A study guide on the Empirical version
of the Rational Method to estimate
peak discharge runoff
Bruce Carey
Soil conservationist
Brisbane, Queensland, Australia
July 2014
bcarey@tpg.com.au
1
This study guide was prepared in 2014 as supplementary material
for the publication Soil conservation measures – Design manual for
Queensland.
The manual was produced in 2004 by the Queensland Department
of Natural Resources and Mines and can be downloaded from the
Department of Environment and Heritage Protection library
catalogue (search for DEHP library catalogue) and from the Landcare
Queensland website.
The manual contains the following chapters:
1 Introduction
2 Soil conservation planning
3 Runoff processes
4 Designing for risk
5 Peak discharge estimation
6 The Empirical version of the Rational Method
7 Darling Downs Regional Flood Frequency version of the
Rational Method
8 Channel design principles
9 Contour banks
10 Diversion banks
11 Waterways
12 Floodplain applications
Carey Bruce and Stone Barry (2004). Soil
conservation measures – A design manual for
Queensland. Queensland Department of Natural
Resources and Mines.
The manual is currently being revised on a voluntary basis by Bruce Carey and will contain the following additional
chapters.
12 Land management on floodplains
13 Stream stability
14 Soil conservation in horticulture
15 Gully control
16 Property infrastructure
Soil erosion had become a major problem in Queensland cropping areas by the late 1940s. Visible evidence of this erosion is
readily apparent from the aerial photography program that the Queensland government began at that time.
There has been considerable progress in the adoption of soil conservation practices in cropping areas since the State
government began an extension program to assist farmers to implement soil conservation measures beginning in the late
1940s. However, the task is by no means complete and with the phasing out of the soil conservation extension service in
the 1990s, the pool of knowledge required to assist farmers to implement soil conservation measures has rapidly declined.
In many ways, we know less about the condition of our land, then we did in the last century, when 50 soil conservation
extension officers working in 30 centres throughout Queensland regularly reported on what was happening in their area.
Of special concern is the lack of young people with soil conservation skills. Tertiary institutions offer minimal, if any, training
in this area and academic staff and scientists generally have a very limited knowledge of this topic – hence the need for the
study guides. They are intended for use by soil conservation practitioners, farmers, students, academics and staff from
industry, NRM regional bodies, Landcare groups and government.
1955
2003
Soil conservation study guides are available on the following topics (additional topics are
planned).
•
•
•
•
•
•
•
Runoff processes
Planning soil conservation layouts
Empirical version of the Rational Method to estimate peak discharge runoff
The Darling Downs Flood Frequency version of the Rational Method to estimate peak
discharge runoff
Design of channels for soil conservation
Contour banks
Grassed waterways for erosion control in cropping lands
These study guides can be downloaded from the Landcare Queensland website at
http://landcare.org.au/resources-links/achieving-soil-conservation-in-queensland/
(from the homepage click on ‘Resources and links’ and then ‘Achieving soil
conservation’.
About the author
Bruce Carey began his career as a soil conservation extension officer with the Queensland
Department of Primary Industries in 1971. He carried out this role in Millmerran, Goondiwindi,
Emerald and Toowoomba before moving to Brisbane in 1988. He maintained his links to soil
conservation while working in several Queensland government agencies until his retirement in 2012.
Like most soil conservationists, he has a keen interest in the relationships between soil, water and
vegetation. His special interest is in documenting the knowledge gained about soil conservation in
Queensland. He is an author of the publications Soil conservation measures – A design manual for
Queensland and the book Managing grazing lands in Queensland. He has written over 50 fact sheets
related to sustainable land management.
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Acknowledgement
Thanks to the Queensland Murray Darling Committee(QMDC) for providing assistance to produce these
study guides and to Landcare Queensland for hosting them on their website.
Thanks also go to the Queensland Department of Science, Information Technology, Innovation and the
Arts (DSITIA) for the use of many of the photographs in this study guide which were taken by soil
conservation extension officers in the 1970s and 1980s.
Google earth
Thanks also to Google earth. Introduced in 2005, we now have a tendency to take this incredible tool for
granted.
In the last century, one of the tools of trade for soil conservationists was aerial photography. This
photography was generally taken every 10 years, for most parts of Queensland since the 1940s. It was
usually black-and-white photography at a fairly broad scale. But it was always consulted before any
property visit. When on the property, it was used as a basis of discussion with the farmer during the
property inspection and while planning and designing soil conservation structures. It provided a base for
the property plans that were produced.
Google Earth is nirvana for anyone interested in soil conservation. For no cost on your home computer, you
can take a closer look at any piece of land in the world and get some indications of how it is being used and
6
managed.
Tips on using this study guide
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It is best to view this PDF file in ‘Full screen mode’ (click on ‘View’ and then ‘Full
screen mode’)
This publication has hyperlinks. From the table of contents you can link to any
section in the study guide. From each section heading you can link back to the
table of contents.
You can go to the next slide by a left click of the mouse or by pressing ‘Page
down’ on the keyboard. You can return to the previous slide by pressing ‘page
up’ on the keyboard.
To exit the publication at any time press the ‘Escape’ button on the keyboard
7
A study guide for the Empirical version of the Rational Method
to estimate peak discharge runoff
Table of Contents
•
•
•
•
Introduction
Factors affecting the peak runoff rate
Designing for risk
Applying the Rational method
A study guide on the Empirical version of the Rational
Method to estimate peak discharge runoff
Return to Table of Contents 
Introduction
There are two components to the design of
soil conservation structures
• How much runoff does the structure need to handle?
– use of the Rational Method
• How big does it have to be to handle this runoff?
– use of the Manning formula
?
?
?
This study guide deals with runoff estimation. Other study guides deals
with the Manning formula for the design of structures.
How many m3/s ???
In soil conservation design, the peak rate of runoff that a structure will
have to accommodate (in m3/sec)needs to be estimated. Such estimates
are needed for structures like contour banks, waterways, dam spillways
and road culverts.
For the design of storage structures like dams for water supply and
irrigation, the volume of run-off (in megalitres) produced by catchment
over a period of time needs to be estimated.
This study guide and the soil conservation design manual only deals with
estimations of peak rates of run-off.
A hydrograph for a single flood event
Peak discharge
A study guide on the Empirical version of the Rational
Method to estimate peak discharge runoff
Return to Table of Contents 
Factors affecting the peak runoff rate
The Rational Formula is said to have been conceived by
an engineer in the 1850s.
If you were that engineer, how would you go about
developing a formula to estimate a peak rate of runoff for
the design of a structure?
The first step might be to think about all of the factors
that affect the production of run-off.
What are they?
Factors affecting the runoff rate
•
•
•
•
•
•
•
•
Rainfall – intensity and amount
Soil types
Slope
Area of the catchment
Shape of the catchment
Land use and management
Storage and detention in the catchment
How wet is the catchment likely to be for the design event?
The proportion of rainfall that becomes runoff is generally
smaller than most people would expect
• Freebairn and Silburn (2004) in Southern Qld, runoff occurs
at the paddock scale on an average of 5 days per year (and a
significant soil movement about once every 2 to 4 years)
• Lawrence and Cowie (1992) Brigalow Research Station
project, average annual runoff under brigalow forest
represented only 3% of the total annual rainfall (6% for
pasture)
• (from section 3.1 of the manual)
Water Balance and Yield
(Greenmount 1978-88)
Bare fallow
Stubble mulch
Evap 67%
Evap 68%
Runoff 12%
Soil Water 20%
Runoff 8%
Soil Water 25%
Extra water 5%
t/ha
3
Crop Yield
extra yield
2.7
Under stubble
mulch an
average of only
8% of the total
annual rainfall
became run-off
2.5
2.25
0
1
Bare Fallow
2
3
Stubble Mulch
18
The hydrologic cycle
Plant Available Soil Water
Courtesy: Department of Atmospheric Sciences at the University of Illinois at Urbana-Champaign,
Catchment shape
These catchments have the same area but they would have different
peak rates of run-off. A contour bay is an unusual shape for a
catchment. Contour banks act like a dam and they detain a
considerable amount of run-off. Run-off along the channel can be very
slow especially when the channel is lined with, a crop or stubble.
Natural
catchments
Contour bay
catchments
During the 16 year period, the
largest run-off events
consistently occurred on land
where the stubble had been
burnt
This event occurred late in the
fallow when the difference in
the amount of cover between
treatments was not so great
So if you were the engineer asked to determine a method of obtaining
the peak rate of run-off from a small catchment, how would you go
about it? Lets forget about a typical catchment for now and look at a
very simple catchment like the roof of a house
Let’s suppose a storm occurs where the rate of rainfall is constant for
the entire event (not very likely in reality). You measure the rate of
flow from the roof as it flows down the downpipe. What would the
resulting hydrograph look like?
Assuming rain falls at a constant rate
Peak
discharge
A hydrograph
At this point,
the whole of
the roof is
contributing
What are the 2 factors affecting the runoff rate from the roof?
(assuming it is impermeable and has no leaks !)
• The rainfall rate (in mm/hr)
• The area of the roof (assume it’s a very
large roof and we’ll use hectares)
These two factors are used in the next equation.
Q = I * A * 0.00278
• Q = the peak rate of runoff in (m3/sec)
• I = the rainfall rate (mm/hr)
• A = the area of the roof (in hectares)
0.00278 balances the units (mm to m3 and hours to seconds)
0.00278 = 1/360. There are 3600 seconds in an hour
ThIs formula is the basis of the Rational Method
To apply it to a catchment, we simply add a C factor which estimates what proportion of
the rainfall becomes runoff during the event. This accounts for “losses” such as
infiltration.
So the Rational Formula becomes
Q = C* I * A * 0.00278 (m3/sec)
The basis of the rational method is that it assumes that a 1
in 10 year runoff event occurs when a 1 in 10 year rainfall
event occurs on a catchment under ‘average’ conditions
So how do we apply this formula to calculate the peak discharge at a
design point in a catchment?
Q = C* I * A * 0.00278 (m3/sec)
• A the catchment area in hectares contributing to the design
point
• C The C value we get from Table 6.2 of the design manual
• I is the rainfall intensity in mm/hr for the design period eg 1 in
10 years
Now we’ll have a closer look at
how we determine values for C and I
Q = Cy* I * A * 0.00278 (m3/sec)
Cy The runoff coefficient
• Defined as the ratio of the peak runoff rate of a given ARI (Annual
Recurrence Interval in years) to the mean rate of rainfall for the
design event
• In essence this is the ‘black box’ – it attempts to take into account all
of the catchment characteristics that affect how much rainfall
becomes runoff during the design rainfall event
• See Tables 6.1 and 6.2 to determine C values. Note that these are
arbitrary values and are not based on hydrological data
First step is to determine the ‘runoff potential’
Second step is to select a C value from this table
The keyword on TV busy on the panel
A roof would have a run-off coefficient of 1, while a deep sand on the
beach would have a runoff coefficient of 0.1.
Equivalent Impervious Area
The Equivalent Impervious Area of a catchment is the area that would produce a design
flood of the same size as that estimated for the catchment if that Equivalent Impervious
Area has a runoff coefficient of 1; this means that all the rainfall falling on the Equivalent
Impervious Area runs off.
It is calculated by dividing a catchment into components having similar runoff producing
characteristics. The Equivalent Impervious Area for each component is then determined by
multiplying its area by its runoff coefficient. The Equivalent Impervious Areas for each
component are then added to determine the Equivalent Impervious Area for the total
catchment.
As Equivalent Impervious Area incorporates both the runoff coefficient and the catchment
area, the Rational Method formula then becomes:
Qy
=
Where
Qy
=
Itc,y
=
equal to
Aei,y
=
0.00278 Itc,y Aei,y Equation 6.2
design peak runoff rate (m3/s), for an ARI of y years
average rainfall intensity (mm/h), for the design ARI and for a duration
the tc (minutes) of the catchment, and
Equivalent Impervious Area (ha) for the design ARI of y years
Example: Determine the Equivalent Impervious Area for a 90 ha catchment which consists
of 20 ha of cultivation (Cy = 0.6), 30 ha of forest (Cy = 0.3) and 40 ha of pasture (Cy = 0.4).
Q = C* I tc,y * A * 0.00278 (m3/sec)
I tc,y The rainfall intensity
• I tc,y = average rainfall intensity (mm/h), for the
design ARI and for a duration equal to the ‘time
of concentration’ tc (minutes) for the design
point
Time of concentration (Tc) is the time estimated for water to flow from
the most hydraulically remote point of the catchment to a design point
The time of concentration for
the area between two
contour banks ( a contour
bay)
The time of
concentration for a
catchment
The Rational Method assumes that the highest peak rate of runoff from the catchment
will be caused by a storm of duration just long enough for runoff from all parts of the
catchment to contribute simultaneously to the design point.
The ‘time of concentration’ is calculated by summing the travel times of
flow in the different hydraulic components. Those components may
include one or more of the following.
• overland flow
• stream flow
• flow in structures (contour banks and waterways)
Several flow paths may need to be assessed to determine the
longest estimated travel time, which is then considered to be the
time of concentration.
Note that stream flow in this situation generally refers to a
drainage line which may only produce runoff on two or three
occasions per year. Streamflow rarely occurs in a paddock with
contour banks flowing into a constructed waterway.
Determining the time of concentration for design point P2
Overland flow
(determined from the
graph on the next slide
Bank flow
(interception
bank)
Waterway
flow
Flow time in the
contour bank
channel and
waterway is
determined by
dividing the length of
the flow path by the
design velocity
Compare the flow times for the red and blue pathways. The time of
concentration (tc) will be the longest of these times.
Poorly grassed
surface
Land slope of
2%
Time of
concentration 15
minutes
100 metres
of overland
flow
Rainfall intensity design chart for
Capella in the Central Highlands
RIFD chart
Design rainfall
intensity of 90
mm/hour
ARI of 10 yrs
(1 in 10 rainfall
event)
Storm duration
of 30 minutes
The storm duration is the
calculated time of concentration
for a design point and is used to
to determine the design rainfall
intensity for the required ARI
(annual recurrence interval)
This data can be obtained for any
location in Australia from the
Bureau of Meteorology
A study guide on the Empirical version of the Rational
Method to estimate peak discharge runoff
Return to Table of Contents 
Designing for risk
When designing a structure to carry or store runoff, it is necessary to consider
how often it will be acceptable for the structure to fail or to surcharge.
The following terms, which refer to both rainfall and runoff, are used when
discussing probability or risk:
•
Average Recurrence Interval (ARI), also referred to as average return
period, is the average number of years (denoted as y years) within which an
event will be equalled or exceeded.
•
Frequency is an alternative way of expressing ARI. A frequency of 1 in
y years means that the event will be equalled or exceeded once in y years on
average.
•
Probability is the inverse of frequency, that is, 1/y. It is often
expressed as percentage probability, this being 100/y %.
It is important to understand that whatever terms are used, they all refer to
long-term averages and that the periods between events are random. This
means, that if an event with an ARI of 10 years occurred last year, the chances of
a similar event occurring this year have not lengthened, they remain the same.
That is, there is a 10% chance (or odds of 10 to 1) of it happening again. This
concept should be fully explained to clients for whom designs are prepared.
For the design of soil conservation structures, the estimation of runoff usually
relates only to very small areas such as a paddock or a small catchment on a
farm. Extremely high rainfall events that are ‘off the scale’ of a district rainfall
intensity chart can occur in very localised areas. So it is likely that in any district,
at the paddock scale, rare events, such as those with an ARI of 100 years, will
occur somewhere in a catchment on a much more frequent basis than 1 in 100
years.
Structures should be designed for ‘average’ conditions. Extreme values of
the parameters of runoff estimation models are used by some operators to
provide safety margins in design. This results in runoff estimates with
unknown ARI’s and increased construction costs. If a more conservative
design is required, it is better to design for a higher ARI.
A study guide on the Empirical version of the Rational
Method to estimate peak discharge runoff
Return to Table of Contents 
Applying the Rational method
Applying the Rational method
1. Decide on the design ARI e.g. a 1 in 10 yr event (see Chapter 4 Design for risk)
2. Allocate locations on the plan for design points (refer to Chapter 2, Soil Conservation
Planning).
3. Estimate the ‘time of concentration’ for the design point.
4. From the IFD diagram for the district, determine the design rainfall intensity relevant
to the ‘time of concentration’ and the required ARI.
5. Identify and measure component areas within the catchment and assign a runoff
coefficient to each.
6. Calculate the design peak discharge by substitution into Equations 6.1 or 6.2 as
appropriate.
The pro forma on the next slide guides you through the process
44
Figure 6.6 Waterway design proforma
Landholder
Date
Contact details
Property description
Farm Code
1
2
3
4
5
6
7
8
9
10
11
12
13
Design Point
Design ARI in years
Length of overland flow (m)
Average slope (%)
Time of travel for overland flow (min)
Length of stream flow (m)
Average slope of stream (%)
Stream velocity (m/s)
Time of travel in stream (minutes)
Length of interception bank flow (m)
Interception bank velocity (m/s)
Time of travel in interception bank (min)
Tc previous design point (minutes)
14
Length of waterway flow (m)
15
Waterway velocity (m/s)
16
17
Time of travel in waterway (minutes)
Time of concentration, tc, (minutes)
18
19
Rainfall Intensity, Itc,y (mm/h)
Area at previous design point
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
Area of pasture & average slope (ha)
Runoff co-efficient
EIA, pasture (ha)
Area of cultivation & average slope (ha)
Runoff co-efficient
EIA, cultivation (ha)
Other area & average slope (ha)
Runoff co-efficient
EIA, other (ha)
Total area (ha)
Total EIA, Aei,y (ha)
Peak discharge, Qy (m3/s)
Design point slope (%)
Retaining bank batters (1:Z (V:H))
Minimum retardance value
Design velocity, V (m/s)
Bottom width, W (m)
Maximum retardance value
Flow depth, d (m)
Settled bank height (m)
Comments
Plan Number
From survey or farm plan
Row 6 / (Row 8 *60)
Row 10 / (Row 11 * 60)
Previous design point
Time
Additional length if Row 13 is
used
Estimated or previous design
point
Row 14 / (Row 15 * 60)
Total Rows 5,9,12, 13, 16 as
applic
From IFD data for this location
Previous point
Total area
Equivalent Impervious Area (EIA)
Additional area if Row 19 is used
Row 20 x Row 21
Additional area if Row 19 is used
Row 23 x Row 24
Additional area if Row 19 is used
Row 26 x Row 27
Rows: 19+20+23+26
Rows: 19+22+25+28
Qy = 0.00278 x I x Aei,y
d + 0.15 m freeboard
Shire
Form used to estimate
peak discharge and
waterway dimensions
for design points along a
waterway
Selecting Design Points
• the commencement and outlet
of waterways
• points where a waterway enters
and exits a property, paddock or
unfenced property lot
• points where there is a
significant change in the
specifications for a waterway
such as:
– at a change in slope
– where two waterways join
– at a bend in a waterway
• where key works are required
for public utilities such as,
road/rail culverts, access inverts
Peak discharge
estimation example
Calculate the peak
discharges for the
waterway design points H3,
H4 and H5 and waterway
H6 – H7 using the design
form and the data provided
on the next slide
Runoff potential
Soil permeability
ARI
Waterway velocity
Contour bank velocity
Overland flow
Location
Topography
220m
2
M
10 years
1 m/s
0.5 m/s
Average grassed
Pittsworth
Rolling
Q = C* I * A * 0.00278
9 ha
350m
4 ha
180m
11 ha
1ha
180m
530m
11 ha
280m
70m
12 ha
14 ha
4 ha
The Excel Spreadsheet RAMWADE allows you to estimate runoff
and design the waterway for a series of design points
Rational Method Waterway Design
Example of the
use of
RAMWADE for
waterway design
The Empirical version of the Rational Method is recommended
for catchments up to 1000 ha. Beyond that, more sophisticated
methods should be considered.
Survey by Mike Stephens (DPI) in 1988
Comparing the ‘Empirical’ and the
Darling Downs Flood Frequency (DDFF) versions of the Rational Method
For the design of soil conservation measures in Queensland, the ‘Empirical’ version of the Rational
Method is usually used. It is named because the parameters it uses (apart from rainfall data) are
arbitrary and are generally based on experience or observation rather than field measurements
obtained over a long period of time.
The publication Australian rainfall and run-off recommends that any method of peak discharge
estimation for design purposes should be based on measured data from a range of catchments. This
data is then used to develop what is known as a ‘statistical’ version of the Rational Method.
However, while we have some streamflow data for major creeks and streams there is very little data
collected from small agricultural catchments. There was a program in place to collect this data from
some small agricultural catchments of Queensland in the 1970s and 1980s but this work has virtually
ceased.
A project carried out in 1987 used all of the runoff data available for the Darling Downs to develop a
statistical version of the rational method ( the DDFF). This version is described in Chapter 7 of Soil
Conservation Measures – Design Manual for Queensland. It is a simpler method than the Empirical
Method because the time of concentration is based entirely on the area of the catchment contributing
to the design point. However, the method has no way of allowing for the reduction in runoff caused by
different land management methods and the use of contour banks.
As a result, the Empirical version of the Rational Method is generally used in Queensland for the design
of soil conservation measures.
52
A study guide on the Empirical version of the Rational
Method to estimate peak discharge runoff
Return to Table of Contents 
End