SWANFAR® is tested in nonstationary (5DVar) mode with a seven-day dataset of wave spectra measured at three instrument locations near Duck, NC. Boundary spectra for the forward model estimates are obtained by applying spectra measured at the 26m-depth Datawell Waverider buoy to the entire offshore boundary of the model domain. Spectra from the 17m-depth Waverider, the 11m-depth AWAC, and the 8m-depth FRF array are assimilated simultaneously at three-hour intervals from August 20-27, 2011 (We gratefully acknowledge the U.S. Army Corps of Engineers Field Research Facility for the provision of these data). The cost function is then minimized for the entire seven-day period.
System performance is measured by (1) comparing model statistics (signficant wave height, mean period, and mean direction), and (2) computing RMS skill scores to cumulatively compare energy levels in all spectral bins. As shown for earlier test cases, the skill score is computed as follows:
in which E denotes spectral energy level in each bin, mod indicates SWANFAR® estimated values, and obs indicates SWAN-generated observations. A perfect spectral match will earn a skill score of 1, while a poor comparison can result in a score of zero or less.
Location 1 -- Waverider Buoy at 17m
The box below shows the overall improvements in estimates of basic wave statistics (i.e., reduction of model-data error) after SWANFAR® assimilation results are used to correct SWAN spectral estimates at Location 1. The three panels on the lower left of the box provide time series of each statistic, with SWAN estimates in green, observations in blue, and post-assimilation estimates in red dashed lines. Top right panel shows bathymetry map with location circled, below which are sample frequency-directional spectra from the time marked by the vertical black dashed line on the time series plots (i.e., 0621hr on 20 Aug). While SWAN achieved a negative overall skill score for the seven-day period, the SWANFAR® assimilation resulted in a significant positive value (0.38).
Location 2 -- AWAC at 11m
The box below shows the improvements in estimates of basic wave statistics at Location 2, where observed spectra were measured with an Acoustic Wave and Current Meter (AWAC). The format is the same as the box above. Post-assimilation estimates show somewhat less improvement for this location than was seen at Location 1. Nevertheless, the SWANFAR® assimilation still improved the initially negative SWAN skill score to a significant positive value (0.33).
Location 3 -- FRF 8m Array
The box below shows the improvements in estimates of basic wave statistics at Location 3, where observed spectra were measured with the FRF's 8m-depth array of pressure sensors. The format is the same as the boxes above. Post-assimilation estimates show more improvement for this location than was seen at Location 2. In the spectral comparison for 0021hr on 27 August (three panels on lower right), the SWANFAR® assimilation (bottom) includes some representation of a bimodal spectrum, which is seen in the observed spectrum (middle) but not in the original SWAN estimate (top).
Development of Error Covariances
Assimilations such as those shown above primarily affect locations close to those of the measurements, and can result in unrealistic distortions of wave energy throughout the rest of the model domain (e.g., lower left panel below). We are in the process of developing and implementing error covariances in SWANFAR®, which will ultimately enable the system to "smooth out" these distortions in both spatial and spectral dimensions. Initial results are promising.
