Evaluation of the CMC regional wave forecasting system against buoy data

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Evaluation of the CMC regional wave forecasting systemagainst buoy dataRoop Lalbeharry aa Recherche en Prévision Numérique, Meteorological Research Branch , MeteorologicalService of Canada , Downsview, ON, M3H 5T4 E-mail:Published online: 21 Nov 2010.

To cite this article: Roop Lalbeharry (2002) Evaluation of the CMC regional wave forecasting system against buoy data,Atmosphere-Ocean, 40:1, 1-20, DOI: 10.3137/ao.400101

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Evaluation of the CMC Regional Wave Forecasting SystemAgainst Buoy Data

Roop Lalbeharry*

Recherche en Prévision Numérique, Meteorological ResearchBranch Meteorological Service of Canada, Downsview ON M3H 5T4

[Original manuscript received 19 September 2000; in revised form 12 April 2001]

ABSTRACT In February 1996 the Canadian Meteorological Centre (CMC) of the Meteorological Service ofCanada (MSC), formerly the Atmospheric Environment Service and Program (AES/AEP), implemented regionalversions of the third generation global ocean wave model WAM Cycle-4 (WAM4) in its operational wave fore-casting system; one for the north-east Pacific and one for the north-west Atlantic. This replaced the first genera-tion Canadian Spectral Ocean Wave Model which had been in operation from December 1990. The 10-m levelwind forcing is obtained from the CMC global atmospheric model for driving the Pacific wave model and fromits regional atmospheric model for driving the Atlantic wave model.

Analyzed and forecast model wave and wind parameters are evaluated against moored buoy-measured data inthe coastal and shelf regions of the Atlantic and Pacific coasts of North America for the period December 1996to November 1999. The evaluation is presented in the form of time histories of the seasonal verification statistics,summary tables, and time series of individual model and buoy data for given periods at selected buoy locationsin order to highlight seasonal differences in model performance and any impacts due to atmospheric modelreplacement and grid changes. The results are further compared with the results from the global WAM4 runningin operational mode at the European Centre for Medium-Range Weather Forecasts (ECMWF) and at the FleetNumerical Meteorology and Oceanography Center (FNMOC) using the same datasets for the same period andfrom the recent study based on the National Centers for Environmental Prediction (NCEP) reanalysis data. Thisis done to assess better the performance of the CMC regional wave models with respect to the global wave mod-els and other regional wave models.

The evaluation results indicate that the Pacific ocean has more wind and wave variability and swells than theAtlantic ocean and that there is seasonal variation in this variability. The skill of the CMC regional WAM4 iscomparable to that of the global WAM4 in operation at other international wave forecasting centres. The resultsare also comparable to those obtained using the NCEP 40-year reanalysis data. The impact on the performanceof the wave model resulting from the replacement of the CMC global and regional atmospheric models and alsofrom the changes made to these models is more or less neutral.

RÉSUMÉ [Traduit par la rédaction] En février 1996, le Centre météorologique canadien (CMC) du Servicemétéorologique du Canada (SMC), anciennement le Service de l’environnement atmosphérique et le Programme(SEA/PEA), a mis en service des versions régionales de la troisième génération du modèle de vagues océaniques,WAM Cycle-4 (WAM4), dans son système opérationnel de prévision de vagues, une pour le nord-est du Pacifiqueet une pour le nord-ouest de l’Atlantique. Ceci a remplacé la première génération du modèle spectral canadiende vagues océaniques qui était en exploitation depuis le mois de décembre 1990. Le forçage du vent à 10 m estobtenu du modèle atmosphérique global du CMC pour exécuter le modèle de vagues du Pacifique et de son modèle atmosphérique régional pour exécuter le modèle de vagues de l’Atlantique.

Les vagues analysées et prévues par le modèle ainsi que les paramètres du vent sont comparés aux donnéesprovenant des bouées ancrées dans les régions côtières et les plate-formes continentales des côtes atlantique etpacifique de l’Amérique du Nord pour la période allant de décembre 1996 à novembre 1999. Les résultats de l’évaluation sont présentés sous la forme de séries temporelles des statistiques de vérification saisonnière, detableaux récapitulatifs et de séries temporelles de données spécifiques du modèle et des bouées pour certainespériodes à des emplacements sélectionnés de bouées afin de mettre en évidence les différences saisonnières dansla performance du modèle et de tout impact dû au remplacement du modèle atmosphérique et aux modificationsà la grille. De plus, les résultats sont comparés avec ceux du WAM4 global fonctionnant en mode opérationnelau Centre européen pour les prévisions météorologiques à moyen terme (ECMWF) et du Fleet NumericalMeteorology and Oceanography Center (FNMOC) en utilisant les ensembles de données pour la même période,et avec ceux de l’étude récente basée sur les données ré-analysées du National Center for EnvironmentalPrediction (NCEP). Ceci a été fait afin de mieux évaluer la performance des modèles régionaux de vagues duCMC par rapport aux modèles globaux et aux autres modèles régionaux de vagues.

ATMOSPHERE-OCEAN 40 (1) 2001, 1–20© Canadian Meteorological and Oceanographic Society

*Corresponding author’s e-mail: [email protected]

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mailto:[email protected]

1 IntroductionIn December 1990, the Canadian Meteorological Centre(CMC) of the Meteorological Service of Canada (MSC), for-merly the Atmospheric Environment Service and Program(AES/AEP), implemented the operational first generation(1G) wave model called the Canadian Spectral Ocean WaveModel (CSOWM) in its forecasting system (Cardone et al.,1976) which operated on two separate oceanic regions, name-ly, the north-west Atlantic and the north-east Pacific. An eval-uation of the performance of the CSOWM against buoy datais presented in Khandekar and Lalbeharry (1996) andKhandekar et al. (1994). The development of the third gener-ation (3G) wave model called WAM (WAMDI Group, 1988)led to a gradual replacement of earlier 1G and 2G (secondgeneration) wave models in most deep water prediction sys-tems since 1988. The current Cycle-4 version of WAM, here-after referred to as WAM4, is based on the ideas of Janssen(1991) in which the winds and waves are coupled, that is,there is feedback of growing waves on the wind profile. Theeffect of this feedback is to enhance the wave growth ofyounger wind seas over that of older wind seas for the samewind. Validation studies (Wittmann et al., 1994, 1995;Cardone et al., 1995, 1996; Janssen et al., 1997; Bidlot et al.,1998) on the performance of WAM4 against buoy observa-tions indicate that the analyzed wave heights generated byWAM4 are of good quality and in good agreement with thebuoy observations while the quality of the wave forecastsshows a slow deterioration with projection time. In February1996, the CMC implemented WAM4 in an operational modein its wave forecasting system, replacing the 1G CSOWM inoperation since December 1990. Two regional versions ofWAM4 were implemented, one for the north-west Atlanticocean extending from 25°N to 70°N and from 80°W to 15°Was shown in Fig. 1a and the other for the north-east Pacificocean bounded by latitudes 25°N and 60°N and longitudes160°E and 120°W as shown in Fig. 1b. Each version has agrid spacing of 1.0° in both latitude and longitude and is dri-ven by 10-m level surface winds provided by the CMC oper-ational global and regional atmospheric weather predictionmodels. The main objective of this study is to evaluate theperformance of the regional version of WAM4 implementedat the CMC during the 3-year period December 1996 toNovember 1999.

The organization of this paper is as follows. Section 2 pre-sents a brief description of the CMC regional wave forecast-ing system and its wind forcing. Changes in the wind forcingdue to changes in the operational weather prediction modelsare also described. The buoy data used for verification and the

generation of the wave model datasets for comparison aredescribed in Section 3. Section 4 presents the results, includ-ing time series of the basic statistical parameters, summarytables, and time series plots of model and buoy-measuredwind/wave parameters at selected buoy locations. Also in thissection the performance of the regional WAM4 is comparedwith the performances of the global WAM4 and other region-al models. Section 5 briefly summarizes the main findings ofthis study.

2 CMC ocean wave model and wind forcinga The Ocean Wave ModelThe ocean wave model in operational use at the CMC is aregional version of the global WAM4 (WAMDI Group, 1988;Janssen, 1991). WAM4 is based on the explicit solution of theenergy balance equation for the two-dimensional surfacewave spectrum written in standard notation as

(1)

where E = E(f,θ,ϕ,λ,t) is the two dimensional spectral energydensity which is a function of frequency f, direction of wavepropagation θ, latitude ϕ, longitude λ and time t. Here, Cg isthe group velocity of the surface waves which can beexpressed in terms of the phase speed C, wavenumber k andwater depth h (Cg = 1⁄2C[1 + 2kh/sinh(2kh)] and C =[(g/k)tanh(kh)]1⁄2). The assumptions made include: no bottomfriction, no shoaling, no depth refraction, no diffraction andreflection, and no ocean currents. The wave spectrum is local-ly modified by the net source term S = S(f,θ,ϕ,λ,t) which rep-resents the physical processes that transfer energy to and fromthe wave spectrum. The source term S can be written as

S = Sin + Snl + Sds (2)

where Sin represents the wind energy input to the wave field,Snl the energy redistribution associated with the nonlinearwave-wave interactions, and Sds the energy dissipation due towhitecapping. All the source terms are functions of E.Equation (2) is solved for 25 frequencies logarithmicallyspaced from 0.042 Hz to 0.41 Hz at intervals of ∆f/f = 0.1 and24 directional bands of 15° each, so that at each model gridpoint, there are 600 spectral estimates at any given time. Thesolution requires specification of the wind forcing at each grid

2 / Roop Lalbeharry

Les résultats de l’évaluation démontrent que l’océan Pacifique possède une plus grande variabilité du vent etdes vagues que l’océan Atlantique et que cette variabilité fluctue en fonction des saisons. La capacité du WAM4régional du CMC est comparable à celle du WAM4 global qui est utilisé de façon opérationnelle dans d’autrescentres internationaux de prévision des vagues. Les résultats sont également comparables à ceux obtenus en utilisant les 40 années de données ré-analysées du NCEP. L’impact sur la performance du modèle de vagues quidécoule du remplacement des modèles atmosphériques globaux et régionaux du CMC ainsi que des modificationsapportées à ces modèles est plus ou moins neutre.

∂∂

+ ⋅( ) =E

tE S∇∇ Cg

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point for each time and the initial model state. The winds areobtained from the numerical weather prediction models. The

model’s boundary points along the coasts are treated as fullyabsorbing. For a regional model with open boundaries the

Evaluation of CMC Regional Wave Forecasting System Against Buoy Data / 3

(a)

(b)

Fig. 1 The CMC regional WAM4 grid areas and geographical locations and identification numbers of the buoys used in this study and shown in Table 1 for(a) the north-west Atlantic and (b) the north-east Pacific.

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integration area is chosen large enough, and the forecast peri-od short enough, to minimize contamination of the wavesinside the area of interest by waves propagating into the areafrom outside. When the model starts from a flat sea, its initialstate is parametrized using an empirically derived spectrum, adirectional spreading function, and the wind speed at runtime. In an operational environment, the initial field is savedafter 12 hours of integration into the forecast for input to themodel’s next run. Both the propagation and integration timesteps are set to 1200 seconds and with the grid resolution of1.0° the Courant-Friedrichs-Lewy stability criterion is morethan adequately satisfied. The solution of Eq. (1) is for deepwater physics in which Cg and C are both functions of fre-quency only. The WAM4 grid spacing ∆φ = 1.0° latitude isequivalent to a spacing of 111 km and ∆λ = 1.0° longitude toa spacing that varies from 100 km at 25°N to 38 km at 70°N.

The WAM4 grid is partially covered with sea ice mainly inthe winter months. For each run the ice field for input toWAM4 is obtained from the CMC sea-ice analyses. TheWAM4 model grid point is considered to be a sea-ice point ifthe ice fraction at that point is >0.5. Once this determinationis made at the beginning of each model run, the ice fieldremains unchanged during the 48-hour forecast period. At allland points, and at all sea-ice points, the wave energy of eachspectral component is set to zero.

b Wind ForcingBoth regional WAM4s were initially driven by winds obtainedfrom the two operational numerical weather prediction modelsin use at the CMC. The Atlantic WAM4 was originally forcedby winds from the regional finite element (RFE) model pro-ducing short-range forecasts up to 48 hours (Mailhot et al.,1995, 1997). The horizontal grid is a variable resolution gridwith a central domain with uniform grid spacing of 50 km cov-ering most of North America and adjacent waters. The verti-cal discretization consists of 28 σ (= p/ps, where p is pressureand ps is surface pressure) levels with the lowest prognosticlevel being σ = 0.995 (about 40 m above the surface). InDecember 1992 the regional data assimilation system (RDAS)based on multivariate optimum interpolation was implement-ed (Chouinard et al., 1994) to provide an analysis at run timefollowing a 12-h spin-up cycle initiated from the global dataanalysis 18 hours earlier. In December 1995 the RFE modelresolution in the central window was increased to 35 km.Details of the RFE model, the changes made to it, and its phys-ical parametrization are described in Mailhot et al. (1995,1997). On the other hand, the Pacific WAM4 was forced bywinds generated by the medium range ( >2 days) globalspectral finite element (SEF) model (Ritchie and Beaudoin,1994). It has a uniform grid spacing of about 0.9° (approxi-mately 100 km), a spectral representation of 199 waves forthe model fields and 21 σ levels in the vertical with thelowest prognostic level being σ = 0.990 (approximately 80 mabove the surface). The SEF model served both as the globaldata assimilation model and the medium range forecastmodel.

The Global Environmental Multiscale (GEM) modelreplaced the RFE model as the regional model on 24 February1997 without an RDAS. It uses the static analysis from theglobal SEF model as its initial conditions to produce short-range (up to 2 days) forecasts. The GEM model has a globalvariable resolution latitude-longitude mesh which can be arbi-trarily rotated to permit resolution to be focused over the areaof interest and 28 η (= (p – pt)/(ps – pt), where pt is the toppressure) levels in the vertical with the lowest prognosticlevel being η = 0.995 (approximately 40 m above the sur-face). The model can be used in uniform resolution mode formedium-range forecasting or in focused mode for short-rangeregional forecasting (Côté et al., 1998a, 1998b). For its initialoperational implementation in the regional cycle, the GEMmodel had a grid resolution of 0.33° (approximately 35 km).On 18 June 1997 a new global 3D variational (3DVAR)analysis (Gauthier et al., 1999) replaced the SEF-driven glob-al optimum interpolation analysis, while in September 1997the 3DVAR data assimilation system was implemented forthe GEM regional analyses (Laroche et al., 1999). InSeptember 1998, the regional model resolution in the uniformwindow was increased to 0.22° (approximately 24 km) and inOctober 1998, the SEF model was replaced by the GEMmodel with the same uniform grid resolution as the SEFmodel. This unified system for short-range and medium-range forecasting allows the global cycle and the regionalcycle to share the same code, the same physics library, andthe same data assimilation system code (Steenbergen et al.,1998). However, the physics options used operationally arenot all the same in the two models.

The CMC weather prediction models use the dynamic vari-ables at their lowest prognostic level (80 m for the SEF modeland 40 m for the RFE and GEM models), the Monin-Obukovsimilarity theory for the surface layer, the surface temperatureand moisture, and the turbulent kinetic energy in the planetaryboundary layer to calculate the fluxes of momentum, heat andmoisture at the surface and the variables at the base of themodels, nominally at σ or η = 1 (Delage, 1988, 1997; Delageand Girard, 1992). The variables at this level are differentfrom those at the surface and represent the winds at the 10-mlevel and the temperature and moisture at the Stevensonscreen level (1.5 m). The surface roughness zo affects all thefluxes. Over the oceans zo is given by the Charnock equationzo = βu*

2/g (Charnock, 1955) in which the Charnock parame-ter β is set to a constant = 0.018 in the RFE and GEM modelsand 0.032 in the SEF model and u* is the friction velocity (u*

2

is the kinematic surface stress or momentum flux). In reality,β is not a constant but a sea state dependent parameter. It canrepresent a coupling parameter between a weather predictionmodel and an ocean wave model in which the latter passes tothe former the variable Charnock parameter and the former tothe latter an updated wind field at regular coupling intervals(Lalbeharry et al., 2000; Desjardins et al., 2000).

Ocean waves play an important role in modulating thetransfer of momentum from the air to the sea. In neutral sta-bility the kinematic surface stress (u*

2) is determined given

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the wind speed at the observation height and zo which is afunction of the air circulation and the sea state dependent β inthe Charnock relation. In the formulation of Janssen (1991) βis a function of the wave-induced stress normalized withrespect to the total stress. The wave-induced stress is thestress exerted by the wave on the wind and is a function of thewind input source term Sin. Given the wave induced-stressand the wind speed, WAM4 determines the total stress atevery integration time step and this allows the computation ofthe variable Charnock parameter β, the roughness length zo,and the sea state dependent drag coefficient. This is a one-way interaction between winds and waves since the β fromWAM4 is never communicated to the weather predictionmodel. Large β implies rougher seas; rougher seas imply larg-er transfer of momentum from air to sea. The value of β =0.032 used in the SEF model corresponds to younger orrougher seas while the value of 0.018 used in the RFE andGEM models corresponds to mature or smoother seas. Inother words, in the GEM models the transfer of momentumfrom air to sea is accomplished by relatively smoother waves.The CMC weather prediction models provide WAM4 withthe 10-m level u- and v-components of the winds interpolatedto the WAM4 grid. WAM4 considers the wind field providedto be the equivalent neutral wind field. Since the wind inputsource term in Eq. (3) requires the u* field in wave generation,the wind speeds are converted internally in WAM4 to u*using the neutral sea state dependent drag coefficient. Thisfield is updated at the end of each integration time step giventhe wave-induced stress and the 10-m level wind speed U10.

3 Model data, buoy data and statistical analysis procedurea Model DataIn late 1995, the European Centre for Medium-RangeWeather Forecasts (ECMWF), the Fleet NumericalMeteorology and Oceanography Center (FNMOC), theUnited Kingdom Meteorological Office (UKMO), and theCMC started a project aimed at exchanging model data atselected geographical locations. They were joined in May1996 by the National Centers for Environmental Prediction(NCEP). All centres use the wave model WAM4, except theUKMO which has its own 2G wave model (Golding, 1983;Holt, 1994), and their own atmospheric models to produce thesurface wind forcing for driving their operational wave mod-els. The model data exchanged in this project are the signifi-cant wave height, wind speed and direction, and the peakperiod. The model two-dimensional spectral energy is inte-grated over all wave directions to obtain the model energy asa function of model frequency only. The frequency corre-sponding to the peak of the one-dimensional energy is definedas the peak frequency and its inverse is the peak period.

The CMC WAM4 for each oceanic basin is run twice dailyat 00:00 and 12:00 UTC and generates wave forecasts at 3-hourly intervals up to 48 hours. For each run and each dayof the month the model data are bilinearly interpolated to theselected buoy locations. The interpolated forecast data valid

for each of three projection times 00 h, 24 h and 48 h from themodel run time are stored in separate files. At the end of eachmonth these files, which contain model monthly time seriesof interpolated data at buoy locations, are transferred by eachparticipating centre via “ftp” to the UKMO computer server,where they are combined with the observations and processedby the ECMWF. The combined data files are then retrievedfrom the UKMO server by each participating centre. Theresults shown in this study pertain to the wind and wave dataprovided by CMC, ECMWF and the FNMOC and processedby the ECMWF in the data exchange project for the periodDecember 1996 to November 1999. The results valid at 00 h,that is, at the analysis or run time, are based on the 00:00 and12:00 UTC model runs while those valid at the 24-h and 48-h projections are based only on the 12:00 UTC

model run. This is done to facilitate comparison with the ver-ification statistics of the ECMWF wave model which is runonce per day at 12:00 UTC. The ECMWF also produces a daily00:00 UTC wave analysis which is used in the computation ofthe 00-h statistics. Hence, for the 24-h and 48-h forecasts thenumber of observations used is approximately half that usedfor the 00-h forecast. In this study, however, only the 00-hstatistics of the ECMWF and FNMOC are used when com-parison is made with the CMC statistics.

b Buoy DataThe Marine Environmental Data Service in Canada and theNational Buoy Data Center in the United States operate a net-work of moored buoys in the coastal and shelf regions of theAtlantic and Pacific coasts of North America. Table 1 givesthe buoy identification numbers and their names and Fig. 1shows their corresponding geographical locations. Thesebuoys which are selected for validation of the model are wellwithin the grids of the two regional wave models in relative-ly deep waters with the North Atlantic (NATL) buoys rang-ing from 63 m to over 4000 m and the North Pacific (NPAC)buoys from 2700 m to over 4000 m. These buoys also have ahigh rate of data availability. With the minimum buoy waterdepth being 63 m, the water depth-wavelength ratio obtainedusing the buoy-measured peak period in this study more thansatisfies the criterion for deep water waves so that the wavesanalyzed are all deep water waves. The buoy data are trans-mitted to the ECMWF via the Global TelecommunicationSystem. From the buoy records, monthly time series of windspeed and direction, significant wave height, and peak periodare constructed and used to perform a basic quality check onthe data. This quality control procedure, described in Bidlot etal. (1998) and Janssen et al. (1997), includes removal of datadue to faulty instruments and removal of outliers. In this studya correction is applied to the buoy wind, usually measured ata height of 5 m, by multiplying it by a factor of 1.07 to adjustit to the 10-m level for a neutrally stable atmosphere (Smith,1988). However, during winter months the atmosphere is gen-erally unstable with cold air over warm waters. This impliesa different wind profile than the neutrally stable one so thatduring these months this adjustment would also have errors(Zambresky, 1989).


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c Statistical Analysis ProcedureThe buoy data provide an independent dataset to evaluate theaccuracy or quality of the model wave forecasts objectively.If F is the model forecast value, O the observed buoyvalue,

–F = 1/NΣF the model mean,

–O = 1/NΣO the buoy mean,

∆F = (F – O) the difference between the model and observedvalues, and N the number of observations, then Table 2 pre-sents the statistics for each of the parameters of wind speed,significant wave height, and peak spectral period as used inthis study. In Table 2 the symmetric slope s is the coefficientof the linear regression line constrained to pass through theorigin and is invariant with respect to an interchange betweenF and O (Bauer et al., 1992; Romeiser, 1993). The modelunderpredicts F for s < 1.0 and overpredicts F for s > 1.0. Theanomaly correlation (AC) measures the correlation betweenthe forecast and observed deviations from climatology, thatis, it measures how much skill the forecast has over climatol-ogy. When it falls below 60%, the wave forecast is regardedto be of little use (Janssen et al., 1997), the same criterion asused in weather forecasts. The reduction of variance (RV) isalso a skill score that compares the mean squared error of theforecast to the mean squared error of the unskilled estimatebased on climatology. For RV > 0 the forecast is better thanclimatology but for RV < 0 climatology gives a better repre-sentation of the forecast. The overprediction ratio Ra givesthe fraction of the total observations N overpredicted by themodel.

4 Results and discussiona Seasonal Variations of Atlantic and Pacific Statistics 1 CMC REGIONAL WAM4 STATISTICS

The data for the verification period (December 1996 –November 1999) are divided into seasons, namely, winter(December – February), spring (March – May), summer (June– August) and fall (September – November). This divisiongives time series consisting of three winters, three springs,three summers, and three falls and permits the examination ofthe seasonal variations of the various statistical parameters foreach of the two oceans and the results of this division are pre-sented in Figs 2 to 5. In each of the figures, the upper panelhighlights the similarities and differences in the NATL and the

NPAC model-generated statistics for the 00-h projection timesince the wind input to WAM4 comes from different CMCweather prediction models. The NATL and NPAC statisticsfor the three projection times 00 h, 24 h and 48 h are shownseparately in the middle and lower panels, respectively.

The statistical parameters of bias, rmse, and scatter index(SI) for the significant wave height (SWH) are shown inFig. 2, those for the wind speed U10 in Fig. 3, and those forthe wave peak period Tp in Fig. 4 using the observations fromthe buoys shown in Table 1. An examination of Fig. 2a indi-cates that the SWH bias has a tendency to be a minimum insummer and a maximum in winter in the two oceans. TheNATL SWH bias is always underestimated and remainsmainly steady close to –0.2 m and throughout the period forthe three projection times. The biases for the 24-h and 48-hforecasts show slight improvements over the 00-h forecastfollowing the implementation of the spin-up cycle of theregional GEM model in fall 1997 but the impact on the biasdue to increased grid resolution after fall 1998 is less obvious.However, the NPAC SWH bias has a more oscillatory behav-iour with distinct crests and troughs in the bias field varyingfrom 0.30 m to approximately –0.5 m. The mainly positivebias gave way to a negative bias after the implementation ofthe global GEM model in fall 1998. This behaviour is moreconsistent with the NATL bias based on the regional GEMmodel. A typical SWH bias in operational wave forecasts isof the order of 0.25 m (Komen, 1999). The SWH bias shownin Fig. 2a is close to, and sometimes better than, this value,except for the NPAC 1999 winter when the bias reached avalue near –0.5 m.

Figure 2b indicates an oscillatory pattern of the rmse val-ues for both oceans with a maximum in winter and a mini-mum in summer. The NPAC winter rmse values, however,are larger than those of the NATL winter, which suggests ahigher variability of the Pacific ocean-wave systems duringthe winter months, while in both oceans the wave systems inwinter are more variable than those in summer. A comparison

6 / Roop Lalbeharry

TABLE 1. Buoy identification numbers and their names

North Atlantic (NATL) buoys North Pacific (NPAC) buoys

Buoy ID Buoy name Buoy ID Buoy name

41001 East Cape Hatteras 46001 Gulf of Alaska41002 South Cape Hatteras 46002 Oregon41010 East Cape Canaveral 46003 South Aleutians44004 Hotel 46004 Middle Nomad44008 Nantuket 46005 Washington44011 Georges Bank 46006 SE Papa44137 East Scotia Slope 46035 Bering Sea44138 SW Grand Banks 46036 South Nomad44139 Banquereau Bank 46059 California44141 Laurentian Fan 46184 North Nomad44142 La Have Bank

TABLE 2. Mathematical definitions of statistics used in this study. Here,bias is the mean error, rmse is the root mean square error, r thelinear correlation coefficient, SI the scatter index, s the symmet-ric slope, AC the anomaly correlation, RV the reduction of vari-ance, Ra the overprediction ratio, σf the standard deviation of Fand σo that of O.

bias = 1/NΣ∆F

rmse = [1/NΣ∆F2]1/2

r = [1/NΣ(F – –F)(O –

–O)]/σfσo

SI = rmse/–O

s = [ΣF2/ΣO2]1/2

AC = Σ[(F – –O)(O –

–O)]/[Σ(F –

–O)2(O –

–O)2]1/2

RV = 1 – [Σ(F – O)2/Σ(–O– O)2]

Ra = δ = 1 for F ≥ O and δ = 0 for F < OΣδN

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of the three Atlantic winter rmse values reveals that the 1997and 1998 values are nearly the same but slightly larger thanthe 1999 value, suggesting that both the RFE and regional

GEM models show little difference in impact on the WAM4output. This is expected because both models have basicallythe same physics and grid resolution. The impact of the


Fig. 2 Seasonal variations of the SWH statistics for the error parameters (a) bias, (b) rmse and (c ) SI for the period winter 1997 – fall 1999. In each panel,the upper plot compares the NATL and the NPAC 00-H forecasts, the middle plot the forecasts for the 00-H, 24-H, and 48-H projection times for theNATL, and the lower plot those for the NPAC. In the figure, the upper case “H” denotes hour, the left vertical dashed line indicates the approximatedate when the regional GEM model replaced the RFE model, the middle one when the RDAS was implemented, and the right one when the global GEMmodel replaced the global SEF model.

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increased grid resolution of the regional GEM model on theNATL SWH rmse is also less obvious as in the case of theSWH bias. On the other hand, the NPAC 1999 winter rmse issomewhat higher than the 1997 and 1998 winter values,which indicates that the implementation of the global GEMmodel and the global 3DVAR analysis did not produce any

positive impact on the NPAC SWH rmse. In the Atlanticthe analyzed rmse varies from 0.4 m to 0.6 m while, in thePacific, it varies from 0.35 m to 0.95 m. In both oceans the24-h forecast is quite reliable as it shows little or nodegradation while the 48-h forecast shows a more significantdeterioration.

8 / Roop Lalbeharry

Fig. 3 As in Fig. 2 but for the wind speed U10.

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In Fig. 2c the analyzed SI for the NPAC shows a moresteady variation from 0.17 to 0.20 than that for the NATLwhich varies from 0.22 to 0.28. If the SI is accepted as a mea-sure of the quality of the forecast (Janssen et al., 1997) then:the Pacific forecasts are of better quality than the Atlanticforecasts; the quality of the forecast during the Atlantic win-

ter is better than that during its summer; and the 48-h forecastis of lesser quality than the 24-h forecast. The quality of theforecast deteriorates more rapidly after 24 h into the forecastperiod. In both oceans the maximum SI occurs in summer andthe minimum in winter, which is the opposite of the SWHrmse behaviour. The smaller Pacific SI is due to the fact that


Fig. 4 As in Fig. 2 but for the peak period Tp.

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the mean observed SWH is larger than that of the Atlanticwhile the smaller winter value in both oceans is attributable tothe fact that the mean winter observed SWH is larger than thatof the summer. It should be noted that the relative change ofSI is the difference between the relative changes of the rmseand the observed mean. Based on near “perfect” hindcast

winds, Cardone et al. (1995) produced the lowest SWH SIvalue, close to 0.15, so that greater accuracy of the wind forc-ing is required to improve the quality of the wave forecasts.

The seasonal variations of the wind speed statistics are pre-sented in Figs 3a–c. The bias, rmse, and SI all exhibit, to somedegree, an oscillatory behaviour. When the regional GEM

10 / Roop Lalbeharry

Fig. 5 As in Fig. 2 but for the anomaly correlation error parameter for (a) SWH, (b) U10 and (c ) the peak period Tp.

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model replaced the RFE model without the spin-up cycle inthe regional analysis in February 1997, the wind speed bias,rmse and SI for the spring and summer of 1997 were unusu-ally large. The improved NATL 00-h forecast statistics fromfall 1997, when coupled with the significant error reductionafter 24 h into the forecast, suggests that this improvement inthe U10 statistics is due largely to the introduction of a spin-up cycle in the RDAS of the regional GEM model inSeptember 1997. Since the NATL 1998 and 1999 winter sta-tistics were lower than those of the 1997 winter, it may beconcluded that the regional GEM model slightly outperformsthe RFE model in operation up to February 1997. Comparisonof Figs 3a and 2a indicates that the 00-h overestimation of U10in the spring and summer of 1997 does not necessarily trans-late into overestimation of the SWH. The high wind speedmay be duration- and/or fetch-limited leading to waves notbeing fully grown. If the 1997 NATL spring and summerbiases are excluded, the magnitude of the analyzed bias forboth oceans is generally < 1.0 m s–1. This is also true for thetwo other forecast projections.

The atmospheric systems in both oceans show more vari-ability in winter than in summer as indicated by the rmse inFig. 3b. The fluctuations of the NPAC winter rmse are signifi-cantly larger than those of the NATL rmse, which indicatesthat the Pacific winter atmospheric systems are more intenseand, hence, show higher variability than the Atlantic ones. Insummer the NATL rmse is slightly larger than the NPAC rmseand this may be the result of the occasional extratropical stormspassing close to the US and Canadian buoy network during theAtlantic hurricane season (June – November). This is alsoreflected in the SWH rmse in Fig. 2b. An examination of theNATL rmse reveals that the rmse improved from fall 1997 andremained steady, close to 2 m s–1, for the rest of the period.This improvement in the rmse is due mainly to the effect of thespin-up cycle of the RDAS using the 3DVAR scheme whichhas now replaced the optimum interpolation scheme. Theimpact of the increased grid resolution of the regional GEMmodel from 35 km to 24 km from fall 1998 is not too notice-able. On the other hand, the switch from the global SEF to theglobal GEM in October 1998 had little or no impact on theNPAC U10 rmse since the physics and grid resolutions of thetwo global atmospheric models are basically the same. ThePacific wind forecasts show more significant deterioration thanthe Atlantic forecasts and this is also reflected in the wave fore-casts. For the Pacific, the maximum rmse varies from 2.5 m s–1

for the 00-h forecast to about 4.0 m s–1 for the 48-h forecastwhile for the Atlantic, it varies from 2.0 m s–1 to 3.25 m s–1 ifthe spring and summer 1997 rmse values are excluded. A com-parison of the NATL winter 1997 rmse value with the corre-sponding 1998 and 1999 values indicates a slightly betterperformance of the regional GEM model over the RFE model.

Figure 3c presents the U10 SI in which the NATL summervalues are significantly larger and the winter values slightlysmaller than the corresponding NPAC values. This is due tothe behaviour of the rmse shown in Fig. 3b and to the buoymean U10 (not shown) being larger for the Pacific than for the

Atlantic with both oceans showing a maximum in winter anda minimum in summer. This trend is also reflected in the twoother forecast projections. The quality of the wind forecast, asgiven by the SI in Fig. 3c, is also reflected in the quality of thewave forecast shown in Fig. 2c since the change in SI is dueto changes in both the rmse and the mean observations. Forthe 00-h forecast the SI ranges from 0.22 to 0.30 for thePacific and from 0.23 to 0.35 for the Atlantic if the 1997spring and summer values are excluded. A reduction in theU10 SI below the values given here requires an improvementin the wind forcing which, in turn, would also lead to animprovement in the wave forecast.

The wave peak period Tp statistics for both oceans aregiven in Figs 4a–c. The analyzed Tp bias in Fig. 4a for theAtlantic is always negative with values ranging from –0.2 s to–1.2 s while for the Pacific they range from –1.4 s to 0.9 s butare always negative following the switch from the global SEFto the global GEM model. The magnitude of the winter biasis generally smaller than that of the summer for both oceans.The wave model has a tendency to predict the winter Tp moreaccurately than the summer Tp due to the poorer model pre-diction of the summer swells as seen, but not shown, in fre-quency analyses of collocated Tp data. There is a closesimilarity in the behaviour of the Tp and SWH biases for thePacific ocean but it is less clear for the Atlantic. Examinationof Figs 4a and 2a indicates that positive (negative) Tp bias isgenerally associated with positive (negative) SWH bias. TheNPAC Tp rmse in Fig. 4b shows larger fluctuations than theNATL rmse. Its analyzed Tp rmse ranges from 2.0 s to a max-imum of 3.5 s in summer while for the Atlantic it is moresteady with a value close to 2.0 s. The mean peak period inTable 3 for the Pacific is larger than that for the Atlantic,making the former more swell dominated. The frequencyanalysis of collocated Tp data mentioned above also indicatesthat the NPAC swells are not well predicted by the regionalWAM4, especially during the summer season leading to largermse, and that they have longer periods than the NATLswells. The peak period SI shown in Fig. 4c exhibits the samefeatures as the peak period rmse for both oceanic basins. It ismore steady for the Atlantic with a nearly constant valueclose to 0.20 throughout the period while it varies from 0.17to 0.35 for the Pacific. This is due to the fact that the Atlanticis more wind sea dominated and the wave model is better ableto predict Tp. It is interesting to note that the Tp bias, rmse,and SI all show little or no degradation with time for bothoceans.

The AC is a verification tool used to examine the qualityand usefulness of a forecast since it is a skill score that pro-vides a measure of how much more skill the forecast has overclimatology. The AC is a good indicator of the quality of theforecast and is considered to be useful if it exceeds the thresh-old value of 0.6 or 60% (Janssen et al., 1997). The AC forSWH, U10, and Tp is presented in Fig. 5 which shows the sea-sonal variations in each of the two oceans. In Fig. 5a the SWHanalyses and forecasts are of good quality since the AC aver-ages close to 90%. However, the 48-h wave forecast tends to


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approach climatology more rapidly than the 24-h forecast butit is still useful. In the Pacific the seasonal fluctuations aremore regular while in the Atlantic the summer fluctuationsare more pronounced indicating that the Atlantic summerwave forecasts are of lesser quality than the winter forecasts.

In Fig. 5b the low AC for the U10 analysis during the Atlanticspring and summer of 1997 is attributable to the absence of aspin-up cycle in the regional GEM model. Except for thisperiod the Pacific and Atlantic analyses are quite comparable,with the AC averaging close to 0.8. The Pacific 48-h forecast,however, is barely useful with the AC hovering near thethreshold value of 60%. Figure 5c indicates that the Tp fore-casts in both oceans are generally of poor quality, especiallyduring the summer when climatology would give an adequateor better representation of the forecast.

2 CMC REGIONAL VERSUS GLOBAL WAM4 STATISTICS

The bias, rmse, and SI obtained from the CMC regionalWAM4 are compared with those obtained from the globalWAM4 in operation at the ECMWF and FNMOC using thedatasets from the global models and the verification data fromthe buoys given in Table 1 for the same period in order toassess how well the regional WAM4 performed against theglobal WAM4. The ECMWF WAM4 has an effective gridresolution of 55 km and a spectral resolution of 25 frequen-cies and 12 directional bands. The model is driven by 10-mlevel winds provided by the ECMWF atmospheric model andincludes assimilation of the European Remote SensingSatellite-2 altimeter wave-height data to generate anenhanced initial wave state. In June 1998 the global WAM4was dynamically coupled to the ECMWF atmospheric model.The FNMOC global WAM4 has a spatial resolution of 1.0° inboth latitude and longitude and a spectral resolution of 25 fre-quency and 24 directional bands. The FNMOC OperationalGlobal Atmospheric Prediction System (NOGAPS) providesthe surface wind stress to the FNMOC WAM4 which is con-verted to a neutral U10 field given the 10-m level neutral dragcoefficient. The latter is obtained using the surface roughnesscomputed from the Charnock relation with the Charnockparameter set to a constant value of 0.0185.

The bias, rmse, and SI for the 00-h forecast for the threecentres are presented in Fig. 6 for the North Atlantic and inFig. 7 for the North Pacific. It should be noted that the 00-hforecast is the analysis at run time and its behaviour may notnecessarily reflect how well the forecasts will perform. Anexamination of these figures indicates that the statistics forthe three centres show generally similar seasonal behaviourfor both oceans whether the wind forcing provided to WAM4is in the form of 10-m level winds or surface wind stress.Figure 6a shows that the models are consistent in their behav-iour in that they all generate negative biases with a tendencyto have larger SWH underprediction in winter than in sum-mer. The SWH biases for the three centres indicate an aver-age of –0.1 m for the FNMOC model and close to –0.2 m forthe CMC model. The ECMWF model exhibits a strong sea-sonal cycle with almost no bias in summer and the largest biasin winter. The agreement among the three models is quitegood for the NATL SWH rmse and SI. No one model signif-icantly outperforms the other two models. In Fig. 6b, if theCMC spring and summer 1997 wind statistics are not consid-ered, the wind fields provided by the three different atmos-


TABLE 3. SWH and Tp verification statistics for the North Atlantic andNorth Pacific for the period December 1996 – November 1999for the forecast hours 00H, 24H and 48H where “H” denoteshour.

North Atlantic wave height statistics

Season Parameter 00H 24H 48HAll Buoy mean (m) 1.991 1.999 2.000

Model mean (m) 1.771 1.801 1.829Symmetric slope s 0.896 0.903 0.914Bias (m) –0.220 –0.199 –0.171Rmse (m) 0.517 0.530 0.623SI 0.235 0.246 0.299r 0.920 0.912 0.868AC 0.902 0.897 0.857RV 0.812 0.804 0.730Ra 0.340 0.373 0.412N (no. of obs) 15721 8053 8052

North Atlantic peak period statistics

Season Parameter 00H 24H 48HAll Buoy mean (s) 8.375 8.386 8.389

Model mean (s) 7.760 7.780 7.791Symmetric slope s 0.926 0.926 0.927Bias (s) –0.615 –0.607 –0.598Rmse (s) 1.888 1.921 1.973SI 0.213 0.217 0.224r 0.655 0.644 0.619AC 0.627 0.617 0.594RV 0.287 0.275 0.237Ra 0.346 0.352 0.365N (no. of obs) 15054 7690 7690

North Pacific wave height statistics

Season Parameter 00H 24H 48HAll Buoy mean (m) 2.900 2.891 2.897

Model mean (m) 2.832 2.794 2.729Symmetric slope s 0.985 0.975 0.950Bias (m) –0.068 –0.098 –0.168Rmse (m) 0.626 0.645 0.766SI 0.215 0.220 0.258r 0.915 0.910 0.873AC 0.914 0.908 0.867RV 0.825 0.814 0.738Ra 0.474 0.447 0.422N (no. of obs) 16782 8429 8397

North Pacific peak period statistics

Season Parameter 00H 24H 48HAll Buoy mean (s) 10.688 10.712 10.721

Model mean (s) 10.473 10.514 10.495Symmetric slope s 0.974 0.975 0.972Bias (s) –0.216 –0.198 –0.226Rmse (s) 2.657 2.696 2.739SI 0.248 0.251 0.255r 0.577 0.566 0.549AC 0.575 0.564 0.547RV 0.226 0.212 0.188Ra 0.527 0.530 0.514N (no. of obs) 16769 8424 8392

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pheric models are also in good agreement with the modelsshowing a near steady rmse value close to 2.0 m s–1 and a biasnear 0.0 m s–1. The slightly larger CMC rmse gives somewhatlarger U10 SI since the buoy mean U10 is the same for the

three models. The Tp biases shown in Fig. 6c are generallysmall, varying from –1.0 s to 1.0 s with the maximum over-estimation/underestimation occurring in summer for all threemodels. FNMOC, which applies a smoother to the model


Fig. 6 Seasonal variations of (a) SWH, (b) U10, and (c ) Tp of the CMC NATL statistics are compared with those of the ECMWF and FNMOC for the peri-od, winter 1997 – fall 1999. In each panel, the upper plot gives the bias, the middle plot the rmse, and the lower plot the SI for the 00-H forecast onlywhere the upper case “H” denotes hour. The vertical dashed line through SP97 indicates the approximate date when the regional GEM model replacedthe RFE model and that through FA97 when the RDAS was implemented.

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peak periods, has somewhat better Tp statistics. The slightlylarger CMC summer Tp bias reflects a general problem ofregional models of not allowing low frequency components toenter the domain at its southern boundary. Except for thesummer of 1999 (SU99) the difference between the ECMWF

and CMC Tp rmse is rather small, suggesting that in the windsea-dominated NATL both models are in good agreement inpredicting Tp. Overall, the performance of the CMC Atlanticregional WAM4 follows the performances of the two globalWAM4s closely.


Fig. 7 As in Fig. 6 but for the NPAC oceanic basin. The vertical dashed line through FA98 indicates the approximate date when the global GEM modelreplaced the global SEF model.

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For the Pacific statistics, Fig. 7a indicates that of the threewave models the ECMWF model is more consistent in its behaviour in that it underpredicts the SWH throughout the period. The other two wave models generate both negativeand positive SWH biases. The magnitude of the CMC SWH bias is in closer agreement with that of the ECMWF.The SWH bias becomes more in phase with that of the ECMWF following the implementation of the globalGEM model in fall 1998. The rmse values for the three models exhibit similar seasonal behaviour. They are also consistent in that they all generate winter values larger thansummer values and NATL summer values slightly larger than NPAC summer values. This confirms the earlier conclu-sion that the Pacific winter wave systems have more variabil-ity than the summer ones and more variability than theAtlantic winter wave systems and on the impact of the occa-sional hurricanes on the NATL summer SWH rmse. TheCMC SWH winter rmse values are larger than those of theECMWF and FNMOC and this suggests that, for the Pacificarea, the global models seem to have an edge over the region-al model. Table 3 indicates that the NPAC wave systems havelonger peak periods than the NATL wave systems, that is, thePacific is more swell dominated and the larger CMC SWHrmse may be partly due to the fact that the two global wavemodels are better able to simulate the Pacific swells than theCMC Pacific WAM4. The FNMOC and CMC WAM4s havethe same grid and spectral resolutions and the FNMOC SWHrmse is in better agreement with that of the ECMWF modelwhich has a finer spatial resolution but coarser spectral angu-lar resolution. The SWH SI values vary from 0.16 to 0.20which is close to the value of 0.15 obtained by Cardone et al.(1995) using near perfect hindcast winds. In Fig. 7b the U10biases for the three atmospheric models vary from –0.7 to 0.5m s–1. The somewhat, but not significantly, larger CMC U10rmse is also reflected in the larger CMC U10 SI and the larg-er SWH rmse in Fig. 7a. In Fig. 7c positive (negative) Tp biasseems to be associated generally with positive (negative)SWH bias in Fig. 7a. The biases all lie within ±1.0 s with theFNMOC bias being close to 0.0 s. The ECMWF and CMCmodels compute Tp the same way. There is a more systemat-ic difference between the ECMWF and CMC Tp rmse. Thefrequency analysis of collocated Tp data mentioned earliershows that NPAC is more swell dominated than NATL and,in this case, the ECMWF global WAM4 with no open bound-aries predicts NPAC Tp more accurately, in particular theswell Tp, than the regional WAM4 with open boundaries. TheCMC Tp rmse and SI statistics lie between those of theECMWF and FNMOC. The analysis suggests that the CMCPacific WAM4 generates wave results that are quite compa-rable with those produced by the two global models runningoperationally at the ECMWF and FNMOC.

b North Atlantic and North Pacific Overall Wave StatisticsThe overall wave statistics for the entire period are presentedin Table 3 for both the North Atlantic and the North Pacific.The rmse values and the buoy and model mean values suggest

that the Pacific wave systems have more variability and aremore intense than the Atlantic systems. They have longerwave periods due to the presence of more swells that are gen-erally not well predicted, thus leading to larger Tp rmse val-ues. The bias, taken in conjunction with the symmetric slopes, indicates that, in the mean, the Pacific WAM4 generateswave heights and peak periods closer to those observed thanthe Atlantic WAM4. The differences in SWH bias and rmsevalues between the two oceans are rather small. The smallerPacific SWH bias, however, may be attributed to the longerPacific fetches. Wave heights are both duration-limited andfetch-limited and need either a long fetch or a long time, orboth, to reach equilibrium values. Fetches associated withPacific storm systems are generally longer than those associ-ated with Atlantic storm systems and this may also accountfor the NPAC SWH Ra being somewhat larger than that ofthe NATL. The SI varies from 0.21 for the 00-h forecast to0.25 for the 24-h forecast and to 0.30 for the 48-h forecast andany improvement in SI would require more accurate specifi-cation of the input wind forcing. The correlation coefficient ris relatively high for SWH but significantly lower for Tp sug-gesting the difficulty the wave model has in generating Tpcloser to that observed.

The SWH AC is well above the threshold value of 60% andthe RV is mostly above 0.5. This indicates that the SWH fore-casts are better than climatology in a meaningful way and thatthey are useful and of good quality. The decay of the SWHAC from 91% for day 1 to 86% for day 2 is in close agree-ment with the typical AC decay from 95% for day 1 to 80%for day 3 as pointed out by Komen (1999) for the NorthernHemisphere. The Tp AC is barely above 60% for the NATLregion and just below for the NPAC region while the RV is> 0 but somewhat small. Hence, the NATL Tp forecasts aresomewhat better than climatology and are more useful thanthe NPAC Tp forecasts.

c Comparison of Statistics With Those Based on NCEPReanalysis Data Cox et al. (1999) obtained two long-term wave hindcastsbased on the National Centers for EnvironmentalPrediction/National Center for Atmospheric Research(NCEP/NCAR) Reanalysis (NRA) project covering a 40-yearperiod from 1958 to 1997 (Kalnay et al., 1996). In the GlobalReanalysis of Ocean Waves (GROW) project the NRA 10-mlevel winds were adjusted for neutral stability using the tech-nique described by Cardone et al. (1990) and interpolatedonto a global 1.25° × 2.5° wave model grid. In the AES40project the adjusted NRA winds were interpolated onto a0.625° × 0.833° latitude/longitude wave-model grid coveringthe entire North Atlantic. These wind fields, however, weremodified for intense extratropical storms using interactivekinematic techniques and for tropical systems using a tropicalboundary layer model including the assimilation of ship,buoy, and satellite wind data. The GROW winds were used todrive the Oceanweather Inc. ODGP2 1G ocean wave modelas described in Khandekar et al. (1994) while the AES40


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winds were used to drive the same ODGP2 wave model butwith 3G WAM Cycle-3 physics. The regional GROW statis-tics are presented in Table 4a, the AES40 statistics in Table4b, and the present study overall SWH and U10 statistics forthe regions that closely approximate the GROW and AES40regions in Table 4c.

The NATL and NPAC statistics in Table 4c are in goodagreement with the GROW statistics in Table 4a and indicatethat the CMC SEF/RFE/GEM winds are of slightly betterquality than those of the NRA winds in terms of rmse and SIat 00 h. The somewhat better NATL and NPAC wave statis-tics may be attributable to the slightly better CMC winds andto the higher grid resolution and 3G physics of WAM4.Comparison of the NATL statistics with the AES40 statisticsin Table 4b indicates that the AES40 winds are of better qual-ity than the CMC winds. This must necessarily be true as theformer winds are enhanced winds and are more representativeof the “ground truth”. In this case the better wave statisticsmay be due to the AES40 enhanced winds and the higher res-olution of the AES40 wave model grid since the physics arebasically the same in both wave models.

d Time Series of Wind/Wave ParametersThe analyzed or 00-h forecast model versus measuredwind/wave time series are presented in Fig. 8a at buoy loca-tion 44011 in the US Atlantic and in Fig. 8b at buoy location46004 in the Canadian Pacific for January 1999 when boththe global and regional GEM models were in operationalmode. The figures indicate that there is good in-phase agree-ment between buoy-measured and model wave and windparameters. The growth and decay phases of the SWH followthe observed phases remarkably well. The wave-height peaksare generally underestimated, leading to negative SWH bias-es for both oceans as shown earlier. This may be partly attrib-uted to the waves not being fully grown because of fetch

and/or duration limitations and also partly to wind speederrors. Assuming unlimited fetch conditions at a given loca-tion, a constant wind speed of 15 m s–1 requires a duration ofclose to 23 h to generate a fully developed sea of 5 m(Komen, 1999). To a large extent the peaks in SWH closelymatch the corresponding peaks in U10. There are more waveswith Tp > 10 s, reaching as high as 17 s, in the Pacific than inthe Atlantic for January 1999, which once again confirms thatthe Pacific is more swell dominated than the Atlantic. Anexample of wave and wind conditions is presented in Fig. 9afor the North Atlantic and in Fig. 9b for the North Pacificvalid at 00:00 UTC 15 January 2000. The figure indicates thatin this case the North Pacific is quieter than the North Atlanticboth in terms of wave and wind conditions and that waveheights in excess of 4 m are found in areas where the windsare strong and the fetches are long. On average, however, thePacific wave systems are somewhat stronger than the NorthAtlantic wave systems as Table 3 indicates.

5 Concluding remarksThe CMC wave forecasting system consists of two regionalversions of the global WAM4, one operating in the NorthAtlantic and one in the North Pacific. During the periodDecember 1996 to November 1999, the 10-m level windsobtained from the operational global SEF/GEM model wereused to drive the Pacific WAM4 while those obtained fromthe operational RFE/regional GEM model were used to drivethe Atlantic WAM4. The significant wave heights and thepeak periods from WAM4 and the wind speeds from theatmospheric models interpolated onto the WAM4 grid arevalidated against wave/wind data measured by buoys locatedin the coastal and shelf regions of the Atlantic and Pacificcoasts of North America for that period. The main conclu-sions from the results presented in this study are briefly sum-marized below.


TABLE 4. Comparison of GROW and AES40 statistics from Cox et al. (1999) with the current study overall statistics for the 00H forecast.

Area N Buoy Mean Model Mean Bias Rmse Stdev SI r

(a) GROW Statistics (see Table 1 in Cox et al., 1999)north-west AtlanticSWH (m) 175256 1.98 2.04 0.06 0.57 0.56 0.28 0.89U10 (m s–1) 179939 7.14 7.54 0.40 2.57 2.54 0.36 0.78

north-east PacificSWH (m) 121793 2.75 3.01 0.26 0.67 0.62 0.23 0.92U10 (m s–1) 121323 7.99 8.04 0.05 2.26 2.26 0.28 0.82

(b) AES40 Statistics (see Table 2 in Cox et al., 1999)north-west Atlantic (US and Canadian data combined)SWH (m) 213734 1.98 2.08 0.10 0.46 0.45 0.23 0.93U10 (m s–1) 219199 7.15 7.45 0.31 1.67 1.64 0.23 0.91

(c ) Current Study Overall Statisticsnorth-west Atlantic (NATL)SWH (m) 15721 1.99 1.77 –0.22 0.51 0.46 0.23 0.92U10 (m s–1) 15419 7.18 7.27 0.10 2.26 2.26 0.31 0.82

north-east Pacific (NPAC)SWH (m) 16782 2.90 2.83 –0.06 0.62 0.62 0.21 0.91U10 (m s–1) 15434 8.30 8.32 0.02 2.12 2.12 0.25 0.85

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Fig. 8 Time series plots of analyzed (or 00-H forecast) model versus buoy-measured wind/wave parameters for January 1999 at (a) buoy 44011 location inthe North Atlantic and (b) buoy 46004 location in the North Pacific. In each panel the upper plot is for SWH, the middle plot U10 and the lower plotTp. The solid line in each plot gives the buoy observations and the dashed line the corresponding CMC WAM4 values.

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The replacement of the global SEF model by the globalGEM model in October 1998 did not show any significantimpact on the verification statistics of the wind and waveparameters, most likely because both models have nearly thesame physics and grid resolution. When the regional GEMmodel replaced the RFE model without the spin-up cycle inthe regional analysis system in February 1997, the wind speedrmse and bias were unusually large but these were signifi-cantly reduced after the spin-up cycle was implemented inSeptember 1997. Although the impact on the SWH in thiscase was not too noticeable, the spin-up cycle is, nevertheless,an important component of the CMC regional data assimila-tion system. The results also show that there was little or noimpact on the wind and wave forecasts following the increaseof the grid resolution of the regional GEM model from 35 to24 km in September 1998.

The Pacific winter atmospheric and wave systems havehigher variability than the winter systems for the Atlantic butin each of the oceans they exhibit higher variability in winterthan in summer. The Pacific has longer period swells through-out the year and is more swell dominated than the Atlantic.WAM4 seems to have some difficulty in predicting the swellssince some of them may originate from well outside the gridarea, especially in the Pacific. The anomaly correlation andreduction of variance analyses indicate that the SWH and U10forecasts are useful and of good quality and show skill when

compared with climatology while the Tp forecasts are lessuseful.

The wave statistics generated by the regional WAM4 arequite comparable with those obtained from the global WAM4run by the international wave forecasting centres at ECMWFand FNMOC. They all show similar seasonal behaviour forboth oceans. Overall, the performances of the CMC regionalAtlantic and Pacific WAM4s closely follow the performancesof the ECMWF and FNMOC global WAM4s, taking intoconsideration the somewhat different wave model grid con-figurations, inclusion of data assimilation to create enhancedinitial sea state, coupled model system, and wind forcingsfrom different atmospheric prediction models. The globalmodels, however, seem to handle the Pacific swells slightlybetter than the regional model. The regional WAM4 statisticsare also compared with those based on the NCEP reanalysisdata. The comparison suggests that the statistics are some-what better than the GROW statistics and this may be attrib-utable to the somewhat better CMC winds and the higher gridresolution and 3G physics of the WAM4. On the other hand,the AES40 statistics are somewhat better than the AtlanticWAM4 statistics, primarily because of the better quality ofthe wind field which is more representative of the groundtruth. This points to the need for more accurate specificationof the wind forcing to ocean wave models by numericalweather prediction models in order to generate more accurate


(a) (b)

Fig. 9 Snapshot of wave and wind conditions valid at 00:00 UTC 15 January 2000 for (a) North Atlantic and (b) North Pacific. The shaded region is the SWHwith contours and central values in metres and the wind vector field is superimposed in meteorological convention with full barbs representing 10 knotsand half barbs 5 knots.

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wave forecasts and better wind/wave statistics. Examinationof time series plots of wind and data for both oceans indicatesreasonably good agreement between model output and thecorresponding buoy-measured parameter. Both regional wavemodels, however, have a tendency to underestimate the wave-height peaks.

AcknowledgementsThe author wishes to express his sincere thanks to LaurieWilson and to Drs Venkata Neralla, Jocelyn Mailhot and

Weimin Luo of the MSC and to Dr. Jean Bidlot of theECMWF for their helpful comments and suggestions for theimprovement of this paper. Thanks are also due to theECMWF and FNMOC for allowing the use of their globalWAM4 data acquired through collaborative exchange.


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Documents

Evaluation of the CMC regional wave forecasting system against buoy data