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Climatic trends in the fluctuations of wind waves power in the Black Sea
Journal Pre-proof Climatic trends in the fluctuations of wind waves power in the Black Sea Boris V. Divinsky, Ruben D. Kosyan PII:
S0272-7714(19)30729-2
DOI:
https://doi.org/10.1016/j.ecss.2019.106577
Reference:
YECSS 106577
To appear in:
Estuarine, Coastal and Shelf Science
Received Date: 22 July 2019 Revised Date:
15 October 2019
Accepted Date: 30 December 2019
Please cite this article as: Divinsky, B.V., Kosyan, R.D., Climatic trends in the fluctuations of wind waves power in the Black Sea, Estuarine, Coastal and Shelf Science (2020), doi: https://doi.org/10.1016/ j.ecss.2019.106577. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
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Climatic Trends in the Fluctuations of Wind Waves Power in the Black Sea Boris V. Divinsky*, Ruben D. Kosyan Shirshov Institute of Oceanology, Russian Academy of Sciences, 117997, 36 Nahimovskiy pr., Moscow, Russia *
Corresponding author: Shirshov Institute of Oceanology Russian Academy of Sciences, 117997, 36 Nahimovskiy pr., Moscow, Russia. Tel.: +7 918 4567922. E-mail address: [email protected] (B.V. Divinsky)
Abstract The research presented in this work allowed us to construct climatic fields of wind wave and swell over the entire Black Sea in the period from 1979 to 2018. The results are based on the calculation of climatic characteristics of the medium and maximum wave power. Possible components of the trend in the climatic fluctuations of the average and maximum wave powers were determined. The main research method is numerical modeling. It has been established that there are statistically significant positive trend components in the climatic fluctuations of the average and maximum surface waves. The greatest contribution to the formation of the wave climate is made by the storm conditions in January, March, and October. The increase in the power of the average waves is observed in the northeastern part of the sea (approximately 0.4 percent per year). The maximum power values tend to increase also in the northeastern region (6-7% / year), and in the southern region west (6-7% / year) and east (56% / year) of Cape Sinop. Keywords Wind waves, swell, wave climate, climatic trends, Black Sea, numerical modeling 1. Introduction Surface wind waves are considered as one of the main natural factors determining the infrastructural, ecological, and recreational potentials of marine systems. During our era of global climate change, the questions about possible climatic variations in wind wave parameters and their trends are the subject of special attention. A modern method of wind waves studying is a mathematical modeling. The modeling is based on the wave energy equation, which reflects the basic physical laws at the stage of nucleation, transformation and attenuation of surface waves. In the world practice, the most common models are WAM (WAMDI, 1988), WAVEWATCH (Tolman, 1991, 2002), SWAN (Booij et al., 1999), DHI MIKE 21 SW (DHI, 2007). The technical aspects of modeling are detailed in (WISE Group, 2007). Spectral wave models are successfully used to study wave processes in a wide range of spatio-temporal variability. A great number of studies on the wave climate of the Black Sea have been published. The researchers used various models of wind waves; they used some of the original surface wind fields and conducted numerical experiments with the tuning parameters of the models (Saprykina et al., 2019; Akpinar A., Ponce de León, 2016; Rusu, 2015; Arkhipkin et al., 2014; Akpinar A., Ihsan Kömürcü, 2013; Aydogan et al. 2013; Galabov, 2013; Polonsky et al., 2011; Rusu, 2009; Cherneva et al., 2008). The list of works, of course, is much broader, but mostly, they are regional or the analysis is based on the limited (in time) input data. We take note that several papers published in the last three years, in which the variability of wind wave parameters over a climatic period for the entire Black Sea area has been investigated. 1. The authors of the paper (Divinsky and Kosyan, 2017) analysed the spatial and temporal variability of the wave climate of the Black Sea from 1979 to 2015. Their main conclusion is as
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follows: over the past 37 years, redistribution of wave energy in the Black Sea occurred along the directions of wave propagation. In the western part of the sea, this is reflected in an increase in the share of waves of the northeastern direction with a decrease in the contribution of the northwestern waves. In the eastern part of the sea, the contribution of the wind waves of the southeastern directions increased together with the weakening of the northwestern waves. 2. The authors of (Akpınar et al., 2017), present maps of the spatial distributions of monthly mean power and coefficients of variation of wind-wave power, obtained from 1979 to 2009. An analysis of trend components was performed at selected points of the coast; no statistically significant climatic trends was detected. 3. The goal of the work (Aydoğan and Ayat, 2018) was to study the spatial variability of longperiod fluctuations of wind waves in the Black Sea (medium values of significant wave heights (SWH) as well as 95% quantile distributions of significant heights as characteristics of extreme waves). An important conclusion was made that the average annual SWH values increase in the eastern part of the Black Sea (up to 1.6% per year), while in the western part there is a negative trend (up to -1.2% per year). In the cases of strong and extreme waves, the linear trend values calculated by the authors are even greater. 4. The paper (Akpinar et al., 2019), studies the temporal variability of wave energy fluxes in the southern and southwestern parts of the sea. It is concluded that for all control points there is a decrease in average and an increase in maximum wave powers. The paper (Rusu, 2019) is devoted to studies of the wave climate of the western part of the Black Sea. The author concludes that no significant trends are detected in the power of wind wave fluctuations (for the region under consideration). Thus, the opinion about the possible trends in the long-period variability of the parameters of the wind waves in the Black Sea can hardly be seen as being established. In this relation, we note that generally the fact that there is a climate change on the planet is not disputed by anyone. The discussions are only related to the scales and signs of variability. The Black Sea, as part of the global climate system, is affected by large-scale atmospheric fluctuations. The goal of this work is to present new results of the research of the climatic fluctuations of parameters of surface waves in the Black Sea and to identify their possible trend components. The main parameter analysed here is the power of wind waves, since this power is simultaneously a function of two main integral parameters of wind waves (height and period) characterizes the energy value of storms, and also allows us to further evaluate the most promising regions in terms of possible utilization of marine energy waves. In the deep water, irregular wind wave power is estimated by the expression (Boyle, 2004): =
ℎ
≈ 0.5ℎ
,
(1)
where hs is significant wave height, te is the energetic wave period, ρ is water density, g is the acceleration due to gravity. The energetic period is defined as the period of a simple monochromatic wave with a power equivalent to the power of a given irregular wave; it is assumed equal to 0.9tp (tp is the period of the spectral peak). If the significant wave height is given in meters, the period is in seconds, the power of the waves will be expressed in kilowatts per meter of the wave front. Since the significant wave heights and periods are determined through the energy spectrum, the estimate of the wind power, of course, completely depends on the correctness and adequacy of the spectral model when reproducing all stages of wave development. Furthermore, we note one more issue. There are actually two main components in the structure of real surface waves and these are pure wind waves related to the local wind field and swell waves propagating beyond the wave generation zones (or moving with a phase velocity exceeding the wind speed). In other words, the energy spectrum of sea waves is formed as a result of the interaction of several wave systems. It is interesting to obtain separate wave statistics for each of the components of the waves. We also note that unlike the open ocean where the simultaneous presence of several different systems of swell waves is possible, the characteristics of the swell in the Black Sea are limited by the limited geographical size and
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isolation of the sea basin. Hence, we do not put forward the task of detailed elaboration and put into the concept of “swell” all surface waves, whose direction of propagation does not agree with the general direction of the wind. We formulate the main objectives of the study: • obtaining climatic fields of wind waves and swell over the entire Black Sea from 1979 to 2018; • calculation of climatic characteristics of the average and maximum wave power; • identification of possible trends in the climatic fluctuations of the average and maximum wave powers. Our main research method is numerical modeling. 2. Numerical model Mathematical modeling is a modern means of analysing parameters of surface waves. In this work, we use the MIKE 21 SW spectral wave model developed at the Danish Hydraulic Institute (DHI, 2007). The model implements the basic physical mechanisms of wind wave generation, transformation, and decay (Sorensen et al., 2004) including initial wave amplitude increase caused by surface wind, nonlinear wave-wave interactions, wave energy dissipation due to breaking, bottom friction and collapse, refraction and diffraction of the wave field, interaction of surface waves and currents. The calculated grid covers the entire basin of the Black and Azov seas; it consists of 20 thousand grid elements (Fig. 1). The morphological features of the Black Sea include the deep-water basin, which occupies the major part of the sea, and the coastal shelf. The northwestern part of the sea is characterized by a relatively wide shelf band up to 200 km wide. The southern and eastern coasts are distinguished by a steep continental slope and shelf, not exceeding 20 km. The central part of the Black Sea basin with a maximum depth of 2,212 m is a relatively flat plain. The depths off the coast of the Crimea and the coast of the Caucasus are rapidly increasing, reaching 500 m already at a distance of a few kilometers from the coastline. The shallow-water Sea of Azov (the maximum depth is about 13 m) is included in the total computational grid. However, the results obtained from this sea are not quite correct and are not considered in this study, since the presence of temporary ice cover in the winter period requires a special approach. The global wind atmospheric reanalysis of ERA-Interim, presented by the European Center for Medium-Range Forecasts (http://apps.ecmwf.int), is used as the initial wind fields. The study region is limited by coordinates: 40° N and 47° N, 27° E and 42° E. The spatial resolution of the wind fields is the same by latitude and longitude (0.25°), the time step is 3 hours. The tuning of the spectral model is optimized for the task of separating the components of the surface waves into wind waves and swell. The main characteristics of the model are as follows: • 50 spectral frequencies are distributed in the range of periods from 1.6 to 17.3 s, using the n relation f n = f 0C (f = 0.055 Hz, С = 1.05, n = 1,2,…50); 0
• the number of discrete directions is 32, i.e. the resolution of the model by directions is 11.25°; • the values of the tuning coefficients determining the energy dissipation due to whitecapping are: Cds = Cds αPM = 5.5; δ = 0.15; m = 4 • the separation of the wave components is performed using a criterion that takes into account the “age” of the waves. These settings allow us to correctly reproduce the extreme wave phenomena in a fast changing synoptic environment. These settings allow us to correctly reproduce the extreme wave phenomena in a fast changing synoptic environment. The MIKE 21 SW model was tuned using the results of various field studies conducted throughout the Black and Azov Seas in a wide range of depths and conditions *
4
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of wave formation. To verify the model, the data of experiments carried out using Datawell Waverider buoys, string wave recorders installed on stationary offshore platforms, ADCP instruments, as well as satellite measurements (altimetry) were used. The results of model verification are explained in detail in the papers (Divinsky and Kosyan, 2017; Divinsky and Kosyan, 2018). 3. Results and discussion 3.1. Climatic characteristics A large array of data was obtained as a result of simulations in the Black Sea basin consisting of fields of wind wave power and swell values with a time step of 1 h covering a period of 40 years (from 1979 to 2018), which allows us to make climatic generalisations. Spatial maps of the average Pmean and maximum Pmax wave power were constructed for further analysis. The 99% values of the power distribution quantiles are taken as the maximum values. Figures 2 and 3 show the average and maximum fields of the power of wind waves, swell, and also mixed waves over a period of 40 years (from 1979 to 2018). It follows from Fig. 2 that the climatic average power of wind waves does not exceed 6-7 kW/m. Such values were estimated in the southwestern region of the sea, adjacent to the Bosporus Strait. The average power of the swell waves is several times smaller; its highest values (in terms of averages) are of the order of 2.0-2.5 kW/m, while the region of the maximum values is shifted to the east of the southwestern region. Mixed waves are characterized by the average highest power values of 7-8 kW/m. The pattern of distribution of maximum wave powers (Fig. 3) is slightly different from the average values. As before, the southwestern region dominates with wind wave powers of the order of 1000 kW/m. In addition, a number of regions with high powers are distinguished: the region adjacent to the southern coast of Crimea; the northeastern part of the sea between the Kerch Strait and Novorossiysk; and the southeastern region of the sea offshore the Turkish coast. The spatial distribution of maximum swell waves is clearly characterized by two regions of maximum wave energy: at the southwestern and northeastern coasts. In these regions, the power of swell waves can be as high as 500 kW/m. Seasonal differences in the spatial distributions of the average and maximum surface wave power are shown in Fig. 4. As shown in from Fig. 4, in the winter months (December, January, February), almost the entire western and central parts of the sea are covered by relatively strong average waves. The strongest waves, on average, are observed in December in the southwestern region (this is related to both wind waves and swell). The calmest climatic months are from April to August. The power of the wind waves in these months rarely exceeds 3 kW/m. January is the stormiest month. In January, the power of wind waves can reach 1100 kW/m, which is an extreme value. In October, due to the restructuring of the atmospheric circulation over the sea and the frequent change of the synoptic situation, severe storms can occur throughout the sea. The previously noted formation of several regions (southwestern, the southern coast of Crimea, northeastern, and southeastern) with characteristic maximum wave power mainly occurs from November to March. At the same time, in November, the northeastern part of the sea is subjected to strong wind waves, with a relative calm region in the southwest. The distribution of swell waves is characterized by two regions of maxima: in the southwest and northeast of the sea. At the same time, the appearance of the first region was caused by the January storms, the second - by the November storms. We also took note of an important detail. The average indices of wave power yield a climatic (annual average) pattern smoothed in space. For each particular month of a particular year, the positions of the center of the maxima of the power distributions of the waves vary quite strongly. As an example, Fig. 5 shows the position of the centers of the regions covered by the highest monthly average storm activity in June (5b) and December (5e) in the period from 1979 to 2018.
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The average annual wave power in June is about 2 kW/m (Fig. 4); in December, it increases to 10-12 kW/m. Figure. 5 shows that in June the expected power of wind waves is 8-12 kW/m (Fig. 5c), and in December in some years the average power values may exceed 50 kW/m (Fig. 5f), as was the case in 1991 and 2001. In other words, in some years, surface waves may develop over the sea regions, whose power is 5-6 times greater than the average long-term values. Figure 6 shows the positions of the centers of the regions of waves with the highest monthly averages (Fig. 6a) and maximum values for the same month (Fig. 6b). Also, as can be seen in Fig. 6, the centers of the regions with the highest average waves are located mainly in the western and central parts of the sea. Storms with maximum wave power can develop in almost any region, while the impact of extreme storms is concentrated in the southwestern part (Bosporus), along the southern coast of the Crimean Peninsula, and also in the northeast and southwest of the sea. 3.2. Analysis of Trends We possess a database of wind wave and swell powers over the last 40 years. On the basis of these data we will try to answer the question: are there any interannual steady trends in the fluctuations of the power of the waves? To answer this question, we use the method described in detail in (Aziz, 2003). This procedure implements the non-parametric Mann-Kendall test. The method does not require knowledge of the law of distribution of initial values and can also take into account the irregular time scale and gaps in the available data. The method considers three basic statistical estimates: • Mann-Kendall statistics (S). It is the sum of the differences between consecutive values; • Confidence factor (CF); • Coefficient of variation (COV). A combination of these three metrics makes it possible to identify trend components in the initial data as well as to evaluate the sign and statistical significance of trends. The interpretation of the results is a probabilistic assessment of the positive (negative) trend in the fluctuations of the parameter being studied: • Increasing, S>0 and CF>95%; • Probably Increasing, S>0 and 90%0 and CF<90%) or (S≤0 and CF<90% and COV≥1); • Stable, S≤0 and CF<90% and COV<1; • Probably Decreasing, S<0 and 90%95%. The application of the terms “No Trend” and “Stable” is adopted from (Aziz, 2003). We will keep in mind that the development of uniform evaluation criteria necessarily requires assuming some fixed values of parameters S and CF. However, there are situations, in which the parameter under study is very close to its boundary value; at the same time, a general analysis (including visual analysis) makes it possible to distinguish the general trend. Therefore, the assessment of “No Trend” will be classified as “Weak (Slight) Increase”, “Stable” as “Weak (Slight) Decrease”. To smooth out the effect of possible random errors, the original data were averaged beforehand over the spatial coordinates; at the same, time a rectangular grid with a step of approximately 40 km was formed. The process of a triangulation grid into a rectangular one transforming was performed by linear interpolation methods using the DHI MIKE internal module. The results of the analysis of possible trends in the fluctuations of the average and maximum power of surface waves are shown in Fig. 7. As follows from Fig. 7, there is a pronounced tendency of increasing the average power of waves: wind waves increase in the northeastern and, partially, in the central parts of the sea; swell waves increase in the eastern part. In the field of mixed waves, the climatic increase in the
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average power in the northeastern region is observed. There are no clear trends in the western part of the sea. Over the past 40 years, statistically significant trends in the increase in the extreme power of waves have been revealed. Three zones of growth of storm activity of wind waves were found: one in the northeastern part of the sea and two in the southern part to the west and east of Cape Sinop The power of swell wave increases in the southeastern part of the sea. The power of mixed waves tends to increase in the open areas adjacent to Novorossiysk, Zonguldak, and east of Sinop. In the western part of the sea, the situation is generally stable, but we note that there is a tendency towards a decrease in the maximum power of the waves. Let us estimate the contributions of different seasons to the formation of the detected trends. Figure 8 presents the estimates of trends in the mean annual fluctuations of the average and maximum power of mixed waves by months. It follows from Fig. 8 that the storm conditions in January, March, and October make the greatest contribution to the formation of the inter-annual trend (and its sign) for the average and maximum power of waves. At the same time, in January, a decrease in storm activity is observed in the entire eastern region. In the last 40 years in March, a steady trend towards an increase in the average and maximum wave power has been observed in the eastern part of the sea. In October, such an increase is typical for almost the entire sea. Thus, the previously noted trend of inter-annual intensification of storm activity in three regions of the sea (one in the northeastern part, two in the southern, west and east of Cape Sinop) is most likely provided by the springautumn processes in the atmosphere associated with restructuring of wind fields and determining the dominance of one or another type of the atmospheric circulation. Figure 9 shows the spatial distributions of numerical estimates of trends over the Black Sea (as a percentage per year) for mixed waves. Judging from Fig. 9 and taking into account Fig. 7, we can conclude that in the northeastern part of the Black Sea, the statistically significant trends in the increase in the average wave power are about 0.4 percent per year. The maximum power values tend to increase: in the northeastern region (up to 6-7%/year) and in the southern part west (6-7%/year) and east (5-6%/year) of Cape Sinop. In the western part of the sea, the long-period fluctuations of obvious trends do not manifest themselves, but perhaps there is a definite tendency towards the weakening of extreme waves. 4. Conclusions The model calculations performed in this work resulted in the fields of the power of wind waves and swell over the entire basin of the Black Sea in the period from 1979 to 2018; we estimated the average and maximum power of wind waves, swell, and mixed waves; possible trend components in long-period oscillations of average and maximum powers were determined. The main conclusions are as follows: 1. The average annual power of wind waves in the Black Sea does not exceed 6-7 kW/m. Similar values are typical for the southwestern region of the sea adjacent to the Bosporus Strait. The average power of the swell waves is several times smaller; its highest values (in terms of averages) are of the order of 2.0-2.5 kW/m, while the region of the maximum values is shifted to the east of the southwestern region. 2. Unlike the average power of waves, the distribution of the maximum wave power in the sea is characterized by several features forming several zones of wind wave generation with extreme characteristics: the southwestern region with wind wave powers of about 1000 kW/m; the region adjacent to the southern coast of Crimea; the northeastern part of the sea between the Kerch Strait and Novorossiysk; the southeastern region of the sea. The formation of regions with characteristic maximum wave power occurs mainly from November to March. 3. The spatial distribution of the maximum swell waves is characterized by two clearly pronounced maxima: at the southwestern and northeastern coasts. In these regions, the
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power of swell waves can be as high as 500 kW/m. At the same time, the existence of the first region is caused by the January storms; the existence of the second is caused by the November storms. There is a pronounced tendency of increasing the average power of waves: wind waves increase in the northeastern and, partially, in the central parts of the sea; the swell waves increase in the eastern part. The average power of mixed waves increases in the northeastern region. There are no obvious trends in the western part of the sea. Over the past 40 years, statistically significant trends to the increase in the extreme power of waves have been observed. Three zones of growth of storm activity of wind waves are revealed: one in the northeastern part of the sea and two in the south, to the west and east of Cape Sinop The increase in the power of the swell waves is characteristic of the southeastern region. The following properties of the interseasonal fluctuations of wave power were found. The greatest contribution to the formation of interannual variability belongs to the storm conditions in January, March, and October. At the same time, in January, a decrease in storm activity is observed in the entire extreme eastern region. In the eastern part of the sea over the past 40 years a steady trend towards an increase in the average and maximum wave power was detected for the month of March. In October, such an increase is typical for almost the entire sea basin. Statistically significant trends in the increase in the average wave power by about 0.4 percent per year exist in the northeastern part of the sea. The maximum power of waves tends to increase also in the northeastern region (up to 6-7%/year), and in the south, to the west (6-7%/year) and east (5-6%/year) of Cape Sinop. In the western part of the sea, there are no statistically significant trends in climatic fluctuations of the maximum wave power, but it is possible that there is still a tendency to weaken extreme waves.
Acknowledgments This work was supported by the Russian Foundation for Basic Research, project no. 18-0580035. The computer calculations were supported by the Russian Foundation for Basic Research (project nos. 19-05-00041, 19-45-230001 and 19-45-230002). Analysis of the results was carried out within the State task program 0149-2019-0014. References 1. Akpınar, A., Bingölbalia, B., Van Vledder, G.Ph., 2017. Long-term analysis of wave power potential in the Black Sea, based on 31-year SWAN simulations. Ocean Engineering 130, 482–497. DOI: 10.1016/j.oceaneng.2016.12.023. 2. Akpinar, A., Ihsan Kömürcü, M., 2013. Assessment of wave energy resource of the Black Sea based on 15-year numerical hindcast data. Applied Energy 101, 502–512. http://dx.doi.org/10.1016/j.apenergy.2012.06.005. 3. Akpinar, A., Ponce de León, S., 2016. An assessment of the wind re-analyses in the modelling of anextreme sea state in the Black Sea. Dynamics of Atmospheres and Oceans 73, 61–75, DOI: 10.1016/j.dynatmoce.2015.12.002. 4. Akpınar, A., Jafali, H., Rusu, E., 2019. Temporal Variation of theWave Energy Flux in Hotspot Areas of the Black Sea. Sustainability 11, 562. DOI: 10.3390/su11030562. 5. Arkhipkin, V.S., Gippius, F.N., Koltermann, K.P., Surkova, G.V., 2014. Wind waves in the Black Sea: results of a hindcast study. Nat. Hazards Earth Syst. Sci. 14, 2883–2897, doi: 10.5194/nhess-14-2883-2014. 6. Aydoğan, B., Ayat, B., 2018. Spatial variability of long-term trends of significant wave heights in the Black Sea. Applied Ocean Research 79, 20–35. https://doi.org/10.1016/j.apor.2018.07.001.
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Figure captions Fig. 1. Grid for numerical simulations and bathymetric map (m) of the Black and Azov seas Fig. 2. The average power of wind seas (a), swell (b), and mixed waves (c) in 1979-2018 Fig. 3. The maximum power of wind seas (a), swell (b), and mixed waves (c) in 1979-2018 Fig. 4. Average and maximum power of wind seas (a, b), swell (c, d), and mixed waves (e, f) by months Fig. 5. Positions of the centers of highest monthly average storm activity in June (a, b, c) and December (d, e, f) Fig. 6. The geographical location of the centers of wave regions with the highest monthly average (a) and maximum (b) power values in the same month (kW/m) Fig. 7. Estimates of trend components in the long-period oscillations of the average and maximum power of wind seas (a, d), swell (b, e), and mixed waves (c, f) Fig. 8. Estimates of trends in the long-period oscillations of the average (a) and maximum (b) power of mixed waves by months Fig. 9. Estimates of linear trends of the average (a) and maximum (b) power of mixed waves
Highlights • the main goal of the research is to identify possible trends in long-period oscillations of the average and maximum wind wave power in the Black Sea; • the method of research is mathematical modeling; • the main result: there are statistically significant positive trends in climatic fluctuations of the average and maximum power of surface waves.
S0272-7714(19)30729-2
DOI:
https://doi.org/10.1016/j.ecss.2019.106577
Reference:
YECSS 106577
To appear in:
Estuarine, Coastal and Shelf Science
Received Date: 22 July 2019 Revised Date:
15 October 2019
Accepted Date: 30 December 2019
Please cite this article as: Divinsky, B.V., Kosyan, R.D., Climatic trends in the fluctuations of wind waves power in the Black Sea, Estuarine, Coastal and Shelf Science (2020), doi: https://doi.org/10.1016/ j.ecss.2019.106577. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
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Climatic Trends in the Fluctuations of Wind Waves Power in the Black Sea Boris V. Divinsky*, Ruben D. Kosyan Shirshov Institute of Oceanology, Russian Academy of Sciences, 117997, 36 Nahimovskiy pr., Moscow, Russia *
Corresponding author: Shirshov Institute of Oceanology Russian Academy of Sciences, 117997, 36 Nahimovskiy pr., Moscow, Russia. Tel.: +7 918 4567922. E-mail address: [email protected] (B.V. Divinsky)
Abstract The research presented in this work allowed us to construct climatic fields of wind wave and swell over the entire Black Sea in the period from 1979 to 2018. The results are based on the calculation of climatic characteristics of the medium and maximum wave power. Possible components of the trend in the climatic fluctuations of the average and maximum wave powers were determined. The main research method is numerical modeling. It has been established that there are statistically significant positive trend components in the climatic fluctuations of the average and maximum surface waves. The greatest contribution to the formation of the wave climate is made by the storm conditions in January, March, and October. The increase in the power of the average waves is observed in the northeastern part of the sea (approximately 0.4 percent per year). The maximum power values tend to increase also in the northeastern region (6-7% / year), and in the southern region west (6-7% / year) and east (56% / year) of Cape Sinop. Keywords Wind waves, swell, wave climate, climatic trends, Black Sea, numerical modeling 1. Introduction Surface wind waves are considered as one of the main natural factors determining the infrastructural, ecological, and recreational potentials of marine systems. During our era of global climate change, the questions about possible climatic variations in wind wave parameters and their trends are the subject of special attention. A modern method of wind waves studying is a mathematical modeling. The modeling is based on the wave energy equation, which reflects the basic physical laws at the stage of nucleation, transformation and attenuation of surface waves. In the world practice, the most common models are WAM (WAMDI, 1988), WAVEWATCH (Tolman, 1991, 2002), SWAN (Booij et al., 1999), DHI MIKE 21 SW (DHI, 2007). The technical aspects of modeling are detailed in (WISE Group, 2007). Spectral wave models are successfully used to study wave processes in a wide range of spatio-temporal variability. A great number of studies on the wave climate of the Black Sea have been published. The researchers used various models of wind waves; they used some of the original surface wind fields and conducted numerical experiments with the tuning parameters of the models (Saprykina et al., 2019; Akpinar A., Ponce de León, 2016; Rusu, 2015; Arkhipkin et al., 2014; Akpinar A., Ihsan Kömürcü, 2013; Aydogan et al. 2013; Galabov, 2013; Polonsky et al., 2011; Rusu, 2009; Cherneva et al., 2008). The list of works, of course, is much broader, but mostly, they are regional or the analysis is based on the limited (in time) input data. We take note that several papers published in the last three years, in which the variability of wind wave parameters over a climatic period for the entire Black Sea area has been investigated. 1. The authors of the paper (Divinsky and Kosyan, 2017) analysed the spatial and temporal variability of the wave climate of the Black Sea from 1979 to 2015. Their main conclusion is as
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follows: over the past 37 years, redistribution of wave energy in the Black Sea occurred along the directions of wave propagation. In the western part of the sea, this is reflected in an increase in the share of waves of the northeastern direction with a decrease in the contribution of the northwestern waves. In the eastern part of the sea, the contribution of the wind waves of the southeastern directions increased together with the weakening of the northwestern waves. 2. The authors of (Akpınar et al., 2017), present maps of the spatial distributions of monthly mean power and coefficients of variation of wind-wave power, obtained from 1979 to 2009. An analysis of trend components was performed at selected points of the coast; no statistically significant climatic trends was detected. 3. The goal of the work (Aydoğan and Ayat, 2018) was to study the spatial variability of longperiod fluctuations of wind waves in the Black Sea (medium values of significant wave heights (SWH) as well as 95% quantile distributions of significant heights as characteristics of extreme waves). An important conclusion was made that the average annual SWH values increase in the eastern part of the Black Sea (up to 1.6% per year), while in the western part there is a negative trend (up to -1.2% per year). In the cases of strong and extreme waves, the linear trend values calculated by the authors are even greater. 4. The paper (Akpinar et al., 2019), studies the temporal variability of wave energy fluxes in the southern and southwestern parts of the sea. It is concluded that for all control points there is a decrease in average and an increase in maximum wave powers. The paper (Rusu, 2019) is devoted to studies of the wave climate of the western part of the Black Sea. The author concludes that no significant trends are detected in the power of wind wave fluctuations (for the region under consideration). Thus, the opinion about the possible trends in the long-period variability of the parameters of the wind waves in the Black Sea can hardly be seen as being established. In this relation, we note that generally the fact that there is a climate change on the planet is not disputed by anyone. The discussions are only related to the scales and signs of variability. The Black Sea, as part of the global climate system, is affected by large-scale atmospheric fluctuations. The goal of this work is to present new results of the research of the climatic fluctuations of parameters of surface waves in the Black Sea and to identify their possible trend components. The main parameter analysed here is the power of wind waves, since this power is simultaneously a function of two main integral parameters of wind waves (height and period) characterizes the energy value of storms, and also allows us to further evaluate the most promising regions in terms of possible utilization of marine energy waves. In the deep water, irregular wind wave power is estimated by the expression (Boyle, 2004): =
ℎ
≈ 0.5ℎ
,
(1)
where hs is significant wave height, te is the energetic wave period, ρ is water density, g is the acceleration due to gravity. The energetic period is defined as the period of a simple monochromatic wave with a power equivalent to the power of a given irregular wave; it is assumed equal to 0.9tp (tp is the period of the spectral peak). If the significant wave height is given in meters, the period is in seconds, the power of the waves will be expressed in kilowatts per meter of the wave front. Since the significant wave heights and periods are determined through the energy spectrum, the estimate of the wind power, of course, completely depends on the correctness and adequacy of the spectral model when reproducing all stages of wave development. Furthermore, we note one more issue. There are actually two main components in the structure of real surface waves and these are pure wind waves related to the local wind field and swell waves propagating beyond the wave generation zones (or moving with a phase velocity exceeding the wind speed). In other words, the energy spectrum of sea waves is formed as a result of the interaction of several wave systems. It is interesting to obtain separate wave statistics for each of the components of the waves. We also note that unlike the open ocean where the simultaneous presence of several different systems of swell waves is possible, the characteristics of the swell in the Black Sea are limited by the limited geographical size and
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isolation of the sea basin. Hence, we do not put forward the task of detailed elaboration and put into the concept of “swell” all surface waves, whose direction of propagation does not agree with the general direction of the wind. We formulate the main objectives of the study: • obtaining climatic fields of wind waves and swell over the entire Black Sea from 1979 to 2018; • calculation of climatic characteristics of the average and maximum wave power; • identification of possible trends in the climatic fluctuations of the average and maximum wave powers. Our main research method is numerical modeling. 2. Numerical model Mathematical modeling is a modern means of analysing parameters of surface waves. In this work, we use the MIKE 21 SW spectral wave model developed at the Danish Hydraulic Institute (DHI, 2007). The model implements the basic physical mechanisms of wind wave generation, transformation, and decay (Sorensen et al., 2004) including initial wave amplitude increase caused by surface wind, nonlinear wave-wave interactions, wave energy dissipation due to breaking, bottom friction and collapse, refraction and diffraction of the wave field, interaction of surface waves and currents. The calculated grid covers the entire basin of the Black and Azov seas; it consists of 20 thousand grid elements (Fig. 1). The morphological features of the Black Sea include the deep-water basin, which occupies the major part of the sea, and the coastal shelf. The northwestern part of the sea is characterized by a relatively wide shelf band up to 200 km wide. The southern and eastern coasts are distinguished by a steep continental slope and shelf, not exceeding 20 km. The central part of the Black Sea basin with a maximum depth of 2,212 m is a relatively flat plain. The depths off the coast of the Crimea and the coast of the Caucasus are rapidly increasing, reaching 500 m already at a distance of a few kilometers from the coastline. The shallow-water Sea of Azov (the maximum depth is about 13 m) is included in the total computational grid. However, the results obtained from this sea are not quite correct and are not considered in this study, since the presence of temporary ice cover in the winter period requires a special approach. The global wind atmospheric reanalysis of ERA-Interim, presented by the European Center for Medium-Range Forecasts (http://apps.ecmwf.int), is used as the initial wind fields. The study region is limited by coordinates: 40° N and 47° N, 27° E and 42° E. The spatial resolution of the wind fields is the same by latitude and longitude (0.25°), the time step is 3 hours. The tuning of the spectral model is optimized for the task of separating the components of the surface waves into wind waves and swell. The main characteristics of the model are as follows: • 50 spectral frequencies are distributed in the range of periods from 1.6 to 17.3 s, using the n relation f n = f 0C (f = 0.055 Hz, С = 1.05, n = 1,2,…50); 0
• the number of discrete directions is 32, i.e. the resolution of the model by directions is 11.25°; • the values of the tuning coefficients determining the energy dissipation due to whitecapping are: Cds = Cds αPM = 5.5; δ = 0.15; m = 4 • the separation of the wave components is performed using a criterion that takes into account the “age” of the waves. These settings allow us to correctly reproduce the extreme wave phenomena in a fast changing synoptic environment. These settings allow us to correctly reproduce the extreme wave phenomena in a fast changing synoptic environment. The MIKE 21 SW model was tuned using the results of various field studies conducted throughout the Black and Azov Seas in a wide range of depths and conditions *
4
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of wave formation. To verify the model, the data of experiments carried out using Datawell Waverider buoys, string wave recorders installed on stationary offshore platforms, ADCP instruments, as well as satellite measurements (altimetry) were used. The results of model verification are explained in detail in the papers (Divinsky and Kosyan, 2017; Divinsky and Kosyan, 2018). 3. Results and discussion 3.1. Climatic characteristics A large array of data was obtained as a result of simulations in the Black Sea basin consisting of fields of wind wave power and swell values with a time step of 1 h covering a period of 40 years (from 1979 to 2018), which allows us to make climatic generalisations. Spatial maps of the average Pmean and maximum Pmax wave power were constructed for further analysis. The 99% values of the power distribution quantiles are taken as the maximum values. Figures 2 and 3 show the average and maximum fields of the power of wind waves, swell, and also mixed waves over a period of 40 years (from 1979 to 2018). It follows from Fig. 2 that the climatic average power of wind waves does not exceed 6-7 kW/m. Such values were estimated in the southwestern region of the sea, adjacent to the Bosporus Strait. The average power of the swell waves is several times smaller; its highest values (in terms of averages) are of the order of 2.0-2.5 kW/m, while the region of the maximum values is shifted to the east of the southwestern region. Mixed waves are characterized by the average highest power values of 7-8 kW/m. The pattern of distribution of maximum wave powers (Fig. 3) is slightly different from the average values. As before, the southwestern region dominates with wind wave powers of the order of 1000 kW/m. In addition, a number of regions with high powers are distinguished: the region adjacent to the southern coast of Crimea; the northeastern part of the sea between the Kerch Strait and Novorossiysk; and the southeastern region of the sea offshore the Turkish coast. The spatial distribution of maximum swell waves is clearly characterized by two regions of maximum wave energy: at the southwestern and northeastern coasts. In these regions, the power of swell waves can be as high as 500 kW/m. Seasonal differences in the spatial distributions of the average and maximum surface wave power are shown in Fig. 4. As shown in from Fig. 4, in the winter months (December, January, February), almost the entire western and central parts of the sea are covered by relatively strong average waves. The strongest waves, on average, are observed in December in the southwestern region (this is related to both wind waves and swell). The calmest climatic months are from April to August. The power of the wind waves in these months rarely exceeds 3 kW/m. January is the stormiest month. In January, the power of wind waves can reach 1100 kW/m, which is an extreme value. In October, due to the restructuring of the atmospheric circulation over the sea and the frequent change of the synoptic situation, severe storms can occur throughout the sea. The previously noted formation of several regions (southwestern, the southern coast of Crimea, northeastern, and southeastern) with characteristic maximum wave power mainly occurs from November to March. At the same time, in November, the northeastern part of the sea is subjected to strong wind waves, with a relative calm region in the southwest. The distribution of swell waves is characterized by two regions of maxima: in the southwest and northeast of the sea. At the same time, the appearance of the first region was caused by the January storms, the second - by the November storms. We also took note of an important detail. The average indices of wave power yield a climatic (annual average) pattern smoothed in space. For each particular month of a particular year, the positions of the center of the maxima of the power distributions of the waves vary quite strongly. As an example, Fig. 5 shows the position of the centers of the regions covered by the highest monthly average storm activity in June (5b) and December (5e) in the period from 1979 to 2018.
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The average annual wave power in June is about 2 kW/m (Fig. 4); in December, it increases to 10-12 kW/m. Figure. 5 shows that in June the expected power of wind waves is 8-12 kW/m (Fig. 5c), and in December in some years the average power values may exceed 50 kW/m (Fig. 5f), as was the case in 1991 and 2001. In other words, in some years, surface waves may develop over the sea regions, whose power is 5-6 times greater than the average long-term values. Figure 6 shows the positions of the centers of the regions of waves with the highest monthly averages (Fig. 6a) and maximum values for the same month (Fig. 6b). Also, as can be seen in Fig. 6, the centers of the regions with the highest average waves are located mainly in the western and central parts of the sea. Storms with maximum wave power can develop in almost any region, while the impact of extreme storms is concentrated in the southwestern part (Bosporus), along the southern coast of the Crimean Peninsula, and also in the northeast and southwest of the sea. 3.2. Analysis of Trends We possess a database of wind wave and swell powers over the last 40 years. On the basis of these data we will try to answer the question: are there any interannual steady trends in the fluctuations of the power of the waves? To answer this question, we use the method described in detail in (Aziz, 2003). This procedure implements the non-parametric Mann-Kendall test. The method does not require knowledge of the law of distribution of initial values and can also take into account the irregular time scale and gaps in the available data. The method considers three basic statistical estimates: • Mann-Kendall statistics (S). It is the sum of the differences between consecutive values; • Confidence factor (CF); • Coefficient of variation (COV). A combination of these three metrics makes it possible to identify trend components in the initial data as well as to evaluate the sign and statistical significance of trends. The interpretation of the results is a probabilistic assessment of the positive (negative) trend in the fluctuations of the parameter being studied: • Increasing, S>0 and CF>95%; • Probably Increasing, S>0 and 90%
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average power in the northeastern region is observed. There are no clear trends in the western part of the sea. Over the past 40 years, statistically significant trends in the increase in the extreme power of waves have been revealed. Three zones of growth of storm activity of wind waves were found: one in the northeastern part of the sea and two in the southern part to the west and east of Cape Sinop The power of swell wave increases in the southeastern part of the sea. The power of mixed waves tends to increase in the open areas adjacent to Novorossiysk, Zonguldak, and east of Sinop. In the western part of the sea, the situation is generally stable, but we note that there is a tendency towards a decrease in the maximum power of the waves. Let us estimate the contributions of different seasons to the formation of the detected trends. Figure 8 presents the estimates of trends in the mean annual fluctuations of the average and maximum power of mixed waves by months. It follows from Fig. 8 that the storm conditions in January, March, and October make the greatest contribution to the formation of the inter-annual trend (and its sign) for the average and maximum power of waves. At the same time, in January, a decrease in storm activity is observed in the entire eastern region. In the last 40 years in March, a steady trend towards an increase in the average and maximum wave power has been observed in the eastern part of the sea. In October, such an increase is typical for almost the entire sea. Thus, the previously noted trend of inter-annual intensification of storm activity in three regions of the sea (one in the northeastern part, two in the southern, west and east of Cape Sinop) is most likely provided by the springautumn processes in the atmosphere associated with restructuring of wind fields and determining the dominance of one or another type of the atmospheric circulation. Figure 9 shows the spatial distributions of numerical estimates of trends over the Black Sea (as a percentage per year) for mixed waves. Judging from Fig. 9 and taking into account Fig. 7, we can conclude that in the northeastern part of the Black Sea, the statistically significant trends in the increase in the average wave power are about 0.4 percent per year. The maximum power values tend to increase: in the northeastern region (up to 6-7%/year) and in the southern part west (6-7%/year) and east (5-6%/year) of Cape Sinop. In the western part of the sea, the long-period fluctuations of obvious trends do not manifest themselves, but perhaps there is a definite tendency towards the weakening of extreme waves. 4. Conclusions The model calculations performed in this work resulted in the fields of the power of wind waves and swell over the entire basin of the Black Sea in the period from 1979 to 2018; we estimated the average and maximum power of wind waves, swell, and mixed waves; possible trend components in long-period oscillations of average and maximum powers were determined. The main conclusions are as follows: 1. The average annual power of wind waves in the Black Sea does not exceed 6-7 kW/m. Similar values are typical for the southwestern region of the sea adjacent to the Bosporus Strait. The average power of the swell waves is several times smaller; its highest values (in terms of averages) are of the order of 2.0-2.5 kW/m, while the region of the maximum values is shifted to the east of the southwestern region. 2. Unlike the average power of waves, the distribution of the maximum wave power in the sea is characterized by several features forming several zones of wind wave generation with extreme characteristics: the southwestern region with wind wave powers of about 1000 kW/m; the region adjacent to the southern coast of Crimea; the northeastern part of the sea between the Kerch Strait and Novorossiysk; the southeastern region of the sea. The formation of regions with characteristic maximum wave power occurs mainly from November to March. 3. The spatial distribution of the maximum swell waves is characterized by two clearly pronounced maxima: at the southwestern and northeastern coasts. In these regions, the
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power of swell waves can be as high as 500 kW/m. At the same time, the existence of the first region is caused by the January storms; the existence of the second is caused by the November storms. There is a pronounced tendency of increasing the average power of waves: wind waves increase in the northeastern and, partially, in the central parts of the sea; the swell waves increase in the eastern part. The average power of mixed waves increases in the northeastern region. There are no obvious trends in the western part of the sea. Over the past 40 years, statistically significant trends to the increase in the extreme power of waves have been observed. Three zones of growth of storm activity of wind waves are revealed: one in the northeastern part of the sea and two in the south, to the west and east of Cape Sinop The increase in the power of the swell waves is characteristic of the southeastern region. The following properties of the interseasonal fluctuations of wave power were found. The greatest contribution to the formation of interannual variability belongs to the storm conditions in January, March, and October. At the same time, in January, a decrease in storm activity is observed in the entire extreme eastern region. In the eastern part of the sea over the past 40 years a steady trend towards an increase in the average and maximum wave power was detected for the month of March. In October, such an increase is typical for almost the entire sea basin. Statistically significant trends in the increase in the average wave power by about 0.4 percent per year exist in the northeastern part of the sea. The maximum power of waves tends to increase also in the northeastern region (up to 6-7%/year), and in the south, to the west (6-7%/year) and east (5-6%/year) of Cape Sinop. In the western part of the sea, there are no statistically significant trends in climatic fluctuations of the maximum wave power, but it is possible that there is still a tendency to weaken extreme waves.
Acknowledgments This work was supported by the Russian Foundation for Basic Research, project no. 18-0580035. The computer calculations were supported by the Russian Foundation for Basic Research (project nos. 19-05-00041, 19-45-230001 and 19-45-230002). Analysis of the results was carried out within the State task program 0149-2019-0014. References 1. Akpınar, A., Bingölbalia, B., Van Vledder, G.Ph., 2017. Long-term analysis of wave power potential in the Black Sea, based on 31-year SWAN simulations. Ocean Engineering 130, 482–497. DOI: 10.1016/j.oceaneng.2016.12.023. 2. Akpinar, A., Ihsan Kömürcü, M., 2013. Assessment of wave energy resource of the Black Sea based on 15-year numerical hindcast data. Applied Energy 101, 502–512. http://dx.doi.org/10.1016/j.apenergy.2012.06.005. 3. Akpinar, A., Ponce de León, S., 2016. An assessment of the wind re-analyses in the modelling of anextreme sea state in the Black Sea. Dynamics of Atmospheres and Oceans 73, 61–75, DOI: 10.1016/j.dynatmoce.2015.12.002. 4. Akpınar, A., Jafali, H., Rusu, E., 2019. Temporal Variation of theWave Energy Flux in Hotspot Areas of the Black Sea. Sustainability 11, 562. DOI: 10.3390/su11030562. 5. Arkhipkin, V.S., Gippius, F.N., Koltermann, K.P., Surkova, G.V., 2014. Wind waves in the Black Sea: results of a hindcast study. Nat. Hazards Earth Syst. Sci. 14, 2883–2897, doi: 10.5194/nhess-14-2883-2014. 6. Aydoğan, B., Ayat, B., 2018. Spatial variability of long-term trends of significant wave heights in the Black Sea. Applied Ocean Research 79, 20–35. https://doi.org/10.1016/j.apor.2018.07.001.
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Figure captions Fig. 1. Grid for numerical simulations and bathymetric map (m) of the Black and Azov seas Fig. 2. The average power of wind seas (a), swell (b), and mixed waves (c) in 1979-2018 Fig. 3. The maximum power of wind seas (a), swell (b), and mixed waves (c) in 1979-2018 Fig. 4. Average and maximum power of wind seas (a, b), swell (c, d), and mixed waves (e, f) by months Fig. 5. Positions of the centers of highest monthly average storm activity in June (a, b, c) and December (d, e, f) Fig. 6. The geographical location of the centers of wave regions with the highest monthly average (a) and maximum (b) power values in the same month (kW/m) Fig. 7. Estimates of trend components in the long-period oscillations of the average and maximum power of wind seas (a, d), swell (b, e), and mixed waves (c, f) Fig. 8. Estimates of trends in the long-period oscillations of the average (a) and maximum (b) power of mixed waves by months Fig. 9. Estimates of linear trends of the average (a) and maximum (b) power of mixed waves
Highlights • the main goal of the research is to identify possible trends in long-period oscillations of the average and maximum wind wave power in the Black Sea; • the method of research is mathematical modeling; • the main result: there are statistically significant positive trends in climatic fluctuations of the average and maximum power of surface waves.