Winter 2009ATM 111
ATM111 - Homework #1
20
pts
1. Basic meteorology review:
a. (3pts) Write down the hypsometric equation and briefly define all terms & symbols.
b. (3pts) Atmospheric temperature is measured by a radiosonde to be T(P)=270+21*cos(P*7x10-5) where T is in K and P is in Pa. What is the mean temperature between 1000 and 500 mb?
c. (1pt) Assume that a radiosonde has a systematic error of 1.2 K, how far off would the geopotential height of 500 hPa surface be if the 1000 hPa surface is estimated correctly? (calculate to nearest cm)
d. (2pts) If the sea level pressure is 1021 mb, what is the elevation of the 1000 mb surface? (Use T definition from part b at the layer midpoint; neglect T change over the 21 mb interval. Neglect moisture effects.)(calculate to nearest cm)
e. (2pts) At the station, the height of the 500 mb surface is 5700 m and the temperature at that level is given by the formula in part b. What is the elevation of the 501 mb surface? (neglect T change over the 1 mb interval)(calculate to nearest cm)
f. (1pt) Compare the elevation change per 1 mb of pressure change for parts d and e.
2. Basic wind review:
a. (3pts) Write down the geostrophic wind equation and briefly define all terms & symbols.
b. (2pts) Looking at the 546 and 552 contours in fig. 3.1c on page 55 of Carlson’s text, the two contours are the equivalent of 3.3 degrees latitude apart just west at 100W longitude. Estimate the geostrophic wind zonal wind between the two contours at 40N. Hint: 1 degree latitude = 111km.
c. (1pt) What is the geostrophic wind for the same spacing at 55 N?
d. (2pts) Compare your answer to part b with an estimated wind speed from the isotachs presented in fig. 3.2c on page 59. What are some reasons for your answer to differ from the value estimated from fig. 3.2c?
Due ____13 January 2009 ______
Winter 2009ATM 111
ATM111L - Lab Exercises #1
18 pts
1. Finding upper level features.
A. Draw a dashed line for each trough in the hemispheric 500 hPa geopotential (Z500) chart: no-color.jpg. This is to be found at the course website from a link on the mainpage. There are two other charts, one has SLP paired with Z500 while the other has vorticity paired with Z500.
B. Draw all surface frontal boundaries showing the correct type (and convention) as well as location on a print of the map: reduced-color.jpg. The map has 1000-500 hPa thickness (h) and sea level pressure (SLP).
Apply the “majority rule” to these properties (not all of this info is available):
i. trough in sea level pressure field
ii. wind shift of direction (typically there is convergence)
iii. at warm air edge of a frontal zone
iv. at moist air edge of a dewpoint gradient
v. may have particular weather or cloud types
vi. barometric tendency (may decrease as front approaches or increase as moves away)
vii. occlusion along 1000-500mb thickness ridge
Also note:
1. designation (warm, cold, stationary) depends on wind direction relative to the front
2. fronts tend to move with speed of air on the cold side of the front
3. there may be other similar features (troughs, squall lines, dry lines, convergence lines) which are not analyzed as fronts.
Grading is based on: having the required information present, and whether it is accurate. Front location error is based on distance from the location given on the key, but also whether important known properties are violated or not.
Due ____13 January 2009 ______
Winter 2009ATM 111L
ATM111L - Lab Exercises #2
23 pts
1. a. (16 pts) Mark the fronts and troughs on the 4-panel forecast chart. Make your marks on the tracing paper provided. Brown lines are SLP; blue (mostly dashed) lines are 1000-500 hPa thickness. The chart is: W08-ua-v3.jpg. These charts and some accompanying upper air charts along with an animation are posted at this URL:
for fronts, mark: location, type, direction of motion (with correct standard frontal symbols).
for troughs: mark location only. Use a dashed line.
Hints:
1. A surface analysis at T=12hr is provided. Fronts have continuity over time.
2. Make your marks lightly at first so you can easily erase and adjust them as needed.
3. Strive to make your locations consistent with as many known properties of fronts as you can. Note that a front that looses its temperature gradient may become a trough.
4. Consult the upper air charts to understand the precipitation areas and front/trough locations.
5. Grading is based on: having the required information present, and whether it is accurate. Location error is based on distance from the location given on the key, but also whether important known properties are violated or not.
b. (5 pts) Provide a brief, most likely explanation for each of these questions. (Hint: the main cause in each case is different.)
Why is there precipitation in central Tennessee in map a?
Why are there scattered showers in western Utah in map a?
Why is there precipitation over eastern South Dakota in map b?
Why is there precipitation in northern New York state in map c? and
What specific factor on the map tells you it is likely to be snow?
2. (2 pts) Make an overlay of 500 hPa geopotential height and a water vapor image using IDV. (Cryptic hints: Start IDV, go to Dashboard window, choose ‘Data choosers’ tab, then ‘catalogs’ on sidebar, then ‘Unidata IDD Model data’, ‘UCAR motherlode’, then Global forecast system model, ‘NCEP GFS Northern Hemisphere’ (otherwise datasets large and plotting is slow), choose the time (e.g. latest if are matching an available satellite image), then add source, pick 3d grid (for an upper air variable, now in ‘Field Selector’ tab), then select the variable, create display. <wait> Then pick proper level. Then modify the region of interest, plotting colors, etc. For example: projections tab, predefined, then North America region, then + magnifying glass to zoom in, etc.
To get satellite data: go to ‘Data Choosers’ tab, pick ‘Images’ sidebar, adde.ucar.edu server with GINICOMP dataset then connect button, image type: ‘WV Multi-composite’ for N Hemis water vapor, absolute time selector choose time to match your upper air chart, <wait>
When image is ready, do a print screen, then open Gimp. In Gimp open ‘file’ menu then ‘acquire’ then ‘paste as new’; you see your screen image. Select the overlay image part, copy that overlay image part and choose ‘paste as new’ again. Now you just have the overlay. Then save that by using: save as; choose a filename that includes your last name, then a file type (.gif) then export to your storage device. Finally, email it to the TA, and print that .gif image.
Due ____20 January 2009 ______
Winter 2009ATM 111
ATM111 - Homework #2
10 pts
1. Consult the “Hard Freeze” 500 mb geopotential height contour pattern at time T=0. (See: ) From that chart, estimate the wavelength between the ridge just off the west coast and the SE United States ridge at φ = 35N and express that in m. Estimate “beta” using β = 2 Ω cosφ r-1 where r is the earth’s radius (6370 km). If the average zonal wind (U) is 30 m/s how fast is the pattern moving according to Rossby’s formula? (Formula in Forecast Notebook) Is your result consistent or not with the persistence of the heat wave?
Due ____20 January 2009 ______
Winter 2009ATM 111
ATM111 - Homework #3
15 pts
1. (10 pts) Consult each “forecast” chart found in the directory given by this URL:
In each case, the forecast verified and a different significant weather event occurred. Make a “forecast” of what that weather event was by identifying:
A. the location/region
- the type of significant weather event
- your reasoning for forecasting that type of significant weather
(.5,1.,1.)
2. (5 pts) Basic vorticity review using information about a point at 32N along the TX/LA border region.
a. From fig. 3.2d (p. 59) there is a max wind along 32N in southern LA of 70 m/s. About 5 degrees longitude to the west the wind drops to about 30 m/s. Using this shear, calculate the shear vorticity in the LA/TX border region.
b. From fig. 3.2d (p. 59) the 300mb height contours are curving. Assuming the flow is parallel to the contours, the estimated curvature at the TX/LA border is roughly an “average” of the 924 (~550 km radius) and 930 (~ almost infinite radius) contours curvature, or about 1100 km. For a wind speed of 50 m/s, what is the curvature vorticity here?
c. Calculate the total absolute vorticity based on your answers from parts a & b. How does that compare with that plotted in fig. 3.1d on page 56?
Due ____27 January 2009 ______
Winter 2009ATM 111L
ATM111L - Lab Exercises #3
60 pts
COMET modules: NWP group.
1. Proceed to the COMET modules on topics related to numerical weather prediction (NWP). The URL is:
You will see a variety of links listed there. Over the next 3 weeks, you are to study the following modules in the following order:
- Model Fundamentals (1-2)
- Understanding Data Assimilation: how models create their initial conditions (3-7)
- Impact of model structure and dynamics (4-8)
- How models produce precipitation and clouds (3-4.5)
- Influence of Model Physics on NWP forecasts (2-4)
- Intelligent use of model-derived products (1-3)(14 -28)
Activities:
A. A list of specific supplementary questions is attached. They are grouped by the module. You are to complete and hand in each group as you finish the relevant module. Note that you are asked to log in the amount of time you spend on each module. Some modules are much longer than others, so preview them first to budget your time.
B. A separate list of 20 questions (file NWP_exam1.doc) is at this website.
i. Download and save a copy of this file.
ii. Review all the questions first.
iii. As you encounter a segment in a module that relates to that question, enter some notes after the question. Two things will be done with those notes.
iv. First, you may refer to those notes when taking the online quizes.
v. Second, you will need to turn in those notes after you have completed all the quizes.
vi. Each of the assigned modules has a quiz. You need to reach a passing score (typically 75%) on each of the modules.
When you take aquiz, you must complete it at one sitting. (It takes 10-20 minutes.) You must enter your full name and Dr. Grotjahn’s email address () where indicated.
You have 3 weeks to complete the questions here, pass the exam, and turn in your online exam notes.
Due ____10 February 2009 ______
Winter 2009ATM 111L
ATM111L - Lab Exercises #3 -- Continued
Specific preparatory questions for online COMET modules: NWP group.
a. Model Fundamentals
i. List 3 groups of “physics” processes in a model.
ii. List 10 different processes that are usually parameterized. Note: “incoming solar radiation”, “vegetation”, “topography”, “surface roughness” and etc. are parameters, not processes.
iii. How much total time did you spend on this module?
b. Understanding Data Assimilation: how models create their initial conditions
i. List a drawback of DA cycling: can perpetuate a bad forecast into later forecasts.
ii. Does tuning vary with observation variable? Does it vary with data source?
iii. How much total time did you spend on this module?
c. Impact of model structure and dynamics
i. For a convective meso-vortex (scale 140 km) in a grid point model (with 20 km grid interval) how many km does a 14 m/s wave lag after 170 min?
ii. Hydrostatic or non-hydrostatic: ____ models can explicitly forecast vertical motion whereas ____ models only diagnose vertical motion fields. _____ models are used especially for forecasting smaller-scale phenomena, such as convection. _____ models are used only over small domains, whereas ______models are used in global and regional models.
iii. Compare and contrast: envelope, silhouette and mean orography.
iv. How much total time did you spend on this module?
d. How models produce precipitation and clouds
i. Compare and contrast: simple versus complex clouds.
ii. Name 2 strengths and 2 limitations of the convective scheme used in the Eta model.
iii. How much total time did you spend on this module?
e. Influence of Model Physics on NWP forecasts
i. Which dominates (physics, dynamics, or both) the forecast of 2 m temperature in the next 12 hours for each of these situations: 1) Center of polar air mass during January, 2) Overrunning area north of a warm front during daylight hours in April, 3) Arctic front to pass your location in the next two hours in February
ii. The largest errors in short- & longwave radiation calculations result from errors in what?
iii. How much total time did you spend on this module?
f. Intelligent use of model-derived products
i. List 6 common derived fields
ii. In which of the following situations is MOS likely to be unreliable? 1) vigorous low-pressure system, 2) squall line, 3) trapped cold air in a mountain valley, 4) clear, clam dry night over the high plains, 5) tropical cyclone
iii. How much total time did you spend on this module?
Winter 2009ATM 111
ATM111 - Homework #4
24 pts
Objective Analysis – Cressman scheme
Problem set up:
i. First guess field is zero.
ii. Synthetic observations are generated from this function: T = cos (πx/2)
iii. grid point range: -3 ≤ x ≤ 3.
iv. For the Cressman scheme, a = 5., R = 10.
v. The problem should be electronically. The entire calculation can be done easily using a spreadsheet program such as Excel.
vi. Submit print outs of answers. To show work, send electronic version of spreadsheet, etc. that you used to generate your answers to the TA for grading.
a. (10 pts) Generate synthetic observations at 11 equally-spaced points from -3. through 3. using a 0.6 interval. Use the Cressman scheme to generate final values at the 21 equally-spaced points over the grid point range using a 0.3 interval. Call this “Set 1”
b. (10 pts) Generate synthetic observations at these irregularly-spaced points:
-2.7, -1.8, -1.5, -1., -0.5, 1.5, 2., 2.1, 2.4, 2.6, 2.9
Use the Cressman scheme to generate values at the 21 equally-spaced points over the grid point range using a 0.3 interval. Call this “Set 2”
c. (2 pts) Use the synthetic observation function to generate final estimates at the 21 equally-spaced points over the grid point range using a 0.3 interval. Call this “Set 3”
d. (2 pts) Plot the 3 sets of values on the same graph. Be sure that your graph as unequivocal labels for curves and axes. Your graph should include the full grid point range.
e. (2 pts) How well do Sets 1 and 2 compare with Set 3?
f. (2 pts) What factors give a better or worse match?
Due ____3 February 2009 ______
Winter 2009ATM 111
ATM111 - Homework #5
21 pts
Understanding Fourier Series.
Here are some simple illustrations of Fourier (cosine) series:
Use NX = 7 grid points defined by xm = (m-1) 2 / NX.
Synthetic data are to be generated by a series of sine functions:
f(xm) = 3 + 2sin(xm) + 2sin(2 xm) + 0.5*sin(3 xm ). (1)
Since NX=7, K=3.
To get full credit on these problems, you must show work (i.e. turn in spreadsheet)
a. (3 pts) find and print the first 6 values (m=1,6) of f(xm)
b. (4 pts) find the 4 values of the Fourier coefficients: c(k). where:
(2) for B=1 for k=0
(3) where B=2 for k>0.
(FYI: For a sine series, sin(0*xm) is identically zero, but one needs the average of f; so that average is included in c(0) but c(0) is treated as a special case and not multiplied by the corresponding sine function.
For a cosine series the average of f is included in c(0) and the term is multiplied by cos(0*xm) which is identically 1; equation 3 is used for all k’s with B=1 for k=0, B=2 for all other k.)
c. (4 pts) make a back transform to obtain the first 4 values of fb after the back transform:
(4)
d. (1 pt) How well do the fb values match the original (f) values at the first 4 grid points?
e. (9 pts) compare treatment of a derivative at the points m=3 and m=4. Obtain the finite difference and spectral estimates of the derivative at that one point using:
versus
and compare (with a brief discussion, 1pt) these estimates with the analytic derivative of f.
Due ____ 10 February 2009 ______
Winter 2009ATM 111
ATM111L - Lab Exercises #4
25 pts
COMET mesoscale weather modules:
1. Proceed to the COMET modules on topics related to mesoscale meteorology. The URL is:
You will see a variety of links listed there. Over the remaining weeks we shall look at several modules.
Over the next two weeks, you are to complete:
(5pts) Mesoscale banded precipitation(3-4)
PLUS (10 pts): Choose 2 from: i) Low Level Coastal Jets, ii) Gap Winds, iii) Mountain Waves & Downslope Winds, iii) Landfalling Fronts and Cyclones, iv)Cold air damming, v) forecasting dust storms, and vi) Coastal Trapped Wind Reversals. (1.5-3 each)
A. Each module has a quiz.When you take the exam, you must complete it at one sitting. (It takes 10-20 minutes.) You must enter your full name and Dr. Grotjahn’s email address () where indicated.
B. In addition to the quizes, answer the following questions.
i.(1 pt) How much time did you need to complete each module (including the final exam)?
ii. (9 pts) Indicate which modules you worked through and for each module:
1) Describe something you learned from each module
2) What did you like most of each module you tried?
3) Was there anything you did not like about a module? If so, please elaborate.
Due ____24 February 2009 ______
Winter 2009ATM 111
Homework #6
22 pts
1. Understanding how a forecast model predicts a future state. Let the initial condition be:
U(x, 0) = 0.125*[1-cos(x )]2(1) where x ranges from 0 to 2.
U(x, 0) = 0(2)where x ranges from 2 to 3
Calculate the model’s forecast using 31 grid points at these locations: xi = 0 to 3 in increments of /10.U’s are nondimensional.Your model is the 1-dimensional nonlinear advection equation: