Residence Time from a Hydrodynamics View Point

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Residence Time from a Hydrodynamics View Point
Edwin (Todd) Cowen Alexandra (Allie)
King Francisco Rueda Nami Tanaka
National Science Foundation Biocomplexity in the
Environment Program Grant number OCE-0083625
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External Forcing Scenarios

• Barotropic forcing from tributaries through
  embayments to LO
• Barotropic forcing from LO to embayments
• Barotropic forcing from embayments to LO
• Baroclinic exchange flow between embayments and LO

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Lake Ontario
Little Sodus Bay
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Residence Time Distributions
Residence time distribution r(t) Q(t)C(t)/V0
May 2002
r(t) (days -1)
t (days since dye release)
Fall 2003
r(t) (days -1)
t (days since dye release)
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Residence Time Distributions are NOT Complete
Only 65 of the dye leaves the pond during our
observations.
May 2002
r(t) (days -1)
t (days since dye release)
Only 61 of the dye leaves the pond during our
observations!
Fall 2003
r(t) (days -1)
t (days since dye release)
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Standard Practice is to Extrapolate the RTD Using
an Exponential Tail
May 2002
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Standard Practice is to Extrapolate the RTD Using
an Exponential Tail
May 2002
Even with the exponential tail, only 66 of the
dye leaves the pond just 1 more than if we
hadnt extrapolated at all!
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How to Extrapolate the May 2002 RTD AND
Understand the Physics?

• 1D Dead-Zone Model
• Originally developed for river modeling in the
  1970s.
• Further developed for wetlands by Andradóttir and
  Nepf (2000).

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1D Dead-Zone Model
Divide Sterling Pond into two zones
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1D Dead-Zone Model

• Divide Sterling Pond into two zones
• Advective Channel
• Length L
• Average cross-sectional area Ac
• Average velocity u and corresponding flow rate Q
  uAc
• Longitudinal dispersion Kx? uh

L
Kx? uh
Ac
QuAc
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1D Dead-Zone Model

• Divide Sterling Pond into two zones
• Advective Channel
• Length L
• Average cross-sectional area Ac
• Average velocity u and corresponding flow rate Q
  uAc
• Longitudinal dispersion Kx? uh
• Stationary Dead Zone
• Average cross-sectional area Ad
• No through-flow (u0)
• Rate of volumetric exchange ?Q between dead zone
  and channel assumed proportional to Q

Ad
?Q?Q
L
Kx? uh
Ac
QuAc
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Results
Mean residence time of 0.88 days
best-fit dead-zone model
May 2002
100 of the dye leaves the pond with the
dead-zone model solution
exponential tail
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Macrophytes Change Things Sort of
May, 2002

• Very strong inflow from Sterling Creek (22
  m3/s).
• Negligible forcing from Lake Ontario.
• Low macrophyte density (40 g/m2).

Fall 2003

• Low inflow from Sterling Creek (2 m3/s).
• Strong barotropic forcing from Lake Ontario
  during Hurricane Isabel.
• Weak upwelling of Lake Ontario followed the
  hurricane.
• Extremely dense macrophytes (190 g/m2)

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Spatio-temporal changes in RT are significant!
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More upwelling events lower flushing times
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Upwelling Driven Exchange Appears to Correlate
with Secchi Disk Depth Reduction Nutrient Flux
Driven Biological Growth?
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Summary range of residence times
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Ongoing Work

• Transitioning to laboratory effort on the effects
  of heterogeneity in macrophyte coverage on
  momentum and mass transport
• Collaborating with Bob Johnson
• Interested in upwelling/event driven work
• Hairston/Bain groups?
• Interested in comparing other approaches at
  estimating residence/flushing times.
• Driscoll/Bain?
• Were hoping to be funded on the first bullet and
  if so can continue to think about the second.

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Center on Cayuga Lake for Education, Athletics,
Research (CCLEAR?)
Ground breaking February 2007 Assistant Professor
Civil Environmental Engineering Director,
DeFrees Hydraulics Laboratory