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METR 3210 – Atmospheric Thermodynamics
Homework 7
Due Tuesday, April 26, 2016 at 11:00 am
Hydrostatics and Atmospheric Stability:
1. What is the geopotential thickness of the 1000-500 mb layer when the virtual temperature
at 1000 mb is 0ºC and the virtual temperature at 500 mb is -30ºC? Assume that the virtual
temperature lapse rate is constant.
2. What is the geopotential thickness of the lowest 200 mb of the atmosphere if the surface
pressure is 1000 mb, the surface temperature is 10ºC, the mean relative humidity through
the layer is 20%, and the lapse rate is dry adiabatic?
3. A meteorological station in the Middle East is located 50 m below sea level. If the surface
pressure at this station is 1020 mb and the mean virtual temperature below the 500 mb
pressure level is 4ºC, compute the height of the 500 mb pressure level above sea level at
this location.
4. Early afternoon surface observations at the Albuquerque airport (elevation 1619 m) for a
date in late spring are p = 840 mb, T = 15ºC, and r = 45%. Compute the sea level pressure
at Albuquerque on this date.
5. The surface observations from Grand Junction, Colorado one afternoon are p = 870 mb,
T = 20ºC, and r = 65%. If the pressure reduced to sea level at this station is 1005 mb, what
is the elevation of Grand Junction?
6. Attached are the pressure, temperature, and dewpoint observations collected by a standard
rawindsonde sounding obtained in the Great Plains during late spring. Obtain a standard
skew-T log-P thermodynamic diagram from the course website or the weather lab.
a.
b.
c.
d.
e.
f.
g.
h.
Plot the temperature profile using a red colored pencil.
Plot the dewpoint temperature profile using a green colored pencil
Compute the geopotential thickness of the 850-600 mb layer.
Describe the environmental lapse rate in the 1000 – 950 mb layer.
Describe the environmental lapse rate in the 950 – 900 mb layer.
Describe the environmental lapse rate in the 800 – 750 mb layer.
Describe the environmental lapse rate in the 600 – 550 mb layer.
In what 50 mb layer(s) would an unsaturated air parcel that is displaced upward be
unstable with respect to the environmental lapse rate? List all such 50 mb layers.
i. In what 50 mb layer(s) would a saturated air parcel that is displaced upward be
unstable with respect to the environmental lapse rate? List all such 50 mb layers.
j. Estimate the level of free convection (LFC) for an air parcel originating at 900 mb.
Note: To receive full credit you must show your work and explain your answers completely. Pay
close attention to units. See the Appendix in your text or the Help Guide provided on the
course website for any unit conversions, values of physical constants, and useful equations.
You may also wish to consult the online Tutorial on Physical Calculations for good
problem solving techniques, as well as consult the online NWS and/or Air Force manuals
about the skew-T log-P thermodynamic diagram.
Pressure
(mb)
1000
950
900
850
800
750
700
650
600
550
500
450
400
350
300
250
200
150
100
Temperature
(C)
20.0
14.0
9.7
6.0
3.0
3.5
-1.0
-5.0
-9.5
-13.0
-24.0
-29.0
-37.0
-43.0
-49.0
-56.0
-59.0
-57.0
-55.0
Dewpoint
(C)
11.0
10.0
7.0
3.5
1.0
-13.0
-16.0
-18.5
-18.0
-23.0
-28.0
-33.0
-40.0
-46.0
-53.0