SAN FRANCISCO STATE UNIVERSITY                                                               Meteorology 430

DEPARTMENT OF GEOSCIENCES                                                      Fall 2010

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Final Examination

250 Points

 

 

 

 

 

 

 

Name _______________________________________________

 

 

                        1.         For questions involving use of equations or calculations, lay out all equations                                                            carefully, show all units, show all steps, number equations sequentially.

 

                        2.         For questions involving analysis or mapping techniques, use proper color                                                                 conventions, use proper mapping techniques (NO grease pencil on final copies).

 

                        3.         This examination is open book, open notes.

 

                        4.         Answer on separate sheets or on back of exam.

 

   

Part A. Application of QG-omega Equation (Map Set A) (140 points)

 

This question refers to the NAM 36 hour forecasts for 0000 UTC 12 December 2010:  (a) 500 mb Heights/500 mb Absolute Vorticity; (b)  the surface isobars overlaid with 1000-500 mb thickness contours for the same date and  time; (c) the absolute vorticity advection at 600 mb, 500 mb and 400 mb; and (d) the temperature advection at 500 mb. 

 

You may assume that real wind is geostrophic and the real absolute vorticity is the same as the absolute geostophic vorticity.

 

 

The simplified quasigeostrophic omega equation is

 

                                              

 

 

(i) Qualitatively discuss the quasi-geostrophic diagnosed omega that would occur at point A at 500 mb on the basis of charts (a) and (b).   Be sure to discuss the contribution of each term, any assumptions you used and the whether the net forcing indicates upward, downward or indeterminate vertical motion.  This is comparable to what we have been doing or have done in Metr 201/400/698.  (50 points)

 

The question asks for a qualitative assessment of the quasigeostrophic forcing for omega at 500 mb at point A.  The charts provided are the 500 mb height and vorticity fields and the 1000-500 mb thickness and surface pressure fields. 

 

Thus, the differential vorticity advection term, which should be assessed on the basis of vorticity advection charts for levels centering at 500 mb, and the temperature advection term, which should be assessed on the basis of the temperature advection at 500 mb, cannot be assessed directly. 

 

On the other hand, since vorticity advection generally is of the same sign but increases in magnitude with height, the sign of the vorticity advection can be estimated on the basis of the sign of the vorticity advection at the level in question.  Also, since temperature advection decreases in magnitude but keeps the same sign from the lower to middle troposphere, the 500 mb temperature advection can be qualitatively estimated on the basis of the temperature advection estimated on the basis of the 1000-500 mb thickness advection by the surface geostrophic wind.

 

With these simplifications/assumptions in mind, there is 500 mb  cyclonic vorticity advection returning forcing for upward motion and cold thickness (temperature) advection returning forcing for downward motion  at Point A.  Thus the two forcing terms are returning forcing for vertical motion of opposite signs, and this case is indeterminate.

 

(ii) Qualitatively discuss discuss  quasi-geostrophic diagnosed omega that would occur at point A at 500 mb on the basis of charts (c) and (d).   Be sure to discuss the contribution of each term in detail.  This is a more accurate assessment of the nature of the forcing functions learned in Metr 430.  (50 pts)

 

Charts (c) provide the actual vorticity advection at levels beneath, at and above the 500 mb level.   Using these charts, one can see that cyclonic (positive) vorticity advection is increasing with height--there is differential cyclonic vorticity advection. This would return forcing for upward motion at Point A.  Chart (d) shows the actual temperature advection at 500 mb.  This is cold advection which would return forcing for downward motion at Point A.

 

Thus, the forcing terms, more accurately assessed qualitatively, return forcing for vertical motion of opposite sign at Point A. Again, the qualitative assessement does not allow us to judge which term will be larger and this case is indeterminate.

 

(iii) Discuss if your Metr 400/698-level analysis (i) would be backed by your Metr 430-level analysis in (ii).  (20 points)

 

The two methods return the same results.  Thus, the assumptions made in (i) appear to be

valid in this case. This case illustrates the justification for using the conventionally available charts equivalent to nam_vort

and nam_thick to assess the relative forcing of the two terms in the middle troposphere is valid.

 

(iv) Discuss how the forcing in the vorticity advection term would be modulated by INCREASING the stability. (20 pts)

 

The static stability parameter is in the denominator of the multiplier for all of the forcing

terms.  Since the parameter is always greater than zero for a stable atmosphere (relative to

the dry adiabatic rate), the greater the stability the larger and more positive the parameter. 

This has the effect of dampening each forcing term. Since, for the case considered, the

vorticity advection term is forcing greater upward motion, the impact of increasing the static

stability will be to decrease the resulting upward motion this term is diagnosing.

 


Part B.  Dines Compensation (Map Set B) (70 pts)

 

Attached find the WXP analyses of the 36 hour forecast NAM 300 mb convergence  and 500 mb vertical velocity for 00Z 12 December 2010.   Examine the pattern at the same location you used in Part A.

 

1.  Compute the 500 mb vertical velocity (in cm/s) that would be expected on the basis of Dines Compensation as expressed in the simplified continuity equation.

                                                            

 

 

 

In this case,  you can assume that divergence at 300 mb is a good estimate of the net divergence in the layer from 500 mb to the tropopause at 300 mb and that 500 mb is the Level of Nondivergence.  The forecast 300 mb height is 888 dm and the forecast 500 mb height is 540 dm. 

 

 

First solve the equation for the 500 mb vertical motion.

 

Substitute the values into the last expression.

 

w500=(3.0 X 10-5 s-1) (3480 m) = 0.104 m s-1 = 10.4 cm s-1

 

2.  Comment on the degree to which the actual vertical velocity field is consistent with your result.  Careful, the vertical velocity plot shows omega, not w.  However, I am only asking you to compare the general nature of your result to the actual NAM forecast vertical velocity.

 

The actual plot of omega indicates a maximum in upward motion at Point A.  My result is c onsistent. The actual values, of course, cannot be compared since omega has a different unit (microbars per second).

 

Part C.  Interpretation of Cross-sections (Map Set C) (40 points)

 

You are given cross-sections of potential temperature, equivalent potential temperature and temperature at the latitude of San Diego stretching along a line of latitude to Florida.  You are  also given (a) a surface chart showing cross section location and fronts (assume that they are correct) and (c) soundings for San Diego, Albuquerque and Tallahassee at 12 UTC.

 

1.  Sketch in the position of the tropopause on the cross-section of potential temperature, and encircle areas where you would expect the value of the static stability parameter would be the greatest. (20 pts) 

 

The areas are shown on the cross-section of potential temperature.

 

2.    Comment on how the cross-section of potential temperature is verified by the tropopause locations on (c). (20 pts)

 

The soundings show that the tropopause is roughly at 200 mb.  This is consistent with the

tropopause location indicated on my cross-section.

 

 

 

 

 

 

Charts For

00 UTC December 12, 2010

 

Part A Charts


 

 

 

Part B Charts

 

 

 

 

 


Part C Charts--Cross-sections