Analysis of Influencing Factors of SST in Tropical West Indian Ocean Based on COBE Satellite Data

Abstract

The time-frequency domain analysis of the sea surface temperature (SST) in the tropical western Indian Ocean was conducted using wavelet analysis, cross wavelet transform (XWT), the Mann–Kendall (MK) test, and other methods based on COBE-SST data for the last 50 years (1974–2020). From the perspective of time-frequency combination, examining the data of precipitation, sea surface heat flux, total cloud cover, and long-wave radiation, helped contribute to exploring the periodic changes of SST. Moreover, the Western Hemisphere Warm Pool (WHWP) was selected to analyze the role of SST from 1974 to 2020. Present results have demonstrated that the SST in the western Indian Ocean was in a stage of rising, particularly in 1998. According to the fast Fourier transform of the filtered SST time series, the tropical western Indian Ocean SST has a short period of 3–6 years, a medium period of about 10 years, and a long period of 40 years. The SST in the tropical western Indian Ocean has a resonance period of 2–6 years with precipitation, a resonance period of 2–6 years with sea surface heat flux, a resonance period of 4–5 years with total cloud cover, and a resonance period of 2–5 years with long-wave radiation. Importantly, SST was negatively associated with precipitation, total cloud cover, and long-wave radiation, and positively for sea surface heat flux before 1997. Seasonal migration activities are significantly correlated with the WHWP and the tropical western Indian Ocean SST. The spatial lattice point correlation coefficient is generally from 0.6 to 0.9, and the inter-annual serial correlation value is more than 0.89. Furthermore, the two exist with a resonance period of 2–5 years.

1. Introduction

The tropical western Indian Ocean’s geographical location is unique; it is at the confluence of the Walker and monsoon circulations, and the Indian Ocean climate has distinct tropical marine and monsoon characteristics. Scholars did little research on the Indian Ocean climate, especially the SST [1], before Saji N H et al. [2] and Webster P J et al. [3] proposed the Indian Ocean Dipole (IOD) [4,5,6,7,8]. The IOD refers to a special meteorological phenomenon that occurs in the Indian Ocean, caused by the difference in SST in different parts of the Indian Ocean. In the “positive dipole” stage, convection is active on the western side of the Indian Ocean, the SST in the west increases, and rainfall occurs in eastern Africa, but the SST on the eastern side of the Indian Ocean drops, and Australia and Indonesia are prone to drought. Saji N H et al. [2] studied the 1997 dipole event and discovered that precipitation reduced in Western Australia while increasing in East Africa during the positive phase of the tropical IOD event. Zhang GL et al. [9] used monthly average Extended Reconstructed Sea Surface Temperature (ERSST) data from 1950 to 2018 to investigate the link between the Indian Ocean Dipole and the El Niño–Southern Oscillation (ENSO). They discovered that the descending branch of the anomalous Walker circulation produces anomalous surface southeasterly winds along the coast of Sumatra and uplifts the thermocline in the eastern tropical Indian Ocean, resulting in an IOD event in the fall. Fathrio I et al. [10] investigated the model bias for SST in the Western Indian Ocean using the Coupled Model Intercomparison Project (CMIP5) models and discovered that about half of the models showed a positive SST bias, similar to the pattern of the Indian Ocean Dipole; the remaining half showed negative SST bias occurring throughout the tropical Indian Ocean and winds shift to the southeast. Zhang RJ et al. [11] employed a neural network-based self-organizing map (SOM) clustering technique to divide the South Indian Ocean SST into 12 patterns from 1901 to 2010, with pattern 1 and pattern 12 representing the southwest and northeast Indian Oceans, respectively. The lateral SST anomalies are opposing and resemble the Indian Ocean’s so-called subtropical dipole. The ENSO and the quasi-decadal-oscillation dominated the tropical Indian Ocean climate change in the twentieth century, according to White W B et al. [12], who evaluated decadal sea surface temperature, surface wind, and wind stress curl data from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR). Gomez AM et al. [13], comparing and analyzing the SST retrieved by three satellites and field observations, observed that the correlation between the inversion value and the observation value is above 0.91, indicating that the satellite value can also be used as a data set for studying SST. Shahi N K et al. [14] developed five multiple linear regression models using the Indian Ocean and Pacific Ocean SST data provided by Hadley Center from 1982 to 2013 and NCEP/NCAR reanalysis precipitation, and verified and used their Model 5 to pass the Indian Ocean SST to predict Indian summer monsoon precipitation. Kämpf J and Kavi A [15] studied the changes in SST in the central area of the Indian Ocean Dipole using multi-platform satellite and ARGO data, and discovered that during the position IOD, a large area of abnormally cold sea surface water on the southwest coast of Sumatra was caused by upwelling favorable winds along the west-central coast of Sumatra (1–3° S). He KJ et al. [16] found that the interannual variation trend of summer precipitation in the eastern and western Qinghai–Tibet Plateau was the opposite, and this phenomenon was significantly correlated with the Indian Ocean SST in spring.

It’s not enough to only look at how a parameter changes in the temporal domain. Xing LT et al. [17] analyzed dynamic monitoring data of groundwater level and precipitation in northern China over the last 40 years using Mann–Kendall, Wavelet analysis, and other approaches, and discovered that precipitation has similar 12-year and 16-year cycles to groundwater level. Amantai N et al. [18] used multi-source remote sensing data to examine the relationship between surface temperature and other meteorological factors of Ebinur Lake watershed in Xinjiang, China, and found that the sharp reduction in open shrubs would lead to an increase in surface temperature. Messié M et al. [19] corresponded the first six modes of global SST using an empirical orthogonal function (EOF) to analyze the El Niño–Southern Oscillation, the Atlantic Multidecadal Oscillation (AMO), the Pacific Decadal Oscillation (PDO), the North Pacific Gyre Oscillation (NPGO), El Niño Modoki, and the Atlantic El Niño six climate phenomena, and time-scale analysis of six modes using wavelet analysis.

From the point of view of time-frequency combination, this article uses a moving average, a sliding t-test, the M–K mutation test, and other methods to analyze the SST in the tropical western Indian Ocean in the time domain, including the interannual trend of the SST time series. It analyzes the cycle nesting phenomenon of SST in the Indian Ocean from the frequency domain through ensemble empirical mode decomposition (EEMD), fast Fourier transform, and more. Drawing on high-quality papers in this field [20,21,22,23], we found that SST is strongly linked to atmospheric parameters such as precipitation, total cloud cover, and long-wave radiation. Thus, in this paper, we choose four parameters—precipitation, sea surface heat flux, total cloud cover, and longwave radiation—to study their connection with SST. Then we use wavelet analysis to study the cycles of precipitation, sea surface heat flux, total cloud cover, and long-wave radiation and compare and analyze them with the SST cycle, finally combining the cross wavelet transform to confirm these four factors in relation to different frequency bands, different time ranges, and SST in the tropical western Indian Ocean. In addition, this article applies a variety of research methods, combined with a long research time range and new data, which can comprehensively reveal the characteristics of SST changes in the tropical western Indian Ocean in the past 50 years.

2. Materials and Methods

2.1. Data and Study Area

The SST data of the tropical western Indian Ocean used in this paper originate from the Physical Sciences Laboratory (PSL), which is a composite SST series that integrates data from ships, buoys, and satellites. Satellite observations are newly introduced for the purpose of reconstructing SST variability over data-sparse regions [24,25]. The consistency of corrected observations and data sparse area values is ensured thanks to the addition of satellite observations. The selected time range is from January 1974 to December 2020 and the mean SST value of the entire tropical western Indian Ocean is regarded as the average annual SST, and the time series is 47 years in total. The precipitation data are ERA5 (ECMWF Reanalysis 5) reanalysis products, and the selected sea surface heat flux, total cloud cover, and long-wave radiation data are NCEP/NCAR reanalysis products. The time range of these four atmospheric parameters is also from January 1974 to December 2020. The data for the WHWP, Oceanic Niño Index (ONI), Pacific Decadal Oscillation (PDO), and the Pacific–North American (PNA) come from the PSL’s monthly average climate index, which spans from 1974 to 2020.

The SST of 400 grid points in the tropical western Indian Ocean (10° S–10° N, 50° E–70° E) is averaged into a value, which is considered to be the mean value of the year. The mean value of each year is sorted as the SST time series (47 years) of the tropical western Indian Ocean.

The majority of the initial SST anomalies were detected in the western Indian Ocean, according to the spatial distribution of global SST anomalies over the last 50 years (Figure 1). Especially noteworthy SST anomalies have always persisted in the western Indian Ocean region from 1974 to 2020, and the anomalies have gotten more intense. The tropical western Indian Ocean (10° S–10° N, 50° E–70° E) is chosen as the study area, with a data spatial resolution of 1 degree (longitude) and 1 degree (latitude) to better understand the law of global SST fluctuations.

2.2. Research Methods

2.2.1. Wavelet Analysis

Wavelet analysis may clearly depict latent multi-cycles in time series and anticipate the short-term future trend by refining the expansion and translation operations of the long-term SST series from the standpoint of time-frequency combination [26,27]. In this study, the Morlet mother wavelet is utilized, and the formula is Equation (1)

$$\mathsf{\phi }\left(\mathrm{t}\right)={\pi }^{-1/4}{e}^{i\omega \mathrm{t}}{e}^{-{\mathrm{t}}^2-1}$$

(1)

In Equation (1), ω is the dimensionless frequency, when it is set as a constant 6 in this article, the wavelet scale and Fourier period are roughly equal, t is the input time series, and the continuous wavelet change expression is Equation (2)

$${\mathrm{W}}_{\mathrm{f}}\left(\mathrm{a},\mathrm{b}\right)={\left|\mathrm{a}\right|}^{-\frac{1}{2}}{{\displaystyle \int }}_{\mathrm{R}}\mathrm{f}\left(\mathrm{t}\right)\overline{\mathsf{\phi }}\left(\frac{\mathrm{t}-\mathrm{b}}{\mathrm{a}}\right)dt$$

(2)

In Equation (2), a is the period length, b is the translation time, a, b∈R, a≠0, f(t) is the input function, the wavelet variance expression is Equation (3)

$$\mathrm{Var}\left(\mathrm{a}\right)={{\displaystyle \int }}_{-\infty }^{+\infty }|W_f\left(\mathrm{a},\mathrm{b}\right){|}^{2}dt$$

(3)

2.2.2. Cross Wavelet Transform

Cross wavelet transform is mainly used to analyze the relationship between the two parameters in the time-frequency domain. It is a new method that combines cross-spectrum analysis and wavelet analysis [28,29]. The expression is Equation (4)

$$W_{XY}\left(\alpha ,\tau \right)=C_X\left(\alpha ,\tau \right)C_Y^{*}\left(\alpha ,\tau \right)$$

(4)

In Equation(4), $W_{XY}\left(\alpha ,\tau \right)$ is the cross wavelet spectrum of the two signals,$C_X\left(\alpha ,\tau \right)$ is the wavelet variation coefficient of one signal, $C_Y^{*}\left(\alpha ,\tau \right)$ is the complex common of the wavelet variation coefficient of the other signal.

Wavelet analysis is the localization analysis of time (space) frequency, it can use the attenuated waveform to refine the time series through the expansion and translation operation, and finally, achieve the time subdivision at the high frequency and the frequency subdivision at the low frequency. In this article, it is mainly used to analyze the changes of four parameters at their specific frequencies (reciprocal of the period). Cross wavelet transform is a new multi-signal and multi-scale analysis technology developed on the basis of traditional wavelet analysis. It can not only analyze the relationship between the two parameters but also reflect their phase structure and detailed characteristics in the time domain and frequency domain. In this article, it is mainly used to analyze the relationship between various parameters and SST. In summary, wavelet analysis can highlight the details and can only discuss a single time series signal. It is difficult to analyze the interaction and time-frequency correlation between multi-factor series signals. The cross wavelet transform can further diagnose the correlation, time ductility, and phase structure of different signals.

2.2.3. Mann–Kendall Mutation Test

UF is a forward SST time series curve, and UB is the reverse SST time series curve which reverses to UF. The two dual SST time series are calculated and plotted in the same graph for the M–K mutation test. If the value of UF > 0, it indicates that the time series has an upward trend; if the value of UF < 0, it indicates that the time series represents a downward trend. The SST time series has neither forward nor reverberation significance if the intersection of the two dual curves falls within the significant test range; there may be an abrupt change in the trend at the intersection if the trend is changing. If the intersection is outside the significant test range, it shows a substantial upward or downward trend, and the time node beyond the significant test range represents the year where major changes occurred [30,31,32,33].

2.2.4. Ensemble Empirical Mode Decomposition

Empirical mode decomposition (EMD) is a technique for decomposing a time series into intrinsic mode functions (IMFs) with different time scales based on the features of the signal’s periodic amplitudes and frequency. EEMD is a better version of EMD that adds a set amount of white noise to the original signal to reduce mode aliasing [34].

3. Results

3.1. Time Domain Analysis

The time series changes of SST in the tropical western Indian Ocean from 1974 to 2020 are depicted in Figure 2a. When combined with the results of the SST series’ 9-year moving average analysis in Figure 2c, it’s clear that the SST has been rising for the past 47 years, with an annual average rate of change of about 0.017 °C/a. The M–K mutation test of the SST time series for the last 47 years is shown in Figure 2d, where UF is the forward time series curve of SST, UB is the reverse time series curve, and the area between the blue horizontal lines is the 95% significant test range. According to Figure 2d, it is found that UF is less than zero from 1974 to 1978, which indicates that the SST in the tropical western Indian Ocean shows a downward trend from 1974 to 1978, whereas UF is greater than zero from 1978 to 2020, indicating that the SST is in a rising stage after 1978, and the intersection of the UF curve and the UB curve is outside the 95% significant test range, indicating that there is no sudden change in the SST time series between 1974 and 2020. The UF curve exceeds the significant test range in 1998, indicating that after 1998, the SST increases significantly. Figure 2b shows the 8-year sliding t-test of the SST series. It can be seen that the SST series exceeds the significant test range between 1996 and 1998, indicating that the SST series may have abrupt changes in 1996 and 1998. Combining with Figure 2d M–K mutation, and the time series changes in Figure 2a, 1998 is determined as the time point when the SST increases significantly rather than a mutation point (Figure 2).

The SST series of the tropical western Indian Ocean is decomposed using the EEMD method from 1974 to 2020, yielding the graph below. In the diagram, there are five IMF components. The first four IMF components represent the SST series’ periodic term at each time scale, whereas the final IMF component represents the SST series’ long-term trend change term. The IMF1 component has the biggest amplitude fluctuation and the poorest periodicity, indicating that the IMF1 component is the major signal occupying the variation of the SST time series. According to the judgment of the long-term trend change term: if the trend item is a monotonically growing or decreasing function, the original signal is non-stationary. The changing process of the SST series in the tropical western Indian Ocean, according to IMF5, is a monotonic function after 1988, indicating that the SST time series is a non-stationary signal. The IMF2-5 components are clearly periodic, with a changing mechanism that resembles that of the sine function. It may be deduced from the long-term trend change term that the period of declining SST in the tropical western Indian Ocean is 1974–1990, and the era of rising SST is 1990–2020 (Figure 3).

3.2. Fast Fourier Transform with Filtering

It is difficult to draw more useful conclusions from analyzing SST series only in the time domain. The Butterworth filter, as well as high-pass, low-pass, and band-pass filters are used to filter the SST time series on this basis, and the acquired analysis findings are given in Figure 4. High-frequency signals are permitted to flow through high-pass filtering, whereas low-frequency signals below the defined critical value are blocked. The high-pass filtering critical value set in this article is 1/3, and the period of the filtered SST time series under 3 years is mainly filtered, so the Fourier transform of the high-pass filtered time series is obtained as shown in Figure 4d, indicating that the SST time series has periods of 2.9 years, 2.5 years, and 2.1 years. Under the condition of low-pass filtering, the signal screening method is opposite to that of high-pass filtering. The critical value for low-pass filtering is set at 1/10, and the filtered SST time series has a period of mostly over 10 years. Figure 4e shows the Fourier transform result, which shows that the SST time series has periods of 40 years and 12.5 years. Under band-pass filtering, signals below the low-frequency critical value and above the high-frequency critical value are blocked, and the filtered SST time series has a period of 3 to 10 years. Therefore, the Fourier transform of the band-pass filtered sequence is shown in Figure 4f, revealing that the SST time series includes periods of 9.5 years, 6.3 years, 5 years, and 3.6 years. According to the magnitude of the amplitude, the periods of 2.5 years after high-pass filtering, 40 years after low-pass filtering, and 5 years after band-pass filtering are the most evident. Because the time series analyzed in this work is 47 years long, neither too long nor too short time scales are appropriate, and the band-pass filter’s selection of 3–10 years is the most appropriate. As a result, the SST in the tropical western Indian Ocean varies with periods of 9.5 years, 6.3 years, 5 years, and 3.6 years in this paper.

3.3. Analysis of Influencing Factors Based on Wavelet Transform

Because the discrete wavelet transform (DWT) with orthogonal wavelet can decompose the SST time series into a spectrally incoherent detail and a slowly varying number and these components have additional variances, the periodicity of the original series can be more clearly deduced and extracted. Considering the characteristics of each wavelet basis function and the actual situation of data, db2 is selected to perform one-DWT decomposition and reconstruction of the SST time series. In the selection of decomposition layers, the more wavelet decomposition layers there are, the better the stability is, but the greater the error is. Therefore, the decomposition layers are generally two to four layers, and three layers are selected in this article. Figure 5a shows the low-frequency approximate part (approximate information) of the original SST series after three-layer decomposition. Figure 5b–d shows the high-frequency detail part (detail signal) after three-layer, two-layer, and one-layer decomposition, respectively. This step completes the transition from the time domain to the wavelet domain.

The main energy of the noise component is often concentrated in the detail signal after wavelet decomposition, so it is necessary to quantify the detail signal threshold, that is, to restore the sub-signal of the detail signal from the wavelet domain and complete the transition from the wavelet domain to the time domain. Figure 6a is the low-frequency signal component of the original signal, and Figure 6b–d shows the high-frequency signal components 3, 2, and 1 after three-layer decomposition.

Finally, the high-frequency coefficient and low-frequency coefficient after threshold quantization are reconstructed to obtain the reconstructed signal, namely, the processed SST correction data. Figure 7a is the original signal, and Figure 7b is the reconstructed signal after correction. The overall trend between the two is consistent, and there is no obvious boundary effect at both ends of the data, which ensures the fidelity of the data.

According to the above operation, the time series of precipitation, sea surface heat flux, total cloud cover, and long-wave radiation are decomposed and reconstructed successively, and the reconstructed original signal is shown in Figure 8a,c,e,g as the original time series of the four, and Figure 8b,d,f,h as the reconstructed series of the four. On the whole, the reconstructed series is consistent with the trend of the original series. The subsequent continuous wavelet transform of precipitation, sea surface heat flux, total cloud cover, and long-wave radiation all use the reconstructed signal after DWT, and the periodicity will be more accurate.

The wavelet analysis of precipitation, sea surface heat flux, total cloud cover, and long-wave radiation in the tropical western Indian Ocean are shown in order. Figure 9a shows that the precipitation of the tropical western Indian Ocean exists in periods of 2 years, 7 years, 14 years, and 24 years. Figure 9c depicts the 4-year, 8-year, 17-year, and 24-year periods in the sea surface flux of the tropical western Indian Ocean. As can be seen in Figure 9e, the total cloud cover of the tropical western Indian Ocean has 4-year, 8-year, 15-year, and 24-year periods. Figure 9g shows that the long-wave radiation in the tropical western Indian Ocean region has 2-year, 9-year, 15-year, and 25-year periods. Figure 9b,d,f,h shows the wavelet variance diagrams of precipitation, sea surface heat flux, total cloud cover, and long-wave radiation in the tropical western Indian Ocean, respectively. From these four figures, we can see that the corresponding variance of precipitation, sea surface heat flux, total cloud cover, and long-wave radiation have multiple peaks, and the size of these peaks and the abscissa corresponding to the peaks represent the main cycle order of these four in the periodic change. Three distinct peaks can be recognized in Figure 9b. These peaks are 24 years, 7 years, and 14 years in size, with corresponding time scales of 24 years, 7 years, and 14 years, respectively. Figure 9d shows peaks and time scales of 8 years, 24 years, and 17 years, respectively. In Figure 9f, the peaks and corresponding time scales are 8 years, 24 years, and 15 years, respectively, and in Figure 9h, the peaks and corresponding time scales are 25 years, 15 years, and 9 years (Figure 9). This shows that in the time scale changes of precipitation, sea surface heat flux, total cloud cover, and long-wave radiation, the first main cycle of precipitation changes is 24 years, the second main cycle is 7 years, and the third main cycle is 14 years; The first main cycle of surface heat flux changes is 8 years, the second main cycle is 24 years, and the third main cycle is 17 years; the first main cycle of total cloud cover changes is 8 years, and the second main cycle is 24 years, the third main cycle is 15 years; the first main cycle of long-wave radiation changes is 25 years, the second main cycle is 15 years, and the third main cycle is 9 years.

The main cycle of the changes in precipitation, sea surface heat flux, total cloud cover, and long-wave radiation is described in the previous article content. The wavelet coefficient change diagram of the corresponding time scale is shown in Figure 10. Specifically, in the process of precipitation change, the 24-year (24a) change period of the first main cycle is about 16 years, and it has experienced about three dry-weather change periods from 1974 to 2020, the 7-year (7a) change process of the second main cycle is relatively complicated and has no research value. The 14-year (14a) change period of the third main cycle is about 9 years, and during the period from 1979 to 2020, it has experienced about five dry-weather change periods. In the change process of sea surface heat flux, the 8-year (8a) change period of the first main cycle is about 5 years, it has experienced about 9 high–low change periods from 1974 to 2020, and the 24-year (24a) change period of the second main cycle is about 16 years, and it has experienced about three high-low change periods from 1974 to 2020. The 17-year (17a) change period of the third main cycle is about 12 years, and it has experienced about four high-low change periods from 1974 to 2020. In the change process of total cloud cover, the 8-year (8a) change period of the first main cycle is about 6 years, and it has experienced about 8 change periods from 1974 to 2020. The 24-year (24a) change period of the second main cycle is about 16 years; from 1974 to 2020, it has experienced about 3 change periods, and the changes of the third main cycle are more complicated, which will not be studied here. In the change process of long-wave radiation, the 25-year (25a) change period of the first main cycle is about 16 years, and it has experienced about three broad–narrow change periods from 1974 to 2020, and the 15-year (15a) change period of the second main cycle is about 9 years. From 1974 to 2020, it experienced five broad–narrow change periods. The 9-year (9a) change in the third main cycle is more complicated, and will not be studied here.

3.4. Analysis of Influencing Factors Based on Cross Wavelet Transform

According to the above analysis of the change process of precipitation, sea surface heat flux, total cloud cover, and long-wave radiation in the tropical western Indian Ocean, there is a multi-period nesting phenomenon among the four, and its changing process may have an impact on the SST in the tropical western Indian Ocean. Therefore, the precipitation, sea surface heat flux, total cloud cover, and long-wave radiation series reconstructed by DWT are respectively subjected to XWT with the SST correction series. Figure 11, Figure 12, Figure 13 and Figure 14 illustrate the findings of the analysis.

The cross wavelet energy spectrum of tropical western Indian Ocean precipitation and SST is shown in Figure 11a, and according to the color bar’s range, the lighter the color (to yellow), the larger the energy spectrum value is. It can also be seen in the figure that the energy spectrum value of precipitation and SST near the time scale of 4–5 years is the largest, and the correlation is the highest in the same period. In the illustration, the black solid line range represents passing the 95% test, and the conical area separated from the shaded half depicts the wavelet cone, which is used to remove border effects. The positive and negative correlations between precipitation and SST are represented by the arrows in the figure. The arrows point upwards, indicating that the precipitation cycle is 1/4 cycle ahead of the change in SST; the arrows point downwards, indicating that the precipitation cycle is 1/4 cycle behind the change in SST; the arrows point left, indicating that the change in precipitation is negatively correlated with the change in SST; the arrows point right, indicating that the change in precipitation is positively correlated with the change in SST. The tropical western Indian Ocean precipitation and the SST have a resonance period of 2–6 years from the cross wavelet energy spectrum; it is found that the resonance energy is only high in the resonance period of 4 years from the cross wavelet condensation spectrum, and the relationship between the two has shifted from a positive correlation to a leading 1/4 period since roughly 1997. This indicates that the rise in SST corresponds to a decrease in precipitation.

Figure 12 shows the cross wavelet energy spectrum (Figure 12a) and condensation spectrum (Figure 12b) of the tropical western Indian Ocean sea surface heat flux and SST. From the cross wavelet energy spectrum, there is a resonance period of 2–6 years (1994–2001) between the SST and the sea surface heat flux in the tropical western Indian Ocean. However, it is found that the resonance energy of the 4–5-year period and the 2-year period are higher. Since 1997, the sea surface heat flux and SST have changed from a negative correlation to a positive correlation.

Figure 13 shows the cross wavelet energy spectrum (Figure 13a) and condensation spectrum (Figure 13b) of total cloud cover and SST in the tropical western Indian Ocean, The cross wavelet energy spectrum shows that there are two resonance periods for total cloud cover and SST in the tropical western Indian Ocean, which are 4–6-year (1982–2000), 2-year (1974–1979), and 4–5-year resonance periods of total cloud cover and SST in the tropical western Indian Ocean (1982–2000), but the 2-year cycle is moot due to boundary effects. From cross wavelet condensation, it is found that the resonance energy of the 6-year period (1987–1998) is higher. The total cloud cover and SST are negatively correlated, which indicated that the higher the total cloud cover, the lower the SST in the tropical western Indian Ocean.

Figure 14 shows the cross wavelet analysis results between the tropical western Indian Ocean long-wave radiation and SST. From the cross wavelet energy spectrum, it can be seen that there are two resonance cycles between the tropical western Indian Ocean long-wave radiation and SST that pass the 95% test, respectively 2–3 years (1994–2000) and 4–5 years (1996–2004). The cross wavelet condensation spectrum shows that the long-wave radiation and the SST in the tropical western Indian Ocean have a significant positive correlation only in a small range around the 2-year period, and other regions have not passed the significance test, which indicates that the influence of the tropical western Indian Ocean in the process of SST changes, and the effect of long-wave radiation is negligible.

The correlation between SST values and WHWP of 400 grid points in the range of (10° N–10° S, 50° E–70° E) was analyzed, and the 400 grid points after correlation analysis are still shown in the region of (10° N–10° S, 50° E–70° E). Figure 15a–d depicts the four-season spatial distribution of the correlation coefficient between the SST in the tropical western Indian Ocean and the WHWP index. The annual spatial distribution is depicted in Figure 15e. The SST in the western Indian Ocean is generally positively associated with the WHWP index, with the spatial correlation coefficient between the two ranging from 0.6 to 0.9. According to the details, there is a seasonal migration in the spatial distribution of the correlation coefficient between the tropical western Indian Ocean and the WHWP index, with the significant positive correlation area migrating to the northeast from spring to summer, and the significant positive correlation area migrating westward from summer to autumn, then the significant positive correlation area relocated to the southwest during the transition from autumn to winter. Finally, its location almost coincided with the significant positive correlation area in spring. This seasonal migration may be related to the seasonal expansion and contraction of the WHWP. According to the analysis in Figure 15e, taking the equator as the dividing line, the spatial correlation between the SST in the western Indian Ocean south of the equator and the 47-year mean value of the western Pacific warm pool is higher than that in the area north of the equator (Figure 15). The correlation between the inter-annual variation of the SST in the tropical western Indian Ocean and the WHWP was analyzed, and the correlation coefficient between the two reached 0.89, which indicated that the WHWP played an important role in the change of the SST of the tropical western Indian Ocean.

The relationship between the SST in the tropical western Indian Ocean and the WHWP is further analyzed by using XWT. The left side of the figure below is the crossed wavelet energy spectrum. According to the crossed wavelet energy spectrum, it is found that in the SST and the WHWP exists a resonance period of 2–5 years (1982–1990, 1994–2000) and shows a good positive correlation. On the right side of the figure is the cross wavelet condensed spectrum, it is discovered that the significant test area accounts for more than 60% of the entire wavelet cone, which indicates that the SST in the tropical western Indian Ocean has an excellent positive correlation with the WHWP (Figure 16).

4. Discussion

A moving average, sliding t-test, and the M–K mutation test are used to examine the interannual variance of the SST time series of the tropical western Indian Ocean over the last 47 years. Meanwhile, EEMD divides the SST time series into numerous fixed frequency components, and monotonicity is a criterion for determining if the SST series is stationary. Then the SST time series after high-pass, low-pass, and band-pass are subjected to a fast Fourier transform to get meaningful periods under the various conditions, and the hidden multi-cycle nesting phenomenon of the SST time series is investigated in the frequency domain. In terms of contributing factors, four atmospheric parameters in the tropical western Indian Ocean are chosen: precipitation, sea surface heat flow, total cloud cover, and long-wave radiation. First, cross wavelet transform is used to examine the periodic nesting phenomena among these four, and the size of the wavelet variance is used to estimate the major cycle order of the respective changes. Second, XWT is used to examine the correlations between precipitation and SST, sea surface heat flux and SST, total cloud cover and SST, and long-wave radiation and SST, as well as the association between these four parameters and tropical western SST. Finally, after removing the four factors, an ocean index (WHWP) is selected to analyze the influencing factors. From the trend changes and correlations, it is concluded that the WHWP is closely related to the SST in the tropical western Indian Ocean.

The advantage of this article is that we can get a comprehensive understanding of the SST variation process in the tropical western Indian Ocean by combining time and frequency domains. The SST in the tropical western Indian Ocean has generally shown an upward trend since 1974, which is consistent with Yadav R K and Roxy M K [35] who found that the reason for the decrease in rainfall of the strong summer monsoon in northern India in the last two decades is the warming of the tropical Indian Ocean, and Qu X and Huang G [36] who found the same conclusion that the Indian Ocean has been warming. In the analysis of the SST cycle change, Jury M [37] found that there is a quasi-decadal oscillation in the SST in the western Indian Ocean, which is consistent with the 9.5-year cycle obtained after screening the 3–10-year cycle by using a band-pass filter in this article. Further subdividing the time scale, it is found that there is a multi-period nesting phenomenon in SST. In the analysis of influencing factors, Yuan J P and Cao J [20] used long-wave radiation data, Joseph P V [21] used sea surface heat flux data, and Khaldun M H I [22] used precipitation data to analyze the influencing factors of Indian Ocean SST. Thus, the precipitation, sea surface heat flux, total cloud cover and long-wave radiation are all integrated on this basis, and their relationships with SST are explored. Crueger T [38] thought that the ENSO and the quasi-decadal oscillation dominated the tropical Indian Ocean climate from 1993 to 2002, and that the tropical western Indian Ocean SST was influenced by the WHWP during 1995, 1998, and 2002. The increase in SST in the Indian Ocean is not attributable to tropical Pacific ENSO zonal atmospheric teleconnections. PDO is linked to the far north Pacific sea level pressure, the Indian Summer Monsoon (ISM), and warm surface temperatures in southern Russia, according to Choudhury, D et al. [39]. Isa N S et al. [40] investigated the long-term climate variability trends of ENSO and the IOD, finding that ONI and IOD had different effects on the sea level temperature of the Malacca Strait and the Andaman Sea in different years. On this foundation, we examine the interannual variation trends of WHWP, ONI, PDO, and PNA from 1974 to 2020, as well as their relationships with the SST in the tropical West Indian Ocean (Figure 17).

The WHWP is found to be highly associated to the SST of the tropical western Indian Ocean in our analysis, and the seasonal movement of the high correlation area is quite similar to the WHWP’s seasonal expansion and contraction. In addition, it is concluded that 1998 was the time node for the significant increase in SST, which is speculated to be related to the 1997/1998 El Niño event. According to the relevant literature, as early as before the El Niño event, the sub-surface SST of the Western Pacific Warm Pool had obvious positive anomalies. The positive subsurface oceanic temperature (SOT) anomaly of the warm pool eastwards along the temperature jump layer to the equatorial eastern Pacific and extending to the marine surface layer is the direct reason for the outbreak of the El Niño event. When the El Niño event occurred, the SOT of the warm pool had a negative anomaly. Subsequently, the eastward propagation of the negative anomaly of the SOT of the warm pool and the expansion of the negative anomaly to the sea surface in the equatorial eastern Pacific led to the occurrence of the La Niña event in 1998 [41]. The ONI index and PNA index have always been in an oscillating range during the research period, and the overall trend was relatively close before 2000, implying that the WHWP has an important role in the change of SST in the tropical western Indian Ocean. In addition, the correlation coefficients of the ONI index, PNA index, and SST series are 0.36 and 0.39, respectively. In terms of interannual variation, the PDO index shows a modest association with the SST trend, with a correlation coefficient of only 0.12. The results of the analysis show that the four ocean indices have varying degrees of influence on the SST of the tropical western Indian Ocean, but the specific year and effect need to be investigated further.

5. Conclusions

After DWT decomposition and reconstruction, the SST, precipitation, sea surface heat flux, total cloud cover, and long-wave radiation time series of the tropical western Indian Ocean retain the authenticity of the original time series, and there is a more accurate periodicity.

From the perspective of the time domain, the SST was in a declining stage from 1974 to 1990 and was in a rising stage from 1990 to 2020. From the perspective of the frequency domain, the SST in the tropical western Indian Ocean has a short cycle of 3–6 years, a quasi-10-year mid-cycle, and a 40-year long cycle. By synthesizing the main periods of precipitation, sea surface heat flux, total cloud cover, and long-wave radiation, it is found that they are concentrated in 7-year, 15-year, and 24-year periods. Considering the short time series in this article, it can be confirmed that their 7-year period is related to the 3–6-year short period of SST in the tropical western Indian Ocean, which is confirmed by the subsequent XWT.

In terms of influencing factors, precipitation, total cloud cover, and long-wave radiation are negatively correlated with SST. However, sea surface heat flux was negatively correlated with SST before 1997 and positively correlated after 1997. Moreover, there is a resonance period of 2–5 years between the WHWP and SST, and the interannual variation correlation is more than 0.89.

Overall, the SST in the tropical western Indian Ocean is influenced by a variety of factors. It has been recognized that the ocean index has a significant impact on climate, including WHWP, ONI, PDO, PNA, and so on. Here, our present data illustrated that the WHWP index was significantly associated with SST in the tropical western Indian Ocean.