1. SO254 - Advection

2. What is advection?
Source:
Advection is the transfer of a property of the air by the wind
There are many things that can be advected: temperature, vorticity (relative and planetary), momentum, moisture
Advection of “A” is mathematically defined as:
is the 3-d velocity vector
is the 3-d del operator
A is what is being advected
We can thus write advection of temperature, relative vorticity, and moisture in the following ways
temperature advection =
relative vorticity advection =
moisture advection =
Advection has a negative sign in front by convention: we prefer advection of a higher quantity toward a lower quantity to give a positive number
Warm-air advection is thus positive; cold-air advection is negative
Cyclonic vorticity advection is positive; anticyclonic vorticity advection is negative ( those are true in the N. Hemisphere only!)

3. More on advection
Wind blowing from the southeast across a region with different temperatures
5°C
7°C
9°C
11°C
If temperature advection = , then the magnitude of the advection depends on several things:
How strong the wind is. Greater wind speeds will lead to more advection
How strong the gradient of T is. If T changes a lot over short distances (i.e., if the isolines of T are close together), then advection will be greater
The angle between the velocity vector and the contours of T
If velocity vector crosses T lines at a 90° angle, then advection will be maximized
If velocity vector crosses at closer to 0° angle, then advection is minimized
If wind blows parallel to lines of T (which is a 0° angle), then there is no temperature advection
5°C
North
7°C
9°C
11°C
East
Wind blowing from the northwest across region with different temperatures
5°C
7°C
9°C
11°C
5°C
7°C
9°C
5°C
11°C
7°C
9°C
11°C
5°C
Wind blowing from the southwest across region with different temperatures
7°C
9°C
11°C

4. More on temperature and relative vorticity advection
Mathematically, the dot product between the velocity vector and the del operator can be expanded. This expansion shows:
advection in the east-west direction by the east-west wind
advection in the north-south direction by the north-south wind
advection in the vertical direction by the vertical wind
temperature advection =
relative vorticity advection =

5. A closer look at vorticity advection in troughs and ridges
In the figure at right, anticyclonic (negative) vorticity is indicated by blue hatching
Cyclonic (positive) vorticity is indicated by red hatching
Winds are indicated by the black arrows
Remember, winds in the upper atmosphere will blow parallel to the height contours, in gradient balance
Vorticity advection is , or
Where will the areas of positive vorticity advection be? Where will the areas of negative vorticity advection be?
Let’s use the math to show PVA and NVA
Negative vorticity in the ridges
Negative vorticity advection
Positive vorticity advection
Positive vorticity in the troughs

6. What is the vorticity advection here in the middle?
Distance 1000 km
Point #2
What is the vorticity advection here in the middle?
Negative rel vorticity
ζ = -1 x 10-4 s-1
Distance 1000 km
Wind speed in the middle: 40 m s-1, from the southwest
Neglect b/c no vertical winds
Point #1
Positive rel vorticity
ζ = +1 x 10-4 s-1

7. Relate temperature advection to changes in wind
One of the neat physical relationships between temperature and wind is called the “thermal wind relationship”
The thermal wind isn’t really a wind. Instead, it is an relationship between vertical wind shear and horizontal temperature gradients:
What does that equation say?
“The geostrophic wind will change as you go up in the atmosphere (in z) if there are horizontal changes in temperature”
The details of this relationship will be taught you in a later course, but for now, let’s relate “veering” and “backing” of the wind profile with temperature advection

8. Counter-clockwise turning
Applying the thermal wind: relating changes in wind with height (veering or backing) with temperature advection (warm- or cold-air advection)
z=5500 m; p=500 mb
z=5500 m; p=500 mb
Clockwise turning
Counter-clockwise turning
z=3000 m; p=700 mb
z=3000 m; p=700 mb
z=1500 m; p=850 mb
z=1500 m; p=850 mb
z=0 m; p=1000 mb
z=0 m; p=1000 mb
This is a veering wind profile. Direction changes clockwise as you go up in the atmosphere. Veering wind profiles are associated with warm air advection.
This is a backing wind profile. Direction changes counter-clockwise as you go up in the atmosphere. Backing wind profiles are associated with cold air advection.