eprintid: 717
rev_number: 10
eprint_status: archive
userid: 17
dir: disk0/00/00/07/17
datestamp: 2018-05-27 16:44:19
lastmod: 2018-05-27 16:44:19
status_changed: 2018-05-27 16:44:19
type: report
metadata_visibility: show
creators_name: Manus, Lorcan Mac
creators_name: Barons, Martine
creators_name: Belica, Matej
creators_name: Chleboun, Colm
creators_name: Dellar, P.
creators_name: Gin, Stephen
creators_name: Gould, Martin D
creators_name: Graf, Isabell
creators_name: Klepek, Karolina Aleksandra
creators_name: Konrad, Bernhard
creators_name: Kwiecinska, Agnieszka Alina
creators_name: Lai, Yi-Ming
creators_name: Luo, Jamie
creators_name: Ockendon, John
creators_name: Sobczak, Grzegorz
creators_name: Sorensen, Troels Bjerre
creators_name: Szerling, Pawel
creators_name: Virmani, Jyotika
corp_creators: Trevor Maynard
title: Modelling hurricane track memory
ispublished: pub
subjects: finance
studygroups: esgi73
companyname: Lloyds
full_text_status: public
abstract: It has been observed that hurricanes that are close in time often follow similar paths. If this can be shown to be statistically significant, it could have implications for how insurance premiums are calculated in areas of the US prone to hurricanes.
We developed two independent path distance metrics and while one suggested that sequential storms within a given hurricane season are more likely to follow each other than any other pair of storms within that season, this conclusion was not supported by the other metric.
Some considerations of how local and large scale air pressure gradients might affect hurricane paths were considered. A point vortex model in the presence of a steering flow field was developed and used to simulate the path of two time displaced vortices. In order for the vortices to follow each other they had to be relatively weak compared to the steering flow field. At realistic vortex strength, the trajectories became chaotic.
In summary, our metrics provided conflicting evidence towards the no- tion of hurricane track memory. A large-scale steering flow field did not appear to provide sufficient explanation for hurricanes following each other, though this does not preclude hurricane track memory being due to localised physical changes following a large storm.
problem_statement: 1.1 Background
(1.1.1) The hurricane seasons of 2004 and 2005 led to extreme losses for the (re)insurance industry. It appeared as though certain large scale atmo- spheric structures (such as the ‘Bermuda High’) were steering storms into the US. If, under some conditions, hurricane tracks are conditional on either previous hurricanes, or other climate variables this could be very significant for the insurance industry. It would suggest that storms may cluster which would lead to a larger variance in financial results than is typically modelled. If the conditions for clustering are expected to either be more or less prevalent under a climate changing world again this is very significant to the insurance industry over the coming decades.
(1.1.2) US landfalling hurricanes result in huge losses to the insurance industry. For instance, Katrina caused USD 45bn worth of damage in 2005 and in the same year, Rita caused USD 6bn and Wilma USD 11bn worth. In 1992, a single hurricane (Andrew) caused USD 22bn and in 2004 a collection of hurricanes caused USD 25bn worth of damage.
(1.1.3) The insurance industry typically models hurricane arrival rates as a Pois- son process and this feeds into further modules that compute the 1 in 200 Value at Risk index, i.e. the value that is at risk in a single year with probability less than 1 in 200.
(1.1.4) Recent storm seasons in the US appear to result in at least some hurricanes following a similar path. One could think of this as storms having a property which makes it more likely that further storms will follow in their wake. If this is indeed the case, then the underlying statistical process assumed to be generating the storms is not well aligned with what is actually occurring.
1.2 Problem Statement
(1.2.1) Within a hurricane season is there a tendency, under some conditions, for groups of hurricane tracks to follow a large scale steering pattern? Can the steering pattern be identified in some sense?
(1.2.2) What is the unconditional probability a steering pattern will exist in a given year? Can this probability be made conditional on large scale climate variables with any skill?
date: 2010
citation:   Manus, Lorcan Mac and Barons, Martine and Belica, Matej and Chleboun, Colm and Dellar, P. and Gin, Stephen and Gould, Martin D and Graf, Isabell and Klepek, Karolina Aleksandra and Konrad, Bernhard and Kwiecinska, Agnieszka Alina and Lai, Yi-Ming and Luo, Jamie and Ockendon, John and Sobczak, Grzegorz and Sorensen, Troels Bjerre and Szerling, Pawel and Virmani, Jyotika  (2010) Modelling hurricane track memory.  [Study Group Report]     
document_url: http://miis.maths.ox.ac.uk/miis/717/1/ESGI73-Lloyds_CaseStudy.pdf