1. METR 2413 31 March 2004

2. Review Hydrostatic balance Ideal gas law p = ρ R d T v, ρ = p / R d T v Take layer average virtual temperature, R and g as constants and integrate LHS

3. Thickness So the height difference, z 2 -z 1, between two pressure levels is where is the average virtual temperature over this layer. This is called the hypsometric equation for the thickness, z 2 -z 1, between two pressure levels, p 1 and p 2 Larger thickness means higher mean temperature in the layer.

4. Thickness Example: Thickness of the 1000 hPa to 900 hPa layer

5. Thickness Most common thickness values are: 1000 – 500 hPa, 1000 – 850 hPa, 1000 – 700 hPa 1000 – 500 hPa thickness used to define “bulk” airmass average temperature 1000 – 850 hPa thickness used primarily for snow probability and maximum daytime temperature forecasting For 1000-500 mb thickness, the 540 dam line (5400 m) is often used as the separator between rain and snow for low terrain - When there is precip in a region of thickness < 540 dam, it is generally snow - If thickness > 540 dam, it is usually rain - Contour intervals are typically 60 m (6 dam)

6. Review Geostrophic wind, pressure gradient force balanced by Coriolis force:

7. Thermal wind In the presence of a horizontal temperature gradient, the tilt of pressure surfaces increases with height. coldwarm ΔzΔz North ugug p=p 1 p=p 2

8. Thermal wind Horizontal temperature gradient  Increasing tilt of pressure surfaces with height  Increasing pressure gradient force on constant height surfaces with altitude  Increasing geostrophic wind with height Vector difference between geostrophic wind at two levels is called the thermal wind.

9. Thermal wind Thermal wind relationship: The vertical gradient of the geostrophic wind is proportional to the horizontal temperature gradient

10. Thermal advection “Advection” – generic term for horizontal transport of some atmospheric property; - typically used in terms of heat transport, but also for moisture To have thermal advection: must have horizontal motion (stronger winds increase thermal advection; little advection under calm conditions) must have horizontal temperature gradient over a large region winds must blow across the zone of strongest horizontal temperature gradient (no advection if wind blows parallel to temperature contours)

11. Thermal advection Warm air advection is occurring in Indiana, cold air advection is occurring over South Dakota and Nebraska

12. Thermal advection Warm air advection (WAA) – movement of warmer air toward a fixed point on a horizontal plane; warm air replaces cold air; Low level WAA is common behind warm fronts and ahead of cold fronts Low level WAA can contribute to rising air Cold air advection (CAA) – movement of colder air toward a fixed point on a horizontal plane; cold air replaces warm air Low level CAA is common behind cold fronts Contributes to sinking air Caution: other lifting and sinking mechanisms can complicate rising or sinking due to advection

13. Thermal advection Thickness charts often used to infer advection thickness used as proxy for temperature geostrophic wind used as proxy for average air motion

14. Thermal advection Thermal wind and thermal advection: Thermal wind – the vector difference between geostrophic flow at 2 different heights (not a real wind!) Thermal wind can be inferred from the thickness field: - thermal wind “blows” parallel to the thickness contours, with cold thickness to the left in the Northern Hemisphere Thermal wind rule (in the Northern Hemisphere): if the geostrophic wind backs (turns counterclockwise with height), cold advection is indicated if the geostrophic wind veers (turns clockwise with height), warm advection is indicated

15. Thermal advection

16. Can use temperatures at 700 mb as an alternative to thickness: temperature at 700 mb close to 1000 – 500 mb thickness 700 mb wind approximates the movement of the 1000 – 500 mb thickness We can use the geostrophic wind and isotherms at 700 mb to estimate mean lower tropospheric thermal advection: 700 mb thermal advection resembles mean thickness advection below 500 mb spacing of height lines at 700 mb is a measure of wind speed wind direction is parallel to height lines Strength of warm or cold air advection is proportional to the area formed by the intersection of the isotherms and the height contours

17. Thermal advection Three factors make thermal advection larger: a strong wind a large temperature gradient a small angle between actual wind direction and temperature gradient (i.e. to maximize heat advection, wind should blow at right angles to isotherms) Very little thermal advection occurs at low latitudes since temperature gradients tend to be very weak.

18. Summary Thickness between two pressure levels is proportional to the layer mean temperature Thermal wind – the vector difference between geostrophic wind at 2 different heights, is proportional to the horizontal temperature gradient Thermal advection occurs for horizontal wind blowing across temperature contours If the geostrophic wind backs (veers) with height, cold (warm) advection is indicated