Summary
of Image Interpretation Tutorials
Summary
of Image Interpretation Tutorials
Over the past two days, we have reviewed multi-channel imagery. Here is a link where you can continue to view some of these derived products. We will continue to have discussions of these types of images. I encourage you to look here regularly when you are reviewing the days weather. If you find particularly interesting images or features on any of these images that you would like to share, save a copy to your homepage and bring it to class for discussion!
Radiative
Transfer Laboratory Activity
In this exercise, I want you to use the Maple software. Maple (produced by Waterloo Maple Software) is a mathematical problem-solving and visualization system available on your workstation (it is also available to use with your Unix accounts, if you have questions check here, manuals should be available in the labs in Thorton Hall, E225, Small Hall 102, and at the ITC Help Desk (235 Wilson Hall, which is downstairs). This software package allows you to solve equations using formal mathematical definitions and returns answers as mathematical objects.
Recall Planck's Function:
You will evaluate and plot this function for a range of wavelenths and temperatures. In a previous feature we discussed the fact that if we differentiate this function with respect to wavelength, and set the result equal tozero, we can find the maximum of this function, that is, wavelength where radiance is maximized for each temperature. This expression was determined empirically by Wilhelm Wein, and is now referred to as Wein's Displacement law:
I would like you to use the software to develop a better understanding of how radiance (the basic quantity that satellites measure) varies with temperature and wavelength. Therefore, I would like you to carry out the following exercise, and ultimately create two separate figures (you will need these figures later as a reference during the first exam).
Exercises
1.) Since Wein's Displacement is a simpler equation, begin by entering it and evaluating F(T) for the following set of temperatures: 5800, 288 and 300, 280, 260, 240, 220 and 200. You will use these results later, so keep track of your answers.
2.) Plot the Planck's radiance versus wavelength for surfaces with temperatures representative of a) the average temperature of the sun (5800K) and b) the average temperature of the earth (288K). Put both curves on one graph. Plot the wavelength region from .1micrometers to 250 micrometers. In order to keep the figures focussed on a reasonable range of radiance values, limit the lowest radiance you plot at 10-6. In order to set the upper limit on the y-axis, you should evaluate the Planck function at the value of maximum wavelength (you determined the maximum wavelength in #1 above) for the highest temperature.
Take a careful look at the range of values you are trying to plot, when both the x and the y axis values range over several orders of magnitude, what kind of plot should you request?
Before you begin, bear in mind the units you should plot are W m-2 um-1, you should do a dimensional analysis to ensure that you get the right units, you will have to use a scale factor.
Radiation Constants
| c1 | 3.74x10-16 W m2 |
| c2 | 1.438x10-2 m K |
3.) Plot the blackbody radiance versus wavelength for surfaces representative of a typical range of tropospheric temperatures, e.g. from 300 K to 200K at 20K intervals. Plot all the curves on one graph. For this set of curves you should only plot the wavelength range from 1micrometer to 100 micrometers. Again, limit your lowest radiance values at 1x10-6.
Once you have made both of these plots, you should save them as postscript files and print them out. Using the plotted curves, plot the wavelength of maximum radiation for each temperature (you calculated these values in #1). You should be able to connect these points with a straight line when you are done.
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