US Navy Global and Regional Wave Modeling

Significant waveheight (m) (colors) and mean direction (arrows) from a Beaufort and Chukchi Seas regional wave model hindcast with WAVEWATCH III (R) during the “Great Arctic Cyclone” of 2012 (2100 UTC August 5, 2012, shown here). Contours indicate ice concentration fraction of 0.3, 0.5, and 0.7, from an operational analysis based on satellite radiometer. 5°N 0°N 75°N 0°N Signi cant Wave Height (m) | 05−Aug−2012 21:00:00 Ice Concentration (contours) ( 0.30 0.50 0.70 )


US Navy Global and
Regional Wave Modeling with these forecasts, but it is reasonably assumed to be in the thousands over the course of the war (Kinsman, 1984).
The methods of Sverdrup and Munk, summarized in Kinsman (1984), were by necessity quite crude, requiring, for example, a forecaster to quantify a single fetch and duration associated with a single wind speed, though winds over the real ocean are non-stationary and non-uniform.Individual forecasts were made using a sequence of charts and nomographs.These simple concepts continued to be used into the era of electronic computing.
In their review of wave modeling at the National Weather Service (NWS), Tolman et al. (2002) state that the first computer-generated wave forecasts for the NWS were made in July 1956, as described by Hubert (1957).The NWS at the time was known as the Weather Bureau, and Hubert was, in fact, a Navy officer detailed to the Joint Numerical Weather Prediction Unit, a joint project by the US Air Force, Navy, and Weather Bureau.These initial computer

INTRODUCTION
Particular attention is given in this article to progress made since an earlier paper of similar theme by Jensen et al. (2002).Center (FNOC; Clancy et al., 1986;Wittmann and Clancy, 1993).By the mid 1970s, FNOC was running its first spectral model, SOWM (Spectral Ocean Wave Model), based on observational and theoretical work of W.J. Pierson and others (Clancy et al., 1986).It was a regional model, subsequently replaced by a global version (GSOWM) in the mid-1980s (Clancy et al., 1986).
Implementation of the first modern (so-called "third generation") wave model, WAM (WAve Model;WAMDI Group, 1988), occurred in the 1990s, with a regional implementation at FNOC in 1990 and a global implementation in 1994 (Wittmann and Clancy, 1993Clancy, , 2004;;Wittmann et al., 1995).By that time, the operational center was known by its current name, Fleet Numerical Meteorology and Oceanography Center (FNMOC).

During this progression of Navy
wave models, the most important breakthrough was arguably the development of the conservation equation for spectral density, sometimes known as the "radiative transfer equation" for wave energy.This was first expressed by Gelci et al. (1956) andHasselmann (1960).
Written in the Cartesian coordinates, the equation is The prognostic variable is the wave action density N, equal to energy density divided by angular relative frequency With the introduction of Equation 1, the sequence of charts and nomographs for manual forecasting were replaced with a single integration.Fetch and duration are not calculated, but are implicit features of the integration.Refraction by bathymetry and currents are included via C σ and C θ , and shoaling effects are included via the ∂/∂x and ∂/∂y terms.
In the case of spherical coordinates, the advection terms are modified to account for Earth's curvature (see WAMDI Group, 1988).Diffraction is customarily disregarded at these scales.
In first generation wave models such as SOWM, the right-hand side of

Boundary forcing consists of directional
wave spectra prescribed at intervals along the boundaries.Nearshore forecasts are important not only for the initial assault, to check against operating thresholds of medium and small craft, but also for so-called "logistics over the shore, " that is, the movement of men and matériel in the subsequent days.In fact, the latter sort of operations is more likely to be restricted by surf conditions (Su and Vincent, 1996).Nearshore forecasts are also utilized for Special Operations in the littoral.

General Features
The 1 An evolved version of WAM, known as ECWAM (Bidlot, 2012), employed at the European Centre for Medium-Range Weather Forecasts, has undergone significant code modernization relative to WAM4.In some cases, features similar to those described herein have been added for WW3, albeit with a slightly different approach.requires that all grids run at once, and so no output is available until the entire system is complete.The second priority implies that regional grids are designed to coincide with regional meteorological models, which are implementations of the Coupled Ocean/Atmospheric Mesoscale Prediction System (COAMPS; Hodur, 1997).This priority contrasts with the approach of NCEP, in which The global model is run to 180 hours, and the regional models forecast to varying lengths, from 36 to 96 hours.
Figure 1 shows the grids included in the WW3 has also been integrated into the COAMPS On-Scene (COAMPS-OS) system (Geiszler et al., 2004).The COAMPS-OS system is a modeling interface that allows for rapid implementation of new areas to meet urgent requests for high-resolution wind and wave forecasts.
Though not yet operational, it also provides a framework to fully couple atmospheric, ocean, and wave models.Eventually, all the regional In October 2012, the assimilation was upgraded from a simple optimum interpolation (OI) to a three-dimensional variational (3DVAR) scheme (Smith et al., 2011).At the time of writing, data are used from three satellite altimeters: CryoSat, ALtiKa, and Jason-2.  the benefit derived from the superior winds of the higher-resolution regional COAMPS implementations via the two-way nesting: waves generated in a regional grid can affect swell predictions at remote coastlines.
FNMOC provides the wind fields.
For the global domain, NAVGEM is provided at 0.5 degree grid spacing, and for regional domains, COAMPS is typically at 0.2 degree grid spacing.Most Figure 4. Layout of the regional domains for the multigrid system running at the Naval Oceanographic Office (NAVOCEANO).The Northeastern Pacific grid is also shown in Figure 5.
WAVEWATCH III Operational Domains at NAVOCEANO

NEXT STEPS: CAPABILITIES FORTHCOMING
During the next two years, NRL will add new grids to the experimental real-time system operated by NRL on the DSRC, and NAVOCEANO will evaluate these grids to determine whether they can be incorporated into the official operational system.As mentioned above, the primary determination of existing regional grids is the availability of COAMPS regional atmospheric model output for a region.Because these COAMPS implementations are by now suitably exploited by the regional WW3 grids, other determinations will be used for the new grids.One example is a polar stereographic (curvilinear) Arctic grid, which is being tested now on the DSRC.The primary motivation for this grid is to avoid the narrowing of grid cells that occurs in the regular grid at high latitudes.Another example is the Australia grid, included in Figure 4, also being tested on the DSRC.In this case, the grid is designed as a so-called "coastal grid" using methods described in Tolman (2008).In this paradigm, the grids are still regular, but sea points far from the coast are masked (i.e., not treated as computational grid points);

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Y W. E R I C K R O G E R S , J A M E S D .D Y K E S , A N D PA U L A .W I T T M A N N Significant waveheight (m) (colors) and mean direction (arrows) from a Beaufort and Chukchi Seas regional wave model hindcast with WAVEWATCH III (R) during the "Great Arctic Cyclone" of 2012 (2100 UTC August 5, 2012, shown here).Contours indicate ice concentration fraction of 0.3, 0.5, and 0.7, from an operational analysis based on satellite radiometer.Height (m) | 05−Aug−2012 21:00:00 Ice Concentration (contours) ( 0.30 0.50 0.70 ) fetch and duration available for generation of wave energy, and (2) the direction and distance of propagation once the waves leave the active generation area.Some information was compiled by the military on wave climatology for certain regions, but no wave forecasts were produced.During the war, the need for wave forecasts was recognized, and action was taken by separate, parallel efforts of the American and British war departments.The most pressing problem was the determination of operability of landing craft within the surf; two-meter breakers were considered likely to cause broaching and sinking (AIP, 1986; Munk and Day, 2002).The US job was given British-American landing of November 8, 1942, on the Atlantic and Mediterranean coasts of Northwest Africa.The methods were subsequently refined by the two researchers after they returned to Scripps in February 1943, and they were taught to officers of the military services, at which time wave forecasting was formally introduced to the US Navy.The methods were applied for the Normandy invasion of June 1944 and a number of other invasions in the Pacific and Mediterranean.It is impossible to estimate the number of lives saved

For a more
detailed review of progress prior to 2002, the reader is referred to this earlier paper.Prior to the Second World War, generation of routine meteorological forecasts for the US military was well underway, with services provided first by the US Army Signal Corps and later by the Army Air Corps Weather Service.At sea, because of the obvious close link between wind and wind-generated seas, these services provided some limited, implicit wave forecasts.For example, a severe winter storm over any significant body of water can reliably be expected to generate large and potentially dangerous waves.However, this linkage is limited because it does not account for important variables that determine wave magnitude both within the storm and at distant locations.The most important of these variables is associated with (1) the temporal and spatial variability of the wind field and the basin geometry, ABSTR ACT.This article reviews the prediction of wind-generated surface gravity waves over the world ocean by the US Navy.The numerical wave model WAVEWATCH III® is used operationally for this purpose at the two primary Navy operational centers, the Fleet Numerical Meteorology and Oceanography Center and the Naval Oceanographic Office.This model is briefly described, and an overview is given of the current operational and near-operational features of global-and regionalscale wave models at the two centers.Planned features are summarized.forecasts were more primitive than the earlier methods of Sverdrup and Munk, representing a step backward of sorts, because they assumed infinite fetch, disregarded swell, and were only beginning to introduce the concept of limited duration.By the mid 1960s, these models had been improved to include simplified swell predictions, and were implemented at the Fleet Numerical Oceanography and for the more general case with or without currents, it is wave action spectral densityN(σ,θ).Phase-resolving wave models are not presently used by the operational Navy for forecasting at any scale, though in principle, it is feasible at smaller scales, particularly if local wave generation and shorter wind sea frequencies are excluded (e.g., see O'Reilly and Guza, 1993).Large-scale wave models have a number of applications operationally, such as for the historical example of an amphibious assault given above.However, large-scale models are rarely used directly for such applications because the spatial resolution is insufficient to represent nearshore bathymetry.Instead, the large-scale wave model is used to create boundary forcing for a telescoping sequence of coastal models.At each step, the resolution is typically increased (improved) by a factor of four to eight.
Offshore, the large-scale models are used more directly, for example, in ship routing and high seas warnings.While the most severe storms can generally be avoided by ships using meteorological forecasts, a wave model is needed to anticipate the swells emanating from these storms.Certain operations, such as ship-to-ship transfer of matériel can be particularly sensitive to long swells, making such forecasts useful for planning.Wave conditions can affect the cost of ship movement.Specific variables pertinent to seakeeping are further discussed below in the context of near-operational products.Other uses for wave forecasts have been proposed but are not operational at the time of writing.Ambient noise is important to undersea warfare; wave forecasts can assist in noise predictions because, along with ship traffic, wave breaking is a primary source of ambient noise.The wave-induced drift current, sometimes called "Stokes drift, " is readily calculated from directional spectra, and is critical for prediction of drift trajectory (e.g., for search and rescue or debris recovery).Waves also play an important role in the dispersion and advection of oil spills.Wave models are, of course, subject to errors.Validation and analysis of sources of errors in hindcasts and operational predictions are a major component of work performed by The Naval Research Laboratory's (NRL's) Oceanography Division.Results from these studies inform subsequent model development efforts.For example, it is useful to know if error is dominated by model forcing vs. errors in the model itself, and if the latter, whether it is in the model physics or numerics.Detailed discussion of this topic is beyond the scope of this paper, but interested readers can find many papers on the topic, for example, Rogers et al. (2005), Cavaleri et al. (2007), and Durrant et al. (2013).WAVEWATCH III: KEY FEATURES AND CODE DEVELOPMENT The WAVEWATCH model was originally developed at Delft University (Tolman, 1991), and its current form, referred to as WAVEWATCH III® (WW3), was developed at the National Oceanic and Atmospheric Administration's National Centers for Environmental Prediction (NOAA NCEP; Tolman et al., 2002).WW3 is free and open source, with license restrictions.At time of writing, the most recent public release was WW3 version 4.18 (Tolman et al., 2014).During the first decade of this century, WW3 evolved from a code written exclusively by a single author into a governing equation of WW3 is a variant of the action balance equation given in Equation 1 above.In addition to the three traditional deepwater source functions mentioned in the paper's first section, the latest version of the model (WW3 version 4) is able to optionally represent a number of other source terms, including the effects of bottom friction, bottom scattering, sea ice, reflection from icebergs and steep shorelines, surf breaking, fluidized mud, and three-wave (triad) nonlinear interactions.In some cases, multiple options exist for the same physical process, allowing different theories, parameterizations, and numerical rigor.In addition to static bathymetry, the model optionally ingests several fields that may be non-stationary and non-uniform: surface currents, water levels, ice characteristics, 10-meter wind vectors, and airsea temperature differences (the last for representation of atmospheric stability).Unresolved islands and ice can be treated with subgrid parameterization.In public release version 3, the multigrid or mosaic approach of Tolman (2008) was introduced.In this approach, nesting is performed using internal communications, and all grids are run within a single executable program rather than the old approach of executing a sequence of programs, one for each grid, communicating via files containing directional spectra.The new approach allows for two-way nesting, exchanging spectra between domains.For example, energy generated in a high-resolution WW3 grid may be propagated out to the lower-resolution global WW3 grid as swell, and then back to another high resolution WW3 grid on the other side of the ocean.Where WW3 version 3 only allowed regular structured grids, WW3 version 4 can perform computations on irregular structured and unstructured grids.Propagation schemes of first-, second-, and third-order accuracy can be selected according to a user's preferences of accuracy vs. computational cost.Output has also been extended to include NetCDF format.Many new variables are added to output, such as momentum flux variables relevant to coupling with atmospheric and ocean models, and wave-breaking statistics such as whitecap coverage.On multiple processors, WW3 can use distributed memory parallelism via Message Passing Interface (MPI), with domain decomposition over both geographic and spectral grids during separate time steps for source term calculation and geographic propagation.One especially noteworthy development is the introduction of the new generation of more physically realistic deepwater dissipation functions in the model by Ardhuin et al. (2010) and Zieger et al. (2011).The latter model is part of a source term package that is essentially identical to the new deepwater physics installed in SWAN by NRL (see Allardet al., 2014, in this issue).Thus, it is possible to use consistent physics between WW3 and SWAN, thereby reducing discontinuities at WW3-to-SWAN nesting boundaries (discussed later in

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THE FNMOC OPERATIONAL SYSTEM IS DESIGNED WITH TWO PRIORITIES IN MIND: (1) RAPID DEPLOYMENT OF THE GLOBAL PRODUCT, AND (2) EXPLOITATION OF HIGH-RESOLUTION METEOROLOGICAL PRODUCTS.MPI methods for parallel processing (Wittmann, 2002), the open source policy of WW3, and WW3's accurate propagation scheme that makes it possible to distinguish separate swell systems in time series of nondirectional spectra (Wingeart et al., 2001).The FNMOC operational system is designed with two priorities in mind: (1) rapid deployment of the global product, and (2) exploitation of high-resolution meteorological products.The first priority implies that the global wave product should be available very soon after the global meteorological product is available, and contrasts with the priorities of the Naval Oceanographic Office (NAVOCEANO; see below).This priority discourages use of the multigrid feature of WW3, which regional models are most often forced by the National Weather Service's Global Forecasting System (GFS).Since February 2013, the global WW3 at FNMOC is forced by the NAVy Global Environmental Model (NAVGEM;Hogan et al., 2014, in this issue).At present, the WW3 grids used at FNMOC are all regular grids.

FNMOC
operational system at time of writing.With the stand-alone WW3 systems such as shown in this figure, wave feedback to the atmosphere (modified surface roughness) is not considered, and coupling with an ocean model is not performed.

FNMOCFigure 2 .
Figure 2. Significant wave height in feet (indicated with color scaling) and mean direction (indicated with arrows) for the 24-hour forecast for October 23, 2013, 00 GMT, from the WW3 West Pacific regional model forced by COAMPS winds.

Figure 4
Figure4shows a layout of domains for a currently tested system.At the time of writing, all domains shown are operational on the DSRC, except for the Arctic and Australia domains, which are currently being tested in the pre-operational developmental system on the DSRC.The global domain is grid spaced at 0.5 degrees, while the regional domains are 0.1 or 0.2 degrees, except the Arctic curvilinear grid, which is at 16 km.Although the global component of the multigrid system completes later than it would if run independently (as at FNMOC), this configuration maximizes

Figure 5 .
Figure 3. Forecast example of differences in geographical location of significant wave heights associated with tropical cyclones.See text for description.Credit: C. Sampson (NRL)

Figure 6 .
Figure 6.Plot of sample results of the crossing seas algorithm for the entire global system including the regional domains.The values are divided into four groupings of significant wave height (in meters) where crossing seas are predicted, with larger numbers indicating greater seakeeping hazard.See text for further description.