SWANFAR® -- Planar Beach Tests of Stationary System

(Note: The following tests are described in greater detail in: Orzech et al. (2012), A 4DVAR data assimilation system for SWAN, in Proceedings of 3rd YOUMARES Conference (Lubeck, Germany, Sept. 2012), pp. 52-53.)

SWANFAR® is tested using a twin experiment format on a planar beach with source and sink terms either neglected or activated. A variety of different boundary spectra are used in fully nonlinear forward SWAN to generate background spectra for the domain and quasi-observations at the 5 locations shown in the figure below. Mean frequencies are varied from swell to wind wave values (i.e., 0.05 - 0.15 Hz). Mean directions range from shore normal to oblique (i.e., 0 to 45 deg). Significant wave heights vary from 0.67 to 2.3 m.

In each test, the SWANFAR® system is provided with the SWAN-generated "observed" spectra at the 5 locations. The system is forced to adopt a zero-energy "first guess" spectrum at all 5 observation locations and then run to convergence, tasked with recapturing the observed quasi-spectra as closely as possible. System performance is measured by (1) comparing model statistics (signficant wave height, mean period, mean direction, and directional spread), and (2) computing RMS skill scores to cumulatively compare energy levels in all spectral bins. 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 very poor comparison can result in a score of zero or less.

Test 1 -- Homogeneous Control Case

For the control case, all nonlinear source and sink terms in SWANFAR® are turned off, resulting in a homogeneous equation for the wave action. In the figure below, the two columns of five panels on the left side show examples of SWANFAR®-estimated (left column) and observed (right column) spectra for a single test case at locations 1-5, following assimilation by the homogeneous system.

The bars in the upper right panel display RMS skill score values, averaged over all test cases, at each location. The very poor mean overall skill score, -0.98, is also displayed.

The four panels in the lower right directly compare modeled and observed spectral statistics for all homogeneous test cases in scatter plots. As can be seen, results are particularly poor for significant wave height and mean period.

Test 2 -- Fully Nonlinear, Stationary Case

In the second test set, all nonlinear source/sink terms in SWANFAR®, including wave breaking, triad and quadruplet interactions, wind forcing, and whitecapping, are activated. The system is reinitialized with the same values as in the first test and again tasked with recapturing the observed spectra. System performance is considerably improved at all five locations, as shown in the figure below.

In the two left columns, sample spectra now match measured spectra much more closely at all five locations (although some nonlinear energy transfer to higher frequencies is not recaptured by SWANFAR® at location 5). RMS skill scores are significantly higher at all five locations, and the system's mean overall skill score has jumped to 0.80. Modeled and observed spectral statistics, including wave heights and periods, are now highly correlated.