It sure is cold outside, or is it?
I created this map at the National Oceanic and Atmospheric Administration (NOAA) website that shows the
relationship between the temperature of places and their latitudes. I guess I always knew that locations near the
Equator were warmer than where I live but I started to wonder if you could predict the average temperature of a place
if you knew its latitude.
http://www.esrl.noaa.gov/psd/cgi-bin/data/composites/printpage.pl
Part A: I used Google Earth to find the latitude and elevation of a range of places on the earth. Then I used the
Weather Underground Trip planner to find the average historical highs and lows of each place in January. (At Weather
underground I asked the range of my temperatures to be from January 1 through January 31.)
Below is my data. Sometimes I added a note to the data when I thought other factors might have affected the
temperatures of that place. I’ve arranged my chart in ascending order of latitudes and created a column called
“average January temperatures” to be the mean of the low and high temperatures.
place
Quito, Ecuador
Kampala, Uganda
Camino Real, Guatemala
Hanoi, Vietnam
Houston, Texas
Tel Aviv, Israel
Kabul, Afghanistan
Tokyo, Japan
Oslo, Norway
Narsarsuaq, Greenland
Longyearbyen, Svalbard
North Pole
latitude
0.2309
.315
14.61
21.033
29.762
32.059
34.4625
43.06
59.91
61.155
78.232
90
average January
low temps in
Fahrenheit
average January
high temps in
Fahrenheit
average of low
and high
temperatures
elevation in
feet
49
67
33
58
45
49
23
37
22
17
10
no data
66
79
56
69
63
64
42
49
30
26
19
no data
57.5
73
44.5
63.5
54
56.5
32.5
43
26
21.5
14.5
9559
3880
3594
59
155
78
7422
409
294
247
434
notes
high elevation
pretty high
high elevation
1. I have entered only some of the average highs, lows, and total averages temperatures in January. Please
finish my chart by calculating the missing data.
See above.
2. To see if there is a correlation, plot the latitude of each of my places along with its average January
temperature on the grid that is on the next page.
3. Does it look like latitude and average temperature have a linear relationship? Yes.
4. Draw a line that you think might be a line of best fit. See above. At first I drew the line a little lower to try to be
between the low points as well. But then I decided that the low points were at places of high elevations. So
they were the outliers in this data.
5. What places and latitudes seem to be outliers? Do you have any theories about why they don’t seem to fit on
your line?
Quito, Ecuador (0.2309) should be warmer.
Camino Real, Guatemala (14.61) should be warmer.
Kabul, Afghanistan (34.4625) should be warmer.
These places are all of high elevation. So, they should be colder places.
Part B: Places that have latitudes that are similar to where I live. I live near Newton, Massachusetts.
latitude
Beijing, China
Chicago, Illinois
Newton, Massachusetts
Khangai Nuruu National Park, Mongolia
Gold Beach, Oregon
Casper, Wyoming
Grand Rapids, Michigan
Lugo, Spain
Monte Carlo, Monaco
Sarajevo, Bosnia
39.96
41.878
42.337
42.37
42.407
42.819
42.963
43.012
43.748
43.84
elevation
in feet
January
lows
January
highs
average of
low and high
53
598
185
4670
46
5197
638
1543
179
2489
15
21
22
-26
42
16
20
44
42
25
32
33
35
-2
54
35
31
55
54
38
23.5
27
28.5
-14
48
25.5
25.5
49.5
33
31.5
notes
near ocean
inland
near Mediterranean Sea
6. Plot my data on the following chart. For each place and latitude make a bar that shows the range from low to
high with a center mark for the mean temperature.
7. Can you come to any conclusions about where you live and how cold it is?
We have a pretty small temperature range. Our lows aren’t even remotely as low as in Mongolia which has a
really high elevation. Our lows aren’t as low has places that have similar elevations. Near large bodies of
water seems to raise the winter temperatures and moderate the extremes.
8. Should I be grateful that it is not as cold as it could be?
Yes.
Part C: Linear Model Section
Refer back to part A to complete the following problems. You should complete this section if you have or
are currently studying linear equations.
9. Determine the slope of the line of best fit. What does the slope represent in this situation?
m = -1 For every increasing degree of latitude the average temperature goes down by 1 degree.
10. Determine the y–intercept of the line of best fit. What does the y–intercept represent in this situation?
b = 78 ish At the equator the average winter temperature is about 78 degrees.
11. I wasn’t able to get temperature data for the North Pole. Can you make an approximate guess at that
temperature from your graph or by using your equation?
From the graph I think the average January temperature at the North Pole might be 0 degrees.
From my equation, y = -1x +78, when x = 90, y = -12
12. The average January temperature in Montreal, Canada is 16 degrees. According to your linear model, at
about what latitude should Montreal be at?
16 = -1X +78
About 52 degrees latitude.
13. The latitude of Atlanta, Georgia is about 33 degrees north of the Equator. According to your linear model,
what is Atlanta’s average January temperature?
y = -1(33) +78
y = 45
14. Go online and check your solutions to problems 13 and 14. How close are your solutions to the actual data?
Why might your solutions be different from the actual data?
Actually, Montreal is at 73° 35' W
Atlanta’s average January temperature is 52.
Extra: Do some research and find out what other variables than latitude can determine the climate of an area. List
those variables below. Do any of these variables influence the climate where you live?
Latitude: Surface temperatures vary with latitude.
Elevation: Climate zones coincide roughly with elevation ranges.
Nearby water: Sea surface temperatures affect land temperatures
Ocean currents
Topography
Vegetation
Prevailing winds
Newton, MA is pretty near the Atlantic Ocean. So, maybe our climate is moderated by the ocean’s warmth.
More sources:
http://www.ncdc.noaa.gov/cmb-faq/anomalies.php
http://www.classzone.com/books/earth_science/terc/content/investigations/es2101/es2101page02.cfm
Bought to you by www.yummymath.com