Determination of a New Coastal ENSO Oceanic Index for Northern Peru

: In 2017, extreme rainfall events occurred in the northern portion of Peru, causing nearly 100,000 victims, according to the National Emergency Operations Center (COEN). This climatic event was attributed to the occurrence of the El Niño Southern Oscillation (ENSO). Therefore, the main objective of this study was to determine and differentiate between the occurrence of canonical ENSO, with a new type of ENSO called “El Niño Costero” ( Coastal El Niño ). The polynomial equation method was used to analyze the data from the different types of existing ocean indices to determine the occurrence of ENSO. It was observed that the anomalies of sea surface temperature (SST) 2.5 ◦ C (January 2016) generated the “Modoki El Niño” and that the anomaly of SST − 0.3 ◦ C (January 2017) generated the “Modoki La Niña”; this sequential generation generated El Niño Costero. This new knowledge about the sui generis origin of El Niño Costero, based on the observations of this analysis, will allow us to identify and obtain important information regarding the occurrence of this event. A new oceanic index called the Paciﬁc Regional Equatorial Index (PREI) was proposed to follow the periodic evolution and forecast with greater precision a new catastrophic event related to the occurrence of El Niño Costero and to implement prevention programs.


Introduction
Globally, El Niño Southern Oscillation (ENSO) events are one of the most important sources of annual climate variability. These phenomena involve large-scale interactions between the oceans and the atmosphere, which consist of an oscillation of atmospheric pressure in the western Pacific [1]. The relationship or coupling between these variables involves great climatic consequences in many parts of the planet [2]. The occurrence of ENSO in the tropical Pacific causes a variation on the oceanic-atmospheric systems in both the North Pacific and the North Atlantic [3]. Without going any further, ENSO is considered the most powerful signal in terms of the interannual variation of the oceanic-atmospheric system [4].
Records indicate that the occurrence of ENSO in South America has shown statistically significant evidence since 1750. However, from the 18th century onwards the chronology of ENSO and anti-ENSO events have occurred with similar chronologies in the literature [5]. Evidence of the widespread impact of ENSO-related events is associated with variables such as (1) sea surface temperatures (exceeding 28 • C); (2) increased rainfall amounts in the central Pacific region; and (3) storm surge in subtropical North and South America. ENSO events, on the other hand, are also associated with droughts in many parts of the world [6,7].
Recent studies focusing on ENSO have shown that changes in the thermocline's depth (i.e., transition layer between warmer water at ocean surface and cooler water deeper down) are the main cause of sea surface temperature (SST) variations, in the time scale and, consequently, the generation of ENSO events [8]. Models made between ocean and reduced deep convection (i.e., less precipitation) in the western tropical Pacific during spring summer reducing wind surface [18].
Coexisting SST anomalies in the equatorial Pacific (and presumably also in the Tropical Atlantic) clearly favored the development of the extreme "coastal El Niño" event and highmagnitude rainfall over Peru in DJFM 2016-2017. The approach and interpretation within a climatic context, shows that the DJFM 2016-2017 rainfall pattern in Peru was highly anomalous, both in terms of its magnitude and the time after a strong El Niño event, which in turn was largely the result of abrupt and unexpected warming above average in the Niño 1 + 2 region. This warming was linked to an anomalous weakening of the western mid-upper level subtropical flow, which in turn led to a weakening of the southeast winds off the coast favoring the warming of the eastern Pacific [19]. This flow is a key ingredient in the subtropical circulation of the SE Pacific, because its blockage by the subtropical Andes leads to a decrease in the flow towards the Equator [18].
A reduction in deep convection in the western central Pacific and zonal air humidity flow in the tropical troposphere may have shifted the ITCZ southward, increasing precipitation along the Andes of northern Peru [15,20]. The Eastern Tropical Pacific also experienced rapid and marked warming in early 2017, causing torrential rains along the west coast of South America with significant social cost in Peru and Ecuador. This strong coastal El Niño was largely unpredictable even a few weeks before its onset, and developed differently than the central or eastern events with a sustained and forced weakening of the western tropospheric free flow impinging on the subtropical Andes driving to a relaxation of the southeast (SE) wind off the coast, which in turn may have warmed the eastern Pacific [20].
A transformation of the El Niño teleconnections has occurred due to climate change and the effect it may have had in the extremely dry conditions during 2015/16 than during 1982/83 and 1997/98. Such a transformation could arise from changes in the atmospheric circulation of forced tropical wave trajectories [21], or from changes in the intensity and length of rainfall from the equatorial Pacific during El Niño events [22].
The occurrence of a coastal ENSO is not common; for example, previous similar event occurred in 1925, that is, it occurred after 92 years and it is stated that its internal dynamics coupled with the ITCZ region was largely the cause for the coastal El Niño of 1925 in the absence of significant external atmospheric forcing [20].
Ocean and atmospheric modeling experiments show that the combined effect of local winds and equatorial Kelvin waves caused the extreme coastal El Niño of 2017, amplified by a positive feedback from Bjerknes that is very important to the extreme coastal ENSO of 2017. Additionally, pre-existing SST warming along the west coast of subtropical South America also favored anomalous north winds. These wind anomalies were favorable for the warming of the coasts south of the equator through weakened upwelling and windevaporation-SST (WES) feedback, setting the stage for the dramatic growth of the extreme coastal ENSO. Furthermore, extreme coastal ENSO frequency changes are independent of future basin-scale changes [23].
After the occurrence of ENSO 2015/2016, the surface of the eastern Pacific Ocean remained ∼0.5 • C warmer than average, experiencing an additional 1.5 • C warming in a series of one-week episodes of duration in the months of January, February and March 2017, which caused torrential rains along the west coast of South America. The behavior of the ocean-atmosphere system during this event differs substantially from the canonical dynamics of ENSO, and a dominant condition of external atmospheric forcing prevails, as well as a sustained and forced weakening of the western tropospheric flow that affects the subtropical Andes, leading to a relaxation of southeast (SE) winds off the coast, which in turn may have warmed the eastern Pacific along weakening outcrops in a near-shore band and decreasing evaporative cooling further offshore [24].
For this reason, this investigation seeks to understand the coastal ENSO and its effects, since there is currently no precise information on the cause that generates it, as well as the interaction with other similar meteorological phenomena that enhance its effects. Knowledge of the occurrence of coastal ENSO would be of great importance for turn may have warmed the eastern Pacific along weakening outcrops in a near-shore ban and decreasing evaporative cooling further offshore [24].
For this reason, this investigation seeks to understand the coastal ENSO and its ef fects, since there is currently no precise information on the cause that generates it, as we as the interaction with other similar meteorological phenomena that enhance its effects Knowledge of the occurrence of coastal ENSO would be of great importance for the pre vention, planning, and management of agriculture, water resources, and natural disasters Thus, the objective of this study is to determine the occurrence of ENSO, but as a variatio defined as "2017 Coastal ENSO". Therefore, our focus was mainly to analyze the differen types of oceanic indices to determine the occurrence of coastal ENSO.

Study Area
The study area corresponds to the north-west territorial portion of Peru, where th coastal ENSO occurred during the months of January, February, and March of 2017 (Fig  ure 1). During these months, the strong warming that developed in the Eastern Tropica Pacific Ocean (abnormal warmth) produced unusually intense rain storms in the area compared to the 1997-1998 and 1982-1983 ENSO events [25].

Methodology
For the development of this study, the oceanic indices that define the occurrence o ENSO have been taken into consideration. Data from different indices correspond to th years 2016 and 2017 (January, February, and March) (Appendix A; Tables A1, A2 and A3

Methodology
For the development of this study, the oceanic indices that define the occurrence of ENSO have been taken into consideration. Data from different indices correspond to the years 2016 and 2017 (January, February, and March) (Appendix A; Tables A1-A3), in order to determine which of these indices is the most appropriate to define the occurrence of the coastal ENSO. It is likewise with the implications of the ITCZ in the generation of rainfall. In Figure 2 a diagram of the methodological procedure is show. in order to determine which of these indices is the most appropriate to define the occurrence of the coastal ENSO. It is likewise with the implications of the ITCZ in the generation of rainfall. In Figure 2 a diagram of the methodological procedure is show. Figure 2. Diagram of the methodological process.

ENSO Data and Index Analysis
For the ENSO 2017 analysis, data from the ENSO's regional indices have been used, which is a standardized measure where the Equatorial Pacific is divided into regions, from which the presence of El Niño or La Niña is deduced. To analyze the behavior of the different types of ENSO index, polynomial equations have been used. The polynomial equation can be expressed in Equation (1): where: -, −1 , and 0 are real coefficients (numbers).
The exponent n is a positive integer that represents the degree of the equation. - x is the unknown variable to be found.
To determine the goodness of fit of each model, the coefficient of determination (R²) was used, which ranges from 0 to 1. The closer its value is to 1, the greater the fit of the model to the variable that is being explained. Conversely, the closer to zero, the less tight (unreliable) the model will be. For the particular case of this investigation, seven indexes were used, corresponding to the years 2016 and 2017 (years in which the ENSO Modoki and the La Niña (LNSO) Modoki were presented: The Modoki ENSO Index, the Trans Niño Index, the Oceanic Niño Index, the Coastal Index (1+2), the Southern Oscillation Index, and the Pacific Equatorial Regional Index. In the case of the Pacific Decadal Oscillation (PDO) index, this has been evaluated from 1976 to 2019 (without calculating any equation) to determine its correspondence with the occurrence of Niño Modoki.

Modoki ENSO Index (MEI)
There have been ENSO events that are not part of the evolution of El Niño, which involve ocean-atmosphere coupled processes that during their evolution present a unique pattern of tripolar pressure at sea level, analogous to the Southern Oscillation in the case of El Niño. Therefore, the total event is called "Modoki ENSO", whose presence significantly influences SST and precipitation in many parts of the world

ENSO Data and Index Analysis
For the ENSO 2017 analysis, data from the ENSO's regional indices have been used, which is a standardized measure where the Equatorial Pacific is divided into regions, from which the presence of El Niño or La Niña is deduced. To analyze the behavior of the different types of ENSO index, polynomial equations have been used. The polynomial equation can be expressed in Equation (1): f (x) = a n x n + a n−1 x n−1 + . . . where: a n , a n−1 , and a 0 are real coefficients (numbers). -a n is different than zero. - The exponent n is a positive integer that represents the degree of the equation. - x is the unknown variable to be found.
To determine the goodness of fit of each model, the coefficient of determination (R 2 ) was used, which ranges from 0 to 1. The closer its value is to 1, the greater the fit of the model to the variable that is being explained. Conversely, the closer to zero, the less tight (unreliable) the model will be. For the particular case of this investigation, seven indexes were used, corresponding to the years 2016 and 2017 (years in which the ENSO Modoki and the La Niña (LNSO) Modoki were presented: The Modoki ENSO Index, the Trans Niño Index, the Oceanic Niño Index, the Coastal Index (1 + 2), the Southern Oscillation Index, and the Pacific Equatorial Regional Index. In the case of the Pacific Decadal Oscillation (PDO) index, this has been evaluated from 1976 to 2019 (without calculating any equation) to determine its correspondence with the occurrence of Niño Modoki.

Modoki ENSO Index (MEI)
There have been ENSO events that are not part of the evolution of El Niño, which involve ocean-atmosphere coupled processes that during their evolution present a unique pattern of tripolar pressure at sea level, analogous to the Southern Oscillation in the case of El Niño. Therefore, the total event is called "Modoki ENSO", whose presence significantly influences SST and precipitation in many parts of the world The TNI index is the one that best represents the occurrence of coastal ENSO. The data used are available at: www.esrl.noaa.gov/psd/data/climateindices/List/#TNI (accessed on 21 July 2019). The TNI index measures the gradient of SST anomalies between the Central and Eastern Equatorial Pacific. When the SST gradient is particularly large (for example, positive anomalies in the ENSO 4 Region and negative anomalies in the ENSO 1 + 2 Regions).

Oceanic Niño Index (ONI)
The Oceanic Niño Index (ONI) is the standard that the National Oceanic and Atmospheric Administration (NOAA) uses to identify warm (El Niño) and cold (La Niña) events in the Tropical Pacific Ocean. The ONI Index uses the same region as the Niño 3.4 Index. El Niño 3.4 is negatively correlated with the Southern Oscillation Index (SOI) detailed further down, that is, when the mean SST in the Pacific is high, the SOI is generally low. The data from the ONI Index have been used to determine its correlation with the presence of coastal ENSO. The ONI data are available at: https://www.esrl.noaa.gov/psd/gcos_ wgsp/Timeseries/Data/nino34.long.data (accessed on 21 July 2019).
ONI index values are normalized according to a statistical series for a single fixed base period of 30 years. There will be multiple-centered 30-year base periods that will be used to define the ocean index (as a deviation from the average or "anomaly"). The NOAA considers El Niño conditions to be present when the ONI index is +0.5 or higher, indicating warmer than normal. When the ONI index is −0.5 or lower, it indicates that the region is colder than normal and suggests the occurrence of La Niña. The methodology for the reconstruction of the SST is described in [26].

Coastal Index (CI)
The location of this index is in the northwestern part of Peru. The data used are available at: https://www.esrl.noaa.gov/psd/gcos_wgsp/Timeseries/Data/nino12.long. Data from the SOI have been used to determine its correlation with the presence of coastal ENSO. SOI data are available at: https://www.cpc.ncep.noaa.gov/data/indices/soi (accessed on 22 July 2019). The SOI or barometric difference is a standardization based on the differences in sea level pressure observed between Tahiti and Darwin (places in the southeast Pacific such as Easter Island, Darwin in Australia, or Jakarta in Indonesia). Its calculation can be performed using Equation (3).

Pacific Regional Equatorial Index (PREI)
The oceanic indices developed and currently used do not define the presence of a coastal ENSO. For this reason, the creation of another index called the Pacific Regional Equatorial Index (PREI) has been proposed in this study, using the set of data from the ENSO Regions 4, 3.4, 3 and 1+2, whose standardization will allow to define or interpret Coastal ENSO in an optimal way. The data are available at: https://www.esrl.noaa.gov/ psd/gcos_wgsp/Timeseries/Data (accessed on 22 July 2019).

Data and Analysis of the Inter-Tropical Convergence Zone (ITCZ)
The ITCZ was another of the factor that caused the extreme rains in northern Peru in 2017. The ITCZ is a band or convective band of low pressures that is not uniform or continuous located in the equatorial zone that ranges approximately between 5 • S and 12 • N during July-November, and 5 • N-5 • S during January to May. It is influenced by the trade winds from the southeast and northeast due to high temperatures; air masses are forced to rise causing abundant cloudiness and heavy rainfall, some accompanied by electrical discharges. Its thickness varies from one site to another, as does its behavior in maritime and continental areas [30,31].
Likewise, satellite images from the Weather Channel (WC) have been used to carry out a qualitative analysis and for comparison to determine the displacement of cloud masses from the ITCZ to the South American continent. The strong convective activity in the ITCZ led to the formation of cloud systems of great vertical development, causing intense rains to the interior of the Ecuadorian and Peruvian coasts [32]. Satellite images were taken for the month of March, the month in which the highest rainfall occurred. In these images, the evolution and displacement of cloud masses were observed, allowing an indirect estimate of rainfall. Images can be obtained from the link: https://weather.com/maps/satellite/ southamerica-weather-map (accessed on 22 July 2019).

Polynomial Equations and Correlation Coefficients of Each Index
Polynomial equations and R 2 values from data analysis for each index are shown in Table 1. The coefficient of determination, denoted R 2 reflects the goodness of fit of a model to the variable to be explained. Table 2 shows pros and cons of the different oceanic indices treated in the present study. The PREI and ONI indexes were those with best fits, being the SOI index the least.

Index
Polynomial Equation It is a sequential period representing regions 4, 3.4, 3 and 1 + 2 The value of the coefficient of determination R 2 = 0.99 obtained in the case of the PREI index is the result of using the polynomial equation of the order "2" and the value of R 2 = 0.99 indicates that the model fits the data, that is, the differences between the observed values and the calculated values are small and not biased. This reflects the quality and goodness of fit of the model. In the next sections, a detailed analysis of each index is provided.
The data used correspond to the years 2016 and 2017, with the exception of the PREI index, which only uses the data for the month of January 2017.

Modoki ENSO Index (MEI)
In 2016 (January through March), an increase in the sea surface temperature of 0.30 • C was observed, indicating the occurrence of Modoki ENSO. Later on, sea temperatures decreased to values as low as −0.60 • C in 2017 (January through March), leading LNSO ( Figure 3). Surprisingly, this large-scale oscillation from warmer to colder SST and in the same central Equatorial zone of the Pacific Ocean clearly defines the presence of Modoki ENSO and Modoki LNSO, whose process and sequence will also serve to define the presence of coastal ENSO.
decreased to values as low as -0.60 °C in 2017 (January through March), leading LNSO ( Figure 3). Surprisingly, this large-scale oscillation from warmer to colder SST and in the same central Equatorial zone of the Pacific Ocean clearly defines the presence of Modoki ENSO and Modoki LNSO, whose process and sequence will also serve to define the presence of coastal ENSO.

Trans ENSO Index (TNI)
The results define the oscillations of the temperature anomalies quite well ( Figure 4). There was an increase in sea temperature with a positive anomaly of 1.3 °C in 2017 (January through March). This index regularly represents the occurrence of coastal ENSO.

Trans ENSO Index (TNI)
The results define the oscillations of the temperature anomalies quite well ( Figure 4). There was an increase in sea temperature with a positive anomaly of 1.3 • C in 2017 (January through March). This index regularly represents the occurrence of coastal ENSO.
decreased to values as low as -0.60 °C in 2017 (January through March), leading LNSO ( Figure 3). Surprisingly, this large-scale oscillation from warmer to colder SST and in the same central Equatorial zone of the Pacific Ocean clearly defines the presence of Modoki ENSO and Modoki LNSO, whose process and sequence will also serve to define the presence of coastal ENSO.

Trans ENSO Index (TNI)
The results define the oscillations of the temperature anomalies quite well ( Figure 4). There was an increase in sea temperature with a positive anomaly of 1.3 °C in 2017 (January through March). This index regularly represents the occurrence of coastal ENSO.  This index uses data from Region 3.4 (central Pacific zone) to define the ENSO and LNSO, and it is currently being used by NOAA. There was an increase in temperature of 2.5 °C during 2016 (January through March). In this same year (September through august), there was a decrease in temperature with an ONI value of -0.7 °C, indicating the presence of Modoki LNSO ( Figure 5). This index adequately represents the presence of Modoki ENSO.

Coastal Index (CI) (Region 1+2)
As can be seen from Figure 6, an average increase of SST of 1.5 °C and, therefore, this index does not contribute to establish the presence of coastal ENSO.

Coastal Index (CI) (Region 1+2)
As can be seen from Figure 6, an average increase of SST of 1.5 • C and, therefore, this index does not contribute to establish the presence of coastal ENSO.
LNSO, and it is currently being used by NOAA. There was an increase in temperature of 2.5 °C during 2016 (January through March). In this same year (September through august), there was a decrease in temperature with an ONI value of -0.7 °C, indicating the presence of Modoki LNSO ( Figure 5). This index adequately represents the presence of Modoki ENSO.

Coastal Index (CI) (Region 1+2)
As can be seen from Figure 6, an average increase of SST of 1.5 °C and, therefore, this index does not contribute to establish the presence of coastal ENSO.

Southern Oscillation Index (SOI)
The SOI is based on atmospheric pressure. Figure 7 illustrates data corresponding to the months of January to March (2016 and 2017). In 2016, negative values were presented, which is consistent with the presence of warm water, defining the presence of ENSO. For the year 2017 (months from January to March), it can be observed that SOI has an average value of "0", i.e., in a neutral position. Therefore, the information provided by SOI is neither useful nor recommended for determining coastal ENSO. The SOI is based on atmospheric pressure. Figure 7 illustrates data corresponding to the months of January to March (2016 and 2017). In 2016, negative values were presented, which is consistent with the presence of warm water, defining the presence of ENSO. For the year 2017 (months from January to March), it can be observed that SOI has an average value of "0", i.e., in a neutral position. Therefore, the information provided by SOI is neither useful nor recommended for determining coastal ENSO.  3.1.7. Pacific Regional Equatorial Index (PREI) Based on the analyzes carried out of the different indices that define the different types of occurrence of ENSO, an index has been defined consisting of the set of data from regions 4, 3.4, 3 and 1+2, which allows us to identify the coastal ENSO for each month and using the corresponding second degree polynomial equation. This index is the one that best represents the evolution of ENSO, in terms of the coastal ENSO. Figure 9 shows a graph of the occurrence of Modoki LNSO and coastal ENSO, during the months of January to March of 2017. In this study we only analyze the behavior of the ENSO Modoki and

Pacific Regional Equatorial Index (PREI)
Based on the analyzes carried out of the different indices that define the different types of occurrence of ENSO, an index has been defined consisting of the set of data from regions 4, 3.4, 3 and 1+2, which allows us to identify the coastal ENSO for each month and using the corresponding second degree polynomial equation. This index is the one that best represents the evolution of ENSO, in terms of the coastal ENSO. Figure 9 shows a graph of the occurrence of Modoki LNSO and coastal ENSO, during the months of January to March of 2017. In this study we only analyze the behavior of the ENSO Modoki and Niña Modoki (2016-2017) and for the months of January to March, (months where the ENSO phenomenon generally occurs); therefore, we do not intend to generalize for other periods.  (Figure 10c), it can be observed that the temperature had an increase of (28.7 °C) in region 1 + 2, also indicating the presence of coastal ENSO.
In 2017 (Figure 10), if we focus on the values of the region 1 + 2, a sequential SST increase can be observed during the months of January, February, and March (of 25.8, 27.9, and 28.7, respectively) and this elevation of the SST in zone 1 + 2 represented the occurrence of coastal ENSO in the northern zone of Peru. Using together all the indices of the Central Pacific Region, better information is obtained to define the Modoki LNSO and, therefore, determine the occurrence of coastal ENSO, the reason for this study.

Projection of TSM values (zone 1 + 2) for the months of February and March 2017
To determine the polynomial equation, the SST data (regions 4, 3.2, 3, 1 + 2) corresponding to the month of January have been used, obtaining the following equation: where: Y = SST value X = Variable considered as a period that represents the oceanic regions (4, 3.4, 3 and 1 + 2)

Projection for the month of February
Taking the observed temperature values for the month of January and considering the value of X = 5, the projection for the month of February of zone 1 + 2 is obtained. The value obtained is 27.05 °C, which would indicate the increase in SST, and compared to the observed value of 27.76 °C, there is a relative difference of −0.71 (Table 3) (Figure 11).

Projection for the month of March
Considering the value of X = 6, we have the projection for the month of March. The value obtained is 29.37 °C , the high value of which would indicate a greater increase in SST, which compared to the observed value of 28.52 °C has a difference of 0.84 °C , which would also indicate an adequate approximation and the usefulness of the equation for predictive purposes (Table 3) (Figure 12) Table 3. Observed data for the month of January and the projected value for zone 1 + 2 (months February and March).

Region
Period "X" "Y" °C Observed (January)  In 2017 (Figure 10), if we focus on the values of the region 1 + 2, a sequential SST increase can be observed during the months of January, February, and March (of 25.8, 27.9, and 28.7, respectively) and this elevation of the SST in zone 1 + 2 represented the occurrence of coastal ENSO in the northern zone of Peru. Using together all the indices of the Central Pacific Region, better information is obtained to define the Modoki LNSO and, therefore, determine the occurrence of coastal ENSO, the reason for this study.

Projection of TSM values (zone 1 + 2) for the months of February and March 2017
To determine the polynomial equation, the SST data (regions 4, 3.2, 3, 1 + 2) corresponding to the month of January have been used, obtaining the following equation: where: Y = SST value X = Variable considered as a period that represents the oceanic regions (4, 3.4, 3 and 1 + 2)

Projection for the Month of February
Taking the observed temperature values for the month of January and considering the value of X = 5, the projection for the month of February of zone 1 + 2 is obtained. The value obtained is 27.05 • C, which would indicate the increase in SST, and compared to the observed value of 27.76 • C, there is a relative difference of −0.71 (Table 3) (Figure 11). Table 3. Observed data for the month of January and the projected value for zone 1 + 2 (months February and March).

Spatial-Temporal Distribution of the ITCZ
In addition to the effects generated by the occurrence of the coastal ENSO, there have also been additional effects from the ITCZ, an area in which convergence between the air masses of the northern and southern hemispheres has been generated. The position of the ITCZ is normally located in the equatorial zone, but it moved further to the south (border

Projection for the Month of March
Considering the value of X = 6, we have the projection for the month of March. The value obtained is 29.37 • C, the high value of which would indicate a greater increase in SST, which compared to the observed value of 28.52 • C has a difference of 0.84 • C, which would also indicate an adequate approximation and the usefulness of the equation for predictive purposes (Table 3) (Figure 12) Figure 11. Example of the sea surface temperature (SST) projection for zone 1 + 2 (Niño Costero) for the month of February.

Spatial-Temporal Distribution of the ITCZ
In addition to the effects generated by the occurrence of the coastal ENSO, there have also been additional effects from the ITCZ, an area in which convergence between the air masses of the northern and southern hemispheres has been generated. The position of the ITCZ is normally located in the equatorial zone, but it moved further to the south (border area between Brazil and Peru), generating the heavy rainfall that occurred in the country.
A qualitative observation and comparison analysis have been carried out using the images provided by the Weather Channel (WC). In these images, the displacement of cloud masses from ITCZ can be observed. The satellite images for the month of March 2017 (Figure 13a-d) show masses of clouds moving over the north of Brazil and towards the Peruvian territory (central and northern part of Peru). The analysis of these cloud bands shows a connection of a cyclonic circulation with the presence of precipitation, further increasing the precipitation generated by coastal ENSO.

Spatial-Temporal Distribution of the ITCZ
In addition to the effects generated by the occurrence of the coastal ENSO, there have also been additional effects from the ITCZ, an area in which convergence between the air masses of the northern and southern hemispheres has been generated. The position of the ITCZ is normally located in the equatorial zone, but it moved further to the south (border area between Brazil and Peru), generating the heavy rainfall that occurred in the country.
A qualitative observation and comparison analysis have been carried out using the images provided by the Weather Channel (WC). In these images, the displacement of cloud masses from ITCZ can be observed. The satellite images for the month of March 2017 (Figure 13a-d) show masses of clouds moving over the north of Brazil and towards the Peruvian territory (central and northern part of Peru). The analysis of these cloud bands shows a connection of a cyclonic circulation with the presence of precipitation, further increasing the precipitation generated by coastal ENSO.
When ENSO occurs, all equatorial convection moves to the east, changing the position of the atmospheric circulation (Walker cell), creating a descending cell over the Atlantic Ocean, and depending on the intensity there may be inhibition in the formation of clouds and consequently the deficiency of rainfall in the ITCZ region [33] In the case of coastal ENSO, there have been thermodynamic patterns or teleconnections of atmospheric circulation (high pressure areas) over the tropical region (equatorial Pacific basin towards the equatorial Atlantic basin), and in the same way the trade winds have contributed to displace the band of clouds from the ITCZ to the northeastern part of Brazil and reaching areas of Peruvian territory.
lantic Ocean, and depending on the intensity there may be inhibition in the formation of clouds and consequently the deficiency of rainfall in the ITCZ region [33] In the case of coastal ENSO, there have been thermodynamic patterns or teleconnections of atmospheric circulation (high pressure areas) over the tropical region (equatorial Pacific basin towards the equatorial Atlantic basin), and in the same way the trade winds have contributed to displace the band of clouds from the ITCZ to the northeastern part of Brazil and reaching areas of Peruvian territory. a b c d

Discussion
In the present study, two main sources that generated heavy rainfall in Peru are proposed. First, the generation of a type of ENSO called "Coastal ENSO"; and second, cloud bands generated in the ITCZ. Next, we develop the explanation and discussion about the generation process of the type of ENSO identified in northern Peru.

Types of ENSO
In recent years, other types of ENSO have been investigated and identified, such as Modoki ENSO, Modoki LNSO, and coastal events, whose occurrence is not very common and also brings different consequences. Therefore, the understanding of these different types of ENSO has a greater degree of complexity when trying to predict their occurrence and, as a consequence, government responses may be inadequate due to contradictory forecast reports and errors in decision making.

Discussion
In the present study, two main sources that generated heavy rainfall in Peru are proposed. First, the generation of a type of ENSO called "Coastal ENSO"; and second, cloud bands generated in the ITCZ. Next, we develop the explanation and discussion about the generation process of the type of ENSO identified in northern Peru.

Types of ENSO
In recent years, other types of ENSO have been investigated and identified, such as Modoki ENSO, Modoki LNSO, and coastal events, whose occurrence is not very common and also brings different consequences. Therefore, the understanding of these different types of ENSO has a greater degree of complexity when trying to predict their occurrence and, as a consequence, government responses may be inadequate due to contradictory forecast reports and errors in decision making.

Definition of Coastal ENSO
A preliminary study carried out by Ramírez [35] mentions that the definition of ENSO was a problem that generated uncertainty and affected the perception of risk and the responses were further complicated by the fact that some regions within Peru were experiencing drought prior to the onset of coastal ENSO. These authors also stated that this "surprise" event developed rapidly and without warning and had catastrophic effects in northern Peru (an ENSO that was not documented since 1925), in addition to contradictory forecast reports (USA and PERU).
Takahashi [36] proposed to classify ENSO into two types: "Global" (e.g., 1982-1983 and 1997-1998) and "Coastal" (e.g., 1925 and 2017). As can be seen, not much literature exist on the occurrence of coastal ENSO in Peru. Similarly, studies carried out by the Multisectoral Commission in charge of the National Study of the"El Niño" Phenomenon ENFEN [11], Heureux et al. [37], and Ramírez [35] proposed to distinguish coastal ENSO from the warm ENSO phase, operationally defining it as "El Niño Costero" based on the seasonal anomaly (SST) of the ENSO 1 + 2 region, the authors also mention that coastal ENSO requires a more in-depth study in terms of its mechanisms and forecast. In the present investigation, based on the analysis carried out, the authors also coincide with the name of "El Niño Costero", mainly due to its form of generation and occurrence.

2015-2016 ENSO
The extreme ENSOs that occurred in Peru are only based on the 1982-1983 and 1997-1998 events. The occurrence of the 2017 coastal ENSO, with different characteristics was preceded by the occurrence of the 2015-2016 ENSO (the first extreme El Niño of the 21st century) [23], which generated many environmental disasters and dramatic impacts on a scale that are consistent with what is expected for an extreme ENSO. However, their occurrence showed different characteristics in relation to the last episodes, confusing previous understanding of an extreme ENSO.

Oceanic Indexes
There are different types of ocean index that have the purpose of observing the occurrence of ENSO, which have not always been effective when predicting the generation of an ENSO event. Each agency examines a wide range of oceanic and atmospheric anomalies to report their updates internationally. The 3.4 ENSO Region, located in the central Equatorial zone of the Pacific Ocean, is perhaps the most common measurement of ENSO, because this region is strongly coupled with the overlying atmosphere and global teleconnections [24]. However, this ENSO 3.4 index did not allow researchers to foresee the occurrence of the 2017 event.

Analysis of the Different Ocean Indices and Creation of the PREI Index
An analysis of the different existing oceanic indices has been carried out in the present investigation, such as Modoki ENSO Index (MEI), Trans ENSO Index (TNI), Oceanic ENSO Index (ONI), Coastal 1 + 2 Index (CI), Southern Oscillation Index (SOI), and Pacific Decadal Index (PDO), in order to determine which of these indices are the most suitable for monitoring and determining the occurrence of an extreme coastal ENSO. From the results of these analyses, it has been determined that these indices do not have an effective application to specify the occurrence of a coastal ENSO such as that which occurred in 2017. For this reason, a new index called the Pacific Regional Equatorial Index (PREI) has been developed in this investigation to specifically determine a coastal ENSO.

Causes of Coastal ENSO Generation
In relation to the causes that generate a coastal ENSO, few studies have been carried out such as that by Takahashi [36], who proposed that the occurrence of coastal ENSO is due to the north winds, which has a crucial role for its development. Likewise, a study carried out by Peng [38] refers that the descending Kelvin waves caused by strong westerly winds over the Equatorial Pacific, together with the anomalous coastal winds from the north, contribute to the formation of the extreme coastal ENSO. Similarly, Peng [38] concluded that the combined effect of local winds and Equatorial Kelvin waves caused the 2017 extreme coastal ENSO. Likewise, Garreaud [18] mentions that the cause was a sustained and forced weakening of the western tropospheric flow that impinges on the subtropical Andes and leads to a relaxation of the southeastern winds off the coast, which in turn may have warmed the eastern Pacific, along the weakening of the outcrops in a near-shore band and decreased evaporative cooling farther from shore.
In this study, the authors differ with the previous explanations, since according to the analysis and results obtained, it has been determined that the occurrence of a coastal ENSO is due to a process of succession of events (Modoki ENSO and Modoki LNSO). In such a way we postulate that the Pacific Decade Oscillation (PDO) in its positive phase (Figure 8), has given rise to coupled ocean-atmosphere processes generating ENSO Modoki and La Niña MODOKI, and the coastal ENSO is a sub-process of La Niña Modoki. the 2017's Modoki LNSO-lower part (Figure 9).
Takahashi [36] studied the coastal event of 1925, suggesting a possibility that the concurrent LNSO conditions in central Pacific could be in favor of atmospheric convection off Peru, reducing atmospheric stability. In this study, the authors partially agree with this hypothesis, changing the term LNSO to Modoki LNSO, since this type of event was the one that generated the coastal ENSO. Given these assertions, we go on to explain some of the causes that generated the Modoki events.

Causes of the Generation of Modoki ENSO/Modoki LNSO
In a study carried out by Ashok [1], the authors state that the Modoki El Niño involves coupled ocean-atmosphere processes that include a unique tripolar sea pressure level pattern, analogous to the Southern Oscillation in the case of El Niño and state that the weakening of the equatorial east winds are related to the zonal weakening of the sea surface temperature gradient that leads to a greater flattening of the thermocline, and that this could be a cause of the more frequent and persistent occurrence of the ENSO Modoki event.
Similarly, Behera and Yamagata [39] mention that Modoki El Niño/Modoki La Niña have a coupled ocean-atmosphere variability in the tropical Pacific Ocean and that the SST anomalies are coupled with a double cell in the Walker anomalous circulation, with upward movement in the central parts and downward movement on both sides of the basin of the tropical Pacific Ocean. Furthermore, they consider that Modoki events are not seasonally locked into a single seasonal cycle like El Niño/La Niña events.
Likewise, Lestari et al. [40] concluded that after an extreme phenomenon of El Niño 2015-2016, a Modoki La Niña event occurred, which had a short duration and was associated with a pattern of SST anomalies in the Indo-Pacific region, with a strengthening of easterly winds in the central tropical Pacific Ocean. The cooling (warming) of SST activated the zone of divergence (convergence) and the downward (upward) atmospheric motion and suppressed (enhanced) convective process in the central tropical Pacific Ocean region.
In the present study on the generation of Modoki El Niño, we agree with the aforementioned authors regarding the explanation of the process, which is due to the oceanatmosphere coupled process that included a unique tripolar sea pressure level pattern, as well as the greater flattening of the thermocline and that do not present a seasonal cycle like canonical El Niño events.
As in the El Niño Modoki generation, the Niña Modoki involves processes of the Atmospheric Ocean in the tropical Pacific Ocean coupled to two cells of the Walker circulation and defining a tripolar pattern; that is, two upward movements (one at the end of region 4, and another in region 1+2) and one downward movement in the middle (regions 3.4 and 3) (Figure 9). This process and the temperature differences of the SST, can be observed in

Decadal Cause
Other studies carried out on the generation of Modoki El Niño explain that they are generated by PDO, such as that carried out by Weng [41], who state that SST gradients result in a two-cell Walker circulation anomalous over the tropical Pacific, with a humid region in the central Pacific and that Modoki El Niño has a large decennial bottom (PDO), while canonical El Niño is dominated by interannual variability.
Li [42] mentions that, in addition to the atmosphere-ocean coupling on intra-seasonal and inter-annual time scales, inter-decennial PDO variations and longer time scales can play an important role (and sometimes a crucial role) in determining the intensity of El Niño. Likewise, Dong [29] indicate that PDO modulations are linked to atmospheric responses and tropical SST anomalies, manifested in the local Hadley and Walker circulations in low latitudes, and the Rossby Wave Train in the extra-tropics, including the Pacific North American pattern (PNA) in the northern hemisphere.
Likewise, Diaz et al. [43] argue that, in regional climates around the world, there have been important changes on a 10-year scale in the general pattern of SST and in the general atmospheric circulation, pointing to the complex interaction between the Canonical ENSO system. Similarly, Magee [44] states that PDO can modulate the genesis of tropical cyclones (TC) during ENSO and Modoki ENSO events, in favor of northeast/southwest modulations typical of positive/negative PDO events, and that Modoki ENSO provides an important piece of the puzzle in understanding where and when the genesis of TC can occur.
In this study, we agree with the assertions mentioned by the previous authors in relation to the fact that the PDO generates the Modoki ENSO. Nevertheless, according to our analysis (from the years 1976-2018), where positive and negative phases can be observed, the longest positive phase was from 1976 to 1988 (12 years), from this date the cycles of both positive and negative phases have had a minor cyclicality of between 4 to 6 years. A positive phase began in 2013, reaching its highest peak (annual anomaly of 1.5 • C) in the years 2015-2016, dates during which Modoki El Niño was generated or appeared ( Figure 8).
Due to the action of the PDO, the surface winds change, generating anomalous wind patterns to propel the ocean in the mid-latitude of the Pacific Ocean. The coastal ENSO is a sub-process of La Niña Modoki, that is, it is a consequence of another larger event (PDO) and also deserves a more in-depth investigation which is beyond the scope of this study. In Figure 8, the behavior of the oscillation of the PDO Index can be observed as explained.
The El Niño Southern Oscillation (ENSO) and the Pacific Decadal Oscillation (PDO) are large-scale climatic phenomena that affect atmospheric and oceanic teleconnections and, therefore, trigger meteorological phenomena at different temporal and spatial scales, both in tropical and extratropical regions. During 11 years (2007-2017) the influence of ENSO events (Canonical and Modoki-in their El Niño, La Niña and Neutral modes) and PDO phases (cold and warm) on meteorological conditions was analyzed [45].
ENSO teleconnections may depend on the phases of the PDO and the characteristics of warming over the central and eastern tropical Pacific, furthermore, the strength of ENSO teleconnections appears to depend on patterns of SST anomalies over the pacific tropical [46].
The frequency and strength of ENSO Modoki events have increased considerably since previous decades , resulting in the need to review climate impacts of varying magnitude from ENSO Modoki, and like ENSO Canonical, ENSO Modoki it also induces a considerable impact in the North Pacific (Atlantic) region [47].

Analysis in the Generation of an Anticyclone
Rodríguez et al. [19] proposed that the probable cause of the anomalous storms generated by the 2017 ENSO is related to the combination of an especially intense wet season over the Central Andes, related to a deep and long-lasting anticyclone located adjacent to the Chilean coast, and the unusual development of warm water off the coast of Peru from El Niño Region 1 + 2. What was explained in the previous study is partially compatible with the occurrence of the ITCZ proposed in this investigation. According to the analysis carried out, we propose that the presence of coastal ENSO in the ITCZ would have generated areas of low pressure, favoring the formation and rise of large masses of humid air, turning into extensive clouds that produced the heavy rainfall in the central and northern areas of Peru. The position of the ITCZ had a variability and moved more towards the southwest of South America (January to March).

Climate Variability-ENSO
The incidence of climate variability in the generation of ENSO is not yet clear, given the existing complexity of the planet's ocean-atmosphere interaction, and only some theories are mentioned in this regard. Tsonis [48], for example, mentions that climate change and ENSO converge in the conclusion that changes in ENSO statistics occur in response to fluctuations in climate (temperature), and the discovery of a correlation between the frequency of El Niño recurrence and temperature change. Similarly, another study carried out by Chowdhury [33], in which they used regional climate models to evaluate future variability of ENSO, indicate that ENSO is correlated with both global and regional climate change scenarios, and that the temperature will continue to increase. In addition to the changing climate, the interannual variability of ENSO would further compound the problems.

Limitations of Data and Methods
In the present study we have carried out an evaluation of the oceanic indices to determine the most appropriate index and to be able to determine a coastal ENSO We are only evaluating two years (2016-2017), because they are the years in which ENSO Modoki, Niña Modoki and "2017 Coastal ENSO" and according to available bibliographic information on coastal ENSO in Peru, there are only two events, a coastal event that occurred in 1925 and the last coastal event in 2017, so there is not much information to make a future evolution or prediction of a coastal ENSO. However, in the case of the PDO index we are evaluating from 1976 to 2018 because we postulate that it could be the cause in the generation of the coastal ENSO.

Conclusions
According to the results obtained in this study, the heavy rainfall that occurred in the northern part of Peru has been caused by the presence of a special type of ENSO, called "Coastal El Niño" (El Niño Costero), as well as the formation of extensive masses of humid air generated in the ITCZ and, therefore, Peru would be affected by three types of meteorological phenomena (in relation to rainfall extremes): the "Canonical El Niño", the "Coastal El Niño", and the ITCZ. It has also been observed that the occurrence of the "Coastal El Niño" is directly related to the occurrence of El Niño Modoki and this, in turn, with the positive phase of the PDO.
To determine the generation and occurrence of "Coastal El Niño", different ocean indices have been analyzed, of which the index that best adapts is the index developed by the authors, called "PREI", through which the probable increases in temperature can be monitored of zone 1+2 that may occur during the months of January to March of a given year and allowing proper management of disaster related to the occurrence of a coastal ENSO. Future research is proposed related to the systematization of the best types of indices that can predict the occurrence of an ENSO, as well as atmospheric modeling to predict and differentiate types of ENSO (Canonical and Modoki) and their variants. Likewise, research is suggested on the behavior of PDO and its probable influence on the generation of "El Niño Modoki".
Author Contributions: E.G. designed this research, collected observed data, wrote the first draft and edited the paper; E.I. provided professional guidance, writing-reviewing. All authors have read and agreed to the published version of the manuscript.
Funding: This research received partial external funding for the first author from Universidad Nacional San Agustin.