Free Standard AU & NZ Shipping For All Book Orders Over $80!
Register      Login
Journal of Southern Hemisphere Earth Systems Science Journal of Southern Hemisphere Earth Systems Science SocietyJournal of Southern Hemisphere Earth Systems Science Society
A journal for meteorology, climate, oceanography, hydrology and space weather focused on the southern hemisphere
RESEARCH ARTICLE (Open Access)

Using Chaos theory fundamentals for analysing temperature, precipitation variability and trends in Northern Patagonia, Argentina

Grethel García Bu Bucogen https://orcid.org/0000-0001-6347-7381 A * , María Cintia Piccolo https://orcid.org/0000-0002-5184-9149 B , Vanesa Yael Bohn https://orcid.org/0000-0002-4050-8664 C and Gabriel Eduardo Huck https://orcid.org/0000-0003-1436-975X A
+ Author Affiliations
- Author Affiliations

A Instituto Argentino de Oceanografía (CONICET-UNS), Bahía Blanca, Buenos Aires, Argentina.

B Instituto Argentino de Oceanografía (CONICET-UNS)–Departamento de Geografía y Turismo, Universidad Nacional del Sur (UNS), Bahía Blanca, Buenos Aires, Argentina.

C Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)–Departamento de Geografía y Turismo, UNS, Bahía Blanca, Buenos Aires, Argentina.

* Correspondence to: grethelgbb@gmail.com

Journal of Southern Hemisphere Earth Systems Science 72(3) 179-190 https://doi.org/10.1071/ES22009
Submitted: 23 March 2022  Accepted: 26 September 2022   Published: 18 October 2022

© 2022 The Author(s) (or their employer(s)). Published by CSIRO Publishing on behalf of BoM. This is an open access article distributed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND)

Abstract

The fundamentals of Chaos theory allow the study of climatic conditions and long-term modifications produced by changes in their spatial and temporal scales. The aim of this work is to analyse the variability and changes produced in the annual cycles of temperature and precipitation in Northern Patagonia, Argentina, applying multifractal analysis as a practical mathematical tool of Chaos theory. Data from the NASA POWER Project (2021) was implemented as an alternative dataset for carrying out climatological studies in the area. Annual mean temperature and precipitation time-series data (1981–2019) were analysed at 72 grid points with 1° of spatial resolution. The Mann–Kendall test was used to calculate the trends through the annual cycles of the meteorological variables. Fractal dimension values were calculated using Multifractal Detrended Fluctuation Analysis. The Hurst exponent, complexity and asymmetry were the multifractal dimensions describing the persistence of time-series trends and climatic variability. The results showed changes in the annual cycles of both variables during the study period. The most significant finding was a large area in the centre and north of the study area, where the decrease in the rainfall regime was persistent. The Hurst exponent detected a sector in the Patagonian Andes mountain range where the temperature increase was constant. This work demonstrates that fractal geometry is useful to describe meteorological variability and obtain better short-, medium- and long-term forecasts.

Keywords: annual cycles, climatic variability, heating, hydric stress, melting, multifractal dimensions, Northern Patagonia, precipitation, temperature, trends.


References

Alencar da Silva Alves KM, Silva Nóbrega R (2017) Tendencia pluviométrica y concentración estacional de precipitación en la cuenca hidrográfica del río Moxotó – Pernambuco – Brasil. Revista Geográfica de América Central 1, 295–313.
Tendencia pluviométrica y concentración estacional de precipitación en la cuenca hidrográfica del río Moxotó – Pernambuco – Brasil.Crossref | GoogleScholarGoogle Scholar | [In Spanish]

Alves TLB, de Azevedo PV, de Farias AA (2015) Comportamento da precipitação pluvial e sua relação com o relevo nas microrregiões do Cariri Oriental e Ocidental do estado da Paraíba. Revista Brasileira de Geografia Física 8, 1601–1614.
Comportamento da precipitação pluvial e sua relação com o relevo nas microrregiões do Cariri Oriental e Ocidental do estado da Paraíba.Crossref | GoogleScholarGoogle Scholar | [In Spanish]

Baranowski P, Krzyszczak J, Slawinski C, Hoffmann H, Kozyra J, Nieróbca A, Siwek K, Gluza A (2015) Multifractal analysis of meteorological time series to assess climate impacts. Climate Research 65, 39–52.
Multifractal analysis of meteorological time series to assess climate impacts.Crossref | GoogleScholarGoogle Scholar |

Baranowski P, Gos M, Krzyszczak J, Siwek K, Kieliszek A, Tkaczyk P (2019) Multifractality of meteorological time series for Poland on the base of MERRA-2 data. Chaos, Solitons & Fractals 127, 318–333.
Multifractality of meteorological time series for Poland on the base of MERRA-2 data.Crossref | GoogleScholarGoogle Scholar |

Bartos I, Jánosi IM (2006) Nonlinear correlations of daily temperature records over land. Nonlinear Processes in Geophysics 13, 571–576.
Nonlinear correlations of daily temperature records over land.Crossref | GoogleScholarGoogle Scholar |

Bianchi E (2016) Dinámica espacio temporal de la relación entre el clima y el funcionamiento de los ecosistemas en Patagonia Norte. PhD thesis, Universidad Nacional de COMAHUE, San Carlos de Bariloche, Argentina. Available at https://ri.conicet.gov.ar/handle/11336/79967 [In Spanish]

Bianchi A, Cravero S (2010) Atlas climático digital de la República Argentina. (Instituto Nacional de Tecnología Agropecuaria: Salta, Argentina) Available at https://inta.gob.ar/sites/default/files/clima_de_arg._cravero_bianchi_elena_bianchi_100517.pdf [In Spanish]

Brendel AS, del Barrio RA, Mora F, León EAO, Flores JR, Campoy JA (2020) Potencial agroclimático actual de la Patagonia moldeado por patrones térmicos e hídricos. Theoretical and Applied Climatology 142, 855–868.
Potencial agroclimático actual de la Patagonia moldeado por patrones térmicos e hídricos.Crossref | GoogleScholarGoogle Scholar | [In Spanish]

Camacho Velázquez R, Vásquez Cruz M (2015) Geometría fractal, Teoría del caos, y sus aplicaciones en la Industria Petrolera. Ingeniería Petrolera 55, 718–729. [In Spanish]

Camilloni I (2018) Argentina y el cambio climático. Ciencia e investigación 68, 5–10. [In Spanish]

Chen D, Chen HW (2013) Using the Köppen classification to quantify climate variation and change: an example for 1901–2010. Environmental Development 6, 69–79.
Using the Köppen classification to quantify climate variation and change: an example for 1901–2010.Crossref | GoogleScholarGoogle Scholar |

Collado A (2012) Desertificación en Argentina: el problema de las 60 millones de hectáreas. [Desertification in Argentina: the problem of 60 million hectares.] (National Institute of Agricultural Technology) Available at https://inta.gob.ar/noticias/desertificacion-en-argentina-el-problema-de-las-60-millones-de-hectareas [In Spanish]

Coronato A, Mazzoni E, Vázquez M, Coronato F (2017) Chapter 3. Clima. In ‘Patagonia: una síntesis de su geografía física’. pp. 101–126. (Universidad Nacional de la Patagonia Austral: Río Gallegos, Argentina) Avaliable at https://www.unpa.edu.ar/publicacion/version-digital-patagonia [In Spanish]

Das P (2009) Nonlinear Analysis of Daily Temperature Data. In ‘2009 ETP International Conference on Future Computer and Communication’, 6–7 June 2009, Wuhan, PR China. INSPEC Accession number 10869078, pp. 273–277. (IEEE)
| Crossref |

Domino K, Błachowicz T, Ciupak M (2014) The use of copula functions for predictive analysis of correlations between extreme storm tides. Physica – A. Statistical Mechanics and its Applications 413, 489–497.
The use of copula functions for predictive analysis of correlations between extreme storm tides.Crossref | GoogleScholarGoogle Scholar |

Endlichter W, Santana A (1988) El clima del sur de la Patagonia y sus aspectos ecológicos. Anales del Instituto de la Patagonia 484, 57–86. Avaliable at http://www.bibliotecadigital.umag.cl/bitstream/handle/20.500.11893/924/Endlicher_Anales_1988_vol18_pp57‐86.pdf?sequence=1&isAllowed=y [In Spanish]

Farr TG, Rosen PA, Caro E, Crippen R, Duren R, Hensley S, Kobrick M, Paller M, Rodriguez E, Roth L, Seal D, Shaffer S, Shimada J, Umland J, Werner M, Oskin M, Burbank D, Alsdorf D (2007) The Shuttle Radar Topography Mission. Reviews of Geophysics 45, RG2004
The Shuttle Radar Topography Mission.Crossref | GoogleScholarGoogle Scholar |

Ferri L, Dussaillant I, Zalazar L, Masiokas MH, Ruiz L, Pitte P, Gargantini H, Castro M, Berthier E, Villalba R (2020) Ice mass loss in the Central Andes of Argentina between 2000 and 2018 derived from a new glacier inventory and satellite stereo-imagery. Frontiers in Earth Science 8, 530997
Ice mass loss in the Central Andes of Argentina between 2000 and 2018 derived from a new glacier inventory and satellite stereo-imagery.Crossref | GoogleScholarGoogle Scholar |

García Bu Bucogen G, Piccolo MC, Bohn VY (2022) Implementación de datos meteorológicos modelados en el norte patagónico argentino. Investigaciones Geográficas 78, 67–87.
Implementación de datos meteorológicos modelados en el norte patagónico argentino.Crossref | GoogleScholarGoogle Scholar | [In Spanish]

García Silva L, Jover ML, Nahas A, Ferri Hidalgo L, Villalba R, Zalazar L, Sánchez R, Marinsek S (2019) ‘Atlas de Glaciares de la Argentina.’ (Ediciones de la Secretaría de Ambiente y Desarrollo Sustentable de la Nación: Mendoza, Argentina) [In Spanish]

Garreaud RD, Vuille M, Compagnucci R, Marengo J (2009) Present-day South American climate. Palaeogeography, Palaeoclimatology, Palaeoecology 281, 180–195.
Present-day South American climate.Crossref | GoogleScholarGoogle Scholar |

Garreaud R, Lopez P, Minvielle M, Rojas M (2013) Large-scale control on the Patagonian climate. American Meteorological Society 26, 215–230.
Large-scale control on the Patagonian climate.Crossref | GoogleScholarGoogle Scholar |

Ghanmi H, Bargaoui Z, Mallet C (2013) Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate. Hydrological Sciences Journal 58, 483–497.
Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate.Crossref | GoogleScholarGoogle Scholar |

Gil Guirado S, Bermúdez F (2011) Tendencia de las precipitaciones y temperaturas en una pequeña cuenca fluvial del sureste peninsular semiárido. Boletín de la Asociación de Geógrafos Españoles 56, 349–371. [In Spanish]

Gómez J, Poveda G (2008) Estimación del espectro multifractal para series de precipitación horaria en los Andes tropicales de Colombia. Revista de la Academia Colombiana de Ciencias Exactas Físico Naturales 32, 483–502. [In Spanish]

González MH, Romero PE, Garbarini EM (2017) Droughts and floods in northern Argentinean Patagonia. The Andes: geography, diversity, and sociocultural impacts. (NOVA Science Publisher Inc.: New York, NY, USA) Available at https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97815361_v_n_p5_Gonzalez

Goossens C, Berger A (1986) Annual and seasonal climatic variations over the northern hemisphere and Europe during the last century. Annales Geophysicae 4, 385–400.

Haro AX, Limaico CT, Llosas YE (2012) Predicción de datos meteorológicos en cortos intervalos de tiempo en la ciudad de Riobamba usando la teoría del caos. Sistemas, Cibernética e Informática 13, 35–41. [In Spanish]

Hena Rani B, Hasan M, Bala SK (2018) Chaos theory and its applications in our real life. Barishal University Journal 1, 123–140.

Huang H-H, Puente CE, Cortis A, Fernández Martínez JL (2013) An effective inversion strategy for fractal–multifractal encoding of a storm in Boston. Journal of Hydrology 496, 205–216.
An effective inversion strategy for fractal–multifractal encoding of a storm in Boston.Crossref | GoogleScholarGoogle Scholar |

IPCC (2021) ‘Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change.’ (Eds V Masson-Delmotte, P Zhai, A Pirani, SL Connors, C Péan, S Berger, N Caud, Y Chen, L Goldfarb, MI Gomis, M Huang, K Leitzell, E Lonnoy, JBR Matthews, TK Maycock, T Waterfield, O Yelekçi, R Yu, B Zhou) (Cambridge University Press)

Johansen KS, Alfthan B, Baker E, Hesping M, Schoolmeester T, Verbist K (2018) The Andean glacier and water atlas: the impact of glacier retreat on water resources. UNESCO: Dataset about Global Resources. (UNESCO: Arendal, Norway) Available at https://unesdoc.unesco.org/ark:/48223/pf0000265810

Kantelhardt JW, Zschiegner SA, Koscielny-Bunde E, Havlin S, Bunde A, Stanley H (2002) Multifractal detrended fluctuation analysis of nonstationary time series. Physica – A. Statistical Mechanics and its Applications 316, 87–114.
Multifractal detrended fluctuation analysis of nonstationary time series.Crossref | GoogleScholarGoogle Scholar |

Kendall M (1975) ‘Rank correlation measures’. p. 120. (Charles Griffin: London, UK)

López-Lambraño A, Carrillo-Yee E, Fuente C, López-Ramos A, López-Lambraño M (2017) Una revisión de los métodos para estimar el exponente de Hurst y la dimensión fractal en series de precipitación y temperatura. Revista Mexicana de Física 63, 244–267. [In Spanish]

Lorenz EN (1963) Deterministic nonperiodic flow. Journal of the Atmospheric Sciences 20, 130–141.
Deterministic nonperiodic flow.Crossref | GoogleScholarGoogle Scholar |

Lorenz EN (1990) Can chaos and intransitivity lead to interannual variability? Tellus – A. Dynamic Meteorology and Oceanography 42, 378–389.
Can chaos and intransitivity lead to interannual variability?Crossref | GoogleScholarGoogle Scholar |

Lorenz EN (1991) Dimension of weather and climate attractors. Nature 353, 241–244.
Dimension of weather and climate attractors.Crossref | GoogleScholarGoogle Scholar |

Lovejoy S, Pinel J, Schertzer D (2012) The global space–time cascade structure of precipitation: satellites, gridded gauges and reanalyses. Advances in Water Resources 45, 37–50.
The global space–time cascade structure of precipitation: satellites, gridded gauges and reanalyses.Crossref | GoogleScholarGoogle Scholar |

Mandelbrot BB (1977) ‘Fractals: form, chance and dimension.’ (Freeman: San Francisco, CA, USA)

Mandelbrot BB, Wheeler JA (1983) The fractal geometry of nature. American Journal of Physics 51, 286–287.
The fractal geometry of nature.Crossref | GoogleScholarGoogle Scholar |

Mann HB (1945) Nonparametric tests against trend. Econometrica: Journal of the Econometric Society 13, 245–259.
Nonparametric tests against trend.Crossref | GoogleScholarGoogle Scholar |

Maofei M, Boming Y, Jianchao C, Liang L (2009) A fractal analysis of dropwise condensation heat transfer. International Journal of Heat and Mass Transfer 52, 4823–4828.
A fractal analysis of dropwise condensation heat transfer.Crossref | GoogleScholarGoogle Scholar |

Martínez Moncaleano CJ (2018) Teoría del Caos y estrategia empresarial. Tendencias 19, 204–214.
Teoría del Caos y estrategia empresarial.Crossref | GoogleScholarGoogle Scholar | [In Spanish]

Masiokas M (2008) Climate and glacier variability during past centuries in the North and South Patagonian Andes of Argentina. PhD thesis, The University of Western Ontario, London, ON, Canada. Available at https://www.collectionscanada.gc.ca/obj/thesescanada/vol2/002/NR39303.PDF?is_thesis=1andoclc_number=665191429

Mazzoni E, Vázquez M (2010) Desertificación en la Patagonia. Developments in Earth Surface Processes 13, 351–377.
Desertificación en la Patagonia.Crossref | GoogleScholarGoogle Scholar | [In Spanish]

Meza L, Corso S, Soza S (2010) ‘Gestión del riesgo de sequía y otros eventos climáticos extremos en Chile.’ (Food and Agriculture Organization of the United Nations: Santiago de Chile, Chile) [In Spanish]

Morales Martínez JL, Segovia-Domínguez I, Rodríguez IQ, Horta-Rangel FA, Sosa-Gómez G (2021) A modified multifractal detrended fluctuation analysis (MFDFA) approach for multifractal analysis of precipitation. Physica – A. Statistical Mechanics and its Applications 565, 125611
A modified multifractal detrended fluctuation analysis (MFDFA) approach for multifractal analysis of precipitation.Crossref | GoogleScholarGoogle Scholar |

Morello J, Matteucci SD, Rodríguez, AF, Mariana S (2012) ‘Ecorregiones y complejos ecosistemicos argentinos.’ (Orientación Gráfica Editorial: Buenos Aires, Argentina) Available at https://www.researchgate.net/profile/Silvia-Matteucci-2/publication/268447092_Ecorregiones_y_complejos_ecosistemicos_Argentinos/links/598333be0f7e9b2ac353f62e/Ecorregiones-y-complejos-ecosistemicos-Argentinos.pdf [In Spanish]

NASA POWER Project (2021) The Prediction of Worldwide Energy Resource (POWER). (NASA Applied Sciences Program within the Earth Science Division of the Science Mission Directorate) Available at https://power.larc.nasa.gov

Nieto HD, Álvarez JE, Rodríguez EL (2016) Análisis de persistencia en acciones financieras en el mercado colombiano a través de la metodología de Rango Reescalado (R/S). Cuadernos Latinoamericanos de Administración, XII 22, 23–32.
Análisis de persistencia en acciones financieras en el mercado colombiano a través de la metodología de Rango Reescalado (R/S).Crossref | GoogleScholarGoogle Scholar | [In Spanish]

Palese C, Lassig J, Cogliati M, Bastanski M (2001) Régimen de Viento y potencia eólica en la región Norpatagónica. In ‘IX Encuentro Latinoamericano y del Caribe sobre pequeños aprovechamientos hidroenergeticos’, 5–9 November 2001, Ciudad de Neuquén, Argentina. Available at https://www.researchgate.net/publication/278403844_Regimen_de_Viento_y_potencia_eolica_en_la_region_Norpatagonica [In Spanish]

Paruelo JM, Beltran A, Jobbagy E, Sala OE, Golluscio RA (1998) The climate of Patagonia: general patterns and controls on biotic processes. Ecologia Austral 8, 85–101.

Pérez SP, Sierra EM, Massobrio MJ, Momo FR (2009) Análisis fractal de la precipitación anual en el este de la provincia de La Pampa, Argentina. Revista de Climatología 9, 25–35. [In Spanish]

Pessacg NL, Flaherty S, Solman S, Pascual M (2020) Climate change in northern Patagonia: critical decrease in water resources. Theoretical and Applied Climatology 140, 807–822.
Climate change in northern Patagonia: critical decrease in water resources.Crossref | GoogleScholarGoogle Scholar |

Pessacg N, Blázquez J, Lancelotti J, Solman S (2022) Climate changes in coastal areas of patagonia: observed trends and future projections. In ‘Global Change in Atlantic Coastal Patagonian Ecosystems’. (Eds EW Helbling, MA Narvarte, RA González, VE Villafañe) pp. 13–42. (Springer: New York, NY, USA)

Plazas Nossa L, Ávila Angulo MA, Moncada Méndez G (2014) Estimación del exponente de Hurst y dimensión fractal para el análisis de series de tiempo de absorbancia UV-VIS. Ciencia e Ingeniería Neogranadina 24, 133–143.
Estimación del exponente de Hurst y dimensión fractal para el análisis de series de tiempo de absorbancia UV-VIS.Crossref | GoogleScholarGoogle Scholar | [In Spanish]

Prohaska F (1976) El clima de Argentina, Paraguay y Uruguay. Climas de América Central y del Sur. In ‘World Survey of Climatology. Vol. 12’. pp. 57–69. (Elsevier Scientific Publishing Company: Amsterdam, Netherlands) [In Spanish]

Quintero Delgado OY, Ruiz Delgado J (2011) Estimación del exponente de Hurst y la dimensión fractal de una superficie topográfica a través de la extracción de perfiles. UD y la geomática 5, 84–91.
Estimación del exponente de Hurst y la dimensión fractal de una superficie topográfica a través de la extracción de perfiles.Crossref | GoogleScholarGoogle Scholar | [In Spanish]

Rangarajan G, Sant DA (2004) Fractal dimensional analysis of Indian climatic dynamics. Chaos, Solitons & Fractals 19, 285–291.
Fractal dimensional analysis of Indian climatic dynamics.Crossref | GoogleScholarGoogle Scholar |

Redondo JM, Grau J, Platonov A, Garzón G (2008) Análisis multifractal de procesos auto similares: imágenes de satélite e inestabilidades baroclinas. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 24, 25–48. [In Spanish]

Rodríguez Aguilar R (2012) El coeficiente de Hurst y el parámetro α-estable para el análisis de series financieras Aplicación al mercado cambiario mexicano. Contaduría y Administración 59, 149–173.
El coeficiente de Hurst y el parámetro α-estable para el análisis de series financieras Aplicación al mercado cambiario mexicano.Crossref | GoogleScholarGoogle Scholar | [In Spanish]

Romero PE, Garbarini EM, González MH (2014) Características hídricas y climáticas del norte Patagónico. In ‘II Encuentro de investigadores en formación en Recursos Hídricos’, 9–10 October 2014, Ezeiza, Buenos Aires, Argentina. (INA: Ezeiza, Buenos Aires, Argentina) Available at https://www.ina.gob.ar/ifrh-2014/Eje3/3.33.pdf [In Spanish]

Santos Burguete C (2018) Física del caos en la predicción meteorológica. In ‘AEMET, 2018. Física del caos en la predicción meteorológica - Agencia Estatal de Meteorología - AEMET’. pp. 13–19. (Editorial del Ministerio de Agricultura y Pesca, Alimentación y Medio Ambiente y editada por el Ministerio para la Transición Ecológica) Available at http://www.aemet.es/es/conocermas/recursos_en_linea/publicaciones_y_estudios/publicaciones/detalles/Fisica_del_caos_en_la_predicc_meteo [In Spanish]

Santos da Silva H, Santos Silva JR, Stosic T (2020) Multifractal analysis of air temperature in Brazil. Physica – A. Statistical Mechanics and its Applications 549, 124333
Multifractal analysis of air temperature in Brazil.Crossref | GoogleScholarGoogle Scholar |

Selvam AM (1993) Universal quantification for deterministic chaos in dynamical systems. Applied Mathematical Modelling 17, 642–649.
Universal quantification for deterministic chaos in dynamical systems.Crossref | GoogleScholarGoogle Scholar |

Selvam AM (2011) Signatures of universal characteristics of fractal fluctuations in global mean monthly temperature anomalies. Journal of Systems Science and Complexity 24, 14–38.
Signatures of universal characteristics of fractal fluctuations in global mean monthly temperature anomalies.Crossref | GoogleScholarGoogle Scholar |

Selvam AM (2013) Nonlinear dynamics and chaos: applications in atmospheric sciences. Journal of Advanced Mathematics and Applications 1, 1–24.
Nonlinear dynamics and chaos: applications in atmospheric sciences.Crossref | GoogleScholarGoogle Scholar |

Selvam AM (2017) Nonlinear dynamics and chaos: applications in meteorology and atmospheric physics. In ‘Self-organized Criticality and Predictability in Atmospheric Flows: The Quantum World of Clouds and Rain’. pp. 1–40. (Springer Atmospheric Sciences: New York, NY, USA)
| Crossref |

Selvam AM, Pethkar JS, Kulkarni MK (1992) Signatures of a universal spectrum for atmospheric interannual variability in rainfall time series over the Indian region. International Journal of Climatology 12, 137–152.
Signatures of a universal spectrum for atmospheric interannual variability in rainfall time series over the Indian region.Crossref | GoogleScholarGoogle Scholar |

Svensson C, Olsson J, Berndtsson R (1996) Multifractal properties of daily rainfall in two different climates. Water Resources Research 32, 2463–2472.
Multifractal properties of daily rainfall in two different climates.Crossref | GoogleScholarGoogle Scholar |

Warren CR, Sugden DE (1993) The Patagonian icefields: a glaciological review. Arctic and Alpine Research 25, 316–331.
The Patagonian icefields: a glaciological review.Crossref | GoogleScholarGoogle Scholar |

Yu J-Y, Kao H-Y (2007) Decadal changes of ENSO persistence barrier in SST and ocean heat content indices: 1958–2001. Journal of Geophysical Research: Atmospheres 112, D13106
Decadal changes of ENSO persistence barrier in SST and ocean heat content indices: 1958–2001.Crossref | GoogleScholarGoogle Scholar |

Yu Z-G, Leung Y, Chen YD, Zhang Q, Anh V, Zhou Y (2014) Multifractal analyses of daily rainfall time series in Pearl River basin of China. Physica – A. Statistical Mechanics and its Applications 405, 193–202.
Multifractal analyses of daily rainfall time series in Pearl River basin of China.Crossref | GoogleScholarGoogle Scholar |

Zalazar L, Ferri L, Castro M, Gargantini H, Giménez M, Pitte P, Ruiz L, Masiokas M, Villalba R (2017) Glaciares de Argentina: Resultados Preliminares del Inventario Nacional de Glaciares. Revista de Glaciares y Ecosistemas de Montaña 2, 13–22. Available at https://notablesdelaciencia.conicet.gov.ar/bitstream/handle/11336/60533/CONICET_Digital_Nro.34d18b29-1b97-4bde-8461-3dd79f4ac4fd_B.pdf?sequence=5andisAllowed=y [In Spanish]

Zhou Y, Leung Y (2010) Multifractal temporally weighted detrended fluctuation analysis and its application in the analysis of scaling behaviour in temperature series. Journal of Statistical Mechanics: Theory and Experiment 6, P06021
Multifractal temporally weighted detrended fluctuation analysis and its application in the analysis of scaling behaviour in temperature series.Crossref | GoogleScholarGoogle Scholar |