SSAC2007.GB1205.NAB1.1
Determining How to Calculate
River Discharge
HOW MUCH WATER IS FLOWING IN THE RIVER?
Quantifying discharge gives us an
understanding of the hydrologic
characteristics and the fluctuations in
the amount of flowing water in river or
stream (lotic) environments. Can you
think of natural and human-derived
factors that would lead to changes in
river and stream discharge?
Core Quantitative Skills
Area of trapezoid
Supporting Quantitative Skills
Number operations: Products and sums
Reading graphs
Prepared for SSAC by
Nicholas A. Baer, Colby-Sawyer College, New London, NH
© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2007
1
Overview of Module
Discharge (Q, the volume of water flowing per unit time past a specific point)
in a river or a stream (lotic environment) is used by scientists to understand
the physical forces and potential impacts on the chemical, physical and
biological aspects of the aquatic environment. For instance, engineers must
know the hydrologic variability of a river before designing and constructing a
bridge. Also, discharge can be used to determine the rate of contaminant
flows, and impacts of an accidental spill into a river. Additionally, ecologists
utilize discharge information to understand the ability of the lotic system to
process nutrients moving through the aquatic environment.
This module will illustrate how to determine discharge, and have you use
relevant field data to calculate stream discharge in two examples.
Slides 3-6 Introduction to concepts and data.
Slides 7-8 Example spreadsheets and measurement tools.
Slides 9-10 Statement of problem, data collection, manipulation, and calculation.
Slides 11-12 Examining rating curves.
Slides 13-14 End-Module Exercise and Pre-Post Test.
2
Slides 15-17 Appendix.
Problem
You will spend the first part of this exercise learning about
river discharge, how it is measured and used in assessing
lotic systems. The module then focuses on expanding your
understanding of discharge as you use Excel spreadsheets
to calculate discharge using an existing data set. Lastly
you will determine the discharge of a river from field data.
You will compile data from a river cross-section and carry
out the calculations using Excel.
Calculate the discharge (Q) of the Ashuelot River using the
data set provided. Then expand your understanding by using
Excel to compile the physical measurements and water
velocities from the Blackwater River in order to determine its
discharge. What additional information do you need about
this river to help resource managers or engineers working
within or around this river system?
3
Understanding Discharge
What environmental factors will alter the
discharge of a river at any given location?
Discharge (Q) of a river continues to
increase as you move further down the
watershed, due to increases in
watershed area and the addition of
tributaries contributing to the flow.
Selecting the same point along the river
to measure discharge over time lets us
know the variability of the flow that is
moving through the watershed.
Photo courtesy of www.geographyalltheway.com
Base flow of a river is considered the discharge due to ground-water seepage
into the river. This low flow level is influenced by season and precipitation.
Horton’s Law of stream ordering classifies increases in stream size by larger
numbers. Stream order number increases only when two or more streams of
the same size meet. For example, a 2nd-order stream starts where two or more
1st-order streams meet. Discharge measurements will depend on the size of
the stream being measured and the size of the watershed contributing to the
4
stream flow.
How to Calculate Discharge
In order to calculate discharge (Q), you need two key pieces of data:
1. The velocity (V) of the water (m/sec) moving by a specific section of the
river, and
2. The cross-sectional area (A) (m2) of the river.
Q= V x A
Where:
Q = Discharge
V = Water Velocity
A = Area
Velocity (V) is measured at 0.6 depth (represented by
the yellow circles) from the water surface, because the
velocity there provides an estimate of the average in
the water column.
River Cross-section with Velocity Points
Water velocity
measured at
0.6 depth.
What forces do you think cause the
average velocity to occur at 0.6 of
the depth?
Friction between the water and the
river bottom substrate slows the
water. Therefore the fastest-moving
water is at the surface and the
slowest-moving water is along the
river bottom. This is one reason why
many organisms have adapted to live
at the river bottom (benthic region)
as the force of the water is reduced
there.
5
How to Calculate Discharge
The cross-sectional area (A) is determined by measuring the area of
smaller geometric shapes across the river section. Since the velocities are
also measured within each of these smaller sub-sections, greater accuracy
of the river discharge can be accomplished.
River Cross-section with Velocity Points
♦ ♦
♦
♦
What one
geometric shape
can be used to
determine the area
for each of these
segments of the
cross-section ?
So: What is this 4-sided
figure with only 2 parallel
sides? Do you remember
the equation for its area?
Once you have calculated discharge (Q) for one segment, then
you sum all the segments together to get total discharge.
Qtotal = Q1 + Q2 + Q3 + …. + Qn
6
Sample River Cross-Section and Spreadsheet
Example Field Data
2
3
4
5
6
7
8
9
10
B
C
D
E
F
G
H
Example Field Data Collected to Calculate Discharge (Q)
Cumulative
Distance Depth1 Depth2
Velocity Discharge
2
Distance (m) (m)
(m)
(m)
Area (m ) (m/s)
(m3/s)
0.5
0.50
0.045
0.00
0
0.18
0.1
1
0.50
0.105
0.02
0.18
0.24
0.23
1.5
0.50
0.1275
0.05
0.24
0.27
0.41
2
0.50
0.1725
0.06
0.27
0.42
0.35
2.5
0.50
0.33
0.07
0.42
0.9
0.21
2.95
0.45
0.2025
0.01
0.9
0
0.05
0.22
Total Q =
= cell with a number in it
= cell with a formula in it
After measuring the
distance across the river
channel, one measures
the water depths at
equally spaced intervals.
The depths and
distances are then used
to calculate the area
within each crosssection segment.
What is the equation for
the area of a trapezoid?
Click for more
information about a
trapezoid.
7
How do we go about measuring water velocity in the stream or river?
There are various tools that can be used to measure the water velocity,
ranging from the simple – floating oranges – to sophisticated acoustic
Doppler technology. All methods are intended to determine how fast
the water is moving per second. This measure of water velocity is then
used along with the cross-sectional data to calculate the volume of
water moving per unit of time (the discharge, Q).
Photo courtesy of www.usgs.gov
Photo courtesy of www.marsh-mcbirney.com
Methods used to measure
water velocity include:
● Timing a floating object
● Propeller rotation speed
● Electromagnetic
● Acoustic Doppler
8
Photos courtesy of www.swoffer.com
Setting up Your Spreadsheet
Depths 1 and 2 represent the
vertical depths on the sides of
the trapezoid (as in Slide 6).
B
C
D
E
F
G
H
2
Field Data from Ashuelot River Hinsdale, NH
2
3
3 Cumulative Distance (m) Distance (m) Depth1 (m) Depth2 (m) Area (m ) Velocity (m/s) Discharge (m /s)
4
0.5
0.50
0
0.13
0.0325
0.061
0.00
5
1
0.50
0.13
0.26
0.0975
0.505
0.05
6
1.5
0.50
0.26
0.37
0.1575
0.427
0.07
7
2
0.50
0.37
0.53
0.225
0.206
0.05
8
2.5
0.50
0.53
0.72
0.3125
0.469
0.15
9
3
0.50
0.72
1.25
0.4925
0.473
0.23
10
3.5
0.50
1.25
1.38
0.6575
0.62
0.41
11
4
0.50
1.38
1.42
0.7
0.78
0.55
12
4.5
0.50
1.42
1.22
0.66
0.88
0.58
13
5
0.50
1.22
1.27
0.6225
1.13
0.70
14
5.5
0.50
1.27
1.14
0.6025
1.41
0.85
15
6
0.50
1.14
1.2
0.585
1.21
0.71
16
6.5
0.50
1.2
1.11
0.5775
1.04
0.60
17
7
0.50
1.11
0.93
0.51
0.86
0.44
18
7.5
0.50
0.93
0.79
0.43
0.62
0.27
19
8
0.50
0.79
0.5
0.3225
0.58
0.19
20
8.5
0.50
0.5
0.46
0.24
0.41
0.10
21
9
0.50
0.46
0.31
0.1925
0.21
0.04
22
9.5
0.50
0.31
0.26
0.1425
0.13
0.02
23
10
0.50
0.26
0.09
0.0875
0
0.00
24
10.2
0.20
0.09
0
0.009
0
0.00
25
Total Q =
5.99
Using the template, calculate
the area and discharge for each
segment of the river crosssection, and determine the total
discharge (Q) of the river.
Click on the Excel icon to
download a datasheet
template to get started.
What types of humanderived influences can alter
the discharge?
9
Calculate Discharge Using Field Data
Now that you have been introduced to calculating discharge, use the diagram below
to create a spreadsheet and calculate the discharge for the Blackwater River. You
will have to estimate the water depths and segment widths based on the diagram.
Water Depth (m)
Cross-section of the Blackwater River, Andover, NH
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0.0
0.01
0.11
0.03
0.0
0.23
0.31
0.47
0.62
0.44
0.39
0.38
0.79
0
1
2
3
4
5
6
Distance Across River (m)
NOTE: Velocity is noted within each segment section and are measured in meters per second (m/s).
7
Click on the Excel icon to download a
datasheet template to get started.
10
Using Discharge Measures to Develop a Rating Curve
A rating curve is determined by taking discharge measures at different flow
rates, during the slow drier periods (base flow) and during the seasonal
floods. In this way we are able to develop a relationship between stream
stage (height of water on the vertical axis) and discharge (on the horizontal
axis). It allows us to evaluate changes in discharge for a flowing water by
simply measuring the height of the water.
See this USGS link for more information:
http://md.water.usgs.gov/publications/presentations/md-de-dc_rt98/sld017.htm
Photo courtesy of www.usgs.gov
Photo courtesy of www.nps.gov
Gaging stations can measure the stream
stage which can then be used to determine
the relative discharge using the rating
curve for that stream.
graph courtesy of www.usgs.gov
Based on the graph above, what
is the discharge if the stream11
stage measures 12 feet in height?
Assessing Changes in Discharge Measures
Collecting discharge measures over a long period of time allows engineers,
resource managers, and scientists to identify when changes in flow rates
occur and the potential causes.
Potential environmental
influences on discharge
include:
Drought
Storm Events
Climate Change
Seasonality
Potential human influences
on discharge include:
Land Use Changes
(agriculture, development)
River alterations
(dams, dikes, diversions)
Photo courtesy of www.noaa.gov
12
End of Module Assignment
1. Turn in the following assignments:
A. Your spreadsheet showing your calculated discharge from the field
diagram exercise.
B. Your responses to the questions for evaluating the graph.
2. The Merrimack River has a base flow of 731 ft3/sec. You just returned from
taking measurements of the area and mean velocity for the river. The area
is 166.2 ft2 and the mean velocity is 3.52 ft/sec. What is the current
discharge (Q)?
3. Based on your calculated discharge in question #2, predict what the time of
year and the climate are when this discharge was measured.
4. Identify three environmental or human factors that would affect a river or
stream discharge.
13
Slide 9 Spreadsheet Template
To access the live spreadsheet, end the slide show so that you can double click on the
template to activate the spreadsheet. You can either work directly in PowerPoint or
copy the table into a blank Excel worksheet. Be sure to save your work.
H
G
F
E
D
C
B
A Day in September Field Data from Ashuelot River Hinsdale, NH
2
3
2
3 Cumulative Distance (m) Distance (m) Depth1 (m) Depth2 (m) Area (m ) Velocity (m/s) Discharge (m /s)
0.061
0.13
0
0.50
0.5
4
0.505
0.26
0.13
0.50
1
5
0.427
0.37
0.26
0.50
1.5
6
0.206
0.53
0.37
0.50
2
7
0.469
0.72
0.53
0.50
2.5
8
0.473
1.25
0.72
0.50
3
9
0.62
1.38
1.25
0.50
3.5
10
0.78
1.42
1.38
0.50
4
11
0.88
1.22
1.42
0.50
4.5
12
1.13
1.27
1.22
0.50
5
13
1.41
1.14
1.27
0.50
5.5
14
1.21
1.2
1.14
0.50
6
15
1.04
1.11
1.2
0.50
6.5
16
0.86
0.93
1.11
0.50
7
17
0.62
0.79
0.93
0.50
7.5
18
0.58
0.5
0.79
0.50
8
19
0.41
0.46
0.5
0.50
8.5
20
0.21
0.31
0.46
0.50
9
21
0.13
0.26
0.31
0.50
9.5
22
0
0.09
0.26
0.50
10
23
0
0
0.09
0.20
10.2
24
Total Q =
25
Return to Module
15
Slide 10 Spreadsheet Template
Use the spreadsheet template below fill in the appropriate values from the
cross-sectional diagram in Slide 10. Use this information to calculate the
area and discharge for each segment of the river cross-section, and
determine the total discharge (Q) of the river.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
B
C
D
E
F
G
H
Field Data from Blackwater River Andover, NH
2
3
Cumulative Distance (m) Distance (m) Depth1 (m) Depth2 (m) Area (m ) Velocity (m/s) Discharge (m /s)
Total Q =
Return to Module
16