This case study describes findings reported by Hunter, Bates et al. (2005). This page provides a brief introduction to this useful paper; however, this is a precis and the interested reader is directed to the full text in order to appreciate the full picture.

This paper provides a useful case study for any practitioner who needs to investigate methods for incorporating different types of data into hydrological model parameter calibration. The paper also describes the benefits and drawbacks of each of the three data types that are used.

Context

The authors used the 2D LISFLOOD-FP model to predict flow and inundation for a 35km reach of the River Meuse near Maarstricht (Belgium). The model was calibrated in a way that would best recreate a severe flooding event that lasted for 20 days beginning on the 22 Jan 1999. The event had a 63 year return period and resulted in extensive inundation of the river valley. Unusually, a good set of data exists to describe the flood event. This data included:

• Internal (to the simulated reach) bulk flow time series.

• External bulk flow time series.

• Vector polygons describing the inundation shoreline from satellite and aerial photography.

• Free surface elevation data at specific point locations.

The intention of the authors was to find a methodology that would permit the inclusion of each type of observational data, described above, into a scheme for estimating the effective parameters of the LISFLOOD-FP model.

The authors chose the Generalized Likelihood Uncertainty Estimation (GLUE) procedure as the overall parameter estimation method. However, within the GLUE approach, a major challenge is to design the cost function that quantifies how well the output of the model compares with observational data. This is especially challenging for spatial data such as inundation extent. A key component of this case study involves developing methods to incorporate spatial information into the model calibration process.

Spatial data: extent of flood shoreline

A major objective of flood risk management is to classify the relationship between stage/discharge and the actual extent of inundation for a given flood event. Within a modelling context, this problem requires a means of providing flood inundation maps that link dynamically with estimates of flow and/or stage.

In the present case study, two forms of flood shoreline data where available: ERS-1 Synthetic Aperture Radar (SAR) satellite images (overpass on 30 Jan), and an air photo survey performed on 27 Jan. The measured downstream discharge on these days was 2631 and 2645 m³ s^-1 respectively. The authors note that this information should provide a rigorous test of the model’s ability to simulate the flood shoreline. However, there are a number of problems including:

• The hydraulic conditions captured by the satellite and aerial survay are not markedly different.

• Different image processing method applied to the satellite and aerial photography introduce quite complex uncertainty into the location of the flood shoreline. The SAR image contains a high degree of noise (speckle). This was processed using the ‘snake’ algorithm (Horritt, 1999). Using this algorithm, the location of the shoreline boundary should be accurate to within 12.5 m although errors can still develop due to misclassification of pixels (i.e., a pixel is classified as water when it is actually dry land).

Incorporating spatially distributed data into model calibration was tackled in the following way:

1. The pattern of cells within the model extent was classified using a binary wet/dry measure.

2. The same pattern was imposed on the observational data and in this way it was possible to define four binary classifications for each cell depending on the yes/no outcome of the following questions:

   • water is present in the model cell and in the data cell

   • water is present in the model cell but absent in the data cell

   • water is absent in the model cell but present in the data cell

   • water is absent in the model cell and in the data cell. This can be summarised with a simple table:

. . . . . . . . . . . . . . . . . Present in data. . . . .Absent in data

. Absent in model. . . . . . . .M₀D₁. . . . . . . M₀D₀

The performance of the model was then defined using the equation:

. . . . . . . eq(1)

Where F⁽²⁾ is a measure of model performance (between 0 and 1), NC is the number of cells.

It may be useful here to include a very simple hypothetical example to illustrate how this works: consider a comparison between the prediction made by a nine cell model and the actual observations describing the nine cells. The shaded regions represent the cells that are predicted or observed to be inundated:

Then, applying eq(1) to these scores produces an F⁽²⁾ score of: (4 - 0)/(4 + 0 + 1) = 0.8

The other available data, namely hydrograph and maximum water surface elevation data (measured at 86 points; although not all within the domain of the digital elevation model (DEM)) where compared with model data using the following methods:

Hydrograph data: the Heteroskedastic Maximum Likelihood Estimator measure was used. This value (as with other goodness-of-fit measures such as Nash-Sutcliffe) was chosen to deal with the non-Gaussian, non-independent nature of the model residuals; however, the authors state the HMLE measure places an emphasis on the recession component of the hydrograph. Calculating HMLE is carried out with the following equation:

. . . . . . eq(2)

Point maximum water surface elevation data: this was compared with model data by collecting the absolute error between either 1) the modelled and observed water surface elevation for wet cells, or 2) between observed water surface elevation and model digital elevation for observed wet but predicted dry cells. This later measure ensures errors are corrected for potential discrepancies in DEM data.

The result of the above work is a set of three separate measures of model fit: one defined from photographic information, one from flow-flow hydrograph data, one from points of maximum water surface elevation. Each data type can be used as a means of calibrating the LISFLOOD-FP model parameters (in this study, the authors aggregated the Manning roughness coefficients of the model into 4 regions: upstream, midsection, downstream and floodplain - with floodplain value fixed; therefore, the tuneable parameter set consisted of the 3 in-channel roughness coefficients).

The study presents the results of 4 sets of 500 realisations of the LISFLOOD-FP model with each parameter set chosen at random from a uniform distribution of roughness coefficients with maximum and minimum values chosen using prior expert opinion. Each set of results presents ‘dotty plots’ of parameter set likelihood determined using: 1) satellite flood shoreline extent; 2) aerial photography flood shoreline extent; 3) hydrograph data; 4) maximum free surface elevation data.

Comment on the results

1. Satellite and aerial photo data. It is not necessary here to provide a specific commentary on the results of the parameter identification (this is best performed with direct reference to the paper); however, the key qualitative findings are summarised. Crucially, the superior accuracy of the aerial photography means that this data provides a more defined constraint on the upstream manning coefficient compared with the results generated from the satellite data. The mid and downstream manning coefficients demonstrated a greater range of acceptable values. It is worth reiterating the authors’ emphasis that the best performing parameter values should not be considered as an optimum set: numerous studies have shown that the best performing effective parameters in hydrological models rarely remain constant when calibrated using alternative data.

2. Hydrograph data. The value of the manning coefficient for each reach was dominated by the data provided by the gauging station directly downstream. Having developed a measure of likelihood for each roughness coefficient, the authors where then able to define a measure of relative confidence in the model output in a manner analogous to confidence intervals defined from a parametric cumulative probability distribution. Comparing a 90% confidence envelope of model forecasts to the observed hydrograph data clearly showed that:

   • stage measures where considerably less well constrained than discharge measures. The authors suggest stage values are more sensitive to parameter variation than discharge;

   • the uncertainty envelope did not contain all the observed data – this was most clearly demonstrated on one particular gauging station where the reach is wide and shallow and therefore most difficult to model;

   • the observed data moves markedly within the uncertainty envelope during the progression of the flood event demonstrating that the expected value of the model drifts away from the observed value during certain periods of the flood event.

3. Point maximum free surface water elevation data. The authors don’t provide too much comment on the parameter conditioning provided by the elevation data other than pointing out that the best performing parameter values fall within the parameter space also identified by the other two data types.

Combining data sets and assessing the contribution to parameter constraint

The authors provide an interesting exploration of the relative contribution of each data type to the constraint of the model parameters. This is performed using Shannon's entropy measure. The authors describe how this measure provides a quantitative measure of the uncertainty of each parameter (akin to the variance of a normal distribution but able to provide information for more awkward non-parametric, potentially multi-modal distributions). The results show that as each data type is incorporated (see below) the Shannon entropy describing the parameters' uncertainty, is reduced.

Bayesian approach

The authors demonstrate a method for refining the parameter calibration by sequentially applying a form of Bayes equation. This approach works by first applying GLUE to the hydrograph data using a uniform distribution for the Manning’s roughness coefficients; the result being a set of posterior distributions – these are then used as the priors for GLUE applied to the flood shoreline data resulting in a refined posterior distribution; finally, this refined distribution is used as the priors for GLUE used with the free surface elevation data resulting in further refinement to the posterior parameter distribution. This is a classic example of the sequential use of Bayes equation to refine prior assumptions based on new information.

Conclusions

1. Internal predictions of stage offer considerable potential for reducing uncertainty of the effective model parameter estimates.

2. Likewise, aerial survey data is useful as this provides a proxy for surface water elevation – particularly when combined with DEM.

3. Discharge data proved less useful for constraining parameter uncertainty due to the inherent mass conservation built into the model and the particular hydrological characteristics of the studied flood event.

4. Model response to calibration is different for high and low flows. The authors emphasise the need to consider the uncertainty in observations as neglecting these could lead to a form of model over-fitting whereby parameter values are unjustifiably constrained by data that presents an unrealistic degree of information.

5. For spatial models, the model uncertainty increases markedly for locations away from sources of conditioning data.

6. The updating process, whereby different data types where used to condition parameter estimates, was shown to reduce the Shannon entropy measure of parameter uncertainty. However, it was noted that this may not be possible in applications where the data types simply can not be incorporated into compatible parameter conditioning schemes.

References

• Horritt, M.S. (1999). "A statistical active contour model for SAR image segmentation." Image and Vision Computing 17: 213-224.

• Hunter, N. M., P. D. Bates, M. S. Horritt, A. P. de Roo and M. G. Werner (2005). "Utility of different data types for calibrating flood inundation models within a GLUE framework." Hydrology and Earth System Sciences 9: 412-430.

Posterior --Thu, 17 Jul 2008 13:04:21 +0100