Mesoscale Meteorology Assignment #3 Q-G Theory Exercise. Due 23 February 2017

Transcription

1 Mesoscale Meteorology Assignment #3 Q-G Theory Exercise 1. Consider the sounding given in Fig. 1 below. Due 23 February 2017 Figure 1. Skew T-ln p diagram from Tallahassee, FL (TLH). The observed temperature ( C) and dew point temperature ( C) traces are given in red and green, respectively. The observed vertical wind profile is given by the wind barbs at right, where a half-barb = 5 kt, full barb = 10 kt, and a pennant = 50 kt. Figure obtained from a. (8 pts) Consider the hpa layer. How does the vertical wind profile change in direction with height over this layer? What does that infer about the sign of temperature advection within this layer? Draw the hodograph for the winds in this layer. b. (7 pts) Graphically compute the thermal wind at 600 hpa using the wind observations at 700 hpa and 500 hpa. Ensure your wind vectors are of appropriate length and include a reference vector. Include a few representative isotherms with appropriate labels. c. (6 pts) Determine the sign and relative magnitude of temperature advection over 100 hpa thick layers at 500 hpa and 700 hpa. From this analysis, what is the inferred sign and magnitude of the geopotential height tendency χ at 600 hpa? d. (6 pts) From the analysis in (a), what is the inferred sign of vertical motion ω at 600 hpa?

2 2. The observed 850 hpa wind at Norman, OK on a late winter s evening was 23.2 m s -1 from just slightly west of due north (350 ). An idealized representation of the hpa layer-mean isotherms at this time are given in Fig. 2. Figure 2. Idealized depiction of the hpa layer-mean isotherms in the vicinity of Norman, OK (denoted by the gold star). The layer-mean isotherms lie 15 off of the x-axis. a. (5 pts) On Fig. 2, draw a vector of appropriate length and direction to represent the 850 v. Include a reference hpa wind observation listed above. Label this vector ( ) vector at lower left (i.e., 10 m s -1 = some distance) to aid with this and later questions. b. (8 pts) Using the thermal wind equation and centered finite differences for its partial derivatives, compute the thermal wind v T = ( u T, vt ) in m s -1 valid at the black star. Show all work and carry all units through your calculations. Please note: f = 8.4 x 10-5 s -1 and R = 287 J kg -1 K -1, where 1 J = 1 kg m 2 s -2. c. (5 pts) Using your answer to (b), draw a vector of appropriate length and direction to represent the thermal wind. Label this vector v T. d. (5 pts) From the observed 850 hpa wind and the thermal wind, compute the 700 hpa v. geostrophic wind (m s -1 ). You should do this only graphically and label it as ( ) e. (5 pts) The observed 700 hpa wind at Norman, OK was 21.1 m s -1 from the northwest (315 ). How does this compare to your result to (d)? g p 0 g p 1

3 3. For this question, use Figs. 3-8 contained at the end of this document. Consider two areas: (#1) Maryland, Delaware, Pennsylvania, New York, and New Jersey and (#2) Illinois, Indiana, Ohio, and Kentucky. a. (6 pts) In the context of the differential potential temperature advection term to the quasi-geostrophic height tendency equation, would you expect height falls or height rises at 500 hpa in region #1? Region #2? Document the evidence in support of your answer. Note: on an isobaric surface, gradients of temperature are exactly equivalent to gradients of potential temperature. b. (6 pts) In the context of the geostrophic absolute vorticity advection term to the quasigeostrophic height tendency equation, would you expect height falls or height rises at 500 hpa in region #1? Region #2? Document the evidence in support of your answer. c. (6 pts) In the context of the potential temperature advection term to the quasigeostrophic omega equation, would you expect ascent or descent at 700 hpa in region #1? Region #2? Document the evidence in support of your answer. d. (6 pts) In the context of the differential geostrophic absolute vorticity advection term to the quasi-geostrophic omega equation, would you expect ascent or descent at 700 hpa in region #1? Region #2? Document the evidence in support of your answer. Note: you may assume that geostrophic absolute vorticity advection is approximately zero at the surface when answering this question. e. (6 pts) Compare your answers to (c) and (d) to Fig. 8. Do your answers agree with the total calculated forcing? Briefly describe. Which term(s) appear to dominate the answer in region #1? Region #2? f. (6 pts) Based on Fig. 7, would you say that the trough at 500 hpa in the eastern United States is amplifying, deamplifying, or translating with no change in amplitude? What about the trough off of the Pacific Northwest coast? Describe why. g. (9 pts) Using Fig. 5, determine the direction and relative magnitude of the Q-vector at three locations: Atlanta, GA; Washington, DC; and northern New Hampshire. Show your work. What is the inferred forcing for vertical motion in this region from your analysis? Note #1: there are wind barbs plotted on the map at each of these locations. Note #2: the map uses a Lambert conic projection, which means that the latitude and longitude lines (thin dashed lines) should be used to determine the cardinal directions (i.e., north is not always straight toward the top of the chart, east is not always straight toward the right edge of the chart).

4 Figure hpa wind (kt, shaded per color bar at bottom; and barbs, half-barb = 5 kt, full barb = 10 kt, and pennant = 50 kt), geopotential height (black contours every 6 dam), and temperature (dashed red contours every 3 C) from the 1 GFS analysis valid 1200 UTC 9 February Image obtained from

5 Figure 4. As in Fig. 3, except for 500 hpa. Note the different shading levels.

6 Figure 5. As in Fig. 3, except for 700 hpa. Note the different shading levels.

7 Figure hpa wind (barbs: half-barb = 5 kt, full barb = 10 kt, pennant = 50 kt), height (black contours every 3 dam), and geostrophic absolute vorticity (x 10-5 s -1 ; shaded per the color bar at bottom) from the 1 GFS analysis valid at 1200 UTC 9 February Image obtained from the same site as in Fig. 3.

8 Figure hpa height (black contours every 3 dam), hpa thickness (green dashed contours every 6 dam), and the total right-hand side of the quasi-geostrophic height tendency equation (x s -3, shaded per the color bar at bottom) from the 1 GFS analysis valid at 1200 UTC 9 February Warm (cold) colors denote forcing for height rises (falls). Image obtained from the same site as in Fig. 3.

9 Figure hpa height (black contours every 3 dam), hpa thickness (green dashed contours every 6 dam), and the total right-hand side of the quasi-geostrophic omega equation (x Pa m -2 s -1, shaded per the color bar at bottom) from the 1 GFS analysis valid at 1200 UTC 9 February Warm (cold) colors denote forcing for ascent (descent). Image obtained from the same site as in Fig. 3.