Flood frequency model-data comparison (in brief)

As has hopefully already been made clear, testing models against the data they are supposed to represent as far as possible is a crucial activity. In this case, given some questions around the utility of the pooled estimates, which it must be remembered come recommended by official guidance, how well the enhanced method seems to fit the data at certain locations was considered. In contrast to the single-site case, when a poor fit may simply be put down to the limited record, should then enhanced single-site curve fit appear poor, there may be an argument for rejecting it in favour of the single-site curve (which will naturally fit the at site data better, but perhaps ‘too well’). In this endeavour, it is important to remember that data plotting positions using the Gringorten formula, for example, can be themselves highly uncertain; an observation which Miller et al. (2013) makes, but which is often overlooked.

In the present study, it was possible to find cases where the enhanced single-site estimates (conducted without the additional peaks, as all enhanced estimates were) do not seem to fit the data well, perhaps due to data of limited relevance being introduced. To aid this discussion, results from two example stations are plotted below (Figure 4.7 and 4.8). Although both these stations (which incidentally have reasonably long records were) affected by high flows in December 2015, it is clear that the model fit is poor more generally, i.e. it is not only the latest peaks which do not fit well.

FIGURE 4.7. AM series (top) and enhanced single-site model without additional data (bottom) for the River Calder at Elland, West Yorkshire (27029). The red curve shows the fitted model and the blue points are the AM observations (plotted using the Gringorten formula).

P ea k fl ow ( m 3 s -1 ) Hydrometric year P ea k fl ow ( m 3 s -1 )

FIGURE 4.8. AM series (top) and enhanced single-site model without additional data (bottom) for the River Eden at Temple Sowerby, Cumbria (76005). The red curve shows the fitted model, and the blue points are the AM observations (plotted using the Gringorten formula).

P ea k fl ow ( m 3 s -1 ) P ea k fl ow ( m 3 s -1 ) Hydrometric year

In these examples, the ‘direction’ of apparent mismatch is potentially worrying; the model, shown by the red line, sits underneath the data. Indeed, since enhanced single site analyses were including the latest peaks was not possible, these peaks are not actually plotted in the lower pane in either Figure 4.7 or 4.8. It is apparent that if they were, the mismatch would become even greater (and the axes would need adjusting).

Contrastingly, in cases where the pooled model-data comparison is poor but the pooled curve sits above the data, then this might be considered reassuring for reasons already deliberated at length. These alternative responses to perhaps similar mismatches in magnitude demonstrate that much scope (or even need) exists to introduce prior knowledge and judgement, perhaps via Bayesian methods, to problems where uncertainty is deep-rooted and pervasive such as flood estimation.

4.2.3. Summary

Overall, it appears that enhanced single-site results may not be capable of consistently raising flood frequency-magnitude curves to levels that appear to be more consistent with the latest observed flows. In this sense, the results presented in this section may be broadly consistent with the underestimation hypothesis. However, the difficulty of testing these types of predictions and reliance on model-model comparisons (since it is often expected that a better model may in fact appear to fit the data poorly) severely restrict the confidence strongly with which any firm conclusions can be drawn. More generally, the previous discussion has highlighted that pooled methodology may be associated with certain drawbacks, especially where the strong influence of local site conditions or lack of independence in the group records challenge the validity of the underlying assumptions.

4.3. Sensitivity to the choice of statistical distribution

Lastly, sensitivity of single-site estimations to the choice of statistical distribution is briefly considered. Results, which are not tabulated in this thesis, are only shown for five stations in each of Group A and Group B (Figures 4.9 and 4.10 respectively).

FIGURE 4.9. Illustration of the impact of choice of distribution of flow frequency magnitude relationships at Group A stations (single-site only). Generalised Logistic (GL), Generalised Extreme Value (GEV) and Gumbel (GEV reduces to the special case of a Gumbel when the shape parameter, ξ = 0) distributions were fitted in case. The ‘without additional peak’ series were used for simplicity. The L-moments fitting method was employed in all cases. The NRFA station reference number is labelled.

FIGURE 4.10. Illustration of the impact of choice of distribution of flow frequency magnitude relationships at Group B stations (single-site only). Generalised Logistic (GL), Generalised Extreme Value (GEV) and Gumbel (GEV reduces to the special case of a Gumbel when the shape parameter, ξ = 0) distributions were fitted in case. The ‘without additional data’ series were used for simplicity. The L-moments fitting method was employed in all cases. The NRFA station reference number is labelled.

These graphs show that broadly speaking, the results demonstrate only limited sensitivity the choice of statistical distribution. Moreover, little systematic difference is apparent between Group A and Group B stations. Certainly variability in estimates at the 1-in-100-year level associated with the different choice of distribution is lower than that associated with that produced in many cases given additional data (Section 4.1) and whether or not pooling was undertaken or not (Section 4.2). These results accord with those of Kjeldsen et al. (2008) who showed that across 600 UK stations,

there was little to choose between the GL and GEV distributions, with the GL being marginally preferred overall. Given all the other difficulties encountered in many flood estimation, this at least provides a little reassurance.