Oceanographic & Meteorological Quantitative Methods SO335 Lab 2 (100 Pts)

Name: ______

Oceanographic & Meteorological Quantitative Methods – SO335 Lab 2 – (100 pts)

Using “real” data in MATLAB

At 9:45 p.m. on the evening of May 4, 2007, the small town of Greensburg, KS was leveled by a very large, EF-5 rated tornado.

The ingredients for tornado formation have been understood for several decades: ample atmospheric instability (measured by the Convective Available Potential Energy, CAPE) and vertical wind shear. One of the more challenging forecasting aspects is to predict whether storms will actually form, as many times the atmosphere has high CAPE and shear, but no storms form. A common culprit for the suppression of severe storm formation is the presence of a strong temperature inversion, colloquially known as a “cap.” To diagnose the cap, meteorologists analyze vertical profiles of temperature and dew point temperature, measured by balloon-launched radiosonde soundings, and these are some of the best tools available to meteorologists in severe storm forecasting. The evolution of the temperature inversion with time can provide clues as to whether the cap is eroding: warming at the surface, often combined with moistening at the surface, and cooling near the top of the inversion, can all signal an eroding cap and point toward an atmosphere that is more conducive to explosive thunderstorm development.

Goal: The goal of this portion of the lab is to: (1) learn to access observed data from internet repositories and import that data into MATLAB; and (2) to plot that data in simple, two-dimensional figures that allow for basic thermodynamic analysis.

Task 1: Simple analysis and plotting.

Visit the University of Wyoming upper-air web page at http://weather.uwyo.edu/upperair/sounding.html. Let’s first examine a graphical representation of the temperatures above Dodge City, KS (DDC; station 72451), which is the closest upper-air station to Greensburg. Make a GIF: Skew-T plot of the 2007-May- 04/12Z temperature data. Remember, 12Z is 7:00 a.m. local time in May in Kansas. The result should look like that shown in the left panel of Figure 1.

1 Now, look at the 18Z “special” sounding from DDC. It is “special” because radiosonde releases in the U.S. typically only occur at 00Z and 12Z, and are released at other times only during extreme events. To view the 18Z data, you first have to look at all of the images between 04/12Z and 05/00Z (you may have to broaden beyond those dates and toggle back and forth – eventually the site will show you the 04/18Z sounding). The Univ Wyoming site is smart enough to look for any special radiosonde data that might have occurred in the off hours, and create plots of those data. Cycle through the observations. Note that at 05/00Z, Dodge City was located behind the dry line, and as such, the temperature profile was dry adiabatic from the surface to nearly 650 mb.

Figure 1: upper-air soundings for DDC for 12Z and 18Z 04 May 2007, day of the Greensburg, KS EF-5 tornado.

The first task of this lab is to locate these data (in text format) and import them into MATLAB. There are many ways to do that; here is one method. In the UWYO web portal, instead of making GIF: Skew-T data, choose Text: List. Highlight with the mouse the 12Z data (no header rows—MATLAB is very picky about mixing letters and numbers!) and copy and paste those data into an Excel workbook. You’ll likely have them paste into Excel all in one column, which is a problem. To create multiple columns, one option (of many) is to use the Text to Columns tool in Excel, which is under the Data menu option. Select the entire column and then use Delimited, with Space as the delimiter. Finish that, and you should have a nice Excel file with 11 columns (A-K) and 71 rows (if Column A comes in as all blanks, you should delete it). Save that excel file as “ddc_12z_04may2007.xlsx” (again, save this file in your MATLAB working folder to save yourself from hunting around for it later).

To import data from the Excel workbook in MATLAB, use the following command: ddc_12z_04may2007 = xlsread('ddc_12z_04may2007.xlsx');

Here, ddc_12z_04may2007 is the output variable from the function xlsread. Double- click on that variable and look at it in the variable editor window.

1. (5 points) What do the first two rows look like? Why are there NaN values in those two rows?

2 2. (5 points) What are the values of row 11, columns 1, 2, 3, 4, 7, and 8? Be sure to include correct units.

3. (5 points) How warm was the atmosphere at 700 mb? One of the famous severe storm meteorologists, Dr. Howard Bluestein of the University of Oklahoma, often says that a 700 mb temperature of +12°C or higher represents an “unbreakable” cap (presumably such a statement is based on his many years of experience with severe storms). Was the 700 mb temperature at 12Z on 04 May 2007 indicative of an unbreakable cap that day in southwest Kansas?

Let’s now plot the data. First, create three new variables from ddc_12z_04may2007, pressure, temperature, and dew point temperature: press_12z = ddc_12z_04may2007(:,1); temp_12z = ddc_12z_04may2007(:,3); dewpt_12z = ddc_12z_04may2007(:,4);

4. (5 points) Execute those three commands above. Describe what they did.

Once you’ve created press, temp, and dewpt, plot both temperature and dew point temperature against pressure. Be sure to add lines of code to include labels for the x- and y-axes, as well as a title. (If you forgot how to do that, look back at Lab 1 and use the internet). Your results should resemble Figure 2. figure(1) clf plot(temp_12z,press_12z,'r') hold on plot(dewpt_12z,press_12z,'g') axis ij legend('12z temperature','12z dew point temperature')

The plot syntax plots an “x” variable against a “y” variable, and then allows for some extra information at the end, like the color of the line (‘r’ stands for red, ‘g’ for green). It 3 also allows for line style. The axis ij command inverted the y axis, making 1000 mb appear at the bottom and 0 mb at the top. The legend command adds legend entries to the figure. The default legend position is in the upper-right corner, although there are many other options (help legend will show them).

Figure 2: Temperature (red curve) and dew point temperature (green curve) above DDC, 12Z 04 May 2007.

5. (5 points) What does the hold on command do?

Let’s do a few other things to “pretty up” the plot: increase the line thickness (default value is 1), and move the x-axis a little more to the right (so the data aren’t scrunched up against the edge): figure(1) clf linewidth=2; plot(temp_12z,press_12z,'r','linewidth',linewidth) hold on plot(dewpt_12z,press_12z,'g','linewidth',linewidth) axis ij legend('12z temperature','12z dew point temperature') xlim([-80 30])

Notice the new variable, linewidth, that is defined as 2. By defining variables and then using them in the code, we can make one quick change, and the rest of the code will reflect it.

6. (5 points) What is the pressure level of the base of the inversion (where the temperature stops climbing and starts falling again)? What is the temperature of that level?

4 Task 2: More simple plotting.

Go back to the University of Wyoming data portal, grab the 18Z text data, and import it into MATLAB, storing it as the variable “ddc_18z_04may2007”. Create similar pressure, temperature, and dew point temperature variables, but this time use the 18Z data: temp_18z, press_18z, dewpt_18z.

Plot the 18Z data in a new figure window (Fig. 2). Again, add appropriate title and axis labels using the title, xlabel, and ylabel commands in MATLAB. This time, instead of solid line, use a dashed line for both temperature and dew point temperature. The code below suggests how to make the lines dashed, using the ‘--’ syntax: figure(2) clf linewidth=2; plot(temp_18z,press_18z,'r--','linewidth',linewidth) hold on plot(dewpt_18z,press_18z,'g--','linewidth',linewidth) axis ij legend('18z temperature','18z dew point temperature') xlim([-80 30])

7. (10 points) Vertical wind shear. As mentioned in the introduction, instability is not the only ingredient needed for severe thunderstorm formation. Vertical wind shear, or the change in wind speed and direction with height, is also critical to generate rotating updrafts. Calculate the surface to 6 km bulk wind shear for DDC at 18Z. Show all work. a. To find the surface-to-6 km bulk wind shear, first find the u and v wind components of the surface (row 3) and 6000 m (row 22) winds. (Note, the sounding doesn’t have wind at exactly 6000 m, but 6096 m is close enough).

Surface: u ______6 km: u ______

v ______6 km: v ______b. Next, find the vector difference in winds, 6 km minus surface (find the and components separately):

5 c. Finally, calculate the magnitude of the vector difference:

d. In the severe storms community, bulk wind shear of at least 40 knots is considered sufficient for supercell thunderstorms (Rasmussen 2003). Comment on the bulk wind shear observed in the 18Z sounding at DDC.

Task 3: Double plotting.

Plot both soundings in the same figure window. Modify the title, legend entries, and axes labels, as appropriate. The 12Z data should be plotted using solid lines, and the 18Z data plotted using dashed lines.

Task 4: Compare two soundings.

For the final task, we want to harness the power of MATLAB to empirically compare the two soundings (not just qualitatively look at them on a figure). The best way to compare the temperatures at 12Z with the temperatures at 18Z is to subtract them. However, if you look at the two different sounding data, you’ll notice that the observations are made at highly irregular pressure levels. For example, while the first observation in each sounding is made at 915 mb (row 3 in ddc_12z_04may2007 and ddc_18z_04may2007), the next observation (row 4) at 18Z is at 853 mb, while row 4 at 12Z is at 901.6 mb. Thus, we cannot simply subtract the two. One solution is to first linearly interpolate the temperature and dew point temperature data. If we choose the same regularly-spaced interpolant for both soundings, then we can subtract the interpolated data (because each row in interpolated data will match).

To do that, we will use the function interp1, which according to MATLAB help command: help interp1

YI = interp1(X,Y,XI) interpolates to find YI, the values of the underlying function Y at the points in the array XI.

6 In plain-speak, that means that if you have a variable Y that is defined at irregular points X, you can interpolate Y onto a smooth variable XI. The new values of Y will be stored in YI.

For us, let’s do the following. First, define our pressure interpolation points. Let’s interpolate every 1 mb, from 915 mb to 15 mb: press_interp = 915:-1:15;

This command creates a variable press_interp that is 1 x 901. Double-click on it in the workspace window and look at it.

8. (5 points) What does 915:-1:15 actually do? What if you put 915:1:15 (instead of -1)? Finally, what would 915:-0.5:15 do? (You can try these in MATLAB and look at them).

Now, let’s interpolate 12Z temp, 12Z dew point, 18Z temp, and 18Z dew point temp, at this new, regularly-spaced pressure variable: temp_12z_interp = interp1(press_12z,temp_12z,press_interp); dewpt_12z_interp = interp1(press_12z,dewpt_12z,press_interp);

For the 18Z data, there is a problem. MATLAB’s interpolator does not know how to interpolate between two points with the same value. For example, the 18Z sounding has two entries at 24.4 mb (rows 67 and 68). That is likely due to a bug in the sounding reporting software that NOAA uses (e.g., how can 24.4 mb have two different values for the data in columns 9, 10, and 11?) To fix this, we need to tell MATLAB to skip row 68, and use only rows 1-67 and 69 to the end. It’s straightforward enough: temp_18z_interp = interp1(press_18z([1:67 69:end],1),temp_18z([1:67 69:end],1),press_interp); dewpt_18z_interp = interp1(press_18z([1:67 69:end],1),dewpt_18z([1:67 69:end],1),press_interp);

The syntax press_18z([1:67 69:end],1) tells MATLAB to grab rows 1-67 and 69 to the “end” (and MATLAB recognizes what “end” means), and column 1, of the variable press_18z.

Plot differences, subtracting the 12Z data from the 18Z data. Scale the x-axis from -20 to 20, and add appropriate titles, axis labels, and legend entry. The resulting difference plot should look like Figure 3.

7 Figure 3: Difference between 18Z and 12Z temperatures (red curve) and dew point temperatures (green curve) at Dodge City, KS on 04 May 2007.

Deliverables:

Be sure to turn in three printed figures (15 points each), your printed and commented MATLAB code (10 points), and the answers to the questions in this lab (45 points worth of questions).