On the isotopic composition of leaf water in the non-steady state

An expression is derived for the isotopic composition of water in leaves under conditions where the composition of water entering the leaf is not necessarily the same as that of water being transpired. The treatment is simplified and considers the average composition of the lamina and of the sites of evaporation. The concept of 'isostorage' is introduced as the product of leaf water content and the isotopic enrichment of leaf water above source water. It is shown that the rate of increase of isostorage is minus the 'isoflux' through the stomata, with the latter expressed as the product of the transpiration flux and the enrichment of the transpired water beyond source water. The approach of the isostorage to the steady state depends on the deviation of the isotopic enrichment of water at the evaporating sites from the steady value, and on the gross (one way) diffusive flux out of the leaf. To achieve model closure, it is assumed that the relationship between leaf water enrichment and that at the sites of evaporation depends on the radial Péclet number in the same manner as in the steady state. The equations have an analytical solution, and we also show how to calculate the results simply using a commonly available computer tool. The form of the equations emphasises that the one-way fluxes of water into and out of the stomata must sometimes be considered separately, rather than as a net outward flux. In this narrow sense we come to the interesting conclusion that more water usually enters the leaf from the air than from the roots.