The influence of Runoff on Recharge

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The influence of Runoff on Recharge

• Keith Beven
• Lancaster University, UK

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The problem of recharge estimation

• Overall water balance constraint
• recharge rainfall evapotranspiration runoff
  
• ( runoff recharge)
• But.Not easy to estimate surface and
  near-surface runoff
• Not easy to estimate evapotranspiration where
  non-homogeneous surfaces
• Not easy to estimate recharge from soil moisture
  characteristics (gradients may be near unity at
  depth but predicted recharge will depend heavily
  on estimate of hydraulic conductivity)
• May be significant short term dynamic recharge
  events due to preferential flows associated with
  a small number of storms in a year at same time
  as runoff

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Horton Macropores and infiltration
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Infiltration into real soils (after Flury et
al., WRR, 1994)
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The problem of recharge estimation

• Traditional split between surface and groundwater
  hydrologists
• Surface water hydrologists calibrate on stream
  discharges as the flow constraint (and have
  tended not to worry too much about spatial
  patterns)
• Groundwater hydrologists calibrate on patterns of
  water table measurements (often averaged to
  steady conditions) with (uncertain) estimates
  of recharge as a flow constraint
• Distributed catchment models have integrated both
  but effects are not easily separated out, there
  are multiple sources of uncertainty, constraints
  are limited, and calibration is difficult.

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A paradox

• Generally, the more physical understanding that
  is built into a model, the more parameter values
  must be specified to run the model
• The more parameter values that cannot be
  estimated precisely, the more degrees of freedom
  that will be available in fitting the
  observations (we cannot measure effective
  parameter values everywhere).
• Therefore the more physical understanding that is
  built into a model, the greater the problem of
  equifinality is likely to be.
• A perfect model with unknown parameters is no
  protection against equifinality

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Binley and Beven, Groundwater, 2003 Application
of GLUE based on SSQ criterion Dotty plot for
parameter qr in layer 4
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Equifinality and the Modelling Process

• Take a (thoughtful) sample of all possible models
  (structures parameter sets)
• Evaluate those models in terms of both
  understanding and observations in a particular
  application
• Reject those models that are non-behavioural
  (but note that there may be a scale problem in
  comparing model predictions and observations)
• Devise testable hypotheses to allow further
  models to be rejected
• If all models rejected, revise model
  structures

This is the essence of the GLUE methodology
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Deconstructing total model error

• Extended GLUE methodology
• insist on model providing predictions within
  range of effective observation error of
  evaluation variables
• specify an effective observation error to take
  account of scale dependencies and
  incommensurability
• models providing predictions outside range are
  rejected as non-behavioural (all models may be
  rejected)
• success may depend on allowing realisations of
  error in input and boundary condition data

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Example Application Modelling Recharge to the
Sherwood Sandstone (with Andrew Binley)

• Large scale estimates of change in water contents
  over time using cross-borehole electrical
  resistance and radar tomographic imaging
• What are the scale dependent effective parameters
  if recharge is to be predicted by a 1-D Richards
  equation model when potential gradients vary due
  to heterogeneity?
• Conditioning on observations based on GLUE Monte
  Carlo methodology and model rejection when
  outside the range of effective observational
  error

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Field site location
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Cross Borehole Radar Profiling - Zero Offset
Profile (ZOP)
Transmitter Antenna
Transmitter Antenna
Receiver Antenna
Time of first arrival measured (t ) allows
calculation of effective relative dielectric
constant between wells separated distance x
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Monte Carlo Simulations
1-D Richards Equation solution with following
parameters treated as uncertain for 4 layers in
the UZ zone (to 15m) qr - residual moisture
content qs - saturated moisture content a and n -
van Genuchten curve parameters Ks - saturated
hydraulic conductivity
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Weighting realisations in GLUE using effective
observation error
Output from each realisation compared with
observed moisture content profile, taking into
account uncertainty in measurement
Goodness of fit
Goodness of fit
Likelihood
q
qmax
qmin
q
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Weighting realisations in GLUE using effective
observation error
5 95 uncertainty limits
Best estimate of q
Upper and lower limits of q
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Dotty plots show behavioural parameter sets
parameter range
Goodness of fit
Goodness of fit
qr
qs
Goodness of fit
Goodness of fit
Ks
a
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Estimate of travel times through sandstone
using uncertainty in model predictions
Weighted behavioural simulations consistent with
effective observational error but remember
assumptions of the analysis
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The Importance of Spatial Patterns
Surface hydrologists have recognized the
importance of spatial patterns of runoff
generation, particularly as driven by topography
(e.g. TOPMODEL, SHE, InHM, POWER, ) But
numerical experiments suggest that even small
rates of recharge to deeper layers can
dramatically influence patterns of wetness
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The Importance of Spatial Patterns
Spatial patterns of evapotranspiration will also
influence net recharge

• Use of remote sensing energy balance closure
  to estimate patterns of land surface to
  atmosphere fluxes
• Greater ET fluxes in valley bottoms
• But is there also greater recharge in valley
  bottoms?

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The Importance of Spatial Patterns
Recharge by river bed infiltration

• LOCAR catchments pattern of gaining and
  losing reaches
• Flood plains as subsurface recharge as well as
  surface water storage areas during periods of
  overbank flow where floods generated by upstream
  rainfall

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Summary

• Spatial patterns are important
• In infiltration, surface and subsurface runoff
  generation, and reinfiltration
• In evapotranspiration
• In river bed recharge
• Data are not adequate to properly calibrate
  models there are too many sources of
  uncertainty, including inputs and representation
  of processes
• Complex models may not necessarily give more
  robust predictions than simple models
• Thus, prediction of change under future
  conditions will be even more uncertain, and it
  might be dangerous to rely on deterministic
  predictions

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and if you might possibly still want to read
more...

• Binley, A and Beven, K J, 2003, Vadose zone model
  uncertainty as conditioned on geophysical data,
  Ground Water, 41(2), 119-127.
• Schulz, K., and Beven, K., 2003. Data-supported
  robust parameterisations in land surface -
  atmosphere flux predictions towards a top-down
  approach, Hydrol. Process., 17, 2259-2277.
• Beven, K. J., 2002, Towards a coherent philosophy
  for environmental modelling, Proc. Roy. Soc.
  Lond., A458, 2465-2484 (comment by Philippe
  Baveye and reply still to appear)
• Beven, K J, 2004, A manifesto for the
  equifinality thesis, J. Hydrology , in press