18.3. Advection

Advection is the horizontal transport of some variable. One of the most common advections that meteorologists investigate is temperature advection. As we saw in the previous section, we can view the change in temperature to be attributable to two different parts, a local time rate of change and an advective component.

\[ \frac{\text{DT}}{\text{Dt}} = \frac{\partial T}{\partial t} + \overrightarrow{u} \bullet \nabla T = \frac{\Delta T}{\Delta t} + u\frac{\Delta T}{\Delta x} + v\frac{\Delta T}{\Delta y} \]

The second term (boxed) on the right-hand side of the equation is the advective term. This basically states that the wind (u, v) will push the temperature gradient (\(\nabla T = \bigg <\frac{\Delta T}{\Delta x}, \frac{\Delta T}{\Delta y} \bigg >\)) around. Depending on the orientation of the temperature gradient and the wind speed and direction we can get warm or cold air advection to occur over a region. Let’s look at this schematically to get a better understanding.

a) Max Advection	b) No Advection

If the arrow gives the wind, the left image clearly has cold air advection as the wind is pushing the cold air into the warmer air. The advection of a variable is maximized when the isopleths of the variable being advected is perpendicular to the wind. In the right image, there is no advection since the isotherms are parallel to the wind, thus the wind is not pushing warmer air into colder air or vice versa.