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Winter 2014 ATM 111 ATM111 - Homework #1 20 pts 1. Basic meteorology review: a. (4pts) Write down the hypsometric equation and briefly define all terms & symbols. b. (2pts) 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 about 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 ____14 January 2014 ___________ Winter 2014 ATM 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: nocolor.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 ____14 January 2014 ___________ Winter 2014 ATM 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: 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 Model data’, ‘NCEP Model Data’, then ‘Global Forecast System’ model, ‘GFS N Hemisphere 381’ (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: ‘GINI 24 km 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 ____21 January 2014 ___________ Winter 2013 ATM 111 ATM111 - 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, a. (2 pts) Estimate the zonal wavelength between the ridges: off the west coast and in the SE United States at φ = 35N. From that calculate the zonal wavenumber: k in m-1 b. (1 pt) Estimate the meridional wavenumber (= M) from the half wavelength as 25N to 70N. c. (1 pt) Calculate the total wavenumber K = (k2+M2) d. (2 pts) Estimate “beta” using β = 2 Ω cosφ r-1 where r is the earth’s radius (6370 km). e. (2 pts) If the average zonal wind (U) is 20 m/s how fast is the pattern moving according to Rossby’s formula? (Formula in Holton; e.g. 2004 ed: eqn 7.92 on p. 216) f. (2 pts) Is your result consistent or not with the persistence of the cold air outbreak? Due ____22 January 2013 ___________ Winter 2014 ATM 111 ATM111 - Homework #2 10 pts 1. Consult the “Heat Wave (onset)” 500 mb geopotential height contour pattern at time T=0. (See: http://atm.ucdavis.edu/~grotjahn/EWEs/heat_wave/heat_wave.htm ) From that chart, a. (2 pts) Estimate the zonal wavelength between the ridges centers at φ = 40N. From that calculate the zonal wavenumber: k in m-1 b. (1 pt) Estimate the meridional wavenumber (= M) assuming the half wavelength is 25N to 70N. c. (1 pt) Calculate the total wavenumber K = (k2+M2) d. (2 pts) Estimate “beta” using β = 2 Ω cosφ r-1 where r is the earth’s radius (6370 km). e. (2 pts) If the average zonal wind (U) is 20 m/s how fast is the pattern moving according to Rossby’s formula? (Formula in Holton; e.g. 2004 ed: eqn 7.92 on p. 216) f. (2 pts) Is your result consistent or not with the persistence of the heat wave? (Persistent means pattern takes more than 4 days to move a distance equaling ½ its wavelength.) Due ____21 January 2014 ___________ Winter 2014 ATM 111 ATM111 - Homework #3 16 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/region B. the type of significant weather event C. your reasoning for forecasting that type of significant weather (.5,1.,1.) 2. (6 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 ____28 January 2014 ___________ Winter 2014 ATM 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: https://www.meted.ucar.edu/training_detail.php?topic=15&pagination=no You will see a variety of links listed there. Find the NWP topic area in the pull down menu. Over the next 3 weeks, you are to study the following modules in the following order: a. Model Fundamentals – version 2 (1-2) b. Understanding Assimilation Systems: how models create their initial conditions –vers. 2 (2-6) c. Impact of model structure and dynamics –vers. 2 (3-6) d. How models produce precipitation and clouds –vers. 2 (can skip Kuo and Kain-Fritsch schemes) (2-4) e. Influence of Model Physics on NWP forecasts –vers. 2 (2-4) f. Intelligent use of model-derived products –vers. 2 (2-3) (Grand total: 12 -25) Activities: A. 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. The typical range of time (in hours) that prior students have needed is indicated above (in small numbers) after each listed module. B. A separate list of questions (file NWP_questions_v2.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, write down your answer(s) 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. (So they will need to be typed and sent as a .doc or .pdf file.) vi. Each of the assigned modules has a quiz. You need to reach a passing score (typically 70%) 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 ([email protected]) where indicated. You have 3 weeks to complete the questions here, pass the exam, and turn in your online exam notes. Due ____11 February 2014 ___________ Winter 2014 ATM 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 assimilation systems: 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 2014 ATM 111 ATM111 - Homework #4 24 pts Objective Analysis – Cressman scheme When using a computer program, email the file to the grader when you turn in the print out of the answer.) Given the following: A. The true or ‘actual’ state is: ZA = tanh(x-d) where d=1.0 B. Observations have systematic error: e = -0.1 sin(2x) Hence, observed values are given by this function: ZO = ZA + e Observations are taken at these points: x = -0.4 0.4 0.7 1.8 2.1 2.7 3.2 3.9 4.4 5.5 C. The first guess is: ZFG = tanh(s*(x-d)+h) where h= π/15 and s=1.1 D. The radius of influence is R = 1. and the coefficient for the weights is a = 1. E. Objective analysis is used to find values ZOA at grid points where x = 0, π/5, 2π/5, 3π/5, 4π/5, and π Make these calculations & plots: a. (6 pts). At the 10 OBSERVATION points, PRINT OUT the following: i) ZO value (1/5 pt ea), ii) ZFG value (1/5pt ea) iii) x value (1/5 pt ea) b. (6 pts). At the 6 GRID points, PRINT OUT the following: i) ZA value (1/6pt), ii) ZFG value (1/6pt) iii) x value (1/6pt) iv) ZOA (1/2pt) c. (3 pts) Print out the sums of the weights at each of the 6 grid points. (1/2pt ea) d. (6 pts) Make one plot showing: i.) ZA , ZOA , and ZFG at the 6 GRID points ii.) Observed values but only in the range: -1. to 4. (part i = 3pts, part ii = 1pt, axes/labels = 2pts) Hint: If using Excel for the plot, try the scatter plot graph type. It is preferable to connect the values of each variable in d.i. with a line but do not connect the observations in d.ii. with a line. Be sure your axes and curves are unambiguously labeled. e. (3 pts) Compare and contrast the objectively analyzed solution with the: first guess, observations, and true (‘actual’) values. Due ____4 February 2014 ___________ Winter 2014 ATM 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) 2π/ NX. Synthetic data are to be generated by a series of sine functions: f(xm) = -2.1 + 1.9cos(xm) – 1.8cos(2 xm) + 0.9*cos(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: c(0) c(k ) NX B NX f (x B NX NX m 1 f (x m m 1 ) (2) for B=1 for k=0 ) cos(kxm ) (3) where B=2 for k>0. m (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: K fb ( xm ) c(0) c(k ) cos(kxm ) (4) k 1 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: df m dx finite.... difference f ( xm1 ) f ( xm1 ) 2x versus df m dx spectral K kc(k ) sin(kx k 1 m ) and compare (with a brief discussion, 1pt) these estimates with the analytic derivative of f. Due ____ 11 February 2014 ___________ Winter 2014 ATM 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: 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 ([email protected]) where indicated. B. In addition to the quizzes, 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 ____25 February 2014 ___________ Winter 2014 ATM 111 Homework #6 26 pts 1. Understanding how a forecast model predicts a future state. Let the initial condition be: U(x, 0) = 0.7*{1/(1.+[x-4]2 ) } (1) where x ranges from 0 to 10. Interval: dx=0.25 for 0≤ x ≤6, and dx=0.5 for 6< x ≤10 (2) Calculate the model’s forecast using 33 grid points at these locations: xi = 0 to 10 in increments of dx. U’s are nondimensional. Your model is the 1-dimensional nonlinear advection equation: Ut + (C+U) Ux = 0 (3) Here C = 0.35 and t and x subscripts are derivatives. Solve (3) subject to the boundary condition: U(0, t) = 0. (4) a. (4 pts) Print the values of x and the corresponding U(x, 0) for all 33 grid points. b. Step (3) forward in time using adjacent cells in a spread sheet program (or using finite differences and looping in a spreadsheet or a: MATLAB, FORTRAN, or C++ program). Use the time interval of dt = 0.25. For the first time step use this form (upstream differencing) for x>0: U(x, dt) = U(x, 0) – dt *[C+ U(x, 0)] * {U(x, 0) – U(x-dx, 0) } / (dx) (5) For all subsequent time steps (j>1) use the form below, written in general form for x≠0: U(x, j*dt) = U(x,(j-1)*dt) – dt*[C+U(x, (j-1)*dt)]*{U[x,(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=8, so that the number of time steps for the given dt value is 32 (not counting t=0). b. (8 pts) Print the values of U(x, 2), U(x, 4), U(x,6) and U(x, 8), make sure your x values are unambiguous. (2pts ea list). c. (12 pts) Plot the values of U(x, 0), U(x, 2), U(x, 4), U(x,6), and U(x, 8) 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. Pay particular attention to the shape, the peak, and the speed the peak moves. Notes: The boundary condition (4) means you do not calculate U at that location, though you do need to have the value there 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 or program, email a copy to the grader when you turn in your assignment. Due ____ 18 February 2014 ___________ Winter 2009 ATM 111 Mix of linear & nonlinear Advection Homework #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 U(x, 0) = 0 (1) (2) where x ranges from 0 to 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: Ut + {c+U} Ux = 0 (3) Where c = 0.25. Solve (3) subject to these boundary conditions: U(0, t) = 0. and U(3, 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 2014 ATM 111 ATM111 - Homework #7 35 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 in the west near 100W. Enter that precise longitude and value in a spreadsheet program, such as Excel. b. (4 pts) Using the maps for all Zp files where P>50 mb, estimate the location of the ridge along 40N in the eastern US, enter those numbers in the spreadsheet. 1/3 ea. c. (4 pts) Using all the maps where P>50 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>50 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 TP and ZP are offset for P > 400 mb. h. (1 pt) Describe how the warm and cold anomaly pattern seen at P=400mb changes across the tropopause. (i.e. how the pattern changes between P=300mb and P=100mb) 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: ___ 18 February 2014 __ Due: ___ 25 February 2014 ____ PAGE 2 . Winter 2014 ATM 111 ATM111L - 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, 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 Profiles vii) Forecasting Aviation Icing: Icing Type and Severity (2.5) 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 ([email protected]) 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: ___ 25 February 2014 __ Due ____4 March 2014 ___________ Winter 2014 ATM 111 ATM111 - Homework #8 32 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 - π L x π L , - π L/2 y π L/2 and 0 p Ps . 2 Note the following: ζg = {g/fo} Zg , Vg = {g/fo} ( -Zg/y , Zg/x ) = (ug , vg ) Assume that: p x y x y Z 1 M Ay B sin( ) cos( ) C cos( ) cos( ) L L L L PS (1.1) Where M, A, B, C, L, and PS are all constants. a. (1 pt) Find the functional form of ∂Z/∂p at any general location (x, y, p) in the domain. b. (3 pts) Find the y derivative of your answer to part a. Find the x derivative of your answer to part a. Next, simplify by setting y = 0 (i.e. consider any location where y=0.) c. (4 pts) Find the functional forms of the 2 components of the geostrophic wind: ug and vg at a general location. Next, simplify by setting y = 0 (i.e. consider any location where y=0.) d. (4 pts) Use the information in parts c and d, applied for any location where y = 0. Derive the individual parts and then multiply them within the curly brackets, then apply the pressure derivative in this advection of temperature term: Z Vg p p Note that it is similar to term 2 on RHS of (4.9). Simplify your answer until obtaining a constant. e. (12 pts) Repeat steps a through d but use this form of Z: p x y x y Z 1 M Ay B cos(rp)sin( ) cos( ) C cos( ) cos( ) L L L L PS (1.2) f. (3 pts) Create a contour plot of Z using equation (1.2) at p = 5x104 Pa for the x and y ranges given using 21 points in x and 11 points in y. Let r = 1.5π/(4Ps). Also, M = 1.1x104 m, A = 2x104 , B = 35, C= -20. m, fo = 10-4 s-1, g = 9.8 ms-2, L = 6x105 m, and Ps = 105 Pa, s~ = 5x10-5 K Pa1 , Rd = 287 m2K-1s-2 . Hence, standard mKs units are used g. (3 pts) Create a single plot showing the following 2 quantities at the indicated P level and for y=0. Hence, x varies on the plot of the: i) zonally-varying part of Z (call that Zp) and ii) temperature advection contribution to the height tendency over 12 hours (call that Ht). Note that Zp = Z minus the average of Z. Assume that the LHS of (4.9) can be written as -2/L2 * χ. Thus, Ht = term 2 in (4.9) times 12 hours divided by -2/L2. Use the values of the various quantities provided above and be sure to keep with mKs units throughout. h. (2 pts) Describe how the two curves in the plot for part g relate. How does this change if you use a higher or lower value for p? (Hint: make p a variable parameter in your code.) Assigned: ___ 25 February 2014 __ Due ____4 March 2014 _________ Winter 2009 ATM 111 ATM111 - 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 . 2 Note the following: ζg = {g/fo} Zg , 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 2014 ATM 111L ATM111L - Lab Exercises #6 20 pts These exercises explore more capabilities of IDV , then ‘Global Forecast System’ model, ‘GFS N Hemisphere 381’ (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. 1 (6 pts). Model comparisons. Create contour plots of Z500 with the CONUS domain. Make 060hour (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 Model data, NCEP Model Data, 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.) (Change contour color by: click color bar, select solid color) NAM has 60hr; GFS more. a.(2) Save a .jpg file of the overlay of the 60 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. (‘Better’ quality is OK. Monitor frame increment to start/stop) 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 file b.(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, wind speed, mixing ratio, 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 grader via email. Use your last name in each filename. Assigned 4 March 2014 Due ____11 March 2014 ___________ Winter 2014 ATM 111 ATM111 Exercises #9 18 pts 1. A strong circular low pressure center is just east of the Continental Divide. See figure and note that the vertical dimension is greatly exaggerated. It responds to the Rocky mountains by migrating southward. 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) pts SE & N are at 900 & 800 hPa. iii) density at SE & N are 1.1 & 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 = 0.9 x10-4 s-1 at both pts. 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 = 1.283x10-4 s-1 distance R from low center to each pt is 500 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 SE (curvature only). d. (2 pts) Find how many hours until the vorticity at pt SE equals the current vorticity at the low center. (Assume that the initial vorticity at SE is entirely the current curvature vorticity at pt SE. 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 total. 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 your question 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 4 March 2014 Due: ___ 11 March 2014 _____ (by 5 pm. No credit if turned in after 5 pm). Winter 2009 ATM 111 ATM111 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 (by 3 pm. No credit if turned in after 3 pm). Due: ___ 12 March 2009 _____ Winter 2014 ATM 111 ATM111L - 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 11 March 2014 Due ____13 March 2014 ___________