Statistical Analysis of Mesoscale Eddy Characteristics in the northwestern Pacific Ocean

In this paper, the mesoscale eddy data set established by Professor Chelton in Oregon State University is used to analyse the statistical characteristics of mesoscale eddies in the Northwest Pacific Ocean. Mesoscale eddies in this region are divided into short-lived, Mid-lived, and long-lived eddies according to their life cycle with the aim of exploring the characteristics of eddies with different life cycles. Those with a life cycle of less than 6 weeks, 6-9 weeks, and more than 9 weeks are defined as short-lived eddies, mid-lived eddies, and long-lived eddies, respectively. The results show that most of the eddies are short lived eddies with a lifetime of 6 weeks or less. Both short-lived eddies and Mid-lived eddies have more cyclonic eddies than anticyclonic eddies. But long-lived eddies have more anticyclonic eddies than cyclonic eddies. In addition, the number of short-lived eddies in the Subtropical Ocean is more than those in the Kuroshio Extension, while the number of long-lived eddies is the opposite.


Introduction
Mesoscale eddy is currently a prominence topic in ocean research.The Northwest Pacific is a high-value region for the generation and disappearance of mesoscale eddies.The mesoscale eddies in the Western Pacific not only have a significant impact on global climate and ocean current systems, but also have mixing and diffusion effects on water masses in the region.Hu et al. (2017) also used satellite altimeter data and Argo data to conduct statistical analysis on the distribution and apparent characteristics of mesoscale eddies in the South Indian Ocean region.They found that the eddy frequency showed a strip along the latitude, with a clear high value range of eddy frequency at 18 ° -30 ° S [1] .Lin (2005) analysed the mesoscale eddies near the Kuroshio and found that 90% of the eddies in the region move westward.At the same time, it was found that the average radius decreases with increasing latitude.The probability of mesoscale eddies appearing in spring is higher and it is smaller in autumn [2] .Wu (2021) found that the western part of the Luzon Strait, the central and eastern part of the basin, and seas along mid-south Vietnam are high-frequency regions for eddy generation, while seas along mid-south Vietnam are highfrequency regions for eddy disappearance [3] .Liu (2021) found mesoscale eddy could influence the spatial distribution and environmental behaviours of semi-volatile organic pollutants in the marine environment [4] .Compared to previous work, this article deepens the level of mesoscale eddy statistical analysis and refines the statistical elements.Following the recommendation in the Lin (2005), only mesoscale eddies with life cycles equal to or greater than 4 weeks are analysed in this paper [2] .

Data
The eddy dataset used in this article is actually the eddy information obtained after extracting and processing satellite altimeter sea surface height data.Professor Chelton from Oregon State University in the United States used a new SSH automatic recognition algorithm and SSH closed contour lines through spatial high pass filtering to track global ocean mesoscale eddies, collect relevant features, and establish a global mesoscale eddy dataset [5] .The data set contains information on eddies with a life cycle of more than 4 weeks and an amplitude of more than 1cm.The data set includes factors of eddy radius, amplitude, time, and geographic location.This article selects data from the Chelton eddy dataset from 1993 to 2017.

Number of eddies
As shown in Table 1, a total of 13744 anticyclone eddies and 14495 cyclone eddies appeared in the study region from 1993 to 2017, including 6919 anticyclone eddies and 7612 cyclone eddies in the Subtropical Ocean (15-30° N), 6825 anticyclone eddies and 6883 cyclone eddies in the Kuroshio Extension (30-45° N).Both the Subtropical Ocean and the Kuroshio Extension have slightly more anticyclone eddies, which is consistent with previous research results [6][7] .Meanwhile, in Table 1, it can be seen that both short-lived eddies and Mid-lived eddies comply with the statistical law of more cyclonic eddies than anticyclonic eddies, while long-lived eddies exhibit an abnormal phenomenon of more anticyclonic eddies than anticyclonic eddies.The possible reason is that anticyclone eddies generally have a larger radius and are more stable, resulting in a longer lifespan of anticyclone eddies.Comparing the statistical results of the two regions, the total number of eddies in the Subtropical Ocean is higher than that in the Kuroshio Extension, and the main contributor to this result is cyclone eddies rather than anticyclone eddies.The number of anticyclone eddies in the Subtropical Ocean is almost the same as that in the Kuroshio Extension, while the number of cyclone eddies in the former is nearly 10% higher than that in the latter.
Comparing different life cycles' eddies, it can be found that firstly, the number of short-lived eddies is significantly large, indicating that most mesoscale eddies in the ocean have a life cycle of less than 6 weeks.Secondly, although the overall number of eddies in the Subtropical Ocean is higher than that in the Kuroshio Extension, the spatial distribution of the three types of life cycle eddies shows different characteristics: short-lived eddies are more common in the Subtropical Ocean than in the Kuroshio Extension, while Mid-lived eddies are similar and long-lived eddies are more common in the Kuroshio Extension than in the Subtropical Ocean.It is demonstrated that the eddies near the Kuroshio Extension are more stable than those in the Subtropical Ocean, possibly due to the fact that the Kuroshio, which has a higher flow velocity, inputs more energy into the mesoscale eddies near it.Fig. 1 shows the spatial distribution of the number of eddies generated and disappeared in the 1°×1° grid in the study area during 1993-2017.Comparing the four images, there is a certain similarity in the distribution of the generation and disappearance of cyclone eddies and anticyclonic eddies, that is, areas with more cyclone eddies generate more anticyclonic eddies, and areas with more cyclone eddies disappear also have more anticyclonic eddies disappear.The high and low value district of the four images is generally consistent.Based on Table 1, this phenomenon can be explained: most eddies have a short life cycle, so their movement distance is not long, and their disappearance is very close to their generation, resulting in the overlapping of the generation high value region and the disappearance high value region.Specifically, in the area east of 170° W, 20-40° N, eddies are clearly high in number of generation and dissipation, which is consistent with the common understanding that the Pacific Ocean is born on the eastern boundary and propagates from east to west, and the number of eddies on the western boundary of the Pacific Ocean is relatively small [5] .In addition, north of 35°N, 135-165° E is also a large high value area for generation and dissipation.By comparing the subgraphs in Figures 1, it can be observed that the western boundary of the Pacific Ocean (along the eastern coast of Japan and the continental shelf of the East China Sea) is a high value area for extinction, but not a high value area for generation.This is because the eddies that reach the boundary cannot continue to move and gradually disappear at the boundary, making the western boundary the "tomb of eddies".At the center of the Kuroshio Extension, there is a low value area for eddy generation and dissipation, and strong ocean currents prevent the generation of eddies.And often the eddies that located the Kuroshio merge into the Kuroshio and disappear.The above analysis analyzed the planar distribution characteristics of the number of eddy generation and disappearance in the northwest Pacific Ocean from 1993 to 2017, and added these parameters by two longitudes or two latitudes and plotted a curve to obtain Fig. 2. The figure shows that there are significant variations in the number of eddy generation and disappearance along the longitude and latitude lines, and the trend of changes in cyclone eddies and anticyclonic eddies is consistent.The generation and disappearance of eddies are distributed in a "bimodal" structure in the meridional direction (Fig. 2a, c), which corresponds to the high value areas of eddy disappearance and generation in the Kuroshio Extension and Subtropical Ocean.In the latitudinal distribution, there is a "three segment" structure characterized by a slow increase of 120° E-150° E, a slow decrease of 150 ° E-170° E, and a slow increase of 170° E-150° W. The number of eddies is slightly higher in the central and eastern Pacific Ocean and is slightly lower in the western Pacific Ocean.

Eddy radius
Table 2 shows that the average radius of cyclone eddies and anticyclone eddies in the entire study area is 83.6 km and 85.1 km respectively.The average radius of cyclone eddies and anticyclone eddies in the Subtropical Ocean is 91.3 km and 94.2 km respectively.The average radius of cyclone eddies and anticyclone eddies in the Kuroshio Extension is 75.3 km and 76.1 km respectively.The radius of anticyclone eddies is generally larger than that of cyclone eddies, which explains in some ways why the number of long-lived anticyclone eddies is greater than that of long-lived cyclone eddies.Fig. 3 (a-c) show the radius distributions of short-lived, Mid-lived, and long-lived eddies respectively.From this, it can be seen that there is a clear low-value area for the radius distribution of mid-lived and long-lived eddies, namely the Kuroshio Extension area south of 35° N.This is a high-value area generated by eddies, but a low-value area of radius size, and the reasons behind it are worth exploring in depth.The difference between Fig. 3 (a-c) is that the radius distribution of long-lived eddies shows a significant small value in the Subtropical Ocean, but the radius distribution of short-lived eddies and Mid-lived eddies does not reflect this significant feature.In addition, the average radius of short-lived eddies is 81.53 km, the average radius of Mid-lived eddies is 93.37 km, and the average radius of long-lived eddies is 100.74 km.This proves the correlation between the life cycle of eddies and the radius of eddies.The larger the radius of eddies, the longer the life cycle of eddies.The article investigated the frequency distribution of eddy radius in the entire study area, Subtropical Ocean, and Kuroshio Extension.The results show that the radius of cyclonic and anticyclonic eddies in various regions have similar frequency distributions.For the entire study area, most eddies have radius between 55 and 120 km, with the highest proportion of eddies with a radius of about 75 km.The frequency of cyclonic eddies is about 9%, while that of anticyclonic eddies is about 9.5%.Afterwards, the frequency of eddies gradually decreases with the increase of radius.The average radius of eddies in the Subtropical Ocean is mainly distributed between 60-140 km, with the minimum average radius of eddies generally not less than 50 km, and very few eddies with an average radius greater than 180 km.Among them, eddies with a radius of about 80 km have the highest frequency, with a maximum frequency of about 8%.Cyclonic eddies and anticyclonic eddies are equivalent.The radius of the Kuroshio Extension eddy is concentrated between 55 and 100 km, with almost no eddies with a radius greater than 140 km.The average radius with the highest frequency is 75 km, with a maximum frequency of about 11%, which is greater than 8% of the Subtropical Ocean.This indicates that the frequency distribution of the Kuroshio Extension eddy radius is more concentrated than that of the Subtropical Ocean, with relatively few eddies with large and small radius.On the contrary, the distribution of eddy radius in the Subtropical Ocean is scattered.Although there are many eddies with larger radius, the average radius is smaller.The size of the eddy radius reflects the strength of the eddy and also the kinetic energy of the eddy.The kinetic energy of the Kuroshio Extension eddy is greater than that of the Subtropical Ocean.Meanwhile, the results show that below a radius of 100 km, the frequency of cyclonic eddies is greater than that of anticyclonic eddies, while above 100 km the frequency of anticyclonic eddies is greater than that of cyclonic eddies, corresponding to that of the anticyclone eddies whose radius is less than that of the cyclone eddies.

Eddy amplitude
Eddy amplitude refers to the difference in sea surface height between the center and edge of the eddy.As shown in Tables 3, the average amplitude of the entire study area's cyclone eddy is 7.0 cm, the average amplitude of the anticyclone eddy is 6.8 cm, the average amplitude of the Subtropical Ocean's cyclone eddy is 6.8 cm, the average amplitude of the anticyclone eddy is 6.5 cm, the average amplitude of the Kuroshio Extension's cyclone eddy is 7.4 cm, and the average amplitude of the anticyclone eddy is 7.2 cm.The average amplitude of eddies is generally greater than that of anticyclonic eddies.Similar to the distribution of eddy radius, there is also a low value range for the amplitude of Mid-lived and long-lived eddies in the centerline area of the Kuroshio Extension south of 35° N.Meanwhile, the average amplitude of the short-lived anticyclonic eddy is 5.99 cm, and the average amplitude of the cyclone eddy is 6.22 cm; The average amplitude of the Mid-lived anticyclonic eddy is 8.20 cm, and the average amplitude of the cyclone eddy is 8.84 cm; The amplitude of the long-lived anticyclonic eddy is 10.84 cm; The amplitude of the cyclone eddy is 10.88 cm.This reflects the correlation between the amplitude of the eddy and its life cycle, with the larger the amplitude, the longer the eddy's life cycle.In addition, the amplitudes of short-lived, Mid-lived, and long-lived eddies near the Kuroshio Extension are greater than those in the Subtropical Ocean.The variation of eddy amplitude with latitude is similar to that of eddy radius.The trend of amplitude variation of cyclone eddy and anticyclonic eddy is consistent, and they also exhibit a "double peak" structure.The difference is that the second peak (Kuroshio Extension) is larger than the first peak (Subtropical Ocean), and the eddy amplitude has no obvious trend of decreasing with increasing latitude.The average amplitude of cyclonic eddies changes with latitude 2-3 degrees faster than that of the anticyclonic eddies.The latitude of the two maximum and one minimum values of the cyclonic eddies amplitude changes with latitude are 2-3 degrees lower than that of the anticyclonic eddies.Similarly, as shown in Fig. 4, the planar distribution of average amplitude also shows that the amplitude of the Kuroshio Extension eddy is greater than that of the Subtropical Ocean, and there is a high amplitude area near the western boundary of the Pacific and Kuroshio Extension, with an average amplitude of over 20 cm.The reasons and mechanisms behind this phenomenon need to be further studied.
For the entire study area, the amplitude of eddies is concentrated between 2-10 cm, with the amplitude with the highest frequency being 3 cm.The frequency of both cyclonic and anticyclonic eddies is about 15% (the frequency of cyclonic eddies is slightly higher than that of anticyclonic eddies), and the frequency of eddies gradually decreases with increasing amplitude.The frequency distribution of eddy amplitudes in the Subtropical Ocean and the Kuroshio Extension has certain similarities with the distribution of the entire region.However, the frequency distribution of eddy amplitudes in the Subtropical Ocean is more concentrated, with almost no eddies with amplitudes greater than 20 cm in

Maximum eddy flow velocity
Table 4 shows that the maximum velocity of cyclone eddies in the entire study area is 21.2 cm/s, the maximum velocity of an anticyclone eddy is 20.0 cm/s, the maximum velocity of cyclone eddies in the Subtropical Ocean is 22.5 cm/s, the maximum velocity of anticyclone eddies is 21.4 cm/s, the maximum velocity of Kuroshio Extension's cyclone is 20.0 cm/s, and the maximum velocity of anticyclone eddies is 18.6 cm/s.The maximum velocity of eddies in the entire northwest Pacific Ocean is mainly distributed between 4-40 cm/s, with the highest frequency being 16 cm/s.The frequency of both cyclonic and anticyclonic eddies is about 9% (anticyclonic eddies are slightly higher than cyclonic eddies).The maximum velocity of eddies in the Subtropical Ocean is mainly distributed between 10-50 cm/s, with high-frequency distribution between 12-28 cm/s, and the highest frequency being 16 cm/s, The highest frequency is around 12% (anticyclonic eddies are slightly larger than cyclonic eddies).The maximum flow velocity of eddies in the Kuroshio Extension is distributed between 4-60 cm/s, mainly between 4-40 cm/s.The maximum flow velocity with the highest frequency is 8 cm/s, and the highest frequency is about 11% (cyclone eddies are slightly larger than anticyclonic eddies).The frequency of anticyclonic eddies with a maximum velocity of less than 20 cm/s in the Subtropical Ocean is greater than that of cyclonic eddies, while the frequency of anticyclonic eddies with a maximum velocity of more than 26 cm/s is lower than that of cyclonic eddies.In the Kuroshio Extension, the frequency of cyclonic eddies with a maximum velocity of less than 10 cm/s is greater than that of anticyclonic eddies, and the frequency of anticyclonic eddies with a maximum velocity of more than 24 cm/s is greater than that of cyclonic eddies.The frequency of eddies with a maximum velocity greater than 20 cm/s in the Subtropical Ocean gradually IOP Publishing doi:10.1088/1742-6596/2718/1/0120058 begins to decrease with the increase of the maximum velocity, while the frequency of eddies with a maximum velocity greater than 8 cm/s in the Kuroshio Extension area gradually begins to decrease with the increase of the maximum velocity.This phenomenon indicates that in the Subtropical Ocean, the frequency of anticyclone eddies is higher than that of cyclone eddies in the low velocity range, while in the high velocity range, the frequency of cyclone eddies is higher than that of anticyclone eddies.In the Kuroshio Extension area, the situation is the opposite.
As shown in Fig. 5, there are more eddies with higher flow velocities along the western coast of the Pacific Ocean and the northern part of the Kuroshio, which coincide with areas with larger amplitude and radius.The maximum velocity of eddies varies with latitude is similar to the amplitude of eddies.Overall, the maximum velocity of eddies does not show a significant increase or decrease trend with increasing latitude, and still presents a "bimodal" structure.The first peak of a cyclone appears near 19 ° N, the second peak appears near 33° N, the first peak of an anticyclonic eddy is near 20° N, and the second peak is near 35° N. The peak at high latitude is greater than the peak at low latitude.The maximum velocity distribution of cyclone eddies with latitude is slightly southward compared to anticyclonic eddies.The two-dimensional distribution of the average maximum velocity of eddies is characterized by a higher maximum velocity north of 35° N, a lower maximum velocity in the latitude zone from the south side of 35° N to 30° N, and a maximum velocity in the range of 15° N-30° N between the first two.

Comparative analysis of eddy characteristics in different life cycles
As shown in Fig. 6, the changes in radius, amplitude, and maximum flow velocity with latitude are all clearly "bimodal" structures, regardless of short, medium, or long-lived eddies.The typical feature of short-period eddies changing with latitude is that the radius decreases continuously with latitude increasing.However, there are two maxima in the Subtropical Ocean and the Kuroshio Extension, and the extreme value of the anticyclone is larger, making the curve of the anticyclone significantly higher than that of the cyclone in the Subtropical Ocean and the Kuroshio Extension, Moreover, the area where the radius of the anticyclonic eddy begins to increase in the Subtropical Ocean is 2 ° lower in latitude than the area where the cyclone begins to increase.Unlike the variation characteristics of radius, the amplitude and maximum flow velocity do not show a clear trend of decreasing with increasing latitude.The extreme values of amplitude and maximum velocity in the Subtropical Ocean are smaller than those in the Kuroshio Extension, and the latitude of the extreme values of cyclone eddies and anticyclone eddies in the Subtropical Ocean is almost the same.However, the latitude of the maximum value of cyclone eddies in the Kuroshio Extension is about 2 ° lower in latitude than that of anticyclone eddies.In addition, the amplitude and maximum flow velocity of cyclone eddies are generally greater than those of anticyclonic eddies, and the difference between the extreme values of the two in the Kuroshio Extension suddenly increases.The extreme value of a cyclone is much greater than that of an anticyclonic eddy.It is speculated that this is related to the occurrence of more cyclonic eddies on the southern side of the Kuroshio and more anticyclonic eddies on the northern side.At 45° N, the average amplitude and average maximum flow velocity of the eddy decrease to a minimum.As shown in Fig. 7, the variation of mid-lived eddies with latitude is similar to that of short-lived eddies.It may be due to the decrease in the number of mid-lived eddies, with more small fluctuations appearing on the curve, which is not as smooth as the curve of short-lived eddies changing with latitude, but the overall trend remains unchanged.At the same time, compared to short-lived eddies, the average radius, average amplitude, and maximum velocity of mid-lived eddies are numerically larger and more pronounced in the Subtropical Ocean and the Kuroshio Extension.As shown in Fig. 8, the typical characteristics of long-lived eddies changing with latitude are similar to the overall variation characteristics of short-lived and mid-lived eddies.Long-lived eddies are consistent with mid-lived eddies, with more small fluctuations appearing on the curve, and are not as smooth as the curve of short-lived eddies changing with latitude, but the overall trend remains unchanged.Compared to short-lived and mid-lived eddies, the growth of the average radius, average amplitude, and maximum velocity of long-lived eddies becomes more pronounced in the Subtropical Ocean and the Kuroshio Extension.At the same time, for the average amplitude and maximum velocity, the anticyclonic eddies have two extreme values in the Kuroshio Extension, with a minimum "trough" appearing at the "peak" of the two extreme values.There is also such a "trough" in the eddy at this location, but it is far less obvious than the anticyclonic eddies, and this phenomenon has already been reflected in the mid-lived eddy.The reasons for this are still worth exploring.As shown in Fig. 9, the same characteristic parameter of short-lived, medium-lived, and long-lived eddies are compared in the same image to obtain the following Fig. 9.It can be seen that the parameter values for long-lived eddies are always greater than those for mid-lived eddies, while the parameter values for mid-lived eddies are always greater than those for short-lived eddies.To some extent, the longer the life cycle of eddy, the larger its radius, amplitude, and maximum flow velocity.However, regardless of the type of life cycle eddy, the overall variation trend of the parameters remains roughly unchanged.

Summary and Conclusion
The article analyses some statistical characteristics (quantity, life cycle, radius, amplitude, maximum flow velocity) of mesoscale eddies in the northwest Pacific Ocean.The main conclusions are as follows:

Spatial distribution
The high value areas of eddy generation and dissipation are located at 170° W-150° W, 20° N-40° N. The western boundary of the Pacific Ocean (along the eastern coast of Japan and the continental shelf of the East China Sea) is also a high value area of extinction quantity, but not a high value area of generation quantity.The overall number of eddies generated in the Subtropical Ocean is higher than that in the Kuroshio Extension.Meanwhile, the number of anticyclone eddies in the Subtropical Ocean is only slightly higher than that of the Kuroshio Extension, but its number of cyclone eddies is nearly 10% higher than that of the Kuroshio Extension.The generation and disappearance of eddies are distributed in a "bimodal" structure in the latitudinal direction (Figure 5a, c), with the "bimodal" corresponding to the high values of eddy disappearance and generation in the Kuroshio Extension and Subtropical Oceans, respectively.Meanwhile, in the Subtropical Ocean and the Kuroshio Extension, there are slightly more cyclonic eddies than anticyclonic eddies.

Changes in eddy characteristic parameters
The characteristic of radius change is that as latitude increases, the radius continuously decreases, and at the same time, in the Subtropical Ocean and the Kuroshio Extension, it reversely increases and then decreases, resulting in two maximum values.The average amplitude of a cyclone eddy is generally greater than that of an anticyclone eddy.Short-lived eddies and Mid-lived eddies have more cyclonic eddies than anticyclonic eddies, but long-lived eddies have more anticyclonic eddies than cyclonic eddies.

Frequency distribution
In the Subtropical Ocean, the frequency of anticyclonic eddies is higher in the low velocity range, while in the high velocity range, the frequency of anticyclonic eddies is higher.The opposite is true in the Kuroshio Extension area.Most eddies have radius between 55-120 km, with eddies with a radius of 75 km accounting for the highest proportion.

Characteristic of eddies with different life cycles
There is a correlation between the life cycle of eddies and their radius.The larger the radius of the eddy, the longer the life cycle of the eddy.Short-lived eddies are more common in the Subtropical Ocean than in the Kuroshio Extension, while Mid-lived eddies are similar and long-lived eddies have more in

Figure 2 .
Figure 2. Changes in the number of eddy and anticyclonic eddy generation and disappearance with latitude and longitude from 1993 to 2017

Figure 6 .
Figure 6.Changes in the characteristic parameters of short-lived eddies with latitude

Figure 7 .
Figure 7.The variation of characteristic parameters of periodic eddies with latitude.

Figures 8 .
Figures 8. Variationof long-lived eddies characteristic parameters with latitude.As shown in Fig.9, the same characteristic parameter of short-lived, medium-lived, and long-lived eddies are compared in the same image to obtain the following Fig.9.It can be seen that the parameter values for long-lived eddies are always greater than those for mid-lived eddies, while the parameter values for mid-lived eddies are always greater than those for short-lived eddies.To some extent, the longer the life cycle of eddy, the larger its radius, amplitude, and maximum flow velocity.However, Figures 8. Variationof long-lived eddies characteristic parameters with latitude.As shown in Fig.9, the same characteristic parameter of short-lived, medium-lived, and long-lived eddies are compared in the same image to obtain the following Fig.9.It can be seen that the parameter values for long-lived eddies are always greater than those for mid-lived eddies, while the parameter values for mid-lived eddies are always greater than those for short-lived eddies.To some extent, the longer the life cycle of eddy, the larger its radius, amplitude, and maximum flow velocity.However,

Figure 9 .
Figure 9. Characteristic parameters of eddies with different life cycles varying with latitude.

Table 1 .
Statistics of the number of eddies in each region

Table 2 .
Statistics of Eddy Radius in Each Region

Table 3 .
Statistics of Eddy Amplitude in Each Region The frequency distribution of eddy amplitudes in the Kuroshio Extension is relatively dispersed, with eddies with amplitudes up to 30 cm present.

Table 4 .
Statistics of maximum eddy flow velocity in each region