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Understanding what controls the water vapor isotopic composition of the sub-cloud layer (SCL) over tropical oceans (delta D-0) is a first step towards understanding the water vapor isotopic composition everywhere in the troposphere. We propose an analytical model to predict delta D-0 motivated by the hypothesis that the altitude from which the free tropospheric air originates (z(orig)) is an important factor: when the air mixing into the SCL is lower in altitude, it is generally moister, and thus it depletes the SCL more efficiently. We extend previous simple box models of the SCL by prescribing the shape of delta D vertical profiles as a function of humidity profiles and by accounting for rain evaporation and horizontal advection effects. The model relies on the assumption that delta D profiles are steeper than mixing lines, and that the SCL is at steady state, restricting its applications to timescales longer than daily. In the model, delta D-0 is expressed as a function of z ong , humidity and temperature profiles, surface conditions, a parameter describing the steepness of the delta D vertical gradient, and a few parameters describing rain evaporation and horizontal advection effects. We show that delta D-0 does not depend on the intensity of entrainment, in contrast to several previous studies that had hoped that delta D-0 measurements could help estimate this quantity.

Based on an isotope-enabled general circulation model simulation, we show that delta D-0 variations are mainly controlled by mid-tropospheric depletion and rain evaporation in ascending regions and by sea surface temperature and z(orig) in subsiding regions. In turn, could SDo measurements help estimate z ong and thus discriminate between different mixing processes? For such isotope-based estimates of z(ori)(g) to be useful, we would need a precision of a few hundred meters in deep convective regions and smaller than 20 m in stratocumulus regions. To reach this target, we would need daily measurements of delta D in the mid-troposphere and accurate measurements of delta D-0 (accuracy down to 0.1 parts per thousand in the case of stratocumulus clouds, which is currently difficult to obtain). We would also need information on the horizontal distribution of delta D to account for horizontal advection effects, and full delta D profiles to quantify the uncertainty associated with the assumed shape for delta D profiles. Finally, rain evaporation is an issue in all regimes, even in stratocumulus clouds. Innovative techniques would need to be developed to quantify this effect from observations.