ESSDEarth System Science DataESSDEarth Syst. Sci. Data1866-3516Copernicus PublicationsGöttingen, Germany10.5194/essd-9-955-2017A multi-decadal wind-wave hindcast for the North Sea 1949–2014: coastDat2GrollNikolausnikolaus.groll@hzg.deWeisseRalfhttps://orcid.org/0000-0001-7449-6166Institute for Coastal Research, Helmholtz-Zentrum Geesthacht, 21502 Geesthacht, GermanyNikolaus Groll (nikolaus.groll@hzg.de)4December2017929559689May201722June20174October20173November2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://essd.copernicus.org/articles/9/955/2017/essd-9-955-2017.htmlThe full text article is available as a PDF file from https://essd.copernicus.org/articles/9/955/2017/essd-9-955-2017.pdf
Long and consistent wave data are important for analysing wave climate
variability and change. Moreover, such wave data are also needed in coastal
and offshore design and for addressing safety-related issues at sea. Using
the third-generation spectral wave model WAM a multi-decadal wind-wave
hindcast for the North Sea covering the period 1949–2014 was produced. The
hindcast is part of the coastDat database representing a consistent and
homogeneous met-ocean data set. It is shown that despite not being perfect,
data from the wave hindcast are generally suitable for wave climate analysis.
In particular, comparisons of hindcast data with in situ and satellite
observations show on average a reasonable agreement, while a tendency towards
overestimation of the highest waves could be inferred. Despite these
limitations, the wave hindcast still provides useful data for assessing wave
climate variability and change as well as for risk analysis, in particular
when conservative estimates are needed. Hindcast data are stored at the World
Data Center for Climate (WDCC) and can be freely accessed using the
doi:10.1594/WDCC/coastDat-2_WAM–North_Sea or via the coastDat web-page http://www.coastdat.de.
Introduction
Multi-decadal wind-wave hindcasts have become a common tool in
supporting the assessment of wave climate variability and change, such as its
extremes, trends or seasonal and inter-annual to decadal variability
e.g.. Data from
wind-wave hindcasts are also frequently used in practically oriented
applications such as in navigation, shipbuilding, offshore design or
strategic planning of logistics for the operation of future offshore wind
farms . Further applications comprise studies such
as evaluating the impact of waves on sea salt emissions or
the evaluation of the potential success or failure of different response
strategies to oil pollution . For all these different types
of applications long, homogeneous and consistent wind-wave data are needed to
derive robust estimates of wind-wave related parameters specific to the
problem. Often such information is unavailable from in situ or satellite data
alone and multi-decadal wind-wave hindcasts have become a common approach in
complementing such analyses.
While formerly wind-wave hindcasts were developed independently using
atmospheric forcing available at that time, they nowadays form an integral
part of global atmospheric reanalysis systems
e.g.. Owing to the limited spatial and temporal
resolution of such global reanalyses, there is, however, still a substantial
number of regional efforts aiming at higher spatial and temporal resolution.
These efforts usually use the traditional approach in which downscaled global
reanalysis wind fields are subsequently used to run a wave hindcast system
over the reanalysis period or sub-periods within that period
e.g..
For the North Sea, there presently exist a number of wind-wave hindcasts
covering at least some decades of years. The first of these multi-decadal
hindcasts was, to our knowledge, developed within the WASA project
while a more recent approach based on the ERA-40 global
atmospheric reanalysis is described in .
Aiming at a consistent description of met-ocean conditions in the North Sea,
developed and described a multi-decadal wind-wave hindcast
for the southern North Sea that is part of a comprehensive met-ocean
downscaling known as coastDat1 . The latter used the global
NCEP/NCAR reanalysis as boundary conditions and provides a
consistent met-ocean data set comprising of regionally downscaled atmospheric
, tide-surge and wind-wave
conditions from which full met-ocean data are available for
every hour over the hindcast period.
Data from coastDat1 have been extensively used for a wide variety of studies. For
an overview, see . While there was and there
still is substantial interest in these data, the effort terminated in 2007
when the atmospheric component of the met-ocean hindcast was discontinued and
consistent atmospheric data to drive the wind-wave and tide-surge models
became unavailable. Up to that time, data from coastDat1 were used by
more than 50 different users with a large variety of applications. About
50 % of the users originated from commercial enterprises, while about
25 % had a more direct scientific interest and another 25 % came from
public authorities . Because of ongoing interest in both
the scientific and the commercial exploitation of the data, eventually a
follow-up effort called coastDat2 was initiated. In this effort, upgraded
models with higher spatial resolution were used and the wind-wave part, in
addition, now also covered the entire North Sea. The atmospheric component of
coastDat2 is described in . In the following, we describe
and evaluate the upgraded wind-wave part that is driven by
the coastDat2 wind fields .
Model setup
For the wind-wave hindcast in coastDat2 the third-generation spectral
wind-wave model WAM version 4.5.4 was used. This
version represents an update and extension of the WAM cycle 4 used in
coastDat1 , the details of which are described in the WAM
documentation available at http://mywave.github.io/WAM/. Apart from
some technical changes such as in the I/O routines, a major change was
introduced by the replacement of the wave dissipation source term with a new
version described in and .
For the coastDat2 hindcast, the wave model was used in a nested version with
a coarse-grid simulation covering most of the northeast North Atlantic and a
fine-grid simulation covering the North Sea from
4.75∘ W to 13.25∘ E and from
50.5 to 59.5∘ N (Fig. ). The grid size of
the coarse grid is 0.5∘ latitude × 0.75∘ longitude
while that of the fine grid nested within the coarse grid is
0.05∘ latitude × 0.075∘ longitude. The latter
corresponds to a grid spacing of approximately 3 × 3 nautical miles.
Model domain and bathymetry used for the fine-grid simulation.
Colours indicate water depth in metres. Circles mark observational sites used
for the model evaluation. For the abbreviations, see Table .
Wave spectra were computed and discretized using 35 frequencies ranging from
approx. 0.042 to 1.067 Hz and 24 directional bins. The
integration time step was set to 3 min, and integrated parameters
derived from the wave spectra such as significant wave height, mean period or
direction were calculated and stored at every full model hour while wave
spectra were kept every 3 h. Boundary conditions were transferred
from the coarse to the fine grid every hour using the full modelled wave
spectra. For both grids, the model was set up and integrated in shallow-water
mode including depth refraction and depth-induced wave breaking. In the
coarse-grid simulation, monthly sea ice conditions from the northeast North
Atlantic were included to account for the varying fetch arising from
variations in sea ice coverage.
External dataForcing data
For both the coarse and the fine grid wind-wave simulations near-surface
marine wind fields at 10 m height were used. These were obtained, taking
atmospheric stability into account, from the high-resolution regional
atmospheric hindcast described in as part of coastDat2. For
the production of this atmospheric hindcast, the regional atmosphere model
COSMO-CLM with a spectral nudging scheme was used to
dynamically downscale the global atmospheric conditions given by the driving
NCEP/NCAR reanalysis . The downscaling was
performed for the North Atlantic/ European region and the model was
integrated on a rotated grid with a grid size of
0.22∘× 0.22∘ corresponding to a spatial resolution
of about 25 × 25 km. Atmospheric wind fields to drive the wave model were
available and used every model hour. Validation of the atmospheric hindcast
is described in . Compared to the driving global reanalysis
an improved representation of marine wind speeds in coastal areas, especially
for higher wind speeds, is noted . Note that the
atmospheric hindcast described in ends in 2012, but it is extended to
2014 to guarantee a consistent forcing data for the presented wave hindcast
simulation.
For the coarse-grid simulation monthly sea ice concentrations provided by the
Hadley Centre Sea Ice and Sea Surface Temperature data set
HadISST1.1, were used. The sea ice concentrations had a
spatial resolution of 1∘× 1∘ and were spatially
interpolated to the coarse wave model grid. Subsequently in the simulation
sea ice was accounted for by treating all model grid points with sea ice
concentrations exceeding 50 % as land for the corresponding time steps.
Reference data
A number of in situ wind-wave observations from platforms and buoys in the
North Sea originating from different sources were available for validation
(Table ). Basic quality control was applied but no attempt to
check homogeneity was done. The data cover different time periods including
gaps and differ in their temporal resolution. Because the model output is
available only at full model hours, the comparison with observations was
limited to data that were measured within ±10 min around full hours.
Location and description of in situ measurements used for
comparison.
SiteLocationDepth (m)Time periodTypeEKO2.6∘ E / 56.5∘ N721980–1998platformK133.2∘ E / 53.2∘ N251980–2008platformNB26.3∘ E / 55.0∘ N421993–2012buoyFN16.6∘ E / 54.0∘ N302003–2012platformHEL7.9∘ E / 54.2∘ N201989–2012buoyELB8.1∘ E / 54.0∘ N251990–2012buoyWES8.2∘ E / 54.9∘ N141993–2012buoy
In addition, wind-wave data derived from satellite provided by the merged
altimeter wave height database version 11.0 were used.
These data originate from the GlobWave project
(http://www.globwave.org) and cover the period 1991 to present. The
satellite data were co-located with the model data using a co-location
criterion of ±10 min at which the position of the satellite was matched
with the nearest grid point of the wave model.
To compare the wave model results in space and time, data from the ERA-Interim
global reanalysis spatially interpolated to the coastDat2
wave model grid were used. More specifically, data from the ocean wave
product of ERA-Interim were used, which originates from a comparable version
of the wave model WAM. Wave data are available every 6 h at 00:00, 06:00, 12:00
and 18:00 UTC and at a spatial resolution of
0.75∘ latitude × 0.75∘ longitude. The atmospheric
part of the ERA-Interim reanalysis has a 30 min time step and a spatial
resolution of about 79 km. For the comparison we use the ERA-Interim data
from 1980 to 2014. ERA-Interim used an assimilation scheme, which includes, among
others parameters, wind data from satellites and in situ observations. Further, from 1990 onwards, wave spectra in ERA-Interim were adjusted using
altimeter data, but no wave buoy data were used in the assimilation scheme
.
In order to avoid biases, only those instances in time are used for
comparison for which both observations and hindcast data were simultaneously
available. In particular, this results in a comparison of 1 h and 6 h
data when coastDat2 hindcast/ERA-Interim reanalysis is involved.
Evaluation
For the evaluation of the wave hindcast the following error metrics were
applied: the mean, the standard deviation (SD), the bias, the root mean
square error (RMSE), the scatter index (SI) and the correlation
coefficient (r). To evaluate the unbiased RMSE the standard deviation of
the error (SDE) was used. All measures were calculated for the entire
data sets if not stated otherwise. In the following, measures are called
errors when simulations are compared with observations and are called
differences when the two simulations are compared. Further details of the
error metrics can be found in Appendix .
Error metrics for the SWH at seven locations derived from in situ
observations (OBS), coastDat2 hindcast (CD2) and ERA-Interim reanalysis
(ERAi), for 1 h (coastDat2) and 6 h (ERA-Interim) data
respectively.
Scatter and quantile–quantile plot of SWH (in metres) between in situ
observation (x-axis) and coastDat2 hindcast data (y-axis). Coloured
squares indicate the number of data in each
0.5 m× 0.5 m bin. Coloured dots represent the
percentile values of the quantile–quantile plots between observed and
coastDat2 hindcast (cyan) and between observed and ERA-Interim reanalysis
significant wave heights (magenta). Note that the comparison is made for
different periods according to data availability (see Table ).
Significant wave height
Significant wave height (SWH) derived from hindcast data and in situ
measurements was compared at seven sites in the North Sea
(Fig. ). Comparison of instantaneous values revealed noticeable
scatter between modelled and observed data with biases ranging between about
0 and 0.25 m. Root mean square errors varied between approximately
0.4 and 0.7 m (Table ). When distributions were
compared, generally a reasonable agreement was inferred for the lower to
intermediate percentiles corresponding to wave heights of up to
2–4 m depending on location (Fig. ). Higher percentiles
were generally found to be overestimated in the hindcast data.
To put these findings into perspective, Fig. , in addition, shows
a corresponding analysis for SWH derived from the ERA-Interim reanalysis.
Here, generally, a tendency towards an underestimation of the higher SWHs can
be inferred. This feature is most pronounced at near-coastal locations such
as at station ELB. An evaluation with a normalized Taylor diagram
(Fig. ) indicates that for both the ERA-Interim and the
coastDat2 SWHs, correlation with observations typically varies around 0.9
with the values being slightly higher for the ERA-Interim reanalysis. The
analysis further reveals that the observed SWH variability is somewhat
underestimated by the ERA-Interim reanalysis and overestimated in the
coastDat2 data set. The centred root mean square errors are slightly above
(below) 0.5 m for coastDat2 (ERA-Interim). Comparing 6 h instead
of hourly values for the coastDat2 SWHs, no substantial differences for the
statistical values used by the Taylor diagram can be found. A more detailed
comparison of error statistics for the seven locations is provided in
Table .
A spatial comparison of the differences between ERA-Interim and coastDat2
SWHs for the common period 1980–2014 is illustrated in Fig. . With
the exception of near-coastal waters, the SWH obtained from the coastDat2
hindcast is on average higher compared to that from the ERA-Interim
reanalysis, with increasing differences from south to north. Largest
systematic differences of up to 0.6 m were found off the Norwegian
coast. A similar spatial pattern is obtained when root mean square
differences are compared. These differences were found to vary between about
0.4 m in the southern North Sea and more than 0.9 m in the
northern parts of the model domain. When the bias is removed from the root
mean square differences, again a similar pattern for the standard deviation
of differences with somewhat smaller values compared to the root mean square
differences is obtained.
Normalized Taylor diagram from 1 h (cyan) and 6 h (blue)
coastDat2 SWHs and from 6 h ERA-Interim (magenta) SWHs at seven
(coastDat2) and at six (ERA-Interim) observational sites. The red circle
represents a perfect model compared to the observations.
When the spatial comparison is made with the SWHs derived from the GlobWave
satellite data set instead of ERA-Interim, differences are less distinct but
still present (Fig. ). Similar spatial features but with smaller
values are found in the southern North Sea and near the coasts. The latter
corresponds to too small wave heights in ERA-Interim when compared to
GlobWave data (not shown). Although the underestimation may reach values of
up to 0.4 m on average, the magnitude of the systematic differences
between ERA-Interim and GlobWave is still smaller than that between the
coastDat2 and the GlobWave data. Note that the robustness of these results is
limited, as the number of available satellite data is small. For most of the
domain less than 100 co-located data points were available for the
comparison. This corresponds to only about 0.1 % of the
potentially available hourly values within the period 1992–2014.
To obtain a more robust figure, an additional comparison of co-located data
from GlobWave and coastDat2 was made, taking all co-located data irrespective
of their location into account. The results are shown in Fig. and
corresponding error statistics are presented in Table .
Altogether, errors statistics obtained and conclusions derived from this
exercise are similar to those based on comparison with in situ observations.
Values for bias and RMSE are slightly enhanced compared to those derived from
comparison with in situ observations. This can be attributed to the fact that
most of the in situ observations were taken in the southern part of the North
Sea, where error statistics of the coastDat2 hindcast are smaller, while the
more northern parts with larger errors have a stronger weight in the GlobWave
comparison.
Spatial distribution (in metres) of bias (a), root mean square distance
(b) and standard deviation of the error (c)
between SWHs derived from the coastDat2 hindcast and the ERA-Interim
reanalysis for the period 1980–2014.
Spatial distribution of bias (a), root mean square error
(b) and standard deviation of the error (c) [m]
between SWHs from the coastDat2 hindcast and the GlobWave data set for the
period 1992–2014 when all available satellite data are used for comparison
(top) and when only data with more than 100 flyovers per grid point are used
(bottom).
Error metrics for the Tm02 period at six locations
derived from in situ observations (OBS) and coastDat2 hindcast (CD2) data for
hourly values.
Error metrics for the MWP at four locations derived from in situ
observations (OBS), coastDat2 hindcast (CD2) and ERA-Interim (ERAi) data for
1 h (coastDat2) and 6 h (ERA-Interim) data,
respectively.
Error metrics for the mean wave direction at three locations derived
from in situ observations (OBS), coastDat2 hindcast (CD2) and ERA-Interim
(ERAi) data for 1 h (coastDat2) and 6 h (ERA-Interim) data,
respectively.
Different definitions for wave periods are used depending on the specific
analysis. Here two of the more frequently used measures are used for
comparison with observations: (i) the mean zero crossing period derived from
the zeroth- and second-order moment of the spectrum (Tm02) and
(ii) the mean wave period (MWP) defined by the ratio of the first- and
zeroth-order moment of the spectrum corresponding to the total energy of the
wave spectrum . The comparison is made based on the
availability of the different data sets.
When observed and hindcast Tm02 periods are compared, an
underestimation (overestimation) for short (long) periods can be inferred for
most locations (Fig. ). Deviations are mostly small and
typically of the order of 0.5 s, except for the near-shore location
WES. Despite the scatter for instantaneous values, hindcast wave periods on
average show a good agreement with the observations. The larger deviations
occurring at the location WES are probably related to the relatively shallow
water depth, which might lead to too small wave dissipation caused by missing
small-scale bathymetric features not resolved at the given spatial resolution
of the wave hindcast model.
A spatial comparison of the MWPs from the coastDat2 hindcast and the
ERA-Interim reanalysis for the period 1980–2014 is presented in
Fig. . On average, the coastDat2 hindcast shows longer MWP (up to
more than 0.6 s) for large areas of the North Sea with the largest
differences occurring in the deeper waters in the northeastern part of the
model domain. In coastal areas, differences are mostly less pronounced. For
the root mean square differences and the standard deviation of the
differences, similar spatial patterns can be inferred.
A comparison between Tm02 period measures derived from
observations and the coastDat2 hindcast is presented in Table .
The MWP measures between observations, coastDat2 hindcast and the ERA-Interim
reanalysis are presented in Table . It can be inferred that,
compared to observations, Tm02 periods are on average
underestimated in the coastDat2 hindcast while MWPs are on average
overestimated. For ERA-Interim no Tm02 data were available. MWPs
are similarly biased high, although with somewhat smaller values. Variability
is generally overestimated in both model simulations with the ERA-Interim
errors again being smaller.
Scatter and quantile–quantile plot of SWH (in metres) between
altimeter (GLOBWAVE) observation (x-axis) and coastDat2 hindcast data
(y-axis). Coloured squares indicate the number of the data in each
0.5 m× 0.5 m bin. Coloured dots represent the
percentile values of the quantile–quantile plots between observed and
coastDat2 hindcast significant wave heights (cyan) and between observed and
ERA-Interim SWH (magenta).
Scatter and quantile–quantile plot of Tm02 wave period
(in seconds) between in situ observation (x-axis) and coastDat2 hindcast data
(y-axis). Coloured squares indicate the density of the data in each
0.5 s× 0.5 s bin. Coloured dots represent the
percentile values of the quantile–quantile plots between observed and
coastDat2 hindcast Tm02 (cyan) wave periods. Note that the
comparison is made for different periods according to data availability (see
Table ).
Spatial distribution (in seconds)of bias (a), root mean square error
(b) and standard deviation of the error (c),
between the mean wave period between from the coastDat2 hindcast and
ERA-Interim reanalysis for the period 1980–2014.
Scatter and quantile–quantile plot of mean wave direction between in
situ observation (x-axis) and coastDat2 hindcast data (y-axis). Coloured
squares indicate the number of counts in each
15∘× 15∘ bin. Coloured dots represent the
percentile values of the quantile–quantile plots between observed and
coastDat2 hindcast mean wave directions (cyan) and between observed and
ERA-Interim mean wave directions (magenta). Note that the comparison is made
for different periods according to data availability (see
Table ).
Wave direction
A comparison between mean wave directions derived from coastDat2, ERA-Interim
and observations was performed at three locations (Fig. ).
Generally, a good agreement was inferred. At FN1 a more systematic deviation
for mean wave directions coming from southerly directions was obtained. Both
model data, coastDat2 and ERA-Interim, show the same systematic error (Table ). This
may point to some bathymetric effects that remain unresolved at the chosen
model resolution or to the installation of wave measurements that might be
sheltered from certain wave directions.
Individual extreme events
In order to illustrate the amount of agreement and disagreement described
above in a more direct and accessible way, modelled and observed wave
parameters during an extreme wave event were compared. Here we used the event
generated by the extra-tropical storm Britta
(31 October 2006–1 November 2006) which caused some structural damage at the
platform FINO1 . Visual inspection of time series of
significant wave height, wave periods and direction reveals that while the
overall development for the days around the storm is reasonably captured by
both the coastDat2 hindcast and the ERA-Interim reanalysis, both data sets
substantially underestimate the peak significant wave height that occurred
during the storm (Fig. ).
Time series of significant wave height (in metres) (a),
Tm02 (in seconds) (b) mean wave period (in seconds)
(c) and mean wave direction (in degrees) (d) at FN1 for
the period 15 October 2006, 00:00 UTC to 15 November 2006, 00:00 UTC.
Observations are shown in black (a–d), the coastDat2 hindcast is
shown in cyan (a–d) and the ERA-Interim data are shown in magenta
(a,c,d).
The underestimation is less severe in the coastDat2 hindcast and
substantially more pronounced in the ERA-Interim reanalysis. Inspection of
the time series further shows that during less stormy periods ERA-Interim
data are generally closer to the observations, while positive systematic
errors are obvious for the coastDat2 hindcast. In detail and for the time
series shown, it was found that (i) peak significant wave heights appear to be
better represented in the coastDat2 hindcast while there generally appears to
be a too rapid increase towards the extremes, (ii) during times with small
wave periods the Tm02 period appears to be reasonable in the
coastDat2 simulation while again a too rapid increase towards the extremes is
observed, (iii) for the MWP a systematic bias towards too high values is
clearly visible that is substantially less pronounced in the ERA-Interim data
and (iv) mean wave directions are very well represented in both simulations.
Extreme value analyses are often based on maximum values occurring within an
interval for which a given threshold is exceeded. For the analysis, the exact
timing of the extreme within this interval is less important. In order to
assess the representativeness of such extremes in the modelled data set, we
defined the duration of an extreme event as the time period for which the SWH
exceeded the 95th percentile of the observed SWH and sampled the maximum SWHs
that occurred during that interval from all data sets; that is, the
observations, coastDat2 and ERA-Interim. The analysis was performed exemplary
for station FN1. It was found that coastDat2 overestimated the observed
maximum SWH by 0.38 m with an RMSE of 1.12 m. ERA-Interim on
the other hand underestimated the observed maximum SWH by -0.63 m
but showed a smaller RMSE of 0.81 m. While the underestimation of
ERA-Interim extremes could partly be related to the coarser temporal
resolution of 6 h, the result indicates that for extreme value analyses
data from coastDat2 would provide a more conservative estimate.
Wind-wave hindcast data are stored at the World Data Center for
Climate (WDCC) and can be freely accessed using the
doi:10.1594/WDCC/coastDat-2_WAM–North_Sea.
Conclusions
To our knowledge, the described data set represents the longest
regional reconstruction of wind-wave climate for the North Sea based on
dynamically downscaled high-resolution atmospheric reanalysis data. It covers
more than 60 years and provides hourly integrated wind-wave parameters and
spectral wave information every 3 h at a spatial resolution of
approximately 3-by-3 nautical miles.
Altogether, the reconstructed data show a good agreement with observations, although the error metrics for the shorter and coarser ERA-Interim reanalysis
show smaller errors for most locations and outperforms the hindcast, especially
for open sea areas. Whereas the ERA-Interim wave product underestimates the
significant wave height, the coastDat2 hindcast overestimates the wave
heights to some extent. This is consistent with marine wind analysis of the
forcing data, which showed a slight overestimation of the observed wind speed
. However, there is some evidence that for extreme
conditions and near-coastal locations, the higher temporal and spatial
resolution of the presented wave hindcast lead to an added value. Due to the
lack of long consistent near-coastal wave observations a detailed analysis of
the added value is not possible. Compared to the coastDat1 wave hindcast
, which ends in 2007, the presented hindcast coastDat2 shows
similar performance with slightly higher values and variability for mean
conditions, but less overestimation during extreme events (not shown). One
benefit of this coastDat2 wind-wave hindcast is the extended period for
which reconstructed data are available, and the more comprehensive set of
wave parameters available (Appendix ). The increased resolution
both in space and time does not necessarily lead to improved simulated wave
conditions. Despite the limitations of the wave hindcast it is still useful
for several applications. The analysis of long-term trend and variability of
wave conditions needs long consistent time series as provided by this
hindcast. A long-term analysis of the forcing wind fields by
showed, as other studies, that the wind speed in the North
Sea region increased towards the end of the 20th century, with no further
increase since then. showed that the forcing global
reanalysis provides good enough homogeneity to analyse long-term climate
trends and variability, especially after 1958. Thus, it can be expected that
the wave hindcast provides homogeneity throughout the simulation periods and
the wave conditions will show comparable trends as shown in the analysis of
the wind forcing data. The more conservative estimates for extreme value
analyses could have some benefits for safety-related assessments in offshore
engineering for extreme events.
As part of a comprehensive approach to consistently reconstruct atmospheric
, tide-surge and wind-wave conditions
(this paper), the hindcast contributes to a consistent met-ocean data set
that provides a useful data source for analysing long-term meteo-marine
climate variability and change. Furthermore, it represents a valuable source
of data for a large variety of related and more applied research in the
industry and administration .
Error metrics
To evaluate the skill of the wave model, standard
statistical measures are used. The mean, the standard deviation (SD), the
bias, the root mean square error (RMSE), the scatter index (SI) and the
correlation coefficient (r) are defined as follows:
mean=E‾=∑i=1nEinSD=∑i=1n(Ei-E‾)2nbias=∑i=1n(Ei-Ri)nRMSE=∑i=1n(Ei-Ri)2nSI=RMSER‾r=∑i=1n(Ei-E‾)(Ri-R‾)∑i=1n(Ei-E‾)2∑i=1n(Ri-R‾)2,
where the overlines indicate mean values over time, n denotes the number of
data pairs, E refers to the estimator (coastDat2 or ERA-Interim) and R
refers to the reference data (in situ or satellite observations). If
coastDat2 is compared to ERA-Interim, the later is used as the reference data
R. Using the decomposition of the mean squared error (MSE) into
variance (VAR) and bias
(MSE=VAR+bias2), the standard deviation of the
error (SDE) is used as an estimate for the unbiased
RMSE and is defined as
SDE=RMSE2-bias2.
Available variables
List of available variables.
Variable nameUnitLong nameStandard name1dddegreewind directionwind_to_direction2dsdegreetotal directional spreadsea_surface_wave_directional_spread3ds_seadegreesea directional spreadsea_surface_wind_wave_directional_spread4ds_swelldegreeswell directional spreadsea_surface_swell_wave_directional_spread5ffms-1wind speedwind_speed6fvms-1friction velocity7hsmtotal significant wave heightsea_surface_wave_height8hs_seamsea significant wave heightsea_surface_wind_wave_height9hs_swellmswell significant wave heightsea_surface_swell_wave_height10nwsnonenormalised_wave_stressnormalised_wave_stress11thqdegreetotal mean wave directionsea_surface_wave_to_direction12thq_seadegreesea mean wave directionsea_surface_wind_wave_to_direction13thq_swelldegreeswell mean wave directionsea_surface_swell_wave_to_direction14tmpstotal mean periodsea_surface_wave_mean_period_from_variance_spectral_density_inverse_frequency_moment15tmp_seassea mean periodsea_surface_wind_wave_mean_period_from_variance_spectral_density_inverse_frequency_moment16tmp_swellsswell mean periodsea_surface_swell_wave_mean_period_from_variance_spectral_density_inverse_frequency_moment17tm1stotal m1-periodsea_surface_wave_mean_period_from_variance_spectral_density_first_frequency_moment18tm1_seassea m1-periodsea_surface_wind_wave_mean_period_from_variance_spectral_density_first_frequency_moment19tm1_swellsswell m1-periodsea_surface_swell_wave_mean_period_from_variance_spectral_density_first_frequency_moment20tm2stotal m2-periodsea_surface_wave_mean_period_from_variance_spectral_density_second_frequency_moment21tm2_seassea m2-periodsea_surface_wind_wave_mean_period_from_variance_spectral_density_second_frequency_moment22tm2_swellsswell m2-periodsea_surface_swell_wave_mean_period_from_variance_spectral_density_second_frequency_moment23tpstotal peak-periodsea_surface_wave_peak_period_from_variance_spectral_density24tp_seassea peak periodsea_surface_wind_wave_peak_period_from_variance_spectral_density25tp_swellsswell peak periodsea_surface_swell_wave_peak_period_from_variance_spectral_density
The authors declare that they have no conflict of
interest.
Acknowledgements
We thank the providers of the observational data, namely, the Bundesamt für
Seeschifffahrt und Hydrographie (BSH), the Norwegian Meteorological
Institute, the Royal Netherlands Meteorological Institute (KNMI), the
European Space Agency (ESA) and the French Research Institute for
Exploitation of the Sea (IFREMER) for their support. We also thank the
providers of the numerical data – namely, the European Centre for Medium-Range
Weather Forecasts (ECMWF) for the ERA-Interim reanalysis data and the Met
Office Hadley Centre for Climate Science and Services for access to the sea
ice data set. The article processing charges
for this open-access publication were covered by a Research
Centre of the Helmholtz Association.
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