Universal Soil Erosion Equation
Author: Laura Swantek
Time: 50 minute class period
Grade Level: 9-12
Background:
Soil is created by the weathering of rock and the decomposition of organic materials. Soils are classified according to the amount of silt, sand or clay they contain. If the soil contains all three sediments, it is
called loam and is modified by the word for the sediment of the highest concentration (e.g. silty loam: loam
with equal amounts of sand and clay but with more silt). Soil forms very slowly and is necessary for sustaining life on earth. It is what our food is grown in! Erosion of this precious resource has been a problem since
people first started farming during the Neolithic and continues to be a problem for farmers today. Poor farming decisions have already caused erosion and desertification of 7.5 million square miles of land. This has
directly affected the food supply of 250 million people. Once land is cleared of trees and shrubs, it becomes
more susceptible to erosion, even if crops are planted in it. The universal soil erosion equation can be used
to determine how much erosion by water will occur in specific areas. Using erosion information from Neolithic
and Bronze Age farming villages in Jordan, we can understand how scientists make sustainable farming decisions for the future.
Objectives:
1- Students will be able to replace variables with numbers in a mathematical equation and solve.
2- Students will be able to determine the rates of erosion for different kinds of landscapes.
3- Students will be able to compare rates for different areas in order to determine which place would be
the most sustainable to farm.
4- Students will understand how climate and the rate of erosion influenced past farming decisions.
5- Students will understand that slowing the rate of erosion through various methods will increase sustainability.
6- Students will be able to read slope, precipitation and soil maps generated with Geographic Information
Systems (GIS) software and use the answers from the soil erosion equations to locate sites on the
map.
Advanced Preparation:
 Print soil erosion equation worksheets
 Print soil, precipitation and slope maps
 Optional: print soil, precipitation and slope maps on transparencies that can be overlaid
Materials:
 Soil erosion worksheets
 Soil, precipitation and slope maps
 Medland Project introduction booklet
Suggested Procedure:
 Introduction using the Medland Project booklet provided
 Read the introduction on the soil erosion equation worksheet together
 Students set up and solve equations and complete erosion worksheet
 Students use the GIS generated maps of an area in Jordan to locate the two sites that were used for the
equations
 Optional: Using the transparencies and an overhead projector, show students how the GIS maps can be
overlaid to give us a complete picture of the landscape
 Discuss soil erosion and sustainability
Mediterranean Landscape Dynamics Project
Questions for Discussion
 How can events in the past help us make more sustainable decisions in the future?
 What can we do individually to make more sustainable decisions?
Evaluation:
Create a bar graph of the values for Cleared Flatland, Cleared Flatland using P factor, Cleared Hillside
and Cleared Hillside using P factor in that order. Determine what happened to the numbers after a sustainable farming method was used.
Extensions:
 Students can change the values for some of the variables to see how they affect the rate of soil erosion.
 Is the U.S. government concerned about erosion? Find out what regulations have been implemented to
control erosion at http://www.nrcs.usda.gov/programs/fppa/pdf_files/FPPA_Law.pdf
 Included at the end of the lesson is a Google Earth Snapshot of the part of Jordan the GIS maps represent. This is the area within the red square. Using Google Earth software available free on the internet,
students can use the latitude-longitude coordinates at the bottom of the snapshot to find this exact place
by typing them into the find command. They can zoom in and see the real watershed the GIS maps show
and how the slope map corresponds to what is actually on the ground.
Resources:
http://ngm.nationalgeographic.com/2008/09/soil/bourne-text “Dirt Poor,” National Geographic article on the
effects of soil erosion on a population.
http://topsoil.nserl.purdue.edu/nserlweb/weppmain/overview/intro.html National Soil Erosion Research Laboratory.
http://en.wikipedia.org/wiki/Sustainable_agriculture Wikipedia article on sustainable agriculture.
Arizona Standards
Science
Inquiry Process
C3-PO1
History and Nature of Science
C1-PO2
Science in Personal and Social
Perspectives
C1-PO1
C1-PO3
C1-PO5
C2-PO5
Mediterranean Landscape Dynamics Project
Math
Number Sense and Operations
C3-PO2
Data Analysis, Probability and Discrete
Mathematics
C1-PO3
C1-PO8
Algebraic Representations
C3-PO2
Social Studies
World History
C1-PO7
C9-PO4
C9-PO5
Geography
C3-PO1
C3-PO3
C4-PO6
C4-PO7
C5-PO3
C5-PO4
Universal Soil Erosion Equation
Worksheet
Beginning 10,000 years ago, during a period called the Neolithic, people started farming in Jordan.
Large groups of people lived together in lowland and hillside landscapes that they had cleared of trees and
shrubs to create farmland. Around 8,000 years ago, the climate changed and more rain began to fall. People
started living in much smaller groups (sometimes only 20 people) and farmed smaller areas because it was
more sustainable. So, what happened that caused people to move to smaller villages? Later, during the
Bronze Age, people adopted more sustainable farming techniques and lived in larger villages.
We are going to use the universal soil erosion equation to see if soil erosion may have been a factor in
the decisions made by early farmers about where to live. After we determine erosion rates, we are going to
use maps to locate the archaeological sites that these numbers correspond to.
Soil Erosion Equation:
A = KR(LS)C
A = Estimate of soil loss rate in tons/hectare/year
K = Soil erodibility factor
R = Rainfall factor
LS = Slope factor
C = Crop management factor
K Factor
The K factor is based on the type of soil that is in the area you are investigating. Soil can be composed of
different types of sediment including sand, silt, and organic matter. These all erode at different rates. The
soil in Jordan has more silt than sand so it is called silty loam and is composed of 2% organic matter.
Because it is dry for most of the year, organic material takes longer to decompose, and it takes longer for soil
to develop in this area.
Soil Texture
Organic Matter Content (%)
Fine Sand
0.5
0.16
2
0.14
4
0.10
Very Fine Sand
0.42
0.36
0.28
Loamy Sand
0.12
0.10
0.08
Loamy Very Fine Sand
0.44
0.38
0.30
Sandy Loam
0.27
0.24
0.19
Very Fine Sandy Loam
0.47
0.41
0.33
Silty Loam
0.48
0.42
0.33
Clay Loam
0.28
0.25
0.21
Silt Clay Loam
0.37
0.32
0.26
Silty Clay
0.25
0.23
0.19
Mediterranean Landscape Dynamics Project
Universal Soil Erosion Equation
Worksheet
R Factor
Very Wet = 90, Moderately Wet = 60, Dry = 30
Jordan was dry during the beginning of the Neolithic, but around 6,000 it changed to a moderately wet climate. These values represent the annual average rainfall.
LS Factor
When hillsides are steep, water and gravity force the soil down the slope faster.
Slope Length (m)
Degree of Slope
LS- Soil Loss Factor
250
200
150
125
110
100
90
60
50
45
1.8˚
3.6˚
5.4˚
7.2˚
9˚
3.6˚
12.6˚
14.4˚
16.2˚
18˚
0.2
0.4
1.5
2
2.5
1.2
4
4
4.5
5
C Factor
Land that is cleared is more susceptible to soil erosion than land that is forested. The values for how susceptible the land is to erosion have been determined by scientists. For our area the values are:
Forest = .005 (low susceptibility)
Cleared Land = 1.6 (high susceptibility)
Mediterranean Landscape Dynamics Project
Mediterranean Landscape Dynamics Project
.42
.42
(1a) Forested Flat
Land
(1b) Cleared
Flat Land
.42
(3b) Cleared
Hillside
(6) Cleared
Hillside with
P
.42
(3a) Forested Hillside
(6) Cleared
Flat Land
with P
K
Land Type
R
LS
1.6
.005
1.6
.005
C
__________
__________
__________
__________
P Factor (6)
A=
KR(LS)C
Universal Soil Erosion Equation
Worksheet
Universal Soil Erosion Equation
Worksheet
For questions 1-7, determine what the rate of soil erosion will be without factoring in sustainability measures
for two different sites in Jordan. Use the formula A= KR(LS)C . This equation provides an estimate of the Soil
Loss Rate in tons/hectare/year. Fill out the chart with the K, R, LS and A amounts, then answer the questions
for each site.
Site #1: Flat Land
1a- Calculate the erosion rate for a forested, flat land site with a 1.8˚slope, length of 250 m and a dry climate.
1b- Then, run the same calculations, but change the C factor to find the erosion rate after the land has been
cleared.
2a- 8,000 years ago, it started to rain more, so the R factor in the equation increased to 60 for wet conditions.
If the R factor increases, estimate whether the erosion rate would increase or decrease, without setting up a
new equation.
2b- Why do you think people would want to live in smaller groups when it started to rain more? Think about
how erosion affects the amount of food that can be produced.
Site # 2: Hillside
3a- Calculate the erosion rate of a forest on a hillside with an 16.2˚ slope and length of 50 m and a dry climate.
3b- Change the C factor to calculate the erosion rate once this land has been cleared in a dry climate.
Mediterranean Landscape Dynamics Project
Universal Soil Erosion Equation
Worksheet
4- Can more
Compare
more soil is
food be produced at the flatland site or the hillside site if the climate is dry?
your answers from Site 1 and Site 2. Remember the higher the value for A, the
being eroded away per year.
P Factor
There is one more factor that can be added to the soil erosion equation. The P Factor represents what people try to do to slow down the rate of erosion, like terrace farming on hillsides and contour farming on flatter
areas. If we add this factor to the equation, we can see how people’s decisions will affect their sustainability:
A = KR(LS)CP
6- Rework the equation for the cleared flatland site (1b) using P =.5 and the cleared hillside site (3b) using
P =.9 . Fill in the answer column of the chart. What happens to the rate of erosion?
7– Based on the examples above, describe how decisions in the past affect our sustainability today?
8- Sustainable farming practices are one way we can use resources without depleting them for future generations. What are some ways we as individuals can be more sustainable in our every day lives?
Terrace Farming
Contour Farming
http://en.wikipedia.org/wiki/File:Rice_terraces.png
http://media-2.web.britannica.com/eb-
Mediterranean Landscape Dynamics Project
Universal Soil Erosion Equation
Worksheet
Now, let’s find the sites for which we calculated erosion rates on the maps.
Beginning with the soil map:
1- Do you think people would put their settlements in areas with good soil that could be farmed or poor soil
that couldn’t? Eliminate settlements in areas you don’t think people would live in.
2- Next, use the slope map to determine which sites have the right amount of slope (based on the information given to you above).
3- One of these sites was settled later in time, after sustainable farming practices were established, which
one do you think it is...the one on the slope or the one on the flatter land?
4- The other was settled after the Neolithic climate change. Using the slope map, why do you think it was established where it was?
5– Indicate on the map which site is the Neolithic site and which is the later site.
Mediterranean Landscape Dynamics Project
Universal Soil Erosion Equation
Map Legend
Use the 3 Legends below to read the Composite, Soil, Slope and Precipitation maps and answer the
questions.
Mediterranean Landscape Dynamics Project
Universal Soil Erosion Equation
Mediterranean Landscape Dynamics Project
Composite Map
Maps
Soil Map
Mediterranean Landscape Dynamics Project
Slope Map
Precipitation Map
Universal Soil Erosion Equation
Google Earth Image of Watershed in Jordan