Mooring data are obtained from three straits: the Makassar Strait, Ombai Strait, and Timor Strait. Among them, the Makassar mooring data is procured from the INSTANT and MITF observation projects, whereas the Ombai and Timor are from the Integrated Marine Observing System (IMOS, 2022).

Four reanalysis datasets are used: Copernicus Marine Environment Monitoring Service (CMEMS), OGCM For Earth Simulator (OFES), Hybrid Coordinate Ocean Model (HYCOM), and simple Ocean Data Assimilation Ocean/Sea Ice Reanalysis (SODA), respectively.

Performances of the four reanalysis datasets are validated by using the mooring observation located at the Makassar Strait, namely the INSTANT and MITF programs. In accordance with the two periods of INSTANT and MITF, the comparative results are divided into two stages, which are January 2004 to late November 2006 and November 2006 to August 2017, respectively. An approximate position at the same latitude as the mooring position is selected to conducted verification when calculating the Makassar Strait flow, which is 117°E–119°E, 2.5°S ( Figure 1 ).

The comparative results are illustrated in Figures 2A, B . In the upper layer, the mean mooring transport is -7.94 Sv (negative means southward transport). It shows a prominent interannual variability. The transport intensified from 2004 to late 2008, with an intensification of -1.53 Sv, whereas from 2009 to mid–2011, it slightly weakened by 0.32 Sv. The transport quickly weakened from mid–2013 to mid–2016, whereas the ITF quickly intensified. The relativity between the upper and lower layers was negative and insignificant (correlation coefficient of -0.30). In the lower layer, the mean transport is -3.10 Sv. The trends of mean transport during 2004–2011 and 2013–2017 were the opposite: there is an intensified (weakened) trend in the former period and a weakened (intensified) trend in the latter period in the upper (lower) layer. In addition, in terms of interdecadal variability, the correlation between the upper layer Makassar flow and PDO and NPO were significantly opposite (Figures not shown). During 2004–2011 and 2013–2017, the correlation coefficients between PDO and flow in the upper layer were 0.78 and 0.75, respectively; whereas the correlation coefficients between NPO and flow changes in the upper layer were -0.44 and -0.35, respectively. All the correlation coefficients pass the 95% significance test. However, the contributions of PDO in the ITF transport are limited in the upper layer inflow and in the decadal timescales, which will not be further considered in this study.

In the upper layer, the correlation coefficients of SODA and CMEMS in the first and second periods are R1 = 0.8 and R2 = 0.96, respectively, and the RMSE is 1.12 Sv, in comparison with the observed data. Similarly, the OFES data in this layer exhibit low correlation coefficients with the observed data in the first half and the second half, where R1 = 0.25 and R2 = 0.7, respectively, and the RMSE is 0.82 Sv. It can be found that between July 2005 and November 2006, the reanalysis data declined more than the mooring observation data, which may be explained by that single point data of Makassar mooring could not accurately reflect the whole change in the entire channel. In the lower layer, the correlation coefficients of OFES and CMEMS with the observed data in the first and second half are R1 = 0.73 and R2 = 0.98, respectively, and the RMSE is 0.89 Sv. The HYCOM data in this layer has relatively low correlation coefficients of R1 = 0.49 and R2 = 0.77, respectively, and the RMSE is 1.35 Sv, in comparison with the observed data. All the correlation coefficients pass the 95% significance test. It can be found that in the upper and lower layers, the correlation between the reanalysis and mooring observation data in the second period is better than in the first period, which may be attributed to the reanalysis datasets dependency and the limitation of mooring observations.

The mooring data of the Ombai and Timor Straits are comprehensively collected to verify the applicability of reanalysis data in the outflow area. Two sections along 125.08°E, 8.33°S–8.83°S and 127.35°E, 8.71°S–10.02°S in the Ombai and Timor Straits, respectively, are selected to conduct the calculation. The low resolution of SODA (only 0.1°) leads to a lack of lower layer data in the Ombai Strait, and hence, only the upper layer of SODA is given below.

Figures 3A, B illustrate the comparison results in the Ombai Strait. For SODA, the correlation with the observed data is low due to the low resolution in the upper layer (R = 0.31, which passes the 95% significance test; RMSE = 0.61 Sv). Apart that, the correlations of the other three reanalysis data are all high. Among them, correlation coefficient of OFES is maximum which reaches 0.90 and RMSE is 0.45 Sv. In the lower layer, HYCOM has the maximum correlation coefficient of 0.80 and lowest RMSE of 0.28 Sv, whereas OFES has a relatively low correlation coefficient of 0.69 and RMSE of 0.43 Sv. The validation results of the Timor Strait data are shown in Figures 3C, D . It is found that CMEMS has the maximum correlation coefficient of 0.71 and lowest RMSE of 0.14 Sv in the upper layer, whereas HYCOM has a relatively low correlation coefficient of 0.38 (passing the 95% significance test) and RMSE of 0.26 Sv. In the lower layer, CMEMS also exhibits a good correlation, with a correlation coefficient of 0.63 and RMSE of 0.11 Sv. However, the correlation coefficients of the other three data are low. Note that, all the correlation coefficients pass the 95% significance test, which demonstrate that all the four reanalysis datasets show consistency with the observations, which gives the confidences to use the reanalysis datasets to show the variability and mechanisms.

Good performance of the eddy-resolving reanalysis datasets reveals, the detailed spatial structures of the ITF in the inflow and outflow.

Among the three inflow cross-sections ( Figures 4A–C ), the Sulawesi Sea has the widest entrance, which spans 3.58°N–5.5°N, 125°E. There are two opposite flows, which are westward in the northern channel and eastward in the southern channel, respectively. As the depth deepens, the eastward flow gradually expands to the north, while the westward flow decreases in scope. The eastward flow mainly exists in the range of 125°E, 1.83°N–3.5°N (the maximum depth is 350 m south of 3.25°N, while it can be extended to 760 m north of 3.25°N), with an average speed of 0.07 m s^-1 and a maximum speed of 0.23 m s^-1 at a depth of 20m near 2.25°N. The westward flow in the 3.58°N–4.66°N region mainly exists above the 115 m layer with an average speed of -0.14 m s^-1. The large value zone of westward flow mainly exists in 4.5°N–5.33°N (the depth can be extended to 760 m) and a maximum speed is -0.59 m s^-1 at a depth of 85 m near 5°N. There is a weak eastward flow near Mindanao Island. The standard deviation of the flow gradually decreases with the increase of depth overall. There has a larger standard deviation in the westward flow, which can reach 0.13 m s^-1, mainly concentrated in the upper 90 m layer of 4.58°N–5.08°N. In the eastward flow range, the standard deviation of the flow can reach a maximum of 0.09 m s^-1, mainly concentrated in the surface layer of 1.91°N–2.83°N.

The opposite flow structure is the same as the Maluku Sea meridional sections ( Figure 4B ). In the western Maluku Sea (125°E–126°E, 0.5°N): above 60 m layer, it flows northward with an average speed of 0.05 m s^-1, and the maximum is 0.16 m s^-1 at a depth of 10 m near 125°E; within a depth of 60 m–300 m, it flows southward with an average speed of -0.02 m s^-1, and the flow gradually decreases as the depth increases; within a depth of 300 m–450 m, there is a weak northerly flow; under 450 m, there is a southward flow, which corresponds well to the observational finding of the Maluku Sea intermediate western boundary current (Yuan et al., 2022). In the eastern Maluku Sea (126°E–127.5°E, 0.5°N): above 60 m layer, there is a weak southward flow with an average speed of -0.03 m s^-1 and the maximum southward flow velocity is -0.07 m s^-1; under 60 m, except for the presence of weak southward flow in depth of 350 m–720 m and range of 126°E–126.41°E, it flows northward in the western side (126°E–126.83°E, 0.5°N) and southward on the eastern side (126.83°E–127.5°E, 0.5°N). The large standard deviation of the flow velocity is mainly concentrated in the western upper layer of Maluku Sea (125°E–126°E, 0.5°N), which can reach a maximum of 0.07 m s^-1. With the increase of depth, the standard deviation gradually decreases. However, below 450 m in the western of Maluku Sea, there is still a relatively large variation zone with a standard deviation of 0.02 m s^-1.

In the Halmahera Sea section (0.5°S) ( Figure 4C ), the flow structures are complicated. In the range of 128.5°E–129.75°E and 129.91°E–130.08°E, there are southward flows, which can reach a depth of 200 m. The maximum velocity (-0.36 m s^-1) appears at 128.83°E and 50 m depth. The flow is northward at both sides of the Halmahera Sea section and in the lower layer. However, the northward flow is relatively weak, with a maximum of 0.08 m s^-1. The large standard deviation of flow velocity is concentrated in the large value region of southward flow, which can reach a maximum of 0.14 m s^-1 in the upper layer of 128.83°E. With the increase of depth, the standard deviation gradually decreases. At the maximum southward flow (at 128.83°E and 50 m depth), the standard deviation reaches 0.12 m s^-1.

In the exit of the eastern equatorial Indian Ocean ( Figure 4D ), the outflow is a significant eastward flow in the 0–110 m range of 114°E, 8.75°S–9.33°S, and the maximum velocity is 0.22 m s^-1 at a depth of 60 m at 8.83°S. The eastward flow corresponds to the upper ocean South Java Coastal Current (SJCC) (Atmadipoera et al., 2009; Sprintall et al., 2009; Liang and Xue, 2020). In the middle section of 114°E, 9.5°S–13.41°S, most of the flow is westward with a maximum of -0.28 m s^-1, which exists at a depth of 10 m at 10.5°S. The eastward flow south of 14°S is closely related with the Eastern Gyral Current (EGC) and the Northwest Shelf Inflow (NWS-inflow) (Liang and Xue, 2020). The large standard deviation values of flow velocity are concentrated in the range of westward flow, which can reach 0.06 m s^-1 in the upper layer.

The comparison results reveal a narrower and stronger inflow and a wider and weaker outflow. This opposite flow among the cross-sections implies complicated flow structures in the high-resolution reanalysis datasets. Detailed flow structures along with additional field experiments should be verified.

To understand the interannual variations of the ITF transport, the upper, lower and full depth layers of the inflow and outflow transport anomaly are illustrated in Figure 5 . The results are averaged from the four reanalysis datasets. In the upper layer ( Figure 5A ), the linear trends of inflow and outflow are -0.08 Sv year^-1 and -0.04 Sv year^-1, respectively (negative linear trend indicates an increase in southwesterly flow). During the strong El Niño event (1997/1998), there was a significant decrease in the upper layer inflow, with a value of -3.38 ± 4.15 Sv. It applies to 2015/2016 as well, when the upper layer inflow is -4.90 ± 1.98 Sv. During positive IOD events (2004–2008), the upper layer inflow increased significantly, from -5.31 ± 2.76 Sv in 2004 to -14.31 ± 4.14 Sv in 2008. However, the upper layer outflow intensified only during 2005–2006, which was significantly weaker than the inflow. In the upper layer outflow, the interannual variation is similar to those of the inflow, the average correlation coefficient between the upper layer inflow and outflow of the four models is 0.63, which passes the 99% significance test. The average flow is more intensified than the upper layer inflow, and the difference is 3.23 Sv. In the upper layer, it can be found that the inflow is smaller than the outflow, which is mainly due to the reason that the South China Sea (SCS) branch of the ITF is not taken into account. Note that, the depth of the Karimata Strait that connects the SCS and Indonesian Sea is less than 50 m, so its inflow mainly contributes to the upper layer.

Unlike the upper layer, the lower layer flow shows no significant trend in the interannual scale ( Figure 5B ). For the lower layer inflow, the flow decreased in 2015 and increased in 2016, but with a much smaller amplitude than that of the upper layer. The lower layer outflow in the same period was also similar. In 1997, the lower layer outflow showed a similar change as the upper layer. In the lower layer, it can be found that the outflow is greater than the inflow, which is closely related to the large inflow of HYCOM.

The total ITF transport is obtained in Figure 5C . The results show that the average ITF transport is -13.33 Sv and -16.62 Sv of the inflow and outflow, with linear strengthening trends of -0.06 Sv year^-1 and -0.05 Sv year^-1, respectively. On average, the outflow value is larger than the inflow. The outflow volume transport estimated in this study is -16.62 Sv, which is close to that by SODA (-16.9 Sv) and the multi-model ensemble means of phase 5 of the Coupled Model Intercomparison Project (CMIP5) (-15.3 Sv) (Santoso et al., 2022). In the Makassar Strait, the mooring average flow of the upper (-9.10 Sv) and lower layers (-3.40 Sv) from 2004 to 2017 (Gordon et al., 2019) are consistent with the reanalysis datasets, which is -9.36 Sv in the upper layer and -1.88 Sv in the lower layer. The difference in the outflow and inflow (3.29 Sv) is larger than in the Makassar Strait (1.26 Sv). Two possible reasons contribute to the mismatch between the inflow and the outflow. First, the SCS branch of the ITF and the inflow along the northern Australia coast are not taken into account in the inflow and outflow calculation, which results in small and large estimates of the inflow and outflow, respectively. Results of the previous particle tracking experiments present the interannual average of the ITF branch in the South China Sea to be approximately 1.6–1.98 Sv (He et al., 2015; Xu et al., 2021). Most of the reanalysis data show that the inflow after adding Karimata Strait flow is comparable to the outflow. And for the high spatial resolution data (CMEMS, HYCOM), the inflow adding Karimata Strait flow is comparable to the outflow after subtracting the inflow along the northern Australia coast. Second, different reanalysis data show large dispersions in the ITF estimation. The full-depth ITF obtained by four kinds of reanalysis data (CMEMS, SODA, OFES, HYCOM) at the inflow position is -14.22 Sv, -15.01 Sv, -6.44 Sv, and -16.94 Sv, respectively. At the outflow position, they are -17.28 Sv, -15.20 Sv, -8.95 Sv, and -24.29 Sv, respectively. The differences are 3.06 Sv, 0.19 Sv, 2.51 Sv, and 7.35 Sv, respectively. The largest deviation between the outflow and the inflow is derived from the HYCOM dataset. In addition, the selection of the outflow section also affects the amount of transport. Overall, it is reasonable to use reanalysis data in this study to reflect the interannual changes of ITF.

Figure 6 illustrates the variabilities of ITF transport in different layers that further explain the correlations between the climate modes and the detailed flow structure. For the upper layer inflow, the correlation coefficients between flow data and Niño 3.4, DMI, and CP indices are 0.73, -0.28, and 0.56, respectively. Among the above results, Niño 3.4 and CP pass the 99% significance test, whereas DMI does not pass the 95% significance test. In the lower layer inflow, the correlation coefficient between flow anomaly and Niño 3.4, DMI and CP indices are 0.23, 0.01 and 0.12, respectively, none of them pass the 95% significance test. This concludes that the influence of the climate index in the upper layer is greater than that in the lower layer.

In the upper layer outflow, the correlation coefficients between flow data and Niño 3.4, DMI, and CP indices are 0.52, -0.55, and 0.32, respectively. Among the above results, Niño 3.4 and DMI pass the 99% significance test, whereas CP does not pass the 90% significance test. In the lower layer outflow, the correlation coefficients of flow anomaly with Niño 3.4 and CP indices are 0.65 and 0.41, respectively, and they pass the 99% significance test, whereas the correlation coefficient with the DMI shows a low correlation (0.12). The correlation between Niño 3.4 and CP indices, and the lower layer is greater than the correlation of the upper layer inflow. Whereas, the correlation between the DMI index and the lower layer with that of the upper layer inflow is the opposite.

Niño 3.4 and DMI have opposite correlations for ITF in comparison with the upper layer inflow and outflow. The linear correlation coefficients between Niño 3.4 and ITF anomalies remained high at 0.73 and 0.52 for the inflow and outflow, respectively. However, the DMI is -0.28 and -0.55 in the inflow and outflow, respectively, and the correlation changes are relatively large. The conclusion is consistent with Li et al. (2020). In the upper layer, the CP index maintains a positive correlation with both inflow and outflow, which is similar to the impact of the Niño 3.4 index. The difference with Li et al. (2020) is that the Niño 3.4 and CP indices have a strong positive correlation with the lower layer outflow, which may be related to the period selected.

To quantitively expose the climate drivers of ITF transport, the RF method is adopted in this subsection. Before that, the dominant periods of the ITF transport should be clarified. The average multi-models flow data in different levels ( Figure 7 ) help to obtain the power spectra of the upper layer and the lower layer inflow and outflow during 1993–2019. Power spectral analysis reveals that the upper layer and the lower layer inflow exhibit peak periods of 4–9 and 5–7 years, respectively. The upper layer and the lower layer outflow exhibit peak periods of 5–7 and 2–6 years, respectively. Overall, the results characterize a common peak period flow of 5–7 years at four different locations. Comparatively, Niño 3.4, as well as DMI and CP indices have peak periods of 2–7, 2–4, and within 10 years (Sullivan et al., 2016; Santoso et al., 2022), respectively.

The calculation of the power spectrum of the four levels of flow data and climate indices concludes that the main change cycle is concentrated in 5–7 years; hence, it is taken as the cycle for RF model training. In addition, to make full use of the data and the experimental results more reliable, the data is recycled (consider the 6-year cycle as an example: 1993–1998, 1994–1999…). Niño and IOD events often occur simultaneously during RF model training. Therefore, the D M I n e w , which removes the influence of the linear trend of Niño 3.4, is adopted and the corresponding RF models by using four model data training are obtained. The relative importance of the RF training results in the period of 5, 6, and 7 years, respectively, are considered. Significant differences are not revealed in the results (figures not given). Therefore, the 6–year period is considered to reveal the relative importance of different climate indices at different levels, beginning with different starting years ( Figure 8 ). Due to the OFES data is up to 2017, the results for the starting year 2013–2014 are obtained from CMEMS, HYCOM, and SODA data. In this study, the dominant index is defined as the importance higher than 33% and which exceeds the other two indices without overlapping.

The RF results show that in the upper layer inflow, starting from 1993–1995 (end of 2008 and 2000), the importance of the Niño 3.4 was significantly higher than that of the other two indices which was greater than 40%. In the 1996–2001 period (end of 2001 and 2006), Niño 3.4 showed more important but insignificant results (shadow regions cover each other) under the average training results of multi-model data. In the starting year of 2002–2003 (end of 2007 and 2008), the DMI became the important index (without overlap of the other two indices). In the periods of 2004–2012 (end of 2009 and 2017), the relative importance of the three indices were comparative and the overlapping shadow covered each other. In the periods of 2013–2014 (end of 2018 and 2019), the importance of the DMI increased, whereas the importance of the Niño 3.4 decreased.

Different from the upper layer, in the lower layer inflow, in the starting year of 1993 (end of 1998), the DMI was relatively important. However, in the starting year of 1994 (end of 1999), the importance of DMI decreased and CP was relatively important. In the starting years of 1995–1999 (end of 2000 and 2004), the shadows of the three indices overlapped each other. On average, the CP was relatively important but insignificant. In the initial years of 2000–2007 (end of 2005 and 2012), the importance of DMI gradually increased, and during 2002–2003 (end of 2007 and 2008), DMI had significant importance. In the later period, starting from 2008–2014 (end of 2013 and 2019), the error bars of the three indices overlapped, and again, there was no dominant index.

In the upper layer outflow, the Niño 3.4 was always at a high level during the 1993–1999 period (end of 1998 and 2004), which implies the dominance of Niño 3.4. During 2000–2001 (end of 2005 and 2006), the influence of the DMI on the upper layer outflow increased, but the importance of the Niño 3.4 decreased. In the starting years of 2002–2004 (end of 2007 and 2009), the DMI became the dominant factor, with an average relative importance of more than 50% between 2002 and 2007. In the initial years of 2005–2007 (end of 2010 and 2012), the average relative importance of the CP increased, but the shadow region coincided with the shadow region of the DMI. In the starting years 2008–2012 (end of 2013 and 2017), the importance of all three indices was relatively close. This indicates the complexity of the influencing factors of ITF during this period, and a significant index was not identified. In the following starting years 2013–2014 (end of 2018 and 2019), the DMI became the dominant factor again, with an average relative importance of more than 40%.

In the lower layer outflow, starting from 1993–1995 (end of 1998 and 2000), the error bars of the three indices coincided, and the significant index was not dominated. In the starting years of 1996–1998 (end of 2001 and 2003) and 2013–2014 (end of 2018 and 2019), the CP was the important index, with an average proportion of 40%. In the starting years of 1999–2000 (end of 2004 and 2005) and 2009–2012 (end of 2014 and 2017), there was no dominating index. In the initial years of 2001–2005 (end of 2006 and 2010), the DMI was the important influence index, with an average proportion of 50%. In the starting years of 2006–2008 (end of 2011 and 2013), the Niño 3.4 was the dominant influence index, with an average proportion of 50% in 2007.

Figure 9 illustrates the relative importance of the different climatic factor indices and their partial dependence in different periods. In the partial dependence plots, the steeper the curve change, the greater the influence of the corresponding index. The results reveal that the curve of Niño 3.4 to be the steepest and the influence on the upper layer inflow to be the greatest during 1993–1998. In 2002–2007, the DMI curve was the steepest and became the dominant index. Similarly, in 2008–2013, the CP and Niño 3.4 were relatively important. During 2014–2019, the importance of DMI increased. The results are consistent with those in Figure 8 . The partial dependences of the climate indices on the lower layer inflow, as well as the upper layer and lower layer outflows are similar to the upper layer inflow (figures not given).