Moisture advection is the horizontal transport of water vapor by the wind. Measurement and knowledge of atmospheric water vapor, or "moisture", is crucial in the prediction of all weather elements, especially clouds, fog, temperature, humidity thermal comfort indices and precipitation.

## Definition

${\displaystyle Adv(\rho _{m})=-\mathbf {V} \cdot \nabla \rho _{m}\!}$

in which V is the horizontal wind vector, and ${\displaystyle \rho _{m}}$ is the density of water vapor. However, water vapor content is usually measured in terms of mixing ratio (mass fraction) in reanalyses or dew point (temperature to partial vapor pressure saturation, i.e. relative humidity to 100%) in operational forecasting. The advection of dew point itself can be thought as moisture advection:

${\displaystyle Adv(T_{d})=-\mathbf {V} \cdot \nabla T_{d}\!}$

## Moisture Flux

In terms of mixing ratio, horizontal transport/advection can be represented in terms of moisture flux:

${\displaystyle \mathbf {f} =q\mathbf {V} \!}$

in which q is the mixing ratio. The value can be integrated throughout the atmosphere to total transport of moisture through the vertical:

${\displaystyle \mathbf {F} =\int _{0}^{\infty }\!\rho \mathbf {f} \,dz\,=-\int _{P}^{0}\!{\frac {\mathbf {f} }{g}}\,dp\,}$

where ${\displaystyle \rho }$ is the density of air, and P is pressure at the ground surface. For the far right definition, we have used Hydrostatic equilibrium approximation.

And its divergence (convergence) imply net evapotranspiration (precipitation) as adding (removing) moisture from the column:

${\displaystyle P-E-{\frac {\partial (\int _{0}^{\infty }\!\rho q\,dz\,)}{\partial t}}=-\nabla \cdot \mathbf {F} \!}$

where P, E, and the integral term are—precipitation, evapotranspiration, and time rate of change of Precipitable water, all represented in terms of mass per unit area (one can convert to more typical units in length such as mm by multiplying the density of liquid water and the correct length unit conversion factor).