This study was undertaken to evaluate the global hindcasting of the WAVEWATCH III model which is intended to mimic the real-time experimental' system running at the US Naval Oceanographic Office (NAVO). This is necessary step before NAVO transitions the real-time system from experimental status to operational status. Although some work was done on comparing the real-time system to the altimetry, hindcasting allows a much more thorough examination. In total 4 hindcast models were run to allow different combinations of wind forcing fields and parameterizations of physical processes (Source Term) packages.
Purpose of this study
This study has been designed to demonstrate how GlobWave data can be used to:
- Validate the global model implementation
- Compare two different source term packages
- To help quantify role of wind field accuracy by comparing hindcasts using two different wind forcing fields. Wind forcing will also be evaluated using the altimeter data.
WAVEWATCH III (WW3) is a 3rd generation wave model developed by NOAA/NCEP in the spirit of the WAM wave model. It is a further development of the WaveWatch I and II models developed at Delft University of Technology and the NASA Goddard Space Flight Centre respectively. WW3 reflects some modifications from its predecessors in terms of the governing physical equations, the physical parameterisations used in these equations, and the numerical methods used to solve these equations. Further details can be found in Tolman (1991, 2009).
Altimeter data & requirements
Altimeter data was used to derived both wind and wave information. This example used altimeter data from the Ifremer Merged Altimeter Database which provides altimetry data for almost 20 years from 7 satellite altimeters.
Please note that the altimeter data should be bias-corrected. Therefore the uncorrected, Fast Delivery (FD) product cannot be used directly.
The first step is to set up the WW3 model using the following major and minor characteristics:
- 0.5 degree resolution (720x361) regular grid (155k sea points)
- 36 directional bins (10 degree resolution), [-5, 5, 15, ...]
- 25 frequency bins, from 0.0418 to 0.4117 Hz (increment factor=1.1)
- Duration: 0000 UTC 1 September 2010 to 0000 UTC 1 January 2011 (4 months). First week treated as spin-up, so effective duration is 115 days
- Global time step: 3600 s
- Time step for x/y propagation: 480 s
- JONSWAP bottom friction with gamma=0.038
- Surf breaking, Miche limiter, bottom scattering, triad interactions not active
- Seeding used in place of linear wind input
- Default settings for propagation, with averaging method for anti-Garden Sprinkler Effect (Tolman 2003)
- Obstruction map used for sub-grid blocking (Tolman, 2003)
- Ice concentrations greater than 75% treated as land, ice concentrations less than 25% treated as open ocean; partial sub-grid blocking otherwise, as described by Tolman (2003)
An objective of this case study was to perform hindcasting comparisons on the WW3 model run with both different wind forcing fields and physics packages. Therefore the model was run a total of 4 times, to allow all combinations of the two wind forcing fields and two physical processes packages.
The two physics packages were contained in the following different Source Term (ST) Packages:
- ST2: physics with default settings as described in Tolman & Chalikov, 1996
- ST4: physics with default settings as described in Ardhuin et al., 2010
The following wind forcing tests were also run:
- CFSR winds: the National Centre for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR) fields were completed over the 31 year period of 1979 to 2009, although have been extended using NCEP's Climate Forecast System Version 2 (CFSV2). Wind and ice fields are on Gaussian grid (which is a type of irregular grid): ni=1152, nj=576. Provided in the GRIB2 (binary) format. Time interval between fields is 1 hour (Saha et al., 2010).
- NOGAPS winds: the Navy Operational Global Atmospheric Prediction System (NOGAPS) winds are given on same grid as WW3, 0.5 degree resolution. Time interval between fields was 3 hours (Hogan & Rosmond, 1991).
The models were run on a Linux cluster containing 48 processors with a run-time between 4 and 15 hours.
For a relevant comparison of model and altimeter data the following steps were undertaken:
Step One: Matching (Time and Space)
- For a given hourly computed global WW3, only altimeter wave data acquired within 30 minutes of model time was selected
- The WW3 hourly results were spatially interpolated into the track locations of selected altimeter data.
- This process was repeated for all hourly WW3 outputs to match WW3 and altimeter data for the entire WW3 model prediction time period.
Step Two: Sorting and Computing
- The temporally and spatially matched global WW3 and altimeter data was regrouped and divide into smaller cells (2 by 2 degrees of longitude and latitude).
- For each cell, comparisons were undertaken between the grouped WW3 and altimeter waves by computing selected statistical variables (correlation coefficient, mean bias, Root Mean Square Error [RMSE], linear slope, etc.)
- These computed statistics were then associated with the centre location of each cell to enable them to be easily displayed graphically.
Fuller results including altimeter, buoy and model comparisons are available in the accompanying results document. Results comparing the altimeter-derived wind speed and Significant Wave Height (Hs) and those from each of the four hindcasts are described below:
Wind speed: As Figure 1, indicates CFSR winds are more consistent with the altimeter values than NOGAPS winds. This is expected, since NOGAPS is an operational product, and CFSR is a reanalysis:
Figure 1: Comparison of altimeter and model wind speeds
Significant Wave Height (Hs): As Figure 2 shows, in contrast to winds, when using the less accurate NOGAPS winds, the WW3 model gives Significant Wave Height values that are more consistent with altimeter values. This is not particularly surprising, since WW3 is calibrated for operational runs using winds that may be similar to NOGAPS in terms of bias.
Figure 2: Comparison of altimeter and model Significant Wave Height (Hs) values
In addition to the actual Significant Wave Height values, a range of selected statistical variables, such as Mean Bias, RMSE and Scatter Index, also confirmed the closer correlation between SWH and model results using NOGAPS.
Figure 3: Mean Bias between altimeter and model Significant Wave Height (Hs)
Figure 4: Normalised Root Mean Square Error (NRMSE) between altimeter and model Significant Wave Height (Hs)
Figure 5: Scatter Index (SI) between altimeter and model Significant Wave Height (Hs)
Based on these results the following comments can be made:
- CFSR winds appear to be more accurate than NOGAPS winds. This is expected, since NOGAPS is an operational product, and CFSR is a reanalysis.
- WW3 is more accurate using the less accurate NOGAPS winds. This is not particularly surprising, since WW3 is calibrated for operational runs using winds that may be similar to NOGAPS in terms of bias.
- Error metrics for WW3 with NOGAPS forcing is acceptable. For example, see accuracy reported by Ardhuin et al. (2010) or Chawla et al. (2011).
ARDHUIN, F., E. ROGERS, A. BABANIN, J.-F. FILIPOT, R. MAGNE, A. ROLAND, A. VAN DER WESTHUYSEN, P. QUEFFEULOU, J.-M. LEFEVRE, L. AOUF, & COLLARD, F., 2010, Semi-empirical dissipation source functions for ocean waves: Part I, definitions, calibration and validations. Journal of Physical Oceanography. 40, 1917-1941.
CHAWLA, A., D. SPINDLER, H. & TOLMAN, L., 2011, A Thirty Year Wave Hindcast Using The Latest NCEP Climate Forecast System Reanalysis Winds, 12th International Workshop on Wave Hindcasting and Forecasting, Kohala Coast, Hawaiâi, HI, 11pp., http://www.waveworkshop.org/ .
HOGAN, T.F. & ROSMOND, T.E., 1991, The description of the U.S. Navy Operational Global Atmospheric Prediction System's spectral forecast models. Monthly Weather Review, 119, 1786-1815.
SAHA, S., ET AL., 2010, The NCEP Climate Forecast System Reanalysis. Bulletin of American Meteorological Society, 91(8), 1015-1056. (DOI: 10.1175/2010BAMS3001.1)
TOLMAN, H.L., 1991, A Third generation model for wind-waves on slowly varying, unsteady, and inhomogeneous depths and currents Journal of Physical Oceanography. 21(6), 782-797.
TOLMAN, H.L., & CHALIKOV, D., 1996, Source terms in a third-generation wind wave model. Journal of Physical Oceanography, 26, 2497-2518. 5, 219-231.
TOLMAN, H. L., 2002, Alleviating the Garden Sprinkler Effect in wind wave models. Ocean Modelling, 4, 269-289.
TOLMAN, H. L., 2003, Treatment of unresolved islands and ice in wind wave models. Ocean Modelling, 5, 219-231.
TOLMAN, H.L, 2009, User Manual and System Documentation of WAVEWATCH III TM Version 3.14. NCEP Technical Note, 220 pp.