problems of inference and uncertainty estimation in hydrologic modelling

Eawag: Swiss Federal Institute of Aquatic Science and Technology

Problems of Inference and Uncertainty Estimation in Hydrologic Modelling

Peter Reichert

Eawag Dübendorf and ETH Zürich

SAMSI meetingOct. 16, 2006

Contents

Motivation

Errors in Hydro-logic Modelling

Suggested Pro-blem Solutions

Working GroupOpportunities

Motivation

Errors and Uncertainties in Hydrologic Watershed Modelling

Suggested Problem Solutions

Working Group Opportunities


Motivation

Motivation

Motivation





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





Motivation

Examples (1):

Aquatic ecosystemmodelling

Motivation




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Mieleitner et al. 2006


Motivation

Examples (2):

Climate modelling

Motivation




Tomassini et al. 2006


Motivation

Examples (3):

Hydrologicmodelling

Motivation




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Yang et al. 2006


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




• 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.


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.

Motivation





Motivation

Hydrologic Modelling:

Watershed hydrologic modelling is a particularly good study area for these problems as

Motivation




• 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.


Errors in Hydrological Modelling


Motivation






Motivation




Overview of Hydrologic Processes

A Simple Hydrologic Watershed Model

More Complex Watershed Models

Sources of Error in Watershed Modelling


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.

Motivation






A Simple Hydrologic Watershed Model (1): Motivation




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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).

Motivation




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.



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).

Motivation






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.

Motivation






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.

Motivation







Motivation







1. „Ad-hoc“ ApproachesApproaches based on increasing parameter uncertainty.(GLUE, SUFI, SUNGLASSES, etc.)

2. Improvement of Output Error ModelAutoregressive output error models.

3. Input and Model Structure Error Models• Storm multipliers.• Bayesian model averaging.• Use of a stochastic hydrological model.• Stochastic, time-dependent parameters.• Multi-criteria optimization.

Motivation






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.

Motivation






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.

Motivation






2. Improvement of Output Error Model (Example)Motivation




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innovations, Box-Cox tr., var. sd.var. corr. time



2. Improvement of Output Error Model (Example)Motivation




Yang et al. 2006

residuals, no transformation

residuals, Box-Cox transf.

residuals, Box-Cox tr., var. sd.

innovations, Box-Cox tr., var. sd., var. corr. time

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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.

Motivation







Motivation






Research Questions / Options for Projects (1)

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.)

2. Develop a better statistical description of rainfall uncertainty.(Option for a collaboration with climate/weather working groups.)

3. Explore alternative options for making parameters time-dependent.(Suggestions so far: storm-dependent parameters, time-dependent parameter as an Ornstein-Uhlenbeck process.)

Motivation







4. 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?)

5. Develop uncertainty estimates when using multi-objective optimization.(How to use information on Pareto set for uncertainty estimation of parameters and results?)

6. 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?)

Motivation







7. 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.)

8. More questions will come up during discussions.

Motivation






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.

Motivation






How to Proceed?1. 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.

2. Discuss and prioritize (according to expected chance of success) the „collection of suggestions“ developed under point 1 above.

3. Use preliminary results of project 1 to stimulte the discussions.

4. Decide on research plans for projects to work on.

5. Organise a workshop for discussing research plans and preliminary results with experts in the field.

6. 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




Eawag: Swiss Federal Institute of Aquatic Science and Technology

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problems of inference and uncertainty estimation in hydrologic modelling

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