Korean Journal of Remote Sensing (대한원격탐사학회지)

Korean Society of Remote Sensing (대한원격탐사학회)
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Study on Dimensionality Reduction for Sea-level Variations by Using Altimetry Data around the East Asia Coasts

  • Hwang, Do-Hyun (Division of Earth Environmental System Science, Major of Spatial Information Engineering, Pukyong National University) ;
  • Bak, Suho (Division of Earth Environmental System Science, Major of Spatial Information Engineering, Pukyong National University) ;
  • Jeong, Min-Ji (Division of Earth Environmental System Science, Major of Spatial Information Engineering, Pukyong National University) ;
  • Kim, Na-Kyeong (Division of Earth Environmental System Science, Major of Spatial Information Engineering, Pukyong National University) ;
  • Park, Mi-So (Division of Earth Environmental System Science, Major of Spatial Information Engineering, Pukyong National University) ;
  • Kim, Bo-Ram (Division of Earth Environmental System Science, Major of Spatial Information Engineering, Pukyong National University) ;
  • Yoon, Hong-Joo (Division of Earth Environmental System Science, Major of Spatial Information Engineering, Pukyong National University)
  • Received : 2021.01.27
  • Accepted : 2021.02.10
  • Published : 2021.02.26
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Abstract

Recently, as data mining and artificial neural network techniques are developed, analyzing large amounts of data is proposed to reduce the dimension of the data. In general, empirical orthogonal function (EOF) used to reduce the dimension in the ocean data and recently, Self-organizing maps (SOM) algorithm have been investigated to apply to the ocean field. In this study, both algorithms used the monthly Sea level anomaly (SLA) data from 1993 to 2018 around the East Asia Coasts. There was dominated by the influence of the Kuroshio Extension and eddy kinetic energy. It was able to find the maximum amount of variance of EOF modes. SOM algorithm summarized the characteristic of spatial distributions and periods in EOF mode 1 and 2. It was useful to find the change of SLA variable through the movement of nodes. Node 1 and 5 appeared in the early 2000s and the early 2010s when the sea level was high. On the other hand, node 2 and 6 appeared in the late 1990s and the late 2000s, when the sea level was relatively low. Therefore, it is considered that the application of the SOM algorithm around the East Asia Coasts is well distinguished. In addition, SOM results processed by SLA data, it is able to apply the other climate data to explain more clearly SLA variation mechanisms.

Keywords

1. Introduction

There are several ways to analyze dimensioning long-term observation data, an empirical orthogonal function (EOF) is the most representative method. Since Lorenz (1956) introduced it at first, it has used in atmosphere, ocean and climate (Qi et al., 2014; Hu and Xu, 2020). EOF analysis described as a value representing the data by finding the axis with the largest variance, and define and extract spatiotemporal modes (Choi et al., 2012). Therefore, the first mode can explain the most data, and the second mode, which is orthogonal to the first mode and has a large variance, can be seen as representing the data second. By using the results for each mode, it is possible to select a physically meaningful mode variation while reducing the data (Zhang and Moore, 2015). However, it is useful for finding the strongest signal of the data, but it is difficult to find the physical interpretation because the condition that all the found signals must be orthogonal to each other must be satisfied.

Recently, as data mining and artificial neural network techniques are developed, techniques for analyzing large amounts of data actively studied. Self organizing maps (SOM) is one of the artificial neural network techniques that use unsupervised classification and is an alternative to EOF analysis (Kohonen, 2001; Jun and Choi, 2013; Jin et al., 2015). It can maintain the topology of the data even if it is classified, and is effective in finding patterns that closely match the neighbors. In addition, cluster analysis and correlation analysis for changes in nonlinear relationships are possible, and data interpretation is easy because both input and output data are imaged. Even if the data contains noise, patterns are able to extract, and various data such as climate change, ocean color, sea surface temperature, and sea level can be applied (Uriarte and Martín, 2005). It is possible to analyze the same event by adding other fields of data based on the clustered results (Grotjahn, et al., 2016).

EOF and SOM algorithm were projected based on visual clustering and were useful for extracting patterns (Liu and Weisberg, 2005; Chattopadhyay et al., 2011). Both used for reducing the dimension by using time series data in this study. EOF analysis is commonly used in the oceanography field, so SOM algorithm results are compared with the EOF results. Therefore, this study proposes a method of using the SOM technique in the oceanography field around the East Asia Coasts.

2. Data and methods

1) Data

Altimetry data provided from the Copernicus Marine Environment Monitoring Service (CMEMS; http://marine.copernicus.eu), used for different altimetry missions. The sea level anomaly (SLA) data is computed with 1993 to 2012 mean sea level. Altimetry data is provided through CMEMS’ Data Unification and Altimeter Combination System (DUCAS). The DUCAS system uses level 2 data as input data, processes the calibrated and generates the multi-gridded level 4 data. Altimetry was observed with Topex/Poseidon (1993-2002), Jason-1 (2002-2008), Jason-2 (2008- 2016), and now Jason-3 (2016-present) satellites. It measured up to 66°N. For global sea level height observations, high latitude data are used ERS-1 (1993-1995), GFO (2000-2008), Envisat (2002-2012), ALtiKa (2013-2015), Cryosat-2 (2011-2013), HY-2A (2014-2016), and Sentinel-3A (2016-present) (Taburet et al., 2019). The study period is a total of 26 years from January 1993 to December 2018, since altimetry data is collected. The resolution is 1/4° with monthly.

The study area is 25-45°N and 117-157°E, which includes the East China Sea around Northeast Asia and parts of the North Pacific Ocean. The Kuroshio Current flows in the study area, which is the second-largest current after the Atlantic Gulf Current. It starts at the eastern part of Taiwan in the western Pacific Ocean and flows to the north of Japan (Wang and Wu, 2019). As the Kuroshio Current flows along the Japan coast toward the Pacific Ocean, it becomes the Kuroshio Extension (KE) (Kida et al., 2015). Part of the Kuroshio Current from the East China Sea flows north to the west coast of Kyushu through the Korea Strait, flows into the East Sea of Korea. In East Asia, climate and environmental changes appear affected by the Kuroshio Current and KE, therefore, the study area selected to investigate sea level variations.

2) Methods

(1) EOF analysis

The EOF analysis is a simple and effective way to analyze the temporal and spatial variability in ocean research. It is mathematically independent in element analysis, a kind of variance technique of time series data, and can explain variance by the sum of functions that are not physically related. Even though the physical meaning of each eigenvector is not accurately identified, the fact that observations are reproduced with only a few eigen-functions is a great advantage of EOF analysis (Na et al., 1997). The first pattern is responsible for the largest part of the variance, and the second pattern is the largest part of the remaining variance. The EOF analysis is as shown in Equation 1, and singular value decomposition was used for patterns that are orthogonal to each other.

\(F(x, t)=\sum e_{i}(x) c_{i}(t)\)       (1)

where i is mode, ei(x) is spatial variations, ci(t) is temporal variations.

As an orthogonal function detects from time series data, numerous orthogonal functions are simultaneously calculated. The spatial structure corresponding to one mode is constant, the time change of the amplitude knows. Therefore, through the EOF analysis method, the temporal and spatial changes of sea level recognize at the same time.

(2) SOM analysis

SOM receives multidimensional data and derives dimensional results as much as the number of N nodes set by the user. A node is an area in which vectors having high similarity to each other are gathered among input vectors, and a reference vector is a vector representing each node in a group of N vectors as many as the number of nodes. The more neighboring nodes are, the greater similarity of the reference vectors appears (Back et al., 2018). The basic structure of SOM has an input layer having multi-dimension and an output layer of one or two dimensions, and it largely subjected to two processes: training and mapping. The training process is a process of determining reference vectors, which are N nodes. The number of reference vectors set in consideration of quantization error (QE) and topographic error (TE). The QE is the average distance between each data point and the node, and the TE is the ratio of the data points that are not adjacent units of the first node and the second node (Kiviluoto, 1996; Kohonen, 2001). In the training process, the weight is randomly set, and then the reference vector is determined through competitive iterations in which the input vector and the Euclidean distance value between the reference vector and the input vector minimized. Each iteration of the training reduces the distance from the weight of the node to the reference vector in which the node appears. This distance must reach the minimum plateau, and many iterations are required until the plateau is reached. At the end of the training process, the input vector classified through a mapping process in which a reference vector with the closest Euclidean distance found and assigned to the closest pattern (Lim and Seo, 2018). The closest distance from the input vector calculated by Equation 2.

\(d_{i j}=\sum\left(X_{i}(t)-W_{i j}(t)\right)^{2}\)       (2)

Where dij is the closest distance, Xi(t)is input vector, Wij(t)is weight.

Whenever an input vector arranged in each node, the reference vector and the neighboring weight updated through equation 3. The above process repeated until the last input vector arranged in the node (Back et al., 2018).

Wij(t+ 1) = Wij(t) + α(Xi(t) –Wij(t))       (3)

Where Wij(t+ 1)is updated weight, α is learning rate.

In this study, SOM Toolbox 2.0 version (http://www. cis.hut.fi/projects/somtoolbox/) provided by Helsinki University of Technology used. The input vectors were the monthly SLA data from 1993 to December 2018. The initial neighborhood radius set 3, training was ended when neighborhood radius became 1. The training length in epochs was 200. The reference vectors of 2 × 2, 2 × 3, 3 × 2, 2 × 4, 4 × 2, 3 × 3 was tested for the training. As the number of nodes increases, the QE decreases, but the TE increases (Pölzlbauer, 2004). Even if the number of nodes increased more than 6 nodes, similar sea level pattern appeared. Therefore, 2 × 3 nodes were selected to represent the study area and classified using the total of 6 nodes.

3. Results

1) EOF analysis

The EOF analysis is a simple and effective way to analyze the temporal and spatial variability in the ocean research. It is divided into modes according to the spatial size distribution characteristics of the largest to the smallest statistically among the variety of data that exist in spatial and temporal. It finds the temporal variation of each spatial distribution characteristic (Choi et al., 2012). Monthly SLA data for 26 years from 1993 to 2018 used. Fig. 1 shows the spatial temporal distributions of SLA data. The first mode explains about 59.7%, the second mode explains about 16.7% and the third mode explains about 13.2%. Because the 1-3 modes account for 89.6% of the total data, three modes used for analysis.

OGCSBN_2021_v37n1_85_f0001.png 이미지

Fig. 1. SLA spatial distribution of EOF (a) mode 1, (c) mode 2, (e) mode 3 and the time series coefficient of (b) mode 1, (d) mode 2, (f) mode 3.

The SLA spatial distribution of the first mode (Fig. 1(a)) was the highest in the 142-152°E, it considered that the effect of the KE flowing to the north along Japan was observed. In the East Sea of Korea, there was the three basins meet and meandering currents in the places where the positive value appears (Naganuma, 1973; Katoh, 1994). The time coefficient of the first mode (Fig. 1(b)) showed annual variations. It was the highest in October and the lowest in March. There was an upward trend in 1997-2002, 2009-2016, and a downward trend in 1993-1996 and 2003-2006. When the first mode of time coefficient analyzed by the power spectrum density, 1 year period and the half-year period were the dominant which was affected by the season.

The SLA spatial distribution of the second mode (Fig. 1(c)) was the highest in the 142-152°E, as in the first mode, but the variance value divided into two. The lowest appeared around the highest value. The time coefficient of the second mode (Fig. 1(d)) showed an upward and downward trend in an 8-10 year cycle from 1998 to 2006 and 2007 to 2016. When the second mode of time coefficient were analyzed the power spectrum density, 1 year period, 3-4 year period and 8-10 year period was the dominant. It showed the long term period.

The third mode of SLA spatial distribution (Fig. 1(e)), the highest was the 136-144°E near the Japan coast and the lowest was around 144°E. When the third mode of time coefficient (Fig. 1(f)) were analyzed the power spectrum density, 2 year period, 4 year period, 6-7 year period was the dominant which was the difference with the first and the second mode.

2) SOM analysis

In order to classify the characteristics of sea level variations around the East Asia Coasts, SOM analysis of 2 × 3 arrays applied. Fig. 2 is an SLA anomaly pattern for each node. Node 1 is the most common pattern of SLA data with a frequency of 20.2%. Most of them have positive SLA values, and especially high values of 0.4 m or more found in the 140-157°E section. Node 2 has a frequency of 14.4%, and the SLA near Honshu, Japan, has close to 0 m. Node 3 occurs the least with a frequency of 12.8%. Node 5 is the second most common pattern with a frequency of 19.6%. Node 5 considered to have a pattern similar to node 3, but the sea level is lower than node 3. Node 4 has a frequency of 14.1%, node 6 has a frequency of 18.9%, and those SLA patterns showed strongly negative among the nodes.

OGCSBN_2021_v37n1_85_f0002.png 이미지

Fig. 2. Spatial distribution of sea level anomaly images by using 2 × 3 SOM algorithm between 1993 and 2018. There are 6 nodes, each node shows frequency (f).

Node 1 showed the most similar pattern to the EOF mode 1 (Fig. 1(a)). The SOM array showed a similar pattern for each neighboring node. For example, Node 1, 3, and 5 were side-to-side neighboring, SLA gradually decreased. In the same way, node 2, 4, and 6 of SLA also gradually decreased. Node 3 and 4 were neighbors, but these arrays were up and down side, that showed the opposite patterns. Node 6 was the diagonally distant from node 1 that showed the opposite pattern. Node 3 and 5 showed the similar pattern with EOF mode 2 (Fig 1(c)).

The number of node occurrences per month showed in Table 1. In January, the node 5 appeared 13 times, and in February, node 5 and 6 appeared 12 and 13 times. In March, node 6 appeared 14 times and node 5 appeared 11 times, and in April, node 5 and 6 appeared 12 times each. Node 6 appeared 10 times and node 5 appeared 9 times in May, and node 3 appeared 10 times in June. Node 3 and 4 appeared 9 times each in July, and node 1 appeared 12 times and node 2 11 times in August. In September, node 1 and 14 and node 2 appeared 11 times, and in October, node 1 appeared 14 times and node 2 appeared 12 times. In November, node 1 appeared 14 times, in December, node 3 appeared 10 times, and node 4 appeared 9 times.

Table 1. The number of node by month using SLA 2 × 3 SOM algorithm between 1993 and 2018

OGCSBN_2021_v37n1_85_t0001.png 이미지

Node 1 and 2 dominantly occurred from August to November, and node 3 and 4 occurred in May to July and December and January when the season changes. Node 5 and 6 considered to occur from February to April. Because of comparison with monthly SLA data from the Korean Peninsula (Hwang et al., 2016), negative SLA patterns showed around Kyushu and Honshu in Japan from January to May, and South East China from August to November. In the East Sea of Korea, positive SLA patterns showed. Therefore, it considered that the SLA patterns by each node well classified because monthly variations reflected.

Fig. 3 showed the monthly mean SLA and each node’s monthly mean SLA. From January to May, the mean SLA was negative, from June to December, the mean SLA was positive. In March, the mean SLA was the lowest at -0.049 m, the mean SLA at node 5 and 6 were -0.039 m and -0.062 m respectively, with a difference of 0.023 m. In October, the mean SLA was the highest at 0.124 m, the mean SLA at node 1 and 2 were 0.146 m and 0.098 m, respectively, with a difference of 0.048 m. The mean difference for each node between March and October was about double. When comparing the mean SLA between nodes with high frequency in Table 1, node 1, 3 and 5 showed higher mean SLA than node 2, 4 and 6. Therefore, node 1, 3 and 5 showed extreme values than the mean.

OGCSBN_2021_v37n1_85_f0003.png 이미지

Fig. 3. Monthly mean SLA for each node. Node 1 (purple), node 2 (blue), node 3 (green), node 4 (yellow), node 5 (orange), node 6 (red) and the black solid line is monthly mean SLA.

Node 1 and 2, 3 and 4, 5 and 6 showed similar monthly distributions, but different SLA patterns. In order to analyze the trend, table 2 showed the frequency of occurrence by dividing the time by 5 years. Node 1 appeared 24 times in 2011-2015, 15 times in 2001- 2005. Node 2 appeared 14 times in 1996-2000 and 13 times in 2006-2010. Node 3 appeared 15 times in 2011- 2015, and node 4 appeared 15 times in 2006-2010. Node 5 appeared 24 times in 2001-2005, 19 times in 2011-2015. Node 6 appeared 23 times in 1996-2000, 17 times in 1993-1995, and 2006-2010. Therefore, node 1, 3, and 5 considered that mainly appeared as recent patterns from the early 2000s and the early 2010s to the present. Node 2, 4, and 6 considered that mainly appeared the late 1990s and the late 2000s. Each node appeared decadal timescale pattern, but node 1, 3, 5 patterns appeared more recently. Although it is difficult to identify the decadal timescale pattern from SLA, sea level declines in the late 1990s and the late 2000s, and sea level rise patterns in the early 2000s and the early 2010s near Japan (Sasaki et al., 2014). China and Korea, sea level variations occurred in 7-11 year cycle (Wang et al., 2018). Therefore, decadal SLA patterns appeared in the East Asia Coasts. Comparing the altimetry period, the rate of sea level rise in the last 10 years was higher than that of the initial observation (Dieng et al., 2017; Cazenave et al., 2018). In addition to decadal timescale pattern, it considered that there are another factors caused sea level rise recently.

4. Discussion

Both EOF and SOM algorithms were performed on SLA data with the same time domain. In order to compare EOF and SOM analysis, nodes clustered as SOM were applied to the result of EOF time series coefficient. Fig. 4 showed the result applied in August-October and February-April, when the change in mean SLA was the greatest.

OGCSBN_2021_v37n1_85_f0004.png 이미지

Fig. 4. Each nodes clustered as SOM were applied to the result of EOF time series coefficient mode 1 and 2. (a) and (b) are SLA mode 1, (c) and (d) are SLA mode 2. (a) and (c) applied from August to October results of SLA and (b) and (d) applied from February to April results. Node’s color is same as Fig. 3.

Fig. 4(a), node 1 and 2 appeared repeatedly, showed upward and downward trends from 1997 to 2008 and from 2009 to 2018 in August to October. If the upward trend was maintained, node 1 showed. Since the early 2010s, the upward trend of SLA has maintained continuously, node 1 was dominant. Fig. 4(b) showed the node 5 and 6 appeared repeatedly, showed the upward and downward trends from 1997 to 2006 and from 2007 to 2018 from February to April. Node 6 appeared the late 1990s and the late 2000s, and node 5 continued in the early 2000s and early 2010s. EOF mode 1 showed 1 year and half-year period where the Kuroshio Current was strong. SOM node 1 and 2 (summer) and node 5 and 6 (winter) indicated the variations of the Kuroshio Current. When the sea level increased in the early 2000s and the early 2010s, the KE was strong. On the other hand, when sea level declined in the late 1990s and the late 2000s, the KE was weak (Sasaki et al., 2015). Depending on the occurrence of each node, node 1 and 5 represented the strength of KE, and node 2 and 6 represented the weak KE.

Fig. 4(c) and 4(d), when the EOF mode 2 of high amplitude maintained, node 1 and 5 appeared. It indicated the patterns in which node 1 and 2, node 5 and 6 were not clearly distinguished in EOF mode 1 (Fig. 4(a) and 4(b)) were divided by strong amplitude. When amplitude was strong, it assumed that the Eddy Kinetic Energy (EKE) was also strong. When the EKE level is low, the KE path is stable, which tends to be less variable (Qiu, 2002; Bessières et al., 2013). The EKE was a stable state in 2002-2005, 2011-2012, 1997- 2001, 2006-2008 was unstable (Wang et al., 2016). It was difficult to find the exact study area and study period, depending on the occurrence of each node, node 1 and 5 represented the stable state of the EKE, and node 2 and 6 represented the unstable state of the EKE.

Node 4 appeared three times in August-October before 2000, it is noteworthy that this node was frequently occurring in February-April since 2010. It appeared when the season changes. As SLA node results are possible to analyze by adding the other data, further study is needed to determine whether node 4 appeared because of the sea level rise or it showed the early season change pattern.

5. Conclusions

In this study, EOF and SOM algorithm were investigated to reduce the dimension by using time series data and found the patterns around the East Asia Coasts. Both algorithms used monthly SLA data for 26 years from 1993 to 2018. EOF recognized the SLA trends and the spatial distribution of SLA data. It was easy to find the maximum amount of variance of EOF modes. However, EOF algorithm was difficult to find the specified the patterns where the minimum amount of variance because the all of SLA variance data was applied.

SOM preserved the topology of the data, which was easy to analyze the results. It was useful to find the change of SLA variable through the movement of nodes. The patterns corresponding to node 1 and 5 appeared in the early 2000s and the early 2010s, mainly appeared when the sea level was high. On the other hand, patterns corresponding to node 2 and 6 appeared in the late 1990s and the late 2000s, mainly appeared when the sea level was relatively low. It was able to summarize the characteristic of spatial distributions of SLA and the periods from EOF mode 1 and 2. Therefore, it is considered that the application of the SOM algorithm around the East Asia Coasts is well distinguished. Most of the ocean data are distributed over the coastline, so it is difficult to compare the in situ data with the satellite data. However, it is considered that comparing the SOM results with the in-situ data will help to compare the results.

The East Asian coastal region was dominated by the influence of the KE and it is estimated that the KE path according to the intensity of the EKE related to the strength of the KE. In addition, SOM results processed by SLA data, it is able to apply the other climate data such as sea surface temperature, wind, etc. It will explain more clearly about the mechanisms caused by SLA variations.

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