in identifying the vein network. Following cuticle removal, leaf sub-sections were photographed using a Nikon microscope (model: SMZ800) at 40× magnification. Finally, minor veins were traced by hand and LVD was calculated as total vein length per unit area (mm mm-2) using ImageJ version 1.48 (National Institutes of Health, USA).

Species-mean values (n=9) for the dominant overstorey species at each location were calculated for δ2H, δ18O, δ13C, and LVD. Relationships between Δ13C and WUEi with DTGW were tested using regression analysis after testing for non-normality (Shapiro–Wilk test, α=0.05) and homogeneity of variances (Bartlett test). A Tukey post hoc test for multiple comparisons across sites was used to test for significance of variation as a function of DTGW. Breakpoints in functions with DTGW were determined using segmented regression analyses whereby the best fitting function is obtained by maximizing the statistical coefficient of explanation. The least squares method was applied to each of the two segments while minimizing the sum of squares of the differences between observed and calculated values of the dependent variables. Next, one-way ANOVA was applied to determine significance of regressions and breakpoint estimates within a given season. We fully acknowledge that the number of plots with shallow DTGW was sub-optimal, but constraints arising from species distribution across the Ti Tree precluded additional sampling.

Mean daily temperature and mean daily vapour pressure deficit (VPD) were largest in summer (December–February) and smallest in winter (June–August) (Fig. 1). Daily sums of rainfall showed that the DTW 8.8 and 49.4 m sites received 265 and 228 mm rainfall, respectively, between the September 2013 and April 2014 sampling dates, representing more than 73 % and 60 % of the total respective rainfall received from January 2013 to June 2014 at these sites.

Xylem water isotope ratios for A. aneura were widely divergent from the bore water stable isotope ratios (Fig. 2a) in both wet and dry seasons, indicative of a lack of access to groundwater. In contrast, δ2H and δ18O of xylem water in E. camaldulensis and C. opaca were predominantly (with two exceptions) tightly clustered around δ2H and δ18O of groundwater in the bores located within 50 m of the trees (Fig. 2b). There was little variation in xylem water composition between the end of the dry season and end of the wet season for either species, reflecting the consistent use of groundwater by these two species.

Δ13C of A. aneura, sampled in the Corymbia savanna and Acacia spp. plots, was not significantly correlated with DTGW, in either season or across all values of DTGW (ANOVA F = 1.78; p>0.05; Fig. 3a, b). As a consequence of these patterns in Δ13C, WUEi did not vary significantly for A. aneura across sites differing in DTGW (Fig. 4a) despite the large variability in WUEi (ranging from 62 to 92 µmol mol-1) across sites and seasons. By contrast, foliar Δ13C of E. camaldulensis and C. opaca declined significantly with increasing DTGW in both seasons at the sites where DTGW was relatively shallow (DTGW < ca. 12 m). Segmented regression analysis shown in Fig. 3c and d yielded breakpoints at 11.17±0.54 m in September (ANOVA F = 11.548; df = 2, 38; P<0.01) and 9.81±0.4 m in April (ANOVA F = 14.67; df = 2, 47; P<0.01), which represent the seasonal maximum depths from which groundwater can be extracted by these species. Thus, WUEi of E. camaldulensis and C. opaca was significantly smaller at the shallowest site than at sites with DTGW > 13.9 m (Fig. 4b), but did not differ significantly across the deeper DTGW range (13.9–49.5 m; Fig. 4b).

As distance from Allungra Creek increased, foliar Δ13C for both E. camaldulensis and C. opaca declined significantly (Fig. 5a), with concomitant increases in WUEi (Fig. 5b). There was no significant relationship for Δ13C or WUEi with distance from the creek for A. aneura (data not shown).

LVD did not vary significantly with increasing DTGW for A. aneura (Fig. 6a), but a significant increase in LVD with increasing DTGW was observed for DTGW < ca. 10 m in the two deep-rooted species (Fig. 6b). The breakpoint for E. camaldulensis and C. opaca (Fig. 6b; 9.36 m ± 0.6 m; ANOVA F = 6.38; P<0.05) agreed well with the two previous estimates (cf. Figs. 3 and 6), although again, constraints imposed by species distributions severely limited the number of samplings available at shallow DTGW sites. As with LVD and DTGW, no relationship was observed between LVD and Δ13C for A. aneura (Fig. 7a), but a significant linear decline in Δ13C with increasing LVD was observed for E. camaldulensis and C. opaca (Fig. 7b).

For the two deep-rooted species (E. camaldulensis and C. opaca), a significant decline in Δ13C (and hence an increase in WUEi) was observed with increasing distance from the creek (Fig. 5a, b). In contrast to the results of O'Grady et al. (2006c) for a steeply rising topography in the Daly River, this is unlikely to be attributable to increased elevation since the change in elevation was minimal across each entire transect (<3 m), and even smaller near Allungra Creek where most of the change in Δ13C was recorded. Therefore the cause of the change in Δ13C with distance from the creek was most likely to be a function of the frequency with which trees receive flood water and hence the amount of recharge into the soil profile (Ehleringer and Cooper, 1988; Thorburn et al., 1994; Villeneuve et al., 2015; Singer et al., 2014). We therefore further conclude that foliar Δ13C can be used as an indicator of access to additional water to that of rainfall, regardless of the source of that additional water (e.g. groundwater, flood recharged soil water storage, irrigation).

In our study, LVD was independent of DTGW for A. aneura, but a breakpoint (9.4 m) was apparent across the combined data of the two deep-rooted species. Increased DTGW reflects a declining availability of water resources (Zolfaghar et al., 2015), especially in arid zones. Uhl and Mosbrugger (1999) concluded that water availability is the most important factor determining LVD. Sack and Scoffoni (2013) also showed LVD to be negatively correlated with mean annual precipitation in a 796-species meta-analysis. Therefore increasing LVD with increasing DTGW is consistent with an increased LVD with a declining water supply, despite similar amounts of rainfall being received along the DTGW gradient.

Both A. aneura and C. opaca in the present study showed LVDs close to the higher end of the global spectrum (Sack and Scoffoni, 2013), consistent with larger LVDs observed in “semi-desert” species. Higher LVDs allow for a more even spatial distribution of water across the phyllode or lamina during water stress, which contributes to a greater consistency of mesophyll hydration in species of arid and semi-arid regions (Sommerville et al., 2012). In turn, this allows continued photosynthetic carbon assimilation during water stress (Sommerville et al., 2010). Presumably, a large LVD also decreases the resistance to water flow from minor veins to mesophyll cells, which is likely to be beneficial for leaf hydration as water availability declines while also facilitating rapid rehydration following rain in these arid-zone species. Large LVDs for A. aneura of semi-arid regions in Australia have been associated with rapid up-regulation of phyllode function with the return of precipitation following drought (Sommerville et al., 2010), and such rapid up-regulation is crucial for vegetation in regions with unpredictable and pulsed rainfall like Ti Tree (Byrne et al., 2008; Grigg et al., 2010).

LVD was negatively correlated with bulk-leaf Δ13C (and thus positively correlated with WUEi) in C. opaca and the data for E. camaldulensis appeared to conform to the regression for C. opaca (Fig. 7b). What mechanism can explain the significant relationship observed between a structural leaf trait (LVD) and a functional trait (WUEi)? The stomatal optimization model (Medlyn et al., 2011) is based on the fact that transpiration (E) and CO2 assimilation (A) are linked via stomatal function. In order to gain carbon most economically while minimizing water loss (i.e. optimization of the ratio A / E), stomata should function such that the marginal water cost of carbon assimilation ∂A∂E remains constant (Cowan and Farquhar, 1977; Farquhar and Sharkey, 1982). This aspect of stomatal control couples the structural traits involved with water flow with traits associated with primary production (Brodribb and Holbrook, 2007) and explains observed correlations between Kleaf and Amax⁡ in a number of studies (Brodribb et al., 2007, 2010, 2005; Brodribb and Jordan, 2008; Sack and Holbrook, 2006; Sack and Scoffoni, 2013). The length of the hydraulic pathway is directly proportional to Kleaf (Brodribb et al., 2007) and the A/gs ratio determines foliar Δ13C (and WUEi) signatures in leaves. Thus, the constraint on Kleaf by LVD affects the coordination between the processes of A and E and thereby might explain significant relationships between structural (LVD) and functional (WUEi) traits. For the two deep-rooted species, having access to groundwater resulted in convergence to a common solution for optimizing water supply through veins with respect to E (Brodribb and Holbrook, 2007).

Several robust and testable predictions arise from the conclusion that E. camaldulensis and C. opaca are functioning at a semi-arid site as though they have access to ca. 1700 or 900 mm rainfall, respectively. Species growing in high-rainfall zones possess a suite of traits, including low-density sapwood, large-diameter xylem vessels, small resistance to vessel implosion, large SLA, and a large maximum stomatal conductance, compared to species growing in arid regions (O'Grady et al., 2006b, 2009; Wright et al., 2004). Therefore, these attributes should be present in E. camaldulensis and C. opaca if they are functioning as though they are growing in a mesic environment. We have previously established (Eamus et al., 2016; Santini et al., 2016) that these predictions are confirmed by field data and therefore conclude that analyses of foliar Δ13C have global application to the preservation and understanding of GDEs.