Download Mapping the return periods of extreme sea levels: Allowing for short

Global and Planetary Change 57 (2007) 139 – 150
www.elsevier.com/locate/gloplacha
Mapping the return periods of extreme sea levels: Allowing for short
sea level records, seasonality, and climate change
N.B. Bernier a,⁎, K.R. Thompson a , J. Ou a , H. Ritchie b
b
a
Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J1
Meteorological Service of Canada, 45 Alderney Drive, Dartmouth, Nova Scotia, Canada B2Y 2N6
Available online 25 January 2007
Abstract
This study of extreme sea levels is motivated by concern over increased coastal erosion and flooding under plausible climate
change scenarios. Extremal analyses are performed on the annual and seasonal maxima from 24 tide gauge stations in the
Northwest Atlantic. At data poor locations, a 40 yr surge hindcast and information from short observation records are used to
reconstruct sea level records prior to the annual and seasonal analysis of extremes. A Digital Elevation Model is used to generate
spatial maps of the return period of extreme sea levels associated with specified flooding probabilities under current conditions and
under projected global sea level rise scenarios for the next century. It is the first time such maps have been produced. Their primary
advantage is that extreme sea levels are expressed in terms of inundated areas as opposed to a critical flood value about an arbitrary
datum. Another novel aspect of this study is that the extremal analyses are carried out for specific seasons.
© 2006 Elsevier B.V. All rights reserved.
Keywords: sea level; extremal analysis; storm surges; spatial mapping of coastal flooding; Digital Elevation Model; climate change
1. Introduction
Over coming decades, projections of global sea level
rise and plausible climate change scenarios (e.g.,
Houghton et al., 2001) point to an increased flooding
risk for many low lying coastal regions. This is
particularly true for areas where subsidence of the
earth's crust combines with global sea level rise to
enhance the rate of relative sea level rise (i.e., with
respect to a fixed land point). In the southern Gulf of St.
Lawrence the projected change of sea level over the next
century is of order 1 m (Bernier and Thompson, 2006).
This creates serious concern for low lying coastal areas
⁎ Corresponding author.
E-mail address: [email protected]
(N.B. Bernier).
0921-8181/$ - see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.gloplacha.2006.11.027
already threatened by instantaneous flood events of the
same magnitude. Unfortunately, many of the regions at
risk have insufficient sea level data available for standard
extremal analysis. It is therefore difficult to evaluate the
distribution of extremes under current conditions and
even more problematic to assess the effect of climate
change on the return period of extremes.
In this study we map the return period of extreme sea
levels using (i) hourly sea level observations, (ii) a
dynamically based surge model, and (iii) a Digital
Elevation Model (DEM). Following in the footsteps of
Pugh and Vassie, 1980, we pay particular attention to the
case of short sea level records (e.g., several years in
length). The surge model has already been extensively
validated for short term forecasts (e.g., Bernier and
Thompson, 2006). The purpose here is to use the model
to generate a 40 yr surge hindcast that can be used to
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N.B. Bernier et al. / Global and Planetary Change 57 (2007) 139–150
calculate extreme statistics, even for locations with few
sea level observations. Thus, our interest is not in short
term surge forecasting but rather the calculation of
extreme statistics, essential information for the development of any sensible adaptation strategy to global sea
level rise and climate change. The DEM is used to
downscale the flooding statistics to the community level
(i.e., to downscale the results of the extremal analysis to a
horizontal resolution of meters). Maps of the return
period of extreme flood levels can then be used by local
authorities to quickly identify lands that will be flooded
on average every 2, 10, or even 100 yr. With this type of
information, communities can, for example, readily
identify areas where development should be prohibited
or the transport network protected.
The DEM maps of return period can also be used by
ecologists to evaluate the impact of floods on the
survival of species at risk. The piping plover is an
example of a species at risk. It is found along the
shorelines of the Northumberland Strait, the Magdalen
Islands and some beaches of Nova Scotia, Prince
Edward Island and Newfoundland. In 2001, there were
about 220 pairs of plovers and only 43 single birds left
(source: Environment Canada Species at Risk: http://
www.speciesatrisk.gc.ca/). Piping plovers arrive at their
nesting grounds in Atlantic Canada in late April. In
addition to predators and human disturbance, loss of
habitat due to storm surges and sea level rise is
considered a major threat to their survival. The
important point with respect to the present study is that
the return periods of extreme sea levels are required for
only one part of the year: the breeding season. In this
paper we show how to allow for seasonality in the
extremal analysis.
The structure of the paper is as follows. In Section 2,
the observed sea level records, standard extremal
analysis, and the reconstruction of sea level records in
data poor locations are described. Extremal analyses are
tailored and performed on seasonal maxima as opposed
to the traditional annual maxima. In Section 3, the
results of the seasonal extremal analyses are downscaled
to the community/ecosystem level using a recently
acquired and prepared DEM. In Section 4, projections of
the return periods of extreme sea levels are made under
climate change scenarios that include changes in the
severity of storms. The results of the study are
summarized and discussed in Section 5.
2. Extremal analysis of observed and hindcast sea
levels
In this section, extremal analyses are performed on
the annual maxima of hourly sea levels in order to
estimate the return period associated with critical flood
Fig. 1. Map of the domain of the storm surge model. The numbers mark the locations of the tide gauges used to validate the storm surge model and the
reconstructed total sea level. Station 14, marks the location for which a Digital Elevation Model is available.
N.B. Bernier et al. / Global and Planetary Change 57 (2007) 139–150
levels (ηc). The sea levels used in this study are for 24
gauges located along the east coast of the United States,
Quebec, and Atlantic Canada (Fig. 1). Two types of
hourly sea level were used: observations and reconstructed records using surge model hindcasts.
2.1. The observed sea levels
The observed hourly sea level records for the 24
locations were subject to thorough quality control prior
to analysis, including visual inspection of all large
recorded values. All records used in this study have a
minimum of 10 yr of observations between 1960 and
1999. The long term means were removed from all
records prior to analysis.
Estimates of the frequency of coastal flooding are
typically based on the analysis of annual maxima (e.g.,
Gumbel, 1958; Leadbetter et al., 1983; Coles, 2001).
Extreme value theory assumes that the variable we are
studying, Mn, is the maximum of n independent,
identically-distributed (iid) random quantities:
Mn ¼ maxfg1 ;: : : ; gn g
ð1Þ
It is further assumed that sequences of location and
scale parameters (an and bn N 0) exist such that Pr
141
(Mn b an + bnηc) converges to a non-degenerate function
as n tends to infinity. Under these conditions the
probability distribution function of Mn is one of three
extreme value types (e.g., Coles, 2001). The Type I
distribution is commonly used in the study of sea level
records (e.g., Dixon and Tawn, 1999; Lowe et al., 2001;
Woodworth and Blackman, 2002; Bernier and Thompson, 2006). The Type I extremal distribution has the
form
PrðMn bgc Þ ¼ expf−exp½−ðgc −an Þ=bn g
ð2Þ
In this study, maximum likelihood is used to estimate
the location and scale parameters from the annual and
seasonal maxima of the hourly sea level observations.
The application of the theory is illustrated for
Charlottetown, one of the few locations in the study
region with a long (1938–present) and a fairly complete
observation record. The annual maxima and minima
(about the annual mean) were first extracted from the
record (top panel of Fig. 2). Note the difference in the
interannual variability of the maxima and the minima and
the offset between the mean sea level and the extremes.
The latter reflects the effect of the tides at Charlottetown.
The maxima and minima were ordered and plotted on
Type I probability paper. The dots show the annual
Fig. 2. Observed sea levels at Charlottetown. The top panel shows the annual mean about the long term mean in meters. Note the trend in annual
means. The adjusted annual maxima and annual minima are also plotted. The average difference between the means and maxima and minima is due in
large part to the tides. The bottom two panels are Type I plots of the maxima and minima about the annual means. The x-axes are the return period in
years and the y-axes are the return level in meters. The dots are the ordered, observed adjusted annual maxima (bottom left panel) and observed annual
minima (bottom right panel) from 1938 to 2004.
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N.B. Bernier et al. / Global and Planetary Change 57 (2007) 139–150
maxima (bottom left panel of Fig. 2) and annual minima
(bottom right panel of Fig. 2). The lines were fit using
maximum likelihood. The shaded area marks the 95%
confidence intervals obtained using the delta method
(e.g., Coles, 2001). Note the difference in the slope of
the return level line (e.g., the difference between the 2 yr
and the 40 yr return period) of the maxima and minima.
The largest differences in the slopes of maxima to
minima are found at the southern most stations where
hurricanes are known to lead to extreme positive
residuals. Other factors such as an increase in frictional
effects associated with a decrease in water depth during
large negative residual events can limit their amplitudes
(e.g., Grant and Madsen, 1979).
2.2. The hindcast sea levels
An important limitation of standard extremal theory
is that it requires the hourly sea level records exceed
about 30 yr in length. Unfortunately this is rarely the
case. In Atlantic Canada, only a small number of such
records is available. For the Gulf of St. Lawrence, a
region that regularly sustains damage due to large flood
events, only one such record is available. Another
problem is that the distribution of both tides and surges
varies considerably over the region. Knowledge of the
distribution of extremes at one location is therefore not a
good estimate of the distribution of extremes at other
locations.
Fig. 3. Evolution of the surge event of December 1972. The top 6 panels are snapshots of the hindcast surges taken 9 h apart. The colorbar is surge
level in meters. The bottom panel shows the observed filtered residuals (black) and the hindcast surges (red) at the gauge location marked by the
yellow dot. The series cover two weeks surrounding the surge event of 17 December 1972. The vertical lines mark the times at which the snapshots
are taken.
N.B. Bernier et al. / Global and Planetary Change 57 (2007) 139–150
Our solution to this problem is to use a validated
storm surge model to reconstruct long sea level records
in data poor regions. The return period of seasonal
extreme sea level are then calculated from the seasonal
maxima of the reconstructed records.
The details of the surge model, and its validation,
are given in Appendix A. The hindcast skill of the
model is illustrated in Fig. 3. The top 6 panels are a
sequence of snapshots of sea surface height. The
bottom panel is a comparison of the hindcasts surge
and observed hourly sea level after removal of the
tide (and filtering to suppress variations with periods
shorter than 12 h that are not resolved by the model).
Overall the surge hindcast is quite accurate; the
hindcast rms error for the period 1960–1999 is
typically 8 cm.
The focus of the present study is not the hindcasting
of particular storm surges; it is the estimation of
flooding probabilities at particular times of the year.
Our approach to this problem closely follows that of
Bernier and Thompson (2006) but includes an
extension to seasonal returns (rather than annual
returns). The steps in the calculation of seasonal return
periods for a location with, say, only 5 yr of data is as
follows:
Step 1: The tides, ηT, are predicted for the first 4 yr
using a tidal package (e.g., Pawlowicz et al.,
2002) and tidal constants fitted to the fifth year
of observations.
Step 2: The observed sea levels, for the 4 yr not used for
the tidal analysis, are written in the form
g ¼ gT þ gS þ g R V
143
synthetic ηR′ record obtained by randomly
sampling with replacement from the binned ηR′
record. To allow for sampling variability, ten
realizations are generated each 40 seasons in
length.
Step 5: The median of the seasonal maxima of the 10
realizations is used in the standard extremal
analysis.
The extremal analysis of the reconstructed seasonal
maxima is shown in Fig. 4 for Shediac (Fig. 1, station
14) for Winter and Spring. There is an offset between the
stormy season of Winter and the quieter season of
Spring and a difference in the slope of the two lines.
Both are primarily associated with weaker cyclone
activity during the Spring season (e.g., Koutitonsky and
Budgen, 1991).
The ability of our approach to estimate seasonal
return periods at all locations is shown in the left
column of Fig. 5. The 40 yr return levels for Spring
based on the reconstructed records are plotted for the
24 gauge locations. Results show good agreement
between the observed and reconstructed seasonal sea
levels (compare top and bottom left panels). The 40 yr
return levels for Spring based on the reconstructed
records are within about 10 cm of the observed Spring
return levels. The 40 yr reconstructed levels for Spring
also show the same station to station variability as the
40 yr observed return levels for Spring. Thus we can
ð3Þ
where ηS is the hindcast surge and ηR′ is a
hindcast error that includes the effect of seiches
and baroclinic effects not captured by the storm
surge model as well as errors in predicting the
tide based on data from another year.
Step 3: The ηR′ are binned by time of year to reflect
seasonality in the distribution of ηR′. We used
two bins in this study: Spring–Summer and
Fall–Winter.
Step 4: We predict the tides for 40 yr using the constants
previously fitted to the fifth year of observations. (Note that the tidal package of Pawlowicz
et al., 2002 does have the option of allowing for
the 18.6 yr nodal modulation. We have verified
that it is recovered in the predicted tides). We
then add, for the season of interest, the 40 yr
predicted record of tides, surge hindcast, and a
Fig. 4. Seasonal return period of extreme total sea levels at Shediac
calculated from the reconstructed seasonal records. The x-axis is the
return period of the seasonal maxima in years where xi = − log(− log
(1 − pi)) for the ith ordered and adjusted seasonal maximum. The yaxis is the seasonal return level in meters. Note, both the offset and
the change in the slope of the return level line between the stormier
Winter period (January–March) compared to the quieter Spring
period (April–June).
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N.B. Bernier et al. / Global and Planetary Change 57 (2007) 139–150
Fig. 5. 40 yr return levels. The x-axis shows the station code. The y-axis is the 40 yr return level for Spring in meters calculated from the Type I
distribution fitted to the adjusted Spring seasonal maxima (Fig. 4). The shaded areas mark the 95% confidence intervals. The top left panel shows the
observed 40 yr return levels. The bottom left panel shows the 40 yr Spring return level obtained using 5 yr of hourly sea level observations and the 40
surge hindcast (Section 2.2). The top right panel shows the 40 yr Spring return level of the filtered residuals with periods below 12 h removed (LηR).
The bottom panel is the 40 yr Spring return level of the hindcast surges (ηS).
generate seasonal extremes with only 5 yr records and
our 40 yr surge hindcast.
3. Downscaling the return periods
In this section, a DEM for an important piping plover
nesting ground (top panel of Fig. 6) is used to downscale
the return period of extreme sea levels for the nesting
season (Spring). The approach is to flood the DEM to a
specified level (ηc), or equivalently return period, to
identify areas at risk. The DEM can therefore be used to
evaluate the extent of any hindcast or forecast flood event.
One subtlety is that flooding is path dependent e.g., a
small valley can only be flooded if the land separating it
from the adjacent ocean is also flooded (hence, there must
be a path to the valley). Another subtlety is that allowance
had to be made for culverts that can affect the extent of
flooding but are not detected by the lidar system that was
used to make the DEM (Webster et al., 2004). We also
note that the DEM is flooded naively in the sense that no
delay is allowed for a flood to propagate through a culvert
or to retire from a flooded region. Models are available for
this purpose and could be used in future studies.
The flooding maps are obtained by first performing an
extremal analysis on the Shediac reconstructed Winter
and Spring record (Fig. 4). The sea level at which each
point in the DEM becomes flooded is then associated
with a return period. The result is a map of the return
period of flood events for the Winter and Spring seasons
(middle and bottom panels of Fig. 6 respectively). Fig. 6
shows the different extents of the return period of
flooding for the Winter (top panel) and Spring (bottom
panel) months. Note how the vulnerable area differs
between seasons. Note also how slowly the spatial extent
of the area at risk grows with increasing return period in
the Spring compared to the Winter. In fact, the 100 yr
Spring return level barely exceeds the 5 yr Winter return
level. This is the first time such maps have been
produced. They have the advantage of simplicity and
show, at a glance, which areas are most vulnerable to
flooding. Note that flooding is now defined in term of
inundated areas (hence landmarks) as opposed to
elevation above some arbitrarily chosen datum such as
mean sea level. The maps are therefore easy to interpret.
Sea level rise is expected to contribute, over the next
25 yr, about 0.2 m sea level increase at Shediac (Section
N.B. Bernier et al. / Global and Planetary Change 57 (2007) 139–150
145
Fig. 6. Digital Elevation Model for Shediac, New Brunswick, and spatial maps of the seasonal return period of extreme events. The top panel is the
DEM for an area located near station 14 (Fig. 1). The colorbar of the top panel indicates elevation above the DEM datum which is located 21 cm
below mean sea level. The horizontal resolution is 1 m and the measured vertical accuracy is better than 0.16 m (Timothy Webster, personal
communication). The middle panel is a return period map of Winter extreme events. The return periods are based on the extremal analysis of the
reconstructed Winter maxima (Fig. 4). The bottom panel is a return period map of the reconstructed Spring extreme events.
4). On the return period plot (Fig. 4), this rise in sea level
will raise the current Spring return level line to roughly
the current Winter line. It is therefore expected that the
risk of flooding will increase during the nesting period
to such an extent that in 25 yr the Spring return period
plot and vulnerability map will resemble the current
Winter return period plot and vulnerability map (middle
panel of Fig. 6).
4. Impact of climate change on the return period of
extremes
This section briefly explores how climate change
may modify the return period of extreme sea levels. The
return levels presented thus far are based on a hindcast
for a fixed observation period. It is possible to extend
our approach to allow for some elements of climate
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N.B. Bernier et al. / Global and Planetary Change 57 (2007) 139–150
change. For example, it is straightforward to approximate the effect of sea level rise by simply adding a
constant height to the return levels as was done in the
previous section. However, in the region studied here, it
is not possible to add a spatially uniform rate of sea level
rise as the effect of vertical crustal movement is spatially
variable (Peltier, 2004) and of the same order as the
generally accepted rate of global sea level rise of 1–
2 mm yr− 1 (Houghton et al. (2001)). Rates of sea level
rise must therefore be station dependent. At Shediac,
close to the location of the DEM, relative sea level is
expected to have risen 0.8 m by 2100 whereas it is
expected to increase by 0.7 m at Halifax. In terms of
changes in storminess, the consensus seems to point
toward an increase in the number of strong wind events
associated with an increase in the number of deep lows,
although the overall number of low pressure events is
expected to decrease (e.g., Lambert, 2004). The impact
of sea level rise and increased storminess on the return
period of extreme sea levels are investigated next.
Three climate change scenarios are discussed below.
They are illustrative rather than definitive and focus on
annual rather than seasonal extremes. We also focus on
Halifax, an important east coast Canadian city with a long
sea level record. The extension of the method to other
locations, and from annual to seasonal extremes, is
straightforward.
For the purpose of this exercise, it is assumed that the
low-pass filtered residuals (see Appendix A) recorded at
Halifax between 1960 and 1999, represent the current
conditions and are denoted by
gpres ¼ Lðg−gT Þ
ð4Þ
where η is the observed sea level about the mean and ηT
is the predicted tide. Hence, the observed sea level
record at Halifax is given exactly by
g ¼ gT þ gpres þ gR V
ð5Þ
where ηR′ includes, as before, the effects of seiches and
baroclinicity. It is further assumed that the impact of
climate change can be expressed simply through a
mathematical transformation of ηpres. The transformed
ηpres will be referred to as ηclim, the climate modified
residuals.
Scenario 1: It is assumed that atmospheric conditions, i.e., winds and pressure forcing, remain unchanged as we progress into the next century. It is
further assumed that sea level at Halifax, the representative station, will have risen 0.7 m by 2100. This sea
level rise is imposed on the present observed residuals
ηpres to obtain ηclim, the climate modified residuals. The
effect on the residuals is illustrated in the left panel of
Fig. 7. The black line shows ηpres plotted against itself
as a reference. The blue line shows ηclim = 0.7 + ηpres i.e.
the present residuals plus sea level rise plotted against
ηpres. In terms of the probability density function (or
similarly the histogram), applying sea level rise shifts
the probability density function of ηclim to the right by
0.7 m (not shown).
The shift in the probability density function increases
the annual maxima by 0.7 m (and also an, the location
parameter of the Type I distribution fit to the annual
maxima). This is illustrated in the Type I plot (right
panel of Fig. 7). The plot is produced by fitting a line
through the ordered annual maxima of η = ηT + ηpres + ηR′
(black line) and η = ηT + ηclim + ηR′ (blue line). The return
period plot shows that the impact of sea level rise is so
important that extreme sea levels with a current return
period of 100 yr are expected to have become regular
events by 2100.
Scenario 2: It is assumed that in combination with sea
level rise, increased storminess will lead to a linear
increase in the climate modified residuals.
Hence, ηclim = 0.7 + αηpres where α is a scaling factor
(α = 1.3 was chosen). The resulting climate residuals are
plotted against ηpres (in green) in the left panel of Fig. 7.
The linear increase in surge intensity has shifted and
stretched the probability density function of ηpres. The
location parameter, an is increased via the inflation of
the annual maxima. The shape parameter bn, a measure
of the spread, is also increased. The return period plot of
the ordered annual maxima of η = ηT + ηclim + ηR′ is
shown in green in the right panel of Fig. 7. The impact of
the linear increase in surge amplitude on the return
period plot is two-fold: the return level line is lifted and
the slope of the return level line is accentuated. The
overall effect is to further reduce the return periods of
extreme total sea levels.
Scenario 3: It is assumed that in combination with sea
level rise, weak cyclones will have a tendency to deepen
more while intense cyclones will remain relatively
unchanged. The effect on the amplitude of surges is
assumed to be as follows: mid-amplitude residuals are
inflated while the largest residuals are left untouched.
This is illustrated in the left panel of Fig. 7 (red line).
The effect of the chosen triangular scaling is to fatten the
probability density function at the mid-range amplitudes
(i.e. in the positive tail of the distribution) while keeping
the range fixed.
The impact of increasing mid-amplitude surges
appears more important than that of a linear increase in
surge amplitude (compare the red and green lines of
Fig. 7). This result confirms that it is rarely the most
N.B. Bernier et al. / Global and Planetary Change 57 (2007) 139–150
147
Fig. 7. Return period of extreme total sea levels into the next century for Halifax. The left panel shows the climate modified residuals, ηclim, against
the present residuals, ηpres. ηpres is plotted against itself in black as a reference. Residuals resulting from sea level rise (blue line) and the combined
effect of sea level rise and changes in storminess (green and red lines) are also plotted. The right panel is the return period plot of extreme total sea
levels associated with each climate change scenario. Each line is based on an extremal analysis of the annual maxima of each climate modified total
sea levels, η = ηT + ηclim + ηR′. The return levels shown are for (i) current conditions (black line), (ii) sea level rise (blue line), (iii) sea level rise and
linear increase of residuals amplitude (green line), and (iv) sea level rise and inflation of mid-range surge amplitude (red line).
extreme residuals that lead to annual maxima; extreme
sea levels are usually the result of a large (but not
unusual) residual coinciding with high tide.
The results shown in Fig. 7 suggest that over the next
century, the continued increase in flooding risk will
primarily be brought about by sea level rise (assuming
that the increase in sea level is comparable to what is
expected for Halifax). The simple sensitivity study
presented here also shows that changes in storminess
should not be overlooked when forecasting flooding risk
into the next century.
5. Conclusions
For locations lacking long sea level records, a storm
surge model can be used in combination with a short
observation record to calculate the return period of
extreme events on an annual or seasonal basis. Type I
extremal analysis of reconstructed seasonal sea levels in
the Northwest Atlantic gave good estimates of the 40 yr
return level. The method was also adapted to calculate
the return period of extreme events over a season of
interest. An important point to note is that this approach
requires only a few years of hourly sea level observations to calculate multi-decadal annual and seasonal
return levels of total sea level.
Given a Digital Elevation Model, it is possible to
downscale the results of an extremal analysis to produce
maps of the return period of flood extent. The extremal
analysis may be performed on the annual or seasonal
maxima of either a long observation record or a
reconstructed record. The maps can therefore be
produced for different periods of the year. Such maps
can then be used, for example, as an indicator of risk to
bird populations during their nesting season. Climate
change effects such as sea level rise and changes in
storminess can also be accounted for and maps of the
extent of floods may be produced under various climate
change scenarios. The maps can then be used to evaluate
how sea level rise may disturb the nesting season of
species at risk or may damage tourist infrastructure.
Thus, DEMs are a powerful way of downscaling the
results of extremal analyses to the community level.
The return period maps presented in this paper have
the advantage of simplicity. They are easy to understand
and allow easy and rapid identification of areas most at
risk of flooding. They can therefore be used by policy
makers to identify zones where development should be
limited, adaptation measures should be put in place, or
ecosystem management should be considered.
Although it has not been discussed in this paper, we
have successfully reproduced the return period of
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N.B. Bernier et al. / Global and Planetary Change 57 (2007) 139–150
minimum sea levels (Bernier, 2005). In areas where
maritime traffic requires a minimum water depth for
ships to enter ports or navigate safely, maps of the return
period and extent of low water levels can also easily be
produced.
Allowing for changes in the severity of storms is
difficult and ultimately such changes should be based on
reliable high resolution forcing from global climate
models. These are currently not available. We therefore
performed preliminary sensitivity studies by modifying
the shape of the distribution of observed surges.
Changes in storminess represented by large increases
in the amplitude of large or mid-range residuals were
found to have less impact on the return period of
extreme sea levels than the realistic sea level rise predicted for some areas of the study region (e.g., Scotian
Shelf ) over the next century. This does not imply that
changes in storm severity will have little impact on the
return period of extreme events. This sensitivity study
rather suggests that in regions where sea level rise is
considerable (order 1 m) it alone will result in a dramatic
reduction in the return period of extreme events over the
next century.
We have assumed throughout this study that tidesurge interaction is negligible in this region. This is
consistent with the generally good estimates of the
extreme seasonal return levels for most tide gauge
locations. Nonetheless, including tidal forcing in the
open boundary condition of the surge model, and thus
allowing for tide surge interactions, could improve the
hindcasts of total sea level in some areas. Preliminary
results suggest that tide surge interactions may be
significant in the southern Gulf of St. Lawrence. This is
the subject of an ongoing study.
Acknowledgements
This work was funded by the Natural Sciences and
Engineering Research Council of Canada and the
Climate Change Action Fund. The Digital Elevation
Model was kindly provided by Tim Webster of the
Center of Geographic Sciences, Nova Scotia. Tim
Webster also inserted the culverts (see text) and was
generous with the provision of advice on processing of
the Digital Elevation Model and also additional
information on its accuracy. Finally, we would like to
thank the reviewers for their constructive comments.
Appendix A. 40 yr surge hindcast
The surge hindcast model is a modified version of the
Princeton Ocean Model (Blumberg and Mellor, 1987). It
is based on the following depth averaged barotropic
momentum and continuity equations
Au
t s −t b
þ udju þ f u ¼ −gjgW þ
þ Aj2 u
At
qh
ðA:1Þ
AgW AðHuÞ AðHvÞ
Ag
þ
¼− P
þ
Ax
Ay
At
At
ðA:2Þ
where u = (u, v) is the depth-averaged horizontal
velocity, f is the upward pointing unit vector scaled by
the Coriolis parameter, τs and τb are the surface and
bottom stress, h is the mean water depth, A is the
horizontal viscosity, and H is the total water depth. The
rest of the notation is standard. The model's sea level
(ηS, where the subscript s denotes surge) has been
written in the form (e.g. Gill, 1982)
gS ¼ gP þ gW
ðA:3Þ
where ηP is the barometer effect due to variations in air
pressure and ηW is the isostatically-adjusted sea level of
the model. In the model, ηW is formulated as the
prognostic variable (Bobanović et al., 1997). ηW is due
to the effect of the wind and the dynamic response of sea
level to air pressure forcing. The kinematic stress
magnitude, cd (W)W2, is given by
1:2 10−3 ;
jW jb8 ms−1
cd ¼
0:68 10−3 þ 0:065 10−3 u; jW jz8 ms−1
ðA:4Þ
where W is the wind speed. The bottom stress
formulation is of the form cdbu(u2 + v2)1/2 where cdb,
the bottom drag coefficient, equals 2.5 × 10− 3.
The model domain extends from 38° N to 60° N and
72° W to 42° W (Fig. 1). It covers the Labrador and
Newfoundland Shelves, the Gulf of St. Lawrence, the
Scotian Shelf, the Bay of Fundy and the Gulf of Maine.
The surge model resolution is 1/12° which corresponds
to a latitudinal resolution of about 9 km.
The surge model was forced with AES40, a set of
high resolution, 6 hourly reanalyzed winds (Swail and
Cox, 2000; Swail et al., 2000) and with AESP40, the
pressure fields inferred from the AES40 surface wind
fields (Bernier and Thompson, 2006). The result is a
40 yr hindcast (1960–1999) of hourly sea levels. Fig. 3
is an example of the model output. It shows the
propagation of a large surge event.
The surge hindcast model is driven by winds and
pressures provided every 6 h. This corresponds to a
Nyquist frequency of one cycle every 12 h (Priestly, 1981).
N.B. Bernier et al. / Global and Planetary Change 57 (2007) 139–150
Fig. A.1. Root mean square hindcast error in meters. The x-axis is
station code (see Fig. 1 for station location). The y-axis is the rms
hindcast error.
Thus, apart from the contribution of nonlinear effects, the
surge model does not generate variability at periods
shorter than 12 h. To compare the hindcast surges and the
observed residuals we removed variability in the residuals
at periods shorter than 12 h using a low-pass filter
LgR ¼ Lðg−gT Þ
ðA:5Þ
where LηR is the low-pass filtered residual. The hindcast
surges were compared against the observed residuals at
149
the 24 available gauges (see Fig. 1 for station locations).
The rms error over the 40 yr of the hindcast was typically
8 cm (Fig. A.1). Rms errors calculated on 1 yr increments
confirmed that the quality of the hindcast remained
comparable throughout the 40 yr of the hindcast (Bernier,
2005; Bernier and Thompson, 2006).
Another way to validate the hindcast is to use the γ2
statistic, a measure of the variance of the hindcast error
upon the variance of the observed residuals (Thompson
et al., 2003). This form of statistic is useful in
determining whether the hindcast captures the general
evolution of the residuals. Fig. A.2 illustrates how γ2
varies spatially (each γ2 is calculated using the selected
observation record and prediction at different model
grid points). As expected, the skill of the model
worsens as we move away from the observation site.
This type of plot can be useful in identifying problems
in areas where the coastline surrounding a gauge is
rugged, a gauge is located in a bay not well represented
by the model resolution, or where two or more grid
points could justifiably be chosen to represent a tide
gauge location.
Fig. A.2. Map of the variance of the hindcast error upon the variance of the filtered observed residuals (γ2) at Rivière-au-Renard. The colorbar
indicates γ2. The location of the LηR record used to measure the γ2 is indicated by the yellow dot. γ2 typically varies slowly at grid points adjacent to
the gauge location. It then increases with increasing distance from the gauge. When γ2 reaches a value of 1, the variance of the hindcast error is as
large as the variance of the signal.
150
N.B. Bernier et al. / Global and Planetary Change 57 (2007) 139–150
The γ2 statistic does not tell us how well any given
large surge event is reproduced. The return period of
surges were therefore compared to return periods of LηR
(Section 2.2). The agreement is good with the hindcast
return levels typically within 10 cm of the observed
filtered residuals for all seasons and for both maxima
and minima (Bernier, 2005), thus confirming the quality
of the hindcast.
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