Spatial autocorrelation inflates the global leaf-wax d2H-precipitation slope

Alexander S. Bradley 

Leaf wax hydrogen isotope ratios (δ²Hwax) are used to make inferences about past hydroclimate, but global calibrations between δ²Hwax and precipitation isotopes (δ²Hprecip) ignore spatial autocorrelation and inflate apparent relationships. This study compiled 1,129 surface sediment and soil measurements of δ²Hwax from n-C29 alkanes and developed hierarchical Bayesian spatial models to separate geographic covariation from isotopic processes. The fitted spatial field accounted for 48–57% of variance and had characteristic length scales of ∼3,600–3,950 km. Accounting for this structure reduces the δ²Hwax–δ²Hprecip slope from a non-spatial baseline of 0.78 to 0.53–0.62, indicating that a substantial fraction of the non-spatial slope estimate reflects confounding by spatial structure rather than the underlying wax–precipitation isotope relationship.

The dominant spatial effects are shifts in regional intercepts. Slopes vary modestly around a near-uniform global mean. Grass and tree cover have negative effects on δ²Hwax, and the δ²Hprecip × tree and × shrub interactions are small but statistically discernible even after spatial adjustment. Elevation, annual precipitation, and C4 fraction effects are weak. Spatial calibrations cut the residual standard deviation in δ²Hwax at the calibration sites by ∼25% (from ∼21‰ to ∼16‰). Inverting through the calibration gives a single-point δ²Hprecip posterior standard deviation of ∼29‰ and, for independent samples within a single record, a 95% detection threshold of ∼81‰. For within-record contrasts, positively correlated calibration residuals can partially cancel, and thresholds are correspondingly lower. These uncertainty and threshold estimates are lower bounds; unmodeled residual confounding, spatial-intercept and covariate uncertainty, and non-stationarity would widen real-world reconstruction errors. Inversions are implemented in the accompanying R package leafwax.