APPENDIX G JOINT PROBABILITY ANALYSIS€¦ · Joint Probability Analysis JULY 2014, 2 In this study, extreme water levels are obtained from existing analysis results, whilst, extreme

Flood Risk Interactions, St Denys Southampton

June 2014

APPENDIX G

JOINT PROBABILITY ANALYSIS

Joint Probability Analysis

JULY 2014 ,

JOINT PROBABILITY ANALYSIS


JULY 2014,

1

1. INTRODUCTION

Among the parameters investigated to consider their significance in influencing (increasing) water levels along the River Itchen (air pressure; wind speed; river flow; and rainfall), high precipitation (rainfall) occurring at times of peak water levels was found to represent the most significant flood risk.

Furthermore, consultation feedback received from local residents during development of the Southampton Coastal Strategy (URS, 2012), coupled with the understanding of processes operating in this area suggest that flooding is likely to be experienced from a variety of means, but predominantly as a result of tidal locking of the local surface water drains and interaction of tidal levels and rainfall preventing surface water draining away.

Therefore, a joint probability analysis has been undertaken to establish the likelihood of occurrence from such a combined event.

2. STUDY APPROACH

Joint probability refers to the chance of two or more conditions occurring at the same time. It provides the probability of the relevant variables taking high values simultaneously. A joint probability assessment was undertaken in the study by using the calculated dependence relationship between the two variables (water level and rainfall) from the available data. This will attribute values to marginal extremes to provide the combinations of water levels and rainfall amounts for a range of joint exceedance events from 1 in 1 year to 1 in 200 year return periods.

The analysis has been conducted in accordance with the guidance provided by the Defra and Environment Agency joint publication: Use of Joint Probability Methods in Flood Management: A Guide to Best Practice – R&D Technical Report FD2308/TR2, 2005. The guide includes a summary of the desk study approach to joint probability analysis, and a software tool for its application. Based on the desk study approach, the problem of joint probability assessment was then reduced to determine the marginal distributions and their dependence. The analysis has been undertaken using the following procedure:

a. Obtaining the marginal distributions for extreme water levels and extreme rainfall. b. Estimation of dependence between water levels and rainfall based on the published

EA dependence mapping of water levels and wave rainfall. c. Estimation of dependence of water levels and daily rainfall using JOIN-SEA

software. d. Calculating the joint exceedance return periods.

3. ANALYSIS RESULTS

Extreme sea levels occur as a result of the combination of tides with storm surges associated with weather systems. URS collected measured sea levels at Dock Head gauge and daily rainfall data at Portswood and Otterbourne from the Environment Agency. The measured water levels at Dock Head are available from 1991 to 2013. Rainfall data at Portswood covers a period of 26 years from 1986 to 2013. Long term daily precipitation figures at Otterbourne in the past 102 years have also been collected and analysed to complement the statistical results.


JULY 2014,

2

In this study, extreme water levels are obtained from existing analysis results, whilst, extreme rainfall heights are evaluated separately and then combined to estimate the joint probability return period. Water levels at Dock Head have been studied as a part of Southampton Coastal Flood and Erosion Risk Management Strategy. URS (2012) presents extreme water levels at Dock Head using the annual maximum water levels for the period 1924 to 2009. The results are listed in Table 1. Analysis of marginal distribution of precipitation at Portswood was undertaken. The collected daily data was used to determine rainfall statistics as shown in Figure 1 and Table 1. To accommodate the broad scale of the study, the extreme water levels at Otterbourne have been estimated based on 102 years annual extreme daily rainfall data. As shown in Figure 2 and Table 1, it can be seen that the outputs at Portswood and Otterbourne are comparable. In order to generate the full suite of marginal return period values required to produce the required range of joint probability combinations, the lower return periods (less than 1 year frequencies) were derived for both water level and rainfall.

Table 1 Extreme Water level and rainfall

Return Period (yrs)

Water Levels

(m, AOD)

Water Levels

(m, CD)*

Rainfall at Portswood

(mm)

Rainfall at Otterbourne (mm)

1 2.45 5.19 26.4 27.4

2 2.56 5.30 33.1 34.3

5 2.67 5.41 41.9 43.4

10 2.76 5.50 48.6 50.2

20 2.84 5.58 55.0 59.3

50 2.94 5.68 64.1 66.2

100 3.02 5.76 70.7 73.1

200 3.09 5.83 77.4 79.9

*A correction of +2.74m from AOD to CD


JULY 2014,

3

Figure 1 Extreme rainfall at Portswood

Figure 2 Extreme rainfall at Otterbourne

The method described in FD2308/TR2 uses a correlation coefficient ‘’ or ‘correlation factor’ (CF) to quantify inter-dependence of the two parameters of interest. The dependence map for two-hourly rainfall and sea level in England and Wales is produced in FD2308/TR2 (Page 24) and reproduced in Figure 3. It suggests that on the south and west coasts of England and Wales, the dependence is consistently characterised as ‘modest’, where the correlation coefficient in the Southampton area is =0.32. This indicates a low correlation between hourly rainfall and sea level.


JULY 2014,

4

Figure 3 Summary of dependence information for rainfall and sea level


JULY 2014,

5

It is worth pointing out here that the dependences in Figure 3 have been mapped for a short duration of rainfall and sea water levels. By comparison, for this study a much longer-term of rainfall data was analysed. The specialist joint probability analysis software ‘JOIN-SEA’ was developed during the Defra-funded programme of research described in Defra (2005a), Defra (2005b), HR Wallingford (2000a) and HR Wallingford (2000b). The software provides a tool to estimate the dependence between rainfall and sea water levels rather than approximating this using Figure 3. Figure 4 shows the results from the application of the JOIN-SEA software. Under the various thresholds, the maximum dependence coefficient was found to be =0.36. The dependence for daily rainfall and water levels is higher than that of the short period measurements shown in Figure 3. The correlation between daily extreme water levels and rainfall is in the range of 0.120.37. The likelihood of extreme water level combining with rainfall is modest. As expected, applying a correlation of 0.36 will produce larger overall values for given joint exceedance return period events compared to the correlation as presented in Figure 3. The value of 0.36 therefore, provides a more conservative assessment of the joint probability conditions.

Figure 4 Dependence vs. thresholds

For the joint return period(s) of interest the appropriate tables for the relevant strength of dependence from the published best practice guidance have been applied to convert the listed joint exceedance extremes from marginal return periods to actual values. Adopting the ‘modest’ dependence coefficient between water levels and rainfall gives the joint probability results presented in Table 2 and Figure 5. Based on the analysis, there would be benefit to further investigating the potential impact for coincident storm tide and rainfall events if and when more data becomes available in the future.

60 65 70 75 80 85 90 95 100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Threshold(%)

!


JULY 2014,

6

Table 2 Joint exceedance of extreme water level and rainfall combinations

1 2 5 10 20 50 100 200

1.87 26.4 33.1 41.9 48.6 55.0 64.1 70.7 77.4

1.95 26.3 33.1 41.9 48.6 55.0 64.1 70.7 77.4

2.05 17.6 25.8 36.7 45.0 53.1 64.1 70.7 77.4

2.16 10.8 19.3 30.0 38.3 46.6 57.4 65.9 74.2

2.25 4.8 12.5 23.5 31.7 40.0 50.9 59.1 67.5

2.36 4.4 14.7 23.0 31.2 42.1 50.4 58.6

2.45 8.2 16.3 24.6 35.5 43.8 51.9

2.55 2.2 9.7 18.0 28.8 37.1 45.4

2.67 1.8 9.3 20.2 28.3 36.6

2.76 3.3 13.4 21.8 29.9

2.84 7.1 15.1 23.4

2.94 6.7 14.6

3.02 0.7 8.1

3.09 2.1

Joint exceedence return period (years)

Water

Level

(m,AOD)

Daily Rainfall (mm)


JULY 2014,

7

Figure 5 Joint exceedance of extreme water level and rainfall combinations

4. INDENTIFICATION OF PAST EXTREME EVENTS

The joint probability study provides a tool to identify past extreme events. The highest 7 combined events were selected from an analysis of the available water levels and rainfall data spanning a 20 year record between 1991 and 2014 as shown in Figure 5 and Figure 6. Note these combined events exclude extreme water level events during periods of low rainfall. The largest combined event from the water level records at Dock head and rainfall at Portswood occurred on 14/02/2014, with an estimated joint exceedance return period of approximately 1 in 200 years.

Dail

y R

ain

fall

at

Po

rtsw

oo

d (

mm

)


JULY 2014,

8

Table 3 Extreme water levels and rainfall

No. Date WL (m, AOD) at

Dock Head

WL (m, CD)* at Dock

Head

Rainfall (mm) at Portswood

Joint Probability Return Period

(yrs)

1 14/02/2014 2.84 5.58 24.2 1 in 200

2 31/01/2013 2.37 5.11 32.8 1 in 25

3 23/12/2013 2.08 4.82 43.0 1 in 10

4 10/03/2008 2.86 5.60 7.0 1 in 50

5 25/12/1999 2.72 5.46 7.6 1 in 20

6 26/11/1995 2.25 4.99 32.4 1 in 10

7 02/01/1995 2.96 5.70 0.4 1 in 60

*A correction of +2.74m from AOD to CD

Figure 6 Extreme events identified on joint probability curves

5. INTERACTIONS BETWEEN WATER LEVEL AND RAINFALL

A modelling exercise has been carried out to illustrate the potential interactions between extreme water levels and rainfall. To quantify the extent of inundation due to storm tides accompanied by a rainfall event, DHI’s MIKE21 model developed for this project has been used to simulate the processes leading to flooding under a combination of sea level and rainfall. The results of the joint probability assessment were used to estimate the ‘worst case’ combinations of rainfall and high tides for a 1 in 200 year return period combined event on 14/02/2014. For the model simulations, the water level is 2.84m at Dock Head (2.94m at St

Dail

y R

ain

fall

at

Po

rtsw

oo

d (

mm

)


JULY 2014,

9

Denys) and the daily rainfall is 24.2mm. To investigate the influence of rainfall on flooding in the area, two models were configured; one including and one excluding rainfall. The models were used to simulate the events which will allow comparison between the two scenarios. To illustrate the situations where flooding may occur, modelled results for each scenario are mapped in Figures 7 and 8. To understand the result of process interactions, Figure 9 shows the difference in water depth between two model runs. The additional contribution to inundation from rainfall can be observed in Figure 9. As no drainage network has been included in the model domain, the results presented may overestimate the impact of rainfall; however it does provide an inundation area for a worst case scenario. A detailed investigation of impact, time series data for water surface elevation and water depth have been extracted at 5 Locations BH2, B, C, D and E. Figures 10-19 show the plots at each location. At Locations BH2, B, C and E, the maximum water depths have been increased by 2.4cm due to rainfall, which is relatively small. A larger increase of 0.50m has been found at location D; this is due to an accumulation of water in a low lying area and the assumption of no ground drainage. Further studies with drainage may be needed to fully address the flooding issues when rainfall is considered.


JULY 2014,

10

Figure 7 Water depth map under water level condition only


JULY 2014,

11

Figure 8 Water depth map under a combination of water level and rainfall


JULY 2014,

12

Figure 9 Difference in water depth


JULY 2014,

13

Figure 10 Comparison of water surface elevation at Location BH2

Figure 11 Comparison of water surface elevation at Location E


JULY 2014,

14

Figure 12 Comparison of water surface elevation at Location B

Figure 13 Comparison of water surface elevation at Location C


JULY 2014,

15

Figure 14 Comparison of water surface elevation at Location D

Figure 15 Comparison of water depth at Location BH2


JULY 2014,

16

Figure 16 Comparison of water depth at Location E

Figure 17 Comparison of water depth at Location B


JULY 2014,

17

Figure 18 Comparison of water depth at Location C

Figure 19 Comparison of water depth at Location D


JULY 2014,

18

6. REFERENCES

Defra (2005a) Joint Probability: Dependence Mapping and Best Practice: Technical report on dependence mapping. FD2308/TR1.

Defra (2005b) Use of Joint Probability Methods in Flood Management: A guide to best practice. FD2308/TR2

HR Wallingford (2000a). The joint probability of waves and water levels: JOIN-SEA: A rigorous but practical new approach. HR Report SR 537.

HR Wallingford (2000b). The joint probability of waves and water levels: JOIN-SEA- Version 1.0, User Manual.

URS (2012) Southampton Coastal Flood and Erosion Risk Management Strategy - Appendix 1A: Conceptual Understanding Report.

Documents

APPENDIX G JOINT PROBABILITY ANALYSIS€¦ · Joint Probability Analysis JULY 2014, 2 In this study, extreme water levels are obtained from existing analysis results, whilst, extreme