Snow Melt, Volume of Precipitation,
and Streamflow
Part
3: Streamflow Prediction
This module is the third
of three which are designed to lead to the prediction of streamflow
for a river in a particular region. Temperature obviously affects the
type of precipitation we get, and the amount of precipitation affects
the amount of water in the river. A model for temperature was developed
in the first module in this series and a model for average precipitation
in the second. In this module, we will use these results together with
the area of the watershed for the river to compute monthly streamflow
figures.
Comprehension
Understanding streamflow, visualizing the method of describing streamflow.
 What is a watershed for
a stream?
 How fast does snow melt?
What are factors that affect the rate of snow melting?
 What type of function
might be used to predict the rate of snowmelt?
 Sketch a graph that might
be used to decide the amount of snow that remains during the time
of year when snow melts.
 Why is snowmelt important
for streamflow for a river?
 Is the area of a watershed
significant in determining streamflow? How could one determine the
area of a watershed?
 Try to sketch a graph
that indicates streamflow over the period of one year for a river
near you.
Acquisition
Mathematical Topics
The mathematical topics required for this study are listed in the menu
to the left. Click on the topics if you need to learn more or refresh
your memory
Information
Snow Melt
Snow melts at a uniform rate for two months after temperature exceeds
32 degrees.
Watershed Area
The watershed for the river is approximately shaped like the figure
shown below with the river running down the middle. Lengths of sides
are labeled, and are measured in miles.
Stream Flow
 Streamflow is the amount
of water that flows through the river measured in cubic feet per month.
 Base flow is is the minimum
amount of water in the river each month, this amount is constant each
month of the year. Base flow for this river is 40 million cubic feet
per month.
 The average person uses
30 cubic feet of water each day.
Application
Apply mathematical tools to analyze snow melt, volume of precipitation,
and streamflow
Questions
 How much snow melts in
the first month? In the second month?
 Use the Law of Cosines
to find the area of the watershed in square feet. Write your answer
in millions rounded to two decimal places. Note: this requires a conversion
from miles to feet, or from square miles to square feet, 1 mile =
5,280 feet.
When answering the following questions refer to the table at the end
and record your answers there. Some answers are already listed; these
were obtained in Part 2, Precipitation. Also the XXX's indicate that
no data should be entered here. (Also see Parts 1 and 2, Temperature
and Precipitation.) All figures in all columns except the first two
should be written in millions.
 Compute the volume of
precipitation over the entire watershed for each month. The unit of
measure will be cubic feet of water. The monthly precipitation figures
from Part 2, Precipitation, are listed in the second column.
 Precipitation falls in
the form of snow from the end of October through the end of April.
(See Part 2, Precipitation.) Compute the total annual volume of water
from snow for the year over the entire watershed. Again, units will
be cubic feet of water.
 Enter the amount of water
from snowmelt in the fifth column in the Table.
 Complete the remaining
columns in the Table. The last column will tell you the monthly amount
of water that can be expected to pass through the river.
 Make points from the
monthly streamflow figures: the first coordinate should be the t value
for month and the second coordinate the streamflow for that month.
Plot these points on the plot screen, then print the screen and connect
the points with a smooth graph. Does this look like some of the graphs
shown in local newspapers for local rivers?
 What is the total annual
stream flow for the river?
 How many people can the
river support with its annual flow?
Month 
Precip.
(Inches) 
Precip
(mil cubic feet)

Rain
(mil cubic ft.) 
Snow
Melt (mil cubic ft.) 
Stream Flow Contribution
(70% of precip) (mil cu ft)

Base
Flow(mil cu ft) 
Total
Monthly Stream Flow (mil cu ft) 
.5
(Jan)

1.29


xxxxxxx

xxxxxxx

xxxxxxx 
40


1.5

1.74


xxxxxxx

xxxxxxx

xxxxxxx 
40


2.5

2.26


xxxxxxx

xxxxxxx

xxxxxxx 
40


3.5

2.71


xxxxxxx

xxxxxxx

xxxxxxx 
40


4.5

2.97





40


5.5

2.97





40


6.5

2.71



xxxxxxx


40


7.5

2.26



xxxxxxx


40


8.5

1.74



xxxxxxx


40


9.5

1.29



xxxxxxx


40


10.5

1.03


xxxxxxx

xxxxxxx

xxxxxxx 
40


11.5

1.03


xxxxxxx

xxxxxxx

xxxxxxx 
40


Reflection
Review the model for reasonableness
and accuracy
 Do you think that the
functions used for steamflow are reasonable?
 Do you think that the
assumptions regarding snowmelt are valid each year?
 What effect would a sudden
heat spell (above 50°) early in the season have on the streamflow?
What if it were followed by a second cold spell which brought more
snow?
 Do you think that your
model should be used for prediction of streamflow for this river next
year?
 Do you know of a function
whose graph might closely fit the streamflow graph?
 Reconsider your answer
to #9 above. Could the river support that many people each month?
What would your strategy be to use the water so as to effectively
support this many people?