River Networks and Floods A Theory to Explain Extreme Flooding

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River Networks and FloodsA Theory to Explain
Extreme Flooding
Ricardo Mantilla Postdoctoral Research Associate
at IIHR-Hydroscience Engineering, University
of Iowa, Iowa City. IA. UI Public Policy
Centers Forkenbrock Series Living With Floods
From Science to Policy. March 11th 2009
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Outline

• Original motivation for developing a Geophysical
  Theory of Floods (The driving question).
• Major progress milestones
• The theory in action. Looking at the 2008
  Eastern Iowa Floods.
• Future work

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Power Laws Q? vs A
One of the most prominent features in Flood Data
is the power-law relation between Flood Quantiles
and Basin Area
Power-Laws form the basis for the technique that
USGS uses to estimate Flood Quantiles in
ungauged/unregulated river basins. It is the
state-of-the-art methodology to determine flood
risk.
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Power Laws Q? vs A
Collection of Formulas found in USGS National
Flood Frequency program http//water.usgs.gov/soft
ware/NFF/
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Power Laws Q? vs A
Are regional flood quantile formulas appropriate
to predict future flood risk?
Q? ? A?
100-year flood for rural streams in Iowa Region 2
(Eash et al. 2001).
Land-Cover? Local Climate? Geology? Local Weather?
Power laws emerge from scale invariant physical
phenomena (Gupta and Dawdy, 1995). What is scale
invariant in the physics of flood generation?
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Theoretical Results
Gupta et al, J. Hydrol., 1996

• Results
• Width Function Maxima Scaling gt Flood Scaling
• Flood Scaling exponent q log3/log40.792

• Questions
• Do results on idealized river networks extend to
  realistic river networks observed in nature?
• 2. Is scaling of peak flows observed for
  individual rainfall-runoff events (from
  individual storms)?

• Simplest type of routing All water moves out
  of the link in Dt.

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Self-similarity in River Networks
Natural River networks are highly heterogeneous
and yet highly organized. Topologic connectivity
exhibits statistical self-similarity (or scale
invariance).
Consider the river network of Whitewaters basin
in Kansas
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Extending to Real Networks
Hillslope-Link Partitioning Mass and Momentum
conservations for each unit
For example, the Cedar River Basin at Cedar
Rapids is a 16,878 km2 basin. It needs to be
decomposed in 170,000 individual control
volumes, interconnected by the river network
giving rise to at least 300,000 nonlinear
ordinary differential equations (ODEs).
See http//cires.colorado.edu/ricardo/cuencas/cue
ncas-google-earth.htm for a description of the
hillslope-link decomposition concept.
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Extending to Real Networks
Hillslope-Link Partitioning Mass and Momentum
conservations for each unit
For example, the Cedar River Basin at Cedar
Rapids is a 16,878 km2 basin. It needs to be
decomposed in 170,000 individual control
volumes, interconnected by the river network
giving rise to at least 300,000 nonlinear
ordinary differential equations (ODEs).
See http//cires.colorado.edu/ricardo/cuencas/cue
ncas-google-earth.htm for a description of the
hillslope-link decomposition concept.
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Extending to Real Networks
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The Floods of 2008 in Eastern Iowa
Estimated Return Intervals
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Flood Severity
Iowa River at Iowa City Basin
Cedar River at Cedar Rapids Basin
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June Rainstorms
IEM, 2008. Iowa Environmental Mesonet. Iowa
State University Department of Agronomy. Ames,
IA. lthttp//mesonet.agron.iastate.edu/gt
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Flood Severity
A different look at data. Peak Flow value as a
function of upstream area
Blue dots correspond to 2008 Floods and Red dots
correspond to annual averages
Power-laws emerge in individual rainfall-runoff
events as a consequence of aggregation vs.
attenuation of flows along a self-similar river
network.
See Mantilla et al. (2006) Role of coupled flow
dynamics and real network structures on Hortonian
scaling of peak flows. Journal of Hydrology vol.
322 (1-4) pp. 155-167 Gupta et al. (2007)
Towards a Nonlinear Geophysical Theory of Floods
in River Networks An Overview of 20 Years of
Progress. Nonlinear Dynamics in Geosciences pp.
121-151
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Average Travel Times in River Network
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Radar Derived Rainfall Products from Hydro-NEXRAD
(Krajewski 2008) Use Google Earth to Explore the
Flood Data http//cires.colorado.edu/ricardo/cu
encas/GoogleEarthLayers/Iowa.kmz
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Theory Guiding Model Construction
A better understanding of primary factors
involved in flood formation allow us to respond
to important questions about future flooding risk
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Challenges Ahead
How do power-laws in individual events connect to
power-laws in flood quantiles?
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Flood Frequencies and Climate
Regional Variability of Exponent ?
Regional Variability of mean P - E
mm
-
As we build our Bottom-Up understanding
connecting physical mechanisms to scaling of
events, we are investigating Top-Down signals
in variability of annual statistics from region
to region.
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Conclusions and Future Work

• Scale invariance in Topology and transport in the
  river network gives rise to scaling in individual
  events
• Physics of flood generation can be connected to
  power law parameters in individual events
• How do power laws in events relate to power laws
  in flood quantiles?
• Understanding region-to-region variation of power
  law parameters can provide links to physics of
  flood generation.
• Iowa floods can be explained by the space-time
  arrangement of storms in relation with the river
  network
• There is a need to move beyond the statistical
  measures of flood risk (100-year flood or
  500-year flood is not a debate for hydrologists).

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Thank you!
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Effect on Streamflow
IEM, 2008. Iowa Environmental Mesonet. Iowa
State University Department of Agronomy. Ames,
IA. lthttp//mesonet.agron.iastate.edu/gt
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Spring Rainstorms
IEM, 2008. Iowa Environmental Mesonet. Iowa
State University Department of Agronomy. Ames,
IA. lthttp//mesonet.agron.iastate.edu/gt
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Empirical Annual IDF-Curve for Iowa
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Soil Moisture Ames, IA