CALIBRATION



Calibration of the relationship between contemporary environmental values (sea-surface temperature) and proxy data (percentage of Globegerina in surficial sediments) permits us to estimate the past temperature when proxy data were deposited. The line in the graph of sea-surface temperature versus Globegerina percent (below) is described by two points (X,Y) 0,0 and 40,20 (Globegerina %, oC ). A fossil sample contains 25% Globegerina, what was the sea-surface temperature at the time (and place) that sample was deposited?

Calibration procedure:
The transfer function for this problem is of the form Y = bX + c where
the slope of the line (b) is (Y2-Y1)/(X2-X1) = b
(20-0)/(40-0) = 0.5
and the Y-intercept (c) is ((Y2+Y1)/2) - b * (X2+X1)/2 = c
20/2 - 0.5 * 40/2 = c
10 - 10 = 0


Therefore, the transfer function is Y = 0.5 * X + 0
(past Sea Surface Temperature equals ½ of the Globegerina percent)

For example, for 25% Globegerina the sea-surface temperature is 12.5 oC

12.5 oC = 0.5 * 25 + 0

For the following five calibrations sets, defined by points 1 & 2, calculate the transfer function (Y = bX + c) by first finding the slope of the line (b) and the Y-intercept (c). Then, calculate the past temperature implied by the percentage of Globegerina in a fossil sample. Hand in a table showing the five pairs of points, b, c, the calculate temperature, and your calculations.
    copy, past, fill-out, and hand this in
    Point 1 Point 2 Transfer Function Fossil % Estim. ºC Varif. ºC Over/Varif/Under
     x, y  x, y (Y = b X + c)
           
    0,0 40,20 Y = 0.5 X + 0 25  12.5 (ex.)  13.0 (ex.)  Under (ex.)
    4,6 24,30 Y = __ X __ 5   ____   13.0   ____
    2,4 18,28 Y = __ X __ 8   ____   13.0   ____
    6,1 16,31 Y = __ X __ 10   ____   13.0   ____
    4,8 36,56 Y = __ X __ 7 ⅓   ____   13.0   ____
    7,7 19,19 Y = __ X __ 14   ____   13.0   ____