Winter 2009 ATM 111ATM111 - 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 2009 ATM 111ATM111L - 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 fieldii. wind shift of direction (typically there is convergence)iii. at warm air edge of a frontal zoneiv. at moist air edge of a dewpoint gradientv. may have particular weather or cloud typesvi. 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 front2. fronts tend to move with speed of air on the cold side of the front3. 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 2009 ATM 111LATM111L - 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:http://atm.ucdavis.edu/~grotjahn/course/atm111/labwk/labwk_2/*

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 2009 ATM 111ATM111 - Homework #2

10 pts

1. Consult the “Hard Freeze” 500 mb geopotential height contour pattern at time T=0. (See: http://atm.ucdavis.edu/~grotjahn/Analogs/hard_freeze/hard_freeze.htm ) 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 2009 ATM 111ATM111 - Homework #3

15 pts

1. (10 pts) Consult each “forecast” chart found in the directory given by this URL:

http://atm.ucdavis.edu/~grotjahn/course/atm111/hwk/hwk3/

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/regionB. the type of significant weather eventC. 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 2009 ATM 111LATM111L - 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:

http://meted.ucar.edu/topics_nwp.php

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:

a. Model Fundamentals (1-2)

b. Understanding Data Assimilation: how models create their initial conditions (3-7)

c. Impact of model structure and dynamics (4-8)

d. How models produce precipitation and clouds (3-4.5)

e. Influence of Model Physics on NWP forecasts (2-4)

f. 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. http://atm.ucdavis.edu/~grotjahn/course/atm111/hwk/hwk3/

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 a quiz, you must complete it at one sitting. (It takes 10-20 minutes.) You must enter your full name and Dr. Grotjahn’s email address (grotjahn@ucdavis.edu) 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 2009 ATM 111LATM111L - Lab Exercises #3 -- Continued

Specific preparatory questions for online COMET modules: NWP group.

a. Model Fundamentalsi. 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 conditionsi. 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 dynamicsi. 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 cloudsi. 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 forecastsi. 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 Februaryii. 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 productsi. List 6 common derived fieldsii. 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 cycloneiii. How much total time did you spend on this module?

Winter 2009 ATM 111ATM111 - 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 2009 ATM 111ATM111 - 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 2009 ATM 111ATM111L - Lab Exercises #4

25 pts

COMET mesoscale weather modules: 1. Proceed to the COMET modules on topics related to mesoscale meteorology. The URL is:

http://meted.ucar.edu/topics_meso.php

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 (grotjahn@ucdavis.edu) 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 2009 ATM 111Homework #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 2p. U(x, 0) = 0 (2) where x ranges from 2p to 3p

Calculate the model’s forecast using 31 grid points at these locations: xi = 0 to 3p in increments of p/10. U’s are nondimensional. Your model is the 1-dimensional nonlinear advection equation:

Ut + U Ux = 0 (3)

Where c = 0.25. Solve (3) subject to these boundary conditions:

U(0, t) = 0. and U(3p, t) = 0. (4)

a. (4 pts) Print the values of x and the corresponding U(x, 0) for all 31 grid points.

b. Step (3) forward in time using adjacent cells in a spread sheet program (or using finite differences and looping in a MATLAB or FORTRAN or C++ program). Use the time interval of dt = 0.1. For the first time step use this form:

U(x, dt) = U(x, 0) – dt * U(x, 0) * {U(x+dx, 0) – U(x-dx, 0) } / (2*dx) (5)

For all subsequent time steps use this form:

U(x, j*dt) = U(x,(j-2)*dt) – dt*U(x, (j-1)*dt)*{U[x+dx,(j-1)*dt] –U[x-dx,(j-1)*dt]} /dx (6)

Where j in (6) ranges from 2 to NT and NT is dictated by the length of the integration. Integrate until t=3, so that the number of time steps for the given dt value is 24 (not counting t=0).

b. (6 pts) Print the values of U(x, 1), U(x, 2), and U(x, 3), make sure your x values are unambiguous.c. (10 pts) Plot the values of U(x, 0), U(x, 1), U(x, 2), and U(x, 3) on ONE chart; make sure your axes are properly labeled (2pt ea curve; 1pt ea axis).d. (2 pts) Comment on how your solution changes over time.

Notes: The boundary conditions (4) mean you do not calculate U at those locations, though you do need to have those values when doing each time step. You only use formulas (1) and (2) to define the values (e.g. in spreadsheet cells) at the initial time, you do not use that formula at any later time step.

Notes: Please remember that you are to do individual work on all lab exercises. It is OK to use a spread sheet, such as EXCEL, if you wish. Either full or no credit is possible if you simply present a table of numbers; so it is recommended that you show your work as much as possible. Points will be deducted if the data are not labeled, incorrectly labeled, labeled ambiguously, etc. If you use a spreadsheet, email a copy to the TA when you turn in your assignment.

Due ____ 17 February 2009 ___________

Winter 2009 ATM 111 Mix of linear & nonlinear AdvectionHomework #6

22 pts

1. Understanding how a forecast model predicts a future state. Let the initial condition be:

U(x, 0) = 0.25*[1-cos(x )]2 (1) where x ranges from 0 to 2p. U(x, 0) = 0 (2) where x ranges from 2p to 3p

Calculate the model’s forecast using 31 grid points at these locations: xi = 0 to 3p in increments of p/10. U’s are nondimensional. Your model is the 1-dimensional nonlinear advection equation:

Ut + {c+U} Ux = 0 (3)

Where c = 0.25. Solve (3) subject to these boundary conditions:

U(0, t) = 0. and U(3p, t) = 0. (4)

a. (4 pts) Print the values of x and the corresponding U(x, 0) for all 31 grid points.

b. Step (3) forward in time using adjacent cells in a spread sheet program (or using finite differences and looping in a MATLAB or FORTRAN or C++ program). Use the time interval of dt = 0.1. For the first time step use this form:

U(x, dt) = U(x, 0) – dt * {c+U(x, 0) }* {U(x+dx, 0) – U(x-dx, 0) } / (2*dx) (5)

For all subsequent time steps use this form:

U(x, j*dt) = U(x,(j-2)*dt) – dt*{c+U(x,(j-1)*dt)}*{U[x+dx,(j-1)*dt] –U[x-dx,(j-1)*dt]} /dx (6)

Where j in (6) ranges from 2 to NT and NT is dictated by the length of the integration. Integrate until t=3, so that the number of time steps for the given dt value is 24 (not counting t=0).

b. (6 pts) Print the values of U(x, 1), U(x, 2), and U(x, 3), make sure your x values are unambiguous.c. (10 pts) Plot the values of U(x, 0), U(x, 1), U(x, 2), and U(x, 3) on ONE chart; make sure your axes are properly labeled (2pt ea curve; 1pt ea axis).d. (2 pts) Comment on how your solution changes over time.

Notes: The boundary conditions (4) mean you do not calculate U at those locations, though you do need to have those values when doing each time step. You only use formulas (1) and (2) to define the values (e.g. in spreadsheet cells) at the initial time, you do not use that formula at any later time step.

Notes: Please remember that you are to do individual work on all lab exercises. It is OK to use a spread sheet, such as EXCEL, if you wish. Either full or no credit is possible if you simply present a table of numbers; so it is recommended that you show your work as much as possible. Points will be deducted if the data are not labeled, incorrectly labeled, labeled ambiguously, etc. If you use a spreadsheet, email a copy to the TA when you turn in your assignment.

Assigned: 10 Feb 2009 Due ____ 17 February 2009 ___________

Winter 2009 ATM 111ATM111 - Homework #7

31 pts

1. Baroclinic tilts. Temperature (T) and height (Z) are offset in a typical developing cyclone. By being offset, the trough and ridge axes have upstream tilt with elevation in the mass fields. This can be shown mathematically from the hypsometric equation.

This assignment compares how ridge and trough axes of P and T compare for an actual storm. In this exercise, you work with real weather data of the large storm in the middle of the US on 8

January 2008 (12 GMT). This directory. http://atm.ucdavis.edu/~grotjahn/course/atm111/hwk/tilts/

contains maps of geopotential height with Z-#### in the file name, where #### is the pressure level. Other maps are geopotential height with the zonal mean removed (Zp), temperature (T), and temperature with zonal mean removed (Tp). There may be ‘redundant’ maps of the same variable and level combination, but a different domain.

a. (12 pts) Using the maps for all the Zp files, estimate the location and value of the main trough at 40N. Enter that longitude and value in a spreadsheet program, such as Excel.

b. (5 pts) Using the maps for all tropospheric Zp files ( P>150 mb) files estimate the location of the ridge in the west of 100W along 40N, enter those numbers in the spreadsheet.

c. (4 pts) Using all the maps where P>250 mb for the Tp files, estimate the location of the coldest minimum between 120W and 60W at 45N. Enter those numbers in the spreadsheet.

d. (4 pts) Using all the maps where P>250 mb for the Tp files, estimate the location of the warmest maximum between 120W and 60W at 45N. Enter those numbers in the spreadsheet.

e. (5 pts) Plot the trough and ridge axes of Zp and Tp found above on ONE plot versus P. Be sure that your plot is fully, unambiguously, and accurately labeled.

f. (2 pts) Plot the magnitude of the Z trough values found in part a as a function of P. Be sure that your plot is fully, unambiguously, and accurately labeled.

g. (1 pt) Describe how the T and ZP are offset for P > 400 mb.

h. (1 pt) Describe how the warm and cold anomaly pattern at P=400mb changes at P=100mb. (i.e. how the pattern changes across the tropopause)

2. Consider figures 4.3a,b from your text. Perform the following tasks with those maps:a. (1 pt) Name a location where WAA and PVA have same sign and thus reinforce each other.b. (1 pt) Name a location where WAA and PVA (or CAA and NVA) have opposite sign and thus oppose each other.

Assigned: ___ 17 February 2009 __ Due: ___ 26 February 2009 ____

PAGE NOT USED IN 2008

Shade blue for CAA, red for WAA (above) using solenoid method. 6.

Shade blue for NVA, red for PVA (below) using solenoid method. 3.

Winter 2009 ATM 111ATM111L - Lab Exercises #5

20 pts

This week the COMET modules will ‘clear the fog’ about … fog.

1. Proceed to the complete list of COMET modules. The URL is:http://www.meted.ucar.edu/resource_modlist.php

You will see a variety of links listed there. This week, you are to complete two modules:

Forecasting Radiation Fog. (2-2.5)

Then choose 1 from this list: i) Synoptic Weather Considerations: Forecasting Fog and Low Stratus, (2.5)

ii) Fog and Stratus Forecast Approaches (2)

iii) Local influences on Fog and Low Stratus (2)

iv) West Coast Fog (2-3)

v) Dynamically Forced Fog (2.5)

vi) Icing Assessment Using Soundings and Wind Profilesvii) Forecasting Aviation Icing: Icing Type and Severity

A. Each module has a quiz that you must pass in order to count this module. When you take a quiz, you must complete it at one sitting. You must enter your full name and Dr. Grotjahn’s email address (grotjahn@ucdavis.edu) where indicated so that scores are reported directly to me.

B. Answer the following questions.

i. How much time did you need to complete EACH module (including the final exam)? (identify each time with the specific module you used)

ii. Describe in words one concept or understanding you learned from each module you chose.

Assigned: ___ 24 February 2009 __ Due ____3 March 2009 ___________

Winter 2009 ATM 111ATM111 - Homework #8

29 pts

1. The purpose of this exercise is to reveal some hidden properties of the RHS terms in the geopotential height tendency equation (4.9).

The domain is -L x L , -L/2 y L/2 and 0 p Ps . Note the following: ζg = {g/fo}2Zg , Vg = {g/fo} ( -Zg/y , Zg/x ) Assume that:

Zg = M(p) - A y {1-p/Ps}) - cos(π y/L) { br cos(π x/L) – bi sin(π x/L) }

Where M(p) = 1.1x104 *(1 – p/Ps), br = B*p/Ps , bi = B*{1-p/Ps} .

To simplify the mathematics, let fo = 10-4, g = 10, L = 2x106, Ps = 105 , s~ = 10-4, Rd = 287, B = 150, and A = 3x10-4 where standard mKs units are used.

Your answers should be expressed in sines and cosines (‘functional form’). You may define and use new variables to equal collections of constants. For example: c= π/L, e= g/fo , N = B/Ps .

a. (3 pts) Create a plot of Zg at p = 6x104 for the x and y ranges given using 21 points in x and 11 points in y. The values should have ‘meteorological’ ranges.

b. (5 pts) Find the functional form and plot ∂Zg/∂p at p = 6x104 for the x and y ranges given using 21 points in x and 11 points in y. For the values should have ‘meteorological’ ranges you must multiply by ( -g p / R). It will show where the warmer and cooler areas are located.

c. (4 pts) Find the functional form and plot ζg at p = 6x104 for the x and y ranges given using 21 points in x and 11 points in y. The values should have ‘meteorological’ ranges. It will show where the trough and ridge are centered.

d. (11 pts) Derive the second term on the RHS of (4.9). This version uses Vg defined from Zg.. Start by making separate definitions of each component of Vg and of ∂Zg/∂p . It takes a bit of work, but you should have most of the terms cancel out in the end. To get full credit, you need to make that simplification. That cancellation is known as ‘geostrophic degeneracy’ and reveals that (4.9) is not as complex as it appears.

e. (3 pts) Plot the function you obtained in part d at p = 6x104 for the x and y ranges given using 21 points in x and 11 points in y. Multiply your values by 1015 to make a simpler plot.

f. (3 pts) Identify the sign of this term at the trough center (vorticity maximum) and deduce whether it would cause height rises or falls. Explain how that might happen or identify which special case in lecture is similar.

Assigned: ___ 26 February 2009 __ Due ____5 March 2009 ___________

Winter 2009 ATM 111L

ATM111L - Lab Exercises #620 pts

These exercises explore more capabilities of IDV

1 (6 pts). Model comparisons. Create contour plots of Z500 with the CONUS domain. Make 0-60hour (11 frames) plots. Use pink contours for NAM (80km) OVERLAID with cyan for GFS (80km). (To load the data do from dashboard: data, new data source, from a catalog, IDV catalog, Unidata IDD model data, UCAR motherlode, choose latest 12z forecast for BOTH models. Caution: GFS runs are present at 18z and 6z, don’t use those since NAM timing does not match.) (To choose contour color do: click color bar, select solid color)a.(2) Save a .jpg file of the overlay of the 72 hour overlay: frame 10 (only).b.(2) Capture a session (do in MapView window: View, capture, movie.) From Movie Capture window you have many options. For example, you manually click through the time sequence first the MapView image, then ‘one image’ button in Movie Capture. Save this as a .mov file. c.(2) Describe in your own words differences you notice between the two fields. Save that as a word document or pdf with the .jpg file inserted in the document as well.

2.(4pts) Model verification. Obtain 60 hour forecasts by NAM and GFS made 2.5 days ago and verifying at the most recent upper air observing time. Obtain the most recent NAM model initialization (e.g. this morning’s 0 hr forecast). a.(2) Create a contour plot of Z500 with the CONUS domain as follows. Overlay the 0 hr forecast (white), the 60 hr NAM (red), and the 60 hr GFS (blue), all verifying at the same time. Save this as a .jpg fileb.(2) Describe in your own words differences you notice between the two fields. Add that to the word document you started in problem 1. Insert this second .jpg file in the document, too.

3.(10pts) Frontal cyclone and adjacent atmospheric structure. Select your case by finding a time, either in observations or in a forecast where there is a developing low pressure center over the central portion of North America. (Weather varies. The better your case, the more you’ll learn from this assignment. You may need to wait for a good date to do this task.)a.(2) CONUS contour plot: Overlay Z500 (cyan), Z1000 (pink), and Z200 (red) for your case. You should see upstream tilt of the trough axis, if not, pick another case!b.(2) Overlay Z1000 (pink), and T850 (default colors) on a CONUS contour plot:. Frontal zones and trough axes should be linked like ‘typical’ warm and cold fronts. If not, pick another case.c.(6) Create contour plan view cross sections for a slice oriented perpendicular to a strong front in your case. (either warm or cold front.) Make separate plots of: temperature, mixing ratio, wind speed, potential temperature (see ‘derived fields’). NOTE: You must use the same cross section end points for each plot. Those end points must be >2000 km apart and far enough from the front to capture many closed contours for wind speed. Save the plot showing the locations of your cross section on a map of T850 (default colors). Mark the front location on every plot. (Note: find Cross sections option on Dashboard, Field selector tab, Displays)d. Save a copy of each plot & insert all 7 into the word document with explanatory captions.

Send the .mov and .doc files to the TA via email. Use your last name in each filename.

Assigned 3 March 2009 Due ____10 March 2009 ___________

Winter 2009 ATM 111ATM111 Exercises #9

18 pts

1. A strong circular low pressure center is crossing Oregon and Washington Cascades. See figure and note that the vertical dimension is greatly exaggerated. It responds to the Cascade mountains by splitting into two centers. Here is a simplified analysis of the situation. Assume: i) the topographically forced vertical motion, s, linearly decreases with pressure to be zero at 300 hPa.ii) points SE and N are at 900 hPa.iii) density at SE and N are both 1. kg/m3 iv) mountain range has constant slope on both sides; the ridge axis is oriented north-south, H = H(x)v) acceleration of gravity is 10 m/s2 vi) QG conditions with no advection.vi) f = 10-4 s-1

Data: surface wind at pt N is E at 15 m/s surface wind at pt S is SW at 14.14 m/s current vorticity, , at low center = 1.25x10-4 s-1 distance R from low center to each pt is 200 km.

a. (6 pts) Find the value of s, at pts N and SE

b. (4 pts) Find the current tendency at pts N and SE

c. (1 pt) Find current at pt N (curvature only).

d. (2 pts) Find how many hours until the vorticity at pt N equals the current vorticity at the low center. (Assume that the initial vorticity at N is entirely the current curvature vorticity at pt N. Assume the vorticity tendency is constant over those hours and equals the current tendency.)

2. (5 pts) Create one or more “final exam” test questions appropriate for use on a final exam for this course. Your question should be worth 5 points. For full credit, you must provide the answer. Your question(s) may be of any standard form: multiple choice, true/false, short answer, matching/labeling, or drawing type. The question must be based on material covered since the midterm exam.

Depending on the questions received, a variation of it may appear on the actual final exam. We shall review the questions and their answers during the final lab session as part of a review period.

Assigned 5 March 2009 Due: ___ 12 March 2009 _____(by 3 pm. No credit if turned in after 3 pm).

Winter 2009 ATM 111ATM111L - Lab Exercises #7

11 pts

This week a COMET module will address some common misconceptions about forecast models.

1. Proceed to the complete list of COMET modules. The URL is:http://www.meted.ucar.edu/resource_modlist.php

You will see a variety of links listed there. This week, you are to complete the module:

Ten Common NWP Misconceptions. (1-2.5)

A. Complete the quiz and answer the following questions.

i. How much time did you need to complete this module?

ii. Briefly summarize in your own words each of the 10 common misconceptions discussed in this module.

Assigned 10 March 2009 Due ____12 March 2009 ___________