Downscaling of wave climate in the western Black Sea

Ocean Engineering 172 (2019) 31–45

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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng

Downscaling of wave climate in the western Black Sea a

a,*

a

Bilal Bingölbali , Adem Akpınar , Halid Jafali , Gerbrant Ph Van Vledder a b c

T b,c

Uludağ University, Department of Civil Engineering, Gorukle Campus, Bursa, Turkey Delft University of Technology, Civil Engineering and Geosciences, the Netherlands VanVledder Consulting, Olst, the Netherlands

A R T I C LE I N FO

A B S T R A C T

Keywords: Waves SWAN Nesting procedure Hindcast Wave modelling South western Black sea

This study presents the south-west Black Sea wave climatology based on a downscaling approach of a long-term 31-year SWAN model wave hindcast using telescoping nested grids. At all domains the SWAN model is forced with the CFSR winds. Sensitivity tests are conducted on domain size, computational resolutions, the physical formulations and their adjustable coefficients for deep water source terms, time step of non-stationary calculation, and wind forcing for all domains. For each nested grid the physical and numerical settings were determined separately by calibration against wave buoy measurements at six locations (Gelendzhik, Hopa, Sinop, Gloria, Filyos, and Karaburun) in appropriate domains. Model validation is also conducted for the long-term data using the unused measurements in the calibration. Using the calibrated nested models, a 31-year long-term wave hindcast is conducted. Two-hourly sea state parameters of significant wave height (Hm0), wave energy period (Tm-10), spectral period (Tm01), zero-crossing period (Tm02), peak period (Tp), wind speed components, and mean wave direction (DIR) were collected over three sub-grid domains. Using this database normal and extreme wave conditions in the three sub-grid domains were determined. Finally, extreme waves with different return periods were determined and compared with those presented in the Wind and Deep Water Wave Atlas of Özhan and Abdalla (2002). The present study demonstrates the sensitivity of the SWAN model towards different GEN3 physics options and its adjustable whitecapping parameter Cds and time step of the non-stationary calculations. It is shown that the developed wave model set-up with a nested grid system performs quite satisfactorily and storms are also well-captured. This study yields higher extreme waves in the western part of our area of interest and lower extremes in the eastern part in comparison with those of the presently used Wind and Deep Water Wave Atlas.

1. Introduction Information on wind wave climate provided by wave hindcasts assists in the understanding of wave behavior that include its short-term variability, long-term trends as well as extremes. The information, which can directly be used, is very valuable when it comes to coastal design and management studies. Especially in regions where measured in-situ data is unavailable, hindcast studies can provide the information required for coastal applications such as the evaluation of wave power (Stopa et al., 2011; Reguero et al. 2012, 2015) and the design of marine structures (e.g. Gouldby et al., 2014) (Weisse et al., 2015). Despite their limited coverage, instrumental data are important for the validation of model simulated wave fields as they provide sea-state parameters directly in specific coastal locations. Altimetry data obtained by satellites (e.g. Izaguirre et al., 2011; Young et al., 2011) give information about significant wave height sea-state parameter for over 20 years. Still,

*

satellite data are not reliable in coastal regions and altimeter products do not give spectral and/or wave period information. The use of numerically generated wave hindcasts is therefore an important alternative for obtaining long-term and mostly homogeneous descriptions of the wave climate (Perez et al., 2017). The WAM (WAMDI Group, 1988), WaveWatch III® (denoted as WW3) (Tolman, 1999), and SWAN (Booij et al., 1999) are some of the most widely used third-generation wave models. These models apply full wave variance spectra and their evolution in time and space obtained by integration of the wave energy (or alternatively wave action) balance equation (Komen et al., 1994). The WAM and WW3 models have been developed particularly to simulate wave generation and evolution at ocean scales. Because of their explicit time integration they are less suited for smaller coastal scales. The SWAN model is especially suited for coastal scales because of its implicit way of solving the action balance equation but it is also able to run on large scales (Reguero et al.,

Corresponding author. E-mail address: [email protected] (A. Akpınar).

https://doi.org/10.1016/j.oceaneng.2018.11.042 Received 27 February 2018; Received in revised form 20 September 2018; Accepted 25 November 2018 0029-8018/ © 2018 Elsevier Ltd. All rights reserved.

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2012; Atan et al., 2017). For that reason, we chose the SWAN model for the transformation of wave conditions from regional to local scales. Information from global wave hindcasts is generally very accurate in the open ocean, however a finer resolution is required in coastal areas to ensure a more precise representation of the coastline and the bathymetry over continental shelf areas. And thus, it provides a better calculation of shallow water processes like bottom friction and depth induced breaking. In addition, it allows for a more accurate definition of the fetch length (Perez et al., 2017). With this in mind, this research focuses on the development of a downscaling methodology using nesting from regional to local scales in the interest of area. Previous studies for the Black Sea (Cherneva et al., 2008; Akpınar et al., 2012, 2016; Akpınar and Kömürcü, 2013; Aydoğan et al., 2013; Arkhipkin et al., 2014; Rusu et al., 2014a; Van Vledder and Akpınar, 2015; Divinsky and Kosyan, 2017) focused mostly on the entire Black Sea for different purposes whereas a limited number of studies focused on western or north-western shelf region of the Black Sea using a grid nesting procedure. Examples are studies for the prediction of extreme wave conditions (Rusu et al., 2006, 2014b), wave energy assessment (Rusu, 2009), influence of spatial wind resolution (Rusu and Butunoiu, 2014), oil spills propagation (Rusu, 2010), wind wave conditions (Valchev et al., 2010), trends in storminess (Valchev et al., 2012), critical storm thresholds for morphological changes (Trifonova et al., 2012), and storm waves (Myslenkov et al., 2016). As seen from here, some of these studies were conducted for different purposes and covering the whole Black Sea use a regular model grid structure while Aydoğan et al., (2013) and Myslenkov et al. (2016) have used an unstructured grid system. In the remaining studies (Rusu et al., 2006; Rusu, 2009, 2010; Valchev et al., 2010, 2012; Trifonova et al., 2012), a higher resolution model was developed for the coastal areas of Romania and Bulgaria based on a telescoping nested grid system. The primary aim of the present study is to develop, calibrate, and validate a high resolution nested wave prediction model focusing on the south-western coasts of the Black Sea which are considered as hotspot areas for harvesting wave energy. To our knowledge such detailed wave predictions have not been done before in this region. In addition, by performing a 31-year hindcast an accurate normal and extreme wave climate could be established in the hot-spot areas. From this point, the paper is organized in six sections. Following the introduction, Section 2 presents the application of the SWAN model to the Black Sea where the materials and methods used in this study are introduced, and Section 3 shows the development, setup and calibration of the wave hindcast model with a telescoping nested grid system. In Section 4 the verification of the developed nested model system against buoy measurements is presented. Wave characteristics along the south western coasts of the Black Sea are presented in Section 5 in terms of normal (mean Hm0, mean Tm-10, different percentile Hm0, probability of exceeding a critical Hm0, and maximum Hm0) and extreme (different return period Hm0) wave conditions. The study is completed with a discussion in Section 6 and some conclusions and recommendations in Section 7.

Fig. 1. Nested grid system (coarse, fine and 3 sub-grid domains, SD1, SD2, and SD3), the Black Sea's bathymetry, locations (black points in sub-grid domains) of measurement data (K: Karaburun, F: Filyos, S: Sinop, H: Hopa, GL: Gloria, G: Gelendzhik) taken into account in calibration and verification of SWAN model, and locations (pink points in sub-grid domains) used at analysis of extreme waves with different return periods.

from the NOAA website at a spatial resolution of 0.3125° in both directions and with a 1-h temporal resolution. Contrary to modelling studies in literature (Akpınar and Kömürcü, 2013; Aydoğan et al., 2013) which used a single domain including the entire Black Sea, in this study, multi-nested grids are preferred to obtain a high resolution and accurate wave hindcasts in the areas of interest as shown in Fig. 1. The position of the measurement locations are also shown in Fig. 1. Their locations, water depths and distance to the coast are summarized in Table 1. As can be seen in Fig. 1 the nested grid system consists of a coarse grid with a spatial resolution of about 0.06977° (approximately 7.8 km) in latitude and longitude including the entire Black Sea, a finer grid with a spatial resolution of 0.02° (about 2.2 km) focusing on the western part of the Black Sea and within this fine grid, and three sub-grids with spatial resolutions of 0.004° 0.006° (approximately 0.4–0.7 km) each focusing on an area around the measurement locations Sinop (SD1), Filyos (SD2), and Karaburun (SD3). Each nested grid obtains its boundary conditions from its host grid in the form of 2D-spectra. A key element in the downscaling approach was to calibrate each (nested) grid separately regarding its physical and numerical settings. This holds for example to the domain size, computational resolutions, the physical formulations and their adjustable coefficients for deep water source terms, time step of non-stationary calculation. Calibration of the coarse grid is performed based on the one-year measurements (1996) at the Hopa, Gelendzhik, and Sinop locations. Measurements from other years at these locations and the measurements at Gloria, Karaburun, and Filyos are used in the model validation of the coarse grid domain. Wave measurements were collected from the three directional wave buoys at Gelendzhik, Hopa and Sinop within the NATO TU-WAVES project (Özhan and Abdalla, 1998). The first measurement location was located in deep water (85 m) in front of the Russian coast near Gelendzhik. The second and the third locations were off the Turkish shore — near Hopa and close to Sinop at depths of about 100 m. The buoys

2. Application of SWAN model to the Black Sea In this study, the state-of-the-art third generation numerical wave prediction model SWAN version 41.01AB (Booij et al., 1999) is used to produce long-term wave data. The bathymetry data used is the General Bathymetric Charts of the Ocean abbreviated as GEBCO (GEBCO, 2014) with the same resolution (30 s) in latitude and longitude produced by the British Oceanographic Data Center (BODC). This data is open for use in scientific studies and was downloaded from the BODC website. For the wind input fields we used the recent atmospheric reanalysis product CFSR wind fields (Saha et al., 2010), these were found to have (presently) the highest quality for wave modelling in the Black Sea (Van Vledder and Akpınar, 2015). The u and v wind components at a height of 10 m for a long-term period of 31 years (1979–2009) were obtained

Table 1 Geographical locations of wave buoys, water depths and (shortest) distance to coast.

32

Location

Latitude (o)

Longitude (o)

Water depths (m)

Distance to coast (km)

Gelendzhik Hopa Sinop Karaburun Filyos Gloria

44°30′27″ 41°25′24″ 42°07′24″ 41°21′0.869″ 41°35′41″ 44°31′00″

37°58′42″ 41°23′00″ 35°05′12″ 28°41′27″ 32°03′29″ 29°34′00″

85 100 100 16 12.5 42

7 4.6 11.6 0.19 1.3 70

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most effective parameter for model calibration. This choice was confirmed by testing the effects of the other processes (triads, bottom friction, and depth-induced wave breaking) and their tunable parameters on model performance. Based on these tests it was found that these shallow water processes did not affect our results at the buoy locations. Due to its complexity we did not consider the quadruplet source term in our calibration. Instead, we applied it unchanged with its default setting. In addition, the numerical settings of each grid domain (spatial resolutions, frequency resolutions, directional resolutions, frequency ranges, sensitivity to choice of wind fields, etc.) were also individually tested for each grid domain. These tests showed that only the choice of a certain time step leads to improved model performance (lower error and higher correlation). Therefore, we present only the results of test runs regarding the time step and whitecapping in the following sections. Since the SWAN model contains different formulations for wind input and whitecapping, five different combinations of formulations describing these two physical processes are considered. The calibration was done pragmatically by varying the coefficients of the whitecapping source terms around their default values. Error statistics for each test run were calculated based on collocated simulated and measured data. The statistical error parameters are presented in Appendix A. The model setting with the lowest error and the highest correlation (the best-setting) is considered as the calibration result. The following combinations were considered: Komen et al. (1994) & Komen et al. (1994), Komen et al. (1994) & Janssen (1989, 1991), Janssen (1989, 1991) & Janssen (1989, 1991), Janssen (1989, 1991) & Komen et al. (1994), Yan (1987) & Van der Westhuysen et al. (2007) for wind input and whitecapping. In the following these combinations are referred to, respectively with the following abbreviations: K-K, K-J, J-J, J-K, and Y-W. It is noted that the Komen and Janssen wind input formulation are different. The default settings (in the SWAN model) whitecapping formulations of Janssen and Komen differ in the choice of the coefficient Cds1 and the Delta parameter. In practice, however, they also differ in the power of the parametric spectral tail being −4 for the Janssen formulation and −5 for the Komen formulation. This will lead to different results in case the same wind input and whitecapping parameters are used. Details of these formulations can be found in above mentioned references but also the SWAN Technical manual (SWAN team, 2016). For the default values of the whitecapping coefficient we used; 2.36 × 10−5 for the Komen formulation, 4.5 for the Janssen formulation, and 0.5 for the Westhuysen formulation. After the calibration of the source terms we determined the optimal time step of the non-stationary calculations for each grid by considering model performance. In the comparison of measured and hindcasted data were ensured that all relevant wave parameters were based on the same frequency interval (0.04–1 Hz).

are able to measure individual wave heights up to the highest encountered in the Black Sea of about 15 m (with a resolution of 1 cm) and periods between 1.6 s and 30 s. Çevik et al. (2006) deployed an ultrasonic DL2 acoustic wave sensor near Karaburun village. The sampling interval, observation time and continuous observation intervals used in the measurements of the Waves Observer were provided as 0.5 s, 10 min and 2 h, respectively. Unfortunately, we could only get wave height information for this station. Another wave measurement campaign by the General Directorate of Railways, Ports and Airports Construction of the Turkish Ministry of Transport (DLH, 1999) was carried out for a new port planned near the Filyos stream located in the western Black Sea. Wave data was collected every 2 h with a sample length of 20 min and a sampling interval of 0.5 s (i.e. a sampling frequency of 2 Hz). A long term measurement campaign has been performed at the Gloria drilling platform, which operates in the western sector of the Black Sea at a Measurements at Gloria have been obtained a 6-h resolution in water depth of about 50 m. The more detailed information on the measurement locations, characteristics of the measurements, and statistical values of measured data can be found in our previous studies (Van Vledder and Akpınar, 2015; Akpınar et al., 2014, 2016). The SWAN model for the fine grid domain is calibrated using the one-year measurements (2006) at Gloria. Boundary conditions for this grid are based on the calibrated SWAN model for the coarse grid domain (Akpınar et al., 2016). Validation of the calibrated SWAN model for the fine grid domain is carried out using the Gloria's measurements unused in the model calibration of the fine grid domain. The innermost grid domains are calibrated individually using the measured data for 1996 at Sinop, 2004 at Karaburun, and 1996 at Filyos. The boundary conditions for each sub-grid are obtained from the calibrated SWAN model for the fine grid domain. Ultimately, a calibrated SWAN model for each grid was determined. Using these models, the GEBCO bathymetry and the CFSR wind fields a 31-year long wind wave simulation was realized. All integral parameters (Hm0, Tm-10, and etc.) needed to determine the wave characteristics, wave energy generation, extreme waves, storms, and etc. are collected at a temporal resolution of 2 h at all computational grid points for the three sub-grid domains. Besides, for selected points in each grid wave data are collected at a 10 min intervals in the Sinop SD1 sub-grid, 30 min in the Filyos SD2 sub-grid, and 20 min in the Karaburun SD3 sub-grid. The SWAN model was run in the third generation and non-stationary mode with different time steps and different spatial regular spherical resolutions for each grid as outlined in Chapter 3. The directional wave variance density spectrum was discretized using 36 directional bins and 30 frequency bins logarithmically distributed between 0.04 Hz and 1.0 Hz. The numerical scheme was the BSBT (first order upwind; Backward in Space, Backward in Time) scheme. For calibrating our wave model, we used different source term formulations for wind growth and whitecapping as discussed in Chapter 3. All other source terms are kept equal in our wave model computations. Quadruplet interactions are estimated using the Discrete Interaction Approximation (DIA) by Hasselmann et al. (1985) using λ = 0.25 and Cnl4 = 3 × 107. The JONSWAP bottom friction formulation (Hasselmann et al., 1973) is used with Cfjon = 0.038 m2s-3 following Zijlema et al. (2012). Depth-limited wave breaking is modelled according to the bore-model of Battjes and Janssen (1978) using α = 1 and γ = 0.73. The triad wave-wave interactions modelled using the Lumped Triad Approximation (LTA) of Eldeberky (1996).

3.1. Coarse grid domain The calibration of the coarse grid was done in our previous study (Akpınar et al., 2016) where detailed information was given on the calibration results. However, we also give, here, some results to show the model performance of previous model. A comparison of the SI, BIAS, and RMSE values of both wave parameters Hm0 and Tm02 at the three buoy locations of Gelendzhik, Hopa, and Sinop is presented in the Fig. 2a and b. This kind of figure shows error measures for each test run such that the best performing combination can easily be identified. As can be seen, the lowest BIAS (−0.01 m), RMSE (0.28 m), MAE (0.20 m), and SI (49%) are achieved in the SWAN model with the Komen formulation for the wind input and Janssen formulation for whitecapping having a whitecapping coefficient (Cds) of 1.5. This test run has also the nearest mean Hm0 (0.57 m) to that of the measurements (0.58 m). Correlations in most of the test runs are between 0.83 and 0.85. In our previous study (Akpınar et al., 2012), the sensitivity of the time step of non-stationary computation was examined during test runs

3. Calibration method The calibration of the nested grid system is done by determining the best physical setting for each grid separately using the available measurement data within each grid. Following Moeini and Etemad-Shahidi (2007), Siadatmousavi et al. (2011), Akpınar and Ponce de Leon (2016) and Akpınar et al. (2016), we chose the whitecapping coefficient as the 33

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Fig. 3. Comparison of error parameters (SI, RMSE, and BIAS) for wave parameter estimates Hm0 and Tm-10 of SWAN model test runs created for different wind input/whitecapping formulation combinations having different values for the whitecapping coefficient at Gloria measurement location in the fine grid domain.

nest are from the calibrated coarse grid model. A comparison of the SI, BIAS, and RMSE values of all SWAN model test runs at Gloria is presented in Fig. 3. Based on the results presented here, the best SWAN setting are the Janssen formulae (1989; 1991) for both wind input and whitecapping using Cds = 3.0. This model setting has the lowest error in comparison with the others in terms of SI (39% and 32% for Hm0 and Tm02, respectively), MAE (0.37 m and 1.09 s for Hm0 and Tm02, respectively), and RMSE (0.53 m and 1.44 s for Hm0 and Tm02, respectively) etc. The optimal time interval for non-stationary computation is found to be 20 min. These results show that nested grid system causes an improvement about 14% for Hm0 and 4% for Tp for 2006 in wave hindcasts in comparison with those of the calibrated SWAN model including all the Black Sea in Akpınar et al. (2016). The percentage (%) improvement was computed based on the scatter index values. It can be expressed as a percentage and thus the % improvement is determined as the percentage by taking the differences of the scatter values obtained.

Fig. 2a. Comparison of error parameters (SI, RMSE, and BIAS) for wave parameter estimates Hm0 and Tm-10 of SWAN model test runs created for different wind input/whitecapping formulation combinations having different values for the whitecapping coefficient at Gelendzhik and Hopa measurement stations in the coarse grid domain.

3.3. Sub-grid domains The performances of the five combinations described above are examined in the individual calibrations of each sub-grid numbered SD1, SD2 and SD3. A comparison of the SI, BIAS, and RMSE values of all SWAN model test runs obtained for the three sub-grid domains is presented in the Fig. 4a and b. According to the results of the calibration process; the best SWAN model performances were obtaining using the Komen formulation for wind and the Janssen formulation for whitecapping at with Cds = 3.0 for SD1, Cds = 9.0 for SD2, and Cds = 2.0 for SD3. The effect of the time step on the model results is also investigated for all three sub-grid domains. Model runs for all three sub-grids were performed using time steps of 30 min, 20 min, 15 min, 10 min and 5 min. The results of the model runs in terms of wave parameter error statistics show that the most accurate results (lowest error) can be achieved by running the SWAN model with a time interval of 10 min in the SD1 sub-grid, a 30-min time interval in SD2, and a 20-min time interval in SD3. Although reducing the time step generally leads to more accurate results, we found different optimal time steps for each sub-grid. As we included the time step as a calibration parameter, these results suggest that errors in physical settings are compensated by errors of opposite sign in the numerical settings. An overview of the calibration for all grids is given in Table 2. The results in this table show that the nested grid system causes an improvement about 1% for both Hm0 and Tp in wave hindcasts in comparison with those of the calibrated SWAN model for the entire Black Sea in Akpınar et al. (2016). Besides, the area where the Filyos measuring station is located is physically different from the other sub-grid

Fig. 2b. Comparison of error parameters (SI, RMSE, and BIAS) for wave parameter estimates Hm0 and Tm-10 of SWAN model test runs created for different wind input/whitecapping formulation combinations having different values for the whitecapping coefficient at Sinop measurement station in the coarse grid domain.

performed for steps of 6 h, 3 h, 1 h, 30 min and 15 min and it was determined that a 30 min time step produced optimal results. Therefore, in this study, the time step for the coarse domain is chosen as 30 min. Ultimately, the best model configuration for the coarse grid domain is found as follows: Komen et al. (1994) & Janssen (1989, 1991) formulations for wind input & whitecapping processes with Cds = 1.5 and Delta = 1.0 where the time interval for non-stationary computation is 30 min and other all physical processes are active in default mode. 3.2. Fine grid domain The calibration of the intermediate Fine Grid domain is done against the measurements from the Gloria station. Boundary conditions for this 34

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areas. At Filyos station, the waves suddenly enter a shallow water from very deep water, which leads to a sudden increase in wave steepness affecting the dissipation behavior. While in other regions the waves slowly enter from deep water to shallow water. It is estimated that due to this effect, a higher whitecapping coefficient is required to be used in the sub-grid SD2 containing the Filyos station. It has been finally determined that whitecapping processes, its coefficient and the computational time step are the most effective modelling choices to improve SWAN model performance at all domains of the nested grid system. We note, however, that no statements can be made of the role of shallow water processes as our measurement location are located in deep water from a wave point of view. 4. Verification of wave hindcast model with a nested grid system Following the calibration of the nested SWAN models, a verification analysis in each grid domain is conducted against measured for a time period that is not used in the calibration to check whether any lasting improvement is achieved. This was done by examining the performance of the calibrated model in each grid domain based on the statistical error indicators (BIAS, RMSE, SI, etc.) presented in Appendix A. 4.1. Coarse grid domain The performance of the calibrated SWAN model for the coarse grid domain is determined using the measured Hm0 and Tm02 or Tp data at Gelendzhik and Hopa and also at the locations Filyos, Gloria, and Karaburun. The data of 1995 and 1996 are used in the Filyos location, the 2006–2009 data for Gloria, the 2003 and 2004 data for Karaburun, 1997–1998 and the 2000–2003 data for Gelendzhik, and the 1997–1999 data for the Hopa location. The error statistics for the simulated Hm0 and Tm02 (or Tp) data with the calibrated and the defaultsetting SWAN models as compared against the measurements at these locations are presented in Table 3. From this table, it is observed that the calibrated SWAN model for the coarse grid domain has a poor performance only at the Gloria location in the peak wave period prediction based on most error parameters except for the correlation coefficient, while the calibrated model has better results for both wave parameters at all other locations. This mismatch may be due to the different sets of locations used in the calibration and validation of SWAN model, respectively. In this coarse domain, the calibration of the SWAN model is based on the measurement locations in the eastern Black Sea (viz. Gelendzhik, Sinop, and Hopa), whereas the validation of this domain is based on measurements obtained in the western part of the Black Sea at the Gloria location. Therefore, the model for the coarse grid domain is tuned especially for the eastern part of the Black Sea. We speculate that the calibrated nested SWAN model will solve this problem and that the calibrated SWAN model with the nested grid system focusing on the western part of the Black Sea will have an improved performance. This notion is discussed in the following parts of the present study. A comparison of the coarse grid calibrated and default-setting SWAN model results against the measurements is shown in the Fig. 5a and b for all locations and for the wave parameters Hm0 and Tm02 (or Tp). The color scheme in scatter diagrams represents the log10 of the

Fig. 4a. Comparison of error parameters (SI, RMSE, and BIAS) for wave parameter estimates Hm0 and Tm-10 of SWAN model test runs developed for different wind input/whitecapping formulation combinations having different values for the whitecapping coefficient at Filyos and Sinop measurement locations for the SD2 and SD1 sub-grid domains.

Fig. 4b. Comparison of error parameters (SI, RMSE, and BIAS) for wave parameter estimates Hm0 and Tm-10 of SWAN model test runs developed for different wind input/whitecapping formulation combinations having different values for the whitecapping coefficient at Karaburun measurement location for the SD3 sub-grid domain.

Table 2 Summary of key model physics' settings for the calibrated SWAN model with nested grid system. Parameter Computational grid Boundary condition Physics

Grid resolution (X × Y) Wave growth (GEN3) Whitecapping Time step

Coarse Domain 0

Fine Domain 0

0.06977 × 0.07 No boundary Komen et al. (1994) Janssen (1989, 1991) Cds = 1.5 and Delta = 1.0 30 min.

0

Karaburun (SD3) 0

0.02 × 0.02 From coarse domain Janssen (1989, 1991) Janssen (1989, 1991) Cds = 3 20 min

35

0

0

0.006 × 0.004 From fine domain Komen et al. (1994) Janssen (1989, 1991) Cds = 2 20 min.

Filyos (SD2) 0

Sinop (SD1) 0

0.006 × 0.005 From fine domain Komen et al. (1994) Janssen (1989, 1991) Cds = 9 30 min.

0.0060 × 0.0040 From fine domain Komen et al. (1994) Janssen (1989, 1991) Cds = 3 10 min.

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Table 3 Error statistics of the calibrated and default-setting SWAN model results for both wave parameters Hm0 and Tm02 or Tpeak against the measurements for validation stage in the coarse grid domain. Location

Year

Model

Parameter

n

r

BIAS

RMSE

MAE

Mean,

SI

NMB

d

HH

Filyos

1995–1996

The calibrated Default-setting The calibrated Default-setting

Hm0 Hm0 Tpeak Tpeak

7811 7811 7811 7811

0.74 0.71 0.62 0.62

−0.13 −0.20 −0.37 −0.49

0.42 0.46 1.21 1.24

0.28 0.30 0.92 0.94

0.62 0.62 5.46 5.46

0.49 0.42 5.09 4.97

0.68 0.74 0.22 0.23

−0.21 −0.33 −0.07 −0.09

0.80 0.75 0.76 0.74

0.61 0.72 0.22 0.23

Karaburun

2003–2004

The calibrated Default-setting

Hm0 Hm0

1390 1390

0.84 0.84

−0.02 −0.12

0.29 0.32

0.20 0.21

0.75 0.75

0.73 0.63

0.38 0.42

−0.03 −0.16

0.90 0.88

0.34 0.40

Hopa

1997–1999

The calibrated Default-setting The calibrated Default-setting

Hm0 Hm0 Tm02 Tm02

4593 4593 4593 4593

0.85 0.85 0.77 0.77

−0.07 −0.15 −0.47 −0.87

0.33 0.36 0.96 1.24

0.21 0.22 0.75 1.01

0.65 0.65 4.06 4.06

0.69 0.51 3.59 3.19

0.50 0.56 0.24 0.30

−0.10 −0.22 −0.12 −0.21

0.90 0.86 0.84 0.79

0.42 0.50 0.24 0.33

Gelendzhik

1997–2003

The calibrated Default-setting The calibrated Default-setting

Hm0 Hm0 Tm02 Tm02

12075 12075 12075 12075

0.88 0.88 0.86 0.85

−0.12 −0.22 −0.40 −0.70

0.41 0.45 0.83 1.07

0.27 0.31 0.67 0.90

0.95 0.95 3.80 3.80

0.83 0.73 3.40 3.10

0.43 0.47 0.22 0.28

−0.13 −0.23 −0.10 −0.18

0.93 0.91 0.90 0.85

0.35 0.41 0.22 0.29

Gloria

2006–2009

The calibrated Default-setting The calibrated Default-setting

Hm0 Hm0 Tpeak Tpeak

5425 5425 5425 5425

0.85 0.85 0.39 0.40

−0.38 −0.50 0.28 0.06

0.67 0.76 1.63 1.59

0.47 0.55 1.26 1.22

1.31 1.31 4.81 4.81

0.93 0.81 5.09 4.87

0.51 0.58 0.34 0.33

−0.29 −0.38 0.06 0.01

0.83 0.77 0.64 0.65

0.51 0.62 0.32 0.32

obs.

Mean,

sim.

with the other locations, is much more agreeable with the measurements than the default-setting model. This illustrates the added value of model calibration for separate grids. 4.2. Fine grid domain The verification of the calibrated model in this grid domain is performed using the measurements from 2007 to 2009 at station Gloria, which are not used in calibration. The reason why the results are not verified in another location is that only one measurement location is available within this grid domain. Error statistics of the estimated Hm0 and Tp data with calibrated and default-setting SWAN models against the measured data are presented in Table 4. The results in this table show that for the intermediate grid improvements based on the calibrated in comparison with the default setting models' results are found of about 11% for Hm0 and 2% for Tp for 2007, 22% for Hm0 for 2008 and 17% for Hm0 for 2009. In comparison with those of the calibrated SWAN model, including the entire Black Sea in Akpınar et al. (2016), improvements are found of 2% for both Hm0 and Tp for 2007, 12% and 8% for Hm0 for 2008 and 2009, respectively. Scatter plots for Hm0 hindcasts from the calibrated and default-setting SWAN models against the measurements at Gloria are presented in Fig. 6. The color scheme is as in Fig. 5a and here a square box of 0.3 m is used in Fig. 6. From the above error statistics and scatter plots, a significant improvement (lower error and higher correlation) is witnessed at the Gloria location, which had poor performance in the calibrated SWAN model developed for coarse grid domain. This results confirm our expectation noted previously.

Fig. 5a. Scatter plots of wave estimates Hm0 of the calibrated (upper panel) and default-setting (lower panel) SWAN models against the measurements at buoy locations for validation stage in the coarse grid domain.

Fig. 5b. Scatter plots of wave period estimates Tm02 or Tpeak of the calibrated (upper panel) and default-setting (lower panel) SWAN models against the measurements at buoy locations for validation stage in the coarse grid domain.

4.3. Sub-grid domains The performances of the calibrated models for the three sub-grid domains are examined using the 1995 measurements of Filyos for SD2 and the 2003 measurements of the Karaburun location for the SD3 subgrid. No verification is done for SD1 sub-grid since all existing data are already used in the calibration. The error statistics of the simulated Hm0 and Tp data from the calibrated and default-setting SWAN models against the measurements for the SD2 and SD3 sub-grid domains are presented in Table 5. Scatter plots for Hm0 and Tp for both sub-grid domains are also given in Fig. 7a and b. From these graphs and error statistics, there has been significant improvements in the model

number of entries in a square box of 0.2 m in Figs. 5a and 0.3 s in Fig. 5b normalized with the log10 of the maximum number of entries in a box. In this way the clustering of data points is highlighted. Each figure contains two lines. The red line is according to the regression model y = cx and the line of perfect agreement is the dashed line. The number of samples N and the names of the buoy locations are shown in the title and in the plot. These graphs also show that the calibrated model, which has only poor performance at the Gloria location in comparison 36

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Table 4 Error statistics for calibrated and default-setting SWAN model results (for Hm0 and Tpeak) against the measurements at the Gloria station for validation stage in the fine grid domain. Location

Year

Model

Parameter

n

r

BIAS

RMSE

MAE

Mean,

SI

NMB

d

HH

Gloria

2007

The calibrated Default-setting The calibrated Default-setting

Hm0 Hm0 Tpeak Tpeak

1353 1353 1353 1353

0.76 0.77 0.39 0.38

0.01 −0.48 −0.04 0.23

0.66 0.81 1.59 1.67

0.44 0.57 1.21 1.27

1.31 1.31 4.63 4.63

1.32 0.83 4.58 4.86

0.51 0.62 0.34 0.36

0.01 −0.37 −0.01 0.05

0.87 0.74 0.64 0.63

0.42 0.66 0.34 0.35

Gloria

2008

The calibrated Default-setting The calibrated Default-setting

Hm0 Hm0 Tpeak Tpeak

1424 1424 1424 1424

0.87 0.88 0.35 0.40

−0.05 −0.54 −0.40 −0.13

0.49 0.79 1.70 1.67

0.36 0.57 1.28 1.27

1.33 1.33 4.93 4.93

1.28 0.79 4.53 4.80

0.37 0.59 0.34 0.34

−0.04 −0.40 −0.08 −0.03

0.93 0.77 0.63 0.66

0.31 0.64 0.35 0.34

Gloria

2009

The calibrated Default-setting The calibrated Default-setting

Hm0 Hm0 Tpeak Tpeak

1296 1296 1296 1296

0.80 0.78 0.28 0.29

−0.07 −0.50 −0.70 −0.40

0.53 0.74 1.84 1.83

0.38 0.55 1.42 1.42

1.23 1.23 5.13 5.13

1.16 0.74 4.44 4.74

0.43 0.60 0.36 0.36

−0.06 −0.40 −0.14 −0.08

0.89 0.73 0.57 0.58

0.38 0.67 0.38 0.37

obs.

Mean,

sim.

Fig. 7a. Scatter diagrams of Hm0 estimates from the calibrated (upper panel) and default-setting (lower panel) SWAN models against the measurements for 1995 and 2003 at Filyos and Karaburun for validation stage in the SD2 and SD3 sub-grid domains, respectively.

Fig. 6. Scatter diagrams of Hm0 and Tpeak estimates from the calibrated (left panel) and default-setting (right panel) SWAN models against the measurements between 2007 and 2009 at Gloria station for validation stage in the fine grid domain.

domain. The different physical and numerical settings also indicate that there is still no overall model setting that provides the best results in all domains.

calibrations in the sub-grids, but a significant improvement has not been achieved in Karaburun SD3 sub-grid domain for Hm0. It is observed, however, that the wave estimates realized with the calibrated nested grid system attained significant improvements. Finally, the results show that the calibration for each grid provides more accurate wave hindcast results compared to choosing one setting for whole

Table 5 Error statistics for results (Hm0 and Tpeak) of calibrated and default-setting SWAN models against 1995 measurements at Filyos and 2003 measurements at the Karaburun for validation stage in the SD2 and SD3 sub-grid domains, respectively. Domain

Location

Model

Parameter

n

r

BIAS

RMSE

MAE

Mean,

SD2

Filyos

The calibrated Default-setting The calibrated Default-setting

Hm0 Hm0 Tpeak Tpeak

3786 3786 3786 3786

0.84 0.85 0.67 0.70

−0.01 0.09 −0.01 −0.02

0.36 0.35 1.11 1.05

0.24 0.26 0.84 0.80

0.65 0.65 5.47 5.47

SD3

Karaburun

The calibrated Default-setting

Hm0 Hm0

324 324

0.70 0.70

−0.14 −0.18

0.46 0.47

0.35 0.35

0.99 0.99

37

obs.

Mean,

SI

NMB

d

HH

0.55 0.54 5.45 5.44

0.55 0.54 0.20 0.19

−0.02 0.14 0.00 0.00

0.89 0.90 0.80 0.82

0.44 0.40 0.20 0.19

0.86 0.81

0.47 0.48

−0.14 −0.18

0.82 0.81

0.45 0.47

sim.

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Fig. 7b. Scatter diagrams of Tpeak estimates from the calibrated (in the left) and default-setting (in the right) SWAN models against the measurements for 1995 at Filyos for validation stage in the SD2 sub-grid domain.

5. Wave characteristics along the south western coasts of the Black Sea The calibrated nested-grid SWAN models were run separately for all three sub-grids and simulations for a period of 31 years (1979–2009). Wind and wave parameters (wind speed components, significant wave height, peak period (Tp), energy period (Tm-10), average period (Tm02), average wave direction, etc.) are accumulated with a time resolution of 2 h at all computational grid points for each sub-grid. The computational requirements of this wave climate reconstruction are as follows. All the SWAN output data collected for the three sub-grid domains requires about 3 TB storage space. The calibrated SWAN model for the coarse and the fine grids need about 4 h and 40 h runtime for a 1-year simulation, respectively. The models are run over an 8 cores i7 processor, at 3.4 GHz. For the detailed grids a 1-year simulation takes about 140 h, 90 h and 110 h for the SD1, SD2 and SD3 grids respectively. Based on the results of the 31-year simulation for all sub-grids the following characteristics are presented: annual, seasonal and monthly average variations of significant wave height, mean wave direction, and wave energy period, spatial variations of 99% and 95% probability of non-exceedance of significant wave heights, the significant wave height being greater than 0.5 m and 4 m, and maximum values of significant wave heights during 31 years over the entire Black Sea. In addition, extreme waves with different recurrence intervals at two locations in each sub-grid domain were determined and the results are compared with those presented in the Wind and Deep Water Wave Atlas of Özhan and Abdalla (2002) which are nowadays still the main source used in the design of coastal structures in Turkey.

Fig. 8. Annual averaged mean significant wave height and mean wave direction for a period of 31 years (1979–2009) for SD1 (Sinop), SD2 (Filyos) and SD3 (Karaburun) sub-grid domains. Pink circles show the measurement locations Karaburun, Filyos, and Sinop.

Fig. 9. Seasonal averaged mean significant wave height and mean wave direction for a period of 31 years (1979–2009) for SD1 (Sinop), SD2 (Filyos) and SD3 (Karaburun) sub-grid domains. Pink circles show the measurement locations Karaburun, Filyos, and Sinop.

the domain during the spring season. The average value decreases to 0.4 m on the eastern side. During the summer season, Karaburun monitoring location is exposed to significant waves of about 0.8 m in height. This value decreases towards the western and eastern sides around this location. In the autumn and winter seasons, waves at 0.8 m and 1 m height are formed on the western side, and 0.4 m and 0.6 m height on the eastern side, respectively. Waves of 0.6 m height form in spring within the Filyos SD2 sub-grid domain along a large part of the shoreline, 0.4 m and below in summer and 0.8 m in winter. In the autumn, waves of 0.6 m in the west of the Filyos monitoring location and 0.8 m in the east are observed. From Baba Burnu Cape to the coast of Karasu in this domain, the region is exposed to the lowest wave height in all seasons. It is also be seen that in the summer, there are higher waves towards the eastern corner of the domain. Within the Sinop SD1 sub-grid domain, in the spring and summer seasons, 0.6 m waves along the entire coast line dominate and decrease in the bay east of Sinop with waves having an average height of less than 0.4 m. In the autumn and winter seasons, there are waves of 0.6 m and 0.8 m in the eastern part of the Sinop cape and in the western coast of İnce Burun cape, respectively. The rest of the coastal areas have mean significant wave heights of 1 m and 1.1 m. At Karaburun and Filyos, north easterly waves are dominant and waves originating from the North at Sinop are

5.1. Mean significant wave height (Hm0) and mean wave direction The spatial variations of long-term averaged annual, seasonal and monthly mean Hm0 and mean wave direction, which is a vectorial mean weighted with variance density (Kuik et al., 1988) are firstly presented in Figs. 8–12. As can be seen from these figures, the highest average significant wave height is approximately 1 m among all the three subgrids is inside the Karaburun SD3 sub-grid. This includes the coast from Şile, Istanbul to the coasts of Bulgaria. From Hisarköy, Bartin coast to İnebolu coast in SD2 sub-grid domain and the coastline between the capes of İnce Burun and Sinop in SD1 sub-grid domain have also high mean significant wave heights of about 1 m (Fig. 8). Waves generally come from a north-eastern direction in the Karaburun and Filyos domains and from northerly directions near Sinop. According to the spatial maps for the seasonal average significant wave height and mean wave direction represented in Fig. 9, winter is the season with the highest average significant wave heights followed by autumn. Summer and spring show very close values. Within the Karaburun SD3 sub-grid domain, the average Hm0 of 0.6 m is simulated in the western region of 38

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Fig. 10. Monthly averaged mean significant wave height and mean wave direction for a period of 31 years (1979–2009) for SD3 (Karaburun) sub-grid domain. Pink circle shows the measurement location Karaburun.

Fig. 12. Monthly averaged mean significant wave height and mean wave direction for a period of 31 years (1979–2009) for SD1 (Sinop) sub-grid domain. Pink circle shows the measurement location Sinop.

Fig. 13. Annual averaged mean wave energy period for 31 years (1979–2009) for SD1 (Sinop), SD2 (Filyos) and SD3 (Karaburun) sub-grid domains. Pink circles show the measurement locations Karaburun, Filyos, and Sinop.

Fig. 11. Monthly averaged mean significant wave height and mean wave direction for a period of 31 years (1979–2009) for SD2 (Filyos) sub-grid domain. Pink circle shows the measurement location Filyos.

5.2. Wave energy period (Tm-10) dominant in all seasons. Fig. 10 shows the spatial distributions of monthly averaged mean significant wave height and mean wave direction for Karaburun SD3 sub-grid domain. Although these spatial distribution maps are similar with that of the averaged mean annual and seasonal spatial distribution map of the entire data in Fig. 8, they differ in magnitude. The monthly maps also show more temporal variations. Further information on the monthly variations of the wave climates is presented in the Figs. 11 and 12, for Filyos SD2 and Sinop SD1 sub-grid domains, respectively.

Spatial variations of long-term averaged mean annual, seasonal and monthly wave energy periods (Tm-10) values are also determined. In the following this wave period measure is denoted as the wave period. The annual variations are presented in Fig. 13 for each of the sub-grids. According to Fig. 13, a large part of the Karaburun SD3 grid domain (from Pazarbaşı cape to the boarder of Bulgaria) is exposed to an average wave period of 4 s, while the Filyos SD2 and Sinop SD1 sub-grid domains mostly have averages of about 5 s periods. In the eastern part of the Karaburun domain, 3.5 s periods are observed in a small section and 4 s periods are seen in the bay area east of Sinop cape and in the region between Baba Burnu Cape and Alaplı Beach. According to the 39

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spatial maps (not included here to reduce the number of figures) of the seasonally averaged mean wave period determined for each sub-grid, the area from the coast of Şile to the border of Bulgaria in the spring season and the region from Akpınar coast to İğneada cape in summer, has 4s wave periods. The value decreases to 3 s towards the eastern region of SD3 sub-grid domain. In the autumn season, 4.5 s period waves dominate in the area between Akpınar and Kıyıköy coastal areas and there are areas exposed to wave periods of 3.5 s and lower toward the east. During the winter season, around the Karaburun monitoring location, there are waves with 4.5 s wave periods, whereas in the other regions of the domain, 4 s wave periods are observed. In the Filyos SD2 sub-grid domain, during the summer, autumn and winter seasons, there are waves having 4.5 s, 5 s and 5.5 s wave energy periods along the entire coastline, respectively. In the spring season, waves with 4.5 s periods in the west of Filyos monitoring location and 5 s in the east are observed. The wave period value decreases toward the far eastern part of the domain to 4.5 s. In the case of Sinop SD1 subgrid domain, most of the coastline, periods of 4 s in the spring and summer, 4.5 s in autumn and 5 s in winter seasons are dominant. In the region east of the Sinop Cape, there are waves having 3.5 s periods in the spring and summer seasons, 4 s in the autumn and 4.5 s in the winter season. In addition, in all sub-grid domains, waves with the highest wave periods occur in the winter season followed by the autumn season and the minimum conditions are in the summer season. 5.3. Spatial variations for significant wave heights with different percentiles From a coastal engineering point of view, information on the most severe sea states is relevant for the design and reliability of coastal structures. Accordingly, in addition to the first analyzed average wave conditions, yearly 95% and 99%-percentile significant wave heights based on the 31 year hindcast have been calculated and the long-term yearly averaged spatial distributions are presented in Fig. 14 for each sub-grid domain. From this figure, it is seen that Hm0 with the 95% and

Fig. 15. Probability of the significant wave height being greater than 0.5 m and 4 m based on the 31-year (1979–2009) data set for SD1 (Sinop), SD2 (Filyos) and SD3 (Karaburun) sub-grid domains.

99% percentiles in the western region of the Karaburun SD3 sub-grid domain is around 2.6 m and 4 m, respectively. The values decrease toward the East to 1.3 m and 2 m in the most eastern part of the domain. In the Filyos SD2 sub-grid domain, the 95%-percentile Hm0 is 1.6 m along the coast and increases to 2 m toward the nearshore, while at open sea this value reaches 2.5 m. The 99%-percentile Hm0 increases along the coast from 2.5 m at a small area to 3 m, 3.5 and 4 m towards the open sea. In addition, the values of 95% and 99% probability of non-exceedance of significant wave heights in the sheltered area on the western side of the cape of Baba Burnu are 1 m and 2 m, respectively. In the Sinop SD1 sub-grid domain, a very narrow area along the coast towards the west of the İnce Burun Cape and east of Sinop Cape areas has a value of about 1.5 m and a lower 95%-percentile for Hm0. It is also found that there are 2 m waves in the nearshore and 2.5 m waves toward the open sea area of the domain with a 95% non-exceedance probability. In this domain, the 99%-percentile Hm0 increased from 3 m, 3.5 m and 4 m along the coast toward the open sea. On the east side of Sinop cape in the bay region, 99%-percentile Hm0 of 2.5 m in the open sea area decreases towards the shoreline to 1 m. In all sub-grid domains, the spatial distributions for 99%-percentile Hm0 values show resemblance to those of 95%-percentile Hm0. 5.4. Spatial variations of the probability of exceeding a critical Hm0 value The probabilities of the significant wave height values being greater than a critical value (0.5 m and 4 m) for each year have been determined and the long-term yearly averaged spatial distributions are presented in Fig. 15 for each sub-grid domain. The probability of the significant wave height being higher than 0.5 m is between 60% and 65% in the Karaburun SD3 sub-grid domain from the Şile coast to the Bulgarian boarder. This value is first between 65% and 70%, then 80% toward the offshore and it decreases to 20% toward the east. The probability of Hm0 being over 4 m increases from 1% along the coast of Şile to the Bulgarian boarder to 4% towards the open sea in the same

Fig. 14. Spatial distributions of 95% and 99% percentile significant wave height based on 31-year (1979–2009) data set for SD1 (Sinop), SD2 (Filyos) and SD3 (Karaburun) sub-grid domains. 40

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Fig. 17. Extreme waves with different recurrent periods based on the 31-year hindcast at 2 locations for each sub-grid domains.

in the Sinop (SD1) sub-grid domains almost coincide. The trend lines of the extreme wave heights also show an increase from the west of Filyos to the western end of the Karaburun (SD3) sub-grid domain, and thus, waves with recurrence intervals increase from east to west. In addition, the 25, 50 and 100-year recurrence interval extreme waves determined for the stations considered in this study are compared to the values presented in the Turkish Coasts' Wind and Deep Sea Wave Atlas (Özhan and Abdalla, 2002). This atlas is currently the only source used in the design of any coastal structure in Turkey (Table 6). The results show that in the present study the values produced in Karaburun (SD3) subgrid domain are higher, and the extreme wave heights determined for the locations in the other two sub-grid domains are lower than the values presented in this atlas. 100-year recurrence interval extreme waves by Özhan and Abdalla (2002) are up to about 2.2 m lower in Karaburun (SD3) domain and up to about 1.2 m higher in the other two sub-grid domains.

Fig. 16. Spatial distribution of maximum Hm0 hindcasted during 31 years (1979–2009) for SD1 (Sinop), SD2 (Filyos) and SD3 (Karaburun) sub-grid domains.

region. Within the Filyos SD2 sub-grid domain, the probability of a significant wave height exceeding 0.5 m over the coast in the western region of the Filyos monitoring location is 50%–55% while it is 55%–60% on the eastern side. The probability of the significant wave height being greater than 4 m in this domain is less than 0.5% along the entire coast. In the Sinop SD1 sub-grid domain, the probability of the significant wave height is less than 0.5 m along the shoreline from the west of İnce Burun cape to İnebolu and in the east of Sinop cape this probability is between 50% and 55%. This value decreases in the eastern part of Sinop in the bay area toward the shoreline to 30%. The probability of the significant wave height being over 0.5 m is 60% over the whole coastal area despite being present along a narrow coastal strip in the western part of the Kerempe cape. This value is 70% toward the open sea. The probability of the significant wave height being over 4 m is less than 0.5% along the western coast of Kerempe cape despite being available on a narrow area. The value is 1.5% toward the offshore. In all sub-grid domains, the spatial distributions of the probabilities of Hm0 values being greater than 4 m and 0.5 m are almost similar however, they vary in value.

6. Discussion This study focused on the development of a wave hindcast model using a calibrated nested grid system along the south-west coasts of the Black Sea with the aim to obtain accurate long-term wave climatology. The results show that in our nested grid setup improved results were found by calibrating the whitecapping source term in connection with choosing the most appropriate wind input source term and time step for each grid system separately, leading to different values per domain. The different calibration results are a consequence of our initial choice in model setup by only considering wind input and whitecapping. Table 7 demonstrates whether there are improvements in model performance for the same years, not used in the calibration, in the same stations among the layers of the developed nested model. It appears that there is a significant improvement in the estimation of the Hm0 especially at the Gloria station as it passes from the coarse grid to the fine grid. At the coarse grid the BIAS, NMB, and HH error indicators are equal to 0.37 m, −0.29, and 0.51 while they are 0.04 m, −0.03, and 0.37 in the fine grid. In this case, we see that a slightly better performance was obtained for all of the error parameters at Filyos location and for some of the error parameters at Karaburun while at Sinop fine grid presents a slightly worse performance. However, it should be noted that we focused on Gloria location in the model calibration. Therefore, it can be expected that an unimproved performance occurs in the south western part of the Black Sea although an improved performance was obtained for some of the error indicators at some locations. Table 7 also shows that, as it passes from the fine grid to the sub-grids, an improved performance in the estimates of Hm0 was obtained at all locations in terms of all error indicators. Scatter indices were determined as 58%, 53%, and 47% in the fine grid while they are 55%, 47%, and 34% in the subgrids at Filyos, Karaburun, and Sinop, respectively. These results show that the nested SWAN model presents an improved performance. On the one hand, the most simple approach for a modeler/engineer is to apply one model for the entire Black Sea to obtain fast and practical solution

5.5. Spatial variation of maximum Hm0 Spatial distribution graphs of the maximum Hm0 values obtained with the maximum values of the significant wave heights at each grid point are separately determined for each sub-grid domains and presented in Fig. 16. From these maps, the largest estimated significant wave heights over 31 years are around 10.5 m along almost the entire coastline of Karaburun sub-grid domain (SD3). At Filyos monitoring station, the maximum Hm0 along the coastal strip was about 8.5 m in the west and 6.5 m in the east. A maximum Hm0 value of 6.5 m was estimated over almost the entire coastline of the Sinop sub-grid domain (SD1). A maximum Hm0 value of less than 5 m was, however, formed in the bay area to the east of Sinop. The value of max Hm0 decreases towards the shore in all the grids due to shallow water effects. 5.6. Extreme wave heights Lastly, extreme value analysis for the selected 2 stations in each subgrid domain was carried out using the estimated annual maximum values for 31 years at the stations based on the Gumbel distribution. Based on this method, extreme wave heights with different recurrence intervals were estimated (Fig. 17). In this figure, the fitted trend lines of extreme wave estimates at the selected stations east of Filyos (SD2) and 41

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Table 6 25-, 50-, and 100-year recurrent-period extreme waves (Hm0, m) computed at 2 locations for each sub-grid domains in the present study against that of Özhan and Abdalla (2002). 25-year

SD1-2 SD1-1 SD2-2 SD2-1 SD3-2 SD3-1

50-year

100-year

25-year

50-year

Özhan and Abdalla (2002)

The present study

Özhan and Abdalla (2002)

The present study

Özhan and Abdalla (2002)

The present study

Difference

7.50 7.64 7.47 7.84 8.42 8.68

6.72 6.71 6.41 7.68 9.42 10.87

8.15 8.19 8.05 8.53 9.26 9.50

7.18 7.18 6.91 8.34 10.27 11.66

8.80 8.74 8.62 9.21 10.08 10.31

7.63 7.65 7.41 9.00 11.12 12.44

0.78 0.93 1.07 0.16 −1.00 −2.19

0.98 1.01 1.14 0.19 −1.02 −2.16

100-year

1.17 1.09 1.21 0.21 −1.04 −2.13

coastal grids. Another limitation of the present study is the coarseness of the coastal zone schematization which does not allow for a proper assessment of shallow water processes because the buoy location are effectively in deep water. Only applying high-resolution grids can correctly represent the effects of these processes. Further nesting or further local refinement of an unstructured grid may solve that problem. On the one hand a (repeated) nesting approach requires more computational requirements than using a single grid, whereas on the other hand more accurate results can now be obtained. This implies that any user should make a careful assessment of the advantages and disadvantages of both approaches.

regarding wave hindcasts. On the other hand, developing an applying a nested SWAN model requires more time to run, but it produces more accurate results in the comparison with the results of using a single model. As our focus was on accuracy, without time constraints, we chose to develop the nested model approach. A more generic approach would be to consider also other source terms, like the one for estimating the non-linear four-wave interactions. This approach, however, is not viable as long as these interactions are crudely estimated using the DIA method. In that way deficiencies in this term are compensated by tuning of other sources (cf. Van Vledder et al., 2000), of which this study is a good example. Another interesting results of our calibration approach is that the time step was included as a calibration parameter, leading to different optimal time steps per subgrid domain. Although it is generally expected that smaller time steps lead to smaller numerical errors, we speculate that numerical errors are partly compensated by errors in the chosen physical processes. In that respect one can also consider using recently developed source term, like the so-called ST4 and ST6 (cf. Stopa et al., 2016; Rogers et al., 2014) source term packages (note the acronym ST refers to Source Term package in the WW3 model). Of these new source terms, the ST6 source term package was included in the 2017 release of SWAN version 41.20. It would be interesting to investigate the effect of using ST6 on model performance. Unstructured grids have become popular in recent years as they provide more flexibility in grid design and savings in computer requirements. In view of the previous discussion it may not be effective as such a grid requires one physical and numerical setting for the entire domain. A limitation of the present study is the scarcity of wave measurements in the Black Sea, both in time and space. To further improve any model setup for the Black Sea more buoy measurements are required, not only along the coast but also further offshore to minimize orographic effects in wind forcing. Another option is to use satellite data for calibration and validation purposes, but these are expected to be only applicable for the coarse grid with limited added value for the

7. Summary and conclusions The development of nested grid system for the south-western part of the Black Sea consisted of the following steps. Firstly, the SWAN model was calibrated per grid based on available measurements by finding the optimal settings of the wind input and whitecapping source terms, their adjustable parameters and time step of the non-stationary simulations. Secondly, the accuracy of the calibrated SWAN model was verified based on measurement data not used in the calibration. Thirdly, a 31year long-term simulation was performed providing a long-term data set containing normal and extreme climate conditions. Results obtained during model development are as follows: ✓ The SWAN model covering the entire Black Sea using the Komen formulation for wind input and the Janssen formulation for whitecapping (Cds = 1.5), is the best model configuration with the lowest error and highest correlation. ✓ The fine-grid model set to Cds = 3 using the Janssen formulae for both wind input and whitecapping processes operating with boundary conditions from the main domain has the best performance. ✓ The SWAN model using Komen for wind and Janssen formulations

Table 7 Error statistics for Hm0 results of calibrated SWAN model in different nested layers. Different colors show the model results that have to be compared within themselves.

Location

Year

n

r

BIAS

RMSE

MAE

Mean, obs.

Mean, sim.

SI

NMB

d

HH

Coarse Grid

Gloria Filyos Karaburun Sinop

2007 - 2009 1995 2003 1996

4073 3797 429 2416

0.84 0.86 0.75 0.85

0.37 0.13 0.16 0.02

0.66 0.38 0.42 0.26

0.47 0.26 0.32 0.19

1.29 0.66 0.99 0.80

0.92 0.53 0.83 0.78

0.51 0.59 0.43 0.33

-0.29 -0.19 -0.16 -0.03

0.82 0.86 0.83 0.91

0.51 0.51 0.42 0.30

Fine Grid

Gloria Filyos Karaburun Sinop

2007 - 2009 1995 2003 1996

4073 3786 324 1828

0.81 0.82 0.65 0.83

0.04 -0.09 -0.11 -0.21

0.56 0.38 0.53 0.38

0.39 0.28 0.40 0.30

1.29 0.65 0.99 0.81

1.26 0.75 1.11 1.02

0.44 0.58 0.53 0.47

-0.03 0.14 0.12 0.26

0.90 0.88 0.80 0.87

0.37 0.44 0.46 0.37

Sub-Grids

Filyos Karaburun Sinop

1995 2003 1996

3786 324 2164

0.84 0.70 0.84

0.01 0.14 0.01

0.36 0.46 0.27

0.24 0.35 0.20

0.65 0.99 0.80

0.64 0.86 0.79

0.55 0.47 0.34

-0.02 -0.14 -0.01

0.89 0.82 0.91

0.44 0.45 0.30

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Wave Atlas (Özhan and Abdalla, 2002), but they are lower in the other sub-grids.

for whitecapping as; Cds = 3 for SD1 (Sinop), Cds = 9 for SD2 (Filyos) and Cds = 2 for SD3 (Karaburun), is found to have the best performance for the three sub-grids operated by taking the boundary conditions from the fine grid. ✓ The most accurate results are achieved by operating the non-stationary computation determined to have an effect on the model performance as 10 min in the SD1 sub-grid, 30 min in the SD2 subgrid, and 20 min in the SD3 sub-grid. ✓ The calibrated nested SWAN model causes an improvement of about 14% for Hm0 and 4% for Tp for 2006 in wave hindcasts at Gloria in comparison with those of the calibrated SWAN model including all the Black Sea in Akpınar et al. (2016). It also provides an improvement of 4% in the estimated wave heights at Filyos against the calibrated SWAN model ran for all the Black Sea in Akpınar et al. (2016).

Based on the results of this study, the following conclusions are formulated: ✓ The most effective calibration ‘knob’ is the whitecapping coefficient. ✓ The use of nested grids in combination with tuning per grid provides more accurate wave hindcast results in comparison with the results of a single wave model covering the entire Black Sea. ✓ The time interval of non-stationary computations has also shown to be effective in model tuning. In general a finer temporal resolution improves model performance, but for some sub-grids this does not always lead to an optimal wave model setting. ✓ The results of the calibration show that different settings were obtained per grid. This indicates that no generic physical wave model setting (yet) exists. ✓ The present Wind and Deep Water Wave Atlas under-estimates extremes in the south west coast of the Black Sea. ✓ This study produced a huge wind and wave dataset for three subgrids focused on the south western part of the Black Sea. This can be used for a variety of different purposes, like guidelines for the development of Wave Energy Convertors and the design of coastal structures.

Results regarding wave climatology are as follows: ✓ Sub-grid domains have a long-term average of 1 m waves in the areas between Şile shore of Istanbul province and Bulgarian border, Bartın province Hisarköy shore to İnebolu shore and between capes of İnce and Sinop. ✓ Between 1979 and 2009, the season with the highest average significant wave height is winter followed by autumn. Slightly lower values are observed in summer and spring. ✓ A large part of the Karaburun grid (from Pazarbaşı cape up to the Bulgarian border) is exposed to a long-term annual average of 4 s wave energy period, while most parts of Filyos and Sinop grids have energy periods of 5 s. ✓ The values of 95% and 99% probability of non-exceedance of significant wave height are 2.6 m and 4 m, respectively in the western region of the Karaburun grid and decrease towards the east. In the Filyos and Sinop grids, the values of both parameters are the lowest along the coast and increase towards the offshore. ✓ The probability of the significant wave height being less than 0.5 m in the Karaburun grid is around 60–65% along the coast from the Şile coast to the Bulgarian border, while it has lower values along the coast in the other grid. The probability of the significant wave height being greater than 4 m is around 1% along the shore from Şile coast up to the border of Bulgaria, but less than 0.5% in other grids. ✓ The largest estimated maximum significant wave height is about 10.5 m along almost the entire coastline of Karaburun sub-grid domain (SD3) and it decreases to about 6.5 m towards to east in other two sub-grids. ✓ Different re-current periodic extreme waves produced in the present study are higher in the western part of Karaburun SD3 sub-grid in comparison with the results of the present Wind and Deep Water

Acknowledgement We would like to thank the Turkish Ministry of Transport (General Directorate of Railways, Ports and Airports Construction) which provided us with wave measurements at Filyos and Karaburun. We also express our appreciation to the NIMRD (Oceanography Department) for supplying us with wind and wave measurements at Gloria. Great acknowledgement should go to Prof. Dr. Erdal Özhan (Director of the NATO TU-WAVES) from Middle East Technical University, Ankara, Turkey, who supplied measurement data of Gelendzhik, Hopa, and Sinop, as well as the NATO Science for Stability Program, supporter of the NATO TU-WAVES project. We are grateful to Dr. Yalçın Yüksel who contributed much on Karaburun measurements, Dr Bergüzar Öztunalı Özbahçeci giving very important statement of opinion on Filyos measurements, and Dr Razvan Mateescu who helped in the provision of Gloria measurements. We also thank the anonymous reviewers for their constructive comments which helped us improving this manuscript. Last but not least, we express our great gratitude to The Scientific and Technological Research Council of Turkey (TUBITAK) which funded the research under the grant number 214M436. The study is part of master's thesis of Bilal Bingölbali.

Appendix A. Definitions of statistical error parameters Model results are evaluated using standard error statistics which include; bias (BIAS), used for the detection of systematic errors, root mean square error (RMSE) and mean absolute error (MAE) used for measuring accuracy of the data, Pearson's correlation coefficient (r) which estimates variance, the scatter index (SI) which measures relative errors, Normalized bias (NMB) which shows the model tendency to over- or underestimation relative to the measurements, the index of agreement (d) introduced by Willmott (1982) which varies from 0 to 1 with higher index values indicating that the simulated values have better agreement with the measurements, and lastly, normalized root mean square error (HH) introduced by Hanna and Heinold (1985) and used by Kazeminezhad and Siadatmousavi (2017) which is not biased toward simulations that under-estimate the average and not sensitive to the mean observed values. They are here characterized as follows: N

r =

∑i = 1 ((Pi − P )(Oi − O )) N

RMSE = [

SI =

N

[(∑i = 1 (Pi − P )2)(∑i = 1 (Oi − O )2)]1/2 1 N

(A.1)

N

∑ (Pi − Oi)2]1/2

(A.2)

i= 1

RMSE O

(A.3) 43

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Ocean Engineering 172 (2019) 31–45

bias = P − O

(A.4)

MAE =

N

1 N

∑ |Pi

− Oi |

(A.5)

i=1 N

NMB =

d = 1−

∑i = 1 (Pi − Oi) N

∑i = 1 (Oi) N ∑i = 1 N ∑i = 1

(A.6)

(Pi − Oi)2

(|Pi − O| + |Oi − O|)2

(A.7)

N

HH =

P =

O =

1 N 1 N

∑i = 1 (Pi − Oi)2 N

∑i = 1 (Pi x Oi)

(A.8)

N

∑ Pi

(A.9)

i=1 N

∑ Oi

(A.10)

i=1

where Oi is the observed value, O is the mean value of the observed data, Pi is the predicted value, P is the mean value of the predicted data, and N is the total number of data. For non-directional parameters we also computed the linear regression lines according to the statistical model

y = cx

(A.11)

for which the coefficients were estimated using a least squares analysis.

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