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Modelling Concepts


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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.

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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  • 1. Models Matter Choice and use of modern stormwater  models
  • 2. Get out your superglue! Image: Enviroscape® classroom kit
  • 3. A topic only an engineer could love
  • 4. 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?
  • 5. What do you want to know? Figure: USGS
  • 6. 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
  • 7. Why model? To keep brilliant consultants in jobs To meet your objectives 
  • 8. 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?
  • 9. Inputs Most typical is rainfall Baseflow/dry weather flow Snowmelt Existing watershed condition Temperature Humidity Wind Sun
  • 10. Responses Infiltration over time Groundwater recharge Runoff over time Flowrate Flow depth Flow velocity
  • 11. 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?
  • 12. Deficit Level Exceedance Level Time Flooded Time Flooded Time w/out water Example River Level Objectives
  • 13. 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
  • 14. 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
  • 15. 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
  • 16. 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
  • 17. 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
  • 18. 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
  • 19. 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?
  • 20. 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
  • 21. Sensitivity Example 100 % Parameter Change %ResultChange 0 100 -100 -100 = mild positive sensitivity = negligible sensitivity = strong negative sensitivity
  • 22. 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
  • 23. Figure: William James, Computational Hydraulics International Calibration Example
  • 24. 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
  • 25. 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?
  • 26. What is your schedule and budget? Consider the cost of making a wrong decision A perfect model a year late is useless
  • 27. Do you need a model? Long term gauge data is preferred, but doesn’t exist many places Image: USACE EM 1110-2-1415
  • 28. OK: you have defined objectives you know you need a model Now what?
  • 29. Model Selection and Proper Application
  • 30. 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
  • 31. 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
  • 32. 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
  • 33. 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
  • 34. 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
  • 35. 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
  • 36. 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
  • 37. Rational Method Example
  • 38. 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
  • 39. 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
  • 40. 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
  • 41. 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.
  • 42. SCS Method Example
  • 43. 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
  • 44. Physical Hydrologic Models: SWMM Has hydrologic, hydraulic and water quality modules Allows for choice of several physical hydrologic  methods
  • 45. SWMM Examples
  • 46. 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
  • 47. 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
  • 48. Necessity of Fieldwork
  • 49. 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
  • 50. 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
  • 51. 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
  • 52. 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
  • 53. Routing Method Choice
  • 54. 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
  • 55. 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
  • 56. 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
  • 57. 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
  • 58. 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
  • 59. 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
  • 60. 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
  • 61. Stream Erosion vs. Deposition
  • 62. Debris Blockage Photo: Lee Gentry Assume that a percentage  of any culvert will be  blocked by debris Check for flooding effects
  • 63. 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
  • 64. 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