CMIP5-Derived Single-Forcing, Single-Model, and Single-Scenario Wind-Wave Climate Ensemble: Conﬁguration and Performance Evaluation

Journal of Marine Science and Engineering

Article CMIP5-Derived Single-Forcing, Single-Model, and Single-Scenario Wind-Wave Climate Ensemble: Conﬁguration and Performance Evaluation

Alvaro Semedo 1,2,*, Mikhail Dobrynin 3, Gil Lemos 2, Arno Behrens 4, Joanna Staneva 4, Hylke de Vries 5, Andreas Sterl 5, Jean-Raymond Bidlot 6 ID , Pedro M. A. Miranda 2 ID and Jens Murawski 7

1 Department of Water Science and Engineering, IHE-Delft, P.O. Box 3015, 2601 DA Delft, The Netherlands 2 Instituto Dom Luiz, Faculdade de Ciências, University of Lisbon, 1749-016 Lisbon, Portugal; [email protected] (G.L.); [email protected] (P.M.A.M.) 3 Institute of Oceanography, Center for Earth System Research and Sustainability (CEN), Universität Hamburg, 20095 Hamburg, Germany; [email protected] 4 Helmholtz-Zentrum Geesthacht Centre for Materials and Coastal Research, D-21502 Geesthacht, Germany; [email protected] (A.B.); [email protected] (J.S.) 5 Royal Netherlands Meteorological Institute (KNMI), Utrechtseweg 297, 3731GA De Bilt, The Netherlands; [email protected] (H.d.V.); [email protected] (A.S.) 6 European Centre for Medium-Range Weather Forecasts, Shinﬁeld Park, Reading RG2 9AX, UK; [email protected] 7 Danish Meteorological Institute, 2100 Copenhagen Ø, Denmark; [email protected] * Correspondence: [email protected]; Tel.: +31-152-152-387

Received: 22 June 2018; Accepted: 25 July 2018; Published: 1 August 2018

Abstract: A Coupled Model Intercomparison Project Phase 5 (CMIP5)-derived single-forcing, single-model, and single-scenario dynamic wind-wave climate ensemble is presented, and its historic period (1979–2005) performance in representing the present wave climate is evaluated. A single global climate model (GCM)-forcing wave climate ensemble was produced with the goal of reducing the inter GCM variability inherent in using a multi-forcing approach for the same wave model. Seven CMIP5 EC-Earth ensemble runs were used to force seven WAM wave model realizations, while future wave climate simulations, not analyzed here, were produced using a high-emission representative concentration pathway 8.5 (RCP8.5) set-up. The wave climate ensemble’s historic period was extensively compared against a set of 72 in situ wave-height observations, as well as to ERA-Interim reanalysis and Climate Forecast System Reanalysis (CFSR) hindcast. The agreement between the wave climate ensemble and the in situ measurements and reanalysis of mean and extreme wave heights, mean wave periods, and mean wave directions was good, in line with previous studies or even better in some areas of the global ocean, namely in the extratropical latitudes. These results give a good degree of conﬁdence in the ability of the ensemble to simulate a realistic climate change signal.

Keywords: Wave climate; ensemble; climate change; EC-Earth; WAM; Coordinated Ocean Wave Climate Project (COWCLIP)

1. Introduction Climate change extends beyond the scientiﬁc community, becoming a key topic in day-to-day public opinion. Matters like sea-level rise, ice-cap melting, extreme storms, droughts and ﬂoods, or coastal erosion, just to mention a few, are now common matters of discussion in the media or even in

J. Mar. Sci. Eng. 2018, 6, 90; doi:10.3390/jmse6030090 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2018, 6, 90 2 of 28 colloquial gatherings. Climate change adaptation and mitigation strategies also now raise increased societal interest. One of the key issues related to climate change, specifically ocean-related, is the potential increase of coastal hazards, like inundation or extreme coastal erosion, particularly when linked to sea-level rise, affecting coastal areas and low-land countries. Ocean surface gravity waves (or wind waves, as they are also called) can be classified as wind sea or swell, depending on their degree of coupling to the overlaying atmosphere [1]. Wind seas are young waves under the influence of the overlaying wind, directly receiving momentum from the atmosphere, to which they are strongly coupled [2,3]. Swell waves are mature waves that propagate away from their generation area by outrunning the overlaying wind speed. Swell waves can propagate thousands of kilometers, across entire ocean basins [4,5] with very little attenuation [4,6–8]. For this reason, the ocean surface wave field is the result of local and remotely generated waves, being strongly dominated by swell [3,9–11]. Therefore, wave climate variability in the open ocean, due to wave propagation characteristics, is often dominated by changes in swell waves carrying the effect of changes in surface winds into remote areas, contributing to changes in the wave climate elsewhere. For that matter, a direct link between the local wind speed and wave field’s long-term variabilities should be done with caution. Wave climate is of fundamental importance to a variety of applications, like the design of offshore and coastal infrastructures, ship design standards, ship routing, and coastal management, among others. Wave climate is also a key factor in determining rates of coastal erosion and sediment budgets. The monitoring of present wave climate conditions is, therefore, a common practice, e.g. [3,7,12–16]. In face of a warming climate due to anthropogenic greenhouse gas emissions [17], a trend that will most probably continue until the end of the twenty-first century due to the inertia of the Earth’s climate and to additional greenhouse gas emissions [18], the study of the impact of climate change in future wave climate is of paramount importance. This study is also important from a scientific point of view, since waves play a key role in the climate system, modulating the exchanges of momentum, heat, and mass across the air–sea interface [14,19–23]. Waves also have an impact on the upper ocean layers and on trough wave-induced turbulence in the mixing layer; they are an important driver in defining the sea surface temperature, with direct impact on the lower atmosphere [24]. Changes in the future wave pattern can, therefore, play an important role in ocean surface heat fluxes. Despite the role of waves in the climate system, up until today no fully coupled ocean-wave–atmosphere climate model exists, albeit some attempts, e.g. [23,25]. For that reason, global wave climate studies still rely on wind forcing (and sea ice coverage) from previous global climate model (GCM) simulations. The study of the impact of climate change on future wave conditions is done following one of two methods: dynamical, using physically based wave models, and statistical, using statistical models, both relying on a priori GCM simulations. Dynamical wave climate simulations use close-to-the-surface wind speeds (usually at 10-m height; U10) and sea ice coverage (SIC) from GCMs to force a physical wave model. Statistical simulations, on the other hand, use mean sea level pressure (MSLP) or U10 wind fields (and SIC) as input to statistical models. Each of the aforementioned methods has its advantages and limitations, with dynamical wave climate projections being computationally more expensive than statistical ones, although producing more accurate and physically sound results. The first dynamical global wave climate projections were done under the auspices of the Coordinated Ocean Wave Climate Project (COWCLIP), supported by the World Climate Research Program—Joint Technical Commission for Oceanography and Marine Meteorology (WCRP-JCOMM) [26,27]. Upon the work of [28], several other global future wave climate projections followed, e.g. [29–34], forced with Coupled Model Intercomparison Project Phases 3 and 5 (CMIP3 and CMIP5) GCM simulations. A concise review of the wave climate projections pursued in the recent past can be found in a review by [35]. Recent climate projections use ensembles instead of single GCM simulations. The use of ensembles has the goal of reducing uncertainties inherent to the simulations that arise from the GCM’s internal variability [36–38]. Uncertainties in climate modeling occur due to errors in the physical parameterizations of the models, to small-scale processes not fully understood, or to processes J. Mar. Sci. Eng. 2018, 6, 90 3 of 28 not resolved due to computational constraints [39]. These uncertainties are often a limiting factor in climate studies, particularly at regional scales [40–42]. By using the GCM ensemble approach, dedicated dynamic ensembles of wave climate simulations were also recently produced, e.g. [43–45]. These dedicated wave climate ensembles relied on multi-forcing suits, i.e., different GCMs were used in the same ensemble, providing forcing to a single wave model (dynamical simulations) or to a statistical model (statistical simulations). In contrast to single wave climate runs and to multi-forcing (multi-GCM) dynamical or statistical ensemble studies of wave climate projections, a different approach was attempted in the present study, where a single-GCM-forced dynamic ensemble was used. An ensemble of seven independent CMIP5 climate simulations, produced with the same GCM (EC-Earth) [46] was used to force the third generation WAM wave model [47], with U10 winds and SIC. The historic period of the seven wave climate simulations span from 1979 to 2005. The future wave climate simulations, not analyzed here, were produced using the EC-Earth representative concentration pathway (RCP8.5; [48]) set-up from 2006 to 2100. The ensemble described in this study is, therefore, a “single forcing-single (wave) model-single scenario” wave climate ensemble, produced with the goal of reducing the variability inherent in using a multi-forcing GCM approach for the same wave model, as in [43], for example. The goal of this study was to present the single-forcing, single-model, and single-scenario wave climate ensemble design, and to assess its performance skills in reproducing the present time wave climate (as represented by the historic period). The ensemble historic period was extensively evaluated through comparison with a set of 72 in situ wave-height observations, with the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis [49], and the wave hindcast generated from the National Centre for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR; [50]). The remainder of the paper is structured as follows: in Section2, the EC-Earth ensemble and the EC-Earth and WAM models, as well as the design of the dynamic wave climate ensemble, are described. The datasets used to evaluate the ensemble historic period (global wave reanalysis and hindcast, and in situ measurements) are also described in Section2. The performance skills of the seven-member ensemble in representing present wind and wave climates are presented in Section3. The summary and conclusions follow in Section4.

2. Models, Data, and Methods

2.1. The EC-Earth GCM The EC-Earth GCM, largely used in global and regional climate studies, e.g. [51], is a full physics seamless coupled atmosphere–ocean–sea ice–land earth system climate prediction model [46]. The EC-Earth was developed from the ECMWF operational seasonal forecast system 3 (ECMWF 2007), albeit with a different ocean model. The atmospheric model is the atmospheric component of the ECMWF Integrated Forecast System (IFS) cycle 31r1 (https://www.ecmwf.int/en/forecasts/ documentation-and-support/changes-ecmwf-model/ifs-documentation, last accessed on June 2018). The ocean general circulation model in EC-Earth is the Nucleus for European Modeling of the Ocean (NEMO) version 2 (OPA9: Océan Parallélisé version 9), developed by the Institute Pierre Simon Laplace [52,53]. See [46] for further details on the EC-Earth performance skills, and [54] for further details on the NEMO ocean model in EC-Earth.

2.2. The WAM Wave Model The WAM wave model version used here is cycle 4.5.3 (C4.5.3), an update of WAM cycle 4, described in [55,56]. WAM cycle 4.5.3 (C4.5.3) includes a source function integration scheme developed by [57], with a new semi-implicit approach developed at the ECMWF. The model updates described in the article by [58] are also included. Additionally, in WAM C4.5.3, the wind generation function and dissipation terms implement the [59–61] formulation, and the nonlinear interaction source functions J. Mar. Sci. Eng. 2018, 6, 90 4 of 28 are evaluated using the DIA (discrete interaction approximation) [62]. Additional details on WAM C4.5.3 can be seen in [63].

2.3. Experimental Set-Up State-of-the-art comprehensive Earth system GCMs, such as the ones used in the CMIP5, rely on ensemble strategies for a more realistic approach to the variability, trends, and extremes of the past, present, and future of the Earth climate. The design of CMIP5 climate experiments [64] led to an extensive list of consistent and comparable GCM simulations of the Earth’s climate, under a number of present climate and future climate change scenarios as the RCPs [48]. Both multi-model ensemble and perturbed physics approaches were used in CMIP5 in order to study or potentially reduce uncertainties in the climate projections. In general, three sources of uncertainties can be distinguished: firstly, the internal model variability or the unforced climate variability; secondly, the uncertainties due to model architecture, parameterizations, and physics; and thirdly, the uncertainties in future emission scenarios [36]. The EC-Earth ensemble, used here to force the WAM wave model, followed a different approach, with the initialization date as the differentiating factor. The seven EC-Earth runs used to force the WAM wave model were taken from the larger EC-Earth ensemble prepared for CMIP5. Each EC-Earth ensemble member integration started in 1850, with the only difference being the initial conditions. The initial conditions are snapshots taken from the long pre-industrial control simulation for CMIP5, each separated by 25 years. The standard set-up of the atmospheric model in the EC-Earth version 2.2 corresponds to a triangular truncation at wavenumber 159 (T159) horizontal spectral resolution (about 125 km at the equator) and a vertical grid spacing with 62 vertical levels of terrain-following mixed sigma-pressure hybrid coordinates, of which about 15 are within the planetary boundary layer. Six of the seven EC-Earth runs used the standard vertical level set-up, while a seventh run, produced at the Danish Meteorological Institute (DMI) was set with an increased number of vertical levels as a differentiating factor. These levels were added in the stratosphere, and the top level of the EC-Earth was raised from 5 hPa to 0.1 hPa. NEMO, the ocean component of EC-Earth, uses a horizontal resolution of roughly 1◦ × 1◦ and 42 vertical layers. The past and present climate EC-Earth ensemble simulations cover the period between 1850 and 1855 to 2005. The future climate runs span from 2006 to 2100, following the RCP8.5 high-emission scenario [65]. Six-hourly 10-m wind speeds ( U10 ) and daily SIC (grid cells with ice coverage less than 0.5 were taken as no ice) with a horizontal resolution of about 1◦ × 1◦, from the seven EC-Earth runs, were used to force seven realizations of the WAM wave model. The WAM runs were performed on a regular global latitude–longitude grid, covering a latitude range of 78◦ N to 78◦ S, with a fixed spatial grid size of 1◦ × 1◦. The spectral domain was discretized into 25 logarithmically spaced frequency bins, from 0.041 Hz to 0.411 Hz, equivalent to wavelengths from about 10 to 950 m. Wave propagating directions were set with a resolution of 15◦. The WAM model was run in shallow-water mode. The 1-min (~0.0168◦) world-gridded elevations/bathymetry ETOPO1 data [66,67] were used to define the depths. The wave model runs were performed using integration time steps of 5 and 10 min for the advection and the source functions, respectively. A suit of 30 wave parameters, in addition to the neutral 10-m wind speed derived from different forms of integrating the outputted wave spectra, were stored every 6 h (see Table A1 in the AppendixA). Having used the same GCM with the same RCP scenario to force a sole wave model, the ensemble described here qualifies as a “single-forcing, single-model, single-scenario” dynamic wave climate ensemble. The WAM realizations were run for the present climate 20th century 1979–2005 period (the historic period). The WAM future climate 21st simulations were run for the 21th century 2006–2100 period. For convenience, the present climate simulations are named in general as PC20, the present climate historic ensemble is named PC20-E, and the individual ensemble members are named PC20-i (where i = 1 to 7). The future climate simulations (not analyzed here) are, on the other hand, named FC21, J. Mar. Sci. Eng. 2018, 6, 90 5 of 28

FC21-E, and FC21-i. Also for convenience, the EC-Earth U10 wind-speed ﬁelds were included in PC20. Table1 presents additional details on the EC-Earth and WAM runs, including the climate centers or research groups responsible for each of the EC-Earth ensemble members.

Table 1. Ensemble details: UL (University of Lisbon), UH (University of Hamburg), SMHI (Swedish Meteorological and Hydrological Institute), DMI (Danish Meteorological Institute), HZG (Helmholtz-Zentrum Geesthacht). PC20—present climate 20th century; FC21—future climate 21st century.

Ensemble Member EC-Earth Run WAM Run PC20 FC21 1 UL UL-HZG 1979–2005 2006–2100 2 DMI UH 1979–2005 2070–2100 3 DMI UH 1979–2005 2070–2100 4 SMHI UH 1979–2005 2006–2100 5 SMHI UH 1979–2005 2006–2100 6 DMI UH 1979–2005 2070–2100 7 SMHI UH 1979–2005 2006–2100

2.4. Global Evaluation Data: ERA-Interim Reanalysis and CFSR Hindcast The performance skills of PC20-E were evaluated through comparison with the ECMWF ERA-Interim reanalysis (Dee et al., 2011) and with the National Oceanic and Atmospheric Administration (NOAA) CFSR wave hindcast [68]. The ensemble signiﬁcant wave heights (Hs) were compared to ERA-Interim and CFSR. The mean wave periods (Tm), mean wave directions (θm), and U10 were compared only to ERA-Interim. The ERA-Interim is a global third-generation reanalysis, produced at the ECMWF using the IFS release cycle Cy31r2 (https://www.ecmwf.int/en/forecasts/documentation-and-support/changes- ecmwf-model/ifs-documentation, last accessed on June 2018), used operationally at ECMWF during the period from December 2006 to June 2007. Here, we used the ERA-Interim period from 1979 to 2005. In addition to atmospheric variables, the ERA-Interim also includes reanalyzed wave parameters, since it was produced using the IFS, a two-way coupled atmosphere–wave model system [69]. The wave model used in this coupled model system is also a modiﬁed version of the WAM model (the so called EC-WAM), albeit different from WAM cycle 4.5.3. ERA-Interim uses an improved data assimilation technique in four dimensions (4D-Var scheme), which outperforms the previous three-dimensional (3D)-Var assimilation technique [70]. ERA-Interim assimilates surface wind speed observations from voluntary observing ships (VOS), buoys, and satellite scatterometery. Satellite altimetry wave heights were also assimilated since 1991. In situ Hs measurements and altimeter winds at 10-m height are not used in the ERA-Interim; thus, they can be used to independently evaluate the merits of the reanalysis. The resolution of the atmospheric model component in ERA-Interim is about 79 km (T255 spectral truncation; ~0.7◦ × 0.7◦), with 60 vertical levels from the surface up to 0.1 hPa. The wave model is set for a resolution of 110 km (~1◦ × 1◦). The temporal resolution of ERA-Interim is 6 h. Additional details about the ERA-Interim reanalysis and its comparison with other global wave hindcasts can be found in articles by [16,49,71,72].The CFSR is the global NCEP third-generation reanalysis [68], produced with a coupled atmosphere–ocean–land surface–sea ice model system. The atmospheric component is the NOAA operational Global Forecast System (GFS). The ocean model coupled to the GFS in the coupled model system is the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model (MOM) version 4p0d [73]. The operational Global Data Assimilation System (GDAS) is used in the assimilation process. The CFSR global atmosphere resolution is ~38 km (T382), with 64 vertical levels up to 0.1 hPa. The global ocean is 0.25◦ at the equator, extending to a global 0.5◦ beyond the tropics with 40 levels. The CFSR reanalysis output is at a T382L64 resolution (~0.5◦ × 0.5◦ horizontal, ~0.266 hPa vertical), running originally from 1979 to 2009. From the CFSR atmospheric reanalysis dataset, a wave hindcast was produced [74] using the WAVEWATCH III wave model (WW3; [75]), the so-called CFSR wave hindcast. Here, we used the three-hourly CFSR hindcast (henceforth just called CFSR, or J. Mar. Sci. Eng. 2018, 6, 90 6 of 28

CFSR hindcast) global domain at a 0.5◦ × 0.5◦ horizontal resolution from 1979 to 2005. Additional details on the CFSR hindcast and its comparison with other global wave data sets can be found in the article by [72]. From here onward, the ERA-Interim reanalysis and the CFSR hindcast are interchangeably referred to as simply “reanalysis”, unless they need to be distinguished. J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 6 of 28 2.5. In Situ Evaluation Data: Wave Observations 2.5. In Situ Evaluation Data: Wave Observations The PC20-E signiﬁcant wave heights (Hs) were also evaluated through comparison with 72 in situ The PC20-E significant wave heights () were also evaluated through comparison with 72 in observations,situ quality-controlledobservations, quality-controlled at the ECMWF, at the ECMW and regularlyF, and regularly used used to evaluate to evaluate the the wave wave forecasting scores of theforecasting operational scores IFSof the [76 operational]. From allIFS the[76]. in From situ all measurements the in situ measurements available available globally globally since 1979, 72 locations, withsince 1979, a long 72 locations, enough with spanning a long enough time-series spanning (at time-series least 10 years) (at least and 10 years) positioned and positioned in relatively in deep relatively deep waters, were selected. Figure 1 shows these locations (see also Table A2 for additional waters, weredetails). selected. Figure1 shows these locations (see also Table A2 for additional details).

Figure 1. Areas and buoy positions. Buoy positions and selected areas: extratropical North Pacific Figure 1. Areas and buoy positions. Buoy positions and selected areas: extratropical North Pacific (ETNP), tropical eastern North Pacific (TENP), tropical western North Pacific (TWNP), tropical (ETNP), tropicalwestern South eastern Pacific North (TWSP), Pacific tropical (TENP), eastern tropicalSouth Pacific western (TESP), Northextratropical Pacific South (TWNP), Pacific tropical western South(ETSP), Pacific extratropical (TWSP), North tropical Atlantic eastern (ETNA), Southtropical PacificNorth Atlantic (TESP), (TNAO), extratropical tropical South South Atlantic Pacific (ETSP), extratropical(TSAO), North extratropical Atlantic (ETNA),South Atlantic tropical (ETSA), North tropic Atlantical North Indian (TNAO), (TNIO), tropical tropical South South Atlantic Indian (TSAO), (TSIO), and extratropical South Indian (ETSI). Further details can be seen in Table A3. extratropical South Atlantic (ETSA), tropical North Indian (TNIO), tropical South Indian (TSIO), and extratropical2.6. Methodology South Indian (ETSI). Further details can be seen in Table A3. The PC20-E was built using a “democratic approach”, with an unweighted mean of the seven 2.6. Methodologyensemble members (PC20-1 to 7) for the period from 1979 to 2005. The six-hourly wind and wave parameters are processed for annual and seasonal means: December to February (DJF), March to May The PC20-E(MAM), June was to built August using (JJA), a and “democratic September to approach”, November (SON). with Here, an unweighted only the extreme mean seasons of the seven ensembleDJF members and JJA were (PC20-1 analyzed. to 7) for the period from 1979 to 2005. The six-hourly wind and wave parameters areIn processed the high latitudes, for annual natural and variations seasonal in SIC means: extent Decembercan seriously to affect February the quality (DJF), of mean March to May (MAM), Junewave to fields, August due (JJA),to a considerable and September reduction to of November data points available, (SON). since Here, the only grid thecells extremeare taken seasonsas DJF land by the wave model when covered with ice for an area higher than 50%. This situation was dealt and JJA werewith analyzed.using one of the procedures proposed by [77] to treat wave statistics for climate purposes. Grid In thecells high with latitudes, full ice concentration natural variations for 30% of in the SIC time extent or more can in the seriously scrutinized affect periods the qualitywere taken of as mean wave fields, dueland, to a and considerable were ruled out reduction of the statistics. of data For points that matter, available, only cells since with thefull gridice concentration cells are taken for as land by the wave70% model or more when of the total covered time series with were ice fortreated an areaas open higher water. than 50%. This situation was dealt with For the comparison of PC20-E (and reanalysis) with the in situ observations, the observational using oneand of the the proceduresmodeled data proposedwere averaged by on [77 a] daily to treat basis. wave The ensemble statistics and for the climate reanalysis purposes. data were Grid cells with full icecollocated concentration with the wave for 30% observations of the time through or more interpolation in the scrutinizedof the nearest periodsgrid points were (bilinear taken as land, and were ruledinterpolation) out of into the the statistics. in situ observational For that matter,positions.only cells with full ice concentration for 70% or more of the totalThe timePC20-E series performance were treated skills we asre openevaluated water. using the following standard statistics: bias— Equation (1), root-mean-square error (RMSE)—Equation (2), mean annual variability (MAV)— For theEquation comparison (3), and ofthePC20-E Arcsin–Mielke (and reanalysis)score (M-Score with)—Equation the in situ(4), all observations, of which are defined the observational below. and the modeled data were averaged on a daily basis. The ensemble and the reanalysis data were collocated with the wave observations through interpolation of the nearest grid points (bilinear interpolation) into the in situ observational positions. J. Mar. Sci. Eng. 2018, 6, 90 7 of 28

The PC20-E performance skills were evaluated using the following standard statistics: bias—Equation (1), root-mean-square error (RMSE)—Equation (2), mean annual variability (MAV)—Equation (3), and the Arcsin–Mielke score (M-Score)—Equation (4), all of which are deﬁned below. 1 N Bias = (PC20 − R ), (1) N ∑i = 1 i i s 2 ∑N (PC20 − R ) RMSE = i = 1 i i , (2) N where N is the number of realizations and R is the reference data (in this case from observations or reanalysis). The MAV [18,72], which is an average of the annual standard deviation normalized by the annual mean, provides an indication of the spread of a climate simulation along the year and also its ability to simulate the seasonal extremes, and it is deﬁned as

r 2 M 1 N 1 N ∑ ∑ PC20ji − ∑ PC20ji ! 1 j = 1 N i = 1 N i = 1 σj MAV = = , (3) M 1 N N ∑i = 1 PC20ji PC20j where M is the number of years in the record and j is the position inside each year. The non-dimensional Arcsin–Mielke score, or M-Score [78,79], used previously for wave climate parameters by [43], is deﬁned as ! 2 MSE = − × M arcsin 1 2 1000 (4) π Vpc20 + VR + (GPC20 + GR) where MSE is the mean-square error, V is the spatial variance, and G is the spatial mean, either of PC20-E or the reanalysis. The M-Score varies from zero (no skill) to a maximum score of 1000 (for virtually no error, i.e., MSE = 0). With the arcsine transformation of the Mielke skill score, introduced by [80], the deviation from unity asymptotes to the RMSE. The statistics were computed for the global ocean, and separately for 13 regional sub-areas, allowing the assessment of the ensemble’s regional performance. Each of these regions, chosen in accordance with [4], can be seen in Figure1, with further details in Table A3. Numerical weather prediction (NWP) strategy has data assimilation as a key element. In climate studies, data assimilation is not present, and climate simulations do not capture the exact time history of the simulated parameters, making the comparison with observations or reanalysis a challenging task. Previous studies used the same overlapping period when comparing present climate wave simulations with reanalysis, e.g., [43], when that was possible. Other studies assumed that wave climate historic simulations, because they are not time-constrained, do not necessarily reproduce the exact same period as the referenced reanalysis; as such, they did not make these periods coincident, e.g., [33]). The problem is enhanced when the comparison is done with observations, e.g., in situ measurements or remote sensing. Most of the time, the periods and the lengths of the climate simulations do not coincide with the observational ones, which can pose additional challenges. That is the case, for example, with in situ observations that are either shorter in time length or have gaps in the data. Differences can also occur in comparisons with remote-sensing observations, which can also have different time lengths compared to climate simulations, or different time resolutions, typically lower than the climate simulations. For that reason, the simple comparison between observations and climate simulations is unfair (to the observations), since, even for overlapping time-slices, the density of the observations is typically lower. A technique where this “unfairness” is corrected, and the historic climate simulation output numbers (densities) and lengths (time-slices) are matched with the observational ones by randomly sampling the climate simulation data, was developed by [80]. Here, we used a similar approach to the comparison between PC20-E and in situ observations (intra-annual variability). To J. Mar. Sci. Eng. 2018, 6, 90 8 of 28 coincide the amount (number of observations and model outputs) and length of the in situ observations with the PC20, ten random Monte Carlo samples were taken of the climate data, and then averaged. This was done for each set of the 72 in situ observations.

3. Evaluation of the Wave Climate Simulation in the Historic Period

Firstly, the PC20-E was evaluated through comparison with the Hs ERA-Interim and CFSR DJF and JJA global climatological means, as seen in the normalized differences shown in Figure2 (PC20-E minus reanalysis normalized by the reanalysis). J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 8 of 28

(a) (b)

(e) (f)

Figure 2. Present climate historic ensemble (PC20-E) 1979–2005 seasonal wave height (; m) means

Figure 2. Presentfor (a) December–February climate historic (DJF) ensemble and (b) June–August (PC20-E) 1979–2005 (JJA). PC20-E seasonal (m) normalized wave height differences (Hs; m) means for (a) December–February(%; PC20-E minus reanalysis (DJF) and normalized (b) June–August by the reanalysis) (JJA). to PC20-E ERA-InterimHs (m) for ( normalizedc) DJF and (d) differences JJA, (%; PC20-E minusand to reanalysis Climate Forecast normalized System Reanalysis by the reanalysis)(CFSR) for (e)to DJF ERA-Interim and (f) JJA. for (c) DJF and (d) JJA, and to Climate Forecast System Reanalysis (CFSR) for (e) DJF and (f) JJA. Compared to ERA-Interim, in most of the extratropical areas, the ensemble overestimated . This overestimation was highest in the North Pacific, around 10–15% in JJA and less than 5% in DJF, and lowest in the North Atlantic, where, in DJF, the differences were negligible or close to zero, and Compared to ERA-Interim, in most of the extratropical areas, the ensemble overestimated Hs. in JJA, they were only slightly overestimated. A slightly larger overestimation (10–15%) can be seen This overestimation was highest in the North Pacific, around 10–15% in JJA and less than 5% in DJF, along the North Atlantic trade-winds path. The seasonal differences of PC20-E to ERA-Interim were and lowestlower in the in the North southern Atlantic, hemisphere; where, in DJF, in DJF,the ensemble the differences overestimated were negligible by less than or 5% close in most to zero, and in JJA, theyof the were South only Atlantic slightly and South overestimated. Indian sub-basins A slightly (for convenience larger overestimation the Pacific, Atlantic, (10–15%) and Indian can be seen along theSouthern North Atlantic Ocean sectors trade-winds are included path. in the The respective seasonal oceans), differences with a slightly of PC20-E higher overestimation to ERA-Interim were in the South Pacific, but less than 10% in almost the entire sub-basin. A similar pattern can be seen in lower in the southern hemisphere; in DJF, the ensemble overestimated H by less than 5% in most JJA in the southern hemisphere, although with lower relative differences, particularlys in the South of the SouthPacific. Atlantic The differences and South between Indian PC20-E sub-basins and ERA-in (forterim convenience wave heights thewere Pacific, highest in Atlantic, DJF in the and Indian Southern OceanNorth Indian sectors Ocean, are includedtoward the inArabian the respective Sea (around oceans), 25%) and with the Bay a slightly of Bengal higher (less than overestimation 15%). in the SouthSimilar Pacific, differences but less in than the North 10% Indian in almost sub-basin the were entire also sub-basin. present in the A comparison similar pattern between can the be seen in ensemble and the CFSR DJF means, although slightly lower. JJA in the southern hemisphere, although with lower relative differences, particularly in the South Contrary to the comparison with ERA-Interim, compared to CFSR, the PC20-E underestimated Pacific. Thewave differences heights (by 5% between or less) or PC20-E showed marginal and ERA-interim differences, close wave to zero, heights in most were of the highest global ocean in DJF in the North Indianin both Ocean, seasons. toward Exceptions, the where Arabian the seasonal Sea (around mean wave 25%) heights and were the overestimated Bay of Bengal by PC20-E, (less than 15%). Similar differenceswere the Arabian in the Sea North and the Indian Bay of sub-basin Bengal in DJ wereA, and also in the present equatorial in the Pacific comparison Ocean in both between the seasons, particularly in the Solomon Sea (10% to 15%). In the extratropical North Pacific, compared ensemble and the CFSR DJF means, although slightly lower. to CFSR, the PC20-E overestimated the mean seasonal by around 10%, and underestimated them in the eastern part by around 5% or less. In the North Atlantic, seasonal mean wave heights were also

J. Mar. Sci. Eng. 2018, 6, 90 9 of 28

Contrary to the comparison with ERA-Interim, compared to CFSR, the PC20-E underestimated wave heights (by 5% or less) or showed marginal differences, close to zero, in most of the global ocean in both seasons. Exceptions, where the seasonal mean wave heights were overestimated by PC20-E, were the Arabian Sea and the Bay of Bengal in DJA, and in the equatorial Paciﬁc Ocean in both seasons, particularly in the Solomon Sea (10% to 15%). In the extratropical North Paciﬁc, compared to CFSR, the PC20-E overestimated the mean seasonal Hs by around 10%, and underestimated them in the eastern part by around 5% or less. In the North Atlantic, seasonal mean wave heights were also underestimated by PC20-E, compared to CFSR, in both seasons by around 10% or less, with the exception of the trade-windsJ. Mar. path Sci. Eng. where 2018, 6, thex FOR mean PEER REVIEW JJA H s was overestimated. Along the extratropical latitudes 9 of 28 in the southern hemisphere, PC20-E underestimated wave heights in both seasons, particularly in JJA. underestimated by PC20-E, compared to CFSR, in both seasons by around 10% or less, with the A similar comparison was done for the global DJF and JJA mean Hs 95% percentiles, as shown in exception of the trade-winds path where the mean JJA was overestimated. Along the Figure3. Theextratropical comparison latitudes with in the ERA-Interim southern hemisphere extreme, PC20-E wave heightsunderestimated showed wave lower heights relative in both differences comparedseasons, to the particularly seasonal inH sJJA.means, with marginal or zero differences or patches of low over- and underestimationsA similar (less comparison than 5%). was Thedone exceptionsfor the global DJF were and in JJA the mean North 95% Atlantic, percentiles, where as shown the ensemble in Figure 3. The comparison with ERA-Interim extreme wave heights showed lower relative underestimated the 95% percentile wave heights by around 5–10% in DJF, and overestimated them differences compared to the seasonal means, with marginal or zero differences or patches of low along theover- trade-winds and underestimations path in JJA, (less in than the 5%). Arabian The ex Seaceptions and were Bay in of the Bengal Northin Atlantic, DJF, and where in the the Solomon Sea in bothensemble seasons, underestimated where extreme the 95% wave percentile heights wa were,ve heights in this by case,around overestimated 5–10% in DJF, by and around 15% overestimated them along the trade-winds path in JJA, in the Arabian Sea and Bay of Bengal in DJF, or more. On the other hand, the comparison between the seasonal PC20-E and CFSR mean Hs 95% and in the Solomon Sea in both seasons, where extreme wave heights were, in this case, overestimated percentiles showed, for both seasons, a generalised underestimation of PC20-E (around 10% or less), by around 15% or more. On the other hand, the comparison between the seasonal PC20-E and CFSR with highermean differences 95% percentiles along the showed, extratropical for both seasons, storm tracks,a generalised where underestimation the underestimation of PC20-E was of the order of 15%(around or even 10% higher.or less), Thewith exceptionshigher differences were, oncealong more,the extratropical the Arabian storm Sea tracks, and thewhere Bay the of Bengal in DJF, and theunderestimation Solomon Sea was in of boththe order seasons, of 15% or where even higher. the 95% The percentile exceptions were, wave once heights more, the were Arabian overestimated Sea and the Bay of Bengal in DJF, and the Solomon Sea in both seasons, where the 95% percentile by the PC20-E compared to the CFSR by 10–15% or more. wave heights were overestimated by the PC20-E compared to the CFSR by 10–15% or more.

(a) (b)

(e) (f)

Figure 3. Present climate historic ensemble (PC20-E) 1979–2005 seasonal wave height (; m) 95% Figure 3. percentilePresent for climate (a) December–February historic ensemble (DJF) (PC20-E)and (b) June–August 1979–2005 (JJA). seasonal PC20-E wave (m) normalized height (H s; m) 95% percentiledifferences for (a) December–February (%; PC20-E minus reanalysis (DJF) normaliz anded (b by) June–August the reanalysis) to (JJA). ERA-Interim PC20-E for (Hc) sDJF(m) and normalized differences(d) (%; JJA, PC20-E and to Climate minus Forecast reanalysis System normalized Reanalysis (CFSR) by the for reanalysis)(e) DJF and (f to) JJA. ERA-Interim for (c) DJF and (d) JJA, and to Climate Forecast System Reanalysis (CFSR) for (e) DJF and (f) JJA. Figure 4 displays the DJF and JJA mean relative differences between the global PC20-E and ERA-Interim (only). As with wave heights, the ensemble overestimated the mean wave periods, although less: globally, around 5% or less in DJF, with slightly higher values in the equatorial regions

J. Mar. Sci. Eng. 2018, 6, 90 10 of 28

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 10 of 28 Figure4 displays the DJF and JJA mean Tm relative differences between the global PC20-E and (moreERA-Interim in the Pacific (only). Ocean) As with and wave in the heights, Arabian the Sea ensemble (but still overestimated within the 10% the range), mean wave with periods,similar behavioralthoughJ. Mar. in less:Sci. JJA, Eng. globally, although 2018, 6, x FOR around with PEER higher 5%REVIEW or lessoverestimations in DJF, with slightlyin the North higher Pacific values (about in the 5–10%). equatorial 10In of DJF, regions28 in the(more North in Atlantic, the Paciﬁc the Ocean) mean and showed in the Arabianalmost no Sea differences (but still compared within the to 10% the ERA-Interim range), with values, similar (more in the Pacific Ocean) and in the Arabian Sea (but still within the 10% range), with similar behavior in JJA, although with higher overestimations in the North Paciﬁc (about 5–10%). In DJF, in and inbehavior JJA, the in overestimation JJA, although with was higher also ratheroverestimations low. in the North Pacific (about 5–10%). In DJF, in the North Atlantic, the mean Tm showed almost no differences compared to the ERA-Interim values, the North Atlantic, the mean showed almost no differences compared to the ERA-Interim values, and inand JJA, in JJA, the the overestimation overestimation(a) was was also also rather rather low.low. (b)

(a) (b)

FigureFigure 4. PC20-E 4. PC20-E 1979–2005 1979–2005 seasonal seasonal wave wave period period ((; s) meansmeans for for (a ()a DJF) DJF and and (b) (JJA.b) JJA. PC20-E PC20-E Figure 4. PC20-E 1979–2005 seasonal wave period (T ; s) means for (a) DJF and (b) JJA. PC20-E T (s) (s) normalized(s) normalized differences differences to ERA-Interimto ERA-Interim (%; (%; PC20- PC20-EEm minus reanalysis reanalysis norma normalizedlized by theby thereanalysis) reanalysis) m normalized differences to ERA-Interim (%; PC20-E minus reanalysis normalized by the reanalysis) for for (c)for DJF (c) andDJF (andd) JJA. (d) JJA. (c) DJF and (d) JJA.

The differences between the global PC20-E and ERA-Interim DJF and JJA mean are The differences between the global PC20-E and ERA-Interim DJF and JJA mean are presented in Figure 5. The seasonal differences are presented in the background contour, and the presentedThe differencesin Figure 5. between The seasonal the global differences PC20-E andare ERA-Interimpresented in DJFthe andbackground JJA mean contour,θm are presented and the ERA-Interim mean DJF and JJA are also presented with arrows of different colors. Most ERA-Interimin Figure5. The mean seasonal DJF differencesand JJA are are presented also presented in the background with arrows contour, of different and the colors. ERA-Interim Most differences were either negligible or close to zero, or between −10° (anti-clockwise) and 10° mean DJF and JJA θ are also presented with arrows of different colors. Most differences were either differences(clockwise) were in eitherbothm seasons. negligible Some or higher close differences to zero, (aboutor between −20° to −20°)10° can(anti-clockwise) be seen in the westand 10° − ◦ ◦ (clockwise)negligibletropical or in Pacific close both toOcean, seasons. zero, in or the betweenSo Arabianme higher Sea10 anddifferences(anti-clockwise) Bay of Bengal, (about and and −20° 10east (clockwise)to of 20°)Australia can ininbe bothDJF, seen and seasons. in in the the Somewest ◦ ◦ tropicalhighermid-latitudinal differencesPacific Ocean, (abouteast in North the−20 ArabianPacific,to 20 in Sea )the can Southand be Bay seen China of in Bengal,Sea, the and west andat tropicalhigh east latitudes of Paciﬁc Australia, as Ocean,in the in BarentsDJF, in the and Sea, Arabian in the mid-latitudinalSea andin JJA. Bay As of with Bengal,east theNorth seasonal and Pacific, east of in Australiaand the South, the in DJF,China comparisons and Sea, in and the mid-latitudinal atwith high ERA-Interim latitudes east, aswereNorth in thebetter Paciﬁc,Barents in the in Sea, the inSouth JJA.North ChinaAs with Atlantic Sea, the and sub-basin.seasonal at high latitudes, and as, the in the Barents comparisons Sea, in with JJA. ERA-Interim As with the seasonal were betterHs and in theTm , Norththe θm Atlanticcomparisons sub-basin. with ERA-Interim were better in the North Atlantic sub-basin. (a) (b) (a) (b)

Figure 5. Cont.

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Figure 5. PC20-E 1979–2005 seasonal wave direction () means for (a) DJF and (b) JJA (arrows not Figure 5. PC20-E 1979–2005 seasonal wave direction (θm) means for (a) DJF and (b) JJA (arrows scaled). PC20-E differences to ERA-Interim, where positive and negative values represent anti- not scaled). PC20-E differences to ERA-Interim, where positive and negative values represent clockwiseanti-clockwise and andclockwise clockwise differences, differences, and and blac blackk (red) (red) arrows arrows represent represent PC20-E PC20-E (ERA-Interim) directions for ( c) DJF and ( d) JJA.

Despite some differences to ERA-Interim and CFSR, at this stage, it can be said that the Despite some differences to ERA-Interim and CFSR, at this stage, it can be said that the agreement agreement between PC20-E and the reanalyzed DJF and JJA mean and extreme wave heights, mean between PC20-E and the reanalyzed DJF and JJA mean and extreme wave heights, mean wave periods, wave periods, and mean wave directions can be considered as relatively good. These differences were and mean wave directions can be considered as relatively good. These differences were lower or lower or in agreement with previous recent studies by [30,32,33,45]. Nevertheless, it is important to in agreement with previous recent studies by [30,32,33,45]. Nevertheless, it is important to reason reason and understand what, to a certain extent, might be behind these differences. Firstly, part of and understand what, to a certain extent, might be behind these differences. Firstly, part of the H the differences between PC20-E and the reanalysis, mostly in the equatorial Pacific Ocean, haves differences between PC20-E and the reanalysis, mostly in the equatorial Pacific Ocean, have to do to do with different land masks used in WAM C4.5.3 set-up in PC20 and in the reanalysis. with different land masks used in WAM C4.5.3 set-up in PC20 and in the reanalysis. Additionally, Additionally, WAM C4.5.3 was proven to not properly damp swell in the light-wind intertropical WAM C4.5.3 was proven to not properly damp swell in the light-wind intertropical areas, which areas, which can sometimes lead to an overestimation of the wave heights compared to the WAM can sometimes lead to an overestimation of the wave heights compared to the WAM version used version used in ERA-Interim and to the WW3 model used in CFSR. Some differences might also occur in ERA-Interim and to the WW3 model used in CFSR. Some differences might also occur due to due to unresolved sub-grid scale bathymetry, which was taken into account in the ERA-Interim unresolved sub-grid scale bathymetry, which was taken into account in the ERA-Interim WAM version WAM version and in WW3, but not in the WAM C4.5.3 version used in the ensemble. Table 2 shows and in WW3, but not in the WAM C4.5.3 version used in the ensemble. Table2 shows a summary a summary of the PC20-E relative differences against the reanalysis. About 67% (84%) of the PC20-E of the PC20-E relative differences against the reanalysis. About 67% (84%) of the PC20-E Hs global global ocean field had relative errors lower than ±10% in DJF compared with ERA-Interim ocean field had relative errors lower than ±10% in DJF compared with ERA-Interim (CFSR). That area (CFSR). That area became about 77% for the comparison with both sets of reanalysis in JJA. Only became about 77% for the comparison with both sets of reanalysis in JJA. Only about 32% (15%) or 22% about 32% (15%) or 22% (21%) of the PC20-E global ocean field in DJF had relative errors higher (21%) of the PC20-E Hs global ocean field in DJF had relative errors higher than ±10%. The PC20-E than ±10%. The PC20-E global scores are similar, with more than 91% (86%) of the global ocean T global scores are similar, with more than 91% (86%) of the global ocean area with errors lower than aream with errors lower than ±10% compared to ERA-Interim in DJA (JJA). The ensemble also ±10% compared to ERA-Interim in DJA (JJA). The ensemble also represented θm well compared to represented well compared to ERA-Interim, with more than 76% (82%) of the ocean area with ERA-Interim, with more than 76% (82%) of the ocean area with errors below ±10◦. errors below ±10°. Table 2. Summary of PC20-E relative differences to the reanalysis. Percentages of global ocean area Table 2. Summary of PC20-E relative differences to the reanalysis. Percentages of global ocean area with as a function of global wave height (Hs), wave period (Tm), and wave direction (θm) relative withdifferences. as a function DJF—December of global wave to February; height ( JJA—June), wave period to August; ( ), and CFSR—Climate wave direction Forecast ( ) relative System differences.Reanalysis; ERA-I—ERA-Interim.DJF—December to February; JJA—June to August; CFSR—Climate Forecast System Reanalysis; ERA-I—ERA-Interim.

PC20-EPC20-E DJF Differences DJF Differences (ERA-I/CFSR) (ERA-I/CFSR) PC20-E PC20-E JJAJJA DifferencesDifferences (ERA-I/CFSR) (ERA-I/CFSR) % Area% with Area with% Area% Area with with % %Area Area with with %% Area Area with %% Area Area with with % Area% Area with with

Error Error < Error |Error− ErrorError > ErrorError < ErrorError |− ErrorError > |5%/◦| |5 − 10%/◦| |10%/◦| |5%/◦| |5 − 10%/◦| |10%/◦| |%/°| %/°| |%/°| |%/°| %/°| |%/°| Hs 16.99/31.82 50.27/52.48 32.74/15.70 35.03/20.36 42.39/57.87 22.58/21.77 16.99/31.82 50.27/52.48 32.74/15.70 35.03/20.36 42.39/57.87 22.58/21.77 Tm 25.12 66.38 8.50 44.67 41.40 13.93 25.12 66.38 8.50 44.67 41.40 13.93 θm 40.80 36.25 22.95 48.94 33.11 17.95 40.80 36.25 22.95 48.94 33.11 17.95

In search of additional justiﬁcation for the differences shown in Figures2–5, the PC20-E and In search of additional justification for the differences shown in Figures 2–5, the PC20-E and ERA-Interim DJF and JJA mean U10 relative differences were computed for the basic wave parameters. ERA-Interim DJF and JJA mean relative differences were computed for the basic wave As can be seen in Figure6, the U10 differences were strikingly low (less than 5%) or close to zero in parameters. As can be seen in Figure 6, the differences were strikingly low (less than 5%) or close most of the global ocean, particularly in the extratropical areas in both hemispheres. These differences to zero in most of the global ocean, particularly in the extratropical areas in both hemispheres. These differences were lower that the ones shown in Figure 2. The relative differences were higher in

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were lower that the Hs ones shown in Figure2. The relative differences were higher in the intertropical the intertropical latitudes, where the mean absolute magnitudes (and respective anomalies) latitudes, where the mean U absolute magnitudes (and respective anomalies) were actually low. were actually low. These differences,10 most pronounced in the equatorial areas, can be attributed to These differences, most pronounced in the equatorial areas, can be attributed to differences in the differences in the placement of the intertropical convergence zone (ITCZ) in EC-Earth, particularly in placement of the intertropical convergence zone (ITCZ) in EC-Earth, particularly in the Atlantic the Atlantic Ocean [46], since slight meridional differences can lead to substantial relative differences Ocean [46], since slight meridional differences can lead to substantial relative differences in the wind in the wind speed there. Nevertheless, as with the mean basic wave parameters, the PC20-E and the speed there. Nevertheless, as with the mean basic wave parameters, the PC20-E and the reanalyzed reanalyzed DJF and JJA differences can be seen as relatively low. The PC20-E relative and DJF and JJA U10 differences can be seen as relatively low. The PC20-E relative Hs and Tm differences in differences in the Arabian Sea can be explained by the ensemble differences compared to the Arabian Sea can be explained by the ensemble U differences compared to ERA-Interim. ERA-Interim. 10

(a) (b)

Figure 6. PC20-E 1979–2005 seasonal wind speed (; s) means for (a) DJF and (b) JJA. PC20-E Figure 6. PC20-E 1979–2005 seasonal wind speed (U10; s) means for (a) DJF and (b) JJA. PC20-E Tm (s) (s)normalized normalized differences differences to ERA-Interimto ERA-Interim (%; (%; PC20-E PC20- minusE minus reanalysis reanalysis normalized normalized by by the the reanalysis) reanalysis) for for(c) ( DJFc) DJF and and (d) ( JJA.d) JJA.

Figure 7 depicts the ensemble’s ability to reproduce the annual variability, as measured by Figure7 depicts the ensemble’s ability to reproduce the H annual variability, as measured by the MAV (Equation (3)), in comparison with the reanalysis. Here,s the comparisons are presented as the MAV (Equation (3)), in comparison with the reanalysis. Here, the comparisons are presented as anomalies (PC20-E minus reanalysis MAVs: −), and not as relative differences. The anomalies (PC20-E minus reanalysis MAVs: MAV − MAV ), and not as relative differences. North Pacific and North Atlantic sub-basins, wherePC 20the−E inter-seasonalR wave height variability is The North Paciﬁc and North Atlantic sub-basins, where the inter-seasonal wave height variability highest [1,3,7] had the highest MAV values (50–60%), followed by the southern hemisphere MAV extratropicalis highest [1 storm,3,7] had paths the (30–40%), highest not countingvalues marginal (50–60%), sea followed areas. Compared by the southern to ERA-Interim, hemisphere the PC20-Eextratropical MAV stormshowed paths small (30–40%), differences: not countingmarginal marginal or inexistent, sea areas. or between Compared −5% to (in ERA-Interim, the lower MAV − latitudes)the PC20-E and 5% showed(in the North small differences:Atlantic and marginal southern or hemisphere inexistent, extratropical or between latitudes).5% (in the When lower comparedlatitudes) to and CFSR, 5% (inthe thedifferences North Atlantic were considerably and southern higher hemisphere (about −10% extratropical to 10%), particularly latitudes). in When the − southerncompared hemisphere to CFSR, the extratropical differences werelatitudes. considerably These differences higher (about might 10%be related to 10%), toparticularly the different in temporalthe southern resolutions hemisphere (6 h extratropicalin PC20-E and latitudes. ERA-Interim, These and differences 3 h in CFSR), might besince related CFSR to is the known different to bettertemporal simulate resolutions extreme (6 hwave in PC20-E heights and compared ERA-Interim, to ERA-Interim and 3 h in [72]; CFSR), however, since CFSRit also is to known slightly to better simulate extreme wave heights compared to ERA-Interim [72]; however, it also to slightly overestimates . These differences in the PC20-E MAV compared to the CFSR were higher in the H MAV Arabianoverestimates Sea (closes. to These 20%). differences in the PC20-E compared to the CFSR were higher in the Arabian Sea (close to 20%).

J. Mar. Sci. Eng. 2018, 6, 90 13 of 28 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 13 of 28

(a)

(b)

(c)

Figure 7. PC20-E mean annual variability (MAV; %; Equation (3)) differences compared to ERA- Figure 7. PC20-E Hs mean annual variability (MAV; %; Equation (3)) differences compared to Interim and CFSR (PC20 minus the reanalysis). (a) PC20-E MAV; (b) difference between the PC20-E ERA-Interim and CFSR (PC20 minus the reanalysis). (a) PC20-E MAV;(b) difference between the and ERA-Interim respective MAVs; (c) difference between the PC20-E and CFSR respective MAVs. PC20-E and ERA-Interim respective MAVs; (c) difference between the PC20-E and CFSR respective MAVs. The PC20-E intra-annual variability was also evaluated through comparison with in situ observations (positions in Figure 1). For that matter, the comparisons were done separately for three of theThe regional PC20-E areas intra-annual shown in variability Figure 1: wasextrat alsoropical evaluated Norththrough Pacific (ETNP), comparison extratropical with in situ NorthHs observationsAtlantic (ETNA), (positions and tropical in Figure North1). For Atlantic that matter, (TNAO). the comparisons The only buoy were in done the tropical separately eastern for three North of thePacific regional (TENP) areas area shown was in included Figure1: extratropicalin the ETNP North for convenience. Paciﬁc (ETNP), The extratropical collocated North(at the Atlantic in situ (ETNA), and tropical North Atlantic (TNAO). The only buoy in the tropical eastern North Paciﬁc measurements positions) daily averaged observations for PC20-E, ERA-Interim, and CFSR (TENP)(averaged area in waseach included of the three in the areas) ETNP plotted for convenience. in a Julian year The are collocated shown in (at Figure the in 8. situ The measurements length of the positions)PC20 time daily series averaged was matchedHs observations with the forobservational PC20-E, ERA-Interim, records following and CFSR [78] (averaged methodology, in each ofas described in Section 2. In the background, the spread of the ensemble members is also shown as a

J. Mar. Sci. Eng. 2018, 6, 90 14 of 28 the three areas) plotted in a Julian year are shown in Figure8. The length of the PC20 time series was matched with the observational records following [78] methodology, as described in Section2. In the background, the spread of the ensemble members is also shown as a grey band. Despite some discrepancies, the intra-annual variability was well captured by the ensemble in the three areas. In the ETNA, the agreement was better, with a slight overestimation (less than 0.1 m). During the last months ofJ.the Mar. yearSci. Eng. (from 2018, 6, x day FOR PEER 250 REVIEW onwards, i.e., from September to December), when 14 wave of 28 heights start to increase in the North Atlantic, the agreement between the PC20-E, the observations, and the grey band. Despite some discrepancies, the intra-annual variability was well captured by the reanalysisensemble was close in the to three ideal. areas. This In the agreement ETNA, the agreem was notent was as better, good with in thea slight ETNP, overestimation where the (lessH s spread between observationsthan 0.1 m). During and reanalysis the last months was alsoof the higher. year (from On day the 250 other onwards, hand, i.e., inthe from first September months to of the year (mostly formDecember), mid-January when wave to April) heights the start agreement to increase wasin the good North in Atlantic, that area; the however,agreement between from there the onwards, PC20-E overestimatedPC20-E, the observations, wave heights and the by reanalysis about was 0.2 m.close This to ideal. overestimation, This agreement aswas mentioned not as good in before, can the ETNP, where the spread between observations and reanalysis was also higher. On the other be explained,hand, to in athe great first months extent, of by thethe year differences (mostly form inmid-January the land to mask April) usedthe agreement in the climatewas good simulations, in with greatestthatdifferences area; however, in from the equatorialthere onwards, Pacific PC20-E Ocean. overestimated For that wave reason, height wavess by about generated 0.2 m. This in the South Pacific Oceanoverestimation, propagate as morementioned freely before, as swell,can be explained, less damped, to a great into extent, the by North the differences Pacific sub-basin,in the land leading to this slightmask overestimation used in the climate of simulations, wave heights with greatest in the differences PC20-E, in mostly the equatorial during Pacific the Ocean. second For half of the that reason, waves generated in the South Pacific Ocean propagate more freely as swell, less damped, year. In theinto TNAO the North area, Pacific with sub-basin, in situ observationsleading to this slight mostly overestimation concentrated of wave in heights the Gulf in the of PC20-E, Mexico and the Caribbeanmostly Sea where during swell the second penetration half of the is lower,year. In the the agreementTNAO area, betweenwith in situ PC20-E observations and the mostly observations and reanalysisconcentrated was good in the for Gulf most of Mexico of the and year. the There Caribbean was, Sea nevertheless, where swell penetration some underestimation is lower, the during the tropicalagreement cyclone between season PC20-E that can and bethe linkedobservations to an and underestimation reanalysis was good of for the most wind of the speeds year. There in JJA in that was, nevertheless, some underestimation during the tropical cyclone season that can be linked to an area, as shownunderestimation in Figure of6d. the wind speeds in JJA in that area, as shown in Figure 6d.

(a)

(b)

Figure 8. Cont. J. Mar. Sci. Eng. 2018, 6, 90 15 of 28 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 15 of 28

(c)

Figure 8. Julian year daily (m) means (January to December intra-annual variability) of the mean Figure 8. Julian year daily H (m) means (January to December intra-annual variability) of the mean (m) at observation spositions for in-situ observations (black line), ERA-Interim (red line), CFSR Hs (m) at observation(blue line), and positions PC20-E (grey for in-situ line) in observations the (a) ETNA, (black (b) ETNP, line), and ERA-Interim (c) TNAO. The (red grey line), band CFSR (blue line), and PC20-Ecorresponds (grey to the line) mean in daily the (spreada) ETNA, of the (sevenb) ETNP, ensemble and members. (c) TNAO. The grey band corresponds to the mean daily spread of the seven ensemble members. The relatively low variability between the ensemble members in Figure 8 (shown in the back as a grey band around the ensemble mean) can now be seen at a global scale in Figure 9, where the The relativelyPC20-E inconsistency low variability (for betweenand ; absolute the ensemble pairwise difference members between in Figure the ensemble8 (shown members in the back as a grey bandPC20-1 around to thePC20-7) ensemble is shown. mean) The can inconsistency now be seen was at relatively a global small: scale about in Figure 0.1 m or9, whereless in the the PC20-E extratropical and high latitudes in DJA (only in the southern hemisphere in JJA), and less than half inconsistency (for H and T ; absolute pairwise difference between the ensemble members PC20-1 to of that values in the mintertropical latitudes and marginal seas in both seasons. The PC20-E PC20-7) isinconsistency shown. The wasH sslightlyinconsistency higher than wasthat of relatively the , or at small: least more about evenly 0.1 distributed m or less in in the the global extratropical and high latitudesocean, with in values DJA (onlylower than in the 0.1 southerns. The highes hemispheret values can inbe JJA),found and toward less the than eastern half oceanic of that value in margins and in the northern sector of the Indian Ocean in DJF, and also in the western South Atlantic the intertropical latitudes and marginal seas in both seasons. The PC20-E Tm inconsistency was slightly in JJA. The intra-ensemble variability, as seen from these values, was, therefore, low as a result of the higher thansingle that GCM-forcing of the Hs, orstrategy, at least and more it was evenlycertainly distributed lower than in in the the multi-forcing global ocean, ensemble with in valuesthe lower than 0.1 s.article The highestby [43]. values can be found toward the eastern oceanic margins and in the northern sector of the IndianThe scatter Ocean plot inin DJF,Figure and 10 compar also ines thethe westernensemble with South the Atlanticin situ inobservations. JJA. The intra-ensemble As in variability,Figure as seen 7, the from ERA-Interim these values, and CFSR was, collocated therefore, wave low heights as a result are also of included. the single The GCM-forcing length of the strategy, PC20-E time series was once again matched with the observational records following the and it wasmethodology certainly lower in [78]. than A quantile–quantile in the multi-forcing (Q–Q) plot ensemble is also included in the in article Figure by10, [with43]. collocated The scatterPC-20-E, plot in situ in observations, Figure 10 comparesand reanalysis. the An ensemble overestimation with of the the inensemble’s situ Hs highestobservations. wave As in Figure7, theheights ERA-Interim can be seen in and the CFSRscatter plot collocated compared wave to the three heights datasets. are Lower also included. wave heights The were, length on of the PC20-E timethe seriesother hand, was slightly once again underestimated. matched The with overesti the observationalmation was mostly records due to the following overestimation the methodology in the North Pacific, and it was hardly present if the comparison was made only for the North Atlantic in [78]. A quantile–quantileobservations (not shown). (Q–Q) It is plot worthy is also of note included that the in CFSR Figure wave 10 ,heights with collocated were closer PC-20-E,to the in situ observations,observations, and reanalysis. slightly Anoverestimating overestimation them, ofwhile the ensemble’sthe ERA-Interim highest underestimated wave heights can (in be seen in the scatteragreement plot compared with [72]). to A the similar three behavior datasets. can be Lower seen in wave the Q–Q heights plot, with were, PC20-E on theunderestimating other hand, slightly underestimated.the lower The quantile overestimation wave heights, was while mostly consistently due tooverestimating the overestimation them in the in higher-order the North ones, Paciﬁc, and it particularly the extreme wave heights. It is also worthy to note the pronounced overestimation of was hardlyextreme present wave if theheights comparison in the CFSR was hindcast made compared only for to the the observations. North Atlantic A summary observations of statistics (not of shown).

It is worthythe of PC20-E note that comparison the CFSR against wave heightsthe observations were closer and reanalysis to the observations, at the observational slightly positions overestimating is presented in Table 3. The high correlation coefficients between PC20 and the observations and them, while the ERA-Interim underestimated Hs (in agreement with [72]). A similar behavior can be reanalysis (consistently higher than 0.93 for the observations and ERA-Interim, and 0.88 for the CFSR) seen in the Q–Q plot, with PC20-E underestimating the lower quantile wave heights, while consistently overestimating them in the higher-order ones, particularly the extreme wave heights. It is also worthy to note the pronounced overestimation of extreme wave heights in the CFSR hindcast compared to the observations. A summary of statistics of the PC20-E Hs comparison against the observations and reanalysis at the observational positions is presented in Table3. The high correlation coefﬁcients between PC20 and the observations and reanalysis (consistently higher than 0.93 for the observations and ERA-Interim, and 0.88 for the CFSR) conﬁrm the good scores of PC20-E, despite the generalized overestimation of wave heights at these positions. J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 16 of 28

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 16 of 28 confirmJ. Mar. Sci. the Eng. good2018, 6 scores, 90 of PC20-E, despite the generalized overestimation of wave heights at16 these of 28 positions. confirm the good scores of PC20-E, despite the generalized overestimation of wave heights at these positions. (a) (b)

(a) (b)

Figure 9. Mean PC20-E intra-ensemble inconsistency (mean absolute pairwise difference between the Figure 9. Mean PC20-E intra-ensemble inconsistency (mean absolute pairwise difference between the seven ensemble members) for (a,b) (m), and (c,d) (s), for (a,c) DJF, and (b,d) JJA. Figureseven ensemble9. Mean PC20-E members) intra-ensemble for (a,b) Hs inconsistency(m), and (c,d) (mTmean(s), absolute for (a,c) DJF,pairwise and (differenceb,d) JJA. between the seven ensemble members)(a) for (a,b) (m), and (c,d) (s), for (a,c) DJF, and(b ()b ,d) JJA.

(a) (b)

Figure 10. (a) Scatter plot of the mean (m) PC20-E (blue squares), ERA-Interim (red triangles), and CFSR (green diamonds) against in situ observations, with the purple cloud dots in the background as Figure 10. (a) Scatter plot of the mean (m) PC20-E (blue squares), ERA-Interim (red triangles), and theFigure Julian 10. year(a) Scatter daily means plot of of the PC20-E mean Hagainsts (m) PC20-Eobservations (blue squares),per in situ ERA-Interim measurement (red (26,280 triangles), dots, andi.e., CFSR (green diamonds) against in situ observations, with the purple cloud dots in the background as 72CFSR in situ (green measurements diamonds) againstover 365 in days). situ observations, (b) Quantile–quantile with the purple(Q–Q) plot cloud of dots PC20-Ein the background (blue circles), as the Julian year daily means of PC20-E against observations per in situ measurement (26,280 dots, i.e., ERA-Interimthe Julian year (red daily circles), means and of CFSR PC20-E (green against circles) observations against in per situ in ob situservations, measurement with 10 (26,280 to 90 quantiles dots, i.e., 72 in situ measurements over 365 days). (b) Quantile–quantile (Q–Q) plot of PC20-E (blue circles), (every72 in situ five measurements quantiles) represented over 365 days).as open (b circles,) Quantile–quantile and 91 to 99 quan (Q–Q)tiles plot (every of Hs quantile)PC20-E (blue represented circles), ERA-Interim (red circles), and CFSR (green circles) against in situ observations, with 10 to 90 quantiles asERA-Interim closed circles. (red circles), and CFSR (green circles) against in situ observations, with 10 to 90 quantiles (every(every five ﬁve quantiles) representedrepresented asas openopen circles, circles, and and 91 91 to to 99 99 quantiles quantiles (every (every quantile) quantile) represented represented as as closed circles. closed circles.

J. Mar. Sci. Eng. 2018, 6, 90 17 of 28

Table 3. Summary statistics of PC20-E, Era-Interim, and CFSR Hs comparisons against in situ measurements. RMSE—root-mean-square error.

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW Bias (m) RMSE (m) r 17 of 28

Table 3. PC20-ESummary vs. statistics Observations of PC20-E, Era-Interim, 0.16 and CFSR 0.39 comparisons against 0.93 in situ measurements.PC20-E RMSE—root-mean-square vs. ERA-I error. 0.22 0.40 0.94 PC20-E vs. CFSR 0.12Bias (m) RMSE 0.46 (m) r 0.88 PC20-E vs. Observations 0.16 0.39 0.93 PC20-E vs. ERA-I 0.22 0.40 0.94 Taylor diagrams of the comparison between PC20-E and observations, separately for the ETNP, PC20-E vs. CFSR 0.12 0.46 0.88 ETNA, and TNAO areas, are shown in Figure 11. The comparison between each of the ensemble members (PC20-1Taylor to diagrams PC20-7) of the and comparison observations, between as PC20 well-E asand similar observations, comparisons separately for for the ERA-Interim ETNP, and CFSR, areETNA, also presented. and TNAO areas, The PC20-Eare shown showed in Figure better 11. The results comparison (higher between correlation each of the coefﬁcient ensemble and lower members (PC20-1 to PC20-7) and observations, as well as similar comparisons for ERA-Interim and RMSE) thanCFSR, any are also individual presented. ensemble The PC20-E members.showed better Theresults variability, (higher correlation as represented coefficient and by lower the standard deviation,RMSE) was similarthan any between individual PC20-E ensemble and members. the ensemble The variability, members, as represented and closer by tothe the standard reanalysis. The correlationdeviation, between was PC20-E similar between and the PC20-E observations and the ensemb was highestle members, in and the closer ETNA, to the and reanalysis. lowest The in the TNAO, despite thecorrelation fact that between the RMSE PC20-E was and lowest the observations in the Caribbean was highest andin the Gulf ETNA, of and Mexico lowest compared in the TNAO, to the other despite the fact that the RMSE was lowest in the Caribbean and Gulf of Mexico compared to the other two areas.two In areas. the TNAO, In the TNAO, the PC20 the PC20 scores scores were were alsoalso more more detached detached from from those thoseof the reanalysis. of the reanalysis.

(a)

(b)

Figure 11. Cont. J. Mar. Sci. Eng. 2018, 6, 90 18 of 28

J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 18 of 28

(c)

Figure 11. Taylor diagrams of (m) PC20-E (blue circles), ERA-Interim (red circles), and CFSR Figure 11. Taylor diagrams of Hs (m) PC20-E (blue circles), ERA-Interim (red circles), and CFSR (green circles) against in situ observations in the (a) ETNA, (b) ETNP, and (c) TNAO. The grey circles (green circles)correspond against to the in seven situ observationsensemble members. in the The ( cosinea) ETNA, of the (angleb) ETNP, in the andpolar (plotc) TNAO. is proportional The grey circles

correspondto the to thecorrelation seven between ensemble the observed members. The (m) and cosine PC20 of (ensemble the angle and in ensemble the polar members), plot is and proportional to the correlationbetween observations between theand observedthe reanalysis.Hs The(m) radius and PC20indicates (ensemble the variability, and as ensemble measured by members), the and between observationsstandard deviation. and The the root-mean-square reanalysis. Theerror radius(RMSE) is indicates presented for the the variability, PC20 and the as reanalysis. measured by the standard deviation.The intra-annual The root-mean-squarevariability of the PC20-E error mean (RMSE) spatial is bias presented (Equation for (1)) the and PC20 mean and normalized the reanalysis. differences (spatially averaged) from the comparison with ERA-Interim and CFSR (daily means The intra-annualshown in a Julian variability year) is presented of the PC20-Ein Figure mean12 for each spatial of the bias 13 regional (Equation areas, (1)) as well and as mean for the normalized global ocean. The ensemble’s overestimation compared with ERA-Interim is clear, as shown in the differencesprevious (spatially Figures, averaged) with a bias from on th thee order comparison of 0.2 and 0.25 with m, ERA-Interimslightly higher during and CFSR the last (daily quarter means of shown in a Julianthe year) year. isThis presented overestimation in Figure toward 12ERA-Interim for each (from of the 9 to 13 11%, regional also higher areas, in the as last well quarter as for of the global ocean. Thethe ensemble’s year), is also overestimationclear in the global normalized compared differences. with ERA-Interim The global agreement is clear, of as the shown PC20-E in with the previous Figures, withCFSR awas bias considerably on the orderhigher, ofwith 0.2 lower and biases 0.25 (from m, slightly−0.1 to 0.15 higher m, and duringmost of the the year last close quarter to of the zero) and also lower normalized differences (between −2% to 4%, but lower for most of the year). year. ThisWhen overestimation looking at the regional toward areas, ERA-Interim the lowest biases (from and 9 normalized to 11%, also differences higher in incomparison the last with quarter of the year), is alsoERA-Interim clear in occurred the global in the normalized extratropical differences.areas, particularly The in global the ETNA, agreement extratropical of the South PC20-E with CFSR wasAtlantic considerably (ETSA), and higher, extratropical with South lower Indian biases (ETSI) (from areas.− The0.1 highest to 0.15 differences m, and occurred most of in the the year close to zero) andPacific also Ocean lower intertropical normalized regions. differences The same occu (betweenrred, with− 2%lower to differences, 4%, but lower for thefor comparison most of the year). with CFSR. Nevertheless, the CFSR comparison displayed a higher bias and relative difference in the When lookingtropical at North the regional Indian (TNIO). areas, the lowest biases and normalized differences in comparison with ERA-Interim occurredThe intra-annual in the variability extratropical of the averaged areas, particularly PC20-E M-Scores in the (Equation ETNA, (4)) extratropical was also computed South Atlantic (ETSA), andglobally extratropical and for each Southof the 13 Indian regional (ETSI) areas, as areas. shown Thein Figure highest 13. The differences highest M-Score occurred values can in the Pacific Ocean intertropicalbe found in the regions. ETNA area The for same the comparison occurred, with with ERA-Interim lower differences, (with an annual for the average comparison of 860; seewith CFSR. Table 4 for mean M-Score values). Similar values can be found for the comparison with CFSR, Nevertheless,consistently the CFSR higher comparison than 820 (annual displayed averagea of higher 827). The bias M-score and relative values for difference the remaining in the tropical North Indianextratropical (TNIO). areas can also be classified as high, particularly during the respective winter season) for The intra-annualthe comparison variability with ERA-Interim: of the averaged consistently PC20-E higher M-Scoresthan 700, (Equationwith the exception (4)) was of also the computed globally andextratropical for each South of thePacific 13 (ETSP) regional area. areas, These asscores shown were insimilar Figure for the13 .comparison The highest with M-ScoreCFSR, values although with lower (higher) scores in the ETSA, ETSP, and ETSI (ETNP)—see Table 4. In the can be foundintertropical in the areas, ETNA the areaM-Scores for were the comparisonstill high, with mean with values ERA-Interim of 778 (696) (with and 664 an (687) annual in the average of 860; see TableTNAO4 andfor TSAO, mean respectively, M-Score values).for the ERA-Interim Similar (CFSR) values comparison. can be found These values for the decreased comparison in with CFSR, consistentlythe intertropical higher Pacific than and 820 Indian (annual Ocean averageareas, for ofboth 827). comparisons, The M-score with the values lowestfor M-score the remaining extratropical areas can also be classified as high, particularly during the respective winter season) for the comparison with ERA-Interim: consistently higher than 700, with the exception of the extratropical South Pacific (ETSP) area. These scores were similar for the comparison with CFSR, although with lower (higher) scores in the ETSA, ETSP, and ETSI (ETNP)—see Table4. In the intertropical areas, the M-Scores were still high, with mean values of 778 (696) and 664 (687) in the TNAO and TSAO, respectively, for the ERA-Interim (CFSR) comparison. These values decreased in the intertropical Pacific and Indian Ocean areas, for both comparisons, with the lowest M-score values occurring in the tropical eastern South Pacific (TESP) area. Globally, the M-Scores were comparable for both sets of J. Mar. Sci. Eng. 2018, 6, x 90 FOR PEER REVIEW 19 of 28 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 19 of 28 values occurring in the tropical eastern South Pacific (TESP) area. Globally, the M-Scores were values occurring in the tropical eastern South Pacific (TESP) area. Globally, the M-Scores were comparablereanalysis (consistently for both sets higher of reanalysis than 750), (consistently with annual higher means than of 808 750), and with 751 annual for the comparisonsmeans of 808 withand comparable for both sets of reanalysis (consistently higher than 750), with annual means of 808 and 751ERA-Interim for the comparisons and CFSR, respectively. with ERA-Interim These M-Scoreand CFSR, values respectively. were comparable These M-Score to or higher values than were the 751 for the comparisons with ERA-Interim and CFSR, respectively. These M-Score values were comparableones shown to in or the higher article than by [the43], ones and shown onsistent in the with article the onesby [43], shown and onsistent for atmospheric with the CMIP5 ones shown GCM comparable to or higher than the ones shown in the article by [43], and onsistent with the ones shown forevaluations atmospheric in the CMIP5 article GCM by [80 ],evaluations showing the in relativethe article high by skill [80], of showing PC20. Additional the relative information high skill can of for atmospheric CMIP5 GCM evaluations in the article by [80], showing the relative high skill of PC20.be seen Additional in Table4 andinformation Figure 14 can, where be seen a graphic in Table display 4 and of Figure regional 14, andwhere global a graphic M-Scores display can beof PC20. Additional information can be seen in Table 4 and Figure 14, where a graphic display of regionalseen simultaneously. and global M-Scores can be seen simultaneously. regional and global M-Scores can be seen simultaneously. (a) (b) (a) (b)

Figure 12. Julian year daily means (January to December intra-annual variability), for the 13 regional FigureFigure 12. 12. JulianJulian year year daily daily means means (January (January to to December December intra-annual intra-annual variability), variability), for for the the 13 13 regional regional areas and for the global ocean, of the (m) PC20-E mean spatial bias (a) against ERA-Interim, and areasareas and and for for the the global global ocean, ocean, of of the the Hs (m) PC20-E mean spatial bias ( a) against ERA-Interim, and and (b) against CFSR. The (m) PC20-E mean normalized differences (c) against ERA-Interim, and (d) ((bb)) against against CFSR. CFSR. The The Hs (m) PC20-E mean normalized differences differences ( (cc)) against against ERA-Interim, ERA-Interim, and and ( (dd)) against CFSR. againstagainst CFSR. CFSR. (a) (b) (a) (b)

Figure 13. Same as Figure 12, but for the M-Scores (a) against ERA-Interim, and (b) against CFSR. Figure 13. Same as Figure 12, but for the M-Scores (a) against ERA-Interim, and (b) against CFSR. Figure 13. Same as Figure 12, but for the M-Scores (a) against ERA-Interim, and (b) against CFSR.

J. Mar. Sci. Eng. 2018, 6, 90 20 of 28 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 20 of 28

FigureFigure 14. 14. M-ScoresM-Scores for for the the 13 13 areas areas and and for for the the global global ocean, ocean, as as listed listed in in Table Table 44..

Table 4.4. SummarySummary of of regional regional and and global global M-Scores. M-Scores ETNP—extratropical. ETNP—extratropical North North Pacific; Pacific; TENP—tropical TENP— tropicaleastern Northeastern Pacific; North Pacific; TWNP—tropical TWNP—tropical western western North Pacific; North Pacific; TWSP—tropical TWSP—tropical western western SouthPacific, South Pacific,TESP—tropical TESP—tropical eastern South eastern Pacific, South ETSP—extratropical Pacific, ETSP—extratropical South Pacific; ETNA—extratropicalSouth Pacific; ETNA— North extratropicalAtlantic; TNAO—tropical North Atlantic; North TNAO—tropical Atlantic; TSAO—tropical North Atlantic; South Atlantic; TSAO—tropical ETSA—extratropical South Atlantic; South ETSA—extratropicalAtlantic; TNIO—tropical South North Atlantic; Indian; TNIO—tropical TSIO—tropical SouthNorth Indian; Indian; ETSI—extratropical TSIO—tropical South South Indian; Indian. ETSI—extratropical South Indian. PC20 vs. ERA-I PC20 vs. CFSR PC20 vs. ERA-I PC20 vs. CFSR

AnnualAnnual DJF DJF JJA JJA Annual Annual DJF DJF JJA JJA ETSA 704 704 714 714 691 691 630 630 713 713 611 611 ETNA 860 861 858 827 824 834 ETNA 860 861 858 827 824 834 ETSP 642 601 659 536 628 428 ETNPETSP 642 765 601 798 659 730 536 796 628 792 428 792 ETNPETSI 765 706 798 708 730 714 796 609 792 658 792 551 TSAOETSI 706 664 708 738 714 597 609 687 658 669 551 739 TNAOTSAO 664 778 738 851 597 715 687 696 669 726 739 662 TESP 404 298 483 490 509 382 TNAOTWSP 778 572 851 540 715 592 696 618 726 597 662 648 TENPTESP 404 485 298 613 483 418 490 608 509 720 382 547 TWNPTWSP 572 650 540 597 592 608 618 676 597 669 648 612 TENPTSIO 485 753 613 634 418 825 608 741 720 757 547 651 TNIO 684 591 808 643 600 681 TWNP 650 597 608 676 669 612 Global 808 768 853 751 760 750 TSIO 753 634 825 741 757 651 TNIO 684 591 808 643 600 681 Figure 15 displays the box plots for the H annual M-scores between the PC20-E and the reanalysis, Global 808 768s 853 751 760 750 globally and for each or the 13 regional areas. The respective annual and seasonal (DJF and JJA) means are also plotted. As a measurement of the intra-annual variability of the regional and global M-score, Figure 15 displays the box plots for the annual M-scores between the PC20-E and the the inter-quartile range (IQR) was lower in the extratropical areas in the comparison with ERA-Interim, reanalysis, globally and for each or the 13 regional areas. The respective annual and seasonal (DJF particularly in the ETNA and ETNP, where the differences between the lower and higher extremes and JJA) means are also plotted. As a measurement of the intra-annual variability of the regional and were also lower, particularly in the ETNA area. While the same occurred in the northern hemisphere global M-score, the inter-quartile range (IQR) was lower in the extratropical areas in the comparison extratropical areas, regarding the CFSR comparison, it was not exactly the same for the southern with ERA-Interim, particularly in the ETNA and ETNP, where the differences between the lower and hemisphere, particularly in the ETSP. The highest IQR (intra-annual variability) can be seen in the higher extremes were also lower, particularly in the ETNA area. While the same occurred in the TESP area (which also had the lowest annual and seasonal M-score means) for both sets of reanalysis. northern hemisphere extratropical areas, regarding the CFSR comparison, it was not exactly the same In Figure 13, it can be seen that the M-scores were comparable in terms of magnitude and variability, for the southern hemisphere, particularly in the ETSP. The highest IQR (intra-annual variability) can be seen in the TESP area (which also had the lowest annual and seasonal M-score means) for both

J.J. Mar. Mar. Sci. Sci. Eng. Eng. 20182018, ,66, ,x 90 FOR PEER REVIEW 2121 of of 28 28 sets of reanalysis. In Figure 13, it can be seen that the M-scores were comparable in terms of magnitudeparticularly and in thevariability, extratropical particularly areas. It in is the interesting extratropical to note areas. that, It while is interesting the mean to M-regional note that, while scores thefor mean the extratropical M-regional areas scores were for higher the extratropical in the comparison areas were with ERA-Interimhigher in the (735,comparison 737, and with 730, forERA- the Interimannual, (735, DJF, 737, and JJAand means,730, for respectively), the annual, DJF, the situationand JJA means, somehow respectively), reversed in the the situation intertropical somehow areas reversedwhen compared in the intertropical to CFSR (680, areas 723, when and 643,compared respectively). to CFSR (680, 723, and 643, respectively).

(a) (b)

Figure 15. M-Score annual box plots for the 13 regional areas and for the global ocean of the PC20- Figure 15. M-Score annual box plots for the 13 regional areas and for the global ocean of the Hs PC20-E E( a()a against) against ERA-Interim, ERA-Interim, and and (b) against(b) against CFSR. CFSR. The boxThe plots box areplots set are between set between the 25% the and 25% 75% and quantiles 75% quantileswith the medianwith the in median between, in andbetween, with and the whiskerswith the betweenwhiskersthe between 5% and the 95% 5% quantiles and 95% belowquantiles and below and above. The blue, green, and red crosses represent the DJF, annual, and JJA mean (m), above. The blue, green, and red crosses represent the DJF, annual, and JJA mean Hs (m), respectively. respectively. 4. Summary and Conclusions 4. Summary and Conclusions The performance skills of a single-forcing (EC-Earth), single-wave model (WAM), and The performance skills of a single-forcing (EC-Earth), single-wave model (WAM), and single- single-scenario (RCP8.5) dynamic wave climate ensemble in reproducing the present time wave scenario (RCP8.5) dynamic wave climate ensemble in reproducing the present time wave climate (as climate (as represented by the historic period) were presented. The ensemble was designed with the represented by the historic period) were presented. The ensemble was designed with the goal of goal of reducing the variability inherent in using a multi-forcing GCM approach to force the same reducing the variability inherent in using a multi-forcing GCM approach to force the same wave wave model. The PC20-E ensemble’s historic period (1979–2005) was extensively compared against model. The PC20-E ensemble’s historic period (1979–2005) was extensively compared against a set of a set of 72 in situ wave-height observations, as well as to the ERA-Interim reanalysis [49] and CFSR 72 in situ wave-height observations, as well as to the ERA-Interim reanalysis [49] and CFSR hindcast hindcast [50]. [50]. It was shown that the differences between the ensemble and the reanalyzed DJF and JJA It was shown that the differences between the ensemble and the reanalyzed DJF and JJA mean mean and extreme Hs, mean Tm, and mean θm can be considered as relatively low, in line with and extreme , mean , and mean can be considered as relatively low, in line with (or lower (or lower than) previous global wave climate studies. The PC20-E comparison with the 72 in situ H than) previous global wave climate studies. The PC20-E comparison with the 72 in situ s observations showed a good agreement, with small biases and high correlation coefficients, as well observations showed a good agreement, with small biases and high correlation coefficients, as well as a good representation of the intra-annual variability. Nevertheless, the ensemble had a tendency as a good representation of the intra-annual variability. Nevertheless, the ensemble had a tendency to overestimate (underestimate) the mean wave heights, in both seasons, compared to ERA-Interim to overestimate (underestimate) the mean wave heights, in both seasons, compared to ERA-Interim (CFSR). The agreement with ERA-Interim was better in the North Atlantic, and with CFSR in the North (CFSR). The agreement with ERA-Interim was better in the North Atlantic, and with CFSR in the Pacific. The comparison with the reanalysis was weaker in the Arabian Sea. Apparently, EC-Earth North Pacific. The comparison with the reanalysis was weaker in the Arabian Sea. Apparently, EC- has some difficulties in resolving the South Asian Monsoon. Nevertheless, most probably due to Earth has some difficulties in resolving the South Asian Monsoon. Nevertheless, most probably due resolution, ERA-Interim winds already had problems in that area, as shown by [81,82]; hence, a to resolution, ERA-Interim winds already had problems in that area, as shown by [81,82]; hence, a dedicated study for this area would be needed. The PC20-E overestimation of extreme wave heights dedicated study for this area would be needed. The PC20-E overestimation of extreme wave heights was lower; in fact, compared to ERA-Interim, the ensemble had almost equal areas of over- and was lower; in fact, compared to ERA-Interim, the ensemble had almost equal areas of over- and underestimation in both seasons. Compared to CFSR, the ensemble extreme H seasonal fields were underestimation in both seasons. Compared to CFSR, the ensemble extreme sseasonal fields were underestimated almost across the entire global ocean. It was shown that ERA-Interim underestimates underestimated almost across the entire global ocean. It was shown that ERA-Interim underestimates extreme wave heights, while CFSR has a tendency to overestimate them [72]. Figure 16 shows the extreme wave heights, while CFSR has a tendency to overestimate them [72]. Figure 16 shows the mean ERA-Interim and CFSR inconsistency (mean absolute pairwise difference). As can be seen, the mean ERA-Interim and CFSR inconsistency (mean absolute pairwise difference). As can be seen, the differences between the reanalysis and the hindcast can reach values of 0.7–0.8 m in the Southern Ocean differences between the reanalysis and the hindcast can reach values of 0.7–0.8 m in the Southern storm belt during the austral winter, and values on the order of 0.6–0.7 m in the extratropical latitudes Ocean storm belt during the austral winter, and values on the order of 0.6–0.7 m in the extratropical of both hemispheres in DJF. These differences are mostly due to the overestimation (underestimation) latitudes of both hemispheres in DJF. These differences are mostly due to the overestimation of the CFSR (ERA-Interim) wave heights. It would be tempting to state that, with the PC20-E H (underestimation) of the CFSR (ERA-Interim) wave heights. It would be tempting to state that, withs seasonal fields somewhere in between, they are closer to reality. Nevertheless, without a third global the PC20-E seasonal fields somewhere in between, they are closer to reality. Nevertheless, wave dataset and further investigation, that cannot be concluded. The ensemble comparison with the without a third global wave dataset and further investigation, that cannot be concluded. The

J. Mar. Sci. Eng. 2018, 6, 90 22 of 28 J. Mar. Sci. Eng. 2018, 6, x FOR PEER REVIEW 22 of 28

ERA-Interimensemble comparison mean Tm seasonal with the ﬁelds ERA-Interim also revealed mean some overestimation; seasonal fields however, also it revealed was lower some than thatoverestimation; seen for the however, mean seasonal it was wave lower heights. than that seen for the mean seasonal wave heights.

(a) (b)

Figure 16. Reanalysis inconsistency for (m) (mean absolute difference between ERA-Interim and Figure 16. Reanalysis inconsistency for Hs (m) (mean absolute difference between ERA-Interim and CFSR) for (a) DJF and (b) JJA. CFSR) for (a) DJF and (b) JJA.

At a regional level, the PC20-E had a rather good performance in the extratropical areas of both Athemispheres, a regional level, particularly the PC20-E in theHs hadNorth a rather Atlantic good sub-basin, performance with in thelow extratropicalbiases and areasrelative of bothdifferences hemispheres, during particularlymost of the inyear, the especially North Atlantic compared sub-basin, to the with CFSR. low These biases skills and relative were lower differences in the duringareas along most the of theequatorial year, especially Pacific Ocean. compared Globally, to the th CFSR.e inter-annual These skills variability were lower of the in biases the areas from along the theERA-Interim equatorial and Pacific CFSR Ocean. comparisons Globally, showed the inter-annual values between variability 0.2 of and the biases0.28 m, from and the−0.1 ERA-Interim and 0.1 m, − andrespectively. CFSR comparisons To a certain showed extent, a values similar between situation 0.2 occurred and 0.28 for m, the and PC20-E0.1 andregional 0.1 m, and respectively. global M- ToScores, a certain i.e., higher extent, M-Scores a similar situationin the extratropical occurred for areas the PC20-E(in this regionalsituation, and slightly global higher M-Scores, for i.e.,the highercomparison M-Scores with inERA-Interim the extratropical than with areas CFSR), (in this and situation, lower slightlyin the tropical higher areas, for the particularly comparison in with the ERA-InterimPacific Ocean, than in line with with CFSR), the multi-forcing and lower in theensemble tropical of areas, [43]. particularly in the Pacific Ocean, in line with the multi-forcing ensemble of [43]. The agreements between the , , and PC20-E and reanalysis, and between PC20-E and The agreements between the Hs, Tm, and θm PC20-E and reanalysis, and between PC20-E and the the in situ observations show that the WAM model, forced by the EC-Earth winds and SIC, inproduces situ Hs considerablyobservations realistic show that results the WAM of the model, global forcedwave climate by the EC-Earthat the end winds of the andtwentieth SIC, produces century considerablywave climate. realisticThese results results give of a the good global degree wave of confidence climate at in the the end ability of the of twentieththe ensemble century to simulate wave climate.a realistic These climate results change give signal. a good Future degree research of confidence on the impact in the ability of climate of the warming ensemble on to future simulate wave a realisticclimate, using climate the change single-forcing, signal. Future single-model, research and on single-scenario the impact of climate dynamic warming wave climate on future ensemble wave climate,is to be conducted using the single-forcing,following the present single-model, study, andincluding single-scenario the impact dynamic on wave wave power, climate and on ensemble the wind is tosea be and conducted swell patterns. following the present study, including the impact on wave power, and on the wind sea and swell patterns. Author Contributions: A.S. conceptually designed the experiment and the ensemble, partially participated in Author Contributions: A.S. conceptually designed the experiment and the ensemble, partially participated in the the wave model set-up and run, processed and interpreted the data and wrote the paper; M.D. and A.B. wave model set-up and run, processed and interpreted the data and wrote the paper; M.D. and A.B. participated in theparticipated experiment in andthe experiment ensemble design, and ensemble and were design, responsible and were for the responsible wave model for set-up the wave and run;model G.L. set-up processed and run; the data;G.L. processed J.S. participated the data; in the J.S. experiment participated and in ensemble the experi designment and partiallyensemble participated design and in partially the wave participated model set-up; in H.d.V.the wave and model A.S. were set-up; partially H.d.V. involved and A.S. in thewere wave partially model involved set-up and in run;the J.B.wave was model responsible set-up forand processing run; J.B. was and providingresponsible the for in processing situ observational and providing data for the the inensemble situ observational evaluation; data P.M.A.M. for the ensemble and J.M. partiallyevaluation; provided P.M.A.M. the EC-Earth forcing data. and J.M. partially provided the EC-Earth forcing data. Funding: Gil Lemos is funded by the Earth Systems Doctoral School at the University of Lisbon, supported by the PortugueseFunding: Gil Foundation Lemos is funded for Science by the and Earth Technology Systems (FCT) Doctoral project School UID/GEO/50019/2013, at the University of Lisbon, University supported of Lisbon. by Alvarothe Portuguese Semedo isFoundation supported byfor the Science project and SOLAR Techno (PTDC/GEOMET/7078/2014),logy (FCT) project UID/GEO/50019/2013, financed by FCT. University of Lisbon. Alvaro Semedo is supported by the project SOLAR (PTDC/GEOMET/7078/2014), financed by FCT. Acknowledgments: This work was done under the auspices of the JCOMM COWCLIP (Coordinated Ocean Wave ClimateAcknowledgments: Project). Model This simulations work was (ensembledone under members the auspices 2 to 7) of at the Universität JCOMM HamburgCOWCLIP were (Coordinated performed Ocean using the high-performance computer at the German Climate Computing Center (DKRZ). Ensemble member 1 was Wave Climate Project). Model simulations (ensemble members 2 to 7) at Universität Hamburg were performed produced at the Instituto Dom Luíz (University of Lisbon) cluster. using the high-performance computer at the German Climate Computing Center (DKRZ). Ensemble member 1 Conflictswas produced of Interest: at the InstitutoThe authors Dom declare Luíz (University no conflict of Lisbon) interest. cluster.

Conflicts of Interest: The authors declare no conflict of interest.

J. Mar. Sci. Eng. 2018, 6, 90 23 of 28

Appendix A Ensemble Output Parameters, and In Situ Measurement and Regional Area Details

Table A1. Integrated output parameters.

Parameter Number Parameter Dimensions −1 1 Wind speed U10 ms 2 Wind direction ϕ degrees from north (toward) 3 Friction velocity ms−1 4 Drag coefficient m 5 Significant wave height m 6 Total peak period s 7 Total mean period s 8 Total Tm1 period s 9 Total Tm2 period s 10 Total mean wave direction degrees from north (toward) 11 Total directional spread degrees 12 Normalized wave stress % 13 Sea significant wave height m 14 Sea peak period s 15 Sea mean period s 16 Sea Tm1 period s 17 Sea Tm2 period s 18 Sea mean wave direction degrees from north (toward) 19 Swell significant wave height m 20 Swell peak period s 21 Swell mean period s 22 Swell Tm1 period s 23 Swell Tm2 period s 24 Swell mean wave direction degrees from north (toward) 25 Goda peakness parameter - 26 Kurtosis - 27 Benjamin Feir index - 28 Normalized maximum wave height m 29 Maximum wave period s 30 Interpolated peak frequency Hz 31 Peak direction degrees from north (toward) 32 Mean square slope -

Table A2. In situ and buoy wave measurements details. Position refers to the mean position of the buoy during its time series. WMO—World Meteorological Organization.

Time Series Time Series WMO ID Position WMO ID Position (Years) (Years) 41004 32.47◦ N, 78.90◦ W 37 46035 57.01◦ N, 177.70◦ W 30 41006 29.32◦ N, 77.35◦ W 14 46036 48.35◦ N, 133.92◦ W 29 41009 28.51◦ N, 80.19◦ W 27 46041 47.36◦ N, 124.63◦ W 28 41013 33.44◦ N, 77.66◦ W 12 46042 36.78◦ N, 122.35◦ W 28 41025 35.08◦ N, 75.35◦ W 12 46047 32.55◦ N, 119.55◦ W 24 41041 14.35◦ N, 46.05◦ W 10 46054 34.25◦ N, 120.45◦ W 22 42001 25.92◦ N, 89.93◦ W 36 46059 38.04◦ N, 129.95◦ W 21 42002 25.64◦ N, 93.96◦ W 36 46063 34.27◦ N, 120.68◦ W 10 42003 25.91◦ N, 85.50◦ W 37 46066 52.70◦ N, 154.98◦ W 15 42019 27.91◦ N, 95.20◦ W 26 46069 33.68◦ N, 120.20◦ W 12 42020 26.97◦ N, 96.60◦ W 26 46075 53.92◦ N, 160.81◦ W 11 42035 29.13◦ N, 94.60◦ W 22 46082 59.66◦ N, 143.54◦ W 13 42036 28.51◦ N, 84.51◦ W 22 46083 58.25◦ N, 138.00◦ W 14 42040 29.01◦ N, 88.15◦ W 20 46086 32.50◦ N, 118.02◦ W 12 J. Mar. Sci. Eng. 2018, 6, 90 24 of 28

Table A2. Cont.

Time Series Time Series WMO ID Position WMO ID Position (Years) (Years) 42056 19.85◦ N, 85.00◦ W 10 46132 49.73◦ N, 127.93◦ W 22 44004 38.69◦ N, 70.36◦ W 29 46147 51.82◦ N, 131.22◦ W 22 44009 38.48◦ N, 74.65◦ W 19 46184 53.93◦ N, 138.84◦ W 28 44011 41.09◦ N, 66.59◦ W 21 46205 54.22◦ N, 133.86◦ W 27 44014 36.60◦ N, 74.82◦ W 25 46206 48.87◦ N, 126.00◦ W 27 44017 40.70◦ N, 72.03◦ W 13 46207 50.88◦ N, 129.91◦ W 26 44024 42.30◦ N, 65.90◦ W 11 46208 52.51◦ N, 132.69◦ W 25 44025 40.25◦ N, 73.19◦ W 24 46213 40.30◦ N, 124.72◦ W 16 44027 44.29◦ N, 67.31◦ W 12 46214 37.93◦ N, 123.49◦ W 19 44138 44.25◦ N, 53.62◦ W 22 46218 34.48◦ N, 120.75◦ W 20 44139 44.21◦ N, 57.36◦ W 25 51202 21.41◦ N, 157.69◦ W 15 44251 46.45◦ N, 53.39◦ W 18 62023 51.40◦ N, 7.90◦ W 15 46001 56.15◦ N, 148.10◦ W 36 62107 50.10◦ N, 6.10◦ W 21 46003 51.92◦ N, 155.85◦ W 19 62116 57.90◦ N, 1.45◦ E 11 46004 50.95◦ N, 135.96◦ W 37 62133 57.15◦ N, 0.95◦ E 17 46005 46.05◦ N, 131.00◦ W 35 62144 53.89◦ N, 1.54◦ E 17 46006 40.85◦ N, 137.70◦ W 37 62145 53.21◦ N, 2.59◦ E 17 46012 37.41◦ N, 122.78◦ W 35 LF4B 60.60◦ N, 3.70◦ E 17 46013 38.22◦ N, 123.32◦ W 34 TFBLK 65.70◦ N, 24.80◦ W 13 46015 42.75◦ N, 124.83◦ W 13 TFGSK 64.10◦ N, 22.90◦ W 13 46026 37.75◦ N, 122.76◦ W 33 TFKGR 65.65◦ N, 13.60◦ W 13 46028 35.75◦ N, 121.80◦ W 32 TFSRT 63.30◦ N, 20.30◦ W 13

Table A3. Regional area limits from Figure1, as in Alves et al. 2006. LAT—latitude; LON—longitude.

AREA LAT (◦) LON (◦) ETSI 78◦ S–25◦ S 21◦ E–145◦ E ETSP 78◦ S–25◦ S 145◦ E–70◦ W ETSA 78◦ S–25◦ S 69◦ W–20◦ E TSIO 24◦ S–0◦ 21◦ E–(100◦ E (N); 135◦ E (S)) TWSP 24◦ S–0◦ (101◦ E (N); 136◦ E (S))–130◦ W TESP 24◦ S–0◦ 129◦ W–65◦ W TSAO 24◦ S–0◦ 64◦ W–20◦ E TNIO 1◦ N–30◦ N 41◦ E–100◦ E TWNP 1◦ N–30◦ N 101◦ E–180◦ E TENP 1◦ N–30◦ N Land TNAO 1◦ N–38◦ N (101◦ W (N); 69◦ W (S))–40◦ E ETNP 31◦ N–78◦ N 101◦ E–102◦ W ETNA 39◦ N–78◦ N 101◦ W–100◦ E

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