Epidemiología de las infecciones respiratorias.

A further dependence analysis was undertaken at Newhaven to define the relationship between astronomical tide, surge and total sea levels using the 98% threshold level. Unlike the previous dependence calculations, tide and surge both occur at the same location, therefore levels are additive with no time-lags required.

Daily maxima observed sea level was plotted against daily maxima surge simultaneously observed at Newhaven (Figure 7.14a), for the period of June 1982 to May 2006. As was expected, there is a trend for the most extreme observed sea levels to occur

simultaneously with high surge events. This was due to the inclusion of the surge in the total sea level record (e.g. predicted astronomical tide plus surge). Figure 7.14b shows a plot of daily maxima predicted tide against daily maxima surge at Newhaven, which displays no obvious trend when the variables are extreme, suggesting independence between the astronomically-driven tide and meteorologically driven surge components.

Daily Maxima Tide & Surge Residual Observational Pairs (June 1982 - May 2006) RIVER OUSE: NEWHAVEN

0 1 2 3 4 5 6 -0.5 0.0 0.5 1.0 1.5

Rec. Newhaven Surge Residual (m)

R e c . N e w h a v e n T id e ( m O D )

Observational Pairs (June 1982 - May 2006)

a.

Daily Maxima Predicted Tide & Surge Residual Observational Pairs (June 1982 - May 2006) RIVER OUSE: NEWHAVEN

0 1 2 3 4 5 6 -0.5 0.0 0.5 1.0 1.5

Rec. Newhaven Surge Residual (m)

P re d ic te d N e w h a v e n T id e ( m O D )

Observational Pairs (June 1982 - May 2006)

b.

Figure 7.14 Scatter plots of a. daily maxima observed sea level versus

daily maxima surge at Newhaven, & b. daily maxima predicted tide

versus daily maxima surge at Newhaven

7.4.2

Dependence Values

Table 7.4 shows the dependenceχ calculated between daily maxima sea levels and daily maxima surge at Newhaven. All values were calculated using the 98% independent POT exceedance threshold level, and show the values ofχ relative to the 5% significance level with lower and upper confidence intervals. The results for observed sea level v surge found a significant level of dependence, with just under 10% of the most extreme tidal events being influenced by surge at Newhaven. This was underlined by the slightly negative dependence value calculated for predicted tide v surge, confirming the

Table 7.4 Dependenceχbetween Newhaven sea level and surge, values ofχcorresponding to the 5% significance level, and the lower and upper confidence intervals

Threshold Selection Confidence Intervals

Gauge / Station

Pair _{(POT %) (value)}

χ

5% Signif.

Level Lower _(5%) Upper _(95%) Newhaven (Sea level) 3.87 mOD Newhaven (Surge) 98% 0.57 m 0.094 0.039 0.021 0.166 Newhaven (Predicted Tide) 3.80 mOD Newhaven (Surge) 98% 0.57 m -0.011 0.008 -0.018 0.035

7.5

Discussion

The dependence modelling exercise utilising daily maxima hydrological datasets from the Ouse system demonstrates how levels of dependence can be successfully employed to categorise the likelihood of simultaneous extreme events and the relative importance of each variable on the production of estuary water levels. When compared to the more straightforward linear statistical correlation exercise in Chapter 5, the calculated R2 and P values show little of the true extremal relationship which exists between the various hydrological pairs determined by theχ dependence measure.

The significant level of dependence calculated for flow v surge at Barcombe Mills and Newhaven of χ =0.338 contrasts with the χ =0.04 level found by Svensson and Jones (2003, 2004a) for the same variable pair. The authors used the original Barcombe Mills flow record (Svensson and Jones, pers comm.) which was found to contain numerous errors, null values and the overtopping of the gauge for flows >20m3/s. To avoid this problem, the synthesised Barcombe Mills dataset was utilised for the dependence calculation in this research (section 5.2.6), which successfully modelled the upper

catchment flows from the four upstream gauges. The use of the recorded Barcombe Mills dataset is likely to have led to the differingχ values.

Although the daily maxima dependence value accurately captured the maximumχ value within any 24-hour period, the likelihood of extreme values from two datasets occurring

hydrodynamic time-lags to be accurately obtained. The use of time-lag algorithms at a high resolution (e.g. 15-minute) for the calculation of the dependence measureχ has been shown to accurately model the hydrological time-lags inherent in the

hydrodynamics of the river system, and determined the time-lag between common meteorological events producing surges and high river flows. The spatial qualities of the Ouse estuary system were found to affect the dependence between downstream sea level and upstream river flow. Unlike coastal sites where tide, waves and surge combine at the same location, the two source variables of river flow and sea level were at two separate locations; it therefore takes time for the peak tide to propagate up the river and river flow to travel down. The time-lag modelling detailed the temporal and spatial factors, enabling an accurate dependence value to be calculated between two variables at different

locations.

It was found that the value of dependence also varied over relatively short distances. Dependence values calculated for two locations at close proximity in Lewes (Corporation Yard and Gas Works), produced differing levels of dependence with river flow and sea level, with extreme water levels at the upstream location influenced to a greater extent by extreme river flows, and the extreme water levels at the downstream location influenced predominantly by sea level. In this instance, it was found that this was due to the

narrowing river channel and Cliffe Bridge structures in between the locations

dramatically effecting the interaction of sea level and river flow during extreme events, altering the dependenceχ values. Dependence values in any river system will therefore respond differently depending on the catchment characteristics and system

hydrodynamics.

To be able to calculate an overall probability of specified extreme water levels occurring from the combination of two (or more) variables producing extreme values at the same time requires the further interpretation and use of the dependence values in a full joint probability analysis, combined with the hydraulic modelling and structure function methods developed in the preceding chapters.