
Citation: | Fang Hou, Zhiyi Gao, Jianguo Li, Fujiang Yu. An efficient algorithm for generating a spherical multiple-cell grid[J]. Acta Oceanologica Sinica, 2022, 41(5): 41-50. doi: 10.1007/s13131-021-1947-3 |
The shortage of fossil fuel and concern of its environmental impact have forced society to seek alternative energy sources with low impact on the environment, such as renewable and sustainable energy. As a result, many maritime countries are interested in ocean energy, especially wave energy. To make full use of wave energy before any exploitation, it requires reliable quantification of wave energy potential. Numerous wave power assessments have been conducted, including global studies (e.g., Gunn and Stock-Williams, 2012; Arinaga and Cheung, 2012) and regional studies, e.g., for coastal waters of the United States (Ahn et al., 2020), Latin American and European coastal waters (Rusu and Onea, 2019), the coastal waters of China (Wan et al., 2020), the western French coast (Gonçalves et al., 2018), the Persian Gulf (Goharnejad et al., 2021), the southwestern Black Sea coast (Bingölbali et al., 2021), the Red Sea (Aboobacker et al., 2017), Thailand (Kompor et al., 2018), Indonesia (Ribal et al., 2020), and the Philippines (Quitoras et al., 2018). Globally, the theoretical wave power is estimated to be about 2.11 Tera Watt at the 95% confidence with a buffer line running 30 nautical miles (Gunn and Stock-Williams, 2012). The total theoretical wave power along the US coasts is estimated to be approximately 2 640 Tera Watt Hours/year, roughly equivalent to 65% of American annual electricity consumption (Jacobson and Hageman, 2011). China is also a country with abundant wave power energy in both offshore and nearshore regions.
In recent years, various studies have been carried out to investigate ocean energy in China. Among them, the development and utilization of wave energy are most concerned by its society. At present, more than 10 scientific research institutions and universities in China are engaged in the development of wave energy conversion devices and technology. However, the critical technologies of reliability, survivability, and the like are still the bottleneck of wave energy technology development. The distribution of wave energy resources in each sea area has its unique characteristics. As early as the 1980s, Ma and Yu (1983), Li et al. (1984), and Wang (1984) estimated the distribution of wave energy resources in the offshore area of China using climatological and synoptic methods and measured data from offshore stations.
Observed data are, however, limited in specific regions, and they lack representativeness. With further development of wave theory and numerical techniques, more and more efforts have been dedicated to wave modeling. For example, the SWAN model (Zheng et al., 2011) and WAVEWATCH-III model (Zheng and Li, 2011) were adopted to estimate the overall spatial and temporal distribution of wave energy resources in the offshore area of China. Lin et al. (2019) evaluated wave energy in the China adjacent seas based on a 20-year SWAN hindcast. Zheng et al. (2011) and Shi et al. (2017) carried out statistical analysis of wave energy distribution along China’s coasts by utilizing years of reanalysis data. Li et al. (2013), Ye et al. (2012), Zhang et al. (2012), and Wang et al. (2016a) discussed wave energy resources in local areas, including the Chengshan Cape, sea area of Fujian, offshore area of Zhejing, and sea area of Weifang based on the SWAN model, respectively.
Although many studies related to wave power have been conducted in some locations of China, comprehensive and accurate assessment of wave energy potential in the Zhe-Min coastal area has not been done. Moreover, most of these works were done using relatively low-resolution models, such as 0.5°−2.5°, which is not enough when applied to regions with complicated shorelines, such as the Zhe-Min coast. The benefit of comprehensive systematic research on wave energy resources in China is that plenty of wind and wave data have been collected at locations off China’s shoreline. This national project includes four regions: OE-W1, OE-W2, OE-W3, and OE-W4 (Fig. 1a). In this study, we carried out an analysis using OE-W2 as an example.
Our study region of OE-W2 is divided into five key areas. We will simulate each area with a high-resolution model, with attention to the complexity of shorelines (Fig. 1b). OE-W2 is located along the Zhe-Min coast in the middle of the East China Sea, with nearshore water less than 50 m deep and offshore water less than 200 m deep. Nearly every key area includes three observation stations to make sure there are good amount of data for numerical model validation. Monsoon climate of the area is characterized by the northerly wind in winter and southeasterly wind in summer.
A three-layer nesting technique was adopted to model waves in our study area using the SWAN (Fig. 1a). The parent grid spans from 10°N to 40°N, and from 110°E to 140°E, with a spatial resolution of 0.5°×0.5°. The resolution was refined to 0.1°×0.1° in the middle layer, which was a rectangle from 24.5°N to 30°N and from 118.5°E to 123.5°E. The inner layer was nested with five small child grids (D5–D9, red boxes in Fig. 1b) at the resolution of 2′×2′. These child grids correspond to the five selected key areas where wave distributions under the effects of complex shoreline, topography, islands, and wind conditions are investigated in detail.
The topography and bathymetry adopted in the model were obtained by integrating the ETOP01 product with spatial resolution of 1′ and digitalized isobaths from offshore marine maps of the China Aviation Insurance Department. By combining these two data sources, the accuracy of topography and bathymetry of offshore area is ensured.
In this study, hourly wind field from the WRF model for 10 successive years (2003–2012) was adopted. By assimilating the measured meteorological data from available offshore gauge stations, important parameters (e.g., wind speed and direction) were modified locally and fed to the wave model to improve odeling results of wave characteristics in the key study area. Comparison between the hindcast and measured data of W1, W4 and W10 (Fig. 1b) shows that the mean absolute error of wind speed is in the range of 1.46–1.73 m/s, and the error in simulated wind speed under normal weather conditions and cold waves is less than that under energetic weather conditions. According to some studies (Wang et al., 2011; Chen et al., 2014; Cai et al., 2019), simulation is considered to be good with absolute error less than 2 m/s or relative error less than 20%. The time range used to verify the accuracy of the input wind covers four seasons, including that from February 25, 2012 to March 26, 2012 and from June 08, 2013 to July 08, 2013 for W1, that from August 01, 2012 to August 30, 2012 and from September 18, 2012 to October 17, 2012 for W4, and that from June 17, 2012 to July 16, 2012 and from September 19, 2012 to October 18, 2012 for W10.
The measured parameters of waves at 13 observation locations within the model domain were collected to assess the model performance (Fig. 1b). Comparison between measured and modelled data shown in Figs 2 and 3 indicates that the simulated significant wave height and mean wave period are in good agreement with measured results. The correlation coefficients of significant wave height and mean wave period are 0.89 and 0.75, respectively, suggesting that the calculation results are reliable for further analysis.
The statistics of simulated significant wave height for the 10 successive years (Fig. 4a) show that the contours of mean annual significant wave height align mostly in parallel with the isobaths, increasing from shallow to deep area and from the northeast to southwest. The maximum annual average significant wave height is 1.47 m in the southeast of key area D9. Seasonal distribution of significant wave height is relatively consistent in three seasons (Figs 4b, d and e) and similar to that of mean annual significant wave height (Fig. 4a). Waves in summer (Fig. 4c) exhibit a different pattern from those in the other seasons and feature a maximum in the northeast and a gradual decrease toward the southwest. Affected by monsoon and tropical storms, waves are in general larger in winter and autumn, and the waves in the coastal area of Zhejiang is the smallest in spring, while the waves in the coastal area of Fujian is the smallest in summer.
Figure 5 shows the distribution of annual average period (Fig. 5a) is more even, and featured by the trend of increasing from the shallow to deep area; the average period is in the range of 4–5 s, and maximum average period is 5.2 s. Figure 5 shows that the average period is the longest in autumn (Fig. 5d), and the shortest in spring (Fig. 5b); and the average period in the north is longer than that in the south in summer (Fig. 5c), and the opposite is true in winter (Fig. 5e).
In order to investigate spatial and temporal variation of wave energy in offshore areas of Fujian and Zhejiang, power density of deep-water waves is estimated following Ma and Yu (1983):
$$ {P_{\text{W}}} = \frac{{\rho g}}{{64\pi }}{H_{\text{S}}}^2\overline T \approx 0.5{H_{\text{S}}}^2\overline T \text{,} $$ | (1) |
where
By integrating the hourly significant wave height and mean wave period of 2003–2012 simulated by the model, the corresponding wave power density
$$ {\overline P _{\rm{W}}}(i, j) = \frac{1}{N}\sum\limits_{t = 1}^N {{P_{\rm{W}}}(i,\ j,\ t)} ,$$ | (2) |
Key area | Spatial mean value$/({\rm{kW}} \cdot {{\rm{m}}^{ - 1} })$ | Maximum$/({\rm{kW}} \cdot {{\rm{m}}^{ - 1} })$ | $ {P_{\text{W}}} $≥2 ${\rm{kW}}/{\rm{m}}$ ratio/% | $ {P_{\text{W}}} $≥4 ${\rm{kW} }/{\rm{m} }$ ratio/% | $ {P_{\text{W}}} $≥6 ${\rm{kW} }/{\rm{m} }$ ratio/% |
D5 | 5.3 | 8.9 | 87.0 | 71.0 | 47.0 |
D6 | 5.7 | 10.2 | 83.7 | 70.3 | 54.0 |
D7 | 6.6 | 10.4 | 93.8 | 82.8 | 65.2 |
D8 | 6.2 | 9.5 | 89.4 | 78.8 | 61.5 |
D9 | 7.0 | 10.1 | 87.0 | 79.7 | 70.3 |
where
Utilizing the above estimates of wave power density, we obtained the distribution of average wave power density of the 10 successive years in study sea area (Fig. 6). Results indicate that the wave power density in Zhejiang coastal area is relatively small, with the average wave power density in key area D5 of 5.3 kW/m. The wave power density in Fujian coastal area, especially in the Taiwan Strait, is the largest, with the average wave power density in key area D9 of 7.0 kW/m. The area ratio of sea area with wave power density greater than 2 kW/m suggests that there are only minor differences among different sea areas. The wave power density is mostly distributed in sea area that is relatively far from the shore. The area ratio of sea area with wave power density greater than 6 kW/m in the south is larger than that in the north; in particular, in the key Area D9 of the Taiwan Strait, it is as high as 70.3% (Table 1). As classified in Zhang et al. (2014), there are four categories for the annual wave power density with value of more than 6 kW/m, between 4 kW/m and 6 kW/m, between 2 kW/m and 4 kW/m, and less than 2, respectively. The first category of > 6 kW/m is considered to be rich in wave power density. From the power abundance view point, the resrouce in Fujian coastal region is better than that in Zhejiang coastal region. According to the distribution pattern, power-rich region is located mostly in the offshore areas, such as areas near the Dachen Island, Nanji Island, Dongtaishan Island, and Dongyin Islands. In addition, some nearshore regions along the Pingtan Island and Nanri Island are also rich in wave power.
To identify the spatial extent of resource abundance based on wave energy, the availability of wave energy resource is analyzed. The criterion for potential wave energy resource is that only a certain range of wave energy is considered, since too small wave energy is not sufficient to support continuous power generation, while excessive wave energy will damage the equipment and therefore cannot be used for power generation. However, there is no standard for defining the ranges of wave parameters for wave energy resource. In this study, waves with significant wave height of 1–4 m (Wan et al., 2015) and mean wave period greater than 2.5 s are assumed to be potential wave energy resource. Using the numerical results of the 10 successive years, the duration that the wave is within the range, i.e., effective duration, was calculated for each year, and the annual average effective duration was obtained by averaging the effective duration of the 10 years. The annual average effective duration is used as an indicator to measure availability of wave energy resource.
Figure 7a shows the annual average effective duration of the sea areas, which, as a whole, tends to be longer in the open sea and shorter in the coastal area, and to be longer in the south and shorter in the north (Table 2). When analyzing distribution patterns of the annual average effective duration, 1 500 h, 3 000 h and 5 000 h are chosen as dividing lines (Zhang et al., 2014). The sea area with effective duration more than 5 000 h shows that key areas D5 and D6 (in Zhejiang coastal area) contributed nearly zero, while key area D9 (in Fujian coastal area) accounts for 65.2%. For key areas D7 and D8 around the border between Zhejiang and Fujian provinces, values of effective duration mostly fall between 1 500 h and 5 000 h.
Key area | Spatial mean value/h | Maximum/h | ≥1 500 h ratio/% | ≥3 000 h ratio/% | ≥5 000 h ratio/% |
D5 | 3 518.1 | 4 784.7 | 90.0 | 76.8 | 0.0 |
D6 | 3 705.2 | 5 009.3 | 87.1 | 75.9 | 0.2 |
D7 | 4 286.2 | 5 135.7 | 95.6 | 90.1 | 13.1 |
D8 | 4 324.8 | 5 277.7 | 95.2 | 87.0 | 34.9 |
D9 | 4 450.5 | 5 350.3 | 89.0 | 85.8 | 65.2 |
To develop and utilize the wave energy, it is also necessary to know the stability of wave power density. Stable wave energy is more conducive to acquisition and conversion by development equipment. The coefficient of variation (
$$ \begin{aligned}{\rm{COV}}(i,j) = &\frac{1}{{{{\bar P}_{\rm{W}}}(i,j)}} \sqrt {\frac{1}{{N - 1}} \left[ {\sum\limits_{t = 1}^N {{P_{\rm{W}}}^2(i,\ j,\ t)} - \frac{1}{N}{{\left( {\sum\limits_{t = 1}^N {{P_{\rm{W}}}(i,\ j,\ t)} } \right)}^2}} \right]} , \end{aligned}$$ | (3) |
where
In the development and utilization of wave energy resource, the frequency of different energy levels is an important measure for the richness of wave power resource. It is generally considered that wave power is available when its density is greater than 2 kW/m, and sea area with value of 20 kW/m is considered to be rich in wave power (Zheng et al., 2011). In this paper, statistical analysis is carried out to define domains of wave power density frequency of more than 2 and 20 kW/m, respectively (Figs 7c and d). More than 50% of the study area shows usable level frequency, which are mostly located in the northern Zhejiang offshore area and southern Fujian coastal area especially around the Pingtan and Nanri Islands. Only less than 15% of the model domain is with rich level frequency, and this percentage is under 10% in the northern Zhejiang coastal area. Wave power resource is relatively rich in the southern Fujian coastal area, with value between 10% and 15%.
The wave power density refers to the wave energy passing the wave crest in a unit length (m), and the total wave energy can be obtained by integrating along the crest line. However, in natural sea conditions, we cannot carry out integration for an individual wave. Considering the randomness and stability of waves, we choose a suitable border line to integrate wave power density, to estimate the reserve N of wave energy resource in the offshore area:
$$ N = \int {{P_{\text{W}}} \cdot {\rm{d}}L}, $$ | (4) |
where
In estimating the reserve of wave energy resource in this sea area, the border line is defined by the following two criteria: (1) in case that the distance between 20-m isobath and the shore is greater than 20 km, the 20-m isobath shall be selected; and (2) in case the distance between 20-m isobath and the shore is less than 20 km, the contour with the distance of 20 m from the shore shall be selected.
Statistical data show that the annual average total reserve of wave energy in the study area is 4.11×106 kW. In the period from June to September, the wave energy reserve in the northern areas is larger, which can be attributed to typhoon impact to a large extent. In the other months, the wave energy reserve in the southern areas is larger (Table 3). From the perspective of spatial distribution, the statistical reserve of the sea area is related to the length of wave crest line used for calculation; the energy per unit length is characterized by an increasing trend from the north to the south (Table 4).
Key area | Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sept. | Oct. | Nov. | Dec. |
D5 | 68 | 61 | 52 | 43 | 41 | 76 | 138 | 212 | 145 | 103 | 68 | 77 |
D6 | 58 | 54 | 44 | 37 | 34 | 62 | 118 | 139 | 109 | 85 | 59 | 63 |
D7 | 62 | 56 | 45 | 35 | 32 | 51 | 92 | 102 | 93 | 85 | 65 | 67 |
D8 | 85 | 72 | 56 | 38 | 32 | 40 | 62 | 75 | 89 | 107 | 91 | 90 |
D9 | 153 | 126 | 102 | 64 | 50 | 60 | 68 | 86 | 115 | 185 | 169 | 163 |
Key area | Annual average reserve of wave energy/(104 kW) | Length of wave crest line/km | Average wave power density along wave crest line/(kW∙m–1) |
D5 | 91 | 174.2 | 5.2 |
D6 | 72 | 131.0 | 5.5 |
D7 | 66 | 124.8 | 5.3 |
D8 | 70 | 117.1 | 6.0 |
D9 | 112 | 157.7 | 7.1 |
OE-W2 | 411 | 704.8 | 5.8 |
The statistical results obtained by Wang and Lu (2009) through general investigation showed that the total reserve of wave energy along Zhejiang and Fujian coasts is about 3.71×106 kW. Although their statistical method was rough estimation by replacing place with point, it is at present the most reliable one. The reserve of wave energy in OE-W2 accounts for 32% of the total value.
In recent years, estimates of the reserve of wave energy in each sea area have been provided by different methods, among them being Luo and Xia (2017) and Jiang et al. (2017), which estimated the reserve of wave energy in the East China Sea to be about 7.71×106 kW using the same method as the one used in this paper. In addition, Wang et al. (2016b) estimated the reserve of wave energy in Zhoushan sea area to be about 0.95×106kW using the 20-m isobath as the border line. Wang et al. (2013) estimated the reserve of wave energy in offshore areas of Zhejiang and Fujian to be about 1.79×106 kW and 1.67×106 kW, respectively, using the 30-m isobath as the border line.
Since the above energy reserves were estimated by different methods, it is not meaningful to carry out direct comparison. However, the estimated values show that they are of similar magnitude.
The wave energy resources in OE-W2 of the offshore areas of Fujian and Zhejiang were estimated and analyzed. The distributions of wave energy resources in the offshore areas were described in a relatively detailed manner using 10-year high-resolution numerical simulation of waves. The analysis gives the following findings:
(1) The sea area is rich in wave energy resource, which is not evenly distributed. The potential wave energy resource is up to 4.11×106 kW. In general, the potential wave energy in the south is more than that in the north. The annual average wave power density in most of the sea areas is more than 2 kW/m, but the wave energy is mainly distributed far from the shore, and it increases offshore.
(2) The surrounding of islands in the open sea is rich in wave energy resource, and the average wave power density around islands in the open sea is more than 4 kW/m. Such abundant wave energy resource provides a promising prospective for future development.
(3) As for the availability of wave energy, its distribution is consistent with the distribution of wave energy resource, and the effective duration increases from the coastal area to open sea.
(4) Due to the impact of frequent typhoons, the stability of wave energy in the study area is relatively poor. With regard to spatial distribution, the wave energy in the coastal area is more stable than that in the open sea, and wave energy in the southern part of the study region is more stable than that in northern part.
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Key area | Spatial mean value$/({\rm{kW}} \cdot {{\rm{m}}^{ - 1} })$ | Maximum$/({\rm{kW}} \cdot {{\rm{m}}^{ - 1} })$ | $ {P_{\text{W}}} $≥2 ${\rm{kW}}/{\rm{m}}$ ratio/% | $ {P_{\text{W}}} $≥4 ${\rm{kW} }/{\rm{m} }$ ratio/% | $ {P_{\text{W}}} $≥6 ${\rm{kW} }/{\rm{m} }$ ratio/% |
D5 | 5.3 | 8.9 | 87.0 | 71.0 | 47.0 |
D6 | 5.7 | 10.2 | 83.7 | 70.3 | 54.0 |
D7 | 6.6 | 10.4 | 93.8 | 82.8 | 65.2 |
D8 | 6.2 | 9.5 | 89.4 | 78.8 | 61.5 |
D9 | 7.0 | 10.1 | 87.0 | 79.7 | 70.3 |
Key area | Spatial mean value/h | Maximum/h | ≥1 500 h ratio/% | ≥3 000 h ratio/% | ≥5 000 h ratio/% |
D5 | 3 518.1 | 4 784.7 | 90.0 | 76.8 | 0.0 |
D6 | 3 705.2 | 5 009.3 | 87.1 | 75.9 | 0.2 |
D7 | 4 286.2 | 5 135.7 | 95.6 | 90.1 | 13.1 |
D8 | 4 324.8 | 5 277.7 | 95.2 | 87.0 | 34.9 |
D9 | 4 450.5 | 5 350.3 | 89.0 | 85.8 | 65.2 |
Key area | Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sept. | Oct. | Nov. | Dec. |
D5 | 68 | 61 | 52 | 43 | 41 | 76 | 138 | 212 | 145 | 103 | 68 | 77 |
D6 | 58 | 54 | 44 | 37 | 34 | 62 | 118 | 139 | 109 | 85 | 59 | 63 |
D7 | 62 | 56 | 45 | 35 | 32 | 51 | 92 | 102 | 93 | 85 | 65 | 67 |
D8 | 85 | 72 | 56 | 38 | 32 | 40 | 62 | 75 | 89 | 107 | 91 | 90 |
D9 | 153 | 126 | 102 | 64 | 50 | 60 | 68 | 86 | 115 | 185 | 169 | 163 |
Key area | Annual average reserve of wave energy/(104 kW) | Length of wave crest line/km | Average wave power density along wave crest line/(kW∙m–1) |
D5 | 91 | 174.2 | 5.2 |
D6 | 72 | 131.0 | 5.5 |
D7 | 66 | 124.8 | 5.3 |
D8 | 70 | 117.1 | 6.0 |
D9 | 112 | 157.7 | 7.1 |
OE-W2 | 411 | 704.8 | 5.8 |
Key area | Spatial mean value$/({\rm{kW}} \cdot {{\rm{m}}^{ - 1} })$ | Maximum$/({\rm{kW}} \cdot {{\rm{m}}^{ - 1} })$ | $ {P_{\text{W}}} $≥2 ${\rm{kW}}/{\rm{m}}$ ratio/% | $ {P_{\text{W}}} $≥4 ${\rm{kW} }/{\rm{m} }$ ratio/% | $ {P_{\text{W}}} $≥6 ${\rm{kW} }/{\rm{m} }$ ratio/% |
D5 | 5.3 | 8.9 | 87.0 | 71.0 | 47.0 |
D6 | 5.7 | 10.2 | 83.7 | 70.3 | 54.0 |
D7 | 6.6 | 10.4 | 93.8 | 82.8 | 65.2 |
D8 | 6.2 | 9.5 | 89.4 | 78.8 | 61.5 |
D9 | 7.0 | 10.1 | 87.0 | 79.7 | 70.3 |
Key area | Spatial mean value/h | Maximum/h | ≥1 500 h ratio/% | ≥3 000 h ratio/% | ≥5 000 h ratio/% |
D5 | 3 518.1 | 4 784.7 | 90.0 | 76.8 | 0.0 |
D6 | 3 705.2 | 5 009.3 | 87.1 | 75.9 | 0.2 |
D7 | 4 286.2 | 5 135.7 | 95.6 | 90.1 | 13.1 |
D8 | 4 324.8 | 5 277.7 | 95.2 | 87.0 | 34.9 |
D9 | 4 450.5 | 5 350.3 | 89.0 | 85.8 | 65.2 |
Key area | Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sept. | Oct. | Nov. | Dec. |
D5 | 68 | 61 | 52 | 43 | 41 | 76 | 138 | 212 | 145 | 103 | 68 | 77 |
D6 | 58 | 54 | 44 | 37 | 34 | 62 | 118 | 139 | 109 | 85 | 59 | 63 |
D7 | 62 | 56 | 45 | 35 | 32 | 51 | 92 | 102 | 93 | 85 | 65 | 67 |
D8 | 85 | 72 | 56 | 38 | 32 | 40 | 62 | 75 | 89 | 107 | 91 | 90 |
D9 | 153 | 126 | 102 | 64 | 50 | 60 | 68 | 86 | 115 | 185 | 169 | 163 |
Key area | Annual average reserve of wave energy/(104 kW) | Length of wave crest line/km | Average wave power density along wave crest line/(kW∙m–1) |
D5 | 91 | 174.2 | 5.2 |
D6 | 72 | 131.0 | 5.5 |
D7 | 66 | 124.8 | 5.3 |
D8 | 70 | 117.1 | 6.0 |
D9 | 112 | 157.7 | 7.1 |
OE-W2 | 411 | 704.8 | 5.8 |