Question

7.4 Characteristics of sea ice melt ponds

Surface albedo is defined as the ratio of solar energy directed upward form a surface over energy incident upon the surface. Surface albedo is a critical climatological parameter of sea ice. The National Snow and Ice Data Center (NSIDC) collects data on the albedo, depth, and physical characteristics of ice melt ponds in the Canadian Artic, including ice type(classified as first year ice, multiyear ice, or landfast ice). Data for 504 ice melts located in the Barrow Straight in the Canadian Artic are saved in the PONDICE file. Environmental engineers want to model the broadband surface albedo level, y, of the ice as a function of pond depth, x1 (meters), and ice type, represented by the dummy vairables , x2 = {1 if first year ice, 0 if not } and x3= {1 if multiyear ice, 0 if not}. Ultimatley, engineers will use the model to predict the surface albedo level of an ice melt pond. Access the data in the PONDICE file and identify the experimental region for the engineers. What advice do you give them about the use of the prediction equation?

Answer 1

In regression analysis, we have to collect two types of data observational and experimental. In observational type the values of independent variable are uncontrolled, whereas in experimental the independent variables are controlled via a designed experiment.

In the given example the environmental engineers want to model the broadband surface albedo level y, of the ice as a function of pond depth xi (meters) and ice type, represented by the dummy variables x2 = {1 if first year ice, 0 if not) and x3 = (1 if multiyear ice, 0 if not). For this regression analysis the experimental region is defined as the values of independent variables. Since ice type is qualitative variable at three levels, we can estimate the experimental region by examining descriptive statistics for depth at each ice type. We use Minitab Software to find the descriptive statistics. The steps are as follows:

1. Go to Stat menu bar. Select "Basic statisticsàDisplay descriptive statistics from dropdown menu. 2. In "Display descriptive statistics" dialog box, select "depth' as "variables" and "ice type" as "By variables". Then click ok.

The result is as follows:

Descriptive statistics: depth

From above results, we can conclude that for ice type "First-year", depth x1 ranges from a minimum of 0.02 meters to a maximum of 0.36 meters, for ice type "Land fast", depth x1 ranges from a minimum of 0.00 meters to a maximum of 0.86 meters, and for ice type "Multi-year", depth x1 ranges from a minimum of 0.07 meters to a maximum of 0.64 meters. These three ranges define the experimental region for the analysis. From above results we have to give the advice as to predict the surface albedo level avoid the depth that outside the intervals (0.02m, 0.36) for "First-year" ice type, (Om, 0.86m) for "Land fast" ice type, and for (0.07m, 0.64m) for "Multi-Year" ice type.