SO254 - Advection

What is advection? Source: http://apollo.lsc.vsc.edu/classes/met130/notes/chapter12/graphics/temp_advection.free.gif 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!)

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

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 =

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

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

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

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.