The Effect of the 18.6-Year Lunar Nodal Cycle on Regional Sea-Level Rise Estimates

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DOI: 10.2112/JCOASTRES-D-11-00169.1
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Abstract
Sea-level rise rates have become important drivers for policy makers dealing with the long-term protection of coastal populations. Scenario studies suggest that an acceleration in sea-level rise is imminent. The anticipated acceleration is hard to detect because of spatial and temporal variability, which consequently, have become important research topics. A known decadal-scale variation is the 18.6-year nodal cycle. Here, we show how failing to account for the nodal cycle resulted in an overestimation of Dutch sea-level rise. The nodal cycle is present across the globe with a varying phase and a median amplitude of 2.2 cm. Accounting for the nodal cycle increases the probability of detecting acceleration in the rate of sea-level rise. In an analysis of the Dutch coast, however, still no significant acceleration was found. The nodal cycle causes sea level to drop or to rise at an increased rate; therefore, accounting for it is crucial to accurately estimate regional sea-level rise.
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The Effect of the 18.6-Year Lunar Nodal Cycle on Regional
Sea-Level Rise Estimates
Fedor Baart
{{
, Pieter H.A.J.M. van Gelder
{
, John de Ronde
{{
, Mark van Koningsveld
{1
,
and Bert Wouters
{{
{
Department of Hydraulic
Engineering
Faculty of Civil Engineering
and Geosciences
Delft University of Technology
Stevinweg 1
2628 CN Delft,
The Netherlands
{
Department Marine and
Coastal Systems
Deltares
P.O. Box 177, 2600 MH Delft,
The Netherlands
1
Department of Environmental
Engineering
Van Oord
P.O. Box 8574, 3009 AN
Rotterdam, The Netherlands
{{
Department of Climate
Research and Seismology
Royal Netherlands
Meteorological Institute
P.O. Box 201, 3730 AE De Bilt,
The Netherlands
ABSTRACT
BAART, F.; VAN GELDER, P.H.A.J.M.; DE RONDE, J.; VAN KONINGSVELD, M., and WOUTERS, B., 2012. The effect
of the 18.6-year lunar nodal cycle on regional sea-level rise estimates. Journal of Coastal Research, 28(2), 511–516. West
Palm Beach (Florida), ISSN 0749-0208.
Sea-level rise rates have become important drivers for policy makers dealing with the long-term protection of coastal
populations. Scenario studies suggest that an acceleration in sea-level rise is imminent. The anticipated acceleration is
hard to detect because of spatial and temporal variability, which consequently, have become important research topics. A
known decadal-scale variation is the 18.6-year nodal cycle. Here, we show how failing to account for the nodal cycle
resulted in an overestimation of Dutch sea-level rise. The nodal cycle is present across the globe with a varying phase and
a median amplitude of 2.2 cm. Accounting for the nodal cycle increases the probability of detecting acceleration in the
rate of sea-level rise. In an analysis of the Dutch coast, however, still no significant acceleration was found. The nodal
cycle causes sea level to drop or to rise at an increased rate; therefore, accounting for it is crucial to accurately estimate
regional sea-level rise.
ADDITIONAL INDEX WORDS: Sea level, subsidence, decadal, tide, trend estimate.
INTRODUCTION
The current and expected rates of sea-level rise are
important drivers for policy makers dealing with the long-
term protection of coastal areas and populations. An example of
an area where sea-level rise is important is the Dutch coast.
There are several measures planned to deal with the expected
acceleration in sea-level rise, which will cost up to J1.6 billion
y
21
until 2050 (Kabat et al., 2009). The long history of tidal
records and the economic value of the area below sea level make
the Dutch coast an interesting case for analyzing sea-level
measurements and scenarios and for comparing local estimates
with global estimates.
LOCAL TRENDS
Sea-level changes are usually reported in the form of trends,
often determined over a period of one or more decades. For The
Netherlands, an important trend was reported after the 1953
flood, when a relative sea-level rise of 0.15 to 0.20 cm y
21
was
estimated for the design of the Delta Works. The first Delta
Committee report (Deltacommissie, 1960) referred to this
change rate as ‘‘relative land subsidence’’. Relative sea level,
the current term, is the sea-level elevation relative to the
continental crust as measured by tide gauges. Absolute sea
level is relative to a reference ellipsoid and is measured by
satellites. A recent estimate (van den Hurk et al., 2007) showed
that relative sea level rose at a rate of 0.27 cm y
21
during the
period 1990–2005. The land subsidence at the Dutch coast
varies around 0.04 60.09 cm y
21
(mean 6standard error of the
mean [SEM]; Kooi et al., 1998).
Local Forecasts
Coastal policy is shifting from observation-based reactions to
scenario-based anticipation (Ministerie van Verkeer en Water-
staat, 2009); it is, therefore, interesting to compare observed
trends with predicted rates. Sea-level scenarios often predict
not only a sea-level rise but also an accelerated rise. The
earliest Dutch scenario, published after the 1953 storm,
forecasted a rise of several meters due to Greenland ice melting
over an unspecified period (Deltacommissie, 1960). Van
Dantzig (1956) used a more concrete number of 70 cm for the
next century in a related publication. The latest study by the
Royal Netherlands Meteorological Institute (KNMI) (van den
Hurk et al., 2007; Katsman et al., 2008) resulted in a low and a
high scenario. The low scenario estimates a rise of 0.25 cm y
21
in the period 1990 through 2050 and 0.32 cm y
21
for the period
DOI: 10.2112/JCOASTRES-D-11-00169.1 received 19 September
2011; accepted in revision 20 September 2011.
Published Pre-print online 15 December 2011.
Coastal Education & Research Foundation 2012
Journal of Coastal Research 28 2 511–516 West Palm Beach, Florida March 2012
2050 through 2100. The high scenario predicts 0.58 cm y
21
and
0.77 cm y
21
for the same periods. A high-end estimate of
2.02 cm y
21
was reported by the second Delta Committee in
2008, based on the Intergovernmental Panel on Climate
Change (IPCC) A1FI scenario for the period 2050 through
2100 (Deltacommissie, 2008, see figure 4, page 24). This
extreme scenario was used to assess the sustainability of the
Dutch coastal policy.
Global Trends
The global measurement of relative sea level started in 1933
when the Permanent Service for Mean Sea Level (PSMSL)
began collecting sea-level data from the global network of tide
gauges (Woodworth and Player, 2003). Trends based on those
measurements vary around 0.17 cm y
21
. For example, Holgate
(2007) reported a 0.145 cm y
21
over the period 1954–2003 and
Church et al. (2008) reported 0.18 cm y
21
over the period 1961–
2003. With the launchof the TOPEX/Poseidon satellite in 1992,
measurements of absolute sea level became available, with
near global coverage and high resolution in time and space.
Those measurements were used in the latest estimates,
summarized in the IPCC report (Bindoff et al., 2007), giving a
0.31 cm y
21
absolute sea-level rise over the period 1993–2003.
Despite the apparent difference, tidal-station measurements
compare well with satellite data when accounting for correc-
tions, start of time window, and the geographical location
(Prandi, Cazenave, and Becker, 2009).
Global Forecasts
Of the global scenarios for future sea-level rise, the most
influential are the current model-based IPCC scenarios (Bind-
off et al., 2007). The estimated rise varies between 0.17 cm y
21
(lower B1) and 0.56 cm y
21
(higher A1FI) over the period 1980–
1999 through 2090–2099 (Meehl et al., 2007). All scenarios
result in a most likely sea-level rise that is higher than the
average rate of 0.18 cm y
21
over the period 1961 to 2003.
Detecting Acceleration
Even though sea-level rise acceleration was expected to
become apparent in the early years of this century (Woodworth,
1990), there is presently no overall, statistically significant
acceleration, other than that in the early 20th century (Church
and White, 2006; Jevrejeva et al., 2008). The probability of
detecting an acceleration in sea-level rise is low because of the
effect of decadal variations (Douglas, 1992; Holgate, 2007).
Accounting for decadal variations can, therefore, enhance our
ability to detect acceleration.
The Nodal Cycle
One such decadal variation is the lunar nodal cycle. The tide
on the Earth is driven by six different forcing components with
periods varying from 1 day to 20,940 years. The fifth component
is the 18.6-yearly lunar nodal cycle (Doodson, 1921). The term
nodal cycle is best explained while looking up from the Earth.
Consider the node as the intersection of the ecliptic plane,
which follows the path of the Sun, and the orbital plane, which
follows the path of the Moon. This node moves westward,
making a circle every 18.6 years.
The main effect of this cycle is that it influences the tidal
amplitude (Woodworth, 1999; Gratiot et al., 2008). There are
indications that the 18.6 yearly cycle also influences regional
mean sea level, for example, at the Dutch coast (Dillingh et al.,
1993) and at a collection of other tidal stations (Houston and
Dean, 2011; Lisitzin, 1957). Global variation studies on tide
gauges using spectral analysis by Trupin and Wahr (1990) and
on satellite data using harmonic analysis (Cherniawsky et al.,
2010) also indicate a cycle in regional mean sea levels.
Observed tide is often compared with the equilibrium tide. The
equilibrium tide is the tide that would exist if the earth were
completely covered by water and if there were no friction. The
equilibrium tide theory builds on the work of Doodson (1921),
Cartwright and Tayler (1971), and Cartwright and Edden (1973).
Following Rossiter (1967), we used Equation (1) for the
equilibrium elevation fand the resulting nodal amplitude A(in
millimeters), with the Mmass of the moon in kilograms, the E
mass of the earth in kilograms, the emean radius of the earth
(in kilometers), the rmean distance between the earth center
and the moon center (in kilometers), the llatitude in radians,
and the Nlongitude of the Moon’s’ ascending node (from ’18u189
to ’28u369). The phase wis 0ufor |l|$35.3uand 180ufor |l|
,35.3u.
f~9
8
M
Eee
r

3
sin2l{1
3

cos N0|0:06552A~26:3 sin2l{1
3
M~5:9736e24
E~7:3477e22
e~6,371,000
r~384,403,000
ð1Þ
Proudman (1960) showed that the nodal tide should follow
the equilibrium tide for friction. The earth tide should also be
taken into account. Rossiter (1967) corrected by a factor of 0.7 to
allow for the effect of a yielding Earth. This is also the approach
used by Pugh (1987) and Cherniawsky et al. (2010). The
correction factor is based on the combined effect of the change
in the height of the equilibrium level above the solid earth,
given by the formula 1 2k2h(V
p
/g), where kand hare the
Love numbers (Love, 1909). The elastic response of the earth
has an amplitude of hV
p
/g, where his a known elastic constant,
V
p
/gis the gravitational potential, and gis the gravity constant.
When the tidal periods become longer, not only the elastic
response but also the viscose response is important, and,
therefore, the factor of 0.7 may not be appropriate (Pugh, 1987).
For regional sea-level rise estimates, the spatial variability of
the nodal cycle is relevant. This spatial variability is also
relevant for estimating the global mean sea level. The global
mean sea level itself is not affected by this cycle, but trend
estimates can be affected because both tide gauges and the
satellites have limited coverage of the world. Tide gauges have
higher coverage in the Northern Hemisphere, and the
altimetry satellites only cover the area between 264uand 64u.
Examining the agreement with the equilibrium tide and the
observed nodal cycle is relevant because it determines the best
512 Baart et al.
Journal of Coastal Research, Vol. 28, No. 2, 2012
method to estimate the local effects of the nodal cycle. Previous
comparisons with the equilibrium tide (e.g., Currie, 1976;
Trupin and Wahr, 1990) have shown agreement.
Accounting for the nodal cycle should increase the probabil-
ity of finding acceleration or deceleration in the rate of sea-level
rise (Baart et al., 2010; Houston and Dean, 2011). In this
article, we determine whether accounting for the nodal cycle
affects sea-level rise estimates locally and analyze how the
nodal cycle varies across the globe.
METHODS
The phase and amplitude of the nodal cycle are estimated by
multiple linear regression using Equation (2). Variable tis time
in Julian years (365.25 d) since 1970, b
0
is the initial mean sea
level (in centimeters), b
1
is the rise (centimeters per year), and a
and bcan be transformed into the amplitude A~ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a2zb2
p(in
centimeters) and the phase w5(arctan a/b) in radians.
Acceleration is tested by comparing the regression model with
the quadratic term b
2
(centimeters per year
2
)withthe
regression model without the quadratic term.
htðÞ~b0
|{z}
mean level
zb1t
|{z}
trend
zb2t2

|fflfflffl{zfflfflffl}
acceleration
zasin 2pt
18:6

zbcos 2pt
18:6

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
nodal cycle
:ð2Þ
We used a spectral analysis only to determine whether the
nodal cycle was the most dominant signal in the spectrum for
cycles with a period greater than a year. The stacking method
was not used because the ‘‘‘‘detrending before fitting the cycle’’’’
approach leads to an underestimate of the amplitude when the
time-series length is not several times as long as the 18.6-year
period. Therefore, we used the same harmonic analysis
approach as Battjes and Gerritsen (2002) and Houston and
Dean (2011).
RESULTS
Local Relative Sea Level
To determine the relevance of the nodal cycle at the Dutch
coast, a spectral analysis was carried out on the yearly means of
six main tidal gauges for the period 1890–2008. The data were
corrected for atmospheric pressure variation using an inverse
barometer correction. The spectral density shows a clear peak
at the 18.6-year period (Figure 1). The multiple linear
regression yields a sea-level rise (b
1
) of 0.19 60.015 cm y
21
(95%), an amplitude (A) of 1.2 60.92 cm, and a phase (w)of
21.16 (with 1970 as 0), resulting in a peak in February 2005
(Figure 2). No significant acceleration (inclusion of b
2
) was
found.
Probability of Acceleration Detection
The nodal cycle explains 9% of the variance in the detrended
mean sea level. Explaining more variance has the advantage
that other effects become clearer. We used this process to
determine the change in the probability of detecting an
acceleration in the rate of sea-level rise. This probability, the
statistical power, is calculated for the lower and higher KNMI
Figure 1. Spectral analysis of the mean of six tidal stations in the period
1890–2008. The dashed line marks 18.6 year.
Figure 2. Annual mean sea level averaged over six Dutch tidal stations
(black dots). Multiple linear regression with a nodal cycle (solid curve),
with a confidence interval (dotted curve), and a prediction interval (dashed
curve). Linear regression line through the period 1890–1990 (light gray).
Linear regression line through the period 1991–2009 (dark gray).
Sea-Level Rise and the Lunar Nodal Cycle 513
Journal of Coastal Research, Vol. 28, No. 2, 2012
scenarios (van den Hurk et al., 2007) for the Dutch coast. The
power was estimated using a simulation, with a generated data
set, based on the broken linear trends from the scenarios in van
den Hurk et al. (2007). In addition, the Dutch nodal cycle was
imposed but with a random, uniform distributed phase, as well
as a random, normal distributed error, based on the residuals
after fitting the nodal cycle for the mean of the Dutch tidal
station measurements. The simulation was performed with
200 samples per condition. The detection of the acceleration
was done by comparing the linear-regression model with a
model with an acceleration term included using an analysis of
variance (ANOVA) with 1 degree of freedom. The probability of
detecting sea-level acceleration for the lower scenario went up
from 46% without the nodal cycle to 48% with the nodal cycle.
The probability of detection in the high-end scenario went up
from 82% without the nodal cycle to 84% with the nodal cycle
included. Generally, 80% is considered an acceptable level.
Thus, it can be concluded that, even without accounting for the
nodal cycle, it is likely that the acceleration in the higher
scenario, if it were present, would have been found.
Local Absolute Sea Level
Repeating the previous analysis on the North Sea satellite
data yielded the same nodal cycle (Figure 3). By including the
nodal cycle, the absolute sea-level rise lowers from 0.23 cm y
21
to 0.07 cm y
21
because, coincidently, the time window starts at
the bottom and ends in the peak of the nodal cycle. This clearly
shows how including the nodal cycle may affect estimates of
sea-level rise.
Global Relative Sea Level
Now that it is known that the nodal cycle is important for
estimates of local sea-level rise, the next question is how the
nodal cycle varies across the globe. The variation in global
relative sea-level was analyzed using the PSMSL tidal gauge
data set. From the 1157 gauges, 511 were selected based on
their recorded history of at least 57 (3 319) years. The analysis
of the spectral densities at the tidal stations was skipped
because it has already been performed in detail (Trupin and
Wahr, 1990), showing a peak at 18.6 years.
Equation (2) was applied to the selected stations, in which 134
stations showed an amplitude (A) that was significantly different
from 0. This confirms the global presence of the effect of the
lunar nodal cycle, with a median amplitude of 2.2. The variation
in global phase and amplitudes are shown in Figure 4.
Global Absolute Sea Level
The phases found at the tidal stations were compared with the
phases found in nearby measurements from altimetry satellites
for verification. This data set was obtained from the Common-
wealth Scientific and Industrial Research Organisation web site
and consists of sea surface heights with inverse barometer (IB)
corrections, seasonal signals removed, and glacial isostatic
adjustments corrected. Because satellite data are only available
for one lunar nodal period, the results are susceptible to other
influences and are not yet stable. The variation in global phase is
plotted in Figure 4. Tidal gauge and satellite measurements
show a reasonable correspondence in the Atlantic Ocean but not
in the Pacific Ocean. The canonical correlation between the
amplitude and the phases of stations and of the nearby satellites
is 0.21, which is low yet statistically significant.
When to Include the Nodal Cycle
The two extra parameters, amplitude and phase, can result
in a less-accurate estimate of the sea-level rise parameter. One
way to approach this is by determining whether the variance
explained by the combination of the two extra parameters is
statistically significant (using an ANOVA with 2 degrees of
freedom). An alternative is to use the Akaike information
criterion.
Another simulation provides a general estimate of what
would be a good period for including a nodal cycle in estimates
of regional sea level. Here, we assumed a sea-level rise equal to
0.2 cm y
21
, a nodal amplitude of 2.2 cm, and a uniform
distributed random phase and a random error of 2.5 cm. By
varying the time period and comparing the root mean square
error of the estimate of nodal fit and linear fit, we find that,
with these conditions, it is useful to include the nodal cycle
terms starting with periods of 14 years and longer. This period
for which it is advisable to include the nodal cycle becomes
longer because the ratio between them is a function of the
random error and the amplitude of the nodal cycle increases. A
Figure 3. Absolute sea level in the North Sea. (Top figure) Linear
regression fitted through corrected satellite observations for the North Sea
from Topex (o), Jason1(n), and Jason2 (+). Dashed line represents the
confidence interval; dotted line represents the prediction interval. (Lower
figure) Seasonal regression (Equation 2) fitted through corrected satellite
observations for the North Sea from Topex (o), Jason1(n), and Jason2 (+).
Dashed line represents the confidence interval; dotted line represents the
prediction interval.
514 Baart et al.
Journal of Coastal Research, Vol. 28, No. 2, 2012
similar discussion can be found in Blewitt and Lavalle
´e (2002)
for the comparable problem of fitting geodetic velocities.
If the goal is to develop an unbiased local estimate of the sea-
level rise parameter, the simplest approach is to use time series
of multiples of 18.6 +9.3 years (integer plus a half). When the
goal is to develop a good estimate of the level or acceleration,
this approach cannot be used.
The goal of including the nodal tide is to fit the nodal cycle, not
other decadal cycles. Therefore, the nodal cycle should only be
incuded in the 18.6 year is within the modal frequency bin of the
multi-year spectrum. In addition, it is advisable to check for the
reliability of the fit, by, for example, splitting up the tidal signal
into two separate parts, which should yield the same nodal cycle
phase. If the estimate of the nodal cycle is based on satellite
measurements, it should be verified using local tide gauges.
CONCLUSIONS
Coastal management requires estimates of the rate of sea-
level rise. The trends found locally for the Dutch coast are the
same as have been found in the past 50 years (Deltacommissie,
1960; Dillingh et al., 1993). Even though including the nodal
cycle made it more likely that the high-level scenarios would
become apparent in the observations, no acceleration in the
rate of sea-level rise was found. The higher, recent rise (van den
Hurk et al., 2007) coincides with theup phase of the nodal cycle.
For the period 2005 through 2011, the Dutch mean sea-level is
expected to drop because the lunar cycle is in the down phase.
This shows the importance of including the 18.6-year cycle in
regional sea-level estimates. Not doing so on a regional or local
scale for decadal length projections leads to inaccuracies.
There is a difference between the nodal cycle phase expected
from the equilibrium and the nodal cycle phase found in tidal
records. This is inconsistent with the results from Trupin and
Wahr (1990), possibly because of the difference between the
stacking approach and the harmonic approach. The difference
here is similar to the differences found by Cherniawsky et al.
(2010). The cause for the difference between the observed nodal
cycle and the equilibrium nodal cycle is not known. It could be a
physical effect but could also be the result of the way our mean
sea levels are measured and computed.
Whatever the cause, if there is a known decadal signal in the
sea-level records, it should be taken into account. Doing so will
provide better estimates of local sea-level rise, but only if it is
determined that the nodal fit is clearly present.
Although the nodal tide does not affect the true global mean
sea level, it can affect global mean sea level estimates. In sea-
level trends from satellites, if one assumes the equilibrium
nodal phase, one would expect a small nodal cycle in the mean
because of the phase distribution in combination with the
limited spatial coverage of the altimetry satellite. The sea-level
trends based on tide gauges can also be affected by the nodal
cycle because of irregular spatial sampling of the tidal gauges.
The observed nodal cycle shows a pattern that is more E–W,
rather than the equator–poles pattern of the equilibrium. The
nodal cycle can thus be safely ignored for global mean sea-level
estimates based on satellites. For global mean sea-level
estimates based on tidal gauges, the distribution of nodal cycle
phases could be checked for approximate, circular uniformness.
Globally, the 18.6-year cycle is observable in one-fourth of the
selected tidal stations, with a varying phase. The phases found,
based on tidal records and satellite data, show a weak
association, probably because of the short period of the satellite
measurements. It is not yet possible to give an accurate
estimate of the effect of the cycle across the globe. Just like a
sea-level rise trend can be very sensitive to the window of
observation, an estimate of a cycle is highly sensitive to
peaks. Without removing such effects, for example, the El
Nin
˜o–Southern Oscillation, short series like the satellite
measurements are not very representative of the effect of the
nodal cycle. A logical follow-up to this research would be to
simulate the effect of the nodal cycle using a global tide model.
Figure 4. Nodal cycle, estimated using Equation (2). Amplitudes in cm
(size of circles) and phases in years (color) of the lunar nodal cycle. (Top
figure) Tide gauges with at least 57 y of measurements. (Middle figure)
Altimetry satellites. (Bottom figure) Equilibrium.
Sea-Level Rise and the Lunar Nodal Cycle 515
Journal of Coastal Research, Vol. 28, No. 2, 2012
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    The relationship between the annual wind records from a weather station and annual mean sea level in an inter-tidal basin, the Dutch Wadden Sea, is examined. Recent, homogeneous wind records are used, covering the past 2 decades. It is demonstrated that even such a relatively short record is sufficient for finding a convincing relationship. The interannual variability of mean sea level is largely explained by the west–east component of the net wind energy, with some further improvement if one also includes the south–north component and the annual mean atmospheric pressure. Using measured data from a weather station is found to give a slight improvement over reanalysis data, but for both the correlation between annual mean sea level and wind energy in the west–east direction is high. For different tide gauge stations in the Dutch Wadden Sea and along the coast, we find the same qualitative characteristics, but even within this small region, different locations show a different sensitivity of annual mean sea level to wind direction. Correcting observed values of annual mean level for meteorological factors reduces the margin of error (expressed as 95 % confidence interval) by more than a factor of 4 in the trends of the 20-year sea level record. Supplementary data from a numerical hydrodynamical model are used to illustrate the regional variability in annual mean sea level and its interannual variability at a high spatial resolution. This study implies that climatic changes in the strength of winds from a specific direction may affect local annual mean sea level quite significantly.
  • Article
    Full-text available
    Rising sea levels due to climate change can have severe consequences for coastal populations and ecosystems all around the world. Understanding and projecting sea-level rise is especially important for low-lying countries such as the Netherlands. It is of specific interest for vulnerable ecological and morphodynamic regions, such as the Wadden Sea UNESCO World Heritage region. Here we provide an overview of sea-level projections for the 21st century for the Wadden Sea region and a condensed review of the scientific data, understanding and uncertainties underpinning the projections. The sea-level projections are formulated in the framework of the geological history of the Wadden Sea region and are based on the regional sea-level projections published in the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR5). These IPCC AR5 projections are compared against updates derived from more recent literature and evaluated for the Wadden Sea region. The projections are further put into perspective by including interannual variability based on long-term tide-gauge records from observing stations at Den Helder and Delfzijl. We consider three climate scenarios, following the Representative Concentration Pathways (RCPs), as defined in IPCC AR5: the RCP2.6 scenario assumes that greenhouse gas (GHG) emissions decline after 2020; the RCP4.5 scenario assumes that GHG emissions peak at 2040 and decline thereafter; and the RCP8.5 scenario represents a continued rise of GHG emissions throughout the 21st century. For RCP8.5, we also evaluate several scenarios from recent literature where the mass loss in Antarctica accelerates at rates exceeding those presented in IPCC AR5. For the Dutch Wadden Sea, the IPCC AR5-based projected sea-level rise is 0.07 ± 0.06 m for the RCP4.5 scenario for the period 2018–30 (uncertainties representing 5–95%), with the RCP2.6 and RCP8.5 scenarios projecting 0.01 m less and more, respectively. The projected rates of sea-level change in 2030 range between 2.6 mm a−1 for the 5th percentile of the RCP2.6 scenario to 9.1 mm a−1 for the 95th percentile of the RCP8.5 scenario. For the period 2018–50, the differences between the scenarios increase, with projected changes of 0.16 ± 0.12 m for RCP2.6, 0.19 ± 0.11 m for RCP4.5 and 0.23 ± 0.12 m for RCP8.5. The accompanying rates of change range between 2.3 and 12.4 mm a−1 in 2050. The differences between the scenarios amplify for the 2018–2100 period, with projected total changes of 0.41 ± 0.25 m for RCP2.6, 0.52 ± 0.27 m for RCP4.5 and 0.76 ± 0.36 m for RCP8.5. The projections for the RCP8.5 scenario are larger than the high-end projections presented in the 2008 Delta Commission Report (0.74 m for 1990–2100) when the differences in time period are considered. The sea-level change rates range from 2.2 to 18.3 mm a−1 for the year 2100. We also assess the effect of accelerated ice mass loss on the sea-level projections under the RCP8.5 scenario, as recent literature suggests that there may be a larger contribution from Antarctica than presented in IPCC AR5 (potentially exceeding 1 m in 2100). Changes in episodic extreme events, such as storm surges, and periodic (tidal) contributions on (sub-)daily timescales, have not been included in these sea-level projections. However, the potential impacts of these processes on sea-level change rates have been assessed in the report.
  • Article
    Full-text available
    The Wadden Sea is a unique coastal wetland containing an uninterrupted stretch of tidal flats that span a distance of nearly 500km along the North Sea coast from the Netherlands to Denmark. The development of this system is under pressure of climate change and especially the associated acceleration in sea-level rise (SLR). Sustainable management of the system to ensure safety against flooding of the hinterland, to protect the environmental value and to optimise the economic activities in the area requires predictions of the future morphological development. The Dutch Wadden Sea has been accreting by importing sediment from the ebb-tidal deltas and the North Sea coasts of the barrier islands. The average accretion rate since 1926 has been higher than that of the local relative SLR. The large sediment imports are predominantly caused by the damming of the Zuiderzee and Lauwerszee rather than due to response to this rise in sea level. The intertidal flats in all tidal basins increased in height to compensate for SLR. The barrier islands, the ebb-tidal deltas and the tidal basins that comprise tidal channels and flats together form a sediment-sharing system. The residual sediment transport between a tidal basin and its ebb-tidal delta through the tidal inlet is influenced by different processes and mechanisms. In the Dutch Wadden Sea, residual flow, tidal asymmetry and dispersion are dominant. The interaction between tidal channels and tidal flats is governed by both tides and waves. The height of the tidal flats is the result of the balance between sand supply by the tide and resuspension by waves. At present, long-term modelling for evaluating the effects of accelerated SLR mainly relies on aggregated models. These models are used to evaluate the maximum rates of sediment import into the tidal basins in the Dutch Wadden Sea. These maximum rates are compared to the combined scenarios of SLR and extraction-induced subsidence, in order to explore the future state of the Dutch Wadden Sea. For the near future, up to 2030, the effect of accelerated SLR will be limited and hardly noticeable. Over the long term, by the year 2100, the effect depends on the SLR scenarios. According to the low-end scenario, there will be hardly any effect due to SLR until 2100, whereas according to the high-end scenario the effect will be noticeable already in 2050.
  • Article
    The relative sea level rates of rise, and their likely accelerations, are estimated for China by analysing the measured relative sea level data of short-term Chinese and long-term worldwide tide gauges. The analysis accounts for the very well-known natural oscillations up to quasi-60 years while also factoring the subsidence of the instrument. It is found that the relative sea levels rose in China during the twentieth century and this part of the twenty-first century from − 1.2 to + 3.2 mm/year, on average + 1.4 mm/year. These results are partially explained by the differential subsidence and the different timings of start/stop of the relatively short records. Because the tide gauges of China are all too short to infer accelerations, the world average values of 0.001–0.003 mm/year² for data sets of average rates of rise of + 1.3 to + 1.8 mm/year are taken as a likely guess. It is then expected that the sea levels may rise of 0–259 mm up to the end of the twenty-first century.
  • Technical Report
    Full-text available
    This report (written in Dutch) discusses the KNMI climate scenarios for The Netherlands. We give arguments why these scenarios will likely not come true. We also explain that most of the warming so far in The Netherlands is due to a jump in the temperature at the end of the 1980-ies.
  • Article
    Our analysis of Global Positioning System (GPS) site coordinates in a global reference frame shows annual variation with typical amplitudes of 2 mm for horizontal and 4 mm for vertical, with some sites at twice these amplitudes. Power spectrum analysis confirms that GPS time series also contain significant power at annual harmonic frequencies (with spectral indices 1 < α < 2), which indicates the presence of repeating signals. Van Dam et al. [2001] showed that a major annual component is induced by hydrological and atmospheric loading. Unless accounted for, we show that annual signals can significantly bias estimation of site velocities intended for high accuracy purposes such as plate tectonics and reference frames. For such applications, annual and semiannual sinusoidal signals should be estimated simultaneously with site velocity and initial position. We have developed a model to calculate the level of bias in published velocities that do not account for annual signals. Simultaneous estimation might not be necessary beyond 4.5 years, as the velocity bias rapidly becomes negligible. Minimum velocity bias is theoretically predicted at integer-plus-half years, as confirmed by tests with real data. Below 2.5 years, the velocity bias can become unacceptably large, and simultaneous estimation does not necessarily improve velocity estimates, which rapidly become unstable due to correlated parameters. We recommend that 2.5 years be adopted as a standard minimum data span for velocity solutions intended for tectonic interpretation or reference frame production and that we be skeptical of geophysical interpretations of velocities derived using shorter data spans.
  • Article
    An update is given of the work of the Permanent Service for Mean Sea Level (PSMSL) during the 1990s, a period in which the number of station-years in the data bank grew by almost one half. A short review is given of the PSMSL's current activities and responsibilities and its interactions with the Global Sea Level Observing System (GLOSS) and other sea and land level monitoring programmes.
  • Article
    The 18.6-year nodal tide is a component of all tide gauge records. It can affect estimates of sea level acceleration, in particular for tide gauge records with lengths of less than 60 years. We provide an analytic solution that shows the effect of the nodal tide on estimates of sea level trend and acceleration. By adding a term to the least squares formulation used to estimate sea level trend and acceleration, we can account for the nodal tide and eliminate its effect on the estimate. Using representative world-wide tide gauge records, we demonstrate that accounting for the nodal tide can improve estimates, particularly of acceleration.
  • Article
    Greenhouse warming scenarios commonly forecast an acceleration of sea level rise in the next 5 or 6+ decades in the range 0.1–0.2 mm/yr2. Long tide gauge records (75 years minimum) have been examined for past apparent sea level acceleration (i.e., deviation from a purely linear rise) and for indication of how long it might take to detect or verify a predicted future acceleration. For the 80-year period 1905–1985, 23 essentially complete tide gauge records in 10 geographic groups are available for analysis. These yielded the apparent global acceleration −0.011 (±0.012) mm/yr2. A larger, less uniform set of 37 records in the same 10 groups with 92 years average length covering the 141 years from 1850 to 1991 gave for acceleration 0.001 (±0.008) mm/yr2. Thus there is no evidence for an apparent acceleration in the past 100+ years that is significant either statistically, or in comparison to values associated with global warming. Estimating how well a global acceleration parameter could be determined in a relatively short time was accomplished by dividing the 1905–1985 data set into four equal time spans. The formal 1σ uncertainty (about 0.2 mm/yr2) of global acceleration from these 20-year periods is more than an order of magnitude larger than for the 80- and 141-year cases owing to the existence of large interdecadal and longer variations of sea level. This means that tide gauges alone cannot serve as a leading indicator of climate change in less than at least several decades. Confirming the prediction of a particular model at the 95% confidence level or differentiating between model predictions will take much longer. The time required can be significantly reduced if the interdecadal fluctuations of sea level can be understood in terms of their forcing mechanisms and then removed from the tide gauge records.
  • Article
    A small error in the computations of Cartwright & Tayler has been corrected, resulting in improved tables of the time harmonics of the principal terms in the tide-generating potential. The correction removes certain previously anomalous features, and otherwise affects the amplitudes in their 5th decimal places.
  • Article
    Nine long and nearly continuous sea level records were chosen from around the world to explore rates of change in sea level for 1904–2003. These records were found to capture the variability found in a larger number of stations over the last half century studied previously. Extending the sea level record back over the entire century suggests that the high variability in the rates of sea level change observed over the past 20 years were not particularly unusual. The rate of sea level change was found to be larger in the early part of last century (2.03 ± 0.35 mm/yr 1904–1953), in comparison with the latter part (1.45 ± 0.34 mm/yr 1954–2003). The highest decadal rate of rise occurred in the decade centred on 1980 (5.31 mm/yr) with the lowest rate of rise occurring in the decade centred on 1964 (−1.49 mm/yr). Over the entire century the mean rate of change was 1.74 ± 0.16 mm/yr.
  • Article
    Based on a careful selection of tide gauges records from the Global Sea Level Observing System network, we investigate whether coastal mean sea level is rising faster than the global mean derived from satellite altimetry over the January 1993-December 2007 time span. Over this 15-year time span, mean coastal rate of sea level rise is found to be +3.3 +/- 0.5 mm/yr, in good agreement with the altimetry-derived rate of +3.4 +/- 0.1 mm/yr. Tests indicate that the trends are statistically significant, hence coastal sea level does not rise faster than the global mean. Although trends agree well, tide gauges-based mean sea level exhibits much larger interannual variability than altimetry-based global mean. Interannual variability in coastal sea level appears related to the regional variability in sea level rates reported by satellite altimetry. When global mean sea level is considered (as allowed by satellite altimetry coverage), interannual variability is largely smoothed out.
  • Article
    An exercise of ‘data archaeology’ of high water tidal information from Liverpool, NW England has resulted in the construction of a time series of ‘Adjusted Mean High Water’ spanning 1768 to the present which can be employed as a record of proxy Mean Sea Level (MSL). The time series, although gappy, is arguably the second oldest sea level-related record in the world, after Amsterdam's (1682, although the data we hold are from 1700 only) and of comparable age to Stockholm's (1774). It describes a secular trend for the period up to 1880 of 0.39+/−0.17 mm/year, a trend for the twentieth century of 1.22plus;/−0.25 mm/year, and an overall low frequency acceleration of 0.33+/−0.10 mm/year/century. When considered alongside geological sea level information from the area, the evidence suggests that the greater secular trend of sea level in the twentieth century, compared to long term projections derived from geological information, is primarily the result of an acceleration towards the second half of the last century, consistent with conclusions inferred from previous analyses of the very small number of other long European MSL records.