Name: ________________________

Final Examination, MEA 443 Fall 2008, Lackmann

If you wish to have the final exam count double and replace your midterm score, place an “X” in the box above. As always, you are allowed to ask me questions during the exam if you require clarification on a given problem. Good luck! 1.) General meteorological analysis and scale analysis questions. Be sure to include units where

appropriate, and show your work.

a.) For synoptic-scale motions, what is the magnitude of the relative vorticity, yu

xv

∂∂

−∂∂ ?

b.) Write a mathematical expression for horizontal vorticity advection, and for synoptic-scale

motions, what is the typical magnitude of this quantity? c.) What is the typical scale for the horizontal temperature gradient across a front?

d.) What is a typical magnitude for the temperature lapse rate, zdTd

− , in the midlatitude

troposphere? e.) Often this semester, we examined horizontal thermal advection on the synoptic scale. Write a

mathematical expression and determine a typical order of magnitude for this quantity. f.) What is a typical value for the 700-mb geopotential height in the midlatitudes during winter? ___________ meters g.) What is an “upper bound” limit for the wind speed in the jet stream for the strongest values

that would be seen in a typical midlatitude winter? _______ kts 2.) Briefly explain the cause of the Earth’s narrow, westerly midlatitude jet streams.

Place an X here to count it double!

3.) True/False questions ____ a.) The process which is responsible for the movement of cyclones is advection. ____ b.) Jet streaks move very rapidly, since they are advected at the speed of the winds within

their core. In other words, jet streaks typically move at the speed of the winds in their core. ____ c.) The energy available for cyclones to convert to kinetic energy is related to the

temperature contrast between the warm and cold air masses surrounding the storm. ____ d.) Ascent in the QG system (upwards omega) is not found when the atmosphere is stable. 4.) Earlier this semester, we discussed the concept of dividing the atmospheric flow into a “background” part (denoted by an overbar), and an “eddy” part, denoted by a prime. We used this framework to study the energetics of troughs and cyclones, in particular to study barotropic energy conversion as a function of positive or negative trough-axis tilt relative to the background flow. Suppose that we were interested in studying ridges and anticyclones instead of cyclones. For the example below, assume that the “eddy” is anticyclonic.

Barotropic term: [ ]

43421B

yuvu

tKe

∂∂′′−∝

∂∂

a.) Is this ridge gaining or losing energy due to the barotropic term? Show your work in the boxes above. ____________ (gaining or losing energy) b.) Recall that for cyclones and troughs, we found that a negative axis tilt when the system was

centered south of the jet core led to growth in energy of the system. Now, extrapolate the finding above for ridges and anticyclones, and state a “rule” like this for ridges south of the jet core.

Ridge or anticyclone 0vu ′′

0yu

∂∂

[ ]0

tK e

∂∂

+y The arrows above represent u

5.) The figure below shows a recent 500-mb height and sea-level pressure analysis from the GFS model. We will focus on three cyclones, labeled A, B, and C on this diagram.

a.) Which of these three cyclones is most likely to be undergoing intensification? ____ b.) In one sentence, justify your answer to a.) below.

c.) What is the sign of the temperature advection in the surface-to-500 mb layer at point D, over

the state of Iowa? _______ (warm, cold, or neutral)

6.) Below is a zoomed-in view of cyclone “B” from above. Based on the available information,

sketch the most likely location of a warm frontal boundary with this system.

C

B

A

500 mb height (thick solid contours at a 6 dam interval) and sea level pressure (thin solid contours at a 2 mb interval).

D

7.) For the cyclone on the previous page, is there evidence of Sutcliffe-Petterssen self-development at this time? ________ (Y or N). Briefly justify your answer below.

8.) The following is a cross section along 45° North, from a GFS forecast.

Thermal Wind Relations: yz

ug

∂∂

−∝∂

∂ θ xz

vg

∂∂

∝∂

∂ θ

a.) Draw the 75-kt isotachs for winds into and/or out-of the section, and label whether the wind is

blowing into or out of the page. Peak wind speeds are ~ 100 kt. Use the letter “J” to mark the location of maximum winds. You may need more than one.

b.) On this diagram, indicate any areas with strong cyclonic or anticyclonic relative vorticity. c.) Indicate with the letter “T” or “R” the expected position of any upper-level trough or ridge

axes at the 400-mb level (draw these on the diagram above). d.) Moving horizontally along the 300-mb level, and accounting for both vorticity and stability,

indicate any areas of anomalously large (cyclone) or small (anticyclonic) potential vorticity (PV). Write “PV+” for large PV, and “PV-” for areas of small PV.

9.) Which of the following are “QG” assumptions? Check all that apply. ___ a.) Vertical advection is neglected ___ b.) The Rossby number is small ___ c.) The planetary vorticity is small ___ d.) The planetary vorticity is constant

10.) Consider the 250-mb map shown below, depicting height (solid contours) and isotachs (shaded).

a.) Based on jet dynamics alone, circle and label any expected regions of ascent and descent in

the vicinity of the jet that is centered over western Canada.

b.) Sketch the expected ageostrophic circulation for section A-B as shown on the map below in

the blank area below.

c.) Is the circulation you sketched for b.) thermally direct or thermally indirect? _______________

B

A

A B

11.) The 3 images above all including the same visible satellite image valid ~18Z yesterday,

12/10/2008. The lower two images, panels b.) and c.), show data for the 300K isentropic surface from the GFS model 6-h forecast valid at that time. If you can’t read these, they are also shown on the projector.

a.) The winds in the two isentropic analyses are storm-relative in one case, and not in the other.

Which panel shows the storm-relative winds? ______ [pick b.) or c.)] b.) Based on the observations and satellite image, sketch the approximate location of the frontal

boundary in panel b.) over the Gulf of Mexico. c.) Based on the data available, is the front over the southern portion of the domain an anafront

or a katafront? _________________ d.) Based on the surface observations shown in panel b.) and your frontal analysis, do you think

the dominant frontogenesis mechanism is shearing, confluence, or both? _________________

a.)

b.) c.)

12.) The two maps below show GFS 500-mb height (solid) and sea-level pressure (dashed) forecasts for the North American region.

a.) Sketch frontal boundaries on the panel two panels for the system in the southeast. b.) On just the right panel, circle and shade all areas of strong QG forcing for ascent, accounting

for frontal circulations, jet circulations, upper waves, etc.

13.) Short answer. Can intensifying tropical cyclones undergo Sutcliffe-Petterssen self

development? _____ (yes or no). Briefly justify your answer below. 14.) It is commonly observed that tropical cyclones, including those that are intensifying, are

“vertically stacked”, with the vortex at the 500-mb level directly above the surface low pressure center. Given that we often state that “stacked” systems are through developing, how can this be? What mechanism(s) are responsible for the deepening? Briefly discuss.

15.) On the following page is a sequence of images showing GFS forecasts of an upcoming

weather event in western Washington State this weekend (details in figure captions). The partial thickness nomogram is included on the last page of the exam for reference.

a.) At the time of the 48-h forecast, do you expect precipitation to be falling at SEA? ____ b.) If precipitation is falling, what precipitation type do you expect at 48-h? __________ c.) At the time of the 72-h forecast, do you expect precipitation to be falling at SEA? ____ d.) If you expect precipitation to be falling, what precipitation type do you expect? __________

GFS forecast images valid 06 UTC Saturday: (a) 500-mb height (thicker solid lines) and sea level pressure (thin solid lines); (b) sea level pressure and 1000-850 mb thickness (dashed); (c) GFS model forecast sounding for Seattle, located at the “S” in panel b above.

As above, except for 72-h forecast valid 06 UTC Sunday, 14 December.

a. b.

c.

c.

a. b.

S

S

16.) Below is a radar image with partial thickness (1000-850 and 850-700 mb) superimposed. This is from 15Z today. Use the partial thickness nomogram on the last page of the exam to make a precipitation-type forecast for the location marked NO (New Orleans) for this time.

_______________________

17.) Fill in the elements of this table. Hydrostatic? Approx. grid spacing Spectral or grid point? NAM GFS ___ 18.) Why is it necessary for numerical models to parameterize cumulus convection?

a.) Because models would otherwise require an unrealistically long time to develop precipitation.

b.) Because the atmosphere would become too unstable due to the neglect of the stabilizing action of sub-grid scale cumulus convection.

c.) Because models must account for the effects of convective precipitation for a more realistic precipitation forecast.

d.) All of the above e.) Only b.) and c.)

____ 19.) Which of the following best fits the definition of “data assimilation”? a.) The practice of using all available data to formulate a weather forecast. b.) The use of observational and short-term model forecast data to construct an analysis. c.) In models, when process that cannot be resolved are represented, this process is known as

“assimilation”. d.) This is where several model runs are used to measure the uncertainty in model forecasts, as

well as produce an ensemble mean which is more accurate than individual forecasts. 20.) List one type of information that is included in MOS that is not numerical model output. ____________________

NO

___ 21.) Which convective scheme is used in the NAM model, the Kain-Fritsch or the Betts-Miller-Janjic scheme? ___________________

___ 22.) True or False. Hydrostatic models do not account for vertical motion effects such as

adiabatic expansion or vertical advection. 23.) True/False cold-air damming questions: ____ a.) A small Rossby radius of deformation would be consistent with a wide CAD cold

dome. ____ b.) Cold-air damming events are also common along the west side of the Appalachians, in

Tennessee and Kentucky. ____ c.) The NAM model is more accurate than the GFS model in handling the initial formation

of cold-air damming. Some additional information for reference: Frontogenesis equation:

4434421443442144344214434421DTermCTermBTermATerm

tdd

yypyv

yyu

xF ⎥

⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

−⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂∂

+⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂∂

+⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂∂

=θωθθθ

Don’t forget to forecast for MCI today- last forecast of the semester!!