Sea Level Anomalies Time Series Research Articles

Lag-WALS approach incorporating ENSO-related quantities for altimetric interannual SLA forecasts in the South China Sea

A novel approach using lag weighted-average least squares (Lag-WALS) is proposed to forecast the interannual sea level anomaly (SLA) in the South China Sea (SCS) using lagged equatorial Pacific El Niño–Southern Oscillation (ENSO)-related quantities. Through empirical orthogonal function (EOF) and wavelet coherence method, we first investigated the relationships between sea surface temperature (SST) and SLA (both steric sea level (SSL) and non-steric sea level (NSSL)) in the equatorial Pacific, and then explored their cross-correlations with the interannual SCS SLA. A robust alignment was found between the first spatiotemporal mode of EOF (i.e. EOF1 and first principal component (PC1)) from SLA/SSL and SST across the equatorial Pacific, both of which exhibited a typical ENSO horseshoe spatial pattern in EOF1. Good consistency between the SCS SLA and the SST/SLA/SSL PC1 was revealed, with the SCS SLA lagging behind the SST, SLA, and SSL by several months at most grid locations. In contrast, the NSSL exhibited large disparities with the SST PC1 or the interannual SCS SLA. The lag-WALS model performed better at the SCS boundaries than in the central region, with an average STD/MAE/Bias (RMSE/MAE/Bias) for internal (external) accuracies of 1.01/0.80/–0.002 cm (1.39/1.13/–0.08 cm), respectively. The altimetric-observed SLA seasonal patterns agreed with the Lag-WALS model-forecasted SLA. A similar situation applies to regionally-averaged SLA time series. These results underscore the ability of the Lag-WALS model to accurately forecast the SCS SLA at the interannual scale, which is crucial for early warning of abnormal sea level changes in the SCS.

Assessment and exploitation of coastal low resolution mode sea level data from CryoSat-2 on the entrance to the Gulf of California

The CryoSat-2 mission (CS2), initially conceived for sea ice measurements, is also useful for sea level monitoring in oceanic and coastal areas. Only specific regions have two high resolution modes (SAR Delay/Doppler and SAR-Interferometric modes), while the rest of the areas are measured in low-resolution mode (LRM). The entrance to the Gulf of California presents this mode of operation. Sea Level Anomalies (SLA) obtained from CS2 are compared with tide gauges at three locations, Cabo San Lucas (CSL) south of the Baja California peninsula, Mazatlán (MZ) and San Blas (SB) on the continental margin. The comparison shows good agreement between SLAs in CSL and MZ, with standard deviations of the differences (SDD) lower than 0.09 m and Pearson’s correlations higher than 0.7 (95% of confidence level). San Blas is in a complex location and with less data, presenting an SDD greater than 0.13 m and a correlation below 0.55. We present the cross-shore seasonal and interannual variability in CSL and MZ using the CS2 SLA time series from 2011 to 2020. The variability shows the presence of events such as El Niño (2015 to early 2016), La Niña (2011) and the warm event of 2014 (nicknamed “the Blob”). Additionally, the residual time series of CS2 obtained after extracting the annual, semi-annual and monthly components, shows the East side (at MZ) is more affected by El Niño/La Niña variability while the West side (at CSL) is more influenced by the Blob/El Niño. Estimated long-term SLA trend at both locations are around 3.1 mm/yr, supporting similar findings by previous studies.

Residual M2 and S2 ocean tide signals in complex coastal zones identified by X-Track reprocessed altimetry data

While the reliability of reprocessed altimetry data from X-Track has been examined for sea level studies, it has not previously been used to study ocean tides in tidally complex coastal zones. Using a new dataset of short-term tide gauges, the aim of this study is to demonstrate the improvements in X-Track reprocessed data for studying ocean tides for the first time in tidally complex regions in northwest Australia. We show that X-Track can be used to evaluate and potentially correct ocean tide models in challenging coastal areas. Our study comprises three components: (1) evaluate the tidal constants from X-Track and RADS datasets using nearby (<12 km) short-term tide gauge data, (2) assess three ocean tide models (FES2014, DTU10, TPXO9) using the X-Track altimetry dataset and (3) extract residual M2 and S2 tidal constants from sea level anomalies (SLAs) computed using the optimal model (FES2014) for ocean tide correction and then use these to predict the residual tidal height to use as an additional correction for the recomputation of the SLAs.Our results show that X-Track data provides users with more valid observations close to coastlines (as close as 5 km) so that the derived M2 and S2 tidal constants show better agreement with nearby tide gauges compared to RADS for both Jason-3 (J3) and GFO missions. In Van Diemen Gulf, where the footprints were 7 km or less from the coast, RADS did not have any valid observations, whereas tidal constants of M2 computed from X-Track J3 and GFO data agreed with the tide gauges within ∼6% of the M2 tidal height. In contrast, X-Track J3 and GFO extracted S2 tidal constants agreed with nearby tide gauges within ∼11–24% (GFO extreme of 47%) of the S2 tidal height. The FES2014-detided SLA time series from X-Track were then analysed to detect the remaining signals of M2 and S2 tidal constituents, with co-range maps suggesting the unmodelled amplitudes for M2 reaches 40 cm and S2 up to 30 cm in Collier Bay. In Van Diemen Gulf, M2 contributes more to the residual tidal signal than S2 with an amplitude of 40 cm compared to 10 cm respectively, in contrast to Joseph Bonaparte Gulf with ∼10 cm for both. When the SLAs, are corrected for the residual tide heights of M2 and S2, the standard deviation of the SLA residuals is decreased by as much as ∼70% in Collier Bay indicating that X-Track altimetry can identify M2 and S2 tidal residuals in complex coastal regions.

Multifractality of global sea level heights in the satellite altimeter-era

Sea level rise is the major concern of climate change research. Beside the positive trends, global sea levels also demonstrate a complex scaling behavior. In this study, multifractal analyses based on the multifractal detrended fluctuation analysis (MFDFA) method are conducted to the global sea level anomaly (SLA) time series in the altimeter-era since 1993. By eliminating the multifractality caused by finite-size effect, the effective multifractality is estimated as the degree of multifractality of SLA time series. The results of show that global SLA time series are multifractals rather than monofractals. Long range dependence was also heuristically demonstrated by both autocorrelation functions and multifractal spectrums, respectively. The complex spatial patterns of sea level changes and multifractality could be partly explained by different mechanisms such as thermal expansion, the shift of ocean currents, and river injections, which are all associated with global climate change.

The Identification and Prediction of Mesoscale Eddy Variation via Memory in Memory With Scheduled Sampling for Sea Level Anomaly

Ocean mesoscale eddies are ubiquitous in world ocean and account for 90% oceanic kinetic energy, which dominate the upper ocean flow field. Accurately predicting the variation of ocean mesoscale eddies is the key to understand the oceanic flow field and circulation system. In this article, we propose to make an initial attempt to explore spatio-temporal predictability of mesoscale eddies, employing deep learning architecture, which primarily establishes Memory In Memory (MIM) for sea level anomaly (SLA) prediction, combined with the existing mesoscale eddy detection. Oriented to the western Pacific ocean (125°−137.5°E and 15°−27.5°N), we quantitatively investigate the historic daily SLA variability at a 0.25° spatial resolution from 2000 to 2018, derived by satellite altimetry. We develop the enhanced MIM prediction strategies, equipped with Gated Recurrent Unit (GRU) and spatial attention module, in a scheduled sampling manner, which overcomes the gradient vanishing and complements to strengthen spatio-temporal features for long-term dependencies. At the early stage, the real value SLA input guides the model training process for initialization, while the scheduled sampling intentionally feeds the newly predicted value, to resolve the distribution inconsistency of inference. It has been demonstrated in our experiment results that our proposed prediction scheme outperformed the state-of-art approaches for SLA time series, with MAPE, RMSE of the 14-day prediction duration, respectively, 5.1%, 0.023 m on average, even up to 4.6%, 0.018 m for the effective sub-regions, compared to 19.8%, 0.086 m in ConvLSTM and 8.3%, 0.040 m in original MIM, which greatly facilitated the mesoscale eddy prediction. This proposed scheme will be beneficial to understand of the underlying dynamical mechanism behind the predictability of mesoscale eddies in the future, and help the deployment of ARGO, glider, AUV and other observational platforms.

Regional sea level changes prediction integrated with singular spectrum analysis and long-short-term memory network

In this paper, the China’s first global ocean Climate Data Records (CDRs) are used to analyze and predict the sea level changes in the Yellow Sea with obvious seasonal changes. Based on the singular spectrum analysis (SSA) method, the spatiotemporal and time series of sea level anomalies (SLAs) in the Yellow Sea are decomposed and de-noised. Then the long short-term memory (LSTM) neural network is combined with the SSA to establish the SSA-LSTM combined model to predict the sea level trends of the Yellow Sea. Compared with the traditional methods, the prediction accuracy of SSA-LSTM combined model is significantly improved with minimum 35.04 mm RMSE values for the SLA time series prediction. For the one-year prediction of spatiotemporal series of SLA, the minimum RMSE values are only 19.68 mm. The law of spatial and temporal differentiation of the sea level change in the Yellow Sea is also analyzed by temporal empirical orthogonal function. It is found that the sea level trend of the Yellow Sea is highly consistent and significantly related to the season and latitude. According to the SSA-LSTM combined model, the sea level rise rate of the Yellow Sea will remain at 3.65 ± 0.79 mm/year in the next ten years.

Sea level anomaly measurements from satellite coastal altimetry and tide gauges at the entrance of the Gulf of California

The Sea Level Anomalies (SLA) obtained from tide gauges and coastal altimetry are compared in four locations around the entrance area of the Gulf of California, Mexico to validate the coastal altimetry data in our region. We perform two analyses using SLA data from X-TRACK coastal altimetry product (1 Hz along track) for the missions Topex/Poseidon (TP), Jason 1–2-3 (Ja), Geosat Follow-On (GFO) and Envisat (EN). The first compares SLA from X-TRACK with the SLA obtained from tide gauge subtracting 31 tidal components. In the second comparison, we start from the total water level envelope for altimetry data, which results from adding the Sea Level Anomalies, tides and atmospheric corrections. A harmonic analysis is performed to subtract only the most relevant tidal constituents in our region. We obtain 18 tidal constituents based on the harmonic analysis of the four tide gauges (16 with amplitudes > 1 cm and including the LDA2 and MM constituent). However, the number of tidal constituents that can be removed from the altimetric data varies due to their tidal alias periods which, in turn depend on their repetition periods and orbits. Therefore, we extract only 18/16/11 constituents for TP-Ja/GFO/EN respectively. The same number of constituents are removed from the tide gauges for comparison. The results show greater similarity between the SLA time series of altimeters and tide gauges for the second analysis, obtaining higher correlations (R > 0.6) and smaller root mean square differences (Rmse < 11 cm) for the TP-Ja and GFO missions and less than 18 cm for the EN mission. The tidal constituents inside the gulf undergo significant changes in amplitude and phase over short distances. Because of this, large differences can be found between the SLA time series of tide gauges when comparing with altimetry points located at distances 40–80 km away. However, when comparing points located less than 30 km away the comparisons are acceptable with differences attributable to the coastal dynamics, and therefore we consider them to be properly validated.

Spectral Analysis of Satellite Altimeter and Tide Gauge Data around the Northern Australian Coast

The north of Australia is known for its complex tidal system, where the highest astronomical tides (HATs) reach 12 m. This paper investigates the tidal behaviour in this region by developing spectral climatology for tide gauge and altimetry data. Power spectral density analysis is applied to detect the magnitude of ocean tides in 20 years of sea-level data from multimission satellite altimeters and tide gauges. The spectra of altimetry sea level anomaly (SLA) time series have their strongest peaks centred at approximately 2.11, 5.88, and 7.99 cycles per year (cpy), corresponding to the diurnal and semidiurnal tidal constituents K1, M2, and O1, respectively. Closer to the coastline, the spectra peak at high-frequency overtide and shallow-water constituents such as M4, MK4, and MK3. There have been many large, high-frequency spectral peaks near the coastline, indicating the difficulty of predicting tidal signals by coastal altimetry. Similar to altimetry observations, there are dominant semidiurnal and diurnal tidal peaks in tide gauge SLA time series accompanying a number of overtides. The semidiurnal and diurnal peaks are mostly higher on the northwest coast of Australia compared with the north and northeast coast. The results from both altimetry and tide gauges indicate that tidal range increases with increasing continental shelf.

Validation of Sentinel-3A SAR mode sea level anomalies around the Australian coastal region

The Synthetic Aperture Radar (SAR) mode sea level anomalies (SLAs) of Sentinel-3A altimetry mission around the Australian coastal region were validated using eight in situ tide gauge sea level records and retracked Jason-3 datasets from a modified Brown-peaky (MBP) retracker. The MBP is a modified version of our existing Brown-peaky retracker aimed at enhancing BP's performance. We compared the noise of Sentinel-3A SLAs averaged across three posting rates (i.e. 1 Hz, 2 Hz and 4 Hz) with the 1 Hz noise of MBP-derived Jason-3 SLAs. At distances >10 km from the coast, the noise level of 1 Hz Sentinel-3A SLAs (~1.2 cm) is lower than that of the MBP-retracked Jason-3 SLAs (~1.7 cm). Moreover, the noise level of 2 Hz Sentinel-3A SLAs is comparable to that of the 1 Hz MBP-derived Jason-3 dataset, indicating that Sentinel-3A can provide precise SLAs at finer spatial scales. The Root Mean Square Error (RMSE) of differences between the tide gauge SLA time series and the equivalent SLA time series at each along-track altimeter point was used to assess pointwise data quality. For both Sentinel-3A and MBP-retracked Jason-3, the along-track RMSEs of 20 Hz SLAs vary between 0.05 m and 0.2 m. The mean and standard deviation (STD) of 1 Hz SLA differences at crossover points were computed for each individual altimetry mission to assess overall data quality. When compared with the crossover analysis results, the quality of Sentinel-3A SLAs is superior to that of the retracked Jason-3 dataset in terms of smaller STDs at crossover points (8.8 cm vs. 10.7 cm).

Sea Level Prediction in the Yellow Sea From Satellite Altimetry With a Combined Least Squares-Neural Network Approach

Accessible high-quality observation datasets and proper modeling process are critically required to accurately predict sea level rise in coastal areas. This study focuses on developing and validating a combined least squares-neural network approach applicable to the short-term prediction of sea level variations in the Yellow Sea, where the periodic terms and linear trend of sea level change are fitted and extrapolated using the least squares model, while the prediction of the residual terms is performed by several different types of artificial neural networks. The input and output data used are the sea level anomalies (SLA) time series in the Yellow Sea from 1993 to 2016 derived from ERS-1/2, Topex/Poseidon, Jason-1/2, and Envisat satellite altimetry missions. Tests of different neural network architectures and learning algorithms are performed to assess their applicability for predicting the residuals of SLA time series. Different neural networks satisfactorily provide reliable results and the root mean square errors of the predictions from the proposed combined approach are less than 2 cm and correlation coefficients between the observed and predicted SLA are up to 0.87. Results prove the reliability of the combined least squares-neural network approach on the short-term prediction of sea level variability close to the coast.

Contemporary sea level rise rates around Malaysia: Altimeter data optimization for assessing coastal impact

The increase of anthropogenic activities has triggered global sea level rise to threaten many low-lying and unprotected coastal areas. Without measures, global sea levels will continue to rise at an accelerating rate in the 21st century. This paper quantifies sea level trends around the Malaysian seas using measurements from multiple altimeter missions over 1993–2015. Sea level anomalies (SLAs) are determined using data from the Radar Altimeter Database System (RADS) covering 8 altimeter missions. We use an enhanced processing strategy to optimize sea surface heights from RADS for the derivation of SLAs, including filtering, data gridding and moving average. Tidal height measurements at eight tide gauge stations around Peninsular Malaysia and East Malaysia are used to assess SLAs from altimetry. Our assessment results in similar patterns of SLAs, high correlation coefficients (>0.9) and small (few cm) root mean square differences (RMSE) between SLAs from altimetry and tide gauges over the same period. Sea level trends are determined by the robust fit regression analysis for the SLA time series. Our result shows that sea level rise trends around Malaysia range from 3.27 ± 0.12 mm yr−1 off eastern Malaysia to 4.95 ± 0.15 mm yr−1 west of Malaysia. Over 1993–2015, the mean rising rate around Malaysia is 4.22 ± 0.12 mm yr−1, and the cumulative sea level rise is 0.05 m. This paper predicts the impact of such rising sea levels on environment, urban planning and climatology in the coastal areas of Malaysia.

The Rossby normal modes in the South China Sea deep basin evidenced by satellite altimetry

ABSTRACTThis study investigates the mechanism of mesoscale eddies observed in the South China Sea (SCS) deep basin, which are characterized by high-frequency occurrence, long life, and regular distribution patterns. Geophysical fluid dynamics predicts that for an enclosed ocean basin, there exist the Rossby normal modes if considering the Earth rotation effect. We use a rectangular ocean basin with a uniform depth to simulate the SCS deep basin and obtain 2D (x − y) sea level distribution patterns of the Rossby normal modes, consisting of alternating cyclonic and anticyclonic eddies, as well as their dynamic parameters. The periods of the modes are evidenced by the Fourier period power density spectra of satellite altimeter sea level anomaly (SLA) data from 1993 to 2015. The 2D normal mode patterns are evidenced by SLA images. The phase speeds are evidenced by that derived from the westward movement of the wave/eddy patterns on SLA time-series images.

Coastal applications from nadir altimetry: Example of the X-TRACK regional products

In the coastal ocean zones, satellite altimetry data processing and interpretation poses specific difficulties, due to the interaction of the radar signal with land topography, inaccuracies in some of the geophysical corrections and to the fast changes in the sea level. In order to optimize the completeness and the accuracy of the sea surface height information derived from satellite altimetry in coastal ocean areas, a dedicated post-processing software, called X-TRACK, has been developed by the Center of Topography of the Ocean and Hydrosphere in Toulouse. It is tailored for extending the use of altimetry data to coastal ocean applications and provides freely available along-track Sea Level Anomaly time series that cover today all the coastal oceans. Here, we present the improvements made in version 2016 of X-TRACK and show the gain in near-coastal data accuracy using in situ tide gauge observations. The correlations between altimeter and tide gauge sea level anomalies are higher (by 15% in average) compared with the previous version of X-TRACK. Three examples of applications are shown. The recent evolutions done in the X-TRACK processing result in an improved observation of the seasonal variations of the boundary circulation in the Bay of Biscay. Along Western Africa, sea-level variations derived from X-TRACK data are observed closer to land (5km) compared to AVISO (10km), and the sea-level statistics are more robust due to the larger and more stable data availability. Along-track empirical tidal constants derived from X-TRACK Sea Level Anomaly time series are also used to validate tidal models. By improving the altimetric data accuracy in coastal areas, we extend the field of marine applications.

Sea Level Changes of China Seas and Neighboring Ocean Based on Satellite Altimetry Missions from 1993 to 2012

ABSTRACT Guo, J.; Hu, Z.; Wang, J.; Chang, X., and Li, G., 2015. Sea level changes of China seas and neighboring ocean based on satellite altimetry missions from 1993 to 2012. The latest satellite altimetry data of TOPEX/Poseidon (T/P), Jason-1 and Jason-2 during the formation flight phase were analyzed. The average difference of sea level anomaly (SLA) was 9.72cm between Jason-1 and T/P, and –11.03 cm between Jason-2 and Jason-1 over the China seas and neighboring ocean. Then SLA time series from 1993 to 2012 were constructed and analyzed with the least squares method. In China seas and neighboring ocean, the average rising rate of sea surface height was about 4.64 mm/yr. The specific average rising rates were 4.44 mm/yr, 2.34 mm/yr, 3.02 mm/yr and 4.25 mm/yr in Bohai Sea, Yellow Sea, East China Sea and South China Sea, respectively. The cycles of sea level changes were also analyzed with wavelet analysis, and results showed that the most significant period of sea level change over each sea was 1 year. A...

On the recent global mean sea level changes: Trend extraction and El Niño's impact

The spatial sampling offered by TOPEX and Jason series of satellite radar altimeters and its continuity during the last twenty years are major assets to provide an improved vision of the global mean sea level (GMSL). The objective of this paper is to examine the recent GMSL variations (1993–2012) and to investigate the correlation between the GMSL and ENSO (El Niño-southern oscillation) episodes. For this purpose, a mean sea level anomalies time series, obtained from TOPEX, Jason-1 and Jason-2 measurements, is used to determine the trend of GMSL changes by using a simplified form of an unobserved components model (namely UCM). Then, to investigate the impact of the ENSO phenomenon on the GMSL changes, we considered the sea surface temperature anomalies (SSTA) index over the Niño3 region (5N–5S 150W–90W). Cross wavelet transform and wavelet coherence analysis are performed to expose common power between the GMSL changes and the SSTA index and their relative phase in the time–frequency space. The results indicate that there are in the estimated GMSL's trend a number of fluctuations over short periods that are least partly related to the El Niño/La Niña episodes. Cross wavelet transform and wavelet coherence analysis indicate that a significant correlation between GMSL and ENSO occurred during 1997–1998, 2006–2007, 2009–2010 El Niño events and 2007–2008 and 2010–2011 La Niña ones. All these areas show in-phase relationship, suggesting that GMSL and SSTA index vary synchronously.

Impact of global ocean model resolution on sea-level variability with emphasis on interannual time scales

Abstract. Four global ocean/sea-ice simulations driven by the same realistic 47-year daily atmospheric forcing were performed by the DRAKKAR group at 2°, 1°, &amp;amp;frac12°, and ¼° resolutions. Simulated mean sea-surface heights (MSSH) and sea-level anomalies (SLA) are collocated over the period 1993–2004 onto the AVISO dataset. MSSH fields are compared with an inverse estimate. SLA datasets are filtered and compared over various time and space scales with AVISO regarding three characteristics: SLA standard deviations, spatial correlations between SLA variability maps, and temporal correlations between observed and simulated band-passed filtered local SLA timeseries. Beyond the 2°−1° transition whose benefits are moderate, further increases in resolution and associated changes in subgrid scale parameterizations simultaneously induce (i) strong increases in SLA standard deviations, (ii) strong improvements in the spatial distribution of SLA variability, and (iii) slight decreases in temporal correlations between observed and simulation SLA timeseries. These 3 effects are not only clear on mesoscale (14–180 days) and quasi-annual (5–18 months) fluctuations, but also on the slower (interannual), large-scale variability ultimately involved in ocean-atmosphere coupled processes. Most SLA characteristics are monotonically affected by successive resolution increases, but irregularly and with a strong dependance on frequency and latitude. Benefits of enhanced resolution are greatest in the 1°−½° and ½°−¼° transitions, in the 14–180 day range, and within eddy-active mid- and high-latitude regions. In the real ocean, most eddy-active areas are characterized by a strong SLA variability at all timescales considered here; this localized, broad-banded temporal variability is only captured at ¼° resolution.

Complex empirical orthogonal functions analysis of ERS‐1 and TOPEX/POSEIDON combined altimetric data in the region of the Algerian current

Maps of sea level anomalies (SLA) relative to the 1993 annual mean sea level combine the data from the two altimetric missions, ERS‐1 and TOPEX/POSEIDON, during the overlap period (October 1992 to December 1993). These regular maps in space and time of residual sea level every 10 days on a 0.2° regular grid are used in the region of the Algerian current where the mesoscale eddies are of primary importance to the circulation of all the Mediterranean water masses. They are first compared with ERS‐1 along‐track scanning radiometer sea surface temperature images to get information on two anticyclonic eddies produced by instabilities of the Algerian current and visible in both infrared and altimetric data sets. Then, an analysis of complex empirical orthogonal functions (CEOFs) is performed on the SLA data set to see the correlation of the different dynamic features of the observed variability. The CEOF analysis is applied to the complex time series formed from the original SLA time series and their Hubert transforms to separate the variability into spatially coherent modes. The spatially correlated signal in the study area (0–15°E and 35°–40°N) was found to be dominated by the first two CEOFs. These first two modes explain nearly 85% of the variability, with 80% of the total variance for the first one and 5% of the total variance for the second one. The temporal phase of the first mode indicates that a constant frequency of one cycle per year is clearly dominant, corresponding to the seasonal signal. The strongest amplitude is obtained in the southern part of the channel of Sardinia and south of the Strait of Sicily. The temporal amplitude and the temporal phase of the second mode show a periodicity of about 6 months which appears to be associated with the variability of the Algerian current as the phase isolines are parallel to the mean current path along the Algerian coast. The strongest amplitude of the second mode is located near the African coast at ∼4°E and 8°E. These two points of high variability could correspond to eddy detachments from the main current.

Observation of equatorially trapped waves in the Pacific using Geosat altimeter data

A spatial integration filtering method is applied to process 4.5 years of Geosat altimeter sea level anomalies(SLA) recorded from 1 April 1985 to 17 September 1989. The integral limits are chosen as ±1.5° latitude centered at the equator and ±4° longitude centered at the each central longitude. These limits are chosen in order to eliminate the random noise and to enhance the equatorially trapped wave signals. The spatial-integration-filtered SLA time series show periodical signals with different time scales. Processing the SLA time series with a Short Time Fourier Transform (STFT) yields the time-frequency spectra of the SLA which show a frequency spectral splitting-combining phenomenon in the periods during and after the 1986–1987 El Niñio-Southern Oscillation (ENSO) event. Analysis of non-linear wave-wave interaction indicates that this phenomenon results from amplitude modulation of the short period oscillations in the 60–100 day band by a long period oscillation with a period of about 500 days. The wave components of the short period oscillations are further analysed using the equatorial wave modes to fit the meridional distribution of the SLA. The results indicate that the downwelling Kelvin wave mode before and during the peak phase of 1986–1987 ENSO and the upwelling Kelvin wave mode during the 1988 La Niña are the dominant components. The first and second Rossby wave modes play important roles for entire time series and occasionally become the dominant components. The mean phase speed of Kelvin wave mode during the 1986–1987 ENSO is 3.0 m s −1 which is 25% higher than those in non-ENSO periods.