The Science of Water Transport and Floods from Theory to Relevant Applications
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This is the presentation given by Riccardo Mantilla at Univerisity of Illinois and about the System for forecasting floods in Iowa.
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The Science of Water Transport and Floods from Theory to Relevant Applications
- 6. DIVISION VI Sec. 15. NEW SECTION. 466C.1 IOWA FLOOD CENTER. 1. The state board of regents shall establish and maintain in Iowa City as a part of the state university of Iowa an Iowa flood center. In conducting the activities of this chapter, the center shall work cooperatively with the department of natural resources, the department of agriculture and land stewardship, the water resources coordinating council, and other state and federal agencies. 2. The Iowa flood center shall have all of the following purposes: a. To develop hydrologic models for physically based flood frequency estimation and real-time forecasting of floods, including hydraulic models of flood plain inundation mapping. b. To establish community-based programs to improve flood monitoring and prediction along Iowa's major waterways and to support ongoing flood research. c. To share resources and expertise of the Iowa flood center. d. To assist in the development of a workforce in the state knowledgeable regarding flood research, prediction, and mitigation strategies.
- 7. • Historical observa/ons of streamflow are needed to calibrate support models for future streamflow forecasts • There is a human forecaster in the loop • Forecasts are issued every 6 hours at loca/ons above ac/on levels CALIBRATION VALIDATION State of the art of flood forecas/ng (Na/onal Weather Service)
- 13. Explicit representa/on of water movement by solving flow transport equa/on at the hillslope-link scale Hillslope-Link Par//oning + Mass and Momentum conserva/ons for each control volume A full model for Iowa would par//on the state into over 3 million individual control volumes (i.e. 15 million ODEs) NSF - CMG Research: On the Quest for Power Laws in Floods: Developing Numerical and Analy/cal Tools, 2010 ($705,320) – A collabora/on with the UI Math Department.
- 16. Transforma/on of a uniform 6 hour uniform intensity (6 mm/hr) rainfall event using different configura/ons* of the ODE system *configura/on refers to a different mathema/cal expression to represent flux-storage rela/ons or a different parameter set dsp dt = p(t)− qpc − qps dss dt = qps − qsc
- 17. Transforma/on of a uniform 6 hour uniform intensity (6 mm/hr) rainfall event using different configura/ons* of the ODE system *configura/on refers to a different mathema/cal expression to represent flux-storage rela/ons or a different parameter set qpc = k2sp qps = kI sp qsc = k3ss Linear Model
- 18. Transforma/on of a uniform 6 hour uniform intensity (6 mm/hr) rainfall event using different configura/ons* of the ODE system *configura/on refers to a different mathema/cal expression to represent flux-storage rela/ons or a different parameter set qpc = k2 sin2 (ω •sp ) qps = kI sp qsc = k3 exp α •ss( )−1( ) Complex Model
- 26. What are the insights? Simple and complex models can have similar capabili/es to predict peak flows, /me to peak, hydrograph /ming. But… Which one is right? Which model provides a more accurate representa/on of flows in the landscape, for example, did most of the runoff entered the channel as subsurface or surface runoff? The answer has important implica/ons for sediment transport, water quality, and ecological models, etc. And more importantly… Why? What makes two models “equivalent”?
- 27. Consider the output of one of the complex model simula/ons ω = 1000, α = 1000 represen/ng water /me of arrival to channel and fit of a log-normal distribu/on with the same moments Best Fit of a log-normal to blue line dsp dt = p(t)− qpl − qpu dss dt = qpu − qsl qpl = k2 sin2 (ω •sp ) qpu = kI sp qsl = k3 exp α •ss( )−1( )
- 28. Hydrographs at the outlet match (5% error) at outlet Error = 1 T h1(t)−h2 (t) h1(t) " # $ % & ' 2 0 T ∫ dt Area = 16875 km2 Area = 0.47 km2
- 29. α = 1000 ω = 1000 ω = 700 ω = 300 ω = 100 Error = 5.7% Error = 5.9% Error = 5.8% Error = 8.3%
- 30. ω = 1000 ω = 700 ω = 300 ω = 100 Error = 22.0% Error = 22.3% Error = 22.8% Error = 20.9% α = 100
- 31. α ω γODE −γLog-Normal γ = E t −µt σt " # $ % & ' 3( ) * * + , - -
- 34. • Preserve the river network structure as it exists on the landscape. • Aggrega/on and asenua/on of flows (in the real system) are equivalent to an averaging process in space. • Superposi/on of signals smoothens out streamflow response at larger scales • Unbiased errors in total volume of rainfall, loca/on and /ming of storms are averaged out by the averaging in the river network. • Unbiased runoff par//on (runoff coefficient) • Then, just follow the water
- 39. Mass Conserva/on Equa/ons Fluxes between control volumes dsp dt = RC *P t( )− qpc −ep dss dt = 1− RC( )*P t( )− qsc −es qpc = k2sp and qsc = k3sp Channel Rou/ng dqc dt = voqc λ1 Aλ1 1− λ1( )l qpc + psc − qc + qu u∈c ∑ $ % & ' ( )
- 40. Mass Conserva/on Equa/ons Fluxes between control volumes dsp dt = P t( )− qpl − qpc −ep dsl dt = qpl − qls −el dss dt = qls − qsc −es qpc = k2sp and qpl = klsp qls = kisl and qsc = k3ss kl = 99 1− sl Sl " # $ % & ' 3 k2 and ki = ρk2 Channel Rou/ng dqc dt = voqc λ1 Aλ1 1− λ1( )l qpc + psc − qc + qu u∈c ∑ $ % & ' ( )
- 54. 0:0012:00 0:00 12:00 18:00 6:00 0:00 12:00 Discharge/MeanAnnualFlood Precipitation(mm/ hr) Date Sloan, Man/lla and Basu (2015) Hydrologic Impacts of Subsurface Drainage at the Field Scale: Climate, Landscape and Anthropogenic Controls, Agricultural Water Management. (In press). Sloan, Man/lla and Basu (2015) Hydrologic Impacts of Subsurface Drainage at the Watershed Scale: Climate, Landscape and Anthropogenic Controls, Agricultural Water Management. (submised).
- 55. • Historical observa/ons of streamflow are needed to calibrate support models for future streamflow forecasts • There is a human forecaster in the loop (forecasted are revised and corrected) • Forecasts are issued every 6 hours at at most 165 loca/ons if above ac/on levels (*need rainfall forecast) CALIBRATION VALIDATION Let’s recall State of the art of flood forecast
- 56. • Validated model structure is fed with real-/me rainfall es/mates (QPE) • No human forecaster in the loop (no rainfall forecast necessary) • Forecasts are issued every 15 minutes for all communi/es in Iowa • So how does this work… Let’s consider the hydrograph predicted for Clear Creek at Coralville Rapid Refresh Flood Forecasts vs. Forecasted Rain Based Forecasts Time in hours Precipita/on Streamflow Minor Flood Level Old Forecast New Forecast Major Flood Level