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Uncertainty in rainfall-runoff simulations

An introduction and review of different techniques

M. Shafii, Dept. Of Hydrology, Feb. 2009

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Overview

  1. Introduction– Different sources of uncertainty

– Non-stationarity

– Calibration and uncertainty

  2. Methods– Probabilistic method

– Monte Carlo simulations (GLUE)

– Fuzzy Logic based method

– Multi-objective calibration

– Bayesian inference

  3. Summary and conclusions...

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Introduction

  Different uncertainty sources– Natural randomness

– Data

– Model parameters

– Model structure

  Note 1. Non-Stationarity– Methods to deal with uncertainty

– Probability rainfall-runoff model

– Monte Carlo Simulations

– Dealing with error series

– Possibilistic approaches

– Hybrid methods

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Introduction

  Note 2. Data uncertainty and calibration– Data errors and uncertainties are transformed to the

model parameters in terms of bias in the parameters (e.g. deviations from their true value).

– Melching (1990) says, data uncertainties need not be explicitly considered in reliability analysis, and instead, they may be assumed to be included in parameter uncertainties.

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Methods

  1. Early methods– Probabilistic methods

– Probability density function of model output

– Potential information:– Sharpness of PDF

– Rule-of-thumb to assess the quality of modeling would be to investigate whether or not the measured values fall within 95% confidence interval of the predictions.

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Methods

  2. GLUE (Monte Carlo Simulations)  Process:  (a) Taking a large number of

samples

  (b) Calculation of likelihood

  (c) Dividing the samples into “behavioral” and “non-behavioral”

  (d) Rescale the likelihood and produce PDF of output

  (e) Determination of Confidene Intervals (CI)

  Keith Beven, “equifinality”

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Methods

  2. GLUE (Monte Carlo Simulations)

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Methods

  3. Input uncertainty and Fuzzy Logic– Maskey et al. (2004): Treatment of precipitation uncertainty in

rainfall-runoff modeling for flood forecasting.

– Fuzzy Logic, Prof Zadeh (1965)

– Crisp and Fuzzy Sets

Crisp Set

Fuzzy Set

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Methods

  3. Input uncertainty and Fuzzy Logic

  Conclusion: using time-averaged precipitation over the catchment may lead to erroneous forecasts

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Methods

  4. Structural uncertainty– Imperfect representation

of catchment processes: structural uncertainty.

– Multi-objective calibration: Pareto front

– Drawbacks of this method!!!

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Methods

  5. Parameter uncertainty, Bayesian Inf.– Bayesian inference: aiming

at deriving the posterior distribution of a future hydrological response allowing for both natural and parameter uncertainty.

– Bayes’ theorem: allowing us to update the “prior” PDF of parameters by observing “data”, resultingin so-called “posterior” PDF.

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Methods

  5. Parameter uncertainty, Bayesian Inf.

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Summary

  Summary and conclusions1. Uncertainty assessment is an essential part of modeling process

and should not be neglected at all.

2. We have to be aware of which kind of uncertainty we are estimating.

3. We, as modelers, should be aware of all possible methods, their peculiarities, and underlying hypotheses.

4. An uncertainty assessment method must be able to take into account any type of useful information (Hybrid methods).

5. To be blunt, there is currently no unifying framework that has been proven to properly address uncertainty in hydrological modeling.

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The End

  Thank you for your attention…

  Any question?

  And then, discussion…