1. Introduction
Wind-generated surface gravity waves (simply called waves henceforth) are a fundamental and ubiquitous phenomenon at the air–sea interface. They have an impact on many aspects of human life (e.g., seafaring, coastal engineering, port operations) and play an important role in many geophysical processes (e.g., momentum exchange at the air–sea boundary layer). Studies of global and regional wave climate are important for both social and scientific perspectives and thus are widely conducted using the data obtained from various sources including numerical model outputs and observations from satellites and voluntary observing ships (e.g., Young 1999; Cox and Swail 2001; Chen et al. 2002; Gulev et al. 2003; Gulev and Grigorieva 2004; Alves 2006; Hemer et al. 2010, 2013; Semedo et al. 2011, 2013; Young et al. 2011, 2012; Fan et al. 2012, 2013, 2014; Aarnes et al. 2015).
Most of these studies focused on important integrated wave parameters such as significant wave height Hs, mean wave period Tm, and mean wave direction θm) Because these parameters are not sufficient to describe mixed sea states with both wind-seas and swells, the Hs, Tm, and θm values of wind-seas (
The wave climate system (WCS) generated by the same wind climate system (e.g., westerlies, trade winds, and polar easterlies in both hemispheres) have different properties from those generated by other wind climate systems. Distinguishing different WCSs generated by different wind climate systems is helpful to have a more comprehensive description of the global wave climate. Alves (2006) presented a technique of simulating the wave climates generated by the wind in different regions separately, which can isolate the contribution of different WCSs to the global wave climate to some extent. However, the method presented by Alves (2006) has four small shortcomings: 1) The way in which the swell generation areas are separated is subjective to some extent. 2) The presented method cannot separate different WCSs generated in the same area (i.e., there might be more than one WCS generated in the same region, e.g., in the monsoon regions). 3) Some physical processes such as swell dissipation are not taken into account. 4) Separating wind forces in different regions may reduce the fetches of some developing waves, which induces error in mean Hs. Notwithstanding these problems, the work of Alves (2006) successfully provides some patterns associated with WCSs generated by different wind climate systems.
Another way of isolating the contribution of different wave systems is to use the wave spectral information. Echevarria et al. (2019) presented the global spectral wave climate using a relatively coarse resolution of 10° × 10°, and they applied the empirical orthogonal function (EOF) to these wave spectra to obtain the seasonal cycle of the spectral wave climate. The long-term wave spectra are directly analyzed in Echevarria et al. (2019), but a major shortcoming of their work is the adoption of a coarse resolution. Portilla (2018) developed an atlas of global spectral wave climate (GLOSWAC) based on the concept of long-term wave spectra and their spectral partitioning. In GLOSWAC, the long-term wave spectrum at a certain geographical location is “partitioned” into different wave systems to classify waves originating from the different wind climate systems. Hereafter, the point-wise wave systems obtained by partitioning long-term wave spectra are referred to as climatic wave partitions (CWPs), and a WCS consists of CWPs at different spatial locations originating from the same wind climate. The mean Hs, Tm, θm, and some other characteristic parameters can be computed separately for each CWP at any point in the ocean.
The mean Hs, Tm, and θm for different CWPs can provide a better description of wave climate than bulk integrated parameters
The rest of the paper is organized as follows. Section 2 introduces the numerical wave model data used in this study and the method of tracking WCSs from CWPs. In section 3, an example is given to demonstrate the limitation of using bulk integrated wave parameters to describe wave climate. The spatial distributions of the tracked WCSs are displayed and discussed in section 4, followed by a summary in section 5.
2. Data and methods
a. Wave hindcast data
Although measured wave spectra are available from the wave mode of spaceborne synthetic aperture radars, the data quality of these wave spectra is still not sufficient for studying wave climate (Jiang et al. 2017). Therefore, long-term global-scale spectral information is only available from numerical wave models. The data used in this study are the spectral partition data obtained from the Integrated Ocean Waves for Geophysical and other Applications (IOWAGA) dataset from 1990 to 2015, a hindcast of WAVEWATCH-III (WAVEWATCH III Development Group 2016) using the physical parameterizations of Ardhuin et al. (2010) forced by the global 10-m wind data from the Climate Forecast System Reanalysis (CFSR). The spatial–temporal resolution of the model output used here is 0.5° × 0.5° × 3 h. The directional spectrum computed in the model is spaced in 32 frequency bins increasing exponentially from 0.038 to 0.72 Hz, and 24 directional bins with 15° spacing. The spectrum at each grid point is partitioned into at most one wind-sea partition and up to five swell partitions using the method developed by Hanson and Phillips (2001). The partitioned Hs, Tm, and θm, which are the data used in this study, are computed for each spectral partition. In this WAVEWATCH-III setup, an explicit swell dissipation source term is included based on the spaceborne observations of Ardhuin et al. (2009). The data show good agreement with observations from both buoys and remote sensing radar altimeters with respect to both overall Hs (Rascle and Ardhuin 2013; Stopa et al. 2016) and partitioned wave information, especially for ocean swells (e.g., Delpey et al. 2010; Stopa et al. 2016; Jiang et al. 2016a). The data are downloaded from the ftp server of IFREMER (ftp.ifremer.fr) where more detailed information about this dataset is also available (Rascle and Ardhuin 2013).
b. Probability density distributions of spectral partitions
The global partitioned Hs, Tm, and θm data of different spectral partitions from the IOWAGA dataset are organized in different seasons here such as: December–February (DJF), March–May (MAM), June–August (JJA), and September–November (SON). For each spectral partition at a given geographical location, the partitioned Tm and θm correspond to a specific position in the two-dimensional frequency–direction space. The frequency–direction positions of all wave partitions in the same location and season are collected. The frequency–direction space is again discretized into the aforementioned 32 frequency bins and 24 directional bins. The number of occurrences for spectral partitions in each frequency–direction bin is then counted without differentiating wind-sea and swell systems, and the result can be regarded as the probability density distributions of spectral partitions (PDSs) in frequency–direction space for different geographical locations and seasons. After that, the spectral partitioning algorithm is again applied on the smoothed PDSs to obtain the CWPs. This method of using PDSs to describe the spectral wave climate in a given geographical location is developed by Portilla et al. (2015) and has been proven to be an effective way to separate CWPs from different wind climate systems at any given location.
c. Integrated wave parameters for CWPs
An alternative method for calculating mean Hs, Tm, and θm of different CWPs is to apply the spectral partitioning algorithm directly to the mean directional wave spectrum. However, the mean wave spectrum at a given location is smoother than the corresponding wave PDS, as pointed out by Portilla et al. (2015). Not all single CWPs are recognizable in the mean directional wave spectrum, especially those with relatively low energy. For example, Jiang and Mu (2019) show that the signature of the California low-level coastal jets (CLCJs) cannot be observed in the mean spectrum in the equatorial region but is well defined in the PDS. Therefore, the author recommends using the aforementioned method based on the partitioned PDS, instead of the mean directional wave spectrum, to calculate the mean Hs, Tm, and θm for each CWP.
d. Spatial tracking of WCSs
The spatial gradients of mean Hs, Tm, and θm are rather limited for the same WCS (CWPs originating from the same wind climate system) at two close geographical locations. This feature can be used to spatially track the same WCS at different locations in the ocean. The spatial tracking algorithm used, presented by Jiang (2019), is originally designed for spatially tracking the wave event generated by the same meteorological event (e.g., a storm) from spectral partitions at different geographical locations. Meanwhile, this method is used in this study to spatially track the WCS generated by the same wind climate system from CWPs at different geographical locations. The procedure of this algorithm is briefly described as follows:
2) If the δ between two CWPs is less than the threshold δth, they can be regarded as the CWPs from the same WCS. The threshold is usually set as δth = 0.01 km−1, which is determined from a tuning process, but this value is sometimes subjectively changed from case to case for a better tracking result.
3) When all neighboring points are searched, extend the above searching process to the second-order neighbor points (i.e., neighboring points of neighboring points) based on the wave parameters of first-order neighbors, and this process is operated recursively to higher-order neighbors (third, fourth, fifth, etc.) until no CWP can be included. After completing the tracking of the current WCS, start from step 1 again to track the next WCS until all systems are tracked.
In this procedure, the CWP is equivalent to the spectral partition in Jiang (2019) and the WCS is equivalent to the wave event in Jiang (2019). More details about this algorithm and its discussion can be found in Jiang (2019).
3. Limitations of bulk wave parameters
An example is shown in Fig. 1 to illustrate the limitation of raw integrated wave parameters
(left) The meridional profile of Hs, Tm (arrow color), and θm (arrow) for the wind-sea (orange line), swells (green line), and overall waves (blue line) at 150°W in DJF. The base map is used as the reference for the location of profile. It is noted that the wind-sea Tm and swell/total Tm share the same color bar but correspond to different values for the same color. (right) The PDS along the same profile at each 6° latitude; the latitudes are marked on the upper left of each subplot. A direction of 0° corresponds to the wave propagation toward the north in this paper.
Citation: Journal of Climate 33, 8; 10.1175/JCLI-D-19-0729.1
(left) The meridional profile of Hs, Tm (arrow color), and θm (arrow) for the wind-sea (orange line), swells (green line), and overall waves (blue line) at 150°W in DJF. The base map is used as the reference for the location of profile. It is noted that the wind-sea Tm and swell/total Tm share the same color bar but correspond to different values for the same color. (right) The PDS along the same profile at each 6° latitude; the latitudes are marked on the upper left of each subplot. A direction of 0° corresponds to the wave propagation toward the north in this paper.
Citation: Journal of Climate 33, 8; 10.1175/JCLI-D-19-0729.1
(left) The meridional profile of Hs, Tm (arrow color), and θm (arrow) for the wind-sea (orange line), swells (green line), and overall waves (blue line) at 150°W in DJF. The base map is used as the reference for the location of profile. It is noted that the wind-sea Tm and swell/total Tm share the same color bar but correspond to different values for the same color. (right) The PDS along the same profile at each 6° latitude; the latitudes are marked on the upper left of each subplot. A direction of 0° corresponds to the wave propagation toward the north in this paper.
Citation: Journal of Climate 33, 8; 10.1175/JCLI-D-19-0729.1
Seasonal averages of CFSR 10-m wind field for (a) DJF and (b) JJA. The arrows are not scaled with the background field.
Citation: Journal of Climate 33, 8; 10.1175/JCLI-D-19-0729.1
Seasonal averages of CFSR 10-m wind field for (a) DJF and (b) JJA. The arrows are not scaled with the background field.
Citation: Journal of Climate 33, 8; 10.1175/JCLI-D-19-0729.1
Seasonal averages of CFSR 10-m wind field for (a) DJF and (b) JJA. The arrows are not scaled with the background field.
Citation: Journal of Climate 33, 8; 10.1175/JCLI-D-19-0729.1
The PDS along the same profile is plotted in the right panel of Fig. 1 at each 6° latitude. It is noted that an “oceanic convention” is used throughout the text that a direction of 0° corresponds to the wave propagating northward. At least three CWPs always coexist at any locations, and each of them corresponds to a remote or local wind climate system (Jiang and Mu 2019). The signatures of swells generated by the westerlies in the North Pacific (NP) can be clearly observed in the South Pacific (SP) (i.e., the WCS at 160°–170°, 0.06–0.08 Hz in Figs. 1k–t). Similarly, the swells generated by the westerlies in the South Pacific (SP) can also be observed in the NP (i.e., the CWP at 20°–30°, 0.06–0.08 Hz in Figs. 1c–j). In the tropical region, four CWPs propagating almost perpendicularly with each other make the mean θm of total/wind-sea/swell loses the representativeness. Moreover, wind-sea and swell events can coexist in the same CWP. For instance, the mean θm of both wind-sea and swell at 57°S are eastward (the left panel), which means the eastward CWP at 57°S (Fig. 1t) consists of both wind-seas generated by the westerlies in the SP and relatively young swells evolved from these wind-seas (swells propagating out of their sources or residual swells when wind diminishes). Because this CWP predominates in the westerlies, the mean θm of both wind-seas and swells are eastward at this location, and the information about the other two CWP is totally absent in the left panel of Fig. 1. This example shows that although traditional bulk wave parameters are useful for many purposes, sometimes they might not be sufficient for a detailed description of wave climates, even after the separation of wind-seas and swells.
The PDS profile in the right panel of Fig. 1 can present more information about the wave climate than the left panel. However, such an “array of wave spectra” is not a good way of data analysis and visualization: First, the PDSs themselves do not contain the energy information for each CWP. Second, and more importantly, it is hard to visualize wave spectra on global scale with a high resolution. The right panel of Fig. 1 is only plotted every 6° of latitude, which is a rather coarse spatial resolution, and it is difficult to increase the resolution within a limited space. Such arrays of wave spectra are used to analyze global spectral wave climate with a 10° × 10° resolution in Echevarria et al. (2019) where the propagation of swells from the westerlies of the two hemispheres is vaguely observable. The global distributions of PDS in DJF and JJA at 10° × 10° resolution is also shown in Fig. S1 in the online supplemental material, where the propagation of some WCSs is also observable. Even with such a low spatial resolution, it is still hard to observe the features of global distributions of wave climate from these arrays. Meanwhile, global distributions of mean Hs, Tm, and θm for different WCSs can provide a better description of global spectral wave climate.
4. Spatial distributions of WCSs
The CWPs at all grid points are spatially tracked in different seasons to obtain global WCSs. Here, only the WCSs in DJF and JJA in the open ocean with a relatively large spatial coverage (larger than 600 1° × 1° grid points) are shown in Figs. 3 and 4, respectively. A label is assigned to each WCS in each season, and each WCS reflects the wave climate generated by a wind climate system. To save space, several WCSs are plotted in the same map and share the same color scale if there is no overlap regarding their spatial extents. The figures with different WCSs plotted with different color scales can be found in the online supplemental material. Their energy contributions to the global (75°S–75°N) wave climate are shown in Table 1. The WCSs shown in Figs. 3 and 4 can explain more than 90% of global wave energy.
Seasonal mean (left) Hs, (right) Tm, and θm (arrows) of the main tracked WCSs (labeled in purple letters) for DJF. The arrows are not scaled with the background fields. The systems without any spatial overlap are plotted on the same map, and the color scales are different for different subplots.
Citation: Journal of Climate 33, 8; 10.1175/JCLI-D-19-0729.1
Seasonal mean (left) Hs, (right) Tm, and θm (arrows) of the main tracked WCSs (labeled in purple letters) for DJF. The arrows are not scaled with the background fields. The systems without any spatial overlap are plotted on the same map, and the color scales are different for different subplots.
Citation: Journal of Climate 33, 8; 10.1175/JCLI-D-19-0729.1
Seasonal mean (left) Hs, (right) Tm, and θm (arrows) of the main tracked WCSs (labeled in purple letters) for DJF. The arrows are not scaled with the background fields. The systems without any spatial overlap are plotted on the same map, and the color scales are different for different subplots.
Citation: Journal of Climate 33, 8; 10.1175/JCLI-D-19-0729.1
Energy contribution of WCSs.
The most interesting features in Figs. 3 and 4 are the patterns of generation and propagation of major WCSs, as the mean Hs, Tm, and θm of different WCSs are shown separately. The regions with highest Hs of different WCSs are in line with the region with high wind speed in Fig. 2. The spatial extent of a WCS can extend far away from their generation areas with the Hs(Tm) decreasing (increasing) along the mean θm. The general propagation routes of these swells are also nicely shown by the mean θm (of the target WCS). For instance, how the waves in system JA travel from the SO to the coasts of California and Alaska along great circles on Earth’s surface can be clearly observed according to the directions of arrows in Fig. 4, providing a good reference for tracking swell propagation using satellite or buoy array. It is already well known that the swells generated by the winter storm in the Southern Hemisphere can sometimes propagate to the coast of California and Alaska (Munk et al. 1963; Snodgrass et al. 1966). The results obtained here can be regarded as the long-term averaged propagation paths of these swells, and the clear land blocking and island shadowing effects are along the direction of waves in this wave climate pattern can support this point of view. The mean Tm of any WCS generally increases with the propagation distance (along the mean θm), primarily because of two reasons: 1) nonlinear wave–wave interaction pumps the wave energy into lower frequencies during the evolution of waves, and 2) high-frequency swells dissipate faster than low-frequency ones (Ardhuin et al. 2009).
Some problems are also found in the results. Theoretically, the mean Hs in the boundaries of all WCSs should be close to zero, and the boundary outlines should be smooth in the open ocean. However, this is not the case for most WCSs. These problems are mainly due to the limitation of watershed-algorithm-based spectral partitioning method used twice in this study. The watershed-algorithm-based partitioning scheme (e.g., Hanson and Phillips 2001; Portilla et al. 2009) is a purely morphological method that does not consider wave dynamics. During spectrum partitioning, when the energy peak of a partition becomes smaller than the tail of a nearby partition, it might be overwhelmed by the nearby partition, and the watershed-algorithm scheme cannot identify it (Ailliot et al. 2013). In addition, it is noted that the WAVEWATCH-III retains at most six partitions at a given location, but sometimes more than six partitions might coexist in modeled wave spectra (although this case does not occur frequently) so that the partition with very low Hs might be also omitted in IOWAGA. Both of the two factors lead to the result that the partitioning with very low Hs might be missed in the dataset, and this affects the computation of PDS. Meanwhile, such a problem also exists during the “partitioning” of PDSs, leading to some discontinuous edges of WCSs. This problem of the spectral partitioning algorithm seems to be difficult to solve at this stage. In spite of this problem, this study presents a reasonable global view of wave climate separating the contributions of different WCSs.
a. Prevailing westerlies–generated WCSs
Systems DA, DB, and DD in Fig. 3 and systems JA, JD, and JL in Fig. 4 are the waves generated by the prevailing westerlies. They are the WCSs with the largest energy contributions to the global wave climate. In DJF, the maximum mean Hs (~5 m) are found in the NP (system DA) and North Atlantic (NA; system DB) owing to the strong winter storm with averaged wind speed higher than 12 m s−1 (Fig. 2a). The waves generated in these regions can gradually turn into swells and propagate to the coast of the Antarctic continent in the Southern Hemisphere (SH). In JJA, these two WCSs have less contribution to the global wave climate. With a maximum mean Hs of ~2 m, only a small amount of energy of systems JL and JD can propagate over the equator due to the strong seasonality of the westerlies in the Northern Hemisphere (NH).
The WCS with the largest spatial extent in both DJF and JJA is generated by storm tracks in SH, because the Southern Ocean (SO) sectors of Pacific, Atlantic, and Indian Oceans are connected to each other. The highest mean Hs in systems JA and DD are both found in the SO Indian sector in all seasons. In JJA, the WCS generated by the westerlies in the SH (system JA) has a maximum mean Hs of more than 5 m and can travel across all the three oceans, and this WCS is overwhelming predominant in global wave climate with an energy contribution of almost 70%. Because the seasonality of the westerlies in the SH is weaker than that in the NH, the WCS generated by the austral summer westerlies (system DD) also has a high mean Hs (~4 m) in the generation areas and can affect the wave climate in the entire Indian Ocean (IO) as well as a large proportion of the Pacific and Atlantic Oceans.
It is somewhat difficult to find the results of global distributions of spectral wave climate parameters in previous studies that can be directly compared to the results obtained in this study. However, the results can be indirectly validated by the wave climate patterns derived from bulk wave parameters in previous studies (e.g., Young 1999; Alves 2006; Semedo et al. 2011; Jiang et al. 2017) and the wind climate patterns in Fig. 2. The patterns of these WCSs at their origins (westerlies) are in line with previous results obtained using bulk wave parameters (e.g., Semedo et al. 2011; Fan et al. 2014). However, because the mean Hs values of these WCSs decline rapidly out of the generation zone, previous studies on wave climate based on wave model hindcast or satellite data did not quantify the impacts of westerlies-generated WCSs on global wave climate in far fields, and even their existence is overwhelmed by the stronger waves generated in the other hemispheres. The results here show clearly that westerlies-generated swells can propagate to the equator in all seasons and can extend to the other end of the basin in hemispheric winters, although they may become less dominant after propagating over large distances. Besides, the mean Tm of the westerlies-generated WCSs can vary from less than 11 s in source regions to more than 15 s in far fields after propagating over more than 10 000 km due to the two reasons mentioned above. A problem of the result herein is that the mean Hs of the westerlies-generated WCSs is observed to increase in the far fields after propagating over 10 000 km, which is unreasonable. This is because the rotating extratropical storms can generate some strong local waves with similar Tm and θm to the waves originating from the other hemisphere, and these local and remote waves are identified as the same WCSs by the partitioning scheme, resulting in the “increase” of mean Hs in far fields. Because of these problems, only one significant digit is maintained in Table 1.
By keeping only the wind in selected oceanic areas active, Alves (2006) eliminates the impact of the waves outside the generation zone. The spatial patterns of mean Hs of systems DA and DB are similar to those of the annual mean Hs of waves originating from the extratropical NP and NA demonstrated in Alves (2006), respectively. According to the distributions of SO westerlies in Fig. 2, it should be more reasonable to consider the SO westerlies-generated WCS as a single system, rather than as three systems that are separated subjectively in Alves (2006). However, the major propagating patterns of these waves are also similar in the two studies, showing the validity of the method and results in this study. The propagation patterns of these WCSs during their less dominant stages are also identified by Echevarria et al. (2019) in the first EOF mode of global wave spectra. But the EOF pattern of Echevarria et al. (2019) shows that the NH-generated swell can propagate into the SH farther than the more energetic SH swell, which propagates northward, which is in line neither with the results of the present research nor with Alves (2006). Checking the long-term PDS (available in Fig. S1), the signatures of the SH westerlies-generated WCSs can be observed to the north of 50°N in both DJF and JJA, whereas those of the NH westerlies-generated WCSs can be observed at 50°S only in DJF, also indicating that the SH-generated swell can propagate farther. It is worth noting that the first EOF mode in Echevarria et al. (2019) mainly represents the seasonality, instead of the strength of wave energy. The NH westerlies-generated swells are observed to propagate farther in Echevarria et al. (2019) simply because they have a stronger seasonality.
b. Trade winds–generated WCSs
Systems DC, DG, DI, DP, and DQ in Fig. 3 are the WCSs along the trade winds in DJF, and systems JF, JG, JH, JC, and JK in Fig. 4 are the corresponding WCSs in JJA. Although the trade winds are stronger in the winter hemisphere, all these five WCSs are clearly observed in all three oceans for all seasons. Because of the lower wind speed compared to the westerlies, both the mean Hs and the mean Tm of the WCSs generated by trade winds are lower than those generated by the westerlies. These trade winds–generated WCSs have the southwestward and northwestward components of mean θm in their southern and northern parts, respectively. The signatures of the regional winds effect along the five eastern boundary currents systems (the California and Canary Currents in JJA, and Humboldt, Benguela, and West Australia Currents in DJF; Carrasco et al. 2014; Semedo et al. 2018) can be observed as a part of these trade winds–generated WCSs (the signals are clearer in the supplemental materials where different WCSs are shown with different color bars), which can be associated with the wind field illustrated in Fig. 2. For instance, the signature of the CLCJ is clearly shown as part of system JC generated by the trade winds in the NP. The range of influence of the waves generated by the CLCJ can reach the eastern tropical Pacific, which is consistent with the results of Jiang and Mu (2019), and can also be confirmed by the PDS array in the eastern tropical Pacific in Fig. S1b in the supplemental material. In addition, the WCS of trade winds in the SP in both DJF and JJA (i.e., systems DG and JG) has two centers of high mean Hs, which is in agreement with the structure of the trade wind zone in the SP. The regions in the “upstream” of the two WCSs have a lower Tm mean, showing that some of the westward waves originating from the trade wind zones to the west of the South America may receive energy again from the local wind in the western side of the basin.
Even in the center of the trade wind zones, the mean Hs of the trade winds–generated WCSs are generally lower than those of the westerlies-generated swells that have not propagated far away from their origins. Therefore, the impact of trade winds on the seasonal averages of total Hs fields is not well defined in either DJF or JJA [e.g., Figs. 2a and 3a of Semedo et al. (2011)] except for the one in the IO in JJA, which has a maximum mean Hs of more than 2.5 m (system JF). After separating the wind-sea and swell climates, these WCSs become observable along the trade wind zones in global distributions of the wind-sea Hs fields [e.g., Figs. 2c and 3c Semedo et al. (2011)]. However, it is difficult to display the trade wind–generated swell systems with lower Hs outside their origins by using bulk wave parameters. In Fig. S1 in the supplemental material, the signatures of the trade winds–generated swells are also well defined in both seasons (e.g., the northwestward and southwestward peaks along the equator). The signals of trade winds are also observed in Echevarria et al. (2019), but the spatial pattern is not that clear. Some of the patterns derived in this study can also be partially validated by the patterns derived by Alves (2006) where the tropical sections of the NA, South Atlantic (SA), eastern NP, eastern SP, and south IO are forced separately. However, the spatial extent of the patterns in Alves (2006) seems to be larger than in the present study. For example, in Alves (2006), the waves generated in the tropical eastern NP can propagate to Antarctic coasts and the waves generated in the tropical South IO can propagate to east coasts of South America. There are at least three reasons which can explain this difference: 1) The swell dissipation term is included in the IOWAGA hindcast whereas it is not taken into account in Alves (2006). Thus, the swell can propagate farther in the model of Alves (2006). 2) Due to the seasonal shifting of the wind belts, the westerlies can sometimes reach south (north) of 30°N (30°S). Therefore, in Alves (2006), some signals of westerlies-generated waves are also displayed in the patterns of waves generated in the tropical oceans. This phenomenon is clearly shown in Fig. 13 of Alves (2006). 3) Even if some swells can propagate farther than the spatial extent shown in Figs. 3 and 4, the occurrence frequency of these swells decrease with the increase of the distance from the origins. The signals of these swells can sometimes be too low to be isolated in the long-term PDS, so that they are not identified in far fields.
c. Indian monsoon–generated WCSs
Systems DE and DJ in DJF and systems JB and JI in JJA are the WCSs generated by the Indian monsoon. Although their spatial extents and energy contributions to global wave climate are relatively small, the Indian monsoon has high wind speeds, especially in JJA, and their signals in the wave fields are well marked (e.g., Semedo et al. 2011; Ranjha et al. 2015). As the Indian monsoon is stronger in JJA, both systems JF and JI have much lower mean Hs and shorter Tm than systems DE and DJ. Within limited fetches, both the mean Hs and Tm of system JB are higher than those of system JI because the Somali coastal jet has higher wind speeds (Fig. 2). The directions of the Indian monsoon are mainly northeastward in JJA; thus, the ranges of influence the two WCSs are mainly the Arabian Sea and Bay of Bengal, respectively. However, it is observed that some of the waves in systems JB and JI can propagate eastward across the IO and reach the northwestern shore of Australia. This phenomenon can be also observed in Alves (2006) where the mean Hs field is forced by the wind in the northern IO.
d. Polar easterlies–generated WCSs
All the aforementioned WCSs correspond to regions with a relatively high local wind speed, which can be clearly observed in Fig. 2 (i.e., the westerlies, trade winds, and monsoon). However, it seems that the source regions of some WCSs are not very clearly characterized in the global distribution of wind speed. According to their spatial patterns, some of these WCSs should be generated by the polar easterlies. In DJF, systems DF, DH, and DK seem to be generated by the easterlies in the Bering Sea, the Norwegian Sea, and the coastal region of Antarctic, respectively, while systems JM and JN are polar easterlies–induced WCSs in JJA. In fact, the corresponding polar wind systems of these WCSs can be observed in the seasonal mean wind in Fig. 2, and the mean wind directions of these wind systems are also consistent with the mean θm of WCSs. However, because the polar easterlies–generated WCSs have a lower wave energy than the westerlies-generated WCSs and their spatial impacting ranges have a large overlap, it seems that the polar easterlies–generated WCSs have often been overlooked in previous studies. Because Alves (2006) does not separate the polar regions and the extratropical regions, these patterns are not observed, either. Another WCS generated by the polar wind system is system DM, which corresponds to the southeastward wind in the Labrador Sea (which is clear in Fig. 2a). This WCS can be partly observed in the distributions of mean Hs and wind-sea Hs at its origin, the Labrador Sea [Figs. 2a and 2c in Semedo et al. (2011)].
No polar easterlies–generated WCS is found in the NP in JJA, because the polar easterlies between 150°E and 120°W are mainly located in the Arctic Ocean in this period, as shown in Fig. 2b, and the Asian and North American continents block the polar easterlies–generated waves in the Arctic Ocean from propagating into the NP. System JN is also observed not to extend to the Pacific Ocean. A potential reason for this phenomenon is that the sea surface polar easterlies in the SO Pacific sector are mainly located in the Ross Sea to the south of 65°S (Fig. 2b), which is frozen in JJA. Therefore, these polar easterlies do not affect the waves in the SP in JJA.
e. Other WCSs
It seems to be relatively difficult to explain the rest of the tracked WCSs, including systems DL, DN, DO, JJ, and JE, because they do not correspond to any wind feature in Fig. 2. A potential reason for the formation of these WCSs is that they are the “remainder” WCSs generated by extratropical storms in the westerlies. Most of the waves generated in the westerlies are eastward, but the rotating winter storms can also generate westward waves, which might form some WCSs. Alves (2006) also shows that the wind in the extratropical regions can generate swell systems that propagate westward against the predominant wave directions. However, the westward wave patterns in Alves (2006) should be the superposition of these remainder WCSs and the polar easterlies–generated WCSs. In regions where systems DN and DO are located, the mean Tm and θm of these WCSs are different from those of the polar easterlies–generated WCSs so that they can be tracked by the long-term PDS. However, in some other regions (e.g., the region near 90°E in the SO), because the Tm and θm of so-called remainder WCSs are similar to those of the polar easterlies–generated WCSs, it is difficult to distinguish them from the long-term PDS.
5. Summary
Several WCSs often coexist at the same location, leading to the complex wave climate in the ocean. Using integrated wave parameters (even if after wind-sea–swell separation) to characterize the global wave climate can only capture the feature of one or two predominant WCSs and often overlooks the WCSs with relatively low energy. In this study, an attempt is made to present a relatively comprehensive global view of wave climate by spatially tracking spectral WCSs in point-wise long-term PDSs. Tens of spatially consistent WCSs essentially independent of each other are tracked and each of them corresponds to a global or regional map of mean Hs, Tm, and θm of waves from the same origins, exhibiting more details of global wave climate. These WCSs reveal the process of how wind-seas gradually turn into swells, as well as the propagation route of global waves. Every region with relatively high wind speeds including the prevailing westerlies, the trade winds, polar easterlies, and Indian monsoon corresponds to an individual WCS. Among these WCSs, those generated by the westerlies, which can travel across the entire basin, play the most important role in the global wave climate. The patterns of these WCSs demonstrate the entire life cycle of ocean waves, from being dominant to become less dominant, from a climatic point of view. Such climatic patterns of global wave propagation obtained in this study can serve as a reference for designing satellite tracks and arranging buoy locations when one wants to track swell propagation using remote sensors (e.g., Jiang et al. 2016b) or buoy arrays (e.g., Snodgrass et al. 1966). Knowing the impacting range of different WCSs may help determine the modeling domain when running a regional wave model. Besides, WCSs from different sources may also have different properties when approaching the coasts, leading to different coastal processes and water-level responses. Therefore, some results of this study may also be useful for coastal research. This study mainly focuses on the seasonal variability of global wave climate while future exploration can be made to regional wave climate using data with higher spatial resolutions and to the interannual/long-term variabilities of each WCS using consistent data with longer time spans. Moreover, with the successful launching of CFOSAT (the China–France Oceanography Satellite) on 29 October 2018, observational global ocean wave spectra will be available from the Surface Waves Investigation and Monitoring (SWIM) sensor. With the accumulation of these remotely sensed wave spectra, the methodology employed in this study can also be used to present observational wave climate patterns in future works.
Acknowledgments
This work is jointly supported by the National Key Research and Development Program of China (2018YFC0309601), the National Natural Science Foundation of China (41806010), Laboratory for Regional Oceanography and Numerical Modeling, Qingdao National Laboratory for Marine Science and Technology (2019A03), and the Guangdong Special Fund Program for Marine Economy Development (GDME-2018E001). The IOWAGA data are downloaded from IFREMER ftp (ftp.ifremer.fr). The author would like to thank Dr. Alexander Babanin, Dr. Alvaro Semedo, Dr. Qingxiang Liu, and three anonymous reviewers for their helpful comments and suggestions.
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