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I gave this talk at a stormwater conference to help people think through some of the reasons for modelling, and how to get the most from their modelling efforts.
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Models MatterChoice 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) downstreamSize my new culvert to ensure that it doesn’t overtopGuide my city’s development to ensure that our streams are not impairedSet our new water intake to ensure that it doesn’t go dryRestore my city’s stream to provide good fishing habitatDo the bare minimum to meet those @#$!@# regulations
Why model?
To keep brilliant consultants in jobs
To meet your objectives
How does a model work?
InputsWhat causes the process?
ResponsesHow does the system respond?
ObjectivesWhat important effects occur?
ErrorHow reliable are my results?
InputsMost typical is rainfallBaseflow/dry weather flowSnowmeltExisting watershed conditionTemperatureHumidityWindSun
ResponsesInfiltration over timeGroundwater rechargeRunoff over timeFlowrateFlow depthFlow velocity
ObjectivesMaximum 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 valuesNumber 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
ErrorHow closely does your model mirror reality?
Error AnalysisHow do your assumptions affect your results?
Sensitivity AnalysisCan you optimize your assumptions to reduce error?
Calibration
Define your objectivesMeet with your consultant
On site if possibleDon’t let him leave until he completely understands your objectives
Define how you will measure successBe clear and conciseWrite 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 moneyIs 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
FEMACorps of EngineersCity engineer
Where do you want to focus?
Be clear about where the critical locations areNon‐critical locations can be modelled more roughlyCritical 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 yearYou may have three 100‐yr storms in a yearEvent 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 playLong‐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 rowMore accurate to say “4%” chance stormA 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 watershedsCan 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 candidateKeep parameters within a reasonable rangeTypically done one at a timeLook at effects over a range of conditionsResults are “sensitive” to a parameter when a change in the parameter makes a large difference in the result
Measured parameters are typically not changedPipe diameterChannel length
Sensitivity Example
100 % Parameter Change
% R
esul
t Cha
nge
0
100
-100
-100
= mild positive sensitivity
= negligible sensitivity
= strong negative sensitivity
Calibration to Increase ConfidenceNeeded especially for physical modelsCompare modelled results with measured results and adjust for better fit using what was learned from sensitivity analysisDegree of fit can be measured using several statistical techniquesFormal calibration can be done with recorded rainfall and flow time seriesInformal 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 siteAt full build‐out per the city 20‐year planWith our 75‐year old culvert collapsed
What expertise is available?Some models require significantly more expertise to operate than othersDoes 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 decisionA 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 atmosphereMany 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 hydrodynamicsHydraulic parameters are typically easier to measure
Hydraulics
Image: Tarleton University Hydraulics Lab
Model selection criteriaAbility 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
RobustnessA robust model will perform well under a wide range of conditions and will remain stable under reasonable conditions
SimplicityModels 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 watershedsConceptual‐based on a conceptual understanding of watershed processesPhysical‐based on physical processes that can be tied directly to measured characteristics
Empirical Hydrologic ModelsDo not attempt to explain the driving processes, they simply transform an input into a result based on statistical analysis of previous resultsCan 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 onlyBe sure to choose the right regionUsually limited by drainage areaNote the prediction error
Empirical Hydrologic Models: Rational Method
Table: NOAA Atlas 14 for University of Tennessee Knoxville Monitoring Station
Q=CiAQ=flow (ac‐in/hr≈cfs)i = rainfall intensity for time of concentration (in/hr)A = area (acres)
Peak flows onlyBest for small urban watershedsCan lead to paradoxical results
Rational Method Example
Rational Method ExampleSite 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 minsPaved shallow concentrated Tc = 2 minTotal Tc = 10 minsCorresponding 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 QuandarySite is 6 acres
2 acres grass (C = 0.12) that flow onto:4 acres paved (C = 0.95)Only consider paved area
TcPaved 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 cfsWhy the flow increase?Tough to determine C for complex watershedsMany communities put a cap on Rational Method area
Figure from Andy Reese, AMEC
Conceptual Hydrologic ModelsExplain driving processes like infiltration and runoff to some extentSeveral inputs may be lumped into non‐measurable factors that replicate processes like infiltrationMany of the processes are still based on regression equations
Conceptual Hydrologic Models: SCSMore sophisticated than the Rational methodConsiders:
Rainfall distributionInitial rainfall lossesLand use (CN) – not a directly measurable parameterTime of concentration (Tc)
Provides peak flows as well as:Total infiltration and runoff volumesOutflow hydrographs
However, several aspects of the model are still based on regression analysis and don’t explain the underlying processes.
SCS Method Example
Physical Hydrologic ModelsModel the actual physical processes that drive the water cycleHave large data requirementsShould be calibrated to some extentExamples
SWMMInfoWorksMike SHE
Physical Hydrologic Models: SWMMHas hydrologic, hydraulic and water quality modulesAllows for choice of several physical hydrologic methods
SWMM Examples
Spatial and Time ScalesLevel of detail should be based on your objectives:
You care about 2 acre watersheds and pipe flow for your new subdivisionYou don’t care about such fine detail for the Mississippi River‐different processes are important
Lumped vs. distributed models
Lumped:Basin is divided into subbasinsThe characteristics of each subbasin are represented by a weighted average
Distributed:Watershed characteristics are determined at each locationLarge amounts of data requiredMost data is satellite derivedLong run times
Necessity of Fieldwork
Design Event ModelsMany design studies are driven using a single storm eventThe 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 runoffWhat 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 ModelsAre calibrated using a long‐term historical datasetRather than run a hypothetical 2% probability design storm, run 50 years of data and perform a flood frequency analysis on the outputLow flow conditions can be examined for water qualityLand use impacts on water supply can be examined for drought periodsThe impact of soil moisture on runoff can be realistically considered
Hydraulic Governing EquationsThe St. Venant equations are used to model flow
Continuity
Momentum
Hydrologic models: continuity onlyHydraulic routing models: continuity and some form of momentumSome situations can be approximated well with simplificationsSome situations require more exacting analysis
Flood Routing MethodsKinematic Wave
Gravity balances frictionIgnores tailwaterFlow is uniformHydrograph is merely translatedOnly for steep, well defined channelsOnly for slowly rising floodwatersCan use long time steps
Diffusion WaveAdds attenuationAllows for downstream boundary conditionAllows for moderately rising floodwaters
Dynamic WaveAllows for convective and local accelerationHandles looped networksRequires short time steps
Routing Method Choice
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 objectivesChosen a model that can analyze for your objectivesSet up the model to take best advantage of the available dataRun the modelPerformed 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 QualityExpand your SWMM hydrology and hydraulics model with water quality parameters to account for pollutants such as sedimentModel contaminant breakdown using models like HSPFUse 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 protectionModelled 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 fullSediment 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 soilsShear stress methodTable methodGeomorphologic method
Stream Erosion vs. Deposition
Debris Blockage
Photo: Lee Gentry
Assume that a percentage of any culvert will be blocked by debrisCheck for flooding effects
Inlet CapacitySimply sizing a pipe to carry flow is not enoughInlets are more often than not the limiting factorFHWA publication HY‐22FHWA 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-VertH-Curb
W
Lo (C)
Lo (G)
WoWP
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)
Q In
terc
epte
d &
Bypa
ssed
(cfs
), Fl
ow S
prea
d T
& T-
Crow
n (ft
), Fl
ow D
epth
(inc
hes)
Q Intercepted (cfs) Q Bypassed (cfs) Spread T (ft), Limited by T-CROWN
Spread T (ft), Not Limited by T-CROWN
Flow Depth d (inches)
Gutter Geometry (Enter data in the blue cells)Maximum Allowable Width for Spread Behind Curb TBACK = 5.0 ftSide Slope Behind Curb (leave blank for no conveyance credit behind curb) SBACK = 0.1000 ft. vert. / ft. horizManning's Roughness Behind Curb nBACK = 0.1000
Height of Curb at Gutter Flow Line HCURB = 6.00 inchesDistance from Curb Face to Street Crown TCROWN = 13.0 ftGutter Depression a = 1.64 inchesGutter Width W = 1.50 ftStreet Transverse Slope SX = 0.0200 ft. vert. / ft. horizStreet Longitudinal Slope - Enter 0 for sump condition SO = 0.0300 ft. vert. / ft. horizManning's Roughness for Street Section nSTREET = 0.0150
Minor Storm Major StormMax. Allowable Water Spread for Minor & Major Storm TMAX = 5.0 10.0 ftMax. Allowable Depth at Gutter Flow Line for Minor & Major Storm dMAX = inchesAllow Flow Depth at Street Crown (leave blank for no) X = yes
Hy
d xS
S wa
S tree t C row n
WT , T .
Tx
Q xwQ
T . C R O W N
C U R B
SBA C K
T .B A C KM AX
Minor Storm Major StormMax. Allowable Gutter Capacity Based on Minimum of QT or Qd Qallow = 1.5 5.5 cfs
Inlet Capacity