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.

  1. What is a watershed for a stream?
  2. How fast does snow melt? What are factors that affect the rate of snow melting?
  3. What type of function might be used to predict the rate of snowmelt?
  4. Sketch a graph that might be used to decide the amount of snow that remains during the time of year when snow melts.
  5. Why is snowmelt important for streamflow for a river?
  6. Is the area of a watershed significant in determining streamflow? How could one determine the area of a watershed?
  7. 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

  1. How much snow melts in the first month? In the second month?
  2. 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.

  3. 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.
  4. 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.
  5. Enter the amount of water from snowmelt in the fifth column in the Table.
  6. 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.
  7. 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?
  8. What is the total annual stream flow for the river?
  9. 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

  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 streamflow? 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. Do you know of a function whose graph might closely fit the streamflow graph?
  6. 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?

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