# A simple way to find out where the moisture for regional rainfall comes from

Moisture tracing is an interesting scientific topic that has fascinated meteorologists and hydrologists for decades. Methods for tracing moisture are numerous, from observations to numerical modelling, from water isotopes to remote sensing, from online tracking to off-line tracking, and both Eulerian and Lagrangian methods are used.

A simple method involves a two-dimensional box model. To build a simple model, assumptions are needed. There are three assumptions:

1. Vapour in the box remains constant at monthly time scales or longer;
2. No matter from where the moisture comes, it is well mixed within the box;
3. Evaporation and precipitation are constant within the box. Then, you can derive a simple relationship from the atmospheric water vapour conservation equation:

ρ = E / E+2Fin

This relationship is developed by Brubaker et al. (1993); ρ is the precipitation recycling ratio, which is the fraction of precipitation within the box that originates as the evaporation from the same box: E is the evaporation with the box and Fin is the horizontal moisture flux into the region, which is vertically integrated through the height of the box.

If the moisture does not come from the evaporation with the box, then it must come from outside in form of the moisture advection. Therefore,

α = 1-ρ = (2Fin)/(E+2Fin)

Where α is the ratio of precipitation arising from advected moisture to the total precipitation within the box.

If we further divide the Fin according to the directions, then we can calculate the contribution of advected moisture from different directions. Together with the contribution from the local evaporation, we can figure out from where the moisture to the precipitation within the box comes.

ρ + αW + αE + αN + αS =1

Where, W, E, N and S represent directions.

Take the central-eastern China for example (Figure 1, left). Applying the aforementioned equations to this region shows the seasonal cycle of the moisture contributions from all directions in Figure 1 (middle). It is clear that the summer monsoon (via the southern boundary) makes a significant contribution during the June-July-August, especially in July (40%). However, the contribution via the western boundary is equivalent or larger. In the winter, the moisture predominantly comes via the western boundary, although the mean precipitation is small (Figure 1, right).

Applying the simple model to a realistic case requires caution. However, similar results have been found from other studies using more sophisticated methods. Besides, a statistical test done by Guo et al. (2018) shows that about 70% of the precipitation interannual variation can be explained by the moisture flux via all these boundaries.

Figure 1 (Left) The study region. The boundary is divided into west (green), east (black), north (red) and south (blue). (Middle) Percentage contributions to precipitation from the moisture influxes from different directions, as well as from the local evaporation in grey. (Right) The mean seasonal cycles of precipitation calculated from the ERA-Interim re-analysis during 1979-2012, units mm/month. The precipitation is separated into colours according to the moisture contributions from each section of the boundary.

#### Guo, Liang, Nicholas P. Klingaman, Marie-Estelle Demory, Pier Luigi Vidale, Andrew G. Tuner, and Claudia C. Stephan, 2018. The contributions of local and remote atmospheric moisture fluxes to East Asian precipitation and its variability. Climate Dynamics, on-line DOI: 10.1007/s00382-017-4064-4.

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