In this study, we extend the work presented in

The accuracy of spectral ocean wave models depends on the
forcing from wind, water level, currents, etc. It also depends on the source
terms and numerical methods

Theoretical models of wave-breaking dissipation have been extensively
reviewed by

However, as more physical processes are being taken into account, expressions
of

In this paper, the improvement of WBLM

According to

The white-capping dissipation expression of KOM

To reduce the energy level at high frequencies, a cumulative term is added to
the dissipation source functions. The cumulative dissipation term
(

Considering the expensive cost of WBLM code in

The unnecessary calculations in the high frequencies were reduced. The WBLM uses 10 Hz
as the maximum frequency, which is only being used for very young waves. Usually, the WBLM
does not have to solve such high frequencies when the energy is so small that their
contribution to the total wave-induced stress is negligible. Therefore, in the new code,
the WBLM only solves the active frequency range which is dynamically changing with the wave
spectrum. Although the maximum frequency is dynamically changing, all the active frequencies
are solved, so there is no influence on the result. Such an adjustment reduces approximately
half of the computation time in the idealized fetch-limited study in Sect.

The standard calculation in SWAN, a sweeping technique is used for the directional propagation of the waves, needs to be swept four times for each time step. Such a sweep is not necessary for the calculation of WBLM because the WBLM has to integrate over all directions of the spectra. Therefore, WBLM only calculates once per time step.

The calculation time of KOM, JANS, the previous WBLM of

The revised dissipation parameter (Eq.

The calibration process is carried out in three steps. In Step 1, we run the
model using the white-capping dissipation parameter as in

SWAN domain for “Reducing
the uncertainty of near-shore wind estimations using wind lidars and
mesoscale models” (RUNE) storm simulation, with domains I at 9 km resolution, II at 3 km
resolution, and III at 600 m resolution. Panels

In addition to the idealized fetch-limited study, the
revised WBLM source terms are also tested in depth-limited wave growth
experiments to check if the new source terms perform well with the
interaction of the other source terms in the wave model, including the bottom
friction and depth-induced wave-breaking dissipation source functions.
Following

In the depth-limited wave growth experiments, we take the measurements of

The new WBLM

SWAN is forced by the National Centers for Environmental Prediction (NCEP)
Climate Forecast System version 2 (CFSv2) 10 m wind

Constants used for all the experiments in Sect.

A summary of model setups for all the experiments in Sect.

Wave spectrum

The significant wave height (

Four groups of fitting parameters (FIT1, FIT2, FIT3, and FIT4) for
Eq. (

Observed (black circles) and parameterized (black line)
non-dimensional wave energy for fully developed waves in shallow water as a
function of non-dimensional depth

The four groups of parameters (FIT1 to FIT4 in Table

One-dimensional wave spectrum measured by

The effect of the ln(

Time series during two winter storms in the RUNE project.

FIT1–FIT3 tend to underestimate

Time series of

Figure

One-dimensional wave spectrum from buoy measurements at RUNE with
all available data during the two storms

The D85 spectra at short fetches (e.g., 1 km) have less energy at high
frequencies (e.g.,

Figure

The one-dimensional wave spectrum in the depth-limited experiment is further
examined after 24 h simulation in Fig.

During the two RUNE storms on 28 November 2015 and 12 August 2015, wave simulation was
done with SWAN forced by CFSv2 wind. The performance of KOM, JANS, and WBLM source terms
are evaluated with buoy measurements in terms of significant wave height

Statistics of simulated significant wave height (

Now we compare the performance of the new WBLM with KOM and JANS source
terms. For

Statistics of simulated significant wave height (

The time series of

The one-dimensional wave spectrum during the whole simulation period at the RUNE site is presented in
Fig.

This study first calibrates the WBLM wind-input and dissipation source terms in idealized fetch-limited cases and further validates the model in idealized depth-limited cases and two real storm cases. In the selected cases, it is proven that the revised WBLM source terms can be used for real cases and can provide certain wave properties better than the original ones in SWAN, such as KOM and JANS. However, two storm cases do not represent all the wave conditions in the ocean; e.g., bimodal waves, slant waves, and swells are not analyzed in detail in this study. Therefore, more comprehensive analysis and validations from different data resources such as satellite data are still necessary in further studies.

The main difference between WBLM and previous wind-input source functions in
SWAN is that the WBLM explicitly considers physics such as the growth rate
reduction of short wind waves in the presence of long waves. This effect
mainly affect the young waves. Moreover, the modification of the dissipation
coefficient is also focused on the young wind waves. Therefore, the
introduction of WBLM source terms to SWAN mainly improves the young wind
waves which are usually found in the coastal areas. This can be seen in
Fig.

As mentioned in

The WBLM source terms is found to improve the prediction of the mean period
significantly. Through analyzing the frequency spectra, it is speculated to
be caused by an improved description of the high-frequency part of the
spectrum. However, the energy from WBLM at high frequencies seems too high in
comparison to measurements. Therefore, the energy distribution in the
high-frequency range needs to be further investigated. One possible way of
reducing this overestimated energy at high frequencies is by tuning the
parameters in the cumulative dissipation source function (e.g.,

This study aims at applying the WBLM source functions of

The new pair of WBLM wind-input and dissipation source functions is calibrated
with fetch-limited and depth-limited simulations. It is proven to be able to
reproduce the benchmark wave growth curve of

The WBLM wind-input and dissipation source functions are validated with
several point measurements during two storms over the North Sea. Results show
that, in comparison to the original wind-input and dissipation source
functions in SWAN, namely

The source code for SWAN used in this study is freely
available at

The D85

Taking

The updated WBLM model was developed by JD. JD, RB, and XGL designed all the numerical experiments, which where performed by JD. RB provided the measurement data of RUNE. The manuscript was written by JD with the assistance of RB, XGL, and MK. All authors worked on the paper.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Coastal modelling and uncertainties based on CMEMS products”. It is not associated with a conference.

This project has received funding from the Danish Forskel project X-WiWa (PSO-12020), the EU CEASELESS project (H2020-EO2016-730030), and the National Key Research and Development Program of China (2017YFC1404200). We are grateful to Jean Raymond Bidlot from ECMWF, Anna Rutgersson from Uppsala University, and Henrik Bredmose from DTU Wind Energy for helpful discussions and inputs. Furthermore, we would like to thank Rogier Floors from DTU Wind Energy for providing the measurement data during Danish ForskEL project RUNE (12263). Edited by: Manuel Espino Infantes Reviewed by: one anonymous referee