Series No. 456

Subject: Wave Forecasting for Alaskan Waters

SIGNIFICANT CHANGES FROM LAST BULLETIN ON THIS SUBJECT NO. 427

Created 08/17/1999;superceded 06/11/2003.

W/NP21: YYC, LDB

This bulletin, prepared by Dr. Y. Y. Chao, Mr. L. D. Burroughs, and Dr. H. L. Tolman of the Ocean Modeling Branch (OMB), Environmental Modeling Center (EMC), National Centers for Environmental Prediction (NCEP), describes automated wave guidance for waters surrounding Alaska alphanumeric and Gridded Binary (GRIB) formats. This guidance has been implemented internally on the new IBM computer and is scheduled for operational implementation after the IBM is moved to Bowie, Maryland sometime in the late fall 1999.

The Gulf of Alaska (GAK; a second generation) regional wave model will be replaced with the Alaska Waters
(AKW; a third generation) regional wave model. The AKW is based on the NOAA WAVEWATCH-III (NWW3)
which is described in detail in Technical Procedures Bulletin (TPB) 453 (Chen, Burroughs, and Tolman
1999) and Tolman (1999a, b, and c). The NWW3 provides the boundary conditions to the AKW. More
specifically, the AKW accounts for wave dispersion within discrete spectral bins by adding in diffusion terms
to the propagation equation (Booij and Holthuijsen 1987); it uses the Chalikov and Belevich (1993)
formulation for wave generation and the Tolman and Chalikov (1996) formulation for wave dissipation; it
employs a third order finite differencing method with a Total Variance
Diminishing limiter to solve wave propagation; its computer code has been optimized to utilize the
Massively Parallel Processing (MPP) structure of the new IBM R/S 6000 SP computer; it uses a higher
spatial resolution (0.50^{o} x 0.25^{o} rather than 30 n mi x 30 n mi), a larger domain (160^{o}E - 124^{o}W by 45^{o}N -
75^{o}N instead of 155^{o}W. - 132^{o}W by 53^{o}N - 61^{o}N), a higher frequency resolution (25 frequencies in place of
20), and a higher directional resolution (24 directions to replace 12).

Various graphics and text products for the AKW are available at
http://polar.ncep.noaa.gov/waves/products.html.
The following wind and wave parameters are available in GRIB format at the web site above, on Family of
Services (FOS), and on AWIPS as GRIB bulletins: H_{s}, D_{m}, T_{m}, peak wave period and direction, wind sea
peak period and direction, wind speed and direction, and u- and v-wind components. Note, however, that
significant wind sea height, significant swell height, and mean swell period and direction are no longer
provided. The peak period and direction replaces the swell period and direction for a large part of
the domain.

Spectral text bulletins for the AKW are available at the web site above. These files are in ASCII and are available by anonymous ftp from the directory ftp://polar.ncep.noaa.gov/pub/waves. These bulletins will be implemented on AWIPS as soon as headers can be derived for them.

The wave guidance will continue to be generated twice daily based on the 0000 and 1200 UTC cycles of the Aviation (AVN) run of the Global Spectral Atmospheric Model.

Technical Procedures Bulletin No. 427 is now operationally obsolete.

WAVE FORECASTING FOR ALASKAN WATERS

By

Y.Y. Chao, L.D. Burroughs and H.L. Tolman^{(1)}^{(2)}

In order to predict wave conditions adequately over the continental shelf and near land boundaries, a regional model which has higher resolution in grid space and possibly in spectral components is required. The regional model also must calculate rigorously the effects of submarine bottom conditions and any currents which may exist on wave growth, transformation and dissipation. A global-scale wave model usually is designed only to provide the general wave pattern over the deep ocean. It does not provide information accurate enough to describe small-scale, complex wave patterns near the coastal areas.

The Alaska Waters (AKW) regional wave model was designed to fill the needs of the Alaska Region which
had requested that the area covered by the Gulf of Alaska (GAK) regional wave model be expanded to
include all the waters that surround Alaska rather than just an interior portion of the Gulf of Alaska. The GAK
is a second generation^{(3)} wave model. As a result, the predicted values over the stormy areas are not as
accurate as those of third generation^{(4)} wave models which describe these conditions more adequately. The
boundary conditions are provided by the NOAA/WAM which is scheduled to be replaced by the NOAA
WAVEWATCH III (NWW3) after the new IBM computer is moved to Bowie, Maryland in the late Fall 1999.

The GAK has been used for operational forecasting of wave conditions over the Gulf of Alaska since April
1994 (Chao 1995) and is scheduled to be replaced with the AKW in May 1999. The AKW is based on the
NWW3 which is described in detail in Technical Procedures Bulletin (TPB) 453 (Chen, Burroughs, and
Tolman 1999) and Tolman (1999a, b, and c). The NWW3 provides the boundary conditions to the AKW.
More specifically, the AKW accounts for wave dispersion within discrete spectral bins by adding in diffusion
terms to the propagation equation (Booij and Holthuijsen 1987); it uses the Chalikov and Belevich (1993)
formulation for wave generation and the Tolman and Chalikov (1996) formulation for wave dissipation; it
employs a third order finite differencing method with a Total Variance
Diminishing limiter to solve wave propagation; its computer code has been optimized to utilize the MPP
structure of the new IBM R/S 6000 SP computer; it uses a higher spatial resolution (0.50^{o} x 0.25^{o} rather than
30 n mi x 30 n mi), a larger domain (160^{o}E - 124^{o}W by 45^{o}N - 75^{o}N instead of 155^{o}W. - 132^{o}W by 53^{o}N -
61^{o}N), a higher frequency resolution (25 frequencies in place of 20), and a higher directional resolution (24
directions to replace 12).

Various graphics and text products for the AKW are available at http://polar.ncep.noaa.gov/waves/products.html.

The following wind and wave parameters are available in GRIB format at the web site above, on Family of
Services (FOS), and on AWIPS as GRIB bulletins: H_{s}, D_{m}, T_{m}, peak wave period and direction, wind sea
peak period and direction, wind speed and direction, and u- and v-wind components. Note, however, that
significant wind sea height, significant swell height, and mean swell period and direction are no longer
provided. The peak period and direction replaces the swell period and direction for a large part of
the domain.

Spectral text bulletins for the AKW are available at the web site above. These files are in ASCII and are available by anonymous ftp from the directory ftp://polar.ncep.noaa.gov/pub/waves. These bulletins will be implemented on AWIPS as soon as headers can be derived for them.

The wave guidance will continue to be generated twice daily based on the 0000 and 1200 UTC cycles of the Aviation (AVN) run of the Global Spectral Atmospheric Model but using data supplied by the AKW.

The AKW model has been run on a Cray computer since August 1998. In the succeeding sections, the established forecasting system along with the model structure will be described, followed by a comparison of predicted results with buoy data and GAK model output for identical locations. Finally, the strength of the new model (AKW) and the available products and dissemination is presented.

**2. Model Description**

Regional wave forecasts for Alaska waters are generated at NCEP by using the AKW model. Fields of directional frequency spectra in 24 directions and 25 frequencies are generated at one hour intervals up to 72 hours. The 24 directions begin at 90 degrees to the east and have a directional resolution of 15 degrees. Note that 12 directions were used by the GAK. The 25 frequencies used by the AKW are given by bin in Table 1.

Figure 1 shows the domain of interest and the depth field which is derived from bathymetric data available
from the National Geophysical Data Center. Required input wave spectral data for the boundary grid points
of the AKW are obtained by linearly interpolating the spectra of neighboring grids of the NWW3. The wind
fields driving the model are obtained from the output of NCEP's operational Global Data assimilation System
(GDAS) and the aviation cycles (AVN) of the global atmospheric spectral model (Kanamitsu *et al.* 1991 and
Caplan *et al.* 1997). The wind fields are constructed directly from spectral coefficients of the lowest sigma
level at 0.5^{o} x 0.5^{o} longitude and latitude resolution, and are interpolated to the resolution of the wave model
grid. They are converted to 10 m winds by using a neutrally stable logarithmic profile.
Air and sea temperature data are obtained from the lowest sigma level air
temperatures of the AVN model and from the 50km SST analysis provided by NESDIS (updated twice per
week) are used in the model wave growth parameterization. Finally, the wave
model incorporates a dynamically updated ice coverage field in the region. These data are obtained from
NCEP's operational automated passive microwave sea ice concentration analysis (Grumbine 1996; updated
daily). Ocean currents are not considered in the model at the present.

The model runs twice daily for the 0000 and 1200 UTC cycles. GDAS wind fields from the previous 12 hours at 3-h intervals (analyses and 3-h forecasts) are used for a 12-h wave hindcast. Winds from the AVN at 3-h intervals out to 72 hours are used to produce wave forecasts up to 72 hours at hourly intervals.

**3. Performance Evaluation**

The AKW has run on the Cray C90 computer since August 1998. The adequacy of the model has been
evaluated by comparing model output of the AKW and the GAK with observed data at NDBC buoys 46001
(56.3^{o}N, 148.2^{o}W) and 46003 (51.9^{o}N, 155.9^{o}W). Figures 2 (a), (b), and (c) show scatter plots of the
significant wave height (H_{s}) produced by the AKW for +00, +24 and +48 hrs forecasts, respectively, for
October 1998. Also shown are the following statistical indices: the mean bias error (bis), root mean square
error (rms), correlation coefficient (cor), and scatter index (sci). The total number of data points(ndp) used
in the analysis combines the results of both buoys for the 00 and 12 UTC cycle runs. Also presented are
scatter plots and statistics for wind speed and direction. Similar results for the GAK are given in Figs. 3 (a),
(b), and (c). It should be noted that wind input to the GAK is slightly different from that of the AKW. Wind
data used in GAK are interpolated to the wave model grid from GDAS and AVN data on 1^{o}x1^{o }grid mesh at
10m height.

Figures 4 (a), (b), and (c) show monthly series of bias, rms and mean wave height for AKW predictions at +00, +24, and +48 hr, respectively, against buoy observations. Similar figures are shown for the GAK in Figs. 5 (a), (b), and (c). It should be mentioned that only three months of concurrent data were available for both models (August-October, 1998). Nevertheless, the results of the comparison show that the AKW's predictions have less statistical error, less scattering and higher correlation with observations than the GAK's.

**4. Available Products and Dissemination**

The following wind and wave parameters are currently available in GRIB format at
ftp://polar.ncep.noaa.gov/pub/waves, on Family of Services (FOS), on the dedicated
communications line (X.25) to Alaska until it's retired, and on AWIPS as GRIB bulletins: H_{s}, D_{m}, T_{m}, peak
wave period and direction, wind sea peak period and direction, wind speed and direction, and u- and v-wind
components. Spectral text bulletins are also available on the web at the site above and will be on AWIPS
as soon AWIPS headers are assigned.

**a. GRIB bulletins**

GRIB bulletins are available for use in AWIPS and for transmission on the Numerical Data Service of FOS.
Table 2 gives the bulletin headers and their meaning. Bulletins are available at 6-h intervals from 00-
through 72-h. Available parameters are H_{s}, D_{m}, T_{m}, peak wave period and direction, wind sea peak wave
period and direction, and u and v components of the wind velocity. A 0.50 x 0.25 degree lon./lat. grid is used
with a domain from 160^{o}E -124^{o}W and 45^{o}N - 75^{o}N.

Spectral text bulletins are presented for numerous points of the AKW. These bulletins are in ASCII and are
available on the INTERNET at present, and, when AWIPS headers are assigned, they will be available to
the field on AWIPS. The line length of the table is 130 characters by 100 lines. The header of the table
identifies the output location, the generating model and the run date and cycle of the data presented. At the
bottom of the table, a legend is printed. The table consists of 8 columns. The first column gives the time
of the model results with a day and hour (the corresponding month and year can be deduced from the
header information. The second column presents the overall significant wave height (H_{s}), the number of
individual wave fields with a wave height over 0.15 m that could not be tracked in the table (x). Individual
wave fields in the spectrum are identified by using a partitioning scheme similar to that of Gerling (1992).
In the remaining six columns individual wave fields identified with their wave height (H_{s}), peak wave period
(T_{p}) and mean wave direction (dir, direction in which waves travel relative to North). Generally, each
separate wave field is tracked in its own column. Such tracking, however is not guaranteed to work all the
time. An asterisk (*) in a column identifies that the wave field is at least partially under the influence of the
local wind, and, therefore, most likely part of the local wind sea. All other wave fields are pure swell.

**5. References **

Booij, N. and L.H. Holthuijsen, 1987: Propagation of ocean waves in discrete spectral wave models. *J. Comput. Phys.*, **68**, 307-326.

Caplan, P., J. Derber, W. Gemmill, S,-Y. Hong, H.-L. Pan and D. Parish, 1997: Changes to the NCEP operational medium-range forecast model analysis/forecast system. *Wea. Forecasting*, **12**, 581-594.

Chalikov, D.V. and Belevich, M.Y., 1993: One-dimensional theory of the boundary layer. *Boundary-Layer Meteor.*, **63**, 65-96.

Chao, Y.Y., 1995: The Gulf of Alaska regional wave model. *Technical Procedures Bulletin No. 427*, National
Weather Service, NOAA, U.S. Department of Commerce, 10 pp. [Available from the Office of Meteorology,
SSMC2, Silver Spring, MD 20910; OBSOLETE]

Chen, H.S., L.D. Burroughs and H.L. Tolman, 1999: Ocean Surface Waves. *Technical Procedures Bulletin No. 453*, National Weather Service, NOAA, U.S. Department of Commerce. [Available at
http://www.nws.noaa.gov/om/tpb/inddraft.htm]

Gerling, T.W., 1992: Partitioning sequences and arrays of directional wave spectra into component systems.
*J. Atmos. Ocean. Technol.*, **9**, 444-458.

Grumbine, R.W., 1996: Automated passive microwave sea ice concentration analysis at NCEP. *Ocean Modeling Branch Tech Note No. 120*, NCEP, National Weather Service, NOAA, U.S. Department of
Commerce, 13 pp.

Kanamitsu, M., J.C. Alpert, K.A. Campana, P.M. Caplan, D.G. Deaven, M. Iredell, B. Katz, H.-L. Pan, J.E. Sela and G. H. White, 1991: Recent Changes implemented into the global forecast system at NMC. *Wea.
Forecasting*, **6**, 425-435.

The SWAMP Group, 1985: *Ocean Wave Modeling*. Plenum Press, New York, 256 pp.

Tolman, H.L. and D. Chalikov, 1996: Source terms in a third-generation wind-wave model. *J. Phys. Oceanogr.*, **26**, 2497-2518.

Tolman, H.L., 1999a: User manual and system documentation of WAVEWATCH-III version 1.18. *Technical
Note No. 166*, Ocean Modeling Branch, NCEP, National Weather Service, NOAA, U.S. Department of
Commerce, 110 pp. [Available at http://polar.ncep.noaa.gov/waves/wavewatch/].

Tolman, H.L., 1999b: WAVEWATCH-III version 1.18: Generating GRIB files. *Technical Note No. 167*, Ocean
Modeling Branch, NCEP, National Weather Service, NOAA, U.S. Department of Commerce, 7 pp. [Available
at http://polar.ncep.noaa.gov/waves/wavewatch/].

Tolman, H.L., 1999c: WAVEWATCH-III version 1.18: Postprocessing using NCAR graphics. *Technical Note
No. 168*, Ocean Modeling Branch, NCEP, National Weather Service, NOAA, U.S. Department of Commerce,
9 pp. [Available at http://polar.ncep.noaa.gov/waves/wavewatch/].

1. H. L. Tolman is a UCAR visiting scientist with OMB

2. OMB Contribution No. 171

3. A second generation wave model uses dynamics in wave generation, but the nonlinear energy transfer mechanism is over-simplified, and the wave growth is artificially limited by the Joint North Sea Wave Project (JONSWAP) spectrum (SWAMP Group 1985).

4. A third generation wave model solves the radiative equation by direct integration of all its components without pre-assumed
constraints to the spectral shape. Previous models rely (partially) on assumed spectral shapes and parameterizations of the integral
effects of the physics of wave growth and decay.