Extreme Sea Levels

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Extreme Sea Levels

• Philip L. Woodworth
• Permanent Service for Mean Sea Level
• with thanks to David Pugh, David Blackman and
  Roger Flather

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Contents

• Introduction
• Annual Maxima method
• Joint Probability method
• Complementary value of tide gauge data and
  numerical modelling
• Changes in extremes with climate change

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INTRODUCTION Coastal planners need to know the
risk of flooding to structures such as houses,
factories and power stations at the coast so that
decisions can made on where to site them and
protect them. High water extreme events
typically result from a high water on a spring
tide and a storm surge.
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Let Q(z) be the Probability of a level z being
exceeded in any 1 year. (Dont worry for now
about how to calculate Q(z)). Then the RETURN
PERIOD T(z) 1/Q(z) is the average time between
which levels higher than z occur. The DESIGN
RISK is the Probability that a given z will be
exceeded during the design life (D years) of the
structure.
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If Q(z) is the Probability of exceeding z in 1
year then (1 Q(z)) is the Probability of NOT
exceeding z in 1 year (1 Q(z)) 2 is the
Probability of NOT exceeding z in 2 years (1
Q(z)) D is the Probability of NOT exceeding z in
D years Then DESIGN RISK 1 - (1 Q(z)) D
e.g. from next figure we see that if engineers
build a structure to a DESIGN RETURN PERIOD T(z)
of 100 years, then if the structure is required
to exist for D 100 years, there will be a 63.5
chance of the level z being exceeded at some
occasion in that time.
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Relationship between the risk of encountering an
extreme sea level with a Return Period of 100
years in the lifetime of the structure, as a
function of the intended period of operation of
the structure
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Note that houses, power stations etc. at the
coast all have D 100 years or thereabouts. To
get a small DESIGN RISK of being flooded in that
time, we have to make the design return period
T(z) as large as possible. For nuclear power
stations, the design T(z) may be 100,000 or
1,000,000 years. In the Netherlands, houses are
constructed with T(z) of 10,000 years. In the UK,
T(z) is often as low as 1,000 years. e.g. if D
100 years, and design risk is required to be just
0.1 (10 chance of flooding at some time during
the 100 years) then a design return period T(z)
of 950 years is needed. (Use the equations on
previous pages to check this.)
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• To calculate Q(z) for a range of values of z, we
  can use
• Tide gauge data plus statistical models
• Numerical modelling information (plus
  statistical models)
• Tide gauge data and numerical modelling in
  combination
• In the following examples we shall use tide gauge
  data from Newlyn.

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Example data used here are taken from
Newlyn (Mean Tidal Range 3 m)
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ANNUAL MAXIMA METHOD We have 84 complete years
of Newlyn data (within 1916-2000), so we have 84
ANNUAL MAXIMUM water levels. These are
histogrammed on next figure. Note that Highest
Astronomical Tide (HAT) (which is at z3.0 m) was
exceeded only 28 times, because in most years the
astronomical tide did not approach HAT and the
surges at high water were not big enough to take
the combined level over HAT. Curve shows Q(z)
Probability of z being exceeded in any 1
year e.g. Q(zHAT) 0.33 28/84
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The Q(z) can be plotted against z for values of
z for which we have data. This is called an
Extreme Level Distribution. Alternatively, and
more normal, is to plot the distribution in
another way z versus log(T(z)). The use of
log(T) is such that it makes the resulting curve
approximately linear see next figure. This
curve can be parameterised easily for
interpolation, but that does not help if we need
to extrapolate it in order to estimate the z
values corresponding to higher T(z) values (or,
if you prefer, very low probabilities Q(z)). To
perform the extrapolation we need to assume one
of the Generalised Extreme Level (GEV) family of
curves.
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The GEV family of curves is derived from the
shapes of the extremes of Gaussian- (or Normal-)
type distributions and have the form z b a
(1 e kX) where z is the level of interest and
X log(T(z)) In the previous example, k gt 0.0.
The special case k0 is called a Gumbel
Distribution and sometimes the GD is preferred as
a simpler choice of curve to fit than the GEV
curve which has the extra parameter (k). Once
the GEV (or GD) curves have been fitted by
least-squares (or, more usually these days,
maximum likelihood) to the available data, then
the curves can be extrapolated to larger T(z)
values.
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In practice, one can extrapolate out to values
of T(z) which are approximately several times the
record length (i.e. several times the 84 years in
this example for Newlyn). Software now exists
which can perform such calculations easily and
produce formal errors on estimates of z
corresponding to extrapolated T(z) values. It is
very important to know such errors.
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Joint Probability Method The Annual Maxima
method is wasteful in that it uses tide gauge
information from only the highest high waters
each year. This ignores all the other data from
the rest of the year, which is a bit crazy! The
JPM uses the fact that the statistics of the tide
and of surges are largely independent (not
completely true) and compiles separate tables of
the distributions of both quantities. So, we can
learn about the statistics of large positive
surges even if they occur at low water, for
example in the Annual Maxima method such surges
would not have contributed to the analysis. An
advantage of the JPM is that it allows to
estimate much smaller probabilities from the data
alone, without need for the gross extrapolations
of the Annual Maxima method. Also much shorter
data sets can be used than in the AM method e.g.
even 4 years might be useful compared to the 84
from before.
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The first step is to perform a tidal analysis
(e.g. from the TASK-2000 package) such that the
time series of (usually hourly) sea level values
for the year is divided into tide and surge
time series. The tidal series has a height
frequency distribution as shown on the next page.
The surge time series will have a distribution
which is approximately Gaussian.
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The first step is to perform a tidal analysis
such that the time series of (usually hourly) sea
level values for the year is divided into tide
and surge. The tidal series has a height
frequency distribution as shown on the next page.
The surge time series has a distribution which is
approximately Gaussian. Then, inside a computer
of course, we can make a 2-dimensional table
which is like a 2-D version of the histogram used
above for the Annual Maxima method. The
following page shows a highly schematic example
of the table, in practice many more rows and
columns would be used. But mostly we need only
consider the higher tide rows which have a chance
of contributing to an overall high water extreme.
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Normalised frequency distributions for tide
(vertical axis) and surge (horizontal axis).
Surge 0.1 for example means surge between 0.05
and 0.15 m. -0.2 -0.1 0.0 0.1 0.2
3.2 0.1 .01 .02 .04 .02 .01 3.1 0.2 .02 .04 .08 .
04 .02 3.0 0.3 .03 .06 .12 .06 .03 2.9 0.3 .03 .06
.12 .06 .03 2.8 0.1 .01 .03 .04 .02 .01 A total
level of 3.4 m (i.e. between 3.35 and 3.45) would
be obtained 11 of the time (of the high tidal
levels represented in the table) from tidesurge
3.20.0 (0.04), 3.10.1 (0.04) and 3.00.2 (0.03)
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The statistics included in this table can be
converted into Q(z) and T(z) form similar as for
the Annual Maxima method enabling similar Extreme
Level Distribution plots to be produced. For more
details, see Pugh (1987) book
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• WHAT CAN YOU DO IF YOU HAVE NO TIDE GAUGE DATA
  FROM A LOCATION WHERE YOU WANT TO HAVE EXTREME
  LEVEL INFORMATION?
• Simple regional approach methods
• Sophisticated spatial approach modelling of
  Coles and Tawn
• Use numerical tidesurge models

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Example of simple methods, where you have data,
define a100 100-year return water level
-------------------------------------------
(HAT 100-year return surge level) If
the large surges always occurred at high
astronomical tide, then this quantity would be
1.0. In practice of course, they do not always,
so it is often much less than 1. Around the UK it
is typically 0.8, falling to 0.7 in the southern
North Sea where tide-surge interaction luckily
causes surges to avoid high water. Once values
of a100 have been acquired for an area, then it
may be possible to use the same value at sites
where there are no good surge data (but some
basic knowledge of the tide is still needed).
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• WHAT CAN YOU DO IF YOU HAVE NO TIDE GAUGE DATA
  FROM A LOCATION WHERE YOU WANT TO HAVE EXTREME
  LEVEL INFORMATION?
• Simple regional approach methods
• Sophisticated spatial approach modelling of
  Coles and Tawn
• Use numerical tidesurge models

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POL NISE model grid (12km) - nested in NEAC
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Storm surge extremes numerical model
approach Model runs forced by long met data sets
produce realistic surge climatology - which can
then be analysed like tide gauge
observations. Two model runs are usually carried
out for 1. tide met (air pressure and wind)
forcing 2. tide only model fields stored hourly
then 1 2 gives the storm surge component. Data
can then be used for Annual Maxima or JPM as for
tide gauge data, or be used with the gauge data
as an interpolation tool.
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• OTHER EXTREME LEVEL TECHNIQUES
• r largest method rather than the 1 largest
  method of Annual Maxima
• Revised JP Method
• Peaks over threshold
• Percentiles

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Some warnings about all methods

• The methods are designed for mid-latitude
  climates where extremes come from winter storms.
• Experience is needed in dealing with data sets
  which have large outlier extremes. It is
  important to decide if they are representative or
  not, as they affect analysis results
  considerably.
• None of the methods work well for really
  extreme events e.g. tsunami
• We have discussed extreme still water levels
  (tides surges) only. Extreme waves, and
  tide-surge-wave interactions, also have to be
  considered. And extreme waves currents for
  off-shore industry.
• Refs. Pugh Tides, surges and mean sea-level,
  1987, chapter 8 UK MAFF reports obtainable from
  http//www.pol.ac.uk/ntslf/

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Tsunami
Scenario Cumbre Vieja volcano, La Palma,
Canary Islands slides into the sea Tsunami waves
O(5-10m) hit NW European Shelf. (Picture from
Benfield Greig Hazard Research Centre, UCL)
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Some warnings about all methods

• The methods are designed for mid-latitude
  climates where extremes come from winter storms.
• Experience is needed in dealing with data sets
  which have large outlier extremes. It is
  important to decide if they are representative or
  not, as they affect analysis results
  considerably.
• None of the methods work well for really
  extreme events e.g. tsunami
• We have discussed extreme still water levels
  (tides surges) only. Extreme waves, and
  tide-surge-wave interactions, also have to be
  considered. And extreme waves currents for
  off-shore industry.
• Refs. Pugh Tides, surges and mean sea-level,
  1987, chapter 8 UK MAFF reports obtainable from
  http//www.pol.ac.uk/ntslf/

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Changes of Extremes and Risk with Climate Change

• Simple approach which considers just a MSL change
  and resulting changes in z vs. T(z)
• ? an order of magnitude increase in risk at
  Newlyn
• Complex approach which models changes of MSL,
  tides, surges etc. in a future climate
• ? conclusions are very dependent on confidence
  in global climate models

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Changes of Extremes and Risk with Climate Change

• Simple approach which considers just a MSL change
  and resulting changes in z vs. T(z)
• ? an order of magnitude increase in risk at
  Newlyn
• Complex approach which models changes of MSL,
  tides, surges etc. in a future climate
• ? conclusions are very dependent on confidence
  in global climate models

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Integrated effects of climate change on UK
coastal extreme sea levels

• (As an example of such a complex approach and
  with a suspicion that things are getting worse)

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Floods in the IoM 2002
Douglas
Ramsey
"the worst in living memory"
4m damage in 3 hours
Pictures from http//www.iomonline.co.im/ftpinc/we
ather/febhightide.asp.
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Aim

• To derive insight into on changes and trends in
  extreme sea levels from existing information
• Changes in extreme SL at the coast result from
• a) global MSL change regional variations
• b) regional land movements
• c) tidal changes due to increased SL
• d) changes in storm surges due to changes in
  "storminess"

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a) MSL change

• UK mean sea level (MSL) is rising
• Plot shows MSL "relative" (to the land) as
  measured by tide gauges
• Corrected for local land movements, the
  "absolute" MSL trend is about 1mm/y
  10cm/century
• IPCC predicts 47cm by 2100

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b) Land movements

• Land subsidence or uplift can result from
• post-glacial rebound
• water extraction
• sediment compaction etc.
• Estimates (mm/y) based on geological data
  (Shennan, 1989) are shown here
• Recent results (Shennan, in press) are not
  included

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c) Tidal changes

• Tides are modified by SL rise
• Increased depth ? longer wavelength
• Figure shows the change in MHW due to an assumed
  50cm rise in MSL
• Changes at the coast are 45 - 55cm

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d) Extreme storm surge

• Computed change in 50-year surge elevation
• "2?CO2"-"control"
• Produced from 30-y runs of surge models forced by
  met data from ECHAM4 T106 time-slice expts.
• Caution! Similar studies with other climate GCMs,
  different sampling and extreme value analysis
  give different results.

(from STOWASUS-2100 EU ENV4-CT97-0498)
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Change in relative extreme SL

• Taking the sum of changes in
  MSL MHW S50 land movement
  (Scottish uplift will decrease
  the change)
• we obtain change in extreme sea level (cm)
  relative to the land for 2075 shown in the plot
• Caution! - uncertainty in each component

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Rate of change of relative SL

• Assuming the changes in relative extreme SL occur
  between 1990 and 2075
• Mean rates are shown c.f. official UK advice
  (boxed numbers)

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Coastal areas at risk

• Areas below 1000-year return period level
• By 2100
• the
• 1 in 1000-y level may become a
  1 in 100-y level

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Conclusions

• Some of the methods used to compute extreme
  levels have been described but see refs. for more
  details.
• Also a case study of possible changes in extremes
  around the UK has been described ? we suggest
  that other countries conduct similar studies.
• Note that the IPCC Third Assessment Report
  discussed extensively changes in MSL, but pointed
  out that it is primarily the extreme events which
  do damage, and that far more study is required
  than has been made so far on extremes and on
  their possible changes in future.
• So the GLOSS community must include this topic in
  its programme of work.