Title: Problems%20of%20Inference%20and%20Uncertainty%20Estimation%20in%20Hydrologic%20Modelling
1Problems of Inference and Uncertainty Estimation
in Hydrologic Modelling
Peter Reichert Eawag Dübendorf and ETH Zürich
2Contents
Motivation Errors in Hydro-logic
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- Motivation
- Errors and Uncertainties in Hydrologic Watershed
Modelling - Suggested Problem Solutions
- Working Group Opportunities
3Motivation
Motivation Errors in Hydro-logic
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Motivation
4Motivation
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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5Motivation
Phytoplanktion biomass
Walensee
Examples (1) Aquatic ecosystemmodelling
Motivation Errors in Hydro-logic
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Zürichsee
Greifensee
Mieleitner et al. 2006
6Motivation
Examples (2) Climate modelling
Motivation Errors in Hydro-logic
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Tomassini et al. 2006
7Motivation
Examples (3) Hydrologicmodelling
Motivation Errors in Hydro-logic
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Yang et al. 2006
8Motivation
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.
9Motivation
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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10Motivation
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.
11Errors in Hydrological Modelling
Motivation Errors in Hydro-logic
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Errors and Uncertainties in Hydrologic Watershed
Modelling
12Errors 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
13Errors 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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14Errors in Hydrologic Modelling
A Simple Hydrologic Watershed Model (1)
Motivation Errors in Hydro-logic
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Kuczera et al. 2006
15Errors in Hydrologic Modelling
A Simple Hydrologic Watershed Model (2)
Motivation Errors in Hydro-logic
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Kuczera et al. 2006
16Errors in Hydrologic Modelling
A Simple Hydrologic Watershed Model (3)
Motivation Errors in Hydro-logic
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Kuczera et al. 2006
17Errors 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.
18Errors 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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19Errors 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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20Errors 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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21Suggested Problem Solutions
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Suggested Problem Solutions
22Suggested 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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23Suggested 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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24Suggested 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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25Suggested 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
26Suggested Problem Solutions
2. Improvement of Output Error Model (Example)
residuals, no transformation
residuals, Box-Cox transf.
Auto-correlation
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residuals, Box-Cox tr., var. sd.
innovations, Box-Cox tr., var. sd., var. corr.
time
Yang et al. 2006
27Suggested 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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28Working Group Opportunities
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Working Group Opportunities
29Working 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.)
Motivation Errors in Hydro-logic
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30Working 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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31Working 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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32Working 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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33Working 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.
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34Thank you for your attention