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1. INTRODUCTION
The El Niño Southern Oscillation (ENSO) is a climatic episode related to the change of the surface temperature of the water at the Pacific. The ENSO occurs when this surface temperature becomes hotter than usual. Their counterpart is “La Niña” episode, which is, on the contrary, the climatic event that is associated with the unusual cooling of the surface water in the aforementioned area (Fredriksen et al., 2020). The ENSO phenomenon is so called because it normally occurs in December. Besides, their appearance implies a warming of the atmosphere, which leads to a variation in wind circulation, especially over the Pacific.
The presence of a strong ENSO directly affects the jet stream which becomes stronger. Bearing in mind that the jet stream is a narrow band of strong wind in the upper atmosphere over the Pacific. Then more intense and frequent storms are generated on the west coast of the USA. And more rainfall than usual appears for the west coast of South America, especially on the coasts of Ecuador and Peru (Toulkeridis et al., 2020). It is necessary to consider that, with the presence of the ENSO phenomenon, the atmospheric balance changes. With more rain on the Americas west coast, there is a shortage of rain in southern Asia and Australia. Consequently, while in the west of the Americas there are torrential rains, in Oceania the climate becomes abnormally dry and periods of drought (Karamperidou et al., 2020) are experienced. In the case of South America, Ecuador was hit in 1982 and 1997 by strong ENSO episodes. In that time ENSO caused the loss of dozens of lives and food shortages due to the destruction of a large part of the territory of crops. Moreover, there were losses for export, loss of road infrastructure and, consequently, milliondollar economic losses (Thielen et al., 2023). Further, with the appearance of excessive rainy conditions, it is necessary to implement fumigation and prevention campaigns to eliminate mosquito breeding sites that transmit dengue and chikungunya (Lovera et al., 2023) diseases that affect the Ecuadorian coastal population. Bearing in mind the above, it is mandatory not only to understand the El Niño and La Niña episodes, but also to be able to predict their appearance and their intensity through the application of current methodologies (Canar et al., 2020; Llugsi et al., 2020). The use of this type of methodologies can speed up decision making in the economic and social sphere, to efficiently and effectively face the presence of the ENSO. For instance, with the proper management of forecasts, implemented with neural networks, it is possible to generate risk maps that clearly identify the most vulnerable places to landslides or floods (Gomez-Tunque et al., 2023) could be clearly defined. These strategies can help prevent impacts on populations through the corresponding activation of shelters in the highest risk populations (Yoo-Geun et al., 2021).
However, in order to generate a methodology for the early detection of the El Niño and La Niña episodes requires first to understand how these episodes are determined by official agencies. This involves identifying the thresholds from which the presence of this episode is ratified. But also, to determine the intensity that they will have based on the first warnings of their presence.
Factoring in, we propose a statistical analysis with neural networks of the El Niño and La Niña episodes and their relationship with carbon dioxide CO 2 and methane CH 4. This is carried out to contrast the presence and impact that the episodes will have. Furthermore, this methodology examines ENSO not only from the historical point of view but also, considering the effect that the presence of gases result from human activity such. Examples of these gases are carbon dioxide (Picano et al., 2022) and methane (Mar et al., 2022) in the atmosphere.
The document is divided as described below. Section 2 presents first the methodology for identification of El Niño and La Niña episodes. In addition, we introduce the statistical methodology that we developed to early determine the presence of these episodes. In section 3 we obtain an analysis of the historical information of CO 2 and CH 4 and we explore a possible relationship between these gases and the temperature anomaly produced in the Oceans by the El Niño episode. We show the results of the correlation analysis between the monthly historical information of Temperature Anomaly. And the records of carbon dioxide and methane to verify a possible relationship. Section 4 is dedicated to defining the theoretical bases of the neural networks that we utilize to obtain the predictions in this work. Section 5 is devoted to show the basis of the experimentation and the results of the forecasts. An analysis of the similarities and differences between the historical and predicted environmental behavior are shown too. And finally, section 6 groups the conclusions of the work as well as the limitations found in the experimentation and some proposals for future research.
2. METHODOLOGY FOR THE IDENTIFICATION OF EL NIÑO SOUTHERN OSCILLATION (ENSO)
2.1 ENSO Description and NOAA approach to Detection
Worldwide the Climate Prediction Center of the National Oceanic and Atmospheric Administration (NOAA) is the group responsible for monitoring and forecasting ENSO events. NOAA monitors and foresees ENSO events utilizing an Average Temperature in the Tropical Pacific (Lopez et al., 2022), see Figure 1.
It is important to remember that Niño 1+2, Niño 3, Niño 3.4 and Niño 4 regions refer to geographic locations where temperature samples are taken to detect ENSO events. Niño 1+2 (0°-10°S, 80°-90°W), Niño 3 (5°N-5°S, 90°W-150°W), Niño 3.4 (5°N-5°S, 120°W-170°W), Niño 4 (5°N-5°S, 160°E-150°W) (Dunkl et al., 2025). To illustrate these locations, Figure 1, taken from Glantz & Ramirez (2020), is presented.
In order to calculate the occurrence of ENSO events, the temperature fluctuations must be considered. These fluctuations cannot be determined based on the use of a specific temperature, but rather with respect to the relative temperatures of a region. These relative temperatures are associated with Seasons which are the product of the moving average of data from a group of 3 months. For example, December January February, January February March, etc.
Using records of seasonal temperature anomalies from 1950, NOAA defines two steps for La Niña or El Niño conditions to develop into a full episode. Firstly, the ENSO occurs when seasonal temperatures appear 0.5°C warmer than the average in the central Tropical Pacific (Lopez et al., 2022). On the other hand, La Niña phenomenon occurs when temperatures are 0.5°C colder than the average temperature in the Tropical Pacific. Finally, confirmation of the phenomenon requires the temperature anomaly to persist for five consecutive seasons and occur consecutively.
The color coded events are shown in Figure 4, according to the information obtained in Lindsey (2023) for the period 2010 - 2023. We use the Figure 4 to visually distinguish the long duration historical ENSO events. And to be able to graphically show the respective classifications and comparisons. To read the map, note that every box represents a certain month of the year (e.g. DJF refers to the period December-January-February).
As stated above, the initial step in defining ENSO events is to determine whether ocean surface temperatures are above or below the average temperature. Allowing for this, it is then necessary to define, first, what the average temperature is.
Because ENSO events are identified by warmer or colder than average temperatures. Until 2012, NOAA used a 30 year average of the three most recent full decades, updated with each new decade. For example, to analyze the 1990s, NOAA employed the average of years from 1961 to 1990, and in the case of the 2000s, the period 1971 to 2000 is averaged. Considering the above, with each change of time period all previous seasonal averages in the historical events table were recalculated using the new base period. The recalculation is performed to ensure that the relative strength of all recorded episodes after 1950 is consistent. Nevertheless, this methodology tends to distort the ENSO climate record with each update of historical events. The distortion consists on that historical cold episodes seem colder and the historical warm ones seem weaker. This happens because the last three decades have been the warmest on record both globally and in the Tropical Pacific.
To solve this problem, in 2013, the aforementioned technique was modified (Lindsey, 2023). It was proposed to begin using fixed 30 year averages of the historical record for the calculation of each five year period. For example, to calculate the period 2001 to 2005, an average of the years 1985 to 2015 is utilized, while, to calculate the period 2006 to 2010, the average of the period 1991 to 2021 is used. The outcome of this modification is observed nowadays in all the information provided by NOAA, for instance like the one shown in Figure 4.
2.2 The Physical Model and Neural Networks
In Figure 2, the “Forecast Chain” to generate an environmental prediction (Canar et al., 2020) shows up in order to deeply understand the process of the ENSO Forecast. The blue fields in the picture show the data acquisition/processing while the red blocks indicate methods. Currently, information from Non Dispersive Infrared Spectroscopy (NDIR) and Gas Chromatography for CO 2 and CH 4 and Contact thermometers, infrared thermometers and satellite sensors for SSTA are considered as the “Observations” in the forecast chain. The “Data assimilation” comprises the combination of data from previous model forecasts. This is to avoid the error related to the lack of information or incompatibilities from indirect measurements.
The “physical model” is a mathematical approach that requires “Initial Conditions”. This is applied to approximate the physical processes governing the evolution of the atmospheric state through the use of two main components the “dynamics” and “physics”. The output called “Raw output” encompasses the data predicted from the Physical Model. The data then needs to be adjusted/corrected with the help of a “statistical postprocessing” or reentered in the physical model to correct predictions. The postprocessing implies the use of a Statistical Forecasting process. This process can be implemented through the use of a ShortWeather forecast system implemented by neural networks. A statistical postprocessing with Neural Netoworks must necessarily take place at the output of the physical model. The Statistical postprocessing carries out a task of calibration. The adjustment is performed to correct the inaccuracies of the model, here is where neural networks can be extremely useful.
Thanks to the environmental information (Time Series) inserted in a Neural Network, a statistical forecast can be directly computed from recently observed values. Such a non-dynamical approach can be helpful for short term forecasts, up to a few hours.
2.3 ENSO Statistical Analysis
As noted earlier, it already exists a methodology that NOAA uses to determine the presence of a El Niño or La Niña full episode. The ENSO occurs when seasonal temperatures appear 0.5°C warmer than the average in the central Tropical Pacific. While La Niña phenomenon will occur when temperatures are 0.5°C colder than the average temperature. As it can be seen in Figure 4, this methodology has been quite successful in establishing the presence of one of the two phenomena. However, can this threshold also be used to early determine a El Niño or La Niña full episode? To answer this question, it is vital to conduct a statistical analysis of the times that the threshold of +/- 0.5°C actually did or did not allow for the early determination of the existence of the episode. To perform the statistical analysis, we make use of the coefficient of determination, also called R-squared factor (R²). The coefficient of determination measures how well a statistical model predicts a certain outcome (Qiang & Ji, 2023).
R-square measures the proportion of variance in the dependent variable explained by the independent variable(s) in the model (Parreno et al., 2021). The r-square is calculated as one minus the ratio of the sum of residual squares to the total sum of squares (R. Llugsi).
Where: RSS: Sum of squared residuals (sum of squared differences between observed and predicted values). SCT: Total sum of squares (sum of squared differences between observed values and the mean of the observed values).
Considering that the R-square measures the proportion of variance of the dependent variable. Table I has sought to investigate what would be, statistically, the threshold with which an ENSO event is best detected.
In our case, we utilize this factor to determine from what threshold the set of data obtained adopts a data distribution closer to a normal distribution. Namely, at what early detection threshold the temperature anomaly will early indicate a high probability of the occurrence of an El Niño or La Niña episode.
Six scenarios of early detection thresholds are proposed for our research. This scenario implies the use of the following thresholds +/-0.5°C, +/-0.4°C, +/-0.35°C, +/-0.3°C, +/-0.2°C, +/-0.1°C. The analysis of the thresholds makes it possible to determine in which case there will be a function more similar to a normal distribution. It has to be said then, that the best scenario will be the one where the coefficient of determination is closer to 1, see Table 1.
In the La Niña case, it can be seen that the -0.5°C threshold is close enough to early determine a full episode. In the case of the El Niño, a 0.2°C threshold allows for the early detection of a full episode. Figure 3 shows the probability distribution derived from the historical temperature anomaly records dating back to the 1950s. On the left, the data set that allows for an early detection of the La Niña episode is shown (early threshold of -0.5°C). On the other hand, the data set that allows for an early detection of the El Niño episode appears to the right (early threshold of 0.2°C).
To understand Figure 3, it is important to mention that the Python environment has generated a curve that represents a normal probability distribution function based on the data trend. Therefore, this curve is generated based on a histogram (bars) constructed considering the number of times a value appears in the time series. With this, the authors sought to verify the number of times an ENSO, El Niño, or La Niña event has been effectively detected with thresholds of 0.5°C and -0.5°C, respectively.
In view of the preceding, we are compelled to assert that, in the case of La Niña events, the data considered above the early detection threshold of -0.2°C help to define a clear trend. Namely, they help to determine a high probability of the appearance of a complete La Niña event, without the need to consider the period of 5 consecutive seasons recommended by NOAA. In the case of the El Niño event, we must acknowledge that the data exceeding the early detection threshold of 0.5°C contribute to defining a clear trend of the episode appearance. Namely, the event has a high probability of occurrence regardless of the period recommended by NOAA of 5 consecutive seasons. Below the indicated thresholds, the data begins to behave like artifacts that do not contribute to obtaining a clear trend that indicates the appearance of a complete event.
To verify the usefulness of this methodology, a modification to the Classification of long lived historical ENSO events is presented in the Figure 4. Blue for La Niña, red for El Niño.
Figure 3 Probability Distribution Adopted by the Historical Temperature Anomaly. To the left, an early detection threshold of -0.2°C for the La Niña episode. To the right, an early detection threshold of 0.5°C for the El Niño episode
Figure 4 is a modification of the images presented by NOAA on their page https://www.climate.gov/news-features/understandingclimate/watching-el-ni%C3%B1o-and-la-ni%C3%B1a-noaaadapts-global-warming. The modification consists of determining when a La Niña event actually occurred and whether the -0.5°C threshold was effective for their detection.
In Figure 4, it can be seen that the statistical methodology presented in this work allows to detect early and week El Niño and La Niña episodes, see Figure 4 (1), (2), (3), and (4). For instance, in Figure 4 (1) it can be seen that the threshold of -0.2°C was reached in May 2010, and a La Niña episode could indeed be predicted. At this point it is crucial to consider that according to the NOAA methodology, this episode ended in June 2011. After this, an apparent new episode of La Niña took place from July 2011 to April 2012. However, with the methodology that we propose, we found that the apparent new episode of La Niña was not a new episode, but was the continuation of the same one that originally appeared in May 2010. The same occurs in (4) where it can be seen that, according to the NOAA methodology, there were two episodes of La Niña. However, according to our methodology, they both can actually be considered as one.
Likewise, with the statistical thresholds for early detection of El Niño or La Niña episodes, we can determine the presence of mild episodes. For example, Figure 4 (5) illustrates the appearance of a mild La Niña episode, which began in December 2012 and ended in March 2014. Finally, Figure 4 (6) also depicts mild episodes of El Niño.
3. PRESENCE AND EFFECT OF CO 2 AND CH 4 IN THE ATMOSPHERE
The gases that contribute the most to Climate Change and that are regulated by the Kyoto Protocol are the following (Gechev, 2020): carbon dioxide (CO 2), methane (CH 4), Nitrous Oxide (N 2 O) and fluorinated gases (HFCs, PFC, SF 6). Water vapor is a powerful greenhouse gas but its natural origin makes it more difficult to control. Researchers such as Chiriboga et al. (2024) and Chiapponi et al. (2024) indicate that CO 2 and CH 4 are the main contributors to the global warming process. It is for this reason that their study and comparison with other types of information is crucial to understanding the climate changes that humanity face and will face in the coming years.
All living beings are based on carbon, so this chemical element constitutes the backbone of life on earth. The carbon regulates the earth’s temperature, contributes to generating food and provides energy (Murawska & Gorynska-Goldmann, 2023). During the day, thanks to sunlight and the process of photosynthesis plants capture atmospheric CO 2 and transform it into the carbohydrates (Asturias-Schaub & Gil-Alana, 2023). They use these carbohydrates to grow and release oxygen at the same time. The process reverses at night capturing oxygen and releasing CO 2 (Omotoso & Omotayo, 2023). It can be said that plants act as carbon stores and are often called carbon sinks.
On the other hand, methane CH 4 is a colorless, odorless natural gas that is produced primarily by the decomposition or digestion of organic matter. Methane is responsible for about 30% of global warming seeing preindustrial times and is proliferating more rapidly than at any time since records began in the 1980s (Flood et al., 2024). In fact, according to data from international agencies of oceanic and atmospheric control carbon dioxide emissions slowed during pandemic related lockdowns in 2020 while atmospheric methane soared (Mannisenaho et al., 2023).
3.1 Carbon Dioxide CO 2
Carbon Dioxide CO 2 is a gas that has existed throughout the existence of life on this planet. This gas is produced during the decomposition processes of organic materials and the fermentation of sugars (Valencia-Molina et al., 2024). However, CO 2 is also produced by the combustion of wood, carbohydrates and fossil fuels such as coal, peat, oil and natural gas (Mominkhan et al., 2023). Whital, this gas appears from various sources such as, the soil at the time of the application of agrochemicals. The agrochemicals are popular nowadays because they alter the physical, chemical and biological characteristics of the soil to promote agricultural performance (Friedlingstein et al., 2023).
Recent analyses conclude that global CO 2 emissions amounted to around 41 billion tonnes in 2023 (Lamboll et al., 2023). This is far from the Paris climate goals. By 2023, it was estimated that around 50% of the CO 2 emitted globally was absorbed on land (e.g. plants, trees, etc.), but especially by the oceans. While the remaining 50% accumulated in the atmosphere, reached an annual average of 419 ppm (Friedlingstein et al., 2023), see Figure 5. With regard to terrestrial absorption of CO 2, it is concluded that the El Niño episode, that began in mid 2023, affected the amount of terrestrial absorption. Probably with 10.4 billion tons of CO 2, a smaller amount than that absorbed in previous years (12.3 billion tons) (Gruber & Gregor, 2023). That is, it can be considered that the influence of El Niño impacts the terrestrial and oceanic absorption of CO 2 and therefore a growth in atmospheric CO 2 levels by 2024 (Venegas et al., 2023).
3.2 Methane CH 4
Methane CH 4 is a hydrocarbon and the main component of natural gas. Methane is also a potent and abundant Greenhouse Gas (GHG) which makes it a major contributor to climate change (Moraes et al., 2024). This gas is emitted during the production and transportation of coal, natural gas and oil (Feng et al., 2023). Gas emissions also result from livestock, agricultural practices, decomposition of organic waste in municipal solid waste landfills and certain wastewater treatment systems (Borisova et al., 2023). Methane is the second most abundant Greenhouse gas after carbon dioxide CO 2 (around 14% of the total global emissions) (Alamoodi et al., 2023). Although methane is emitted into the atmosphere in smaller quantities thanCO 2, its global warming potential (e.g., the gas ability to trap heat in the atmosphere) is 25 times greater (Nisbet et al., 2023), see Figure 5. Consequently, methane emissions currently contribute more than a third of current anthropogenic warming (Rocher-Ros et al., 2023).
On the other hand, it could be considered that the information from methane measurements could constitute a problem. Because measurements agone 1980 are considered when carrying out the modelling task with neural networks. However, it is unavoidable to consider two factors, 1) That the NOAA carries out formal CH4 measurements from the time of the 80s of the last centuries (CarbonTracker CH4 Program) (Mannisenaho et al., 2023). And 2) that the authors consider that the information to be entered into the Neural Network allows modelling of the most recent effects of the phenomenon. While it is true, the more information available, the modelling through the Neural Network is closer to reality, but in this work we do not seek. For instance, to model the effect that CH 4 exclusively produced by wetlands had in the past and compare it with the present, but rather to study the effect that CH 4 and CO 2 can have on the detection of an ENSO event.
3.3 Correlation Analysis BetweenCO 2 andCH 4 and Temperature Anomaly
The relationship between ENSO Sea Surface Temperature Anomalies (SSTAs) and CO 2 has already been proven by several studies (Chylek et al., 2018; Petch et al., 2024). Moreover, beyond SSTA variation is related to ENSO events, it can be said that CO 2 emissions are related to the occurrence of ENSO events (Petch et al., 2024). Precisely for this reason, Earth System Models (ESMs) already exist that can represent this relationship; however, there is little consensus regarding the processes underlying this relationship. For example, correctly reproducing atmospheric CO 2 variability in SSTA forced assimilation series does not necessarily indicate a good representation of atmospheric circulation patterns and biogeochemistry. We attribute this high uncertainty in the ENSO-NBP relationship to our limited understanding of the sensitivity of terrestrial carbon fluxes to climate (Dunkl et al., 2025; Zhang et al., 2025). This can be resolved by considering that instead of adjusting the ESM with local observations of carbon flux data, large scale patterns induced by ENSO are used. On the other hand, we cannot ignore that CH 4 is a more potent greenhouse gas than CO 2 in the short term but with a shorter atmospheric lifetime. In Zhu et al. (2025), it is highlighted that the ENSO phenomenon influences CH 4 emission anomalies in wetlands. Specifically, ENSO events suppressed CH 4 emission anomalies, while LNSO events intensified them (Lin et al., 2024). Considering the above, it can be said that there is a relationship between both events, and in this case the causality would be doubly related, with an effect of ENSO on CH 4 and of CH 4 on ENSO because it is a greenhouse gas.
Currently, there are several methodologies that can be used to analyze and roughly predict an ENSO event, using models from the European Centre for Medium Range Weather Forecasts (ECMWF) (Pinheiro et al., 2022) and new technologies such as neural networks (Jiménez-Carrión et al., 2018). From January 1, 2023, the representation of ENSO trend is based on the ECMWF’s fifth generation reanalysis (ERA5) for global climate and weather, using eight decades of historical information (Pinheiro et al., 2022). The reanalysis combines model data with global observations and physical models. This paper does not aim to conduct an in depth study of the operation of atmospheric models for prediction, but rather the use of variables in addition to the ENSO event for prediction. However, in general terms, it can be said that ECMWF models base their operation on the use of complex climate models that consider the physics and chemistry of the atmosphere and ocean to understand and predict El Niño (Zuo et al., 2019). The above procedure is called data assimilation, and is currently the method used by numerical weather prediction centers, where every certain number of hours (12 hours at ECMWF) a previous forecast is combined with newly available observations. The regions from which data are taken for the analysis of an ENSO event are four and are located over the Equatorial Pacific Ocean as follows: Niño 1 + 2 (0 ° -10 ° S, 80 ° -90 ° W), Niño 3 (5 ° N-5 ° S, 90 ° W-150 ° W), Niño 3.4 (5 ° N-5 ° S, 120 ° W-170 ° W), Niño 4 (5 ° N-5 ° S, 160 ° E- 150 ° W) (Dunkl et al., 2025). On the other hand, there are works that show the use of neural networks. Commonly, in this approach the application of 5 stages is proposed as a methodology: 1) data collection, 2) preliminary data processing, 3) Neural Network modelling, 4) code development and 5) stability analysis of artificial neural networks (ANN’s). In JiménezCarrión et al. (2018), it is mentioned that the data for modelling and predicting the ENSO event comes from the monthly record of sea surface temperatures (°C) of the Niño 1+2, Niño 3, Niño 4 and Niño 3.4 zones, the trade wind speed (m/s) in the Peruvian area and the information corresponding to the precipitation (mm) obtained at the Miraflores meteorological station located on the university campus of the National University of Piura in Peru. In both cases, both with the ECMWF modelling and with the use of new technologies such as neural networks, it is seen that the adequate management of historical information is extremely useful when proposing a methodology for analyzing an ENSO event. To begin the analysis, we must consider that the most rapid fluctuations in temperature and humidity appear in the pleposphere, also known as the Planetary Boundary Layer (PBL). That is, greenhouse gases are mainly mixed in the boundary layer, which will later appear with a certain concentration at ground level. Considering the above, it is important to analyze to what extent changes in temperature and humidity will affect the concentration of greenhouse gases at ground level.
On the contrary, it is also important to remember that in an El Niño episode, there is a general increase in sea surface temperature in much of the Eastern and Central sector of the Equatorial Pacific. This results in a decrease in atmospheric pressure in the Eastern South Pacific (coast of South America) and their corresponding increase in the Oceania region.
Consequently, it is significant to establish the relationship that may exist between the El Niño episode and the concentration of CO 2 and CH 4 in the atmosphere. In Figure 5, we can see the behavior of the temperature anomaly, CO 2 and CH 4 together on the same graph.
Figure 5 was constructed based on data from the NOAA databases to CO 2 (https://gml.noaa.gov/ccgg/trends/data.html), CH 4 (https://gml.noaa.gov/ccgg/trends_ch4/) and SSTA
(https://origin.cpc.ncep.noaa.gov/products/analysis_monitoring/ ensostuff/detrend.nino34.ascii.txt). Over and above that, Figure 5 shows the analysis graphically. In this way we highlight the importance of studying greenhouse gases, especially due to their increasing tendency.
The correlation analysis between the monthly historical information of temperature anomaly, carbon dioxide and methane, is shown in Table 2.
While the correlation between CH4 and CO2 is high (0.947), but the correlation values with the temperature anomaly are low (-0.092 and -0.096). This is explained considering that CH 4 is related to both the generation of ocean warming, as well as, warming, is related to the generation of a greater volume of CH 4. That is, there is a double relationship between ocean warming andCH 4. In the first case, it is evident thatCH 4 is a greenhouse gas, so its relationship with global warming is clear. In the second case, the increase in temperature is also related to the generation of CH 4 through methanogenesis. Which consists of the decomposition of organic matter in the absence of oxygen (anaerobic conditions produced by microorganisms called methanogenic archaea) and produces CH 4 as a by product. Given the foregoing, the authors did not perform additional statistical significance tests to determine whether these correlations obtained are really useful for the model. However, special care was taken when considering the neural networks to be used. Since it has been proven in other works that they allow obtaining an adequate forecast independently of the seasonality and stationarity that the data may have.
From the brief analysis presented above, the following observations emerge: Firstly, in Figure 5 a drastic variation of methane in the atmosphere between 1980 and 2006 is shown. This can be understood considering that while CO 2 remains in the atmosphere for hundreds or thousands of years,CH 4 only takes about a decade to decompose (Alves et al., 2021). Secondly, from Figure 5 and Table 2 it can be seen that there is a clear relationship (Correlation coefficient of 0.947) between the concentration of CO 2 and CH 4. Nevertheless, a possible relationship between the temperature anomaly resulting from an El Niño episode and the GHG is not very clear. Now we propose the application of a statistical analysis to study in depth whether or not the previous relationship exists. The analysis technique that is proposed in this work is based on the use of neural networks.
4. EXPERIMENTATION
To implement the research tasks proposed, the NOAA databases have been used to collect information on CO 2 (https://gml.noaa.gov/ccgg/trends/data.html), CH 4 (https://gml.noaa.gov/ccgg/trends_ch4/) and SSTA (https://origin.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/detrend.nino34.ascii.txt). The measurement of CO 2 and CH 4 involves the use of various instruments and techniques, mainly Non Dispersive Infrared Spectroscopy (NDIR) and Gas Chromatography (NOAA_A, 2024), (NOAA_B, 2024). While the surface temperature record is carried out with marine sensors installed in buoys at the Niño 1 + 2, Niño 3, Niño 3.4, Niño 4 regions (NOAA_C, 2024).
Data normalization was not performed because the authors have previously published other works considering temperature anomalies with neural networks. These studies have shown that the network training algorithm is sufficiently efficient to find the optimal weights for learning the networks. These trials were successful without requiring a rescaling of the input vector. Moreover, special care was taken when considering the neural networks used in this work, as previous studies by the authors have shown that they provide an adequate forecast regardless of the seasonality and stationarity that the data may have. However, a review of possible artifacts or noise in the network was carried out to avoid any errors during the Neural Network training phase.
The use of LSTM and Convolutional Encoder Decoder models has been resorted to, because they have been widely used by the authors. The fields of application were focused on the treatment and analysis of environmental information, Telecommunications, as well as for pattern recognition for the detection of fraudulent information or the analysis of economic information (Llugsi et al., 2021, 2022).
4.1 Long Short Term Memory (LSTM)
The Long Short Term Memory (LSTM) Neural Network is a type of Recurrent Neural Network (RNN) widely used for the treatment of Time Series with historical information (Canar et al., 2020). The Long Short Term Memory (LSTM) network allows to solve the gradient fading problem. This is related to the calculation of the division for zero in the own derivation that is carried out when executing the Backpropagation algorithm (Llugsi et al., 2020). This problem leads to the inability to archive long term memory when dealing with extensive historical series. Considering the above, LSTM networks allow Recurrent neural networks to be scaled to long term Time Series and capture long term trends. In their basic (vanilla) form, the LSTM model consists of a cell and three doors called input, output, and forget (Llugsi et al., 2022). In general, it can be said that the memory block is made up of the cell, which records and remembers the values of each of the gates. While, the gates regulate the transmission of information associated with the cell.
4.2 LSTM Multilayer
A deep hierarchical model allows more abstractions to be represented and therefore define a more reliable model. The deeper version of LSTM is called Stacked LSTM. This type of LSTM architecture involves stacking multiple layers that allow for a more realistic representation of time series data. In the Stacked LSTM architecture, the layer where data is processed in L(n) is fed with inputs from the previous LSTM layer L(n−1). The precision and reliability of the Stacked LSTM model leads to the use of a smaller number of neurons in each layer because it also makes use of the information from the previous layer, which consequently reduces training time (Kreuzer et al., 2020). Considering that N is the total number of LSTM layers used in a Stacked LSTM model, it can be said that the activation of an intermediate LSTM layer n with N ≥ n has the form of the matrix a n =σ(ω n a n−1 +b n ) (Li et al., 2019). Being ω n the weight matrix that sums the output a n−1 of the layer n−1 above n and b n the column matrix of biases. The function σ() is usually the sigmoid function, but others can be chosen such as the hyperbolic tangent. If the intermediate quantity obtained by applying the sum is called z n =ω n a n−1 +b n then the activation of the last LSTM layer N is a N = σ(z N ). Therefore the sum in the neuron i of the LSTM layer n is equal to z N i = ∑ω ij N a N j −1+ b N i . Being z N i the averaged input to the activation function of the neuron i at the LSTM layer N. Therefore, the Error Cost (Llugsi et al., 2022). Function (C) in the final LSTM layer N is
4.3 Convolutional Encoder Decoder Architecture
The Encoder Decoder architecture for Recurrent neural networks is a Neural Machine method that comprises a sequence tosequence prediction. This architecture was successfully tested in Llugsi et al. (2021) through the use of LSTM networks. We develop an Encoder Decoder architecture whose data is preinputted into two convolutional layers. That is, given the inputs x 1,x 2,...,x t−1 with x t ∈ R n (Wang et al., 2023), several convolutions can be applied independently on each of the network inputs to learn the interactions between the different components of x t (Sagheer & Kotb, 2019). The output sequence from the convolutional networks is read in its entirety and encoded with an LSTM network to a fixed length internal representation. Then an LSTM network acting as a decoder uses this internal representation to generate a new sequence that becomes the forecast. LSTM networks were used for both the encoder and decoder.
4.4 Statistical Analysis of the Series
To determine the impact that an El Niño episode will have, one can initially consider the historical series of temperature anomalies divided by complete decades from 1950 and look for similarities between them. At first glance, we can see that two temperature anomaly series look quite similar, the 1960s and the 2010s series and the 1970s and 1980s series, see Figure 6.
Nevertheless, to formally determine the similarities between the series, we utilize two types of test The Correlation Coefficient (r) and the T-Student test. The Pearson correlation coefficient is an index that measures the degree of covariation between different linearly related variables.
The Pearson correlation coefficient ranges between 0 and 1. The range of values indicates a perfect negative correlation with 1, no correlation with 0, and a perfect positive correlation with 1. Their calculation is based on the covariance and standard deviations of the variables (Olmos et al., 2019). Mainly the coefficient refers to the average of the cross products of the standardized scores of two series X and Y. By offering a quantitative metric of the relationship between two variables, the Correlation Coefficient becomes an essential tool to understand patterns and trends in Time Series (Llugsi et al., 2022).
On the other hand, the T-test quantifies the difference between the arithmetic means of the Time Series of Temperature Anomaly per decade. The p-value obtained from this test allows to quantify the probability of observing such or more extreme values assuming that the null hypothesis is true. Considering the above, a p-value greater than the 5% threshold indicates that the similarity is likely to have occurred by chance. Therefore, we do not reject the null hypothesis of equal population means. On the other hand, if the p-value is less than our threshold, then we have evidence against the null hypothesis and can conclude the similar statistical means.
Figure 6 Visual Comparison between Temperature Anomaly by decades. At the top a possible relationship between the historical records from the 1960s and the 2010s is presented. While in the lower part a possible relationship between the historical records of the 1970s and 1980s is shown.
The Correlation Coefficient (r) obtained from the series comparison is shown in Table 3.
From this statistical analysis, we can conclude that the series from the 1970’s and 1980’s are related because they have a correlation coefficient of 0.654 and a p-value of 0.020. This does not occur when we analyze the 1960’s and 2010’s series. In this case, the correlation coefficient is 0.513 and the p-value is equal to 0.114. Although it is true, the correlation coefficient is relatively high, however, the p-value exceeds 5%, which confirms the null hypothesis.
Although Table 3 suggests similarities between some decades (e.g., 1970-1980 with r = 0.654), certain decades tend to be more similar to each other, and this serves as the basis for NOAA’s ENSO forecasting methodology. It is important to note that this part of the paper does not attempt to perform an in depth analysis of the NOAA methodology, modify it, and detect ENSO events based on decadal analysis. What the authors propose is an analysis based on modified ENSO detection thresholds. Therefore, no further statistical analysis of the decadal data is presented, including, for example, p-values to complement the correlation information. Thus, p-values should be included to validate whether the correlations are statistically significant. The discussion on why certain decades appear more similar to each other and how this could be used in ENSO forecasting could be improved.
The analysis by decades appears to be interesting, however there is no formal relationship that can give us a concrete clue about the behavior of an El Niño episode. To boot, we must state that this initial relationship of decades does not contribute to determining a possible relationship with GHG. This occurs because methane has begun to be measured back in 1980. This is why we propose the use of neural networks to implement a temperature anomaly forecast based on the relationship between anomaly temperature and GHG.
4.5 Walk Forward Validation
In this research, we employ the Walk Forward technique (Ladyzynski et al., 2018) to manage the prediction approach. This technique involves the utilization of a shifting moving window that is applied over a variable size subset of the training set to execute the optimization in the forecast. This approach allowed to obtain an out of sample prediction extend and to improve the basic approach of dividing the available data in training and validation/testing sets (Hyndman & Athanasopoulos, 2018).
Where: TW: Testing Window.
t W L i : Window length for test per iteration.
4.6 Analysis with Neural Networks
First of all, so that the CO 2 and CH 4 series can contribute to the statistical analysis with neural networks, they have been differentiated so that the series do not have stationarity problems. Then the data entered in the neural networks was configured with the following parameters: data distribution for training, validation and testing is 70%, 15%, 15%, respectively. Epoch and Batch size were 50 and 6, respectively. We determine these values experimentally. The LSTM model uses a Vanilla LSTM with 50 neurons while the LSTM stacked model (Multilayer) uses a structure of 75-75 neurons. Finally, the Convolutional Encoder Decoder model works with a 64 filter at the convolutional layers and 50 neurons at the layer LSTM. To bring about a proper optimization at the neural networks, we adopted the ADAM Optimizer with α = 0.001,β −1 = 0.9,β −2 = 0.999 y ε = 1×10−8 and the Dropout regularization P i was 0.25 (Llugsi et al., 2021). The hyperparameters of the neural networks used have been experimentally modified until finding the optimal result (number of nodes per layer, number of layers used in the neural networks, batch size and number of epochs).
Three stages were proposed for the experimentation. In the first stage, only the water surface temperature anomaly time series was utilized. We entered this historical information into the three models proposed. From the analysis, the predicted series that most closely resembles the real series is the one obtained with the Convolutional Encoder Decoder model. To graphically and statistically confirm this result, the boxplot of the experiment with the result of the series obtained is presented in Figure 7. We can also see that the median of the boxes (horizontal bar in the center of the box) shows that the error tends to the upper quartile of the data in almost all cases.
Looking at whisker graph, the correlation coefficient and the error metrics, it appears that the Convolutional Encoder Decoder model offers unique advantages over the other models.
Reviewing Figure 7, we can observe that neural networks tend to more easily detect ENSO events related to a 0.5°C variation. This corresponds to what was reviewed in Figure 3, where the relationship between the aforementioned threshold and the onset of an El Niño event was more clearly defined. However, it is evident that there is difficulty for the networks to predict a La Niña event. This can occur in a weak type of event where, despite the ocean surface temperature still being colder than average, the climatic effects of a La Niña event on a global level are less intense than in a strong event. This could be considered a slight advantage of the Convolutional Encoder Decoder model. In view of the fact that it presents a tendency more oriented towards the detection of La Niña event.
In the second stage, we utilize the historical information of Temperature Anomaly syne 1980. We are compelled to assert that at a global level there is only historical information onCH 4 from 1980 onwards, which limits the effectiveness of working with neural networks.
From the analysis, the predicted series from the Convolutional Encoder Decoder model appears a quite good alternative to forecast the temperature anomaly of the ocean. Despite the apparent good degree of correlation, the predicted series shows error metrics of MSE = 0.269, RMSE = 0.518, MAE = 0.415. Consequently, the Convolutional Encoder Decoder model looks like a not precise alternative to forecast the temperature anomaly. This happens because the temperature anomaly has been truncated from the 1980’s. In the third stage, we use the historical information of CO 2 and CH 4 to study the effect that said information can have on the forecast with the Convolutional Encoder Decoder model. This is where the limitation appears in the experimentation, for the reason that it is essential to argue that at a global level there is only historical information on CH 4 from 1980 onwards, which limits the effectiveness of working with neural networks. The Forecast Series Comparative and the Forecast Analysis for the second stage of the experiments appears in Table 4.
At this point, it is worth mentioning that the authors have considered neural networks with which they already have prior experience, and whose benefits have been proven both in terms of obtaining forecasts and in terms of resource consumption. Regarding computational resources, it has been verified (Llugsi et al., 2022) that the networks proposed can be implemented on a Raspberry Pi, and in this environment, they have proven to be fast (Llugsi et al., 2021).
Additionally, as it can be seen in Table 4, the predicted series from the Convolutional Encoder Decoder model appears a quite good alternative to forecast the temperature anomaly of the ocean. Aforementioned, the statistical analysis offered by Neural Networks is very useful when performing statistical post processing in a prediction chain. The high correlation (0.996) obtained in the Convolutional Encoder Decoder model indicates that statistical post processing is ideal for correcting the output of the Physical Model used to predict an ENSO event. Nevertheless, as seen in Table 4, the predicted series from the Convolutional Encoder Decoder model shows the highest error metrics from all the stages of the experiment (MSE = 1.095, RMSE = 1.046, MAE = 0.962).
5. CONCLUSIONS
This work corroborates the findings made by Chylek et al. (2018), Petch et al. (2024) and Zhu et al. (2025). That is, it is proven the existence of a relationship between ENSO Sea Surface Temperature Anomalies (SSTAs) and CO 2 (Chylek et al., 2018; Petch et al., 2024), and the influence of an ENSO event on CH 4 emission anomalies in wetlands presented in Zhu et al. (2025). This work shows a very promising methodology to bring off the statistical post processing stage of a Forecast Chain. Consequently, this approach is interesting to implement the early detection of an El Niño and La Niña episodes. This methodology has been generated based on statistical thresholds and the use of neural networks. In the case of La Niña events, an early detection threshold of -0.2°C helps to define a clear trend. Namely, they help to determine a high probability of the appearance of a complete La Niña event. In the case of the El Niño event, we can conclude that with an early detection threshold of 0.5°C, we can define a clear trend of the episode appearance. In both cases, the event has a high probability of occurrence regardless of the period recommended by NOAA of five consecutive seasons.
We exploit the benefits of three Neural Network models and we analyze the correlation between the obtained series and the real one as well as the respective error metrics. The outcome shows that a Convolutional Encoder Decoder model is the most suitable structure to carry through this purpose. This methodology shows a correlation coefficient of 0.996 and error metrics of MSE = 1.095, RMSE = 1.046, MAE = 0.962. The limitation of the work is based on the lack of official information on CH 4 from NOAA, nevertheless it can be said that the results are quite promising. Since they allow to verify the findings made in Chylek et al. (2018); Petch et al. (2024) and Zhu et al. (2025).
As future work, it is proposed to investigate more complex statistical models. We can relate neural networks taking into account the effect that CH 4 has on the generation of tropospheric Ozone. The authors propose this based on that the methane is also a key precursor to the formation of tropospheric ozone (ozone in the lowest layer of the atmosphere), which is a harmful pollutant for health and the environment.
