Snow
Melt, Volume of Precipitation, and Streamflow
Part
3: Streamflow Prediction
In this module,
we will determine the streamflow for a river. It will first be
necessary to find out how much snow contributes to the streamflow,
then we will need to know the volume of water distributed over
the watershed for the river.
Comprehension
Understanding streamflow, visualizing the method of describing
streamflow.
 What type
of function would be appropriate to predict the rate of snowmelt?
 Why is
snowmelt important?
 Why is
it important to predict streamflow or the amount of water in
a river at a given time?
 What are
some factors that might affect streamflow?
 How can
we predict the streamflow for a river?
 How can
we describe streamflow, i.e., what units would be appropriate?
 How could
mathematics be used to predict future streamflow?
Acquisition
Mathematical Topics
Learn or review mathematical concepts and skills needed to study
snowmelt and streamflow. See the Menu to the left.
Information
Watershed Area and Snowmelt
 The area
of the watershed is approximately 335 million square feet.
 Precipitation
is uniform over the entire region.
 Average
temperatures are above freezing from the end of April through
midOctober (See Part 1, Temperature).
 Snow melts
at a uniform rate for two months after temperature exceeds 32
degrees F.
Streamflow
 Stream
flow is the amount of water that flows through the river
measured here in cubic feet per month.
 Base
flow is the minimum amount of water in the river each month,
this amount is constant each month of the year. Base flow comes
from precipitation and for this river is 5 million cubic feet
per month.
 In addition
to base flow, 70% of the precipitation other than gets to the
river bed.
 During
months when temperature is below freezing, the only streamflow
is base flow.
 Each person
uses approximately 30 cubic feet of water each day.
Application
Apply mathematical tools to analyze snow melt, volume of precipitation,
and streamflow
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 are in millions.
Watershed
Area, Volume of Precipitation, Snowmelt, and Streamflow
(Write your answers in millions and enter in the appropriate
column in the Table.)
 Compute
the volume of precipitation over the entire watershed for
each month. The unit of measure will be cubic feet of water.
 There
is an average total of 12.70 inches of water from snow each
year(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
(cubic
feet)

Rain
(cubic ft.) 
Snow
Melt (cubic ft.) 
Stream
Flow Contribution (70%)

Base
Flow 
Total
Monthly Stream Flow 
.5 (Jan)

1.98


xxxxxxx

xxxxxxx

xxxxxxx 
5


1.5

2.59


xxxxxxx

xxxxxxx

xxxxxxx 
5


2.5

3.20


xxxxxxx

xxxxxxx

xxxxxxx 
5


3.5

2.89


xxxxxxx

xxxxxxx

xxxxxxx 
5


4.5

2.58





5


5.5

2.27





5


6.5

1.96



xxxxxxx


5


7.5

1.65



xxxxxxx


5


8.5

1.34



xxxxxxx


5


9.5

1.03



xxxxxxx


5


10.5

0.72


xxxxxxx

xxxxxxx

xxxxxxx 
5


11.5

1.33


xxxxxxx

xxxxxxx

xxxxxxx 
5


Reflection
 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 watershed? 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?
 Reconsider
your answer to #7 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?