Snow Gauge Lab

Your assignment is to write an instruction sheet (max one page) for a lab technician on how to use the calibrated snow gauge in winter months. Include an easy-to-use graph for determining snow density from gain.

Accompany the instruction sheet with a technical appendix (max two pages) that defends the methodology you have used to calibrate the gauge. Include up to four graphs and two tables.

You may work in pairs, for this assignment.

• Use the data to fit gain, or a transformation of gain, to density.
  • Add the least squares line to the scatter plot.
  • Do the residuals indicate any problems with the fit?
• Develop a procedure for adding bands around your least squares line that can be used to make interval estimates for snow-pack density from gain.
• To check how well your procedure works, omit the set of measurements for the density 0.508, apply your calibration procedure to the remaining data, and provide an interval estimate for density for an average reading of 38.6.
• Consider fitting a polynomial in density to the data. How well does it fit? Compare this model to the simple log-linear model. Consider fit, predictive ability, physical model, and any other factors that might be relevant. Include your comparison in the technical appendix.

To assist you in the lab, you will use the latest version of the descriptive stats GUI:

• R
• library(descriptiveStats2)
• descriptiveStats()

Additional features have been added to the GUI for this lab assignment.

• The Regress command now has options for polynomial regression and zero intercept regression.
• A scatter plot can now be annotated with lines and curves. To do this, bring the scatterplot that you wish to annotate to the foreground of the plots and click on the Annotate button.
  • If you wish to add a line to the plot, enter the intercept and slope in the appropriate boxes and push the Apply button.
  • If you wish to add a curve to the plot, enter the function in the large text area. Use the x argument for your function, e.g. 3 + 2*x + 4*(x-1)^2
  • If you have made a syntax error in your statement, when the Apply button is pushed, an error message will be displayed and no curve will be added to your plot.

NOTE:

• The numerical statistics can help you figure out sum(x - xBar)^2.
• The output from the regress command can help you determine sigma as well as the equation for the line (or polynomial).
• There are functions such as log(), sqrt(), exp() available to you.
• Be sure to check that the order of operations is correct and that parenthesis are properly placed in your curve function.
• If you want to remove a line that you have added to your plot, you will have to start with a new plot. Soon there will be a way to remove annotations from a plot...
• The curve function only works for x in a range from 0 to 1. soon you be able to specify the range.
• If you annotate your plot but nothing shows up on the plot then check to see if the line/curve is out of the range of values displayed.
• There is a calculator on the computer that you can use if needed.