Temporal and spatial distribution characteristics of ocean temperature front in Antarctic Circumpolar Current waters

This article uses satellite data and reanalysis data to study the spatiotemporal distribution characteristics of ocean temperature fronts in the Antarctic Circumpolar Current (ACC) waters under the proposed new classification standard using an optimized dynamic gradient threshold method based on Bayesian decision theory. The permanent oceanic front is mainly distributed between 40°S-65°S, with an average intensity of 1.5 °C per 100 kilometers; The average intensity of a semi permanent ocean front is 1.2 °C per 100 kilometers; The average intensity of the short-term oceanic front is around 1 °C per 100 kilometers. The determination of the optimal threshold in the ocean front recognition method adopted in this article is adaptive to the temperature distribution of the studied sea area, effectively reducing the subjectivity of threshold selection.


Research background and progress
Ocean temperature fronts are narrow transition zones with large temperature level gradients between two or more water bodies with significant differences, mainly located in the surface and subsurface layers of the ocean [1].It is widely recognized by scholars that there are three polar-orbiting oceanic fronts within the Antarctic Circumpolar Current (ACC) waters [2], which are, in order from south to north, the South Antarctic Circumpolar Current Front (SACCF), the South Antarctic Polar Front (SAPF), and the Sub Antarctic Front (SAF).
The study of oceanic fronts began in the mid-19th century, and so far they have been shown to play an important role in various aspects such as climate change, ocean circulation, and biochemistry [3].In the research direction of ocean fronts in the ACC waters, Moore [4] et al. used the temperature gradient greater than 1.35°C per 50 km as the criterion to determine the position of PF; Dong [5] et al. used the temperature gradient greater than 0.015°C per km as the criterion to consider the southernmost position greater than this threshold as the position of PF.Domestic and foreign scholars have analyzed and studied the characteristics of ocean fronts in Antarctic waters based on different definitions, but there is no uniform standard for identifying ocean fronts in Antarctic waters [6].In addition, there are scholars using other methods for the identification of ocean fronts.Ping [7] proposed a gravitational model front detection algorithm based on the gravitational edge detection algorithm, which realizes the effective detection of the front information while reducing the noise interference.
The idea of this paper is as follows.In the second chapter, two kinds of data and ocean front recognition methods are introduced.In the third chapter, a frequency based ocean front classification

Hydrographic characteristics of the study area
The study area of this paper is the ACC waters (40°S-80°S,180°W-180°E), and from figure1, we know that the isothermal lines around the Antarctic continent are distributed in a closed quasi-circle, and the temperature decreases from north to south.From figure 2, it is known that the mean sea surface temperature change in the ACC waters in 2019 has obvious seasonal characteristics, with higher temperatures in the first half of the year and lower temperatures in the second half of the year, reaching the highest and lowest values in mid-February and mid-August, respectively.It is noteworthy that a significant fluctuation in the sea surface temperature occurs at around day 100, suggesting that some scale of drastic weather changes occurred in the study area near day 100, resulting in anomalously high temperatures.Coraltemp is a sea surface temperature data provided by Coral Reef Observation Center of National Oceanic and Atmospheric Administration (NOAA), which is acquired by satellite remote sensing methods for monitoring global coral reef thermal stress.The spatial resolution of the data is 0.05° × 0.05°, the temporal resolution is 1 day, and the data period is from January 1, 2019 to December 21, 2019.The WOA18 data is also provided by NOAA, and the monthly average of temperature from the WOA18 data is used in this study.The spatial resolution of the data is 0.25° × 0.25°, the temporal resolution is 1 month, and the data period is 1955-2017.

Identification of ocean temperature fronts
2.2.1.Dynamic gradient thresholding method based on Bayesian decision theory.The sea surface temperature gradient is computed using the Sobel operator (2-1), a first-order discrete differential operator for edge detection that detects and linearly superimposes image edges in both the horizontal and vertical directions.In equation 2-1 is the matrix to be processed, is the result of horizontal edge detection, is the result of vertical edge detection, and is the gradient value after linear superposition.In this project, the Sobel operator is used to convolve the daily sea surface temperature data to obtain the temperature gradient for subsequent threshold selection. (2-1) The threshold interval is set according to the gradient cumulative probability density curve, and then find the optimal threshold value [8].In this project, the high and low threshold points of the threshold interval are set at 0.9 and 0.8 of the corresponding cumulative probability density, and their corresponding horizontal coordinate values are the high and low thresholds.Taking the data of January 1, 2019 as an example ( figure 3), the gradient corresponding to the high threshold is 0.91386, and the gradient corresponding to the low threshold is 0.62821.For all pixel points in the operation sea area, if the gradient value of a pixel point is greater than the high threshold, the pixel point is categorized as an ocean front; if its gradient value is less than the low threshold, the pixel point is categorized as a nonocean front; and if its gradient value is in the threshold interval, it is categorized as a candidate pixel point.

Figure 3. January 1, 2019 Selection of Threshold Intervals in Ocean Front Identification Methods
Pixel points for which classification is determined are not processed for the time being.For the pixels within the threshold interval (candidate pixels), this paper adopts the conditional probability method to calculate the probability of belonging to the ocean front and the probability of belonging to the nonocean front, and the gradient value corresponding to the pixel when the results of the two are equal is the optimal threshold value.
Taking the pixel in the temperature gradient data of a certain day as an example, the priori probability that pixel belongs to the ocean front can be calculated by equation (2-2): Where is the gradient value at point A of the pixel, and and are the lower and upper limits, respectively.Similarly, the prior probability that pixel belong to the nonocean front pixel can be calculated by equation (2-3): In the process of finding the optimal threshold this paper adopts the bifurcation method for algorithmic optimization, which reduces the space-time complexity of the people's operation.

Advantages and Disadvantages of methods.
The traditional ocean front identification method generally uses the static threshold method, i.e., a fixed threshold is artificially specified for the identification of ocean fronts, and pixels with a temperature gradient value greater than this threshold are categorized as ocean fronts, while pixels with a temperature threshold value less than this threshold are categorized as non-ocean fronts.This method is simple and easy to operate, but due to its strong subjectivity, the problem of inapplicability occurs when time and space changes.Taking figure 4 as an example (in an ideal situation), the fixed threshold can only identify the ocean front in zone A, but cannot identify the ocean front at zone B. The setting of the threshold interval in the ocean front identification method of this paper comprehensively utilizes all the data in the study sea area, so that the use of the dynamic threshold method can not only identify the stronger ocean fronts, but also take into account the weaker fronts to achieve the global optimal solution.

Characterization of the temporal and spatial distribution of ocean temperature fronts
Based on the ocean front identification method in Chapter 2, ocean front identification and feature extraction are carried out in this chapter for the ACC waters, and the frequency of ocean fronts appearing in the ACC waters in 2019 is shown in figure 5: The red color in the figure 5 represents the high frequency of oceanic fronts, and the blue color represents the low frequency of oceanic fronts.
In terms of the spatial distribution of oceanic temperature fronts, the distribution of oceanic temperature fronts in the ACC waters is basically in the form of a closed ring, and the direction of the fronts is roughly the same as that of the latitudinal direction.In addition, the distribution of oceanic fronts is basically concentrated in the 60°S-40°S ring, but the distribution in each sea area is slightly different: the distribution of oceanic fronts in the range of 0°-120°E (South Indian Ocean) is generally northward, the distribution of oceanic fronts in the range of 150°E-90°W (South Pacific Ocean) is generally southward, and the distribution of oceanic fronts in the range of 60°W-0° (South Atlantic Ocean) is more centered.The distribution of ocean fronts in the range of 60°W-0° (South Atlantic) is more centered.
The temporal distribution of oceanic temperature fronts varies considerably among sea areas.From the longitudinal point of view, the frequency of oceanic fronts is higher in 60°W-30°W (Scotia Sea), 0°-120°E (South Indian Ocean), and 150°W-120°W (South Pacific Ocean), and lower in 120°W-90°W (Southeast Pacific Basin).From the latitudinal point of view, the frequency of oceanic fronts in the range of 60°S-40°S is high, while the frequency of oceanic fronts in other areas is low.

3.2.1.
Definitions of permanent, semi-permanent, and short-critical ocean temperature fronts.In order to analyze the temporal and spatial distribution characteristics of ocean temperature fronts in the ACC waters, this paper classifies the ocean fronts into three categories according to the number of days of the ocean fronts in a year: permanent ocean fronts, semi-permanent ocean fronts, and short-term ocean fronts, and the classification criteria of these three categories of ocean fronts in this study are shown in table 1 6, the distribution area of permanent ocean fronts is relatively small, in addition to sporadic fronts in some areas of the sea is basically distributed in a band.The direction of the front axis is also more consistent, generally latitudinal distribution, in the east side of the American continent, the south side of the African continent, there is a stronger, wider north-south span of the ocean front area, while in other longitudes at the permanent ocean fronts north-south span is narrower, the strength of the relatively weaker.According to figure 7, it can be found that the distribution of the axis of permanent ocean fronts is consistent with the direction of isothermal lines, and there is a better consistency with the density of isothermal lines, which on the one hand indicates that the results of the identification of ocean fronts using this method are more reliable, and on the other hand, it also indicates that the influence of the annual mean sea surface temperature on the spatial distribution of permanent ocean fronts is more obvious.In addition, from figure 6 and figure 7, we can also intuitively find that the distribution of permanent oceanic fronts in the South Atlantic Ocean and the South Indian Ocean is more northward, while the distribution in the South Pacific Ocean is more southward.Moreover, the permanent oceanic fronts in the South Atlantic and South Indian Ocean are stronger and more continuously distributed than those in the southern Pacific Ocean.From figure 8, it can be seen that there are six obvious high fronts in the permanent oceanic fronts according to the longitudinal statistics, which are at 175°W, 140°W, 50°W, 10°W, 20°E, 50°E, and the intensity is the greatest at 50°W and 50°E.While some areas (near 100°W and 125°W) did not even have permanent oceanic fronts.In addition, the highest value of the frontal intensity reaches 2.5 times of the lowest value.From figure 9, it can be seen that the permanent oceanic fronts are mainly concentrated between 40°S and 65°S, and their latitudinal intensity distribution tends to decrease from north to south, but peaks occur near 48°S, 58°S, and 63°S.The above shows that there are large spatial differences in the intensity of permanent ocean fronts in both longitudinal and latitudinal directions.
From figure 10, it can be found that the permanent ocean front is almost a flat curve at other times, except for an obvious jitter at about 100 days (early April).The intensity of permanent ocean fronts basically showed an increasing trend in the first half of the year and a decreasing trend in the second half of the year, with the turning point of the change on the 200th day (mid-June).The average intensity of permanent ocean fronts was relatively strong at around 1.1°C per 100 km.11 show that the spatial distribution of semi-permanent oceanic fronts is relatively broad, with the whole of them circling the Antarctic in a closed loop.Overall, the semi-permanent oceanic fronts are basically distributed between 40°S-65°S, and they are distributed in all longitudes.Semi-permanent oceanic fronts have a wider distribution area than permanent oceanic fronts, but the overall intensity is small, indicating that the intensity of semi-permanent oceanic fronts is slightly smaller and the fluctuation between sea areas is not large.The axes of the semi-permanent ocean fronts are not plotted because of their irregular distribution shape and more holes.Figure 12 shows that the intensity of semi-permanent oceanic fronts varies in a continuous curve in terms of the intensity of oceanic fronts.The average intensity of semi-permanent oceanic fronts by longitude varies between 1 and 1.5°C per 100 km, with smaller fluctuations than those of permanent oceanic fronts (figure 8).Although the intensity of the semi-permanent fronts is more uniformly distributed, there are two peaks (50°W and 50°E) in the longitudinal statistics, which are close to the locations of the two largest peaks (50°W and 50°E) of the permanent oceanic fronts.From figure 13, it can be found that the intensity change of semi-permanent ocean fronts is also a continuous curve in terms of the intensity of ocean fronts when counted by latitudinal direction.The average intensity is also between 1-1.5°C per 100 km, with smaller fluctuations than that of permanent ocean fronts (figure 9).In addition, when the statistics are made by latitude, the intensity changes of semi-permanent ocean fronts and permanent ocean fronts basically follow the same trend of decreasing intensity from north to south, but the semi-permanent ocean fronts have a peak near 65°S, which is farther south than the maximum peak of permanent ocean fronts (48°S).In general, the semi-permanent oceanic fronts show a similar trend compared with the permanent oceanic fronts, but the permanent oceanic fronts are more intense and the intensity fluctuates more sharply along the longitudinal and latitudinal directions.
From figure 14, it is easy to find that similarly, the semi-permanent ocean front also showed a large fluctuation at the 100th day (early April), but apart from this fluctuation, the overall change of the semipermanent ocean front was more moderate, with only a slight downward trend at the end of the year.The average strength of the semi-permanent ocean front was around 0.7°C per 100 km, which was relatively weak.From figure 16, it can be seen that the short-advance oceanic fronts are distributed from 180°W to 180°E, and the average value is around 1℃ per 100 km, and there are two insignificant peaks in the statistics by longitude, which are at 40°W and 25°E, respectively.From figure 17, it can be seen that short-advance oceanic fronts are distributed between 40°S-80°S, which, combined with the previous results according to longitude, indicates that oceanic fronts are more common in the sea area around the Antarctic.In terms of intensity, it can be divided into three regions when analyzing the statistics by latitude.The intensity of short-proximity oceanic fronts between 40°S and 60°S remains stable without major fluctuations; the intensity gradually increases between 60°S and 70°S, and reaches a peak at 70°S; and then decreases gradually from 70°S to 80°S.
Combining figure 16 and figure 17, it is not difficult to find that the distribution of the intensity of short-advance oceanic fronts has a similar trend to that of permanent and semi-permanent oceanic fronts in longitude, but shows a different phenomenon in latitude.
From figure 18, it is easy to find that the short-advancement ocean front also has a large fluctuation at the 100th day (early April), but except for this fluctuation, the overall change of the semi-permanent ocean front is more moderate.Unlike the other two types of ocean fronts, the intensity of the shortadvancement ocean fronts, except for the strong fluctuation on the 100th day (early April), shows a generally decreasing trend before the 270th day (early September), and then an increasing trend after the 270th day until the end of the year.The average intensity of the short-proximity ocean front was weak at about 0.3°C per 100 km.

Summary and Discussion
In this paper, ocean temperature fronts in the ACC waters are identified using the dynamic gradient threshold method based on Bayesian decision theory, and the spatial and temporal distributions of permanent, semi-permanent, and short-advective ocean fronts are defined and analyzed.The main conclusions drawn from the study are as follows: In terms of ocean front identification methods, this study optimizes the subjectivity of gradient threshold selection using the dynamic gradient threshold method based on Bayesian decision theory.The method is able to adaptively select the optimal thresholds when recognizing ocean fronts in different spatial and temporal ranges, but the setting of high and low thresholds will have an impact on the recognition results.Meanwhile, the use of bifurcation method in the process of recognizing ocean fronts can effectively improve the computational efficiency.
Regarding the spatial and temporal distribution characteristics of ocean fronts, this study extracts the features of three types of ocean fronts from the perspective of location and intensity.Among them, the permanent ocean fronts are mainly distributed in the sea area between 40°S-65°S, and their intensity is the largest and fluctuates significantly with latitude and longitude changes.The average intensity of the permanent ocean front is 1.5℃ per 100 km, and the fluctuation range is between 1-2.5℃ per 100 km, in addition, it also has the characteristics of small area and regular shape.Semi-permanent ocean fronts are mainly distributed in the sea area between 40°S-65°S, and their intensity is larger, and the change of intensity with latitude and longitude is more moderate.The average intensity of the semipermanent ocean front is 1.2℃ per 100km, and the fluctuation range is between 1-1.5℃ per 100km, in addition, it also has the characteristics of wider distribution area and more holes.The short-proximity ocean front is distributed between 40°S-80°S, basically covering the whole study sea area.Its intensity is the smallest, with an average intensity of about 1°C per 100 km.In addition, the short-advancement ocean front is characterized by the largest distribution area and gentle changes.

Figure 4 .
Figure 4. Disadvantages of the static threshold method

Figure 5 .
Figure 5. Distribution of ocean temperature fronts in 2019 (Numerical value represents probability) Figure 6.Intensity of permanent ocean fronts and their axial distribution

Figure 7 .
Figure 7. Distribution of sea surface temperatures and axes of permanent ocean fronts in 2019

Figure 8 .Figure 9 .Figure 10 .
Figure 8. Intensity distribution of permanent ocean fronts across longitudes Figure 9. Intensity distribution of permanent ocean fronts at various latitudes Figure 10.Plot of intensity of permanent ocean fronts over time

Figure 11 .
Figure 11.Intensity distribution of semi-permanent ocean fronts

Figure 12 .Figure 14 .
Figure 12.Intensity distribution of semi-permanent oceanic fronts across longitudes Figure 13.Intensity distribution of semi-permanent oceanic fronts across latitudes Figure 14.Plot of the intensity of semi-permanent ocean fronts over time Figure15shows that the short-advance oceanic fronts are distributed in a faceted manner, with the largest area of distribution, a blueish overall color, and a small average intensity.The intensity of short-advance oceanic fronts does not differ significantly among sea areas, with the southernmost part of the Atlantic Ocean and the southernmost part of the Pacific Ocean having relatively greater intensity, while the ICFOST-2023 Journal of Physics: Conference Series 2718 (2024) 012004 IOP Publishing doi:10.1088/1742-6596/2718/1/0120048 intensity in other sea areas is smaller.Because of the large area and surface distribution of the shortadvance oceanic fronts, the axes of the fronts are not plotted.

Figure 15 .
Figure 15.Intensity distribution of short-range oceanic fronts

Figure 16 .Figure 18 .
Figure 16.Intensity distribution of semi-permanent oceanic fronts across longitudes Figure 17.Intensity distribution of semi-permanent oceanic fronts across latitudes Figure 18.Plot of the intensity of semi-permanent ocean fronts over time

Table 1 .
: Criteria for classification of ocean temperature fronts Characterization of the spatial and temporal distribution of permanent ocean fronts.As seen in figure