From AMS Glossary
The process of transport of an atmospheric property solely by the mass motion (velocity field) of the atmosphere; also, the rate of change of the value of the advected property at a given point.
Advection may be expressed in vector notation by
where u is the wind vector, φ the atmospheric property, and ∇φ the gradient of the property. In three-dimensional Cartesian coordinates, it is
where u, v, and w are the wind components in the eastward, northward, and vertically upward directions, respectively. The first two terms compose the horizontal advection and the last term is the vertical advection. Also, it should be noted that the property φ may itself be a vector field. Often, particularly in synoptic meteorology, advection refers only to the horizontal or isobaric components of motion, that is, the wind field as shown on a synoptic chart. Regarding the general distinction (in meteorology) between advection and convection, the former describes the predominantly horizontal, large-scale motions of the atmosphere, while convection describes the predominantly vertical, locally induced motions. In oceanography, advection refers to the horizontal or vertical flow of seawater as a current.