METR 2413 31 March 2004. Dynamics II: Thermal wind and thermal advection. 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. Thickness.
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31 March 2004
Thermal wind and thermal advection
Ideal gas law p = ρ RdTv, ρ = p / RdTv
Take layer average virtual temperature , R and g as constants and integrate LHS
So the height difference, z2-z1, between two pressure levels is
where is the average virtual temperature over this layer.
This is called the hypsometric equation for the thickness, z2-z1, between two pressure levels, p1 and p2
Larger thickness means higher mean temperature in the layer.
Example: Thickness of the 1000 hPa to 900 hPa layer
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)
Geostrophic wind, pressure gradient force balanced by Coriolis force:
In the presence of a horizontal temperature gradient, the tilt of pressure surfaces increases with height.
Thermal wind relationship:
The vertical gradient of the geostrophic wind is proportional to the horizontal temperature gradient
Warm air advection is occurring in Indiana, cold air advection is occurring over South Dakota and Nebraska