Spatial-temporal characteristics of temperature in Indonesian Sea based on a high-resolution reanalysis data

Influenced by both the Pacific and Indian Oceans, the temperature field in the Indonesian Sea are complicated. In order to reveal the spatial-temporal variability, the surface, thermocline and intermediate layers of the temperature field are studied based on the global ocean reanalysis data of Copernicus Marine Environment Monitoring Service (CMEMS) from 1993 to 2019 and the Empirical Orthogonal Function (EOF) analysis method. The results show that there is a warming trend of 1.36×10−2 °C /year in the surface layer. The first two modes both show reverse changes close to the Pacific and Indian Oceans. The correlation coefficients between the first and second modal time coefficients and the Niño 3.4 index are 0.62 and 0.48, respectively. And the correlation coefficient between the second modal time coefficient and the ITF inflow is -0.45. In the thermocline, there is a warmer trend, which is 4.78×10−2 °C /year. The correlation index of the first and second modal time coefficient with the Niño 3.4 and DMI indices are 0.87 and 0.43, respectively. The correlation index between the first and second modal time coefficient and the ITF inflow are -0.60 and 0.38, respectively. In the intermediate layer, the warming trend is 2.18×10−2 °C /year. From 1993 to 1999, from 2000 to 2016 and from 2017 to 2019, the Sulu Sea and northern Halmahera Sea experienced three periods of warming, cooling and warming, respectively. The study is helpful for further understanding the variation of the temperature field in the Indonesian Sea.


Introduction
The Indonesian Sea occupies an important position in the global climate system, which is an important conduit connecting the Pacific and Indian Oceans at low latitude.Temperature change between the two oceans can be balanced through the Indonesian Throughflow (ITF) [1], [2], which can carry 0.24~1.15PW (1 PW = 10 15 W) in the sense of annual average [3]- [5].Hirst et al. [6] suggest that closing the Indonesian strait can warm the Pacific Ocean and cool the Indian Ocean.
Due to the location of Indonesian Sea (Figure 1), its temperature changes are both related to El Niño-Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD) events [7].At the same time, the Walker circulation, which is closely related to the ENSO event in the Pacific Ocean, will affect the temperature field change in the Indonesian Sea, especially precipitation activities brought by it will greatly change the temperature field change in the upper layer of the Indonesian Sea [8].In addition, the Indonesian Sea is also a key link in surface compensation for deep Atlantic water bodies [9], and an important component of thermohaline exchange in the global ocean [10].Related studies [11]- [13] have shown that the temperature field in the surface of the Indonesian Sea is more correlated to ENSO and IOD events.However, due to the sparse observations and low-resolution of reanalysis data in the Indonesian Sea area and bathymetric topography (the area with red borders is the area studied) In this study, the spatial-temporal variation characteristics of the temperature field in the Indonesian Sea were studied using Copernicus Marine Environment Monitoring Service (CMEMS) reanalysis data.Since climate variability mainly affects the temperature field changes in the middle and upper layers, this study will focus on the temperature fields of the surface (0m), thermocline (109m) and intermediate layer (318m) of the Indonesian Sea.

CMEMS Global Ocean Reanalysis Data
CMEMS global reanalysis data (GLOBAL_MULTIYEAR_PHY_001_030) are used in this study, which are monthly average from 1993 to 2019.The Reanalysis Data has a spatial resolution of 1/12°×1/12° and a total of 50 layers in the vertical direction, which covered the whole ocean and assimilated the available observations.The time range covers the most recent period of altimeter data, which is from 1993 to 2020.The CMEMS data are also used to study the ITF and can better model the changing characteristics of the main strait flow field [14], [15].The CMEMS data used in this study are accessed from https://resources.marine.copernicus.eu.

Empirical Orthogonal Function (EOF)
EOF is applied to the meteorological fields by Principal Component Analysis (PCA).The method can objectively and quantitatively reflect the changes of the element field and the statistical coordination relationship between the elements [16].
Suppose a known spatial range of SST field, which contains  station information, each space In the matrix, a single SST value   represents the SST observations at a certain station , at time .The next step is to decompose the individual SST   into a linear superposition of the products between the independent time and space parts.
= ∑    =1 =  1  1 +  2  2 + ⋯ +     , ( = 1,2, ⋯ , ;  = 1,2, ⋯ , ) (2) The   is the part that only changes with space, also known as the spatial function, which does not change with the change of time point , but only depends on the space station .For the resulting SST data matrix , it can be written as a matrix product of space and time, i.e  =   = ( where  represents the matrix of the spatial part and  represents the matrix of the time part.The spatial functions are all unit column vectors, there are: The same spatial function is multiplied by its own transpose matrix as a unity matrix, i.e.  ′  =  (5) Using the transpose matrix  ′ left-by-sea temperature data matrix  formula of the spatial function (3), according to the above properties, there are:  =  ′  (6) The first few independently principal components can be used to interpret and analyze the initial field, which is arranged according to the variance contribution rate.

Significance test
The significance test is required after the eigenvalues are obtained.North et al. [17] proposed the test method, which used the calculated eigenvalue error range.The error range of the eigenvalue   is: where  is the sample size.If the next eigenvalue  +1 satisfies the following equation: ) That is, the orthogonal function corresponding to these two eigenvalues is considered a valuable signal.

Linear Trend
Figure 2 shows spatial distribution of linear trends at different level.At different levels, there are certain differences in the linear trend of temperature.In the surface (Figure 2A), almost the whole Indonesian Sea shows a warm trend.There is a temperature increase of 0.03°C/year in the eastern Sulu Sea, northern Sulawesi Sea, western Maluku Sea, eastern Banda Sea, and near the Sunda Strait.Among them, the temperature rise trend in the sea near the Sunda Strait is most prominent.Most of the Sulu Sea, Sulawesi Sea and its eastern sea and the Maluku Sea showed an increase of 0.02°C/year, as well as in the southern part of the Java Sea and the outflow of Lombok, Ombai and Timor Straits.The Makassar Strait, the eastern part of the Java Sea, the central and western parts of the Banda Sea, and the Timor Sea have smaller temperature increases at a rate of 0.01°C/year.The south-western part of Sulawesi, the entrance to the Ombai Strait and the south-eastern sea of Timor Island have the smallest temperature rise of around 0.005°C/year.In the intermediate layer (Figure 2C), there is no obvious trend of temperature change in most of the Indonesian Sea.There is a weak temperature trend of -0.03°C/year in the western and eastern parts of the Sulu Sea, the south-central part of the Sulawesi Sea, the northern sea of Central Sulawesi Province and the outflow of the Sunda Strait.The northwestern, northeastern and eastern parts of the Banda Sea and a small part of the Timor Sea have a temperature increase of 0.05°C/year.In order to obtain the average temperature change in the whole region, Figure 3 shows that each layer has a rising trend.In surface (Figure 3A), the growth rate is 1.36×10-2 °C /year.In 2016, the average temperature was the highest (29.5 °C ).In 1994, the average temperature was the lowest (28.6 °C ).In 1998, 2010 and 2016, the average surface temperature increased by more than 0.4°C compared with the previous year.It is maybe related to the occurrence of El Niño with lag.1997~1998, 2009 and 2015 are extremely strong El Niño years, which will bring warm water from the eastern Pacific Ocean.
In thermocline (Figure 3B), the rising trend is 4.78×10 -2 °C /year.In 2008, the average temperature of the interannual was the highest, about 23.2°C.In 1997, the average temperature of the subsurface layer was the lowest, about 19.6°C.From 1997 to 1999, the average temperature of the subsurface layer increased by 3.4 °C, and the annual change rate reached 1.7°C /year.
In intermediate layer (Figure 3C), the growth rate is 2.18×10 -2 °C /year.In 2008, the average temperature reached its highest, about 11.4°C.In 1993, the average temperature reached its lowest, about 10.2 °C.In 1993~1996, 1997~2000 and 2006~2009, the average temperature of the middle layer increased significantly, increasing by 0.6 °C, 0.6 °C and 0.7 °C respectively.In order to further study the interannual variation of surface temperature in the Indonesian Sea, EOF analysis was carried out and its significance was tested.To emphasize seasonal variation, winter average data from 1993-2019 were taken for EOF analysis.From the distribution of variance ratios of different modes (Figure 4), it can be calculated that the first, second, third and fourth modes account for 47.1%, 18.7%, 10.9% and 4.5%, respectively.It can be determined that the interannual distribution of surface temperature is determined by the first and second modes.(A) is the first mode, (B) is the second mode) Figure 5 shows the spatial and temporal fields of the first two modes in the EOF analysis of the surface temperature field in the Indonesian Sea.In the first mode of spatial distribution (Figure 5A), the east-central Sulu Sea, which connects the Pacific Ocean, the east-central Sulawesi Sea, the northcentral Maluku Sea, and the Halmahera Sea, which connects the Indian Ocean, show inverse phase changes to form a "seesaw" pattern.Among them, the western Pacific Ocean in the northern part of the Java Sea and the Maluku Sea are the two regions with large positive and negative phase changes.Combined with the time coefficient, it can be found that in El Niño years (1994,1998,2002,2006,2015,2019), the surface temperature of the connecting Pacific Sea has a decreasing trend due to the cooling of the western Pacific Ocean, especially in the strong El Niño years (1997/1998, 2015), and there is a lag.In these years, the areas connected to the Indian Ocean show a warming trend.Conversely, in La Niña years (1995,1999,2000,2011,2018), the surface temperature of the contiguous Pacific Ocean tended to increase due to warming in the western Pacific.The correlation index between the first modal time coefficient and the Niño 3.4 index is 0.62 and passes the 99% significance test.

Surface
For the second mode of spatial distribution (Figure 5B), the Sunda Strait outflow area connecting the Indian Ocean and the Timor Sea form an inverse phase trend with other seas.Among them, the Sulu Sea and the Timor Sea have large negative and positive phase changes, respectively.In El Niño years (2002,2006,2015,2019), the surface temperature of the connecting Pacific Ocean tends to decrease due to cooling in the western Pacific.Conversely, in La Niña years (1999,2000,2011), there was a tendency for surface temperatures in the Pacific Ocean to increase due to warming in the western Pacific.The correlation coefficient between the second modal time coefficient and the Niño 3.4 index reached 0.48, and passed the 95% significance test.By using EOF, Ju J et al. [11] also derived the inverting phase variation characteristics of the surface temperature field in the Indonesian Sea connecting the Pacific and Indian Oceans.Since ITF is also an important factor affecting the temperature change in Indonesian Sea, combined with the research of Li et al. [14], the correlation coefficient between the second modal time coefficient and the annual change of ITF inflow is -0.45, and passed 95% significance test.Combined with its spatial distribution, when the ITF strengthened, the Indonesian Sea near the Pacific Ocean showed a warming trend.

Thermocline
Figure 6.same as Figure 4 but for thermocline From the distribution of thermocline different modes (Figure 6), it can be calculated that the first, second, third and fourth modes account for 82.3%, 4.5%, 4.1% and 1.9%, respectively.The distribution of thermocline temperature is mainly determined by the first and second modes.7 shows the spatial and temporal fields of the first two modes in the EOF analysis of the thermocline temperature field in the Indonesian Sea.
For the first mode of spatial distribution (Figure 7A), almost all of the Indonesian Sea are in negative phase.Among them, there is a negative phase maximum in the western Pacific Ocean north of the Maluku Sea.The first mode of the thermocline is also influenced by ENSO.During El Niño events (1994, 1997/1998, 2002, 2004, 2006, 2015, 2019), the trend of temperature reduction near the western Pacific Ocean was more pronounced.Conversely, during La Niña events (1999/2000, 2011), the western Pacific showed a warming trend.The correlation index between the first modal time coefficient and the Niño 3.4 index is 0.87 and passes the 99% significance test.And the correlation coefficient between the first modal time coefficient and the annual change of ITF inflow is -0.60, and passed 99% significance test.Combined with its spatial distribution, when the ITF strengthened, the Indonesian Sea near the Pacific Ocean showed a warming trend.
For the second mode of spatial distribution (Figure 7B), the western Pacific Ocean in the northern Maluku Sea, the northwestern Sulawesi Sea, the Makassar Strait and the Sulu Sea are positive phase, while the central Sulawesi Sea, the Banda Sea, the Timor Sea and the outflow of the Ombai Strait are negative phase.Among them, there are positive phase maximum in the western Pacific Ocean in the northern Maluku and northern Sulawesi Seas, and negative phase maximum in outflow of the Ombai Strait.The second mode of the thermocline shows a strong correlation with IOD events.During the positive IOD event (2006/2007), there was a cooling trend in the lower Makassar Strait, the Banda Sea and the Timor Sea, which connect the Indian Ocean.However, during the negative IOD event (2016), the seas connecting the Indian Ocean showed a warming trend.The correlation index between the second modal time coefficient and the DMI index was 0.43 and passed the 95% significance test.The correlation coefficient between the second modal time coefficient and the annual change of ITF inflow is 0.38, and passed 90% significance test.Combined with its spatial distribution, when the ITF strengthened, the Indonesian Sea near the Pacific Ocean showed a warming trend.8), it can be calculated that the first, second, third and fourth modes account for 38.1%, 18.0%, 11.1% and 6.5%, respectively.It can be determined that the interannual distribution of thermocline temperature in the Indonesian Sea is mainly determined by the first mode.IOP Publishing doi:10.1088/1742-6596/2718/1/0120419 thermocline temperature field in the Indonesian Sea.For the first mode of spatial distribution (Figure 9A), the Sulu Sea and northern Halmahera Sea are positive, while the Sulawesi Sea, Makassar Strait, Maluku Sea, Banda Sea and Timor Sea are all negative phase changes.Among them, there is a maximum negative phase in the eastern part of the Banda Sea.Combined with the change of time coefficient, it can be found that the temperature changes in the Sulu Sea and the northern part of the Halmahera Sea are roughly divided into three stages at different times: 1993-1999, 2000-2016, and 2017-2019, respectively, they experienced three periods of warming, cooling and warming.

Summary and Conclusion
Based on the CMEMS reanalysis data from 1993 to 2019, the temporal and spatial variation characteristics of the surface, thermocline and intermediate temperature fields in the Indonesian Sea are studied, and the following conclusions are obtained: (1) In the surface, almost the whole Indonesian Sea shows a strong warming trend.There is a temperature increasing trend of 0.03°C/year in the sea near the Sunda Strait.The spatially averaged warming rate is 1.36×10 -2 °C /year.The SST field is mainly controlled by the first two modes, which both show reverse changes close to the Pacific Ocean and close to the Indian Ocean.The correlation coefficients between the first and second modal time coefficients and the Niño 3.4 index are 0.62 and 0.48, respectively.The correlation coefficient between the second modal time coefficient and the ITF inflow is -0.45.
(2) In the thermocline, the long-term warming trend has strengthened.There is a warming trend of 0.05°C/year in the central part of the Sulu Sea, central and western part of the Sulawesi Sea, southeastern part of Mindanao, central and western part of the Banda Sea, and Timor Sea.The spatially averaged growth rate is 4.78×10 -2 °C /year.The first two modes dominate the temperature variation.In the first mode, almost all of the Indonesian Sea are negative phase.The correlation index of the first modal time coefficient with the Niño 3.4 index is 0.87.The second mode shows a reverse change close to the Pacific and Indian Oceans.The correlation of the second modal time coefficient with the DMI index is 0.43.The correlation index between the first and second modal time coefficient and the ITF inflow are -0.60 and 0.38, respectively.
(3) In the intermediate layer, the temperature interannual growth rate is 2.18×10 -2 °C /year.The temperature increasing trend of 0.05°C/year mainly exist in the northwestern, northeastern and eastern parts of the Banda Sea and a small part of the Timor Sea.The space field is mainly controlled by the first mode.The Sulu Sea and northern Halmahera Sea are inverse-phase changes with other seas.From 1993 to 1999, from 2000 to 2016 and from 2017 to 2019, the Sulu Sea and northern Halmahera Sea experienced three periods of warming, cooling and warming, respectively.
Through this study, it can be found that the first two modes of surface, first mode of thermocline and second mode of thermocline are significantly correlated with the Niño 3.4, Niño 3.4 and DMI indices, respectively, which may be related to a series of phenomena caused by ENSO and IOD events.ITF also have an important impact on temperature changes in Indonesian Sea.In addition to ENSO, IOD events and ITF, factors such as ocean acidification are also responsible for the temperature rising in Indonesian Sea [18].This study only focuses on the temperature changes in the middle and upper layers, but does not study the temperature changes at full depth in the Indonesian Sea.In addition, the salinity changes in Indonesian Sea can also be obtained by such methods.

Figure 1 .
Figure 1.Indonesian Sea area and bathymetric topography (the area with red borders is the area studied) In this study, the spatial-temporal variation characteristics of the temperature field in the Indonesian Sea were studied using Copernicus Marine Environment Monitoring Service (CMEMS) reanalysis data.Since climate variability mainly affects the temperature field changes in the middle and upper layers, this study will focus on the temperature fields of the surface (0m), thermocline (109m) and intermediate layer (318m) of the Indonesian Sea.

Figure 2 .
Figure 2. Spatial distribution of linear trends at different levels in Indonesian Sea from 1993 to 2019.(A-C) are surface, thermocline, and intermediate layer, respectively.In the thermocline (Figure2B), there is a temperature increase of 0.05°C/year in the central part of the Sulu Sea, central and western part of the Sulawesi Sea, south-eastern part of Mindanao, central and western part of the Banda Sea, and Timor Sea.In the intermediate layer (Figure2C), there is no obvious trend of temperature change in most of the Indonesian Sea.There is a weak temperature trend of -0.03°C/year in the western and eastern parts of the Sulu Sea, the south-central part of the Sulawesi Sea, the northern sea of Central Sulawesi Province and the outflow of the Sunda Strait.The northwestern, northeastern and eastern parts of the Banda Sea and a small part of the Timor Sea have a temperature increase of 0.05°C/year.

Figure 3 .
Figure 3. Spatial average interannual linear trends at different levels in Indonesian Sea from 1993 to 2019.(A-C) are surface, thermocline, and intermediate layer, respectively.In order to obtain the average temperature change in the whole region, Figure3shows that each layer has a rising trend.In surface (Figure3A), the growth rate is 1.36×10-2 °C /year.In 2016, the average temperature was the highest (29.5 °C ).In 1994, the average temperature was the lowest (28.6 °C ).In 1998, 2010 and 2016, the average surface temperature increased by more than 0.4°C compared with the previous year.It is maybe related to the occurrence of El Niño with lag.1997~1998, 2009 and 2015 are extremely strong El Niño years, which will bring warm water from the eastern Pacific Ocean.In thermocline (Figure3B), the rising trend is 4.78×10 -2 °C /year.In 2008, the average temperature of the interannual was the highest, about 23.2°C.In 1997, the average temperature of the subsurface layer was the lowest, about 19.6°C.From 1997 to 1999, the average temperature of the subsurface layer increased by 3.4 °C, and the annual change rate reached 1.7°C /year.In intermediate layer (Figure3C), the growth rate is 2.18×10 -2 °C /year.In 2008, the average temperature reached its highest, about 11.4°C.In 1993, the average temperature reached its lowest, about 10.2 °C.In 1993~1996, 1997~2000 and 2006~2009, the average temperature of the middle layer increased significantly, increasing by 0.6 °C, 0.6 °C and 0.7 °C respectively.

Figure 4 .
Figure 4. Distribution of variance contribution rate of the first four modes of EOF analysis in the surface temperature field of Indonesian Sea (red indicates passing the significance test)

Figure 5 .
Figure 5. Spatial and temporal fields of the first two modes (left is space, right is time;(A) is the first mode, (B) is the second mode) Figure5shows the spatial and temporal fields of the first two modes in the EOF analysis of the surface temperature field in the Indonesian Sea.In the first mode of spatial distribution (Figure5A), the east-central Sulu Sea, which connects the Pacific Ocean, the east-central Sulawesi Sea, the northcentral Maluku Sea, and the Halmahera Sea, which connects the Indian Ocean, show inverse phase changes to form a "seesaw" pattern.Among them, the western Pacific Ocean in the northern part of the Java Sea and the Maluku Sea are the two regions with large positive and negative phase changes.Combined with the time coefficient, it can be found that in El Niño years(1994, 1998, 2002, 2006,  2015, 2019), the surface temperature of the connecting Pacific Sea has a decreasing trend due to the cooling of the western Pacific Ocean, especially in the strong El Niño years(1997/1998, 2015), and there is a lag.In these years, the areas connected to the Indian Ocean show a warming trend.Conversely, in La Niña years(1995, 1999, 2000, 2011, 2018), the surface temperature of the contiguous Pacific Ocean tended to increase due to warming in the western Pacific.The correlation index between the first modal time coefficient and the Niño 3.4 index is 0.62 and passes the 99% significance test.For the second mode of spatial distribution (Figure5B), the Sunda Strait outflow area connecting the Indian Ocean and the Timor Sea form an inverse phase trend with other seas.Among them, the Sulu Sea and the Timor Sea have large negative and positive phase changes, respectively.In El Niño years(2002, 2006, 2015, 2019), the surface temperature of the connecting Pacific Ocean tends to decrease due to cooling in the western Pacific.Conversely, in La Niña years(1999, 2000, 2011), there was a tendency for surface temperatures in the Pacific Ocean to increase due to warming in the western Pacific.The correlation coefficient between the second modal time coefficient and the Niño 3.4 index reached 0.48, and passed the 95% significance test.By using EOF, Ju J et al.[11] also

Figure 7 .
Figure 7. same as Figure 5 but for thermocline Figure7shows the spatial and temporal fields of the first two modes in the EOF analysis of the thermocline temperature field in the Indonesian Sea.For the first mode of spatial distribution (Figure7A), almost all of the Indonesian Sea are in negative phase.Among them, there is a negative phase maximum in the western Pacific Ocean north of the Maluku Sea.The first mode of the thermocline is also influenced by ENSO.During El Niño events(1994, 1997/1998, 2002, 2004, 2006, 2015, 2019), the trend of temperature reduction near the western Pacific Ocean was more pronounced.Conversely, during La Niña events (1999/2000, 2011), the western Pacific showed a warming trend.The correlation index between the first modal time coefficient and the Niño 3.4 index is 0.87 and passes the 99% significance test.And the correlation

Figure 8 .
Figure 8. same as Figure 4 but for intermediate layer From the distribution of variance ratios of different modes (Figure8), it can be calculated that the first, second, third and fourth modes account for 38.1%, 18.0%, 11.1% and 6.5%, respectively.It can be determined that the interannual distribution of thermocline temperature in the Indonesian Sea is mainly determined by the first mode.

Figure 9 .
Figure 9. Spatial and temporal fields of the first mode in the intermediate layer (left isspace, right is time) Figure9shows the spatial and temporal fields of the first two modes in the EOF analysis of the station corresponds to  times of SST observation data.The SST values are arranged regularly in matrix form, i.e