# Temporal Variation of the Wave Energy Flux in Hotspot Areas of the Black Sea

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{ds}). Therefore, the model was adjusted based on these formulations and the C

_{ds}to give the best prediction performance on each grid. For these parameters, the best performances in the different grid domains were obtained as follows. The Komen [16] formulation for wind input and the Janssen [17,18] formulation for whitecapping with C

_{ds}=1.5 were implemented in the coarse domain representing the entire Black Sea. Janssen [17,18] with C

_{ds}=3 for both wind input and whitecapping was set in the fine-grid model representing the western Black Sea using boundary conditions from the main domain. Komen [16] for wind and Janssen [17,18] for whitecapping were implemented in the three sub-grids as C

_{ds}=3 for SD1 (Sinop), C

_{ds}=9 for SD2 (Filyos), and C

_{ds}=2 for SD3 (Karaburun) and based on boundary conditions from the fine grid. For sensitivity analysis, the numerical settings of each grid domain (domain size, computational 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, in each domain, different time steps were used as shown in Bingölbali et al. [13]. In all grids, in the nesting procedure, all other source terms were kept as the default in our wave model computations because they have no obvious effect. The Discrete Interaction Approximation (DIA) method by Hasselmann et al. [19] was used in the estimation of quadruplet interactions with λ=0.25 and C

_{nl4}=3×10

^{7}. The value C

_{fjon}=0.038 m

^{2}s

^{−3}for bottom friction from following JONSWAP [20] was used following the work by Zijlema et al. [21]. For depth-limited wave breaking, α=1 and γ=0.73 values were adopted following the bore-model of Battjes and Janssen [22]. The Lumped Triad Approximation (LTA) method by Eldeberky [23] was adopted for triad wave-wave interactions modelling.

_{m0}) and wave energy period (T

_{m-10}) are the fundamental parameters used in the calculation of wave power resource (P

_{w}) in deep water. The wave power (P

_{w}) is given as energy flux per unit of the wave crest length in kW per meter as:

^{3}has been chosen for the Black Sea based on spatial and temporal changes affected by salinity and temperature. The wave energy flux per unit crest length, therefore, becomes:

## 3. Results and Discussion

_{i}is the observed value, $\overline{\mathrm{O}}$ is the mean value of the observed data, P

_{i}is the predicted value, $\overline{\mathrm{P}}$ is the mean value of the predicted data, and N is the total number of data. The error statistics between hindcasts and measurements are given in Table 1. The results show that model results are well in agreement with the measurements in terms of both wave parameters at three buoy locations. Bias varies between 0.01 m and 0.03 m, and the correlation coefficient is about 0.85 for H

_{m0}. At Sinop, bias and correlation coefficient for the mean period are 0.08 s and 0.73. At Filyos, peak period is slightly underestimated. Scatter plots and time series comparison of model hindcasts against the measurements at three buoy locations in the sub-grid domains are also presented in Figure 2 and Figure 3.

## 4. Conclusion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Map of the Black Sea. The computational domain for the Simulating Waves Nearshore (SWAN) model is enclosed by the black rectangles (the nested grids). The outermost black rectangle represents the computational coarse domain. Inner black rectangle shows the boundaries of the finer grid and the innermost black rectangles are presented as the sub-grid domains SD1, SD2, and SD3; (

**b**) Mab of the sub-grid domain SD1; (

**c**) Mab of the sub-grid domain SD2; (

**d**) Mab of the sub-grid domain SD3. The measurements in white points are used in the model development, calibration, and validation. The letters GL, G, H, S, F, and K refer Gloria, Gelendzhik, Hopa, Sinop, Filyos, and Karaburun buoy locations, respectively. The positions of the stations selected in three sub-domains are shown by pink circles and color bars and color maps present bathymetries for the entire Black Sea and three sub-grids. φ and λ represent latitudes and longitudes.

**Figure 2.**Scatter plots between model hindcasts and the measurements at three buoy locations in the sub-grid domains. The data for the first six months of 1996 and 1995 at (

**a**) Sinop and (

**b**) Filyos buoy locations in SD1 and SD2 sub-grid domains, respectively, and between March and June 2004 at (

**c**) Karaburun in SD3 sub-grid domain is used. The color scheme in scatter diagrams represents the log10 of the number of entries in a square box of 0.2 m and 0.2 s for H

_{m0}and T

_{p}and T

_{m02}, respectively, 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 three lines. The solid blue line is the linear regression line according to the model y = a + bx, the red line according to the 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.

**Figure 3.**Time series comparison of model hindcasts against the measurements at three buoy locations in the sub-grid domains. The data for the first six months of 1996 and 1995 at (

**a**) Sinop and (

**b**) Filyos buoy locations in SD1 and SD2 sub-grid domains, respectively, and between March and June 2004 at (

**c**) Karaburun in SD3 sub-grid domain is used. The names of the buoy locations are shown in the title.

**Figure 4.**(

**a**) Long-term hourly variations during the day for average wave power, (

**b**) average maximum power and (

**c**) the highest maximum power values determined depending on values of maximum wave power for each year for the period 1979 to 2009 at the selected locations in SD3 (Karaburun) sub-domain.

**Figure 5.**(

**a**) Long-term hourly variations during the day for average wave power, (

**b**) average maximum power and (

**c**) the highest maximum power values determined depending on values of maximum wave power for each year for the period 1979 to 2009 at the selected locations in SD2 (Filyos) sub-domain.

**Figure 6.**(

**a**) Long-term hourly variations during the day for average wave power, (

**b**) average maximum power and (

**c**) the highest maximum power

**c)**values determined depending on values of maximum wave power for each year for the period 1979 to 2009 at the selected locations in SD1 (Sinop) sub-domain.

**Figure 7.**(

**a**) Monthly and seasonal variations for average wave power, (

**b**) average maximum power and (

**c**) the highest maximum power values determined depending on values of maximum wave power for each year for the period 1979 to 2009 at the selected locations in SD3 (Karaburun) sub-domain. In the subplots, indicating the seasonal variations (from the right side), 1 indicates Spring, 2- Summer, 3- Autumn and 4- Winter.

**Figure 8.**(

**a**) Monthly and seasonal variations for average wave power, (

**b**) average maximum power and (

**c**) the highest maximum power (

**c**) values determined depending on values of maximum wave power for each year for the period 1979 to 2009 at the selected locations in SD2 (Filyos) sub-domain. In the subplots, indicating the seasonal variations (from the right side), 1 indicates Spring, 2- Summer, 3- Autumn and 4- Winter.

**Figure 9.**(

**a**) Monthly and seasonal variations for average wave power, (

**b**) average maximum power and (

**c**) the highest maximum power (

**c**) values determined depending on values of maximum wave power for each year for the period 1979 to 2009 at the selected locations in SD1 (Sinop) sub-domain. In the subplots, indicating the seasonal variations (from the right side), 1 indicates Spring, 2- Summer, 3- Autumn and 4- Winter.

**Figure 10.**Annual maximum and average wave power variations and linear trends for selected stations in Karaburun SD3 sub-domain for the years 1979 to 2009. (

**a**) station SD3-1; (

**b**) station SD3-2; (

**c**) station SD3-3; (

**d**) station SD3-4; (

**e**) station SD3-5; (

**f**) station SD3-6.

**Figure 11.**Annual maximum and average wave power variations and linear trends for selected stations in Filyos SD2 sub-domain for the years 1979 to 2009. (

**a**) station SD2-1; (

**b**) station SD2-2; (

**c**) station SD2-3; (

**d**) station SD2-4; (

**e**) station SD2-5.

**Figure 12.**Annual maximum and average wave power variations and linear trends for selected stations in Sinop SD1 domain for the years 1979 to 2009. (

**a**) station SD1-1; (

**b**) station SD1-2; (

**c**) station SD1-3; (

**d**) station SD1-4; (

**e**) station SD1-5; (

**f**) station SD1-6.

Locations | BIAS | MAE | SI | r | |
---|---|---|---|---|---|

Sinop | H_{m0} (m) | 0.01 | 0.20 | 0.34 | 0.84 |

Filyos | −0.03 | 0.24 | 0.58 | 0.85 | |

Karaburun | −0.01 | 0.15 | 0.34 | 0.88 | |

Sinop | T_{m02} (s) | 0.08 | 0.59 | 0.19 | 0.73 |

Filyos | T_{p} (s) | −0.03 | 0.88 | 0.22 | 0.68 |

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**MDPI and ACS Style**

Akpınar, A.; Jafali, H.; Rusu, E. Temporal Variation of the Wave Energy Flux in Hotspot Areas of the Black Sea. *Sustainability* **2019**, *11*, 562.
https://doi.org/10.3390/su11030562

**AMA Style**

Akpınar A, Jafali H, Rusu E. Temporal Variation of the Wave Energy Flux in Hotspot Areas of the Black Sea. *Sustainability*. 2019; 11(3):562.
https://doi.org/10.3390/su11030562

**Chicago/Turabian Style**

Akpınar, Adem, Halid Jafali, and Eugen Rusu. 2019. "Temporal Variation of the Wave Energy Flux in Hotspot Areas of the Black Sea" *Sustainability* 11, no. 3: 562.
https://doi.org/10.3390/su11030562