1. This work is supported by the National Science Foundation’s Transforming Undergraduate Education in STEM program within
the Directorate for Education and Human Resources (DUE-1245025).
The math you need:
- rates of change
- drawing trend lines
- anomalies
Unit 2: Part 2

2. What is a rate?
Any change with respect to time is called a
rate.
Examples in the geosciences?
• plate tectonic velocities (distance over time)
• crystal growth rates (change in crystal size over time)
• river and groundwater discharge (volume change over time)
• decay rates (change in number of parent isotopes over time)

3. Rates of change – Determining rates from a graph
6.0 - 2.5 billion people
2000 - 1950 years
0.7 bill. people/yr==
Calculate the rate of
population growth
from 1950 to 2000.

4. Draw a trend line
Why and when do I need one?
• Most exercises that ask you to construct a best-fit line have to do
with wanting to recognize relationships among variables on Earth
or to predict the behavior of a system.
• Also called: best-fit line, linear regression
http://serc.carleton.edu/ma
thyouneed/graphing/bestfit.
html

5. Draw a trend line
http://serc.carleton.edu/mathyouneed/graphing/bestfit.html
A best-fit line is meant to mimic the trend of the data. In many cases, the line
may not pass through very many of the plotted points. Instead, the idea is to
get a line that has equal numbers of points on either side.
1.Plotalldata
2.Drawshape
aroundalldata
3.Bisectthe
areawitha
line
4.DONE!

6. What are anomalies?
Anomalies are the difference between a reference temperature (or some
long-term average) and the temperature that is recorded for a particular year.
temperature data
temperature
anomaly data
(anomaly with respect
to 1980–2000 data)
Created using data from: http://data.giss.nasa.gov/gistemp/graphs_v3/

7. What are anomalies?
Anomalies are the difference between a reference temperature (or some
long-term average) and the temperature that is recorded for a particular year.
Anomaly from
1960–1980
temperatures
http://data.giss.nasa.gov/gistemp/graphs_v3/