Modelling Concepts

Models Matter
Choice and use of modern stormwater
models

Get out your superglue!
Image: Enviroscape® classroom kit

A topic only an engineer could love

Getting what you need from
stormwater studies
Are your consultants not answering the questions that
matter to you?
Are they answering questions you didn’t ask?
Are they ensuring the long‐term function of your
project?
Are they presenting the material in a form you can
understand?
Are they considering the environmental impacts?

What do you want to know?
Figure: USGS

Common drainage study objectives
Develop my property without causing flooding (and
lawsuits) downstream
Size my new culvert to ensure that it doesn’t overtop
Guide my city’s development to ensure that our streams
are not impaired
Set our new water intake to ensure that it doesn’t go dry
Restore my city’s stream to provide good fishing habitat
Do the bare minimum to meet those @#$!@# regulations

Why model?
To keep brilliant consultants in jobs
To meet your objectives

How does a model work?
Inputs
What causes the process?
Responses
How does the system respond?
Objectives
What important effects occur?
Error
How reliable are my results?

Inputs
Most typical is rainfall
Baseflow/dry weather flow
Snowmelt
Existing watershed condition
Temperature
Humidity
Wind
Sun

Responses
Infiltration over time
Groundwater recharge
Runoff over time
Flowrate
Flow depth
Flow velocity

Objectives
Maximum values
What will be the peak flood level for a given storm?
Minimum values
Will I have any flow in my stream during an August drought?
Total values
How much rain will infiltrate the soil in a given year?
Average values
Number of exceedances
How many times is my building likely to flood in 100 years?
Number of deficits
How many times is my pond likely to dry up in 100 years?

Deficit Level
Exceedance Level
Time
Flooded
Time
Flooded
Time w/out
water
Example River Level Objectives

Error
How closely does your
model mirror reality?
Error Analysis
How do your assumptions
affect your results?
Sensitivity Analysis
Can you optimize your
assumptions to reduce
error?
Calibration

Define your objectives
Meet with your consultant
On site if possible
Don’t let him leave until he completely understands
your objectives
Define how you will measure success
Be clear and concise
Write objectives into the contract
His recommended modelling plan should address all
of the aspects that follow

What data currently exists?
Surveying, constructing, testing, and calibrating a model
for a large watershed takes a lot of time and money
Is the existing dataset detailed enough?
Is the existing dataset reliable?
Does the existing data require significant re‐formatting?
Often there are existing studies that can provide a
starting point
FEMA
Corps of Engineers
City engineer

Where do you want to focus?
Be clear about where the critical
locations are
Non‐critical locations can be
modelled more roughly
Critical locations will require
more detail
Take care in applying existing
models: they may have been
made for a different purpose

Under what range of conditions?
100‐yr storm
Has a 1% chance of occurring in a given year
You may have three 100‐yr storms in a year
Event modelling – hypothetical storms
A 100‐yr storm doesn’t necessarily produce a 100‐yr
runoff; soil moisture, storm duration, rainfall
distribution and several other factors come into play
Long‐term rainfall/runoff conditions
Continuous modelling – calibrates model with recorded
data and tests future case against the long‐term rainfall

What exactly is a 25‐yr storm?
You may encounter a 25‐year storm two years in a row
More accurate to say “4%” chance storm
A rainfall distribution is required to understand how the
total rainfall depth falls over time

How certain do you need to be?
Figure: Cooperative Research
Center for Catchment Hydrology
75%?
99%?
Within 0.5 feet elevation?
Within 100 cubic feet per second?
Which parameter will be used for
calibration and error analysis?
Flow?
Water elevation?
Perform sensitivity analysis and
calibration to increase confidence
Data is hard to find for small
watersheds
Can another similar watershed be
used for calibration?

Sensitivity Analysis to Increase Confidence
Change uncertain model parameters and examine the
effects on the results
Infiltration parameters are usually a good candidate
Keep parameters within a reasonable range
Typically done one at a time
Look at effects over a range of conditions
Results are “sensitive” to a parameter when a change in
the parameter makes a large difference in the result
Measured parameters are typically not changed
Pipe diameter
Channel length

Sensitivity Example
100 % Parameter Change
%ResultChange
0
100
-100
-100
= mild positive sensitivity
= negligible sensitivity
= strong negative sensitivity

Calibration to Increase Confidence
Needed especially for physical models
Compare modelled results with measured results and
adjust for better fit using what was learned from
sensitivity analysis
Degree of fit can be measured using several statistical
techniques
Formal calibration can be done with recorded rainfall
and flow time series
Informal calibration can be performed with measured
total rainfall and high water marks

Figure: William James, Computational Hydraulics International
Calibration Example

What future scenarios?
After construction of a 1.5 acre restaurant site
At full build‐out per the city 20‐year plan
With our 75‐year old culvert collapsed

What expertise is available?
Some models require significantly more expertise to
operate than others
Does your staff or consultant:
Have a thorough understanding of the processes
involved in your watershed?
Have a solid foundation in the model being employed
and the algorithms driving it?
Have the community relations skills to present your
project to the public?
Have the availability to perform the work?

What is your schedule and budget?
Consider the cost of making a wrong decision
A perfect model a year late is useless

Do you need a model?
Long term gauge data is preferred, but doesn’t exist many places
Image: USACE EM 1110-2-1415

OK: you have defined objectives
you know you need a model
Now what?

Model Selection and Proper Application

Hydrology
Hydrology: the science dealing with the occurrence,
circulation, distribution, and properties of the waters of the
earth and its atmosphere
Many hydrologic parameters are hard to measure
= part of a simple drainage study
Modelling other parts of the
water cycle helps us to
understand the long‐term
environmental impacts of land
use decisions
Hydrology

Hydraulics: the science dealing with the laws governing water or other
liquids in motion and their applications in engineering; practical or
applied hydrodynamics
Hydraulic parameters are typically easier to measure
Hydraulics
Image: Tarleton University Hydraulics Lab

Model selection criteria
Ability to explain past observations
Can be improved through calibration
Ability to predict future observations
Cost of creation and use
Especially for models that will be maintained into the future
Robustness
A robust model will perform well under a wide range of
conditions and will remain stable under reasonable conditions
Simplicity
Models with the fewest number of parameters are usually best
for a given error level

Model Structure
Figure: Cooperative Research
Center for Catchment Hydrology
Empirical‐based on statistical analysis of other watersheds
Conceptual‐based on a conceptual understanding of watershed
processes
Physical‐based on physical processes that can be tied directly to
measured characteristics

Empirical Hydrologic Models
Do not attempt to explain the driving
processes, they simply transform an
input into a result based on statistical
analysis of previous results
Can provide reliable results if used
within the constraints of the original
study:
Studies typically provide bounds of
applicability based on factors like
location, rainfall distribution, or land
use
Robust and simple, but high error

Empirical Hydrologic Models:
Regional Regression
Table and Figure: USGS Water Resources Investigation Report 03-4176
Peak flows only
Be sure to choose the right region
Usually limited by drainage area
Note the prediction error

Empirical Hydrologic Models:
Rational Method
Table: NOAA Atlas 14 for University of Tennessee
Knoxville Monitoring Station
Q=CiA
Q=flow (ac‐in/hr≈cfs)
i = rainfall intensity for time
of concentration (in/hr)
A = area (acres)
Peak flows only
Best for small urban watersheds
Can lead to paradoxical results

Rational Method Example
Site is 6 acres
2 acres grass (C = 0.12) that flow onto:
4 acres paved (C = 0.95)
Overall C = 0.67
Time of Concentration (Tc)
Grass sheetflow Tc = 8 mins
Paved shallow concentrated Tc = 2 min
Total Tc = 10 mins
Corresponding intensity = 6.8”/hr for 100‐yr storm
Q = CiA = 0.67*6.8*6 = 27.5 cfs
Figure from Andy Reese, AMEC

Rational Method Quandary
Site is 6 acres
2 acres grass (C = 0.12) that flow onto:
4 acres paved (C = 0.95)
Only consider paved area
Tc
Paved shallow concentrated Tc = 2 min (use 5‐min intensity)
Corresponding intensity = 8.5”/hr for 100‐yr storm
Q = CiA = 0.95*8.5*4 = 32.3 cfs
Why the flow increase?
Tough to determine C for complex watersheds
Many communities put a cap on Rational Method area
Figure from Andy Reese, AMEC

Conceptual Hydrologic Models
Explain driving processes like infiltration and runoff
to some extent
Several inputs may be lumped into non‐measurable
factors that replicate processes like infiltration
Many of the processes are still based on regression
equations

Conceptual Hydrologic Models: SCS
More sophisticated than the Rational method
Considers:
Rainfall distribution
Initial rainfall losses
Land use (CN) – not a directly measurable parameter
Time of concentration (Tc)
Provides peak flows as well as:
Total infiltration and runoff volumes
Outflow hydrographs
However, several aspects of the model are still based
on regression analysis and don’t explain the
underlying processes.

Physical Hydrologic Models
Model the actual physical processes that drive the
water cycle
Have large data requirements
Should be calibrated to some extent
Examples
SWMM
InfoWorks
Mike SHE

Physical Hydrologic Models: SWMM
Has hydrologic, hydraulic and water quality modules
Allows for choice of several physical hydrologic
methods

Spatial and Time Scales
Level of detail should be based on your
objectives:
You care about 2 acre watersheds and
pipe flow for your new subdivision
You don’t care about such fine detail for
the Mississippi River‐different processes
are important

Lumped vs. distributed models
Lumped:
Basin is divided into subbasins
The characteristics of each
subbasin are represented by a
weighted average
Distributed:
Watershed characteristics are
determined at each location
Large amounts of data required
Most data is satellite derived
Long run times

Design Event Models
Many design studies are driven using a single storm
event
The chosen event is often chosen based on a regulated
design storm with a specified probability of occurrence
(e.g. 2% probability storm)
Remember: a 2% probability storm does not mean a 2%
probability runoff
What happens between storms?
What about the regional water balance?
What about water quality?
Soil moisture conditions at the start of the storm must
be assumed

Continuous Stormwater Models
Are calibrated using a long‐term historical dataset
Rather than run a hypothetical 2% probability design
storm, run 50 years of data and perform a flood
frequency analysis on the output
Low flow conditions can be examined for water
quality
Land use impacts on water supply can be examined
for drought periods
The impact of soil moisture on runoff can be
realistically considered

Hydraulic Governing Equations
The St. Venant equations are used to model flow
Continuity
Momentum
Hydrologic models: continuity only
Hydraulic routing models: continuity and some form of
momentum
Some situations can be approximated well with simplifications
Some situations require more exacting analysis

Flood Routing Methods
Kinematic Wave
Gravity balances friction
Ignores tailwater
Flow is uniform
Hydrograph is merely translated
Only for steep, well defined channels
Only for slowly rising floodwaters
Can use long time steps
Diffusion Wave
Adds attenuation
Allows for downstream boundary condition
Allows for moderately rising floodwaters
Dynamic Wave
Allows for convective and local acceleration
Handles looped networks
Requires short time steps

Overall Complexity
“Things should be made as simple as possible, but not any
simpler” ‐Albert Einstein
Modelling Costs
Modelling Error
Modelling Value
Model Complexity
Optimum Model Complexity
ComplexSimple

Making the most of your
modelling investment
So far, you have:
Defined your study objectives
Chosen a model that can analyze for your objectives
Set up the model to take best advantage of the available data
Run the model
Performed sensitivity and/or error and calibration analysis to
give an idea of the certainty your model can provide
Now, try to get as much useful information as possible
from the model you have worked so hard on

Water Quality
Expand your SWMM hydrology
and hydraulics model with water
quality parameters to account for
pollutants such as sediment
Model contaminant breakdown
using models like HSPF
Use your long‐term continuous
model to:
Examine what happens to
pollutants during low flows

Outlet Protection
Photo: Mary Halley
A random pile of gravel
does not make for good
outlet protection
Modelled outlet velocity
and tailwater conditions
can be used to design
proper outlet protection
given the local soils

Culvert Flushing
Photo: Greg Wilson
Use model to check that
culvert flow velocities are
high enough (>2.5 ft/s) to
flush culvert when flowing
partially full
Sediment traps and low‐
flow barrels can be used to
ensure flushing

Low Flow Channels
Typical stream crossing: improperly
sized culvert
New properly sized and
positioned culvert with
additional bankfull culvert to
allow stream to stay
connected to its floodplain at
times of bankfull and beyond
bankfull flow

Streambank Erosion
Photo: Mary Halley
Use model to check that
natural streams will be
kept in equilibrium (e.g. no
net erosion or deposition)
Requires knowledge of soils
Shear stress method
Table method
Geomorphologic method

Stream Erosion vs. Deposition

Debris Blockage
Photo: Lee Gentry
Assume that a percentage
of any culvert will be
blocked by debris
Check for flooding effects

Inlet Capacity
Simply sizing a pipe to
carry flow is not enough
Inlets are more often than
not the limiting factor
FHWA publication HY‐22
FHWA or other curves can
be used in a dual‐drainage
model to correctly model
overland flow

Design Information (Input) MINOR MAJOR
Type of Inlet Type =
Local Depression (additional to continuous gutter depression 'a' from 'Q-Allow') aLOCAL = 1.0 1.0 inches
Total Number of Units in the Inlet (Grate or Curb Opening) No = 1 1
Length of a Single Unit Inlet (Grate or Curb Opening) Lo = 6.00 6.00 ft
Width of a Unit Grate (cannot be greater than W from Q-Allow) Wo = N/A N/A ft
Clogging Factor for a Single Unit Grate (typical min. value = 0.5) Cf-G = N/A N/A
Clogging Factor for a Single Unit Curb Opening (typical min. value = 0.1) Cf-C = 0.10 0.10
Denver No. 14 Curb Opening
H-Vert
H-Curb
W
Lo (C)
Lo (G)
Wo
WP
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Q for 1/2 Street (cfs)
QIntercepted&Bypassed(cfs),FlowSpreadT&T-Crown(ft),FlowDepth(inches)
QIntercepted(cfs) QBypassed(cfs) SpreadT (ft),Limited
byT-CROWN
SpreadT (ft),Not Limitedby
T-CROWN
FlowDepthd(inches)
Gutter Geometry (Enter data in the blue cells)
Maximum Allowable Width for Spread Behind Curb TBACK = 5.0 ft
Side Slope Behind Curb (leave blank for no conveyance credit behind curb) SBACK = 0.1000 ft. vert. / ft. horiz
Manning's Roughness Behind Curb nBACK = 0.1000
Height of Curb at Gutter Flow Line HCURB = 6.00 inches
Distance from Curb Face to Street Crown TCROWN = 13.0 ft
Gutter Depression a = 1.64 inches
Gutter Width W = 1.50 ft
Street Transverse Slope SX = 0.0200 ft. vert. / ft. horiz
Street Longitudinal Slope - Enter 0 for sump condition SO = 0.0300 ft. vert. / ft. horiz
Manning's Roughness for Street Section nSTREET = 0.0150
Minor Storm Major Storm
Max. Allowable Water Spread for Minor & Major Storm TMAX = 5.0 10.0 ft
Max. Allowable Depth at Gutter Flow Line for Minor & Major Storm dMAX = inches
Allow Flow Depth at Street Crown (leave blank for no) X = yes
H
y
d xS
S wa
S treet
C row n
W
T , T .
Tx
Q xwQ
T .C R O W N
C U R B
SBA C K
T .B AC K
M AX
Minor Storm Major Storm
Max. Allowable Gutter Capacity Based on Minimum of QT or Qd Qallow = 1.5 5.5 cfs
Inlet Capacity

Modelling Concepts

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