Turn in answers to the underlined items.

Problem 1. SURFER has some built-in tools that help you visualize data that might be difficult to contour. For example, consider the data shown below:
 
 

The data represent five periods of measurements where the upper line shows the day of the month and the left column shows soil depth in feet. The “z” variable (bold font) is soil moisture, shown in percent. These values were obtained from depths ranging from 1 to 5 feet below the surface (shown as –1 to –5). Notice on day 18 it rained and a 30% moisture content was recorded at –1 ft. Also notice that the moisture from the rain infiltrated to greater depths on later days, while drying somewhat at the surface.

We want to have SURFER contour the soil moisture (“z”) as a function of time (x-axis) and depth (y-axis). To do this, create an xyz file in either Excel or SURFER’s worksheet. You should have 25 records in the xyz data set.

Next, grid this using SURFER’s "Inverse Distance to a Power" algorithm and its associated defaults. Create and print the resulting map. It is important at this point to think conceptually about the process of infiltration. Can you see on the contoured time-depth profile the movement of the infiltration front through time? It should appear as a front that moves downward with time. It should NOT have bulls-eyes or be overly controlled by dates.

SURFER’s defaults do not do a very good job because of the strong anisotropy in the data set. Define "anisotropy." The data set greatly lacks continuity between the measurement dates. Therefore, SURFER's defaults give you great contours within a narrow vertical interval centered on the data collection dates, but lousy results between dates.

Try re-gridding by using Kriging and modifying the anisotropy under advanced options. In this case you will flatten the ellipse. This will make SURFER give more weight to the horizontal relationships among the data. (Although SURFER has some built in tools to set the ellipse quantitatively, you may prefer to simply work by trial and error to come up with a best fit contour map of the depth vs. time data.) Does the grid density make a difference in the resulting grid?.  Turn in a copy of you final profile and explain why it is better than the profile generated by SURFER’s default parameters.

Problem 2. Other maps and images can be brought into a SURFER plot. For example, download the zipped DRG (digital raster graphic) map of the Lake Louise quadrangle northwest of Jamestown. This is in the heart of North Dakota’s prairie pothole country, an area of very hummocky topography and extensive wetlands. Unzip the map and save both the TIF and TWF files that constitute the map to your G-drive. Open a new plot window in SURFER and add the DRG as a “Basemap.” Click OK when it asks about the bit map.

Notice that SURFER puts its own grid on the map, based on one map unit equivalent to one image pixel, with (0,0) in the lower left corner. When you want to overlay GPS (global positioning satellite) data onto the USGS quadrangle, however, you are going to want to use lat-long or more common UTM coordinates. (Please be sure to read through the information given in this link if you are unfamiliar with UTM coordinates). If you zoom in on the margin of the TIF topographic map, you will see the UTM coordinates; they are in a small, blue font and look something like “52₁₈”. These numbers refer to the distance in thousands of meters from the UTM zone's principal baseline and meridian. So  “52₁₈” means 5,218,000 m north of the baseline. SURFER's coordinates are unrelated to the UTM coordinates that you need to work with.

To better understand the problem at hand, download and unzip the USGS digital elevation model (DEM) for the same quadrangle. This is simply a big grid of elevations that cover the area of the quadrangle. Open a new plot document and, because it is already a grid, bring this in as a new contour map. Notice that the x and y axes now reveal the UTM coordinates (these are in meters, by the way).

The "Select All" and "Overlay Maps" command will not work at this point. So how can we overlay the DEM and the digital raster image?

The bit map image has two files associated with it: the actual image has a TIF extension. The other file, which is much smaller, has a TFW extension and can be viewed in Notepad. The TFW file includes the UTM information for the upper left corner of the TIF map and the number of map units per pixel. (The image, when really zoomed in, shows up as little squares or pixels). The Lake Louise DRG’s TFW file contains six lines of text with the following format:

2.43840000..............x-resolution
0.00000000..............amount of translation
0.00000000..............amount of rotation
-2.43840000..............y-resolution
461214.56479510..............x-ground coordinate of pixel 1,1 (upper left)
5219724.88142852..............y-ground coordinate of pixel 1,1 (upper left)

Open the file and check to make sure these are correct. With this information, we know that that the xMin is 461214.56479510 and the yMax is 5219724.88142852. In addition, to set the coordinates correctly in SURFER, we need to calculate the xMax and yMin. Get the size of the TIF file in pixels by going back to the quadrangle map image and double clicking on the map to display the image coordinates in the Base Map dialog box. Note that the number of pixels across the width is 4554 and the number of pixels along the height is 6723. How many pixels make up the map image? The xMax and yMin are calculated as follows:

xMax = (x-resolution * #pixelsAcrossWidth) + xMin

yMin = (y-resolution * #pixelsAlongHeight) + yMax

Once you have these calculated, enter all four of the image map corner coordinates into the “Image Coordinates” section of the Base Map dialog box. Click OK and now the DEM and DRG should overlay correctly. To overlay the maps, click on "Select All" and then "Overlay Maps."

Adjust the values under the levels tab so that the DEM (in meters) has the same values and interval as the DRG contours, which are in feet. (Note: 1 foot = 0.3048 meters and the contours on the DRG vary from 1720 to 1980 feet with a 10 ft. interval). Magnify an area and turn in a screen dump.

If the DRG already shows contours, why would anyone want to import and overlay another map, the DEM, that also shows topography? (What is the fundamental difference in the format that this topographic information is stored digitally?)

Problem 3. Finally, we will use SURFER's volume estimation capability. Use the Grid Extract command on the Lake Louise DEM to create a new digital elevation map that covers the big pothole in the northeastern corner of the map bounded by 5216310 on the south, 5217180 on the north, 468000 on the west, and 469500 on the east. Bring this map into the plot window, overlay the maps, and turn off the large DEM.

Next, use SURFER's Grid Volume command to estimate the volume and area of the pothole as water fills it up. Use the new truncated grid when the command prompts to open a grid, set the bottom grid to a constant near the base of the pothole (558 m would probably be a good choice). Click on OK and check the report. There's quite a bit of information here, but the two really important numbers are the negative cut and fill volume and the negative planar area. Write these down and then consecutively run the Volume command for 559, 560, 561, and 562 m. Record the volume and area for each and plot them in Excel, with volume on the x-axis and area on the y-axis. Fit the data to a 2nd order polynomial. Turn in a plot of your Excel graph, showing the data points, the 2nd order trend line, equation, and correlation (R^2).