# 7.4 Characteristics of sea ice

7.4 Characteristics of sea ice melt ponds

Surface albedo is defined as the ratio of solar energy directedupward 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 thealbedo, depth, and physical characteristics of ice melt ponds inthe Canadian Artic, including ice type(classified as first yearice, multiyear ice, or landfast ice). Data for 504 ice meltslocated in the Barrow Straight in the Canadian Artic are saved inthe PONDICE file. Environmental engineers want to model thebroadband surface albedo level, y, of the ice as a function of ponddepth, x1 (meters), and ice type, represented by the dummyvairables , x2 = {1 if first year ice, 0 if not } and x3= {1 ifmultiyear ice, 0 if not}. Ultimatley, engineers will use the modelto predict the surface albedo level of an ice melt pond. Access thedata in the PONDICE file and identify the experimental region forthe engineers. What advice do you give them about the use of theprediction equation?

In regression analysis, we have tocollect two types of data observational and experimental. Inobservational type the values of independent variable areuncontrolled, whereas in experimental the independent variables arecontrolled via a designed experiment.

In the given example theenvironmental engineers want to model the broadband surface albedolevel y, of the ice as a function of pond depth xi (meters) and icetype, represented by the dummy variables x2 = {1 if first year ice,0 if not) and x3 = (1 if multiyear ice, 0 if not). For thisregression analysis the experimental region is defined as thevalues of independent variables. Since ice type is qualitativevariable at three levels, we can estimate the experimental regionby examining descriptive statistics for depth at each ice type. Weuse Minitab Software to find the descriptive statistics. The stepsare as follows:

1. Go to Stat menu bar. Select”Basic statisticsàDisplay descriptive statistics from dropdownmenu. 2. In “Display descriptive statistics” dialog box, select”depth’ as “variables” and “ice type” as “By variables”. Then clickok.

The result is as follows:

Descriptive statistics: depth

From above results, we can concludethat for ice type “First-year”, depth x1 ranges from a minimum of0.02 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 0.86meters, and for ice type “Multi-year”, depth x1 ranges from aminimum of 0.07 meters to a maximum of 0.64 meters. These threeranges define the experimental region for the analysis. From aboveresults we have to give the advice as to predict the surface albedolevel avoid the depth that outside the intervals (0.02m, 0.36) for”First-year” ice type, (Om, 0.86m) for “Land fast” ice type, andfor (0.07m, 0.64m) for “Multi-Year” ice type.

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