Analyses of Antarctic ice cores revealed that temperature changes preceded changes in CO₂ concentrations by hundreds to thousands of years in past glacial and interglacial cycles [1] . However, the Intergovernmental Panel on Climate Change (IPCC) states that modern warming differs from past natural climate changes in that it is the result of a rapid increase in atmospheric CO₂ concentrations caused by human activity, which has intensified the greenhouse effect and caused the Earth’s temperature to rise [2] . This means that the increase in CO₂ may precede the increase in Earth’s temperature, and the Earth’s temperature may continue to rise.

Humlum et al. [3] examined the relationship between changes in CO₂ concentration and land-sea surface temperature over the period from January 1980 to December 2011 and reported that changes in CO₂ always lag changes in temperature by 10 - 12 months. Wang et al. [4] analyzed the relationships between the Mauna Loa atmospheric CO₂ growth rate and tropical land climatic elements. They reported that the Mauna Loa CO₂ growth rate lags precipitation by 4 months, leads temperature by 1 month, and correlates with soil moisture with a zero.

On the basis of our recent analysis [5] , the temperature change and rate of CO₂ change are correlated with a temperature-leading time lag. The correlation was investigated by calculating a correlation coefficient r of these changes for selected ENSO events in the study. Annual periodical increases and decreases in the CO₂ concentration were considered, with a regular pattern of minimum values in August and maximum values in May each year. An increased deviation in CO₂ and temperature was found in response to the occurrence of El Niño, but the increase in CO₂ lagged behind the change in temperature by 5 months. This pattern was not observed for La Niña events. An increase in global CO₂ emissions and a subsequent increase in global temperature proposed by the IPCC were not observed, but an increase in global temperature, an increase in soil respiration, and a subsequent increase in global CO₂ emissions were noticed. This natural process can be clearly detected during periods of increasing temperature, specifically during El Niño events. The results cast strong doubts that anthropogenic CO₂ is the cause of global warming.

When El Niño events occur, an increase in the global temperature is usually observed several months later [6] [7] . El Niño is a climate phenomenon characterized by the warming of sea surface temperatures in the central and eastern Pacific Oceans. While the exact causes of El Niño events are complex, several key factors that contribute to El Niño occurrence may be summarized as follows [8] - [10] . El Niño events are driven primarily by a weakening of Pacific trade winds, which disrupts normal ocean-atmosphere interactions. This weakening allows warmer water from the western Pacific to spread eastward, leading to positive sea surface temperature anomalies in the central and eastern equatorial Pacific. These warmer surface waters then deepen the thermocline, further reinforcing warming and atmospheric changes. While influenced by natural climate cycles, the critical factors are the initial weakening of trade winds, the subsequent ocean-atmosphere feedback, and the resulting changes in sea surface temperatures and thermocline depth.

The Oceanic Niño Index (ONI) is an index that reflects fluctuations in sea surface temperatures in the equatorial Pacific Ocean. The National Oceanic and Atmospheric Administration (NOAA) considers El Niño conditions to be present in the ocean when the ONI in that area, known as the Niño-3.4 region (see Figure 1 ) [11] , is +0.5 or higher, meaning that surface waters in the east-central tropical Pacific are 0.5˚C warmer than average. Oceanic La Niña conditions exist when the ONI is −0.5 or lower, indicating that the region is 0.5˚C or greater, which is cooler than average. The Niño-3.4 region is the east-central equatorial Pacific between 5N-5S, 170W-120W, which is approximately 6.179 × 10⁶ km² and 1.2% of the Earth’s surface area, approximately 510.1 × 10⁶ km².

Our recent research [5] [12] - [16] has shown that global temperature changes precede changes in CO₂ concentrations by 5 months. Therefore, rising temperatures may induce increased CO₂ emissions. This phenomenon is due mainly to the promotion of soil respiration. Large amounts of “thermally induced CO₂” are emitted, especially from midlatitude forests. “Thermally induced CO₂” is more temperature dependent than the amount emitted from tropical rainforests. Moreover, its amount significantly exceeds anthropogenic emissions. This process can be organized as shown in Figure 2 [16] . This differs from the view of the IPCC.

The IPCC proposed that anthropogenic CO₂ is causing global warming through the greenhouse effect. The observed temperature-leading process suggests a natural phenomenon via soil respiration, casting doubt on the theory that anthropogenic CO₂ is the only cause. Considering the important role of temperature-dependent soil respiration, it is necessary to consider whether the current efforts to reduce anthropogenic CO₂ emissions are effective in lowering global CO₂ concentrations [16] . The purpose of this paper is to further clarify and confirm the process summarized in Figure 2 . To do so, we focus on the ONI, which is an index of the ENSO process. We then consider the time-dependent changes in the ONI, global temperature, and CO₂ concentration and the processes by which they change.

The ONI data are reported by the National Oceanic and Atmospheric Administration (NOAA), and all the original data were downloaded [11] . The three-month average ONI values were used.

Since 1979, the University of Alabama in Huntsville (UAH) has updated global temperature datasets that represent the piecing together of temperature data from a total of fifteen instruments flying on different satellites. Further details are available [17] . Temperatures here were obtained from the datasets, and the 13-month average of lower troposphere anomaly values was used, where the temperatures were averaged over the 6 months before and after each specific month.

In general, the correlation coefficient r between variables x and y can be defined as follows:

$r=\frac{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)}}{\sqrt{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{\left(x_i-\bar{x}\right)}^2}}\sqrt{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{\left(y_i-\bar{y}\right)}^2}}}$ (1)

For convenience, r can be easily calculated via built-in functions in Microsoft Excel®. This calculated r is used to show correlations between two variables throughout this paper.

The annual mean growth rate of CO₂ in a given year is the difference in concentration between the end of December and the start of January of that year reported by NOAA. Further details are available on their website [18] . Because of the seasonal changes in CO₂ concentrations, the annual means and the monthly data are compared.

Monthly average temperature data in Japan were obtained from 15 locations selected from meteorological observation stations that have been conducting observations since 1898 by the Japan Meteorological Agency, with little impact from urbanization and without bias toward specific regions. For each location, the deviation of the monthly average temperature (observed monthly average temperature minus the 30-year average from 1991to 2020) is calculated [19] .

The 13-month average global and ocean temperatures based on satellite observations are available from the UAH database [17] . Figure 3 compares these results between 1979 and 2023. Both results are well correlated, with a correlation coefficient of 0.993. This means that the global temperature is almost completely controlled by the ocean temperature.

Figure 4(a) compares the changes in the ONI values obtained from NOAA and satellite-based global temperatures between 1979 and 2023. The correlation coefficient between the two is 0.143. The global temperatures lag behind the ONI. Therefore, the correlation coefficient between the ONI and global temperature was investigated by changing the lag time (in months). Figure 4(b) shows the result. The value at which the correlation coefficient is maximized indicates that the global temperature changes with a lag of approximately five months compared with the ONI value.

Oceanic gyres are large systems of circular ocean currents [20] driven primarily by global wind patterns and the Coriolis effect, which deflect moving water. Oceanic gyres are broadly shown in Figure 5 [21] . While gyres are generally stable, their formation and characteristics can be significantly influenced by phenomena such as the El Niño-Southern Oscillation (ENSO).

The Niño 3.4 region shown in Figure 1 , which is used to monitor the ONI, is located near the equator, and the ocean currents flowing through this region head westward. Then, at the western end of the Pacific Ocean, they turn northward in the Northern Hemisphere, whereas in the Southern Hemisphere, they turn southward. The warm current flowing east of the Japanese Islands is called the Kuroshio Current. During El Niño events, the Kuroshio Current may cause an increase in temperature near the Japanese Islands. Therefore, the relationship between the ONI and temperature changes in Japan was investigated during two El Niño events. Figure 6(a) compares the changes in the ONI values obtained from NOAA and the temperature anomalies in Japan from the Japan Meteorological Agency between Jan. 2015 and Dec. 2016. The correlation coefficient between the two is 0.0194. The global temperatures lag behind the ONI, and the correlation coefficient between the two is 0.855 after moving temperatures by 5 months ahead. Similarly, Figure 6(b) compares the changes in the ONI and temperature anomalies in Japan between September 2022 and August 2024. The correlation coefficient between the two is 0.809 and 0.843 after moving temperatures by 5 months ahead. The local temperature changes with a lag of five months compared with the ONI value during these El Niño events.

We found here that temperature changes can be observed at a global scale and in selected places where warm currents flow. They are particularly noticeable when El Niño events occur. We next investigate ONI fluctuations, subsequent fluctuations in global temperature, and how CO₂ changes due to fluctuations in global temperature.

Global temperature anomalies and CO₂ annual growth rates are correlated over 40 years, as reported in our recent paper [5] . The 12-month average CO₂ annual growth rates are reported by NOAA [18] . The latest correlation between July 1979 and December 2023 is shown in Figure 7 . Its correlation coefficient r is 0.744, and the correlation is relatively good.

Since the 13-month average of temperature change and the annual average of the rate of CO₂ increase are used in Figure 7 , a time lag within 12 months between two variables cannot be effectively analyzed. Figure 8(a) compares global temperature anomalies and CO₂ monthly growth rates instead of CO₂ annual growth rates between 1980 and 2023. The correlation coefficient between the two is 0.664. The CO₂ growth rates lag behind the global temperatures. Therefore, the correlation coefficient between the CO₂ growth rates and global temperatures was investigated by changing the lag time (in months). Figure 8(b) shows the result. The value at which the correlation coefficient is maximized indicates that the CO₂ growth rate changes with a lag of approximately four months compared with the global temperature.

Figure 9 shows the correlation between global temperature anomalies and monthly CO₂ growth rates during two El Niño events between (a) Jan. 2015 and Dec. 2016 and (b) Sep. 2022 and Aug. 2024. The correlation coefficients between the two variables increased (a) 0.901 from 0.705 and (b) 0.973 from 0.822 when time lags of (a) five months and (b) four months were considered. The temperature change and rate of CO₂ change are correlated with a time lag, as reported in a previous paper [5] . The time lag of CO₂ behind the change in temperature was five months. The time lags of four and five months in Figure 9 are coincident with the results in the previous paper [5] .

The results summarized here show that there is a correlation between ONI (or ENSO) variations, changes in global temperature, and changes in CO₂ concentration. There is a time lag between these correlations. The overall results are consistent with the results reported in previous papers and can be summarized, as shown in Figure 10 , from the results in Figure 4(a) and Figure 8(a) . The results show that changes in CO₂ concentration do not cause changes in global temperature but rather that changes in global temperature cause changes in CO₂ concentration.

Our recent research has shown that soil respiration and ocean CO₂ emissions significantly contribute to atmospheric CO₂ concentration changes as global temperatures rise, which is based on the global CO₂ balance [13] [14] [16] . The general process changes are shown in Figure 2 . The quantitative investigation of ocean emissions is a future challenge. When ONI changes are large, ENSO appears. This event is characterized by small fluctuations in the atmospheric CO₂ concentration [16] . Compared with these CO₂ balance amounts, the amount of CO₂ emissions due to anthropogenic activities is small [16] .

The ONI is an index that indicates the variation in sea surface temperature in the equatorial Pacific Ocean. When the ONI varies greatly, El Niño or La Niña phenomena occur. Changes in global temperature appear approximately 5 months after ONI variations ( Figure 4 ). El Niño events cause the temperature to rise, whereas La Niña events cause the temperature to decrease. There are peculiar places where the direction of the warm current has changed, such as the western end of the Pacific Ocean, such as the Japanese Islands. In these peculiar places, during El Niño events, the temperature changes 5 months later than the ONI value changes ( Figure 6 ).

Additionally, changes in the global CO₂ concentration appeared approximately 4 months after the global temperature change ( Figure 8 ). The CO₂ concentration tends to increase with increasing temperature. El Niño or La Niña phenomena are small perturbations in the atmospheric CO₂ concentration. This is mainly due to increased plant respiration and accelerated decomposition of organic matter in soil due to rising temperatures and is thought to be largely due to CO₂ emissions from the ocean. A quantitative investigation of emissions from the ocean is a future task. Compared with these CO₂ budgets, CO₂ emissions from anthropogenic activities are small.

Our recent results, including those of this work, reveal that temperature and CO₂ changes are correlated, but CO₂ changes are the result of temperature changes, and we have not found that CO₂ changes cause temperature changes ( Figure 2 ).