Improving the understanding of the in�uencing factors on sea level on various time scales based on wavelet coherence and partial wavelet coherence

The relationship between sea level change and a single climate indicator has 15 been widely discussed. Despite this, few studies focused on the relationship between 16 monthly mean sea level (MMSL) and several key impact factors, including CO 2 17 concentration, sea ice area, and sunspots, on various time scales. In addition, research 18 on the independent relationship between climate factors and sea level on various time 19 scales is lacking, especially when the dependence of climate factors on Niño 3.4 is 20 excluded. Based on this, we use wavelet coherence (WC) and partial wavelet coherence 21 (PWC) to establish a relationship between MMSL and its influencing factors. The WC 22 results show that the influence of climate indices on MMSL has strong regional 23 characteristics. Sunspots affect MMSL on a scale of more than 64 months. The 24 influence of the sea ice area on MMSL in the northern hemisphere is opposite to that in 25


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Sea level is an important indicator of climate change and varies at broad spatial 38 and temporal scales (Meng et al., 2019). It is necessary to analyze the relationship 39 between sea level and climate indices on temporal and spatial scales to reveal the 40 relationship between sea level and its influencing factors. Significant interannual and 41 interdecadal changes occur in the sea level, exhibiting variation characteristics on 42 multiple time scales. Therefore, using analysis methods with a robust periodic analysis 43 ability is crucial for analyzing the relationship between sea level and its influencing 44 where 1 c and 2 c are normalization constants, and  is the rectangle function.

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The factor 0.6 is the empirically determined scale decorrelation length for the Morlet 139 wavelet (Torrence and Compo, 1998). 140 It should be noted that we evaluate the performances of single factors and 141 combined factors using the average wavelet coherence (AWC, the average of the 142 coherence value in the significant coherence region) and the percentage of the 143 significant coherence area (PASC, 100*significant coherence area/(significant 144 coherence area + insignificant coherence area)). The larger the AWC and PASC, the 145 more important that single factor or combination of factors is. 146

Partial wavelet coherence 147
PWC and partial correlation analysis are similar. However, PWC can be regarded 148 as a partial correlation analysis on a given time scale. Assuming that y is affected by x1 149 and x2, one can find the WC results between the two time series y and x1 after 150 eliminating the influence of time series x2. In short, we determine the influence degree 151 of x1 on y after excluding the effect of x2 .  152   2  1 2   2  1, 2   2   , 1  ,  ,  2  2  2  1 2 ,

Study area and data sources
159 All data sources used in this study are listed in Table 1. 160 It can be seen that the trend of the sea level change is very different in different 165 regions. The rate of increase in the sea level is the largest in the South Atlantic (3.50 166 mm/year) and the smallest in the Black Sea (2.08 mm/year). The rate of increase in the 167 global sea level is 3.42 mm/year. The sea-level change exhibits strong regional 168

characteristics. 169
In addition, the MMSL in the southern hemisphere, the South Pacific, and the 170 globally was abnormal around 1997-1998, which was due to the influence of the ENSO. 171 Sea level anomalies globally and locally in a certain period are also primarily affected 172 by ENSO events. 173

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Previous studies primarily focused on the driving mechanism of the Pacific, 176   The sea-level rise caused by sea ice melting is greater in the northern hemisphere than 203 in the southern hemisphere, which may be one of the reasons for this abnormal 204

phenomenon. 205
The significant correlation between NHSA, SHSA and MMSL for 16-32 months 206 is not as strong as that for 12 months, indicating that NHSA and SHSA do not control 207 the change in MMSL for 16-32 months. 208 In addition, we also found that NHSA has significant coherence with the South 209

WC results of MMSL and climate factors 215
The WC between the climate factors and MMSL is shown in Fig. 3 and Fig. 4. 216

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(c) WC between MMSL and AO 222 Fig. 3. WC between MMSL and OTI, DMI, and AO (the 5% significance level against 223 red noise is shown as a thick contour. The relative phase relationship is shown as arrows 224 (in-phase pointing right, anti-phase pointing left, and monthly mean sea level leading 225 influencing factors by 90 pointing straight down)) 226 In terms of the significant coherence region, the OTI has a more significant effect 227 on MMSL in the Indian Ocean and South Pacific and a smaller effect in the Black Sea 228 (the significant coherence region of the Black Sea is the smallest among the 10 regions). 229 In addition, we identified a 72-120-month effect scale of OTI on MMSL in eight regions 230 (all except the Black Sea and the North Pacific). 231 The DMI had a relatively large impact on MMSL in the South Pacific, Indian 232 Ocean, and southern hemisphere, and the most significant impact on MMSL in the

Main driving factors of MMSL in the 10 regions 299
The relationship between the carbon dioxide concentration and MMSL on various 300 time scales is described in the discussion section. The higher the percentage of the 301 PASC, the greater the impact of a factor on MMSL is. The larger the AWC, the stronger 302 the correlation between the influencing factor and MMSL is. We summarized the PASC 303 and AWC values corresponding to the influencing factors (Fig. 5) Table 2. 326   The PWC between the AMO and MMSL is shown in Fig. 9.

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It is well known that global warming is caused by carbon emissions, but it also 407 affects the sea level. However, since the time scale dependence of the CO2 408 concentration and MMSL relationship is unclear, we used WC to analyze the influence 409 of CO2 concentrations on MMSL at various time scales. 410 411 Fig. 11. Globally averaged monthly mean carbon dioxide (CO2) concentration at marine 412 surface sites (elsewhere in the text, we refer to the globally averaged monthly mean 413 carbon dioxide concentration) 414 The WC between CO2 concentration and MMSL is shown in Fig. 12 The PASC and AWC values between the MMSL and CO2 concentration were 436 higher than those between the MMSL and OTI, NHSA, and SHSA, indicating that CO2 437 is the most important driving factor of MMSL change. The correlation between CO2 438 concentration and MMSL was positive. Decision-makers in various countries should 439 take measures to slow down CO2 emissions to mitigate sea-level rise. 440 Furthermore, the WC and PWC results may be affected by the length of the MMSL 441 sequence. In a future study, we will analyze MMSL changes and the influencing factors 442 on a longer time scale and integrate data obtained from tide level stations. In addition, 443 we only removed the influence of Nino 3.4 from the PWC results, but other variables 444 may also affect PDO, AMO, DMI, SOI, and MMSL. We will consider these effects in 445 a future study. This paper focused on improving our understanding of the independent 446 relationship between climate indices and MMSL on various time scales after excluding 447 the dependence of the five climate indices on ENSO. 448

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We used WC and PWC to analyze the relationship between MMSL and its