Temperature Advection In general, one likes to use potential temperature instead of temperature in the thermodynamic equation. Why? For a dry adiabatic process,

Temperature Advection B C x 10 oC 15 oC 20 oC 100km Warm or cold temperature advection? cold T adv

Temperature Advection In nature coordinates, these equations are written as: s n V s n x s + Ds s - Ds V

Temperature Advection Looking at the equation for the horizontal temperature advection On a constant p surface, it can be written as (From the Poisson equation!)

Thermal Wind (VT) Estimate the temperature advection and the change of static stability using a hodograph VT Vg1 : lower-level geostrophic wind Vg2 : upper-level geostrophic wind COLD WARM Tv: Virtual Temperature The thermal wind equation:

Temperature Advection Let us use the natural coordinate and choose the s direction along the thermal wind (and along the isotherms with cold air to the left). Now rotating the x axis to the s direction, we get the temperature advection equation as where is the average wind speed perpendicular to the thermal wind. The sign of      VT VT - +

Temperature Advection WARM VT VT COLD - + COLD WARM - - Warm temperature advection Cold temperature advection If the wind veers with height,      is positive and there is warm advection. If the wind is back with height,      is negative and there is cold advection.

Temperature Advection Procedure to estimate the temperature advection. 1. Plot a hodograph showing the upper- and low-level wind and the thermal wind. 2. For the layer of interest, measure      , the wind speed perpendicular to the thermal wind. Be sure that   is positive if the wind veers with height (warm advection) and negative is the wind is back with height (cold advection) 3. Estimate temperature advection. This procedure can be used to determine the temperature change due to advection in any layer. If there is warm advection in the lower layer, or cold advection in the upper layer, or both, the environment will become more unstable.

Temperature Advection Temperature advection using 1000-500 mb thickness The hypsometric equation: where H=z2-z1 is the thickness. Using the conclusion that, for a fixed layer where ln(p1/p2) is a constant, the thickness is proportional to the layer averaged temperature. Take derivative with respect to n, we get

Temperature Advection Again ignore the difference between temperature and virtual temperature, we can get: n s Vg1, Vg2 , and    all have the same Vn, the wind component perpendicular to the thermal wind (or in the n direction). The component along the thermal wind (or in the s direction) does not contribute the temperature advection. (so lets’ just use 1000 mb wind)

Temperature Advection Using the surface pressure and 1000-500 mb thickness chart to compute advection. The sea level pressure pattern should be similar to the 1000 mb geopotential height pattern and the geostrophic wind on these two maps should be similar. The following explanation is quite straightforward in vector calculus. Using the geostrophic wind balance equation in nature coordinates We have two components of wind here because now the s direction in not along the wind.

Temperature Advection Substitute the Vn equation into the temperature change equation We get In finite difference form, it is

Temperature Advection Dp= 400 Pa and DH = 60 m. Ds is the distance between points a and b, and Dn is the distance between the points b and b'. DsDn is therefore the area of the rhomboid (abcd). We can conclude that the temperature advection is inversely proportional to the AREA formed by the intersection of the isobars and thickness lines.

Temperature advection Warm T Advection ? Almost no T advection ? Warm T Advection ? Cold T Advection

Temperature Advection The effect of temperature advection on vertical velocity Horizontal maximum warm advection is one of the key factors in creating upward motion. In an area of warm advection, cold air is replaced by the warm air and the surface pressure will have to fall. That will create a low pressure in this area, which in turn will create convergence and upward motion. The magnitude of the upward motion is proportional to the intensity of the warm advection and inversely proportional to the area of warm advection. The first point is obvious. The second point can be illustrated below:

Temperature Advection Suppose the pressure is constant at the beginning. The two circles are areas of warm advection and the pressure drop due to the warm advection. Even though the pressure drops are the same, the pressure gradient in area B is 2/3 of that in area A. The magnitude of the convergence and vertical velocity in area B will be proportionally smaller. Cold advection will increase the surface pressure and produce divergence and downward motion.

Temperature Advection Temperature advection and the change of atmospheric stability? Absolute unstable! Warm advection Destabilized the layer Cold advection Stabilized the layer

Temperature Advection The effect of vertical advection on temperature In area of warm advection, the associated upward motion will cool the atmosphere and partially offset the effect of the warm advection. The temperature change due to vertical velocity can be estimated first using the potential temperature change and then converted to temperature change using the Poisson equation.