Figure 2

Summary output of mechanistic models developed to describe a causal relationship between VPD and δ¹⁸O:δ¹³C slopes in tree-ring cellulose (a–d) and in relation to our own observations of modern trees across biomes (e). Modeled δ¹⁸O and δ¹³C ratios are calibrated for Pinus radiata trees when: (a) and (c) vapour pressure deficit (VPD) varies; (b) and (d) stomatal conductance (g_s) varies, under constant source water (δ¹⁸O at − 8.0‰; model adapted from Barbour et al.⁸). Air temperature was kept constant at 20 °C, and stomatal conductance (g_s) varied between 0.02 and 0.48 mol m⁻² s⁻¹. Photosynthetic capacity (V_cmax) at the given temperature varied between 24 and 34 mmol m⁻² s⁻¹; V_cmax variation alone showed little influence on δ¹⁸O and δ¹³C⁸. Model defaults were vapour pressure deficit = 0·94 kPa, g_s = 0.19 mol m⁻² s⁻¹ (on a projected leaf area basis) and V_cmax = 30 mmol m⁻² s⁻¹ and constant source water δ¹⁸O of – 8.0‰. (e) Shows the modeled relationships between vapour pressure deficit (VPD) and the change in slope of the δ¹⁸O and δ¹³C relationship when variation in δ¹³C is driven by changes in g_s alone, or by large changes in both g_s and V_cmax, or by small variation in g_s and large variation in V_cmax. We plotted our compiled global observations (triangles) of cellulose δ¹⁸O:δ¹³C slopes and annual average VPD in contemporary needle-bearing taxa from around the world which showed a positive and significant relationship between δ¹⁸O and δ¹³C (Table S5). For ease of comparison with the Barbour et al. model⁸, here we plotted our modern cellulose data to show δ¹⁸O:δ¹³C slopes (S^-1), whereas δ¹³C:δ¹⁸O slopes (S) are used as previously suggested for paleo-VPD estimates (see Methods for details).