Hydrology and Water Resources, UO
Geography 4/525
Exercise 6: Modeling runoff with the Rational Equation
authored by Paul Blanton and W. Andrew Marcus
You have been hired as a hydrologic consultant by the City of Discordia on the outskirts
of Portland, Oregon to perform a historical analysis of runoff as related to land use/land
cover change over time. The City Planning Office has provided you land use/land cover
maps (posted on-line with this lab) that include the basin drained by Chaos Creek, which
is a tributary of the Discord River.
Your analysis will require you to undertake the following steps:

Become conversant with the Rational Model through the readings posted on the
web site.

Select appropriate “rational runoff coefficients” for all the land cover types in
Chaos creek.

Use the C coefficients and the Rational Model to calculate runoff and changes in
runoff for a basin in 1900, 1950, and 2000.
The materials you will turn in to the City Planning office (also known as the Geog
425/525 GTF) are:

A table with your values of land use type, proportional areas, weighted rational
coefficient values, final C values, and estimated peak runoff for 1900, 1950, and
2000.

Your answers to the questions at the end of this lab.
Please turn in your table and answers by the time posted on the class web site. Late assignments will be penalized 15% per day, unless you have a documented excuse. Answers to the questions must be typed to receive credit.
Applying the Rational Model
According to the Handbook of Hydrology, the Rational Model is to this day the most
widely used runoff model in the world for estimating effects of land cover change in
small urban and suburban basins. It is commonly used by developers and city planners to
estimate runoff impacts of small (<200 acres) developments.
Application of the Rational Method is simple. To “run” the model you (1) identify the
land cover types, (2) select a rational coefficient value for each land cover type; (3)
measure the basin area and the proportion of the basin area covered by each land cover
type; (4) calculate the weighted C factor for the entire basin; and (5) run the model for a
rainfall intensity of a given recurrence interval to estimate the flood discharge of the same
recurrence interval (e.g. use a 2–yr precipitation event that has a duration equal to the
time of concentration for the basin to estimate a 2-yr peak discharge – see Dunne and Leopold for further explanation). .
Go through the following sequence of steps for the 1900 map, then repeat the procedure
for the 1950 and 2000 map. Maps are posted on the web site.
1. Identify land cover types
Look over your land cover map for 1900 and identify which land uses shown in Table 109 of Dunne and Leopold (1978) are also included on the map. In Excel create a table that
lists the land cover types down column A. The heading should be “Land Cover Type”
2. Select C values for each land cover type
Using the range of values provided in Table 10-9 and based on your best professional
judgment (which is guided by the information provided below ), choose a C value for
each coefficient for each land cover type for 1900. Enter these values down column B
with a heading titled: “C in 1900.” (Add new columns later when you calculate C values
for 1950 and 2000.)
For all time periods: Soils in this basin are sandy or gravelly. In the absence of
other information, assume a median C value for each category.
1900: The Light Industry down by the river is very sparse, and should have a
very low C value. The only exception is the mill area which should have the maximum light industry value. Even though the mill is tiny, still give it a weighing
factor of 0.01 (to represent its disproportionate impact).
Small businesses are quite clustered on the north side of the railroad, with virtually no open space.
1950 During World War II, an aluminum smelter and munitions factories were
built by the river. This resulted in a high degree of impervious surface (as well as
other environmental concerns).
The business sector grew and dispersed, and should have a median ‘neighborhood
district’ value.
The suburban area was a planned development, with lawns and open space.
2000: The railroad was converted to a ‘rails-to-trails’ park.
Subsequent suburban development was not planned particularly well, and overall,
Discordia’s suburbs should now receive a high c-value.
3. Calculate the proportional area of each land cover type
For each land cover type, add up the number of squares and divide by 780 (the total number of squares in the basin). Enter these values in column C under a heading titled:
“Weighting factor.”
4. Calculate the weighted C factor for the entire basin.
In column D, determine each land cover type’s relative impact on runoff by multiplying
the weighting factor (column C) by the land cover’s C value (column B). Title the column D: “Weighted C.”
Sum all the Weighted C values for all land uses on map. This is your final C value for
the entire watershed.
5. Run the Rational Model
Now you can solve the rational runoff for the time period, using an area of 195 acres and
a rainfall intensity of 5”/hr using the rational equation:
R=CAI
where R is the peak rate of runoff in cfs, A is area in acres, I is rainfall intensity in inches
per hour, and C is the weighted C factor for the entire basin.
To solve the rational runoff for the 3 time periods, use a total basin area of 195 acres and
a rainfall intensity of 5”/hr.
6. Repeat for the 1950 and 2000 maps.
‘nuff said.
Answer the questions on the following page.
Questions
Name:
Exercise 6, Rational model
Turn in:
- a table with your values of land use type, proportional areas, weighted C, and final
C values for 1900, 1950, and 2000.
- your answers to the questions below. Please type your answers.
Questions:
1. What runoff values (in cfs) did the rational runoff equation generate for 1900, 1950,
and 2000?
2. Give your interpretation of the pattern of change in runoff in terms of changing land
use/land cover. What are the primary drivers of the changes in runoff?
3. Think over the discharge estimation/modeling labs we have done in the past few
weeks. What are two other methods/models you might use to estimate discharge from
the basin? What would be the advantage(s) to using more than one methods/model to
estimate peak runoff?
4. What are the primary limitations of the Rational Model in this particular example –
i.e., what might be some major sources of uncertainty in your results? Be sure to read
over Dunne and Leopold before answering.