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.

  1. What type of function would be appropriate to predict the rate of snowmelt?
  2. Why is snowmelt important?
  3. Why is it important to predict streamflow or the amount of water in a river at a given time?
  4. What are some factors that might affect streamflow?
  5. How can we predict the streamflow for a river?
  6. How can we describe streamflow, i.e., what units would be appropriate?
  7. 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 mid-October (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.)

  1. Compute the volume of precipitation over the entire watershed for each month. The unit of measure will be cubic feet of water.
  2. 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.
  3. Enter the amount of water from snowmelt in the fifth column in the Table.
  4. 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.
  5. 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?
  6. What is the total annual stream flow for the river?
  7. 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

  1. Do you think that the functions used for steamflow are reasonable?
  2. Do you think that the assumptions regarding snowmelt are valid each year?
  3. 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?
  4. Do you think that your model should be used for prediction of streamflow for this river next year?
  5. 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?