This model builds on earlier reactive transport work (Hendricks et al., 2000; Chamberlain et al., 2014; Winnick et al., 2014) by adding energy balance constraints and rainout over topography. The model is initialized with landscape and climate data (“model inputs” in figure) and simulates the balance of precipitation, evapotranspiration, and moisture transport, as well as the δ18O of these fluxes, over space.

In our model, evapotranspiration (ET) is limited by potential evapotranspiration (E0) such that ET/P (precipitation) depends on whether the landscape is water-limited (P < E0) or energy-limited (P > E0). This constraint limits the number of possible climate solutions for a given (non-zero) isotope gradient, making it possible to quantify climate from the spatial change in δ18O. It also helps explain why δ18O decreases along a storm track. Overwhelmingly, P > E0 along storm tracks where δ18O decreases (e.g. in tropical monsoon regions and over mountain ranges).

Chamberlain et al., (2014) defined the isotopic hydrostat—the point of aridity where δ18O loses sensitivity to hydroclimate. In our work, we map the hydrostat into Budyko space to show that δ18O is more sensitive to hydroclimate in different landscapes. For each line, a landscape is below the hydrostat (higher δ18O sensitivity) down and to the left, and above the hydrostat (no δ18O sensitivity) up and to the right. This analysis quantifies how δ18O is less sensitive to hydroclimate behind coastal mountain ranges than inland mountain ranges.

We simulate three temperature-dependent processes that affect precipitation δ18O along a mountainous storm track. (1) Vapor content usually increases faster than precipitation with warming (“hydroclimate effect” in figure); (2) Higher temperatures decrease isotope fractionation over mountains (“orographic effect”); (3) Warming increases the initial δ18O of an air-mass (“temperature effect”). Because each process affects a different part of the storm track, the overall change in δ18O with temperature varies over space.

The model has been mostly applied to oxygen isotope gradients between speleothem (cave calcite) sites. Oxygen isotopes in speleothems can resolve relatively small signals in δ18O (often less than 1‰) so climate trends are easier to identify and simulate. For example, I applied the model to quantify past Amazon rainfall using the δ18O gradient (Kukla et al., 2021). Others used it to test for consistency between GCM results and a spatial gradient in speleothem δ18O in the Middle East (Carolin et al., 2019), and test the role of topography in precipitation δ18O over Vietnam (Wolf et al., 2020).