Oceanography 450
Homework Set #5.
Due Monday, FEB 27 (note that
you have extra time for this one).
Name__________________________
1. As discussed in class, there is a difference between 'calendar years' (which are
calculated) and measured 'C-14 years' (which are measured).
a. Why does this difference exist?
b. An empirical relationship between calendar years (CALyrs) and C-14
years (C14yrs) is
CALyrs  1807  1.39  (C14 yrs )  (5.85 106 )  (C14 yrs ) 2
Implement this equation in Excel, and tabulate the values at 1000 year intervals
from 0 to 30,000 years. Then, plot C14 yrs (on the horizontal x-axis) vs CALyrs
(on the y-axis) for the interval between 10,000 and 30,000 C14 yrs. Turn in this
Excel plot.
c. Convert the following events, from measured C-14 years to calendar
years, using your Excel spreadsheet, turn in the completed table.
Heinrich event H-1
Lake Missoula floods, start
LIS collapse via Hudson
Bay
Younger Dryas, end.
C-14 years
14,300
15,700
7,700
calendar years
10,000
d. Why would this equation be an inappropriate relationship to use for
modern (0 to 1000 years) times?
2. The relationship between the area of the surface of the earth (either above
sealevel, or below it) and altitude/depth is called the 'hypsographic curve'. A
typical plot is shown on an attached page. Also shown on that page is a table of
representative points taken from this curve.
a. Enter this data into your Excel spreadsheet.
b. Plot area of the earth (in the horizontal x-axis) vs altitude/depth (in the
vertical y-axis) between +1000 meters and –1000 meters (like the graph
on the last page of this homework sheet).
c. Fit a 4th order polynomial curve (i.e., trendline) through this data and give
the equation below. This will give you the functional relationship of
DEPTH = as a function of (AREA). Turn in this plot with the trendline
shown. HINT: if you haven’t done curve fitting before, search the Excel
HELP for the word ‘trendline’.
d. Now, invert the data, so you have an equation that gives AREA = as a function
of (DEPTH). The easiest way to do this is to break the data up into two
sections: (i) ABOVE sea level and (ii) BELOW sea level and treat them
separately. Then plot DEPTH/ALTITUDE on the x-axis (horizontal) and
AREA on the y-axis (vertical). You will need to make two plots, one 0 to
+1000 meters (altitude), and the other -1000 meters to 0 (depth below sea
level). Fit a 4th order polynomial equation through each of these, and write
these equations below.
i. Above Sea level ____________________________________________________________
ii. Below Sea level_____________________________________________________________
e. Finally, assume that all the ice in the Greenland Ice Cap (2.6 x 106 km3) and Antarctic Ice
Cap (3.01 x 107 km3) melts. Ignore temperature changes in the water and the fact that some of
these ice caps are below sea level or floating. Use the standard 'Rule of Thumb' that 1 km3 of
ice melt raises sea level by 0.24 x 10-2 millimeters. Calculate the area of the earth that would
be flooded by this melting. Total area of the earth is approximately 5.1 x 108 km2 and total
area of the ocean is 362 x 106 km2. HINT: just use the 0 to +1000 meter plot in section d
above. Calculate the total volume of new melt water, calculate the new elevation of sealevel
(use Excel or your calculator, if you need to), then use your trendline fit (4th order polynomial)
equation from the plot in part d(i) above.
Write your answers below (show your work on another piece of paper)
Sea level change for Greenland and Antarctic melt _________________________________
Area of newly flooded regions
______________________________________
Percentage of earth’s surface that would be newly flooded. __________________________
depth or
altitude
above or
below
sealevel in
meters
1000
850
750
600
500
400
300
200
150
100
50
0
-75
-100
-150
-200
-300
-400
-500
-600
-750
-850
-1000
area of
earth in
units of
108 km2
0.56
0.6
0.65
0.7
0.76
0.8
0.85
0.92
1
1.12
1.25
1.43
1.59
1.64
1.69
1.75
1.81
1.85
1.88
1.9
1.93
1.94
1.95
Hypsographic curve of the earth; total
area is approximately 5.1 x 108 km3