Simple physics-based adjustments reconcile the results of Eulerian and Lagrangian techniques for moisture tracking

The increase in the number and quality of numerical moisture tracking tools has greatly improved our understanding of the hydrological cycle in recent years. However, the lack of observations has prevented a direct validation of these tools, and it is common to find large discrepancies among the results produced by them, especially between Eulerian and Lagrangian methodologies. Here, we evaluate two diagnostic tools for moisture tracking, WaterSip and UTrack, using simulations from the Lagrangian model FLEXPART. We assess their performance against the Weather Research and Forecasting (WRF) model with Eulerian Water Vapor Tracers (WRF-WVTs). Assuming WRF-WVTs results as a proxy for reality, we explore the discrepancies between the Eulerian and Lagrangian approaches for five precipitation events associated with atmospheric rivers and propose some physics-based adjustments to the Lagrangian tools. Our findings reveal that UTrack, constrained by evaporation and precipitable water data, has a slightly better agreement with WRF-WVTs than WaterSip, constrained by specific humidity data. As in previous studies, we find a negative bias in the contribution of remote sources, such as tropical ones, and an overestimation of local contributions. Quantitatively, the root-mean-square-error (RMSE) for contributions from selected source regions is 5.55 for WaterSip and 4.64 for UTrack, highlighting UTrack's narrowly superior performance. Implementing our simple and logical corrections leads to a significant improvement in both methodologies, effectively reducing the RMSE by over 50 % and bridging the gap between Eulerian and Lagrangian outcomes. Our results suggest that the major discrepancies between the different methodologies were not rooted in their inherently different nature, but in the obviation of basic physical considerations that may be easily straightened out.