1 / 15

Evaluating the risk of spatially extensive flooding

Evaluating the risk of spatially extensive flooding. Duncan Reed duncanreed@dwrconsult.demon.co.uk. An index of collective risk (4). … a c ollective r isk in dex for ge neral use:. But how is the effective number of independent sites, N e , defined?. If sites independent.

inge
Download Presentation

Evaluating the risk of spatially extensive flooding

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Evaluating the risk of spatially extensive flooding Duncan Reed duncanreed@dwrconsult.demon.co.uk

  2. An index of collective risk (4) … a collective risk index for general use: But how is the effective number of independent sites, Ne, defined?

  3. If sites independent The clever bit … MAGNITUDE Distribution of maxima over N sites Distribution of maxima at a typical site Standardised extreme value x lnN FREQUENCY Gumbel reduced variate, y = - ln ( - lnF)

  4. If sites partially dependent MAGNITUDE Distribution of maxima over N sites Distribution of maxima at a typical site lnNe Standardised extreme value x FREQUENCY Gumbel reduced variate, y = - ln ( - lnF)

  5. CRINGE = 1 (fully dependent) CRINGE = 0 (fully independent) Network maximum curve – actual MAGNITUDE Standardised extreme value x lnNe lnN FREQUENCY Gumbel reduced variate, y = - ln ( - lnF)

  6. A practical approach CRINGE = 1 – lnN/lnNe Ne = NCRINGE = 0 Ne = 1 CRINGE = 1

  7. Spatial dependence model for rainfall extremes CRINGE = 0.919- 0.085 lnAREA+ 0.051 lnN+ 0.027 lnD where: Nnumber of sites in network AREAarea spanned by network (km2) Drainfall duration (days) [Re-expression of Dales & Reed, 1989]

  8. Definition of area spanned dbaris mean inter-site distance Spanning area taken as AREA = 2.5 (dbar)2 1 d12 d13 2 d23 3

  9. Example: 1-day maximum rainfall AREA km2 CRINGE Number of insured units

  10. Example: 90-day maximum rainfall AREA km2 CRINGE Number of insured units

  11. Why effect greater for floods • Extreme rainfalls that lead to flooding tend to be those occurring when soils are already primed. Such conditions tend to be strongly seasonal and – when they occur – more spatially widespread than typical rainfall extremes. • Highly permeable catchments struggle to flood other than spatially extensively.

  12. Spatial dependence in floods (1) • Koltun & Sherwood (1999) study pairwise dependence in flooding for streamflows in Ohio • They index dependence by a ratio of counts: • They have to make quite a lot of assumptions about what constitutes an “event”

  13. Spatial dependence in floods (2) • Koltun & Sherwood relate their index to: • Inter-catchment distance • Mean size of the catchments • Relative size of the catchments • Inter-catchment orientation • They use logistic regression to force the dependence to lie between the independent and fully dependent cases.

  14. Suggested developments (1) • Use Dales & Reed model of spatial dependence in rainfall extremes to compare CRINGE factors for Portfolios A and B • Adopt nominal values of rainfall duration, such as: • D = 0.05 days for storm-sewers • D = 30 days for groundwater-fed rivers • D = 1.0 otherwise

  15. Suggested developments (2) • Generalise a spatial dependence model for river flooding, taking the best from the Dales & Reed and Koltun & Sherwood approaches • Vary the method to allow CRINGE to reflect the much larger insured units at some sites • Consider applications to extreme values of other variables, especially drought

More Related