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Problems%20of%20Inference%20and%20Uncertainty%20Estimation%20in%20Hydrologic%20Modelling

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Title: Problems%20of%20Inference%20and%20Uncertainty%20Estimation%20in%20Hydrologic%20Modelling


1
Problems of Inference and Uncertainty Estimation
in Hydrologic Modelling
Peter Reichert Eawag Dübendorf and ETH Zürich
2
Contents
Motivation Errors in Hydro-logic
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  • Motivation
  • Errors and Uncertainties in Hydrologic Watershed
    Modelling
  • Suggested Problem Solutions
  • Working Group Opportunities

3
Motivation
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Motivation
4
Motivation
Practice of Environmental Modelling
Mechanistic, deterministic description of system
behaviour with a simple, additive, independent
(measurement) error model
Strong autocorrelation of residuals, if
temporal resolution of data is high. This severe
violation of statistical assumptions leads to
unreliable error estimates. The problem is
aggravating, as temporal resolution of data and
measurement accuracy are increasing.
Motivation Errors in Hydro-logic
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Motivation
Phytoplanktion biomass
Walensee
Examples (1) Aquatic ecosystemmodelling
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Zürichsee
Greifensee
Mieleitner et al. 2006
6
Motivation
Examples (2) Climate modelling
Motivation Errors in Hydro-logic
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Tomassini et al. 2006
7
Motivation
Examples (3) Hydrologicmodelling
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Yang et al. 2006
8
Motivation
Cause of the Problem and Challenges The cause
of this problem is not the inadequatemodel of
the measurement process, but the neglection of
input and model structure errors that are
propagated through the model and dominate
prediction uncertainty. Both input and model
structure errors lead to very similar pattern in
the residuals. The challenges are
Motivation Errors in Hydro-logic
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  • to find good statistical descriptions of the
    random contributions of both error sources,
  • to find procedures to support finding model
    structure improvements, and
  • to separate the two error contributions.

9
Motivation
Universality of the Problem This problem is
typical for nearly all fields of dynamic
modelling in the environmental sciences. The
causes and techniques for problem analysis can be
expected to be the same for different application
areas, despite application-field specific
interpretations and identified error models.
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Motivation
Hydrologic Modelling Watershed hydrologic
modelling is a particularly good study area for
these problems as
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  • Data at high temporal resolution are available.
  • Essentially the same problems occur with complex
    and very simple watershed models.(see next part
    of the talk for a justification of this
    statement.)

? It seems to be a reasonable strategy to analyse
the problem and test solutions with simple
watershed models and transfer the promising
solutions to the more complex case.
11
Errors in Hydrological Modelling
Motivation Errors in Hydro-logic
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Errors and Uncertainties in Hydrologic Watershed
Modelling
12
Errors and Uncertainties in Hydrologic Watershed
Modelling
Motivation Errors in Hydro-logic
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  • Overview of Hydrologic Processes
  • A Simple Hydrologic Watershed Model
  • More Complex Watershed Models
  • Sources of Error in Watershed Modelling

13
Errors in Hydrologic Modelling
  • Overview of Hydrologic Processes
  • The water balance in a watershed is affected by
  • rainfall,
  • runoff,
  • infiltration into the soil,
  • evapotranspiration,
  • transport through the soil (vertically and
    laterally),
  • transport to shallow ground water,
  • lateral transport in ground water,
  • transport to deep ground water,
  • exfiltration from soil and groundwater to surface
    water,
  • transport in surface water.

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Errors in Hydrologic Modelling
A Simple Hydrologic Watershed Model (1)
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Kuczera et al. 2006
15
Errors in Hydrologic Modelling
A Simple Hydrologic Watershed Model (2)
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Kuczera et al. 2006
16
Errors in Hydrologic Modelling
A Simple Hydrologic Watershed Model (3)
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Kuczera et al. 2006
17
Errors in Hydrologic Modelling
  • More Complex Watershed Models
  • Parameterization by soil properties (soil
    thickness, porosity, texture, conductivity,
    etc.).
  • Higher vertical resolution of soil profile
    (layers, continuous vertical resolution).
  • Higher horizontal resolution of watershed
    (accounting for variation in soil properties,
    land use, etc. within the watershed).

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More complex models (with a higher spatial
resolution) are primarily required for the
prediction of the effect of land use change, not
to improve the quality of the fit. These models
are usually highly overparameterized, but do
nevertheless not very much improve the fit.
18
Errors in Hydrologic Modelling
  • Sources of Error in Watershed Modelling
  • Input uncertaintyPoint measurements from rain
    gauges and potential evapo-transpiration
    measurements are extrapolated to the watershed
    area despite high local variation in rain
    intensity.
  • Model structure uncertainty
  • Many different storage systems in parallel are
    represented by an average storage or by storage
    systems parameterized using soil properties.
  • All storage systems within a sub-basin are
    subject to the same input.
  • Parameterization of storage function.
  • Output uncertaintyMeasurement error of stream
    flow (gauging curve and random error).

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Errors in Hydrologic Modelling
  • Difference Simple vs. Complex Models
  • As simple and complex models usually use the same
    input, they face the same problems outlined
    above.
  • Only the use of higher (spatial) resolution in
    input could reduce some of these problems, not
    increase in model complexity (which was
    introduced for other reasons).
  • It is a trend in real-time hydrologic modelling
    to do this with the aid of radar data. But still
    most of the hydrologic modelling studies must be
    based on rain gauge data.

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Errors in Hydrologic Modelling
  • Results for Simple Error Model
  • When using an independent error model the result
    will usually be a small prediction uncertainty
    for the mean and a large standard deviation of
    the error term.
  • The resiudals will show strong deviations from
    the indepencence assumption.

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Suggested Problem Solutions
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Suggested Problem Solutions
22
Suggested Problem Solutions
  • Suggested Problem Solutions
  • Ad-hoc ApproachesApproaches based on
    increasing parameter uncertainty.(GLUE, SUFI,
    SUNGLASSES, etc.)
  • Improvement of Output Error ModelAutoregressive
    output error models.
  • Input and Model Structure Error Models
  • Storm multipliers.
  • Bayesian model averaging.
  • Use of a stochastic hydrological model.
  • Stochastic, time-dependent parameters.
  • Multi-criteria optimization.

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Suggested Problem Solutions
1. Ad-hoc Approaches Approaches such as GLUE,
SUFI, SUNGLASSES, etc. increase parameter
uncertainty to cover most of the observations
with a prediction uncertainty band. This is
either done by introducing a generalized
likelihood function, the values of which are
normalized and then interpreted as probabilities
or by ad-hoc selection of parameter subsets
that lead to an adequate coverage of
observations. Despite the poor statistical
foundation, such techniques are quite popular in
hydrology. ? This is not the approach I would
like to follow in the working group.
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Suggested Problem Solutions
2. Improvement of Output Error Model Use of an
autoregressive error model instead of the
independent error model. This approach is quite
successful in the fulfilment of statistical
assumptions (see example). However, it describes
only the effect and not the cause of the errors
and may lead to statistical description of
physical phenomena (description of recession
curves from storages by the auto-regressive
error model). ? This is a nice intermediate step,
but the effort must be on a description of the
actual error sources.
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Suggested Problem Solutions
2. Improvement of Output Error Model (Example)
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residuals, no transformation
residuals, Box-Cox transf.
residuals, Box-Cox tr., var. sd.
innovations, Box-Cox tr., var. sd.var. corr.
time
Yang et al. 2006
26
Suggested Problem Solutions
2. Improvement of Output Error Model (Example)
residuals, no transformation
residuals, Box-Cox transf.
Auto-correlation
Motivation Errors in Hydro-logic
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residuals, Box-Cox tr., var. sd.
innovations, Box-Cox tr., var. sd., var. corr.
time
Yang et al. 2006
27
Suggested Problem Solutions
  • 3. Input and Model Structure Error Model
  • Only recently better error models have been
    suggested. The essential elements are that
  • the high input uncertainty in total rainfall and
    potential evapotranspiration over the watershed
    must be considered explicitly,
  • a deterministic description is not adequate due
    to stochastic distribution of input over the
    watershed (the different storage systems),
  • model structure (systematic) errors must be
    distinguished from random errors.
  • ? It would be an interesting SAMSI activity to
    discuss how to best do this and compare results
    of different approaches.

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Working Group Opportunities
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Working Group Opportunities
29
Working Group Opportunities
  • Research Questions / Options for Projects (1)
  • Compare results when making different model
    parameters stochastic and time-dependent.
    (Ongoing with a postdoc in Switzerland extending
    earlier work with continuous-time stochastioc
    parameters.)
  • Develop a better statistical description of
    rainfall uncertainty.(Option for a collaboration
    with climate/weather working groups.)
  • Explore alternative options for making parameters
    time-dependent.(Suggestions so far
    storm-dependent parameters, time-dependent
    parameter as an Ornstein-Uhlenbeck process.)

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Working Group Opportunities
  • Research Questions / Options for Projects (2)
  • Investigate on how to learn from state estimation
    of stochastic hydrological models.(Can the
    pattern of state adaptations lead to insights of
    model structure deficits or input errors?)
  • Develop uncertainty estimates when using
    multi-objective optimization.(How to use
    information on Pareto set for uncertainty
    estimation of parameters and results?)
  • Analyse differences in results of suggested
    approaches when using different models.(Is there
    a generic behaviour of different techniques when
    they are applied to different models/data sets?)

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Working Group Opportunities
  • Research Questions / Options for Projects (3)
  • Improve the efficientcy of posterior maximisation
    and posterior sampling.(Efficiency becomes
    important when having complex watershed models in
    mind. Efficient global optimizers and sampling
    from multi-modal posterior distributions becomes
    then important.)
  • More questions will come up during discussions.

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Working Group Opportunities
  • Practical Considerations
  • State estimation of time-dependent OU-parameters
    as well as the simple hydrological model are
    implemented in the UNCSIM package by PR.This
    package also provides a simple interface to
    complex hydrological models.
  • Jasper Vrugt (LANL) can provide implementations
    of several simple hydrological models and
    analysis techniques in Matlab.
  • The simple hydrological models can also easily be
    implemented in any other computing environment.

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Working Group Opportunities
  • How to Proceed?
  • Initiate a reading group for discussing key
    papers and suggestions of how to attack the
    problems.This could be a separate working group
    or a subgroup of the methodology working group.
  • Discuss and prioritize (according to expected
    chance of success) the collection of
    suggestions developed under point 1 above.
  • Use preliminary results of project 1 to stimulte
    the discussions.
  • Decide on research plans for projects to work on.
  • Organise a workshop for discussing research plans
    and preliminary results with experts in the
    field.
  • Plan the group activities for the remaining part
    of the subprogram that lead to results to be
    published and presented at a closing workshop.

Motivation Errors in Hydro-logic
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34
Thank you for your attention
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