Global Mean Sea Level Variation On Interannual-Decadal Timescales: Climatic Connections


 We investigate the influences of the climatic oscillations on global mean sea level (GMSL) on interannual-decadal timescales. We conduct correlation analyses on the GMSL-ID time series, which is obtained upon removing numerically the long-term trend and seasonal variations from satellite radar altimeter data since 1992, with several climatic oscillations represented by their respective meteorological indices, including El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), Atlantic Multidecadal Oscillation (AMO), Arctic Oscillation (AO), Antarctic Oscillation (AAO). From the time-domain correlation and frequency-domain coherence, we find: (i) High correlation between GMSL and ENSO on timescales longer than 1.5 years, especially w.r.t. the Central-Pacific type of El Niño, evidently related to changes in dynamics of the ocean mixed layer and in land-sea distribution of precipitation. (ii) Moderate correlations of GMSL with PDO and AMO, respectively on timescales of over 4 years and 2-10 years, where AMO’s correlation peaks at 8 months earlier in phase than GMSL. (iii) Weak correlation of GMSL with AO implying exchanges of the Arctic water with other oceans even though the altimetry data do not include Arctic sea,. (iv) Practically no correlation between GMSL and AAO. Finally, we least-squares fit the above five indexes to GMSL to assess the relative contribution of each oscillation in causing the interannual GMSL variations, which would lead to a better understanding of the GMSL under the on-going climate changes.


Introduction
The sea level varies with time anywhere in the ocean on all timescales for a myriad of reasons.
Conventional tide gauges monitor long-term sea level but only relative to the local ground at sparse coastal sites. Modern satellite radar altimetry on the other hand measures absolute sea level in the terrestrial reference frame uniformly over open oceans on global scales. One important product has been the averaged global mean sea level (GMSL) anomaly as a continuous single time series referenced to the time-mean value.
In terms of time dependence, the most prominent variations in the GMSL are the secular sealevel rise and the seasonal fluctuations. A subject of active research, the secular rise is a consequence of the global warming in the form of thermal expansion of the surface water and additional water inflow from land; the latter includes melting glaciers and ice-sheets, modified by anthropogenic effects of artificial-dam water impoundment and groundwater discharge (e.g., Cazenave et al., 2018;Frederikse et al., 2020). The seasonal signals follow the climatology of water exchanges of the ocean with land and atmosphere plus steric variations (e.g., Chen et al., 2005;Vinogradov et al., 2008;Garcia-Garcia et al., 2020).
In this paper we turn attention and target the non-secular and non-seasonal variability of GMSL on the interannual-to-decadal timescale, henceforth referred to as GMSL-ID. Studying the GMSL-ID, which reflects processes of the global water cycle that are related to climate variabilities (cf. Cazenave and Remy, 2011), is a scientific pursuit toward better understanding and monitoring of the on-going climatic changes. Evidences of such connections have been reported on specific basis especially with respect to extreme events. For example, Chambers et al. (2002) detected signature of El Ninos in GMSL along with certain 10~12-year variabilities. Willis et al. (2008) examined the anomalous GMSL budget during 2004-2005. Boening et al. (2012 found unequivocal link of GMSL with the strong 2011 La Nina event of the El Nino/Southern Oscillation (ENSO) which retained a great amount of water on land lowering the GMSL by as much as 5 mm. Cazenave et al. (2012) and Haddad et al. (2013) assessed the influence of ENSO and identified signatures of several El Nino/La Nina episodes in GMSL. Jin et al. (2012) and Zhang and Church (2012) reported possible connections of Pacific sea level variations with ENSO and Pacific Decadal Oscillation (PDO); Hamlington et al. (2013; found significant contribution of PDO to GMSL; Kuo et al. (2021) contrasted the influence of two different El Ninos on GMSL. Conversely, Wahl and Chambers (2016) and Rohmer and Le Cozannet (2019) made statistical studies on GMSL's connection and impacts on extreme climatic events.
In the present paper we aim to "explain" GMSL-ID following the approach of Chao et al. (2020) in understanding the variations in Earth's oblateness J2. We shall assess and quantify the contributions of the major climatic oscillations in the ocean-atmosphere system to the observed GMSL-ID, and do so via correlation investigations in both time-and frequency-domains.

Data Preparations and Methodology
Several versions of the GMSL time series have been solved by different agencies based on different treatments of systematic corrections in the satellite altimetry observation. Figure 1(a) presents the GMSL time series that we shall use, courtesy of U. Colorado. It is obtained by averaging the sea level height between 66°S and 66°N (on account of the orbit inclination of the Topex/Jason satellite series, covering about 95% of the world's ice-free ocean area), at sampling interval of 10 days (Topex/Jason's orbit repeat cycle); the timespan is from 1992.9 (Topex's launch year) to 2020.75. We first model the GMSL time series as a linear combination of various numerical terms: where angular frequency ω = 2π/(365.25 days). The term a + bt is to represent the secular sea-level rise in the form of the mean + linear trend, while the four sinusoidal terms account for the seasonality at annual and semi-annual periods. The coefficients a, b, …, f are then solved by linear least-squares regression on the GMSL(t) data ( Figure 1a) by minimizing the variance of the residual, which is our wavelet spectrum of GMSL-ID(t) (e.g., Chao et al., 2020), where two quasi-periodic signals stand out: one around 4 years growing in strength after ~2005, and one around 10.5 years which only sees ~2.5 cycles as limited by the data timespan. Figure  Counterpart to AAO, the AO (also known as the Northern Annular Mode) is closely related to and encompassing the conventional North Atlantic Oscillation (NAO; Wallace & Gutzler, 1981). It is to be interpreted as the surface signature of modulations in the strength of the polar vertex aloft the Arctic (Thompson & Wallace, 2000), while the AO Index is constructed by projecting the 1000 hPa height anomalies poleward of 20°N.
Despite the difference in their primary timescales, PDO and ENSO carry considerable correlation between their conventional indices because of the geographical juxtaposition in the Pacific Basin; for example, they show corresponding decadal behaviors evident in their wavelet spectra in Figure 2. Wanting mathematical orthogonality, that makes identifying the individual contributions to GMSL troublesome. Therefore in the processing to be conducted below we take the filtered version of the indices to accentuate the signal frequency contents as follows: the Indices of ENSO, ENSO-CP, ENSO-EP are high-pass filtered at the period of 8 years (see Figure 2 a, b, c, the blue curves), whereas the PDO Index low-pass filtered at 8 years ( Figure 2d).

Results for GMSL-Climate Correlation
We conduct the correlation analyses of GMSL-ID(t) with respect to the Indices of the aforementioned climatic oscillations in Figure 2. Figure 3 shows the time-domain cross-correlation functions, as functions of relative time shift (in months) where positive time shift means the oscillation leading GMSL-ID(t) in phase. Figure 4 shows the corresponding frequency-domain coherence spectra. We shall discuss these results in Section 4. The lack of GMSL-AAO correlation, which presumably implies that Antarctica continent's land ice mass melting does not follow AAO in a linear fashion. On the other hand, the lack of significant GMSL-AO correlation (or at most a weak correlation of AO at a 14-month lag to GMSL-ID) warrants further mention: Excluding the Arctic Ocean (above the 66N latitude), our GMSL data (including the seasonality and trend) would actually reflect any water exchanges of Arctic Sea with the rest of the oceans. Prandi et al. (2012; see also Cheng et al., 2015) estimated the sea level variations of the Arctic Sea (from multi-satellite altimetry), and found no correlation with climatic indices; our present result is consistent with theirs. In this regard, our results are also consistent with a finding by Chao et al. (2020), that it is the atmospheric, not the oceanic, mass transports that are responsible for the intra-seasonal to interannual (non-seasonal) ΔJ2 associated with AAO and AO variability.  The consequent Residual(t) time series (in Equation 2) is plotted in Figure 6 along with its wavelet spectra. It represents the remnant after the optimal combination of the known climatic oscillation effects are removed from GMSL. Now buried in relatively high noises, it in principle contains signals missed or unaccounted for by the major climatic oscillations, presumably including anthropogenic influences from artificial reservoirs water impoundment (Chao et al., 2008) and underground water withdrawal (Wada et al., 2012).
Our treatment of the climatic influences in terms of indices does not distinguish between the steric-and the mass-induced effects, the two main contributions to GMSL variations. To that end in pursuit of more insights into the responsible mechanisms, one would resort to additional global data types than the present ocean altimetry. A general prospective practice is to combine the GRACE satellite time-variable gravity data such as in Llovel et al. (2010) and Kuo et al. (2021) along with other types of in situ data or numerical model output.