NHESSNatural Hazards and Earth System SciencesNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus PublicationsGöttingen, Germany10.5194/nhess-18-2675-2018Implementation and validation of a new operational wave forecasting system of the Mediterranean Monitoring and Forecasting Centre in the framework of the Copernicus Marine Environment Monitoring ServiceImplementation and validation of a new operational wave forecasting systemRavdasMichalisZacharioudakiAnnaazacharioudaki@hcmr.grKorresGerasimosHellenic Centre for Marine Research, P.O. Box 712, 19013 Anavyssos, Hellas, GreeceThese authors contributed equally to this work.Anna Zacharioudaki (azacharioudaki@hcmr.gr)22October201818102675269526January20181February201813September201825September2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://nhess.copernicus.org/articles/18/2675/2018/nhess-18-2675-2018.htmlThe full text article is available as a PDF file from https://nhess.copernicus.org/articles/18/2675/2018/nhess-18-2675-2018.pdf
Within the framework of the Copernicus Marine Environment Monitoring Service (CMEMS),
an operational wave forecasting system for the Mediterranean Sea has
been implemented by the Hellenic Centre for Marine Research (HCMR) and
evaluated through a series of preoperational tests and subsequently for 1
full year of simulations (2014). The system is based on the WAM model and it
has been developed as a nested sequence of two computational grids to ensure
that occasional remote swell propagating from the North Atlantic
correctly enters the Mediterranean Sea through the Strait of Gibraltar.
The Mediterranean model has a grid spacing of 1/24∘. It is driven with
6-hourly analysis and 5-day forecast 10 m ECMWF winds. It accounts for
shoaling and refraction due to bathymetry and surface currents, which are
provided in offline mode by CMEMS. Extensive statistics on the system
performance have been calculated by comparing model results with in situ and
satellite observations. Overall, the significant wave height is accurately
simulated by the model while less accurate but reasonably good results are
obtained for the mean wave period. In both cases, the model performs
optimally at offshore wave buoy locations and well-exposed Mediterranean
subregions. Within enclosed basins and near the coast, unresolved
topography by the wind and wave models and fetch limitations cause the wave
model performance to deteriorate. Model performance is better in winter when
the wave conditions are well defined. On the whole, the new forecast system
provides reliable forecasts. Future improvements include data assimilation
and higher-resolution wind forcing.
Introduction
In recent years the requirements of the marine industry for real-time wave
forecasts have increased substantially. Various sectors such as, for example, maritime transport, shipping, and offshore mineral industry require
accurate wave forecasts in order to secure operations at sea, save fleet
fuel consumption using more accurate routing, and prevent from potential ship
and platform oil spill drift. In addition, a detailed wave information along
coastal regions is crucial for coast guards and port authorities as there is
the need to anticipate wave conditions that could interfere in ships
arriving and leaving the harbours. Furthermore, wave forecasting provides
significant advantages for the offshore wind and the wave energy so as to
schedule installation and maintenance activities, to define control
strategies according to the predominant wave conditions, or to plan for
storm events. Scientifically, waves are a bridge between the ocean and the
atmosphere, playing a key role in air–sea interaction and are also an
important mixing agent with an active role in erosion and resuspension processes.
The dramatic increase in computing power and the enhanced understanding of
the physical processes responsible for wave generation, evolution, and
dissipation have resulted in third-generation wave models which use first
principles in the integration of an action or energy balance equation
(Tolman, 1992) based on the sophisticated physics pertaining to wave
generation, propagation, and decay mechanisms. Wave models like WAM (WAMDI
Group, 1988; Komen et al., 1994), WAVEWATCH III (Tolman, 1991, 1999), and
SWAN (Booij et al., 1999) are being used by many meteorological and
oceanographic operational centres and have been reasonably successful in
operational wave predictions at the global, regional, and coastal scales. One
of the pioneers in the implementation and the development of wave analysis
and forecast systems is the European Centre for Medium Weather
Forecasts (ECMWF),
which has provided daily medium-range global wave forecasts
up to 10 days ahead since 1992. With time, more centres (e.g. UK Met Office, the
Service Hydrographique et Océanographique de la Marine (SHOM), and
several others) began to use state-of-the-art third-generation numerical
wave models in operational forecasting. In addition, an international wave
forecast inter-comparison project was established (Bidlot, 2007),
coordinated by the ECMWF, to evaluate forecast quality and performance and
identify areas of potential improvement (Breivik et al., 2015).
The EU-funded Copernicus Marine Environmental Monitoring Service (CMEMS)
driven by the requirements of a large user panel in need of wave information
in all ocean basins has enriched its portfolio since early 2017 with the
provision of open, cost-free, and quality-controlled wave products for the
global ocean and regional European seas. CMEMS is based on a strong
European partnership with more than 50 marine operational and research
centres in Europe involved in marine monitoring and forecasting services
and their evolution, providing a wide range of marine measurements of social and
environmental value such as ocean currents, temperature, salinity, sea
level, pelagic biogeochemistry, and waves. The backbone of the CMEMS relies
on a Central Information System (CIS) and an architecture of production
centres inherited from the MyOcean projects for both observations (Thematic
Assembly Centre – TAC) and modelling–assimilation (Monitoring and
Forecasting Centre – MFC). The MFCs are distributed according to the
marine area covered and generate model-based products including analysis of
the current situation, forecasts of the situation a few days in advance, and
the provision of retrospective data records (reanalysis). Detailed
information on the systems and products is on CMEMS web site:
http://marine.copernicus.eu/ (last access: September 2018). The Mediterranean Sea (Med) MFC is composed of
INGV (Italy), HCMR (Greece), OGS (Italy), and the Euro-Mediterranean Centre
on Climate Change (CMCC, Italy). It is an expert consortium with profound
expertise in the Mediterranean phenomenology and dynamics, from waves to
currents, and biogeochemistry, and it provides regular and systematic information
about the physical state of the ocean and the dynamics of the marine
ecosystem of the basin.
In this study we present the wave component of the Med MFC, a high-resolution
operational wave forecasting system (hereafter called Med-waves), which has
been developed by HCMR and provides daily accurate products – wave simulations and 5-day forecasts – of
the wave environment of the Mediterranean Sea to the general public through the CMEMS
portal. The system employs the WAM
Cycle 4.5.4 (Günther and Behrens, 2012), a modernized and improved version
of the WAM model. In this study, a modelling system consisting of a nesting
sequence of two computational grids (North Atlantic and Mediterranean) has
been developed with the fine-grid model covering the Mediterranean Sea and
the coarse-grid model the North Atlantic. A nesting approach of this kind
enables us to properly simulate the effect of the remotely generated Atlantic
swell into the Mediterranean Sea as it passes through the Strait of Gibraltar.
In fact, Cavaleri and Sclavo (2006) pointed out that the narrow Strait of Gibraltar appreciably affects the wave climate in the close-by area of the
Alboran Sea and it is often neglected in wave modelling systems of the
Mediterranean Sea. Moreover, the system incorporates offline coupling with
general circulation models (CMEMS global and Mediterranean analysis and
forecast systems) to provide surface currents for wave refraction to both
nests of the modelling system. Refraction due to surface currents impacts the wave spectrum to
some extent. Its impact on improving the wave forecast is
addressed by Osuna and Wolf (2005), Clementi et al. (2013, 2017), and Mao and
Xia (2017). Thus, while in the last years few operational centres have
already developed and implemented regional wave forecast systems for the
entire Mediterranean, none of these take into account the sensitivity of
Mediterranean wave dynamics to the nesting with the Atlantic, at the same time incorporating
the surface currents effect on wave refraction. In addition,
the system offers an extended set of freely available wave products and has
a spatial and spectral resolution high enough to describe with sufficient
accuracy the wind wave dynamics over the Mediterranean Basin.
Despite the diversity of wave generation models as well as of atmospheric
models, obtaining good quality of short-term wave forecasts for the
Mediterranean Sea is still a difficult task due to the large spatial and
temporal variability in the surface wind field over the basin (e.g. Bidlot,
2017). Wind-wave models are very sensitive to wind field variations, which
result in one of the main source of errors in wave predictions. The
sensitivity of wave model prediction to variations in wind forcing fields
has been studied by several authors (Komen et al., 1994; Teixeira et al.,
1995; Holthuijsen et al., 1996; Ponce and Ocampo-Torres, 1998). This is
particularly true for the Mediterranean where the limited contribution of
swell to the wave spectrum makes the regional wind conditions the most
important factor in determining the local wave state. Bearing in mind this
context, the complex structure of the Mediterranean Sea due to the presence
of large mountainous islands, protruding peninsulas, jagged coastlines, and
sharp orography gradients deeply influences the wind and wave dynamics,
especially close to the coast, making the local forecast particularly
challenging. Many authors have highlighted the fact that forecasted winds in
the Mediterranean are not as accurate as in the open ocean (Cavaleri and
Bertotti, 2003, 2004; Bolaños et al., 2005; Signell et al., 2005; Ardhuin et
al., 2007; Bolaños-Sanchez et al., 2007) and advocate the necessity of
further improvement on the wind field quality as well as the increase in its
spatial resolution, especially in enclosed basins such as the Mediterranean
Sea (Cavaleri et al., 1991; Cavaleri and Bertotti, 2004, 2009a, b;
Bentamy et al., 2007; Lionello et al., 2008). Today, the full coupling of
different geophysical models (e.g. atmospheric, ocean, wave) is also a
favoured approach to reduce the wind forecasting error, especially in
dynamically complicated coastal areas, as it accounts for the complex
interactions of waves, currents, and the atmosphere (Wahle et al., 2017). For
the Mediterranean Sea, the added value of coupled air–sea models has been
demonstrated by many research groups (Artale et al., 2009; Renault et al.,
2012; Katsafados et al., 2016; Varlas et al., 2018) particularly in the
region of the Adriatic Sea (Pullen et al., 2006; Carniel et al., 2016;
Licer et al., 2016; Ricchi et al., 2016) where the synoptic wind regimes are
difficult to forecast. However, despite the rapid progress and the
encouraging results of this field, there are still open scientific issues
such as missing physics and poor parameterizations for the coupled
atmospheric–ocean–wave processes in the air–sea interaction zone, especially
under extreme wind and ocean conditions (Chen et al., 2007; Soloviev
et al., 2014). Furthermore, the coupled models are still computationally
expensive and even with increased computational potential to date only few
major meteorological and oceanographic centres have the capability to
incorporate these high computationally demanding systems at fine
spatiotemporal resolution and at large spatial scales into their operational
weather–ocean forecasting chains. The recent white paper by Cavaleri et al. (2018)
analyses in detail the various aspects and problems affecting the
performance of wave models in enclosed and inner seas including the
Mediterranean Sea. In this framework, the selection of an appropriate wind
forcing is a vital step in the operational wave modelling of the
Mediterranean Sea. As such, the Med-waves system in particular uses the
analysis and forecast wind fields produced by the ECMWF Integrated Forecasting
System (IFS). The quality and appropriateness of ECMWF 10 m winds for wave
simulations and forecasting in different areas has been demonstrated by many
studies. On a global scale, repetitive statistics have shown that the ECMWF
products are, and have been for a long while, the best ones in the world
(Bertotti et al., 2011). However, for semi-enclosed basins, the quality of
ECMWF wind fields decreases and the wave model underestimates the high wave
heights because of the underestimation of high wind speeds (Cavaleri and
Bertotti, 2004; Signell et al., 2005; Cavaleri and Scalvo, 2006; Saket et
al., 2013) and/or overestimates the lower ones because of the overestimation
of low wind speeds by ECMWF (Moeini et al., 2010). In our system, this
underestimation of wind is compensated for by reducing the energy loss due to
whitecapping, performing a fine tuning of the free parameters of the
dissipation function.
We present here the first comprehensive documentation of the system and the
evaluation of its accuracy over a period of 1 year (2014). The rest of the
paper is organized as follows. A detailed description of the Med-waves
modelling system is given in Sect. 2. Section 3 outlines the methodology
followed in the model validation, and Sect. 4 is devoted to the
validation results including both hindcast and forecast skill evaluation
against in situ and satellite observations. Finally, a summary and some
concluding remarks are given in Sect. 5.
The wave forecasting system
As previously stated, Med-waves is based on the WAM Cycle 4.5.4 wave model, a
state-of-the-art third-generation wave model which is a modernized and
improved version of the well-known and extensively used WAM Cycle 4 wave
model (WAMDI Group, 1988; Komen et al., 1994). Cycle 4.5.4 has been released
during the MyWave (“A pan-European concerted and integrated approach to
operational wave modelling and forecasting – a complement to GMES MyOcean
services”) EU FP7 research project and is freely available to the entire
research and forecasting community. WAM solves the wave transport equation
explicitly without any presumption on the shape of the wave spectrum. Its
source–sink terms include the wind input, whitecapping dissipation,
non-linear transfer, and bottom friction. The wind input and whitecapping
dissipation source terms of the present cycle of the wave model are a
further development based on Janssen's quasilinear theory of
wind-wave generation (Janssen, 1989, 1991). The non-linear transfer term is a
parameterization of the exact non-linear interactions as proposed by
Hasselmann and Hasselmann (1985) and Hasselmann et al. (1985). Lastly, the
bottom friction term is based on the empirical JONSWAP model of Hasselmann
et al. (1973).
The Med-waves set-up includes a coarse-grid domain with a resolution of
1/6∘ covering the North Atlantic Ocean (NA) from
75∘ W to 10∘ E and from 10 to 70∘ N and a nested fine-grid domain with a resolution
of 1/24∘ covering the Mediterranean Sea from
18.125∘ W to 36.2917∘ E and from
30.1875 to 45.9792∘ N. The areas covered
by the two grids are shown in Fig. 1, which is a schematic of the Med-waves
system. The bathymetric map has been constructed using the GEBCO 30 s
bathymetric data set (GEBCO, 2016) for the Mediterranean Sea model and the
ETOPO2 2 min bathymetric data set (NGDC, 2006) for the North Atlantic model.
Schematic of the Med-waves system.
The Mediterranean Sea model receive the full wave
spectrum at hourly intervals at its Atlantic Ocean open boundary from the North Atlantic model. The latter
model is considered to have all of its four boundaries closed with no wave
energy propagation from the adjacent seas. Because of the wide geographical
coverage of the North Atlantic model, the consideration of closed boundaries
does not affect the swell propagation towards the open boundary of the
Mediterranean model, which is the main interest of this nesting approach.
The wave spectrum is discretized using 32 frequencies, which cover a
logarithmically scaled frequency band from 0.04177 to 0.8018 Hz at
intervals of dff=0.1 and 24 equally spaced directions
(15∘ bin size).
The Mediterranean model runs in shallow-water mode considering wave
refraction due to depth and currents in addition to depth-induced wave
breaking. The North Atlantic model runs in deep-water mode with wave
refraction due to currents only. The North Atlantic model additionally
considers wave energy damping due to the presence of sea ice.
Following ECMWF (2015), the tunable whitecapping dissipation
coefficients Cdis and δ have been altered from their default
values. Specifically, the values of Cdis=1.33 (Cdis=2.1
default) and δ=0.5 (δ=0.6 default) have been
adopted. The aim of this tuning is to produce results which are in good
agreement with data on fetch-limited growth and with data on the dependence
of the surface stress on wave age.
The atmospheric forcing of the Med-waves system is the operational 10 m wind
analysis and forecast from the ECMWF global meteorological forecasting system
(ECMWF, 2017) that are disseminated at a horizontal resolution of
1/8∘. The quality of the ECMWF forecasts is regularly evaluated
(Haiden et al., 2016). Sea ice coverage fields are also obtained from ECMWF
IFS at the same horizontal resolution as the wind fields. An issue here
concerns the temporal resolution of the disseminated ECMWF wind fields as
these data are provided on a 3-hourly basis for the first 3 days of the
forecast while it is expected that higher-temporal-resolution wind forcing
can better capture storm events, especially if the latter have a short
duration. For example, Alomar et al. (2014) have shown that on the southern
Catalan coast (NW Mediterranean Sea), the best wind speed estimations,
compared with the observations, corresponded to a grid size of 4 km and a
temporal resolution of 1 h.
Surface current forcing is accounted for in Med-waves. The Mediterranean
Sea model is forced by surface currents obtained from the physical
forecasting system of the CMEMS Med-MFC at 1/16∘ horizontal
resolution (CMEMS, 2016a) and the North Atlantic model by surface currents
obtained from the physical forecasting system of the CMEMS Global-MFC at
1/12∘ horizontal resolution (CMEMS, 2016b). Both physical
forecasting systems are based on the Nucleus for European Modelling of the
Ocean (NEMO) ocean physics model, which is a state-of-the-art free-surface
primitive equation model (Madec, 2008). NEMO is free software used by a
large community.
Med-waves is run once per day starting at 12:00:00 UTC. It produces 5-day
forecast fields initialized by a 1-day hindcast. The wave hindcast is forced
by 6-hourly analysis wind fields and daily averaged analysis current fields.
The 5-day forecast is forced by 3-hourly forecast wind fields for the first
3 days and 6-hourly forecast wind fields for the rest of the forecast cycle.
Daily averaged forecast currents are used over the entire wave forecast. Sea
ice coverage fields are updated at daily frequency and remain constant
during the forecast cycle.
Wave buoys' location and unique ID code.
Med-waves generates hourly wave fields over the Mediterranean Sea at
1/24∘ horizontal resolution. These wave fields correspond either
to wave parameters computed by integration of the total wave spectrum or to
wave parameters computed using wave spectrum partitioning. In the latter
case the complex wave spectrum is partitioned into wind sea and primary and
secondary swell. Wind sea is defined as those wave components that are
subject to wind forcing while the remaining part of the spectrum is termed
swell. Wave components are considered to be subject to wind forcing when
c≤1.2×28u*cos(ϑ-φ),
where c is the phase speed of the wave component, u* is the wind
friction velocity, θ is the direction of wave propagation, and
φ is the wind direction. As the swell part of the wave spectrum can
be made up of different swell systems with quite distinct characteristics, it
is further partitioned into the two most energetic wave systems, the so-called primary and secondary swell. Swell partitioning is carried out following the
method proposed by Gerling (1992), which finds the lowest energy threshold
value at which upper parts of the spectrum get disconnected, with the process
repeated until primary and secondary swell is detected.
Total spectrum and partitioned wave parameters produced by Med-waves and
disseminated though CMEMS include spectral significant wave height (Hm0),
spectral moments (-1, 0) wave period (Tm-10), spectral moments (0, 2) wave
period (Tm02), wave period at the spectral peak or peak period (Tp), mean wave
direction (Mdir), wave principal direction at spectral peak, surface
Stokes drift U, surface Stokes drift V, spectral significant wind wave
height, spectral moments (0, 1) wind wave period, mean wind wave direction, spectral significant primary swell wave height, spectral moments (0, 1)
primary swell wave period, mean primary swell wave direction, spectral
significant secondary swell wave height, spectral moments (0, 1) secondary
swell wave period, and mean secondary swell wave direction.
Validation framework
Med-waves has been validated against in situ and satellite observations,
focusing on its performance in the Mediterranean Sea. Model output and
observations corresponding to the year 2014 have been compared, focusing on
the fundamental wave parameters of significant wave height, Hs, and mean
wave period, Tm.
In situ measurements of Hs and Tm for 2014 were extracted from the
Copernicus In Situ Thematic Assemble Centre (INS-TAC), a component of CMEMS
which aims at providing a research and operational framework to develop and
deliver in situ observations and derived products based on such
observations. Hs measurements from 32 wave buoys within the Mediterranean
Sea were available in the examined year. Figure 2 depicts their location and
unique ID code. Tm measurements were available from a subset of the
depicted buoys which excludes all the buoys offshore from the Italian
coastline. To collocate model output and buoy measurements, in space model
output was taken at the grid point nearest to the buoy location. In time,
buoy measurements within a time window of ±1 h from model output
times at 3 h intervals (0, 3, 6 …, etc.) were averaged. Prior to model–buoy
collocation, the in situ observations were filtered so as to remove those
values accompanied by a bad quality flag (quality flags included in the data
files provided by the INS-TAC). After collocation, visual inspection of the
data was carried out, which led to some further filtering of spurious data
points. In addition, Tm data below 2 s were omitted from the statistical
analysis since 0.5 Hz (T=2 s) is a typical cut-off frequency for wave
buoys. It is noted that WAM, in contrast to the wave buoys, does not
implement a high-frequency cut-off in the computation of Tm but instead
includes a high frequency tail extending the calculation to infinity. As a
result, model Tm is anticipated to be somewhat biased towards lower values
compared to measured Tm.
Mediterranean Sea subregions for qualification metrics.
Satellite observations of significant wave height, Hs, and wind speed,
U10 (used to obtain Hs-U10 quality associations), for the year 2014 were obtained
from a merged altimeter wave height database set-up at CERSAT – IFREMER (France).
This database contains altimeter measurements that have been
filtered and corrected (Queffeulou and Croizé-Fillon, 2013). Here,
measurements from three satellite missions, Jason-2, Cryosat-2, and SARAL,
were used. To collocate model output and satellite observations, the first
two
were interpolated in time and space to the individual satellite tracks. For
each track, corresponding to one satellite pass, along-track pairs of
satellite measurements and interpolated model output were averaged over
∼50 km (0.5∘) grid cells, centred at grid points
of the forcing wind model (0.125∘× 0.125∘). This
averaging is intended to break any spatial correlation present in successive
1 Hz (∼7 km) observations and/or in neighbouring model grid
output (Pierre Queffeulou, personal communication, 2015).
Metrics that are commonly applied to assess numerical model skill and are in
alignment with the recommendations of the EU FP7 project MyWave (Saulter,
2014) have been used to qualify the Med-waves system within the
Mediterranean Sea. These include the RMSE, bias, scatter index (SI), Pearson
correlation coefficient (CORR), and best-fit slope (slope). The SI, defined
here as the standard deviation of errors (model – observations) relative to
the observed mean, as well as being dimensionless, is more appropriate to evaluate the
relative closeness of the model output to the observations at different
locations compared with the RMSE, which is representative of the size of a
“typical” error. The slope corresponds to a best-fit line forced through the
origins (zero intercept). In addition to the aforementioned core metrics,
merged density scatter and quantile–quantile (QQ) plots are provided.
Metrics are computed for the Mediterranean Sea as a whole, for the
individual wave buoy locations shown in Fig. 2, and for 17 subregions of
which one is in the Atlantic Ocean and 16 are in the Mediterranean Sea (Fig. 3):
(atl) Atlantic, (alb) Alboran Sea, (swm1) West South-West Med, (swm2) East
South-West Med, (nwm) North West Med, (tyr1) North Tyrrhenian Sea,
(tyr2) South Tyrrhenian Sea, (adr1) North Adriatic Sea, (adr2) South Adriatic Sea,
(ion1) South-West Ionian Sea, (ion2) South-East Ionian Sea, (ion3) North
Ionian 3, (aeg) Aegean Sea, (lev1) West Levantine, (lev2) North-Central
Levantine, (lev3) South-Central Levantine, and (lev4) East Levantine. All
metrics are evaluated over a period of 1 year (2014). In addition, metrics
associated with the full Mediterranean Sea are evaluated seasonally.
Validation resultsHindcast significant wave heightComparison with in situ observations
Table 1 shows results of the comparison between hindcast Hs (model data) and
in situ observations (reference data), for the Mediterranean Sea as a whole,
for the entire year of 2014, and seasonally. In the table, “Entries” refers
to the number of model–buoy collocation pairs; i.e. to the sample size
available for the computation of the relevant statistics, R¯ is the
mean reference value, M‾ is the mean model value, and SD R and SD M are
the standard deviations of the reference and model data respectively. The
remaining quantities are the qualification metrics defined in the previous
section. Figure 4 is the respective merged QQ–scatter plot (left), together
with the QQ plot alone (right) for visual clarity, for the full 1-year
period. In the figure, the QQ–plot is depicted with black crosses. Also
shown are the best-fit line forced through the origin (red solid line, left
plot) and the 45∘ reference line (red dashed line).
Med-waves Hs evaluation against wave buoy Hs,
for the full Mediterranean Sea, for a 1-year period (2014) and seasonally.
QQ–scatter plots (a) and QQ plot alone (b) of
Med-waves output Hs versus wave buoy observations, for the full
Mediterranean Sea, for a 1-year period (2014): QQ plot (black crosses), 45∘
reference line (dashed red line), least-squares best-fit line (red line, a).
Table 1 shows that the typical error (RMSE) varies from 0.17 m in summer to
0.25 m in winter. However, the scatter in summer (0.26) is about 2 %
higher than the scatter in winter (0.24) whilst a lower correlation
coefficient is associated with the former season. This suggests that the
model follows the observations in “stormy” conditions better, with
well-defined patterns and higher waves. A similar conclusion has been
derived by other studies (Cavaleri and Sclavo, 2006; Ardhuin et al., 2007;
Bertotti et al., 2013) with respect to wind and wave modelling performance
in the Mediterranean Sea. Like summer, autumn is characterized by lower
mean wave height, higher scatter, and a lower correlation coefficient compared
to winter and spring. Relative bias (BIAS/R‾) has an approximate
variation of 2.5 % (spring) to 5 % (autumn) and is always negative.
Accordingly, slopes are also below unity with small variation among
seasons. These values are indicative of an underestimation of the wave
height in the Mediterranean Sea by the model, a result which is in agreement
with the results of a number of operational or preoperational models for
the Mediterranean Sea (e.g. Bidlot, 2015; Donatini et al., 2015) and is
linked to an underestimation of the wind speed by the ECMWF forcing wind
model (see Fig. 7). Overall, the spring statistics are the ones closest to
the year-long statistics for the Mediterranean Sea.
Figure 4 depicts the pattern of the agreement between hindcast and observed
Hs for different Hs value ranges. The figure reveals that the
Hs underestimation by the model mainly occurs for wave heights below 4 m
and is rather small. It also shows a QQ plot that is really close to the
reference line over most of the Hs range observed, which means that waves of
a specific wave height have a very similar probability of occurrence in the
hindcast and in the observations. The “outliers” present in the scatter
plot, i.e. a number of measured waves of 2–4.5 m in height which are not
simulated by the model (not enough evidence was found to remove the depicted
outliers from the calculation of the statistics as faulty), correspond to
buoy location 61218 in the Adriatic Sea (Fig. 2) and mostly belong to a
single storm.
Med-waves Hs evaluation against wave buoy Hs,
for each individual buoy location, for a 1-year period (2014).
QQ–scatter plots of Med-waves output Hs versus wave buoy
observations at specific wave buoy locations, for a 1-year period (2014): QQ plot
(black crosses), 45∘ reference line (dashed red line), and least-squares
best-fit line (red line).
Table 2 shows results of the comparison between hindcast Hs and in situ
observations for each of the wave buoys depicted in Fig. 2 (buoys listed
from west to east). The table reveals that RMSE varies from 0.16 to 0.44 m
with the highest values (>0.3 m) observed in the North Adriatic
Sea at buoy location 61218 (0.44) and offshore of the French coastline at buoy
location 61021 (0.35). Both locations are associated with poor overall
qualification metrics, with location 61218 in particular displaying the
poorest overall statistics. Thus, SI, which varies between 0.17 (61197) and
0.53 (61218), also obtains its highest values – indicating a poorer model
performance – at locations within the North Adriatic Sea. Locations SARON
and 61021 follow with values of 0.4 and 0.32 respectively. In general,
SI values above the mean value for the whole Mediterranean Sea (0.25) are
obtained at all wave buoys located near the coast that are sheltered by land
masses to their west (e.g. western French coastline, eastern part of Corsica,
and eastern part of Italy). With respect to the Italian buoys, this result
is in close agreement with Cavaleri and Sclavo (2006), who found that the
performance of the operational ECMWF wave model deteriorated at those
Italian wave buoys facing east. This is because the resolution of the
forcing wind model is not capable of reproducing the fine interaction
between the prevailing north-northwesterly winds in the northern
Mediterranean Sea with the complex orography sheltering the northern
Mediterranean coastline well. An underestimation of wind speeds and consequently
of wave heights (also the case herein) is commonly observed at such
locations (Ardhuin et al., 2007). In addition, the buoys are often located
only a few kilometres from the coastline; thus, in these conditions,
i.e. when the wind is blowing from the coast, the approximation of the wave model
grid size can lead to non-negligible fetch differences. Similar SI values
are found within enclosed basins characterized by a complex topography such
as the Adriatic and Aegean seas. In general, the closer the location to the
coastline (e.g. 61187) and/or the more complex the surrounding topography
(e.g. SARON), the poorer the model performance expected. As explained in
several studies (e.g. Cavaleri and Sclavo, 2006; Bertotti et al., 2013;
Zacharioudaki et al., 2015; Cavaleri et al., 2018), in these cases, the
spatial resolution of the wave model is not adequate to resolve the fine
bathymetric features, whilst, as mentioned above, the spatial resolution of
the forcing wind model is incapable of reproducing the fine orographic
effects, introducing errors to the wave hindcast. The correlation
coefficient (CORR) largely follows the pattern of variation of the SI. It
ranges from 0.79 (61218) in the Adriatic Sea to 0.98 (61213) at a location
west of Sardinia which is well exposed to the prevailing north-westerly
winds in the region. Bias varies from -0.13 m at location 61218 in the
Adriatic Sea to 0.11 m at location 61021 offshore of the French coastline.
It is mostly negative, indicating an underestimation of the observed wave
height by the model, with positive bias observed at only six out of the
32 buoy locations examined. In most of the cases of relatively high positive
bias, this is because the wave model resolution has missed or has partly
captured important bathymetric features in the surroundings of the relevant
locations, thus missing or reducing the shadowing effects produced by these
features. For example, at shoreward buoy 61021 where the largest positive bias
is observed, there are a few small islands that are almost entirely missed by
the model. Also, at buoy 61221, similar to in Bertotti et al. (2013), the
coastal geometry is not well represented by WAM. Bertotti et al. (2013)
state that the buoy position is exposed to the easterly waves more than is
actually the case, leading to the observed overestimate by the model.
Similar conclusions stand for the SARON buoy in the Aegean Sea. Overestimation
at buoy 61198 in the Alboran Sea is part of a general overestimation of the
wave heights in the Atlantic and Alboran regions as it will be seen later in
the comparison with the satellites. In accordance with bias, best-fit slopes (slope)
vary from 0.77 at buoy location 61218 in the Adriatic Sea to 1.1 at
buoy location 61021 offshore of France. Slope values above unity coincide
with locations of positive bias; otherwise they are below unity, confirming
an overall underestimation of the observations by the model. In general, the
pattern of variation in slope is close to the pattern of variation in bias.
Med-waves Hs evaluation against satellite Hs,
for the full Mediterranean Sea, for a 1-year period (2014).
Med-waves Hs evaluation against satellite Hs,
for each Mediterranean Sea subregion shown in Fig. 3, for a 1-year period (2014).
Up to now, the overall performance of the Med-waves modelling system at the
different wave buoy locations has been analysed independently of the
severity of the conditions. Figure 5, similar to Fig. 4, shows the
QQ–scatter plots of hindcast Hs versus measured Hs at three buoy locations,
exhibiting model performance over the different wave height ranges. The
results at these three locations are reasonably representative of the
different behaviours of the wave model at the different wave buoy locations
in the Mediterranean Sea shown in Fig. 2. Thus, the top left plot shows the
behaviour of the model at location 61188, offshore from the border between
France and Spain, backed on the west by the Pyrenees Mountains. It is seen
that model underestimation occurs throughout the measured Hs range except
from the highest percentiles of Hs at which model overestimation is observed.
This distribution, with a smaller or larger model underestimate and with a
more or less pronounced convergence or overestimate towards the highest
waves, is observed at the majority of the wave buoy locations. The bottom
left plot corresponds to location 61221, south of the island of Sardinia.
There, the model overestimates the observed Hs over the entire Hs range,
even more so in the upper end of this range. Considerable model
overestimation, mostly over the middle and higher Hs ranges, is observed at
all wave buoys associated with unresolved bathymetric features in their
surroundings (e.g. 61021, SARON). Over the lower Hs range, convergence or
underestimation is also observed in these conditions. At SARON (not shown),
the surrounding topography is highly complex, including both orographic and
bathymetric effects, resulting in highly scattered data around the reference
line. The right plot shows results at buoy location 61197 east of the
Balearic Islands. This is a well-exposed offshore wave buoy; consequently,
the behaviour of the model at this location is expected to be representative
of its performance at well-exposed offshore sites. Relatively small
scatter of the data points is shown in the plot with QQ crosses and the best-fit
line laying close to the reference line. More specifically, the model
converges to the observations for wave heights below about 2 m, somewhat
underestimates the observations for wave heights between 2 and 4 m, and tends to
overestimate Hs for higher waves. A very similar distribution is found for
location 61430 west of the Balearic Islands. Other well-exposed offshore
locations present QQ–scatter patterns that are not far from the one shown
for location 61197.
Comparison with satellite observations
This subsection starts with the comparison of Med-waves hindcast Hs with
satellite observations of Hs separately for each satellite. This is carried out
for a
1-year period (2014) for the full Mediterranean Sea and for the different
subregions defined in Fig. 3. Respective results are shown in Table 3 and Fig. 6.
Table 3 shows that even though the model–satellite comparison behaves
similarly for the three different satellites in terms of SI and CORR, a
substantially more (>10 %) negative model bias associated with
a considerably lower slope is found for Cryosat-2. RMSE is also higher for
this satellite. Figure 6 shows that these results are largely consistent
among the different Mediterranean subregions although they are more
pronounced in the western Mediterranean and the Adriatic Sea. A lower model
underestimate of the Cryosat-2 measurements is observed in the Ionian Sea
and the eastern Mediterranean. The statistics of model–Jason-2 and
model–SARAL comparisons are comparable, with the model exhibiting its best
performance when compared to the observations of SARAL.
Med-waves Hs evaluation against satellite Hs
(Jason-2 and SARAL), for the full Mediterranean Sea, for a 1-year period (2014) and seasonally.
QQ–scatter plots of (a) ECMWF forcing wind speed U10 versus
satellite U10 (Jason-2) and (b) Med-waves Hs versus satellite Hs
(Jason-2 and SARAL), for the full Mediterranean Sea, for a 1-year period (2014).
It was decided to exclude the observations of Cryosat-2 from the analysis.
Apart from the aforementioned discrepancies, there are other results in the
literature to support this decision. Specifically, satellite–buoy
comparisons performed by Sepulveda et al. (2015) have shown that SARAL Hs is
of better quality than Jason-2 and Cryosat-2 Hs at both open-ocean and
coastal buoy sites. In fact, SARAL data are of very high quality with no
need of corrections whilst corrections are applied to Jason-2 and Cryosat-2
Hs observations (corrected data are used herein). After corrections, Jason-2
Hs has been found to approximate SARAL Hs well whilst less accurate results
have been obtained for Cryosat-2, particularly for wave heights below 1.5 m.
For these reasons, in what follows, the comparison of Med-waves Hs is
performed against merged satellite observations from the SARAL and Jason-2
satellites, which are of similar accuracy.
Table 4 shows statistics from the comparison of the Med-waves hindcast Hs
and satellite observations of Hs, for the full Mediterranean Sea, for a 1-year
period and seasonally. Figure 7b shows the corresponding QQ–scatter
plot for a 1-year period, for the full Mediterranean Sea. Figure 7a
shows an equivalent QQ–scatter plot resulting from the comparison of the
ECMWF forcing wind speeds, U10, and Jason-2 measurements of U10 (no
U10 available from SARAL or Cryosat-2).
Figure 7a shows that the ECMWF forcing wind model mostly
underestimates observed U10, even more so at high wind speeds. An overall
model underestimation of 8 % associated with a slope of 0.9 has been
computed. Figure 7b also shows an overall Med-waves model
underestimation of observed Hs by about 5 % associated with a slope of 0.96.
Nevertheless, in this case, the model somewhat underestimates observed Hs
over the lower Hs range (<2 m), converges to the observed Hs
over the middle Hs range (2–3.5 m), and, generally, somewhat overestimates
the larger waves in the data records. This apparent discrepancy between wind
and wave scatter distributions is a consequence of the modification of the
default values of the whitecapping dissipation coefficients in WAM as
described in Sect. 3. A QQ–scatter plot obtained before this modification (not
shown) is indeed very similar to the one of the ECMWF wind speeds in Fig. 7.
On the whole, Fig. 7 shows that the performance of Med-waves at offshore
locations in the Mediterranean Sea (satellite records near the coast are
mostly filtered out as unreliable) is very good. Comparing to the equivalent
results obtained from the model–buoy comparison (Fig. 4), a very similar
pattern of scatter distribution is observed in the two plots, also evident
from the orientation of the best-fit lines and the curvature of the
QQ plots. A smaller scatter (by about 6 %) with a larger overall bias (by
about 2 %) is associated with the model–satellite comparison. SI values
compare well at the more exposed wave buoys in the Mediterranean Sea.
Med-waves Hs evaluation against satellite Hs
(Jason-2 and SARAL), for each individual Mediterranean Sea subregion shown in
Fig. 3, for a 1-year period (2014).
Table 4 shows the seasonal variation in the Med-waves model performance.
RMSE varies from 0.17 m in summer to 0.24 m in winter. SI is highest in
summer (0.2) and lowest in winter (0.17). Correlation coefficient varies
accordingly. In general, as explained in the previous subsection, a lower
scatter with a higher correlation is expected the more well-defined the
weather conditions are. Similar to in the model–buoy comparison, bias is negative
in all seasons. Its highest relative value (BIAS/R‾) of 7.7 % is
computed for autumn and its lowest of 3.5 % for summer. Slope varies from 0.95
in spring and autumn to 0.97 in winter. Overall, Table 4, like Table 1,
reveals that the statistics of spring are the most representative of the
year-long statistics for the Mediterranean Sea.
Table 5 shows the statistics of the comparison of the Med-waves hindcast Hs
and satellite observations of Hs for the different subregions of the
Mediterranean Sea defined in Fig. 3. For visualization purposes, Fig. 8b maps the statistics shown in Table 5. In addition, equivalent
statistics are mapped for the ECMWF – satellite comparison of wind speeds
(Fig. 8a). It is noted that the relative bias (BIAS/R‾) is
displayed in the figure. This quantity allows for a more straightforward
comparison among the different sub-basins in terms of percentage
deviations from the observed mean value. It is also highlighted that the
spatial coverage of the model–satellite wind collocations (measurements only
from Jason-2) is much more limited than the spatial coverage of the
model–satellite wave collocations (measurements from both SARAL and
Jason-2). As a consequence, the wave statistics are expected to be more
representative of the subregions under consideration compared to the wind
statistics. This is particularly true for the Adriatic, the Ligurian, and the
Alboran Seas. In addition, the wave statistics have been computed using a
sample size of at least 400 data points whilst the wind statistics have been
obtained with a minimum sample requirement of 200 data points. Thus, the
confidence associated with the wave statistics is higher than the confidence
associated with the wind statistics. For the above reasons, the wind metrics
presented in Fig. 8 are interpreted with caution.
ECMWF U10(a) and Med-waves Hs(b)
evaluation against satellite U10 (Jason-2) and satellite Hs
(Jason-2 and SARAL) respectively: maps of metric values over the Mediterranean
Sea subregions shown in Fig. 3, for a 1-year period (2014).
Figure 8b shows that the typical error (RMSE) varies from 0.18 m
in the South-Central Levantine Basin (lev3 in Fig. 3) to 0.24 m in the
Alboran Sea, the North West Mediterranean (nwm), and the North Adriatic
subregions up to 0.29 m in the Atlantic subregion. In terms of SI, the
highest value (0.28) is obtained in the North Adriatic Sea followed by the
Aegean Sea (0.24). The South Adriatic, Alboran, Ligurian (tyr1), and East
Levantine (lev4) seas also have relatively high SI values (0.21–0.23). The
lowest values are found over the south-eastern Mediterranean Sea (0.15–0.16)
and in the Atlantic subregion (0.15). SI and CORR have a similar pattern of
variation, a notable difference being that the correlation coefficient
obtains its worst value in the East Levantine and, in general, it has
relatively lower values in the well-exposed regions of the Levantine Basin
compared to the well-exposed regions to its west. In accordance with the
above results, Ratsimandresy et al. (2008), examining model–satellite
agreement over coastal locations of the western Mediterranean Sea, found the
worst correlations in the Alboran Sea and east of Corsica. Bertotti
et al. (2013), in a comparison of high-resolution wind and wave model output
with satellite data over different subregions of the Mediterranean Sea,
also found the largest scatter and lowest correlations in the Adriatic and
the Aegean seas. In agreement, Zacharioudaki et al. (2015), focusing on the
Greek seas, have shown a considerably larger scatter in the Aegean Sea than
in the surrounding seas when model output was compared to satellite
observations. As explained in the previous subsection (model–buoy
comparison), it is difficult for wind models to reproduce
orographic effects and/or local sea breezes well and difficult for wave
models to resolve complicated bathymetry that introduces errors in these
fetch-limited, enclosed regions, often characterized by a complex
topography, well. Indeed, comparison with the equivalent results for the ECMWF
wind speeds confirms these difficulties. For example, the pattern of SI and
CORR variation for U10 largely resembles that for Hs, corroborating the
conclusion of many studies that errors in wave height simulations by
sophisticated wave models are mainly caused by errors in the generating wind
fields (e.g. Komen et al., 1994; Ardhuin et al., 2007). Nevertheless, some
differences do exist. For instance, the Hs SI in the Aegean Sea is
relatively higher than the corresponding U10 SI. This is most probably
because in this region of highly complicated bathymetry with many little
islands the error of the wave model increases in relation to the error of
the wind model. Similarly, in the East Levantine, Hs SI is lower than that
implied by U10 SI. In this case, the wind model may not simulate local
wind patterns, characterized by local sea breezes and easterly directions, well
(Galil et al., 2006); however, the wave regime which is dominated by waves
from the west sector (Galil et al., 2006) is better reproduced by the wave
model. Negative bias and slope below unity are the case in all subregions
except for the Atlantic Ocean and Alboran Sea.
Med-waves Tm evaluation against wave buoys' Hs,
for the full Mediterranean Sea, for a 1-year period (2014) and seasonally.
In the last two regions, the wave
model overestimates the observations by 5 %–6 %. Otherwise, it
underestimates the observations by about 2 % in the East South-West
Mediterranean (swm1) and Aegean seas to about 15 % in the Adriatic (adr2).
In general, the largest biases are found in the Adriatic (adr1, adr2), the
North Ionian Sea (ion3), and the Levantine Basin (lev2, lev3, lev4) with values
of 7.5 %–15.2 %. Slope varies accordingly with values between 0.88 in the
South Adriatic Sea (adr2) and 0.99 in the Aegean Sea and up to 1.05 in the
Alboran Sea. Comparing with the equivalent results for the ECMWF wind speed,
it is evident that although there are similarities in the relative bias and
slope distributions, there are also considerable differences. In general, in
terms of absolute value, the relative bias associated with the wind field is
larger than that associated with the wave field except for the South
Adriatic Sea, the Alboran Sea, and the Atlantic. In fact, in the last two
regions, a change of sign from negative to positive is observed between wind
and waves. As already mentioned, this is a consequence of the modification
of the whitecapping dissipation coefficients from default values in WAM,
which has led to an important offset of the negative bias associated with
the ECMWF wind speeds, especially over the high Hs range. Thus, in regions
where the ECMWF underestimate has been small, as in the Atlantic,
modification of the dissipation coefficients has eventually led to an
overshoot of the observed Hs. This is a robust pattern obtained for the
whole Atlantic area simulated by the nested Med-waves model (up to
-18.125∘ W; Fig. 1). The increase in negative Hs relative bias in
the South Adriatic Sea relative to the respective U10 relative bias is
somewhat puzzling; however, as mentioned above, small confidence
pertains to the results of U10 in the Adriatic Sea due to a limited
observational coverage by Jason-2.
Hindcast mean wave period
Table 6 presents the statistics of the comparison between the Med-waves
hindcast mean wave period, Tm, and in situ observations of mean wave period,
for the full Mediterranean Sea, for a 1-year period (2014) and seasonally.
Figure 9 shows the corresponding QQ–scatter plot for the year-long
statistics. It is shown that the model exhibits greater variability than the
observations (SD in Table 6). RMSE varies from 0.8 s in summer to 1.07 s in
winter. In relation to the mean of the observations, the error is about
17 %–19 %, with winter and spring being at the low end of this range and
autumn at the high end. SI varies from 0.12 in winter and spring to 0.14 in
summer and autumn. The non-trivial deviation of SI from relative RMSE (RMSE/R‾)
indicates that a substantial part of the error is caused by
bias. CORR has its minimum value (0.78) in summer and its maximum (0.87) in
winter and spring. As before, these results indicate that the model wave
period, like the model wave height, better follows the observations in
well-defined wave conditions of higher waves and larger periods. Bias is
negative with values that correspond to a model underestimate of about
11.5 %–13 %. Correspondingly, slope has a small variation of 0.87–0.89. Like
for wave height, spring statistics are the most representative of the
year-long statistics. Figure 9 clearly shows that the wave model
underestimates the observations throughout the observed Tm range.
Measurements of Tm<4.5 s are especially underestimated while those
of relatively high Tm are better approximated by the model. As mentioned in
Sect. 3, part of the model underestimation of observed Tm, especially over
the lower Tm range, may be attributed to the absence of a high frequency
cut-off in the model in contrast to the observations.
QQ–scatter plots of Med-waves output versus wave buoy observations,
for the full Mediterranean Sea, for a 1-year period (2014).
Med-waves Tm evaluation against wave buoy Tm,
for each individual buoy location, for a 1-year period (2014).
Table 7 gives the statistics of the model–buoy comparison at the individual
wave buoy locations. The typical error relative to the mean of the
observations (RMSE/R‾) has its lowest values of 12 %–16 % over the
western part of the Mediterranean Sea, west and south of France, with the
two locations nearest to the Gibraltar Straight being at the low end of this
range. Otherwise, this error is 17 %–23 %, reaching up to 29 % at location 61187
near the French–Italian border. At this location, all qualification
metrics obtain their worst value. This is because wave buoy 61187 is located
at a distance less than 2 km from coast and is affected by winds blowing from
land. As already explained in the model–buoy wave height comparison, in this
situation, the simulated fetch may differ substantially from the actual
fetch because of the wave model grid size approximation; moreover, wind
speed and wave height are considerably underestimated. RMSE is mainly caused
by bias, which is negative at all locations. Thus, according to the RMSE,
the relative bias is below 10 % over the western Mediterranean and is
14 %–20 % otherwise reaching up to 23 % at location 61187. It is only
at location 61197, offshore from the eastern Balearic Islands, that the
scatter of the data appears to contribute more to the typical error than the
bias. This is a well-exposed offshore location where bias (2 %) and slope (0.97)
have their best values and where model performance has been found to
be optimal for wave height. The relatively high SI (0.15) and moderate
correlation (0.86) at this location could be associated with the appearance
of two density peaks in the density scatter plot (not shown), indicative of
a double-peaked frequency spectrum. Density scatter plots with two peaks,
although less distinct, have also been obtained for locations 61289 and 61021,
offshore from France. In general, a close examination of the
QQ–scatter plots (not shown) corresponding to the different locations has
revealed that the model largely underestimates the observed Tm over the
lower wave period range at all locations. Over the higher range, the model
converges or overestimates the observed Tm in the western Mediterranean Sea,
west and south of France. Otherwise, the model underestimates all observed Tm
values with some convergence towards higher values. Slope mostly follows the
pattern of variation in bias with values between 0.76 and 0.97. SI is
relatively small with values between 0.09 (ATHOS) and 0.18 (61187) while
CORR varies from 0.65 (61187) to 0.9 (61430, 68422). Generally, similar to
the wave height results, the lowest correlations are found at coastal
locations affected by fetch differences between model and reality due to a
complex surrounding topography. Conversely, the highest correlations
are obtained at the most exposed wave buoy locations.
Forecast skill
In the previous section, the performance of the Med-waves system has been
characterized through the comparison of hindcast wave parameters with
observations. In this section, the forecast skill of the Med-waves system is
explored by comparing forecast wave parameters with observations at
different forecast lead times. Hence, Fig. 10 shows Med-waves forecast skill
for Hs (Fig. 10b, c) together with ECMWF forecast skill for U10 (Fig. 10a). The latter is evaluated against satellite observations, the former is
evaluated against satellite (Fig. 10b) and buoy (Fig. 10c) observations.
It is noted that in the model–buoy comparisons, each lead time represents a
single point in time, whist, in the model–satellite comparisons, each
lead time represents a full forecast day; i.e. +0 h represents forecast
day 1 containing data from 0 to 24 h forecast. This approach is dictated
by the scarcity of satellite observations in time.
ECMWF U10 forecast skill evaluated against satellite observations (a)
and Med-waves Hs forecast skill evaluated against satellite (b)
and buoy (c) observations, for the full Mediterranean Sea, for a 1-year period (2014).
Med-waves Tm forecast skill evaluated against buoy
observations, for the full Mediterranean Sea, for a 1-year period (2014).
Figure 10 shows that Hs SI grows with forecast lead time at a constantly
increasing growth rate. At the same time, CORR decreases with forecast
lead time, with the decrease being more notable after the third day of
forecast (+48 h). These patterns, which are consistent between model–buoy
and model–satellite observations, mostly agree with the equivalent U10
patterns and manifest the deterioration of the forecast in time. A small
difference between U10 and Hs forecast skill is the somewhat more linear
increase in SI with forecast lead time in the first case, which results in a
smaller overall U10 deterioration over the length of the forecast (14 %)
compared to the respective Hs deterioration (19 % for model–satellite
comparisons). This is indicative of the sensitivity of wave height to even
limited variations in the input wind intensity. Conversely, waves
seem to be less sensitive to wind misfits in time and space, which is
manifested by the higher and more persistent Hs CORR over the forecast range
compared to the respective U10 CORR. Contrary to SI and CORR but also to
U10 bias, the evolution of Hs bias with forecast lead time in not monotonic.
This apparent discrepancy between wind and wave bias evolution is attributed
to the modification of the default values of the whitecapping dissipation
coefficients in WAM, which, as shown in Sect. 4.1.2, have an impact on the
bias of the wave model output relative to the observations. In any case, for
both winds and waves, the variation in bias with forecast range is small and
does not exceed 2 %.
Figure 11, like Fig. 10c, shows Med-waves forecast skill for Tm
evaluated against wave buoy observations. Similar to Hs, SI increases with
forecast range, CORR decreases, and bias exhibits a non-monotonic variation
analogous to the one of Hs. In this case however, the variation in SI over
the forecast period is small (5 %) compared to the respective Hs variation
(25 %). This agrees with the finding that Tm errors are mainly caused by
bias (Sect. 4.2).
Conclusions
The CMEMS Mediterranean wave forecasting system, Med-waves, has been operational
since April 2016, providing short-range forecasts over the Mediterranean Sea
at hourly intervals and at a horizontal resolution of 1/24∘.
The development and the evaluation of the performance of the system has
been presented in detail in this paper. In the framework of this evaluation,
the wave parameters of significant wave height and mean wave period have
been evaluated against in situ and satellite observations over a period of
1 year (2014). Both hindcast quality and forecast skill have been
assessed. In the former case, evaluation statistics have been provided for
the Mediterranean Sea as a whole, at individual buoy locations and over
predefined Mediterranean subregions. In the latter case, evaluation
statistics have been provided only for the entire Mediterranean Sea. The
main findings of this evaluation assessment are summarized below.
Overall, the significant wave height is accurately simulated by the model.
Considering the Mediterranean Sea as a whole, the RMSE is 0.21 m and the
bias is -0.03 m (3.7 %) when the model is compared to in situ observations
and -0.06 m (5.5 %) when it is compared to satellite observations. In
general, the model somewhat underestimates the observations for wave heights
below 4 m whilst it mostly converges to the observations for higher waves.
The scatter index, indicative of the scatter of the data around their
regression line, is 25 % for the model–in situ comparison and 19 % for
the model–satellite comparison, demonstrating a reduced scatter off the shore
(where satellite measurements are mostly located) compared to near the shore
(where in situ measurements are mostly obtained). The correlation
coefficient is 0.95–0.96 and so is the best-fit slope. Model performance is
better in winter when the wave conditions are well defined. Spatially, the
model performs optimally at offshore wave buoy locations and well-exposed
Mediterranean subregions. Within enclosed basins and near the coast,
unresolved topography by the wind and wave models and fetch limitations
cause the wave model performance to deteriorate. In particular, the model
has an optimal performance along most of the southern Mediterranean Sea. Its
performance is less good in the Alboran, Ligurian, Adriatic, Aegean, and
Eastern Levantine seas, with the worst evaluation statistics obtained in the
Adriatic. In terms of bias, the model overall underestimates the
measurements in the Mediterranean Sea. The smallest underestimate is
observed in the Aegean Sea while overestimate is observed in the Alboran Sea
and in the Atlantic.
Poor wave model statistics were strongly linked to poor wind forcing
statistics. Naturally, it is expected that an improved orographic
representation of the ECMWF forecasting system will improve the quality of
the surface wind fields near the coast while a higher temporal resolution of
wind forcing would be beneficial to the model to resolve the high wind and
wave variability in the Mediterranean Sea, providing more accurate wave
fields. Moreover, the atmospheric model of ECMWF, which was not coupled with
an ocean model (coupling was performed only with the wave component) by the time
of this study, did not consider some vigorous air–sea interaction processes
(large heat fluxes or strong ocean mixing processes) that occur in regions
which are usually affected by extreme weather events such as the northern
part of the Adriatic during strong wind events (Bora, Sirocco). As a
result, it failed to properly reproduce the spatial structure of the wind
fields. To overcome this limitation, many studies (Carniel et al., 2016;
Ricchi et al., 2016, 2017) show that the use of a fully coupled atmosphere–ocean–wave
model can be considered appropriate for these regions for
properly representing the air–sea interactions and for providing a more
realistic and consistent evolution of the atmospheric and oceanic fields. It
is noted at this point that substantial progress has been made since the year 2014 – the
year the results of this study are obtained for – by ECMWF
regarding spatial and temporal resolutions and coupling. Specifically, the
spatial resolution of the ECMWF winds has increased since spring 2016 from
16 to 9 km. Also, in June 2018, it was decided that ECMWF can provide
hourly forecasts up to a forecast step of 90 h (Jean Bidlot, personal communication, 2018).
Finally, in June 2018, the ECMWF forecasting system is a fully coupled
atmosphere–waves–ocean–sea ice system (ECMWF, 2018). As a consequence of
these improvements, a future validation of the Med-waves system is expected
to yield better validation results.
The mean wave period is reasonably well simulated by the model. The RMSE is
0.7 s and is mainly caused by model bias, which has a value of -0.48 s
(12 %). In general, the model underestimates the observed mean wave period
and exhibits greater variability than the observations. A relatively larger
model underestimate is found for mean wave periods below 4.5 s. The scatter
index is 13 %, the correlation coefficient is 0.85 and the best-fit slope
is 0.88. Model performance is a little better in winter when wave conditions
are well defined. Spatially, the model somewhat overestimates the highest
mean wave period values in the western Mediterranean Sea, west and south of
France. Otherwise, model underestimate is widespread. Similar to the wave
height, the model performance is best at well-exposed offshore locations and
deteriorates near the shore mainly due to fetch limitations.
The forecast skill of the model over the Mediterranean Sea deteriorates with
forecast range. The growth of error in the wave forecast is mainly due to
the growth of error in the forcing wind fields. The scatter index of the
significant wave height deteriorates by 19 and 25 % over the 5-day
forecast for model–satellite and model–buoy comparisons respectively. The
equivalent deterioration for mean wave period is only 5 % (model–buoy
comparison). A monotonic decrease in correlation is also observed. On the
contrary, the evolution of bias with forecast range shows some variability
with no clear trend. Nevertheless, this variability does not exceed 3 %
over the forecast period.
In the next version of the system an optimal interpolation data
assimilation scheme is added to the Med-waves system in order to blend
satellite along-track significant wave height measurements with model
background forecasts. Although wave data assimilation is known not to be
particularly beneficial in areas where wind sea conditions are dominant, we
expect that wave forecasts in certain sub-areas of the Mediterranean Sea
where swell propagation is quite frequent, will be improved at +24 h and
perhaps +48 h lead time. The enhanced Med-waves system with the data
assimilation system module is going to produce 3-hourly wave analyses on a
daily basis for the Mediterranean Sea by assimilating Sentinel-3 and Jason-3
altimeter measured significant wave heights and surface winds. The
assimilation is based on the inherent data assimilation scheme of WAM Cycle 4.5.4
model, which generates an updated wave field by distributing the
information from the observed significant wave height and surface wind data
within a given time window over the entire model grid. The Med-waves data
assimilation component is integrated into the Med-waves system since April 2018.
Lastly, more work will be devoted to improve the offline coupling between
waves and currents by including as a next step the variations in the sea
level as predicted by the physical component of the Med MFC system. In
parallel the full online two-way coupling between Mediterranean waves and
currents will be developed and implemented into the Med MFC system, with a
target to enter into the operational chain in future versions of the
Copernicus Marine Service, improving the forecasting skill of the models in
various coastal areas of the basin.
The in situ wave buoy observations used in this study have
been obtained from the Copernicus Marine Environment Monitoring Service (CMEMS)
IN-SITU Thematic Assembly Centre (INS TAC) archive and are available from
http://marine.copernicus.eu/services-portfolio/access-to-products/?option=com_csw&view=details&product_id=INSITU_MED_NRT_OBSERVATIONS_013_035
(CMEMS, 2018a). The satellite observations have been obtained from a merged altimeter wave
height database set-up at CERSAT – IFREMER, France, and are available from
ftp://ftp.ifremer.fr/ifremer/cersat/products/swath/altimeters/waves/data/ (CERSAT-IFREMER, 2017).
The model outputs for the year 2014 are available upon request from the authors.
Model outputs since 2016 are available through CMEMS from
http://marine.copernicus.eu/services-portfolio/access-to-products/ (CMEMS, 2018b).
GK and MR decided on the set-up and initial configuration
of the wave forecasting system and designed a number of sensitivity runs to
help reach a conclusion on the final model configuration. MR collected the necessary model
inputs and performed all simulations. AZ performed all validation so as to
decide together with the co-authors on the final version of the wave model.
She also prepared the paper with contributions from all co-authors.
GK coordinated all activities.
The authors declare that they have no conflict of interest.
Acknowledgements
This work has been supported by HCMR (https://www.hcmr.gr/en/, last access: September 2018) and Copernicus Marine
Environment Monitoring Service (CMEMS) (http://marine.copernicus.eu/, last access: September 2018). CMEMS
is implemented by Mercator Ocean through a delegation agreement with the
European Union. The authors want to acknowledge the CMEMS for providing
ocean current data and in situ observations, the Italian Meteorological
Service for providing ECMWF wind data, and CERSAT – IFREMER for the
satellite observations for validating the system.
Edited by: Piero Lionello
Reviewed by: Jean-Raymond Bidlot and one anonymous referee
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