Transcript Extreme Sea Level Analysis

Extreme Sea Levels
Philip L. Woodworth
Permanent Service for Mean Sea Level
with thanks to David Pugh, David Blackman and Roger Flather
Contents
•
•
•
•
Introduction
Annual Maxima method
Joint Probability method
Complementary value of tide gauge data and numerical
modelling
• Changes in extremes with climate change
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.
Let Q(z) be the Probability of a level z being exceeded in any 1 year.
(Don’t 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.
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.
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.)
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.
Example data used here are taken from Newlyn
(Mean Tidal Range 3 m)
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 z=3.0 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(z=HAT) = 0.33 = 28/84
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.
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 > 0.0. The special case k=0 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.
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.
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.
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.
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.
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 tide+surge 3.2+0.0 (0.04), 3.1+0.1 (0.04) and 3.0+0.2
(0.03)
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
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 tide+surge models
Example of simple methods, where you have data, define:
α100 = 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 α100 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).
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 tide+surge models
POL NISE model grid (~12km) - nested in NEAC
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.
OTHER EXTREME LEVEL TECHNIQUES
• ‘r largest’ method rather than the ‘1 largest’ method of Annual
Maxima
• Revised JP Method
• Peaks over threshold
• Percentiles
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/
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)
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/
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
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
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’)
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/weather/febhightide.asp.
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"
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
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
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
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 timeslice expts.
• Caution! Similar studies
with other climate
GCMs, different
sampling and extreme
value analysis give
different results.
(from STOWASUS-2100 EU ENV4-CT97-0498)
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
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)
Coastal areas at risk
• Areas below 1000year return period
level
• By 2100:
the
1 in 1000-y level
may become a
1 in 100-y level
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.