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### Lab06

Course: ATM OCN 311, Spring 2008
School: Wisconsin
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Word Count: 853

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311 AOS Lab 6 The Weather Model: Grid Resolution Objective: Gain appreciation for the limitations imposed on a grid-model when attempting to simulate the behavior of a continuous fluid. Observe the effect of grid resolution on model variables. Motivation: One of the core complications of a weather model is the way in which information is processed on a grid. The real atmosphere is a continuous fluid, and...

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311 AOS Lab 6 The Weather Model: Grid Resolution Objective: Gain appreciation for the limitations imposed on a grid-model when attempting to simulate the behavior of a continuous fluid. Observe the effect of grid resolution on model variables. Motivation: One of the core complications of a weather model is the way in which information is processed on a grid. The real atmosphere is a continuous fluid, and therefore it cannot be represented as a set of discrete points. Yet this is the way most computer forecast models simulate the weather. Specifically, derivatives cannot be represented on a discrete grid. The center difference approximation (CDA) is used to estimate the value of derivatives, hopefully within a tolerable amount of error. Assignment: The assignment for this lab includes GEMPAK and MATLAB: PART 1 GEMPAK Exercise This exercise is simply comparing plots of 500 hPa vorticity and geopotential heights between two different grid resolutions. This is also the first GEMPAK exercise where I don't tell you exactly what the parameters are. However, I will give you some suggestions. Use GDPLOT to create the following plot: Vorticity (fill pattern) at 500 hPa and geopotential heights (contoured) at 500 hPa for 00Z 07 March 2008. Use the data file: /labdata/data/gemdata/hds/08030700_eta211.gem Suggestions: 1) Set the GAREA to the continental U.S. centered on Topeka, KS (GAREA=TOP--) 2) The plot contains two variables (vorticity and heights), so several things must be set twice (once for each variable). The way this is done is to separate individual parameters by an exclamation point (!). This lets GDPLOT know that the setting before the exclamation point is for the first variable, and the setting after the exclamation point is for the second variable. Here is a list of all of the variables that must be set this way: GFUNC Set the first variable to vorticity of the observed wind, and the second to heights SCALE CTYPE Set this to CTYPE = F!C which ensures that vorticity is a fill-pattern and heights are contoured. 3) Make the following additional settings: FINT = 8;12;16;20;24;28 sets the interval for the fill-pattern FLINE = 0;18;15;12;9;6;3 sets the colors for the fill-pattern CLRBAR = 1/V sets the color-bar for the fill-pattern PROJ = UTM sets the map projection CINT Set this to the contour interval for the heights DEVICE = XW Create a plot in the X-window (the colors of the fill-pattern won't look great, but they will when the plot is printed). When you have all of the parameters set the way you want, type SAVE PLOT1 and hit ENTER to save the settings. Then the save file as a postscript and go through the printing procedure. REMEMBER TO TYPE `gpend' AFTER EXITING OR ELSE THE FILE WON'T BE CREATED. When you have the plot, go back into GDPLOT and type RESTORE PLOT1 and hit ENTER to get to your original settings. Then create an identical plot using the following data file: /labdata/data/gemdata/hds/08030700_eta212.gem Create a postscript and print this plot as well. QUESTIONS 1) Using the definitions for the geostrophic wind components in pressure form: ug 1 , vg f y g 1 f 2 x Show for (f = fo = constant) that 1 fo 2) The NAM 211 model uses an 81 km grid spacing, while the NAM 212 model uses a 40 km grid. Comment on the differences between vorticity at the two different 2 resolutions and heights at the two different resolutions. Given that for A B, B appears as a "smoothed" field based on the characteristics of A (e.g. minimums in B appear where there are maximums in A, and vice-versa), explain why the vorticity differences are much larger than the height differences between the two plots. PART 2 MATLAB Exercise For this exercise, you simply need to construct a table of values describing how the error inherent in the center difference approximation changes with changing grid resolution. MATLAB is then used to plot these values. Perform a center-difference approximation on a simple equation using various values of x . Using the equation: F ( x) x 2e x dF at x = 1 and calculate the dx error in the approximation (i.e. the difference between the calculated value and the actual dF value of at x = 1). Fill in the following table: dx CDA Error x x2 Approximation 0.2 0.15 0.1 0.05 0.01 0.001 Calculate the center-difference approximation value for In MATLAB, plot x versus error on a logarithmic plot, and compare it to the values of x versus x 2. You can plot them both at the same time by using the following command in MATLAB: loglog(dx,err,'r',dx,dx2,'b') Where: dx = array of values for x err = array of values for the calculated error dx2 = array of values for x 2 The plot of dx versus error will appear in red, and the plot of dx versus dx2 will appear in blue. QUESTION 3) From the plots you've created in MATLAB, explain how you can see that model error is a function of the square of the grid resolution. Grade Breakdown: Plots (2 GEMPAK plots + 1 MATLAB plot): Question 1: Question 2: Question 3: 30% 20% 30% 20% Additional copies of this handout will be made available on the course website: http://aurora.aos.wisc.edu/~hoover/AOS311.html Due Date: At the beginning of class on Friday, 28 March 2008.
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