Module_11_F23_Homework

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1 Engin 112 – Fall 2023 Homework 11: Remote Sensing Due: 5:00 pm Friday, December 8 1.) A radar sensor operating at a frequency of 1.25 GHz is carried on a satellite that is orbiting at 700 km altitude above the Earth’s surface. What is the Doppler shift for the three directions in parts a through c. Note: to make this problem easier, do not assume that the satellite is looking down, rather it is looking in front, to the side, or at the 45 degree angle. a) a forward-looking direction ( 𝜃 = 0° ) b) a side-looking beam ( 𝜃 = 90° ) c) a squinted beam with 𝜃 = 45° d) if a police-radar uses the Doppler frequency to determine velocity, which direction will be least-sensitive to a speeding driver ( 𝜃 = 0°, 45°, or 90° ) 2.) The equation for the orbital velocity, derived from Keppler’s laws of motion, applies to much more than artificial satellites. For this problem, use the internet to look up the mass of the Sun, the mass of the Earth, and the distance of the Earth to the Sun. Using these values, and values from the lecture and class notes, do the following: a) Determine the equivalent mass of the Sun, stated in units of equivalent masses of Earths. In other words, how many Earths would it take to come up with the equivalent mass of the sun? To get some appreciation for how large a number this is, provide your answer to the nearest whole number and do not use exponential notation (e.g. use 10,000 instead of 10e3 or 10 x 10 3 ) b) Ignoring the mass of the Earth, calculate the orbital velocity of the Earth around the Sun. Provide your answer in units of m/s. c) Use the value from part b, to determine the length of time that it takes for the Earth to orbit the Sun. Provide your answer in units of days and compare to the known value of 365.25 days. 3.) The optical spectrum (red-green-blue to the mid-infrared) looks different for the three basic land- cover types (water, vegetation and soil). The first three “thematic” bands of Landsat are for red, green and blue, are bands 3, 2 and 1 respectively (or TM3, TM2 and TM1). Sometimes the contrast between these bands is not very useful in highlighting the differences between the landcovers (see figure below). a) Using the graph from the figure, calculate the ratio of reflectivity (reflection percent) of band 2 to band 1 for Water, Vegetation and Soil (approximate the graph as being constant within the bands). Call these variables, 𝑅 ?𝑎?𝑒? 21 , 𝑅 ?𝑒𝑔 21 , and 𝑅 ?𝑜𝑖𝑙 21 . b) Using the graph from the figure, calculate the ratio of reflectivity of band 5 to band 1 for Water, Vegetation and Soil. Call these variables, 𝑅 ?𝑎?𝑒? 51 , 𝑅 ?𝑒𝑔 51 , and 𝑅 ?𝑜𝑖𝑙 51 . For water in band 5, assume that the reflectivity value is zero. c) Compare the differences between water, vegetation and soil for the 21 spectral ratios and the 51 spectral ratios. That is, see how 𝑅 ?𝑎?𝑒? 21 and 𝑅 ?𝑒𝑔 21 are different from one another compared to 𝑅 ?𝑎?𝑒? 51 and 𝑅 ?𝑒𝑔 51 , and similarly for comparison between soil and vegetation, and soil and water. These differences are what creates

2 the increased “contrast” in the image at right compared to the natural color image. For the 51 spectral ratios, which of the two land cover types have the greatest contrast (i.e. vegetation from water, vegetation from soil, or soil from water)? 4.) As you have seen so far, MATLAB is a very useful tool for many disciplines. It is like that for remote sensing too. We are going to use MATLAB in the next three problems to look at data collected by an airborne lidar called LVIS (Land, Vegetation and Ice Sensor; pronounced like the name of the famous rock singer). To help you with these problems, there is a dataset called lvis.mat that has been uploaded to the module section on the course Moodle page. Locate this file and download it to your computer. It is a binary file in MATLAB structure format. Once you have download the file, load it into MATLAB by double-clicking on it or typing in the command load(‘lvis.mat’) . Within the file is the data structure called lvis. Within that structure are different variables with names like ‘shot_number’, ‘time’, ‘lon’, ‘lat’, etc. You can see these variables by double-clicking on the lvis structure in the Workspace panel of the MATLAB window, or just typing ‘ lvis ’ in the command window . Note that each variable looks like a one- dimensional array (Nx1) of numbers. In the case of the provided file, there are 10,000 entries for each variable. Our goal is to make a plot of the lidar return as a function of the vegetation height, for one of the lidar pulses (or shots). After transmitting one lidar pulse, the returned power from the lidar is recorded as a function of time in units of 2 nanoseconds. For the LVIS sensor, the time window goes from 0 to 862 nsec. a) Make a plot of the 4102 nd lidar return as a function of time by typing in the following commands: tt = (0:431)*2; plot(tt,lvis.wave(4102,:))

3 xlabel('Time (nsec)') ylabel('Lidar counts (-)'); title('Lidar power versus time <your-name-here>'); Make a screen capture of your plot and include it as part of your homework submission. Your plot should look something like the following (without the annotations). b) Use the magnifying glass feature of the MATLAB figure window to determine the time of the top of canopy return and ground return in units of nanoseconds. Using the table below, record these values, and then calculate the time difference between the bottom of canopy return and the top of canopy return. By multiplying the time difference (in units of seconds) by the speed of light ( 3 × 10 8 m/s), convert into a difference of round-trip distances in units of meters. Now divide this difference in round-trip distances by two to determine the height. This is the height of the trees in the area where the lidar pulse was recorded. Top of canopy time (nsec) Ground return time (nsec) Time difference (nsec) Round-trip difference (m) Height of trees (m) c) Create a more intuitive plot of the lidar return as a function of power as a function of height by typing in the following commands into the MATLAB command window: zz = tt/1e9*3e8/2; plot(lvis.wave(4102,:),84-zz) xlabel('Lidar counts (-)') ylabel('Height above ground (m)');

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4 title('Lidar power versus height <your-name-here>'); Note that the time in nanoseconds is divided by 1 × 10 9 in order ot put the time in units of seconds. The value of 84 in the plot command is referenced to the distance from the sensor to the ground return, hence making the ground return to be defined as a zero height for the ground. 5.) To put the data into Geographic context, we will use GoogleEarth to locate where the data were collected. First, we will find out the location of something a) Use the Search window in GoogleEarth to find what is located at the latitude, longitude pair: 42.3773, -72.5360. Provide a screen shot of this location in your homework submission. b) Use the command lvis.lat(4102), and lvis.lon(4102) to determine the latitude and longitude of the lidar return that created the above waveform. Put these values in the table below Latitude (deg) Longitude (deg) c) Use the GoogleEarth program to find the location of the lidar shot by entering the latitude & longitude values from above into the Search window of GoogleEarth, and provide a screen shot in your homework submission of the area from where the data were collected. 6.) Lastly, we are going to make some plots of the path that the LVIS sensor took when collecting the data set. a) Use MATLAB to plot lvis.lon, lvis.lat onto a single graph. The longitude should be along the x-axis and latitude along the y- axis. Create axis labels that say “Longitude (deg)” and “Latitude (deg)”, as above. Also, include a title that says “LVIS flight plath, plotted by <your-name- here>”. Create a screen shot and include with your homework. b) Next, we will take this same data and create a file that can be read in by GoogleEarth. To do this, type the following commands in the MATLAB command window: out = [lvis.lat, lvis.lon]; fid = fopen('lvis_flightpath.txt','w'); fprintf(fid,'latitude longitude\n'); fprintf(fid,'%.6f %.6f\n',out'); fclose(fid);

5 Once finished, use the File menu to Open the ‘ lvis_flightpath.txt’ file in GoogleEarth (the downloaded program, not the on-line version). To do so, you can just use the default settings for space delimited text. If GoogleEarth indicates that the number of features may be too large, still try to “import all”, and say “No” to applying a style template to the data. If nothing shows up in GoogleEarth, you may have to click on the check-box to actually show the data that has been imported into the Temporary Places part of GoogleEarth. What you should see is a screenshot that looks like the image below. Use the ruler tool in GoogleEarth to calculate the length and width of the data (in units of kilometers) collected by LVIS, and report this number in your homework. As you can see, there is a lot that we can do with a data set like this. For now, we will finish our analysis here and leave you to explore the data set based on your curiosity. For instance, look at how the waveforms change for different latitude/longitudes. You can also use this opportunity to learn more about MATLAB’s “find” command, which will help you locate specific latitude/longitudes in a large dataset like the one provided. It is not necessary to turn anything more in than your own screen shot version from above, and your measurement of the dimensions of the data collection area.