1 Introduction

Variations in Earth rotation are excited by multiple internal and external sources, spanning a wide range of timescales from sub-diurnal to monthly, annual, and even decadal periods. In that context, we understand internal sources refer to processes in the Earth's interior, i.e., electromagnetic coupling, gravitational coupling, earthquakes, etc.; the external sources refer to both the surface fluids and lunisolar torques. Among these causes, the contributions from geophysical fluids, i.e., atmospheric and oceanic angular momentum (AAM, OAM) have been extensively studied, and the changes in AAM are thought to be the most dominant contributor (Zotov et al. 2020; Chen et al. 2019; Yan and Chao 2012). In this paper, we discuss the axial component of Earth rotation (length-of-day changes ΔLOD, m3) and zonal AAM variations (as conveyed by the excitation function χ3) on interannual scales.

The El Nino-Southern Oscillation (ENSO) is a quasi-periodic oscillation of the climate system along the tropical Pacific zone occurring roughly every 2–7 years. As a coupled ocean–atmosphere phenomenon, ENSO accounts for the seesaw between warm and cold phases in the surface water of the equatorial central-eastern Pacific. El Nino corresponds to the warm anomaly and La Nina to the cold anomaly. In the atmosphere, ENSO appears among other effects as a southern oscillation (SO), which is a fluctuation in the pressure difference at the sea surface between the eastern and western Pacific (Fang and Yu 2020; Timmermann et al. 2019; López-Parages et al. 2016). In terms of AAM fluctuations, weakened trade winds during El Nino provide less counteraction to the westerly AAM, thereby slowing down the solid Earth; on the contrary, the solid Earth is accelerated during La Nina phases (Haddad and Bonaduce 2017; Dickey et al. 2007). These arguments are in keeping with the angular momentum conservation of the Earth ocean–atmosphere system, that is, AAM variations in the axial direction cause opposite angular momentum perturbations in the solid Earth, resulting in LOD changes (ΔLOD). Thus, ENSO, AAM changes, and ΔLOD are closely related (Zotov et al. 2017; Dickey et al. 1992, 2007).

The advance of space geodesy over past decades has greatly improved the accuracy of Earth rotation observations and helped identify geophysical causes (Ratcliff and Gross 2019; Gambis 2004). Using high temporal and spatial resolution data, numerous studies have been conducted to analyze the correlations between ΔLOD, AAM and ENSO. The primary results can be summarized as follows: (1) due to the hemispheric asymmetry of seasonal circulation, the AAM motion term becomes the primary source of the interannual, seasonal, and sub-seasonal variations (Haddad and Bonaduce 2017; Zhou et al. 2008). On ENSO timescales (2–7 years), the AAM contribution to ΔLOD is found to be 0.1 ms on average for the motion term and 0.01 ms for mass term (Zotov et al. 2017); (2) although the interannual variations of the three subject data sets typically show a high degree of correlations, the ENSO indices usually precede ΔLOD and AAM by approximately 1–2 months (Dickey et al. 2007, 1992); (3) since 1980, three extreme El Nino events occurred during 1982–1983, 1997–1998 and 2015–2016, causing approximately 0.91, 0.78 and 0.81 ms anomalies in ΔLOD (Lambert et al. 2017). Extreme El Nino events are identified in the observational record every time the equatorial Pacific sea surface temperature anomaly (SSTA) is greater than 2.0℃ for more than 5 months. Interestingly, the strongest El Nino events occurring every ~ 20 years may be associated with the quasi-20 years cycle found in the regional patterns of atmospheric excitation (Zotov and Bizouard 2015).

Regarding regional AAM contributions, extensive investigations have been carried out to polar motion excitation (Zotov and Bizouard 2015; Nastula et al. 2009; Nastula and Salstein 1999). By contrast, regional AAM contributions to the ΔLOD excitation have been rarely examined in the available literature. In this study, we estimate the continental and oceanic AAM contributions to ΔLOD separately (throughout this paper, the continental and oceanic AAM refer to the AAM over the land and ocean, respectively). The results show that the oceanic AAM contributions to ΔLOD corresponding to the three extreme El Nino events are more than twice as large as those of the continental AAM.

On interannual timescales related to climate variations, there are three signals (at ~ 6, ~ 7, ~ 8 years) in ΔLOD interpreted as internal causes (Hsu et al. 2021; Ding et al. 2021; Duan and Huang 2020; Duan et al. 2018). These internally driven oscillations have been estimated to be of appreciable magnitude (~ 0.2 ms), and therefore they will affect the ΔLOD variations associated with climatic causes. Thus, we extract and deduct the three interannual signals in ΔLOD series, to obtain the sought-for rotation rate variations. After removing the three internal-caused oscillations, the discrepancy between AAM and ΔLOD is reduced. Furthermore, we investigate the latest 2020–2021 La Nina event emerging in interannual AAM and climate-related ΔLOD.

The structure of the paper is as follows: the data processing and analyses are introduced in Sect. 2; the results are assessed and discussed in Sect. 3; a summary of the main findings is provided in Sect. 4.

2 Data processing and analyses

Considering that ENSO is a quasi-periodic oscillation roughly every 2–7 years, we focus on timescales of 1.5–10 years to retain all the climatic contributions in interannual ΔLOD. The data sets are reduced to monthly mean series. To arrive at the wanted interannual ΔLOD series, we use a differential method to eliminate effects from the long-term variations in ΔLOD and the three interannual oscillations associated with internal causes (Sect. 2.3). Further processing steps include an Auto-Regressive (AR) model that is used to extrapolate the respective time series by 10 years (120 months) in both forward and backward directions. Afterward, a 2-order Butterworth filter is passed through the extended data. Finally, we obtain the climate-related interannual ΔLOD by integrating the filtered series (Brockwell and Davis 1996; Akaike 1971).

The employed ΔLOD series range from January 1962 to October 2021 and come from the International Earth Rotation and Reference Systems Service (IERS) (Ratcliff and Gross 2019; Gambis 2004). The AAM series are calculated based on the data from the National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis data set R1(Kalnay et al. 1996; Salstein et al. 1993). The ENSO indices are from the National Oceanic and Atmospheric Administration (NOAA).

2.1 ENSO indices

The complexity of ENSO makes it difficult to accurately determine its duration and intensity. The commonly used criteria for ENSO is presented by NOAA (Fang and Yu 2020; Timmermann et al. 2019; Capotondi et al. 2015). Here, the Nino 3.4 of ocean Nino index (ONI) and standardized southern oscillation index (SOI) from NOAA are selected to represent the ENSO variations. The SOI characterizes the southern oscillation and represents the standardized monthly mean pressure difference between Tahiti (tropical eastern Pacific) and Port Darwin (tropical western Pacific). The Nino 3.4 index denotes the SSTA with a moving average of 3 consecutive months. Moreover, the current SSTA on the ONI is based on the fifth version of NOAA's reconstructed extension sea surface temperature (ERSSTV. 5), which provides a rolling update of the climate state every 5 years, excluding effects from SST long-term warming trend in the Nino 3.4 sea area. The monthly mean time series of the SOI and Nino 3.4 from January 1962 to October 2021 are compared in Fig. 1, and the positive and negative regions are colored in red and green, respectively.

Fig. 1
figure 1

Monthly mean series of the SOI and Nino 3.4 from January 1962 to October 2021. The blue square frames mark the three extreme El Nino events. a SOI and b Nino 3.4

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As Fig. 1 indicates, the SOI presents a negative correlation with Nino 3.4 and shows higher frequency fluctuations. Moreover, it should be noted that the ENSO intensity variations in both panels differ somewhat. For example, seen across the three extreme El Nino events in 1982–1983, 1997–1998 and 2015–2016, the SOI exhibits decreasing amplitudes while Nino 3.4 behaves in the opposite way (i.e., events in recent years are stronger). Considering a nonlinear response of zonal winds in the central Pacific to SST anomalies, two distinct El Nino/La Nina patterns, Eastern Pacific (EP) and Central Pacific (CP) were defined (López-Parages et al. 2016). The 1982–1983 and 1997–1998 El Nino events were identified as an EP types, and the 2015–2016 El Nino event was suggested to be a mixed EP/CP type (Lambert et al. 2017; de Viron et al. 2014). Because of the negative correlation between SOI and Nino 3.4, the minus southern oscillation index (MSOI) is used hereafter.

2.2 AAM sequence

The expressions for the axial AAM function (AAMF), split up into the pressure (mass) and wind (motion) terms are as follows (e.g., Eubanks et al. 1993):

$$ \chi_{3}^{{\text{p}}} = \frac{{0.753R^{4} }}{{gC_{{\text{m}}} }}{\iint }p_{{\text{s}}} cos^{3} \varphi {\text{d}}\lambda {\text{d}}\varphi $$
(1)
$$ \chi_{3}^{{\text{w}}} = \frac{{0.998R^{3} }}{{gC_{{\text{m}}} \Omega }}\iiint {ucos^{2} \varphi {\text{d}}p{\text{d}}\lambda {\text{d}}\varphi } $$
(2)

where \(u\) is the zonal westerly wind, \(p_{s}\) is the surface atmospheric pressure, \(R\) is the radius of the Earth, \(\Omega\) is the Earth average rotation rate, \(g\) is the gravitational acceleration, \(C_{{\text{m}}}\) is the principal axial inertia moment of the mantle, \(\lambda\) is longitude, and \(\varphi\) is latitude.

Surface atmospheric pressure and horizontal wind field data used in Eqs. 1 and 2 were obtained from the NCEP/NCAR reanalysis data set R1 (Kalnay et al. 1996; Salstein et al. 1993). The output data interval is 6 h (starting at 00 UTC), the grid resolution is 2.5° × 2.5°, and the vertical wind field is from 1000 to 10 hPa with 17 levels in total (Kalnay et al. 1996; Salstein et al. 1993). It is worth noting that in calculations of the mass term, the sea level height changes with the air pressure. Therefore, we use the inverted barometer (IB) approximation, which assumes that variability of the atmospheric pressure over the ocean is modified by an isostatic ocean response that quickly readjusts sea level due to the overlying atmospheric loading. In evaluating Eq. (1), the IB correction is made by substituting mean value of the atmospheric pressure overlying the ocean for atmospheric surface pressure at every over-ocean point. As for the motion term (Eq. 2), influences of the topography are accounted for (Zhou et al. 2006, 2008; Chen 2005). Finally, the axial AAMF χ3 is obtained as a sum of the mass and motion terms, and a scaling factor of 8.64 × 107 ms/rad is applied to be consistent with unit of the observed ΔLOD (ms). We also calculated the global, continental, and oceanic AAM with same period as ΔLOD, and compare their 1.5–10 years filtered monthly time series in Fig. 2. Similar to ΔLOD, we obtain the interannual AAM series with edge effects eliminated.

Fig. 2
figure 2

Interannual series of the global (green curve), continental (orange curve) and oceanic (blue curve) AAM from January 1962 to October 2021. The red square frames mark the three extreme El Nino events. a Mass terms; b motion terms; and c combined mass-motion terms

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Figure 2 displays the decomposed and combined AAM mass-motion variations over the globe (green curve), ocean (blue curve) and land (orange curve). As apparent from panels (a) and (b), the AAM motion terms are approximately one order of magnitude stronger than the mass terms in all three cases. Panel (c) shows that the oceanic AAM contributes more to the global AAM with larger amplitudes and longer periods than the continental AAM. Furthermore, the three extreme 1982–1983, 1997–1998 and 2015–2016 El Nino events are clearly evident in both the AAM motion and combined series but not in the mass terms. In summary, the AAM motion term over the ocean is the most significant contributor to global AAM changes, especially during periods of extreme ENSO events.

2.3 ΔLOD series

Changes in Earth's rotation rate contain variations on multiple timescales from different driving agents. For the interannual ΔLOD, the relevant geophysical processes comprise internal sources, surface fluids and lunisolar torques (Ding et al. 2021; Duan and Huang 2020; Chen et al. 2019).

To obtain the climate-related interannual ΔLOD without effects from other factors, i.e., the Earth’s interior signals and lunisolar torques, we need to remove the zonal tidal terms and the three internal-caused oscillations. First, the tidal and AAM contributions are subtracted from ΔLOD. Second, the derivative of the residual ΔLOD series (corrected for tidal effects and AAM contributions) is taken, and the three interannual oscillations (at ~ 5.9, ~ 7.2, ~ 8.6 years) are extracted by the frequency domain stepwise regression (FDSR) method (see Hsu et al. 2021 for more details). Finally, the derivative of the residual ΔLOD series (corrected for tidal effects and internal causes) is passed through by band-pass filtering, and the sought-for interannual ΔLOD are obtained by integrating the filtered series. The data processing flowchart (hereafter, the major data processing is abbreviated as the difference + FDSR method) is presented in Fig. 3. The monthly tidal-corrected ΔLOD series, the derivative series and the final climate-related variations are presented in Fig. 4. To show the superiority of the difference + FDSR method, the traditional least square polynomial-fitted terms (with periods longer than 10 years), the residual ΔLOD series (corrected for tidal and polynomial-fitted terms) and the original interannual ΔLOD series (obtained without using the difference + FDSR method) are also displayed in Fig. 4.

Fig. 3
figure 3

Flowchart illustrating the processing chain from the monthly averaged ΔLOD observations to the climate-related ΔLOD series

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Fig. 4
figure 4

Monthly averaged ΔLOD series from January 1962 to October 2021. a Tidal-corrected ΔLOD series (orange curve), least square polynomial-fitted terms (purple curve) and tidal- polynomial-corrected ΔLOD series (blue curve); b derivative of tidal-corrected ΔLOD series (green curve); c original interannual ΔLOD (light-blue curve) and final climate-related ΔLOD (black curve), where the red square frames mark the three extreme El Nino events

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As shown in panel (a), due to the combination of excitation sources and different periodicities included, the least square fitting model (purple curve) has difficulties in recognizing all the long-term components in the ΔLOD series (orange curve). Some of the remaining long-period signals in the residual ΔLOD series (corrected for tidal and polynomial-fitted terms) will affect the interannual filtered results and therefore the estimations of the three internal-caused signals. Thus, we apply the differential method to minimize the impact of these long-term variations. The derivative of tidal-corrected ΔLOD series (green curve) is shown in panel (b). As can be seen, this differential series is stable, similar to white noise, and is more suitable for the AR extrapolation model. After removing the three internally induced signals, as well as band-pass filtering and integrating, we obtain the sought-for interannual ΔLOD series (black curve). The original interannual ΔLOD series (light-blue curve) is also included in panel (c). We can see exceptionally prominent oscillations in the climate-related ΔLOD, during periods over the 1982–1983, 1997–1998 and 2015–2016 El Nino events. By contrast, different cases are discovered in the original interannual ΔLOD, i.e., prominent oscillations are presented during the periods over 1982–1983, 2009–2010 and 2015–2016 El Nino events. Moreover, the anomalies in climate-related ΔLOD corresponding to the three extreme El Nino events here (~ 0.43, ~ 0.36, ~ 0.42 ms) are about half of the magnitude of previous estimates (~ 0.91, ~ 0.76, ~ 0.81 ms) (Lambert et al. 2017). These discrepancies can be ascribed to the utilized differential scheme and particularly our approach of subtracting length-of-day changes associated with interior processes.

3 Results

3.1 Continental and oceanic AAM contributions to ΔLOD

To illustrate the effects of the different excitation patterns on ΔLOD caused by the continental and oceanic AAM, monthly time series of the interannual ΔLOD as well as the global, continental, and oceanic AAM are compared in Fig. 5. Besides, the amplitudes of these series and the AAM contribution ratios to ΔLOD, corresponding to the three extreme El Nino events are estimated in Table 1.

Fig. 5
figure 5

a Interannual time series of the global AAM and ΔLOD from January 1962 to October 2021. The red square frames mark the three extreme El Nino events. b Similar to (a) but for the continental, oceanic AAM and ΔLOD

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Table 1 Amplitudes of the interannual ΔLOD, and the global, oceanic, continental AAM series, as well as AAM contribution ratios to ΔLOD, corresponding to the three extreme El Nino events
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There are two findings from the closely related results in Fig. 5 and Table 1. First, the interannual variations of ΔLOD and the global AAM exhibit a notable degree of consistency. In particular, the AAM contribution ratios to ΔLOD corresponding to the three extreme El Nino events are 80%, 93% and 68%, respectively. The discrepancy between the interannual ΔLOD and AAM suggests that there are other small contributors, e.g., oceanic and hydrological angular momentum.

Second, the oceanic AAM shows variations with larger amplitudes and longer periods than the continental AAM. It is worth noting that the contribution ratios of the oceanic AAM to ΔLOD corresponding to the three extreme El Nino events are more than twice as large as those of the continental AAM. Based on the fact that AAM contributes in the form of topographic torques over the land, the prominent oceanic AAM contributions (primarily the motion term) reveal the important role of ocean–atmosphere processes in redistributing the atmosphere mass, and then exciting the Earth rotation changes, particularly during periods of extreme ENSO events (Zhou et al. 2008; Dickey et al. 2007; Ponte and Rosen, 1999).

3.2 The three internal-caused oscillations removed in ΔLOD

The FDSR parameter estimates of the three interannual harmonic oscillations (at ~ 5.9, ~ 7.2, ~ 8.6 years) are listed in Table 2, by the sine convention of \({\text{ Asin}}\left( {\frac{{2{\uppi }\left( {{\text{t}} - {\text{t}}_{0} } \right)}}{{\text{T}}} + {{\varphi }}} \right)\). Here \(A\) is amplitude, \(T\) is period, \(\varphi\) is phase, and the epoch \(t_{0}\) with 0° phase is 1962.0. The three internal-caused signals are jointly illustrated in Fig. 6. To quantify the agreement before and after subtraction of the three internal oscillations, the correlations between the two interannual ΔLOD series with global AAM are also compared in Fig. 6.

Table 2 FDSR parameter estimates of the three interannual harmonic signals in tidal-AAM-corrected ΔLOD series
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Fig. 6
figure 6

Interannual time series from January 1962 to October 2021. a The three signals interpreted as internal causes in ΔLOD (red curve); b correlations between the global AAM and the ΔLOD before removing the three oscillations (black curve), the ΔLOD after removing the three oscillations (blue curve)

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As shown in Table 2, among the three internal-caused signals, the 6-year peak is most prominent with an amplitude of more than 100 \({\mu s}\); the 7-year and 8-year oscillations are smaller with amplitudes in the order of 30–70 \({\mu s}\). The three oscillations are combined in panel (a) of Fig. 6 (red curve), and the total amplitude is ~ 200 \({\mu s}\). As can be seen in panel (b), the correlation coefficient between global AAM and ΔLOD after removing three oscillations is 0.88 (blue curve), higher than that between AAM and ΔLOD before removing three oscillations (0.66, black curve). These findings reveal that the three signals associated with internal causes are relatively large ΔLOD contributors and should be subtracted to isolate the climate-related rotation rate variations.

3.3 The latest La Nina event detected during 2020–2021

To investigate prominent changes in the ENSO indices (MSOI and Nino 3.4), and corresponding anomalies in the climate-related ΔLOD signals as well as in the interannual AAM, the three data sets from January 1962 to October 2021 are compared in Fig. 7. In the ENSO indices, distinct positive regions are marked in red and negative ones are marked in blue, indicating the potential ENSO events.

Fig. 7
figure 7

Time series from January 1962 to October 2021. The red square frame marks periods when the latest 2020–2021 La Nina event occurred. a Interannual ΔLOD (black curve) and AAM (green curve); b original MSOI; and c Nino3.4

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Figure 7 illustrates that the interannual ΔLOD and AAM have pronounced anomalies that align well with similar positive and negative fluctuations in the ENSO indices. These fluctuations denote the speed decelerations and accelerations in Earth rotation, and correspond to the El Nino (warm) and La Nina (cold) events in climate change, respectively. According to the NOAA determination (SSTA ≥ 0.5℃ or SSTA ≤ -0.5℃ for more than 5 months), there were 19 El Nino and 18 La Nina events from 1962 to now. These warm and cold phases of ENSO exhibit a significant asymmetry in their decay speed. In particular, the decay speed during La Nina is slower, as the system's relaxation from the generally weaker cold anomalies is less drastic than for the strong positive anomalies during El Nino (Song et al. 2019).

To be specific, the clearly descending areas in the interannual ΔLOD and AAM, as well as in the original ENSO indices are enclosed with a red square frame, pointing to the latest 2020–2021 La Nina event. As depicted in Fig. 7, this recent phenomenon lasted 10 months from August 2020 to May 2021; and the minimum SSTA of approximately -1.4℃ occurred in November 2020, which could be classified as an event of intermediate strength. Similar to the seesaw performances between previous ENSO events, this 2020–2021 La Nina is a second-year cooling after the 2018–2019 El Nino (Feng et al. 2020). Moreover, this cold event contributed a minimum value of approximately -0.21 ms to ΔLOD and -0.11 ms to AAM. The discrepancy between the ΔLOD and AAM estimates for this event may be ascribed to other small contributors (e.g., oceanic and hydrologic angular momentum). In addition, Zotov et al. (2022) found that the Earth started to accelerate since the 2015–2016 El Nino event and reached the maximal velocity in 2020. The detected La Nina could be a potential indicator of the Earth rotation acceleration and series of extreme weather events (e.g., cold waves and strong rainfalls) in the recent 2 years.

4 Discussion and conclusion

The history of civilization has been accompanied by global climate change, and an increasing number of extreme weather events have been reported in recent years. Exploring the relationships between ENSO phenomena and corresponding anomalies in the AAM and ΔLOD is important for understanding the ocean–atmosphere interactions, and the coupling between the solid Earth and its fluid envelope.

Using the latest data series from January 1962 to October 2021, we have applied the difference + FDSR method to isolate the ΔLOD components related to climatic oscillations, and investigate the weather events reflected in both ΔLOD and AAM. Unlike in previous studies, the contribution to ΔLOD by the AAM over the ocean is estimated separately from that over the land; and the ~ 6-, ~ 7-, ~ 8-years internal-caused oscillations are removed to obtain the climate-related interannual ΔLOD for the first time. The comparative results reveal that the oceanic AAM (primarily the motion term) contribute more to ΔLOD than the continental AAM, with larger amplitudes and longer periods, especially during periods of strong ENSO events. The climate-related ΔLOD matches AAM better than the ΔLOD series without removing the three internal-caused signals; and the ENSO-driven anomalies in the ΔLOD obtained here are half as strong as those found in previous studies.

In addition, an intermediate La Nina event from August 2020 to May 2021 was detected in both the climate-related ΔLOD and the interannual AAM, with the corresponding minimum values being approximately -0.21 ms and -0.11 ms, respectively. Besides, another follow-up La Nina event is likely occurring, indicating strong ocean–atmosphere activities in the central Pacific. Considering a series of severe weather events over the past 2 years, the whole society need to remain vigilant. We will continue to focus on this phenomenon in subsequent studies. In summary, although ENSO has proved to be a robust indicator of climate variables, other climate indicator such as the quasi-biennial oscillation (QBO), and other fluid contributors such as the oceanic and hydrologic angular momentum have not yet been fully explored. These questions are left for future investigations.