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SAN FRANCISCO STATE UNIVERSITY Spring 2005
DEPARTMENT OF GEOSCIENCES Metr 503
Midterm 1
200 points
Part I. Quasigeostrophic Omega Equation (75 points)
The quasigeostrophic omega equation is
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where the effects of friction (Term D) and diabatic heating (Term E) are also included.
1. (a) Discuss why all the forcing terms EXCEPT Term E can be neglected during the
summer in the lower mid-troposphere over the center of North America (40 points) (now amended to include information that should appear in your answers after careful reconsideration...i.e., the extra credit);
The first two forcing terms, differential vorticity advection and temperature advection, are significant only for baroclinic systems (i.e., if the jet stream is present). This is because significant vorticity advection is associated with the jet, and significant temperature gradients and advection are found with the pressure patterns that are found associated with troughs and ridges in the jet as well. Thus Terms B and C would be zero, since the baroclinic patterns associated with the jet stream generally are absent in the summer. The entire quasigeostrophic forcing would lie with the diabatic heating term, which is interpreted in much the same way that the temperature advection term is---a maximum returns forcing for upwards omega. Since the resulting vertical motion fields are associated with equivalent barotropy (which in itself suggests that Terms B and C would be small). The upward motion associated with the diabatic term is associated by continuity with the surface low pressure area that is climatologically found over southwestern portions of North America int he warm season.
(b)
Examine the potential temperature pattern below. Assume that the pattern represents the average daily DIURNAL HEATING (in other words, assume that the chart shows the heating that produces a change in potential temperature from morning to afternoon). Given your answer in (a) discuss the average daily nature of the forcing for 700 mb qg omega over the western United States (35 points) (now amended to include information that should appear in your answers after careful reconsideration...i.e., the extra credit);
For the pattern shown, the Laplacian of the diabatic heating would return forcing for upwards motion at 700 mb. The pattern shows a maximum of heating in the western United States. The Laplacian of this heating pattern would return a negative value. The minus sign at the front of the term converts it to positive. Thus, the pattern is forcing negative (upward) omega. This is consistent with both the observed vertical motion fields in the lower mid troposphere over western North America in the warm season, and, by continuity, the presence of a surface low pressure area in the same area, the North American thermal low.
Part II. Gigantic, Stupendous Case Study (125 points)
Attached at rear of exam find the following charts for 00 UTC 3/13/99:
(a)
500 mb heights/Absolute Vorticity
(b)
Sealevel Pressure/1000-500 mb Thickness
(c)
Surface Analysis
(d)
850 mb Heights and Isotherms
(e)
500 mb Heights and Isotherms
(f)
850 mb Q-vector Convergence
(g)
Radar Composite
(h)
Enhanced Infrared Sat Image
1.
Using (a) and (b), characterize the QG-forced w at 850 mb over south-central Tennessee. Please be careful to list the assumptions you made in using these charts to estimate the nature of the 850 mb QG-forced w. (35 pts)
To assess the differential vorticity advection term, one needs to assume that vorticity advection is negligible near the ground and increases upward. The pattern depicted shows either neutral conditions (since the area of south-central Tennessee can be thought of as the center of a ab vort minimum) or weakly positive centering on the 850 mb level, even though the level shown for the vorticity field is the 500 mb level.
To assess the impact of the temperature advection term, one needs to remember that temperature advection tends to weaken with height, but maintain its sign. Thus, the area of south-central Tennessee is in an area of warm advection at all levels of the lower troposphere, including 850 mb. The temperature advection forcing term would contribute to upward omega.
On balance, this is not an ambiguous case. The forcing is for upwards omega in south central Tennessee at 850 mb.
2.
Using charts (c), (d) and (e), briefly describe the evidence that this system is occluded. (15 pts)
(Basic: The system is closed off at all levels.) (Advanced: A thickness tongue extends northward from the apex of the surface low.)
3.
Describe how the pattern shown in chart (f) is consistent/inconsistent with your results from (1). (10 pts)
The Q-vector convergence field suggests upward motion over south-central Tennessee. This result is consistent with the result from (1) above.
4. Analyze the surface chart. (40 points)
5.
Using (h), analyze a deformation zone in the relative mid/upper1 tropospheric wind field for the portion of the image in the southeastern quadrant of the image. (Be sure to show relative streamlines, neutral point, axes of dilatation and contraction). (25 pts)
1In this case the mid and upper tropospheric relative wind fields are in phase.
6. Explain whether the relative winds (as indicated by the deformation shown) SHOULD be a representation of the ACTUAL winds for this case in the mid and upper troposphere. (10 pts)
The system is closed off at all levels above the surface. In this restrictive circumstance, the relative winds are the same as the actual winds since
Actual Winds = Mean Zonal Flow + Relative flow
For closed systems, there is no mean zonal flow. Occluded systems are closed at all levels of the troposphere. Hence, the relative flow south of the axis of dilatation in this case should approximate the actual flow..
7.
As an illustration of (6), find ONE of the charts that provides corroboration of your answer in (6). (10 pts)
The 500 mb chart shows the same actual wind pattern as the relative wind flow depicted in (5).
