On the dialog between experimentalist and modeler in catchment hydrology

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On the dialog between experimentalist and modeler
in catchment hydrology
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• Jeff McDonnell
• Department of Forest Engineering
  Oregon State University

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How the experimentalist and modeler view the
rainfall runoff process
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The experimentalist
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has described a morass of process
complexity! has done little to whittle down
complexity or identify first order controls
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The modeler
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• has been guilty of a having a disparity between
  the scale of measurements and the scale of model
  sub-units.

http//hydrology.pnl.gov/forest.asp

• Or if a conceptual model, parameters
  represented are often not physically-based or
  related to physical properties, and therefore
  cannot be established prior to a model
  calibration.

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If the experimentalist was to build a model
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After much whittling down, this is my most
parsimonious model structure.
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If the modeler went into the field
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?????
as my subgrid scale parameterization
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Outline
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• Experimental evidence how complex is it?
• Some recent work on how to use process knowledge
  for model calibration
• Some new thoughts on residence time and how it
  might subsume much flowpath heterogeneity
• Residence time as a model state variable
• Residence time as a scalable value

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A note on my examples todaywhere P Q E
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Your AZ sites
My examples
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How complex is it?
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How complex is it?
Weiler and McDonnell, in prep
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How complex is it?
Freer et al., 2002 WRR
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How complex is it?
Tromp van Meerveld and McDonnell, 2004 WRR
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Hillslope to catchmentHow complex is it?
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McGlynn and McDonnell, 2003a WRR
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Hillslope to catchmentHow complex is it?
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McGlynn and McDonnell 2003b WRR
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Catchment to catchment How complex is it?
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Parshall Flumes
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Catchment to catchment How complex is it?
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Weiler and McDonnell, in prep
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This is the PUB problem
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Wagener et al., in press EOS
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Soft data
Evaluation rules
Experimentalist
Modeler
Values for evaluation rules (ai)
a2
a3
1
a4
a1
0
Degree of acceptability
Seibert and McDonnell, 2002 AGU Monograph
Seibert and McDonnell, 2002 WRR Freer et al.
2004 JoH
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Soft data
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Seibert and McDonnell, 2002 WRR
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Virtual Experiments
Weiler and McDonnell 2004 JoH
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A posteriori parameter rejection
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• A poorly gauged watershed in Chile
• An example of an additional criterion
• Percent new water in a storm hydrograph

Efficiency
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A posteriori parameter rejection

• Red dots new water gt 50
• Black dots new water lt 50
• Identifies parameter sets that produce the
  efficient results for the wrong reasons

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Efficiency
Vache et al., 2004 GRL
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New work in a new direction
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A case for water residence time
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What is residence time?
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remember from your shower this morning
Temperature (deg C)
Flow rate (L/s)
A very different type of information!
t1 residence time t2
Time (seconds)
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Residence time distributions in watersheds

• As an experimentalist, I concede that the
  subsurface is unknowable (with current meas.)
• - There are an infinite array of flowpaths

• The distribution quantifies the flowpath
  heterogeneity
• For models that link water quantity and water
  quality, flowpath reasonableness is key

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Mean residence time
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• Simply the mean of these distributions

x
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Some reported mean residence times
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• Small Experimental Watersheds
• Dischma Catchment, AU, 33 km2, 4.1 yr
• Pukemanga Catchment, NZ, 0.3 km2, 12 yr
• Panola, GA, 0.4 km2, 4.5 yr
• Rietholzbach, CH 3.5 km2, 1.1 yr
• Large River Basins
• Colorado R, UT, 75,000 km2, 14 yr
• Mississippi R., MN, 253,000 km2, 10 yr
• Neuse R., NC, 11,000 km2, 11, yr
• Sacramento R, CA, 277,000 km2, 10 yr

Sources Michel, 1992 Burns et al. 1999 McGlynn
et al., 2003 Vitvar et al., in press Stewart
and Mehlhorn, in press
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Why mean residence time is important?
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Burns et al., 2003 Groundwater
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How do we compute residence time?
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Tracers and Age Ranges
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• Environmental tracers
• added (injected) by natural processes, typically
  conservative (no losses, e.g., decay, sorption),
  or ideal (behaves exactly like traced material)

We will focus on this
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A quick stable isotope primer
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• Isotopes are atoms of the same element that have
  different numbers of neutrons.
• 18O and 2H are constituent part of natural water
  moleculesthey are the water molecule
• Applied naturally during precipitation events
• Conservative at ambient temperatures
• Only mixing can alter concentration

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The crazy parts per mil nomenclature
Ratio sample
Ratio standard
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Delta Isotope (i.e. d in o/oo )
x 1000
Ratio standard
Dont let this throw you off they could have
used ppm!
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18O Natures tracer
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Convolution Integral
Plummer et al., Chem. Geology 2001
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Convolution integral
Input Function Derived from precipitation d18O
signal Represents d18O in water that contributes
to recharge
System Response Function Time distribution of
water flow paths
Predicted or simulated output d18O signature
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The rest of the talk in a nutshell
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A model proof- of-concept
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Maimai The simplest of our various experimental
watersheds
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Planar slope
hollow
3 ha catchment
17 ha catchment
Hillslope throughflow trench
Stream and riparian zones
Downstream
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The simplest of models to start
Grid-based, highly simplified with 3 tunable
parameters
The volume of water within each reservoir is
accounted for using the familiar continuity
equation
Vache et al., 2004 GRL
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Model output
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Nash Suttcliffe Efficiency 0.83
1750 runs, cutoff 0.75
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Tracer in the model
NATO ARW Moscow
Then defined as a mass balance of some arbitrary
conserved tracer
The mean residence time is derived by the
concentration breakthrough
i.e. time averaged C normalized by total mass of
the tracer
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Simulated tracer breakthrough
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Directly simulated MRT over the prior parameter
range varied from 30 to 95 days.
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the tradeoff between between high discharge
efficiency and more realistic MRT
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Spatial model output
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Soil water sampling for residence time computation
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Modeling residence time a lysimeter near the
divide
NATO ARW Moscow
MRT 13 days
Stewart and McDonnell, 1991 WRR
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MRT and distance from the divide
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Regionalized MRT to the entire basin based on a 2
meter elevation grid using a single direction D8
algorithm
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Model output from before
We reject this simple model
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Adding more model complexity Simulated values
incorporating soil depth
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MRT A scalable value?
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Residence time as a scalable parameter
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• Is residence time related to basin area?
• .a recent breakthrough weve had from the HJ
  Andrews (0.1 to 64 km2)

PhD work of Kevin McGuire at HJA
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Model Input Precipitation and d18O
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Model Simulations
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s0.13
s0.18
s0.27
s0.34
s0.11
s0.23
s0.14
McGuire et al. 2004 WRR
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Topographic Distributions
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Topographic Distributions
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McGuire et al. WRR in review
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Mean Residence Time and Topography Relationships
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McGuire et al. 2004 WRR
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MRT as a scalable value
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21 ha
6200 ha
500 m/y (1.6E-05 m/s)
581 ha
60 ha
101 ha
10 ha
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Conclusions 1
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• Hillslope processes are complex
• Highly threshold dependent, not steady state
• Networks dominate subsurface flux during events
• Residence time is something that can be
  quantified with data
• Residence time represents flowpath heterogeneity
  and makes sense across all scales
• Residence time probes a different axis in
  different information spaceit is non-redundant
• Our recent work in Oregon suggests that MRT
  scales with readily available terrain indices
• This may help to define the connection between
  the headwater catchments and their mesoscale
  basin.

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Conclusions 2
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• Residence time is a measurable observable that
  can be a good system constraint
• Provides a rationale for making the model more
  complex
• We are now exploring spatial variation in soil
  properties, explicit inclusion of an immobile
  domain, unsaturated zone coupling
• Perhaps we need to
• Move beyond the status quo where we go into the
  field, collect data, build a model and declare
  victory.
• Deal with the disparity between the scale of
  measurements and the scale of our physically
  based model sub-units.