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Rodrigo Abarca del Rio
  • Departamento de Geofisica
    Universidad de Concepcion
    Concepcion, Chile
  • 56-41-2203107
ABSTRACT El presente trabajo estudia eventos de inundaciones en el pasado, asociándolos a indicadores climáticos y precipitaciones durante la fecha de los eventos adversos. Se estudiaron lo hechos ocurridos durante la segunda mitad del... more
ABSTRACT El presente trabajo estudia eventos de inundaciones en el pasado, asociándolos a indicadores climáticos y precipitaciones durante la fecha de los eventos adversos. Se estudiaron lo hechos ocurridos durante la segunda mitad del siglo XX en la zona Central de Chile (32ª a 37º S). Se usaron registros de inundaciones recopiladas por Aldunce en el año 2009 y dos indicadores climáticos: Se usó la variabilidad del El Niño-Oscilación del Sur (ENOS) reflejada en la anomalía nino3.4 y como segundo indicador la anomalía de la oscilación antartica (AAO), adicionalmente se usó las anomalías de los datos globales de precipitación de Willmott. Para el estudio se usó como herramienta dos tipos de distribuciones, en este caso distribuciones logit y probit. Los modelos Logit y Probit tienen la ventaja de ser lineales por lo cual su estimación es simple. Se logró establecer que para anomalías positivas de AAO y nino3.4 existe una mayor probabilidad de inundación, según la fdp establecida mediante ambas regresiones lineales. Conocer la función de distribución de probabilidad asociada a los eventos adversos de inundaciones bajo distintas condiciones, permitiendo manejar de mejor manera los recursos durante las distintas subetapas de preparación.
Interdecadal oscillations in Atmospheric Angular Momentum variationsGlobal Atmospheric Angular Momentum (AAM) is an intrinsic index for describing processes that affect the atmospheric circulation on time scales ranging from intraseasonal... more
Interdecadal oscillations in Atmospheric Angular Momentum variationsGlobal Atmospheric Angular Momentum (AAM) is an intrinsic index for describing processes that affect the atmospheric circulation on time scales ranging from intraseasonal to secular. It is associated with length-of-day (LOD) variability through conservation of global angular momentum in planet Earth and thus is of considerable importance for quantifying how the Earth acts as a system. The availability of lengthy AAM time series computed from the recent 20th Century atmospheric reanalyses (1870-2008), complemented by the NCAR-NCEP reanalysis in the overlapping period of 1948-2008 allows the investigation of the role of decadal and interdecadal cycles as well as the recent overall trend in AAM. Thus, we extend to the entire 20th century (and prior, back to 1870) results concerning decadal time scales and a secular positive trend detected over recent decades by different authors. In addition, we also note that AAM has ...
We analyse phase lags between the 11-year variations of three records: the semi-annual oscillation of the length of day (LOD), the solar activity (SA) and the cosmic ray intensity (CRI). The analysis was done for solar cycles 20–23.... more
We analyse phase lags between the 11-year variations of three records: the semi-annual oscillation of the length of day (LOD), the solar activity (SA) and the cosmic ray intensity (CRI). The analysis was done for solar cycles 20–23. Observed relationships between LOD, CRI and SA are discussed separately for even and odd solar cycles. Phase lags were calculated using different methods (comparison of maximal points of cycles, maximal correlation coefficient, line of synchronization of cross-recurrence plots). We have found different phase lags between SA and CRI for even and odd solar cycles, confirming previous studies. The evolution of phase lags between SA and LOD as well as between CRI and LOD shows a positive trend with additional variations of phase lag values. For solar cycle 20, phase lags between SA and CRI, between SA and LOD, and between CRI and LOD were found to be negative. Overall, our study suggests that, if anything, the length of day could be influenced by solar irrad...
... Past sea-level reconstruction and variability of sea-level trend patterns. W. Llovel, A. Lombard, A. Cazenave, P. Rogel, Th. Penduff 1 , Rodrigo Abarca Del Rio 2. (2008). 1 : Laboratoire des écoulements géophysiques et industriels... more
... Past sea-level reconstruction and variability of sea-level trend patterns. W. Llovel, A. Lombard, A. Cazenave, P. Rogel, Th. Penduff 1 , Rodrigo Abarca Del Rio 2. (2008). 1 : Laboratoire des écoulements géophysiques et industriels (LEGI). ...
... Analysis of images from 2000 to 2010 has also showed high inter-annual amplitudes of ... 4] Töyrä, J., Pietroniro, A. and Martz, LW Multisensor Hydrologic Assessment of a ... IEEE JSTARS, Special Issue on Microwave Remote Sensing for... more
... Analysis of images from 2000 to 2010 has also showed high inter-annual amplitudes of ... 4] Töyrä, J., Pietroniro, A. and Martz, LW Multisensor Hydrologic Assessment of a ... IEEE JSTARS, Special Issue on Microwave Remote Sensing for Land Hydrology Research and Applications ...
ABSTRACT Complementary analysis of satellite mission data (altimetry, Moderate Resolution Imaging Spectroradiometers (MODIS)) and climate fields over 2000–2009 was conducted to investigate the variability of the water cover surfaces and... more
ABSTRACT Complementary analysis of satellite mission data (altimetry, Moderate Resolution Imaging Spectroradiometers (MODIS)) and climate fields over 2000–2009 was conducted to investigate the variability of the water cover surfaces and the geographical source of water inflowing into the Lake Poopó system. The results suggest that over the time span of 2000–2009 a great part of the variability of the Poopó system originates from geographic sources other than Lake Titicaca. Possible alternative causes include climate change inducing increased temperatures and greater evaporation rates along the Altiplano; increased glacier and snow melting over the Andes Cordillera; and a potential increased anthropogenic water use (such as irrigation, minery, etc.) throughout the path of the Desaguadero River (which connects lakes Titicaca and Poopó). This change in the hydrology of this region could lead to a collapse of water supplies and endanger the already fragile Poopó system as well as the regional socioeconomic system, which closely depends upon it.
... CK Shum g , F. Nino b , M. Bergé-Nguyen a , S. Fleury h , P. Gegout i , R. Abarca Del Rio j & P. Maisongrande a pages 291-318. ... 200910. Crétaux, JF, Calmant, S., Romanovski, VV, Shabunin, A., Lyard, F.,... more
... CK Shum g , F. Nino b , M. Bergé-Nguyen a , S. Fleury h , P. Gegout i , R. Abarca Del Rio j & P. Maisongrande a pages 291-318. ... 200910. Crétaux, JF, Calmant, S., Romanovski, VV, Shabunin, A., Lyard, F., Berge-Nguyen, M., Cazenave, A., Hernandez, F. and Perosanz, F. 2009. ...
Climate change scenarios are computed on a large scale, not accounting for local variations presented in historical data and related to human scale. Based on historical records, we validate a baseline (1962–1990) and correct the bias of... more
Climate change scenarios are computed on a large scale, not accounting for local variations presented in historical data and related to human scale. Based on historical records, we validate a baseline (1962–1990) and correct the bias of A2 and B2 regional projections for the end of twenty‑first century (2070–2100) issued from a high resolu‑ tion dynamical downscaled (using PRECIS mesoscale model, hereinafter DGF‑PRECIS) of Hadley GCM from the IPCC 3rd Assessment Report (TAR). This is performed for the Araucanía Region (Chile; 37°–40°S and 71°–74°W) using two different bias correction methodologies. Next, we study high‑resolution precipitations to find monthly patterns such as seasonal variations, rainfall months, and the geographical effect on these two scenarios. Finally, we compare the TAR projections with those from the recent Assess‑ ment Report 5 (AR5) to find regional precipitation patterns and update the Chilean `projection. To show the effects of climate change projections, we compute the rainfall climatology for the Araucanía Region, including the impact of ENSO cycles (El Niño and La Niña events). The corrected climate projection from the high‑resolution dynami‑ cal downscaled model of the TAR database (DGF‑PRECIS) show annual precipitation decreases: B2 (−19.19 %, −287 ± 42 mm) and A2 (−43.38 %, −655 ± 27.4 mm per year. Furthermore, both projections increase the probability of lower rainfall months (lower than 100 mm per month) to 64.2 and 72.5 % for B2 and A2, respectively.
Research Interests:
We show that the monthly recorded history (1866–2014) of the Southern Oscillation Index (SOI), a descriptor of the El Niño Southern Oscillation (ENSO) phenomenon, can be correctly described as a dynamic system supporting a potential... more
We show that the monthly recorded history (1866–2014) of the Southern Oscillation Index (SOI), a descriptor of the El Niño Southern Oscillation (ENSO) phenomenon, can be correctly described as a dynamic system supporting a potential nonlinear predictability well beyond the spring barrier. Long-term predictability is strongly connected to a detailed knowledge about the topology of the attractor obtained by embedding the SOI index in a wavelet base state space. By utilizing the state orbits on the attractor, we show that the information contained in the SOI is sufficient to provide nonlinear attractor information, allowing the detection of predictability for longer than a year: 2, 3, and 4 years in advance throughout the record with an acceptable error. This is possible due to the fact that the lower-frequency variability of the SOI presents long-term positive autocorrelation. Thus, by using complementary methods, we confirm that the reconstructed attractor of the low-frequency part (lower than 1/year) of SOI time series cannot be attributed to stochastic influences. Furthermore, we establish its multifractality. As an example of the capabilities of the methodology, we investigate a few specific El Niño (1972–1973, 1982–1983, 1997–1998) and La Niña (1973–1974, 1988–1989 and 2010–2011) events. Our results indicate that each of these present several equivalent temporal structures over other eras of these 149 years (1866–2014). Accordingly, none of these cases, including extreme events, presents temporal singularity. We conclude that the methodology’s simplicity of implementation and ease of use makes it suitable for studying nonlinear predictability in any area where observations are similar to those describing the ENSO phenomenon.
Research Interests:
Research Interests:
In 2000, the World population was 6.2 billion people; it reached 7 billion in 2012, and is expected to reach 9.5 billion (± 0.4) in 2050, 11 billion (± 1.5) in 2100, according to the 2012 UN projections (Gerland et al, in Science... more
In 2000, the World population was 6.2 billion people; it reached 7 billion in 2012, and is expected to reach 9.5 billion (± 0.4) in 2050, 11 billion (± 1.5) in 2100, according to the 2012 UN projections (Gerland et al, in Science 346:234–237, 2014). The trend after 2100 is still one of global demographic growth, but after 2060, Africa is the only continent where the population would still increase. The amount of water consumed annually to produce the food necessary to meet the needs of the populations varies greatly between countries, from about 600 to 2500 m3/y per capita (Zimmer  in L’empreinte eau. Les faces cachees d’une ressource vitale. Charles Leopold Meyer, Paris, 2013), depending on their wealth, their food habits, and the percentage of food waste they generate (on average, 30% of the food produced is wasted). In 2000, the total food production was on the order of 3300 million tons (in cereal equivalents). In 2014, it is estimated that about 0.8 billion inhabitants of the planet suffer from hunger (FAO in World agriculture: towards 2030–2050. FAO, Rome, 2014. http://www.fao.org/docrep/004/Y3557E/y3557e00.HTM) 2014) and do not get the nutrition they need to be in good health or, in the case of children, to grow properly (both physically and intellectually). This food deficit was on the order of 40 million tons of cereal equivalents in 2014. The number of inhabitants with a food deficit was about 0.85 billion before the 2008 crisis and was decreasing annually, but it increased abruptly after 2008 up to 1 billion inhabitants, and is slowly decreasing now. Assuming a World average water consumption for food of 1300 m3/y per capita in 2000, 1400 m3/y in 2050 and 1500 m3/y in 2100, a volume of water of around 8200 km3/y was needed in 2000, 13000 km3/y will be needed in 2050 and 16500 km3/y in 2100 (Marsily in L’eau, un tresor en partage. Dunod, Paris, 2009). Can bioenergy be added to food production? Will that much water be available on earth, and where will it come from?  Is climate change going to modify the answers to these questions? Can severe droughts occur? Can there be conflicts related to a food deficit? Some preliminary answers and scenarios for food production will be given in this paper from a hydrologist viewpoint.
Research Interests:
We predict flood events by fitting two simple logistic regression models between mesoscale rainfall and El Niño-Southern Oscillation (ENSO) index with local scale flooding into the Biobío River Basin in Chile from 1948 to 2002. Two... more
We predict flood events by fitting two simple logistic regression models between mesoscale rainfall and El Niño-Southern Oscillation (ENSO) index with local scale flooding into the Biobío River Basin in Chile from 1948 to 2002. Two different and complementary logistic models were studied: Logit and Probit. The models perform alike suggesting that the methodology is robust. The best model is most accurate during the autumn over 80% hit rate and in winter 66% hit rate, which are the seasons with high risk of floods. This work represents a first step in the development of a complete hydrological framework for the Biobío River Basin. The Logit distribution shows better results; thus, we suggest to use this distribution to relate flood events with mesoscale precipitation and ENSO index in the Biobío River Basin. Finally, these results explain the flood events and its relation with risk management. In forthcoming studies we will extend the methodology over this region and Chile taking advantage of the availability of higher resolution (temporal and spatial) weather products along with investigating climatic patterns and Intergovernmental Panel on Climate Change (IPCC) climate change scenarios.
In ungauged basin, space-based information is essential for the monitoring of hydrological water cycle, in particular in regions undergoing large flood events where satellite data may be used as input to... more
In  ungauged  basin,  space-based  information  is  essential  for  the  monitoring  of  hydrological  water  cycle,  in
particular in regions undergoing  large flood  events where  satellite  data  may  be  used  as input to  hydrodynamic
models. A method for near 3D flood monitoring has been developed which uses synergies between radar altimetry
and high temporal resolution multi-spectral satellite. Surface Reflectance from the MODIS Terra instrument are
used to map areas of open water as well as aquatic vegetation on a weekly basis, while water level variations in the
inundated areas are provided by the radar altimetry from the Topex / Poseidon (T/P) and Envisat satellites. We
present this synergistic approach to three different regions: Niger Inner delta and Lake Tchad in Africa, and Ganga
river delta in Asia. Based mainly on visible and Near Infra Red (NIR) imagery is suitable to the observation of
inundation extent. This method is well adapted for arid and semi arid regions, but less for equatorial or boreal ones
due to cloud coverage.
This work emphasizes the limitations of current remote sensing techniques for full 3D-description of water storage
variability in ungauged basins, and provides a good introduction to the need and the potential use of the future
SWOT (Surface Water and Ocean Topography) satellite mission.
Global Atmospheric Angular Momentum (AAM) is an intrinsic index for describing processes that affect the atmospheric circulation on time scales ranging from intraseasonal to secular. It is associated with length-of-day (LOD) variability... more
Global Atmospheric Angular Momentum (AAM) is an intrinsic index for describing processes that affect the atmospheric circulation on time scales ranging from intraseasonal to secular. It is associated with length-of-day (LOD) variability through conservation of global angular momentum in planet Earth and thus is of considerable importance for quantifying how the Earth acts as a system. The availability of lengthy AAM time series computed from the recent 20th Century atmospheric reanalyses (1870-2008), complemented by the NCAR-NCEP reanalysis in the overlapping period of 1948-2008 allows the investigation of the role of decadal and interdecadal cycles as well as the recent overall trend in AAM. Thus, we extend to the entire 20th century (and prior, back to 1870) results concerning decadal time scales and a secular positive trend detected over recent decades by different authors. In addition, we also note that AAM has features of interdecadal time scales that modulate the lower frequency variability. These interdecadal time signals oscillate with periods of about 30-50 years, and we found an indication of an 80-90 year period. Short term signals interact with the long-term (secular) trend. Particularly over the years 1950-1985 the global positive trend in AAM appears to result from a conjunction of constructive positive slopes from all lower frequency signals (interdecadal short-term trends and the long-term positive secular trend). Since the mid 1980s, however, the interdecadal oscillation short-term trend contribution decreases, as does the total signal in global AAM. These oscillations appear as two interdecadal modes originating within the Pacific (associated principally with the Pacific Decadal Oscillation and also ENSO) from which they propagate poleward, with differing characteristics in each hemisphere.
The influence of inter-decadal and secular variability on the annual mean air surface temperature variability over France is characterized for the period 1880–2005, together with a description of their regional distribution. After a... more
The influence of inter-decadal and secular variability
on the annual mean air surface temperature variability over
France is characterized for the period 1880–2005, together
with a description of their regional distribution. After a
descriptive study of temperature linear trends over the
century, the oscillatory components of the series are
investigated through continuous and discrete wavelet
transform. This study reveals the importance of inter-
decadal time scales (40–60 and 60–80 years) and
particularly the evolution of their phase shift in the latest
epoch of the high temperatures rise over France (since
1980).
Located within the Altiplano at 3,686 m above sea level, Lake Poopó is remarkably shallow and very sensitive to hydrologic recharge. Progressive drying has been observed in the entire Titicaca-Poopó-Desaguadero-Salar de Coipasa (TPDS)... more
Located within the Altiplano at 3,686 m above sea level, Lake Poopó is remarkably shallow and very sensitive to hydrologic recharge. Progressive drying has been observed in the entire Titicaca-Poopó-Desaguadero-Salar de Coipasa (TPDS) system during the last decade, causing dramatic changes to Lake Poopó’s surface and its regional water supplies. Our research aims to improve understanding of Lake Poopó water storage capacity. Thus, we propose a new method based on freely available remote sensing data to reproduce Lake Poopó bathymetry. Laser ranging altimeter ICESat (Ice, Cloud, and land Elevation Satellite) is used during the lake’s lowest stages to measure vertical heights with high precision over dry land. These heights are used to estimate elevations of water contours obtained with Landsat imagery. Contour points with assigned elevation are filtered and grouped in a points cloud. Mesh gridding and interpolation function are then applied to construct 3D bathymetry. Complementary analysis of Moderate Resolution Imaging Spectroradiometer (MODIS) surfaces from 2000 to 2012 combined with bathymetry gives water levels and storage evolution every 8 days.
Complementary analysis of satellite mission data (altimetry, Moderate Resolution Imaging Spectroradiometers (MODIS)) and climate fields over 2000–2009 was conducted to investigate the variability of the water cover surfaces and the... more
Complementary analysis of satellite mission data (altimetry, Moderate Resolution Imaging Spectroradiometers (MODIS)) and climate fields over 2000–2009 was conducted to investigate the variability of the water cover surfaces and the geographical source of water inflowing into the Lake Poopó system. The results suggest that over the time span of 2000–2009 a great part of the variability of the Poopó system originates from geographic sources other than Lake Titicaca. Possible alternative causes include climate change inducing increased temperatures and greater evaporation rates along the Altiplano; increased glacier and snow melting over the Andes Cordillera; and a potential increased anthropogenic water use (such as irrigation, minery, etc.) throughout the path of the Desaguadero River (which connects lakes Titicaca and Poopó). This change in the hydrology of this region could lead to a collapse of water supplies and endanger the already fragile Poopó system as well as the regional socioeconomic system, which closely depends upon it.
" We analyse phase lags between the 11-year variations of three records: the semi-annual oscillation of the length of day (LOD), the solar activity (SA) and the cosmic ray intensity (CRI). The analysis was done for solar cycles 20–23.... more
" We analyse phase lags between the 11-year variations of three records: the semi-annual oscillation of the length of day (LOD), the solar activity (SA) and the cosmic ray intensity (CRI). The analysis was done for solar cycles 20–23. Observed relationships between LOD, CRI and SA are discussed separately for even and odd solar cycles. Phase lags were calculated using different methods (comparison of maximal points of cycles, maximal correlation coefficient, line of synchronization of cross-recurrence plots). We have found different phase lags between SA and CRI for even and odd solar cycles, confirming previous studies. The evolution of phase lags between SA and LOD as well as between CRI and LOD shows a positive trend with additional variations of phase lag values. For solar cycle 20, phase lags between SA and CRI, between SA and LOD, and between CRI and LOD were found to be negative. Overall, our study suggests that, if anything, the length of day could be influenced by solar irradiance rather than by cosmic  rays."
The analysis of variability in Atmospheric Angular Momentum (AAM) and Length of day (LOD) of Abarca del Rio et al. [Ann.Geophys.18 (2000) 347 ] is extended to investigate a possible connection with solar activity fluctuations from... more
The analysis of variability in Atmospheric Angular Momentum (AAM) and Length of day (LOD) of Abarca del Rio et al. [Ann.Geophys.18 (2000) 347 ] is extended to investigate a possible connection with solar activity fluctuations from interannual to secular time scales. The southern oscillation index and records of sea surface temperature are used as proxy series in this analysis during the era prior to the availability of AAM analyses. At  interannual times scales, the variability in AAM and LOD agrees with that in solar activity with regard to the decadal cycle in the stratospheric quasi biennial oscillation and solar activity but whose phases are slowly shifting from one another with time, while the stratospheric quasibiennial cycle agrees with the solar quasibiennial cycle, though led by 6years. At decadal times scales, AAM varies statistically with the solar decadal cycle over much of the last century since 1930–1940. The decadal mode in AAM is suggested here to be generated by upward propagation of surface atmospheric modes, from the surface throughout the troposphere through the stratosphere. Equatorial Sea Surface Temperature (SST) variability may be considered a proxy index for AAM variability because of the relationship to the El Nino/SouthernOscillation; its analysis over the last three centuries (1730–2000) and that of LOD since 1830 confirm the agreement found over the last part of the 20th century,as well as the general disagreement before.
The tendency of the atmospheric angular momentum (AAM) is investigated using a 49-year set of monthly AAM data for the period January 1949-December 1997. This data set is constructed with zonal wind values from the reanalyses of... more
The tendency of the atmospheric angular momentum (AAM) is investigated using a 49-year set of monthly AAM data for the period January 1949-December 1997. This data set is constructed with zonal wind values from the reanalyses of NCEP/NCAR, used in conjunction with a variety of operationally produced AAM time series with different independent sources and lengths over 1976-1997. In all the analyzed AAM series the linear trend is found to be positive. Since the angular momentum of the atmosphere-earth system is conserved this corresponds to a net loss of angular momentum by the solid earth, therefore decreasing the Earth rotation speed and increasing the length of day (LOD). The AAM rise is significant to the budget of angular momentum of the global atmosphere-earth system; its value in milliseconds/century (ms/cy) is +0.56 ms/cy, corresponding to one-third of the estimated increase in LOD (+1.7 ms/cy). The major contribution to this secular trend in AAM comes from the equatorial Tropopause. This is consistent with results from a previous study using a simplified aqua-planet model to investigate the AAM variations due to near equatorial warming conditions. During the same time interval, 1949-1997, the global marine + land-surface temperature increases by about 0.79 °C/cy, showing a linear correspondence between surface temperature increase and global AAM of about 0.07 ms per 0.1 °C. These results imply that atmospheric angular momentum may be used as an independent index of the global atmosphere's dynamical response to the greenhouse forcing, and as such, the length of day may be used as an indirect indicator of global warming.
Research Interests:
Understanding present-day global sea level rise requires a correct evaluation of past sea level field variability. We use sea level height fields obtained by satellite altimeters between 1992 and 2006, sea level height fields from recent... more
Understanding present-day global sea level rise requires a correct evaluation of
past sea level field variability. We use sea level height fields obtained by satellite
altimeters between 1992 and 2006, sea level height fields from recent reanalyses
of oceanic circulation (SODA) and worldwide tide gauges series for the time
interval 1958–2006, to investigate the limitations inherent in reconstructing the
past ~50 years of sea level variation using empirical orthogonal function (EOF)
decomposition. To understand some of the weaknesses we found, we tested the
influence of the spatial distribution of tide gauges as well as the ability to properly
reconstruct sea level in certain frequencies bands. The presence of the particularly
strong 1997–1998 El Nin˜o event, and the short time span of the base period
(1992–2006), limits the determination of other spatial teleconnections and then
the reconstruction over preceding epochs. More particularly, during the pre-
satellite era and outside the tropics, the non-stationary characteristics of heat
transport at interannual time scales and other low frequencies oscillations
associated with sea level height fields undermine the methodology.
Research Interests:
We propose an alternative approach for the em- bedding space reconstruction method for short time series. An m-dimensional embedding space is reconstructed with a set of time delays including the relevant time scales charac- terizing... more
We propose an alternative approach for the em-
bedding space reconstruction method for short time series.
An m-dimensional embedding space is reconstructed with a
set of time delays including the relevant time scales charac-
terizing the dynamical properties of the system. By using
a maximal predictability criterion a d-dimensional subspace
is selected with its associated set of time delays, in which
a local nonlinear blind forecasting prediction performs the
best reconstruction of a particular event of a time series. An
locally unfolded d-dimensional embedding space is then ob-
tained. The efficiency of the methodology, which is mathe-
matically consistent with the fundamental definitions of the
local nonlinear long time-scale predictability, was tested with
a chaotic time series of the Lorenz system. When applied to
the Southern Oscillation Index (SOI) (observational data as-
sociated with the El Ni˜no-Southern Oscillation phenomena
(ENSO)) an optimal set of embedding parameters exists, that
allows constructing the main characteristics of the El Ni˜no
1982–1983 and 1997–1998 events, directly from measure-
ments up to 3 to 4 years in advance.