Transcript Characterizing impact of local sea level rise through

Extreme value analysis of storm surges
along the US coast
and the role of rising sea level
Claudia Tebaldi
ASP Summer Colloquium, June 2011
Statistical Assessment of Extreme Weather Phenomena under Climate
Change
NCAR, Boulder, CO
Aim of our study
Using gauge measurements from a set of
locations along the lower US coasts and only
global average temperature projections,
– Estimate the magnitude of extreme storm surges in
terms of return levels for 10,25,50,100 yr return
periods.
– Estimate local sea level rise out to 2050.
– Combine the two to assess changes in the risk of
extreme sea levels from storm surges under sea level
rise.
Outline
• Extreme value statistics of storm surges along the Atlantic, Gulf and
Pacific Coasts.
• Future sea level rise by “downscaling” the semi-empirical model
proposed by Vermeer and Rahmstorf (PNAS 2009).
• Combining the two under the assumptions of independence and no
change in extreme storm surge statistics.
• Extension to include tidal (and seasonal) component.
• Many possible directions for improvements.
Data
55 gauges with almost complete hourly data over the 30 years 1979-2008, and
monthly data over 1959-2008.
Data at each gauge comes as two parallel time series: actual and predicted values:
actual, what was recorded at that hour, that day;
predicted, what NOAA anticipated on the basis of tidal patterns.
We will work with the actual observed but also by recombining the residuals,
(actual-predicted), representing the weather effect on water level, with the
predicted, through a bootstrap procedure.
Tide gauge
From NOAA website on tides and currents
Hourly time series for a gauge,
over a period of 5 days
Tide histograms for the same gauge
Data basics
Several components in the observed time series
(actual values, the black line):
 Long term trend (increasing if sea level is
rising, decreasing if it is receding, possibly
flat);
 Seasonal variations;
 Tidal (hourly) variations;
 Weather driven disturbances.
Data analysis steps
• We work with the observed time series of
hourly data (30 years) and a corresponding
observed time series of monthly data (50
years).
• We use the longer time series to detrend the
shorter time series by estimating and
subtracting a linear fit (and saving its linear
coefficient).
Extreme Value Analysis
• We compute daily maxima of hourly data after detrending.
• We separate winter from summer months conducting two analyses
separately (Nov-Apr vs. May-Oct).
• We perform a “peak-over-threshold” analysis choosing, after trial
and error, the 99th percentile of the daily maxima distribution as
the threshold, fitting the Generalized Pareto Distribution to the
values exceeding the threshold after declustering*.
* This turns out to be in almost all cases redundant since the spell length of these exceedances
rarely exceedes a handful of hours, so the daily maxima are rarely over consecutive days
because of a single storm straddling multiple days.
Results from GPD analysis
Winter 50-yr return levels
Summer 50-yr return levels
Note: these are values with reference to MHW
Results from GPD analysis
Winter 100-yr return levels
Summer 100-yr return levels
Note: these are values with reference to MHW
Sea Level Rise Component
• Vermeer & Rahmstorf (2009): A semi-empirical
model estimating the relationship between global
average temperature change, T-T0, the fast
component of temperature change, dT/dt, and the
rate of global sea level rise, dH/dt, as in
dH
dT
= a(T - T0 ) + b
dt
dt
In the VR09 equation a,b
and T0 are estimated from
past observations.
Then, a simple model
(MAGICC) can be run to
produce current and future
global average temperature
projections exploring
uncertainties related to
model climate sensitivity,
carbon cycle, scenarios.
We use 342 simulations of
global average temperature
change (19 model
configurations reproducing
CMIP3 GCMs, 3 strengths of
carbon cycle response and 6
SRES scenarios):
For each of the MAGICC
trajectories of global
average temperature
change we determine a
corresponding trajectory
for the rate of sea level rise
during the 1959-2008
period, whose average rate,
G, we can compare with the
local rates, Hk’s, of SLR at
the gauge locations.
We can then compute the
local component of SLR at
gauge k as Lk such that by
assuming an additive
model, the local sea level
rise (Hk) is the result of
offsetting the global signal
G by the local Lk as in
Hk=G+Lk
G
(3.4
mm
/yr)
We are going to use the gauge specific Lk’s
to revise future global SLR projections
upward or downward
Now we have all that we need to talk about
changes in return levels/return period in the
future.
We can estimate return level curves, and we can incorporate sea level rise by 2030 or 2050
as an offset to get a first order estimate of how return levels would change with SLR
Changes in return levels/return periods by 2050
Changes in return levels/return periods by 2050
What we saw in the observations was just one
particular combination of weather and tides.
What if a different combination had taken place?
We may want to think about constructing new series
of synthetic hourly values by recombining predicted
with residuals (actual--‐predicted) from observations.
Bootstrapping away…
• What we saw in the observations was just one particular
combination of weather and tides
• What if a different combination had taken place?
• We can construct new series of synthetic hourly values by
recombining predicted with residuals (actual-predicted from
observations). Remember that green line and the red line?
Bootstrap procedure:
• We compute a time series of residuals, as actual minus
predicted values;
• we then choose randomly a point in the series that we use as
our initial time, say t0;
• we "wrap-around" the time series of residuals so that it now
starts at that point in time and ends at t0 - 1;
• we sum this "shifted" time series of residuals (shifted green
line) to the original series of predicted values (red line),
forming a synthetic series of actual values (synthetic black
line);
• we apply the extreme value analysis to this new series
(compute daily maxima, compute 99th percentile threshold,
perform POT fitting).
What does one (or six) of the return
level curve/bootstrap look like?
What should we confirm or disproof in order to
assess the validity of our bootstrap?
Over all gauges and by season, do those red dots
fall randomly within the bootstrapped pdfs?
• Compute empirical CDF at red mark
• Do the 55 empirical quantiles appear as a sample from a
Uniform distribution?
• Preliminary results seem to suggest so, at least in terms of the
produced R2…less convincingly so in terms of the coefficient
beta (*)
(*)
What does it look like if we change our analysis
from observed surges to – for example – the
median results of the bootstrapped surges, or
the 95% bootstrap envelope?
Basic assumptions and shortcoming of
the analysis this far
• 30 year of data may be a little short for 100 yr events.
• Assuming that storm intensity won’t change may be too
optimistic.
• Sea level rise projections assume a constant additive offset of
the local rates with respect to the global rates
• Vermeer and Rahmstorf 2009 assume the same relative
importance going forward of the ice melting and thermal
expansion components.
• For locations on the Atlantic coast changes in the MOC
(projected by models to slow down) has been shown to be
anticorrelated to sea level rise. VR09 does not capture that.
Bromirski et al. 2011 recently argued similar importance of
currents for West coast.
Open questions/improvements
• Alternative representation of local sea level rise,
including ocean circulation changes where relevant
(esp., along the Atlantic coast).
• Data fusion of a larger network of gauges with more
missing data and/or longer daily or monthly record;
satellite record available for short time period
assessing slr at high resolution; model results
representing possible changes in future extremes’
statistics.
• Spatial interpolation of extremes at non observed
locations, taking into account coastal morphology and
peculiar characteristics like estuary regions.
Finally, harking back to Philippe’s talk on
Tuesday, what about modeling the joint
behavior of the extremes among predicted
(tides) and residuals (weather superimposed
storms)?
To be continued…