La precipitación intensa vista desde la criticalidad auto-organizanda y las transiciones de fase continuas: un nuevo enfoque de estudio
Contenido principal del artículo
Resumen
La criticalidad auto-organizada, en inglés Self-Organized Criticality (SOC) es un modelo teórico reciente que describe a los sistemas complejo y ocurre generalmente cerca de las transiciones de fase continuas. Según esta teoría, un parámetro de orden se incrementa siguiendo una ley de potencia cuando un parámetro de sintonización pasa por un valor crítico; al acoplarse estos parámetros, el punto crítico se convierte en un atractor y resulta una SOC. Asimismo, la escala del parámetro de orden diverge. Aunque este concepto ha sido aplicado a campos muy diversos, que van desde la geofísica hasta la economía, los fenómenos climáticos aún se siguen considerando como sistemas caóticos cuyo comportamiento, marcado por el cuasi-equilibrio de Arakawa y Schubert (1974), está lejos de la auto-organización. Bajo este contexto, la presente revisión busca dar un formulismo efectivo a los fenómenos que involucran las precipitaciones intensas, utilizando la teoría de la SOC y las transiciones de fase. Así, se argumenta que al llegar a un valor crítico de vapor de agua (el parámetro de sintonización) se genera una transición de fase continua fuera del equilibrio hacia un régimen de convección y precipitación intensas (el parámetro de orden), con regiones de correlación con magnitudes de decenas a cientos de kilómetros (Peters y Neelin, 2006b). Así se logra una relación de potencia entre la precipitación intensa y los datos el vapor de agua.
Palabras Clave
Criticalidad auto-organizada, transiciones de fase continuas, precipitación intensa.
Citas
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Raup, M. D. 1986. Bilogical extinction in earth history. Science, 251: 1530–1532.
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Wolff, D. B., D. Marks, E. Amitai, D. Silberstein, B. Fisher, A. Tokay, J. Wang y J. Pippitt. 2004. Ground Validation for the Tropical Rainfall Measuring Mission (TRMM). American Meteorological Society.
Xu, K. y K. Emanuel. 1989. Is the tropical atmosphere conditionally unstable? . Monthly Weather Review, 117: 1471–1479.
a
Yeomans, J. 1992. Statistical Mechanics of Phase Transitions. Clarendon, Oxford.
Zhang, G., U. Tirnakli, L. Wang y T. Chen. 2011. Self organized criticality in a modified Olami-FederChristensen model. The European Physical Journal B, 82: 83–89.
Zhang, Y. y S. Klein. 2010. Mechanisms Affecting the Transition from Shallow to Deep Convection over Land: Inferences from Observations of the Diurnal Cycle Collected at the ARM Southern Great Plains Site. Journal of atmospheric sciences.
Arakawa, A. y W. Schubert. 1974. Interaction of a cumulus cloud ensemble with the large-scale environment, part I. . Journal Atmospheric Science, 31: 674–701.
Bak, P. 1996. How Nature Works: The science of self-organized criticality. Copernicus.
Bak, P. y K. Chen. 1991. Self-organized criticallity. Science Amercian, 246(1).
Bak, P. y K. Sneppen. 1993. Punctuated equilibrium and criticality in a simple model of evolution. Physical Review Letters, 71(24): 4083–4086.
Bak, P., C. Tang y K. Wiesenfeld. 1987. Selforganized criticality. Physical Review A, 38(1): 364–374.
Benjamin, Grell, Brown, Smirnova y R. Bleck. 2004. Mesoscale weather prediction with the RUC hybrid isentropic-terrain-following coordinate model. Mon. Weather Rev., 132: 473–494.
Bleck, Benjamin, Lee y MacDonald. 2010. On the use of an adaptive, hybrid-isentropic vertical coordinate in global atmospheric modeling. Mon. Weather Rev., 138: 2188–2210.
Bretherton, C., M. Peters y L. Back. 2003. Relationships between Water Vapor Path and Precipitation over the Tropical Oceans. Journal of Climate, 17.
Bretherton, C., M. Peters y L. E. Back. 2004. Relationships between water vapor path and precipitation over the tropical oceans. Journal Clim., 17.
Bunde, A., J. Eichner, R. Govindan, S. Halvin, E. Koscienly-Bunde, D. Rybski y D. Vjushin. 2003. Power-Law persistence in the Atmosphere Analysis and Applications. Nonextensive Entropy-Interdisciplinary Applications, New York Oxford University Press, 17.
Chistensen, K., H. J. Jensen y H. C. Fogedby. 1991.
Dynamical and Spatial Aspects of Sandpile Celluar Automata. J. Stat. Phys., 63: 653–681.
Condom, T., P. Rua y J. C. Espinoza. 2011. Correction of TRMM 3B43 monthly precipitation data over the montainous areas of Peru during the period 1998-2007. The European Physical Journal B, 82: 83–89.
Cowan, G., D. Pines y D. Meltzer. 1994. Complexity: Methaphors, Models and Reality. SFI Studies in the Sciences of Complexity. Addison Wesley.
Grabowski. 2003. MJO-like coherent structures: Sensitivity simulations using the cloudresolving convection parameterization (CRCP). Journal of Atmospheric Sciences, 60: 847–864.
Ibañez, J. 2007. Física de Fractales, Geosfera, Edafosfera y Biosfera (La Criticalidad AutoOrganizada). MI+D.
Jaynes, E. 1957. Information theory and statistical mechanics. Phys. Rev., 105: 620–630.
Kagan, Y. 1992. Seismicity: Turbulence of solids. Nonlinear Sci. Today, 2: 1–13.
Kron, T. y T. Grund. 2009. Society as a Selforganized Critical System. Cybernetics and Human Knowing, 16: 65–82.
Liu, Y., C. Liu y D. Wang. 2011. Understanding Atmospheric Behaviour in Terms of Entropy: A Review of Applications of the Second Law of Thermodynamics to Meteorology. Entropy, 13: 211– 240.
Lucas, C. 1999. Self-Organizing Systems. Usenet group comp.theory.self-org-sys.
Mandelbrot, B. 1982. The Fractal Geometry of Nature. W.H. Freeman, San Francisco.
Marro, J. y R. Dickman. 1999. Nonequilibrium Phase Transitions in Lattice Models. Cambridge Univiversity Press, Cambridge.
Neelin, D., O. Peters y K. Hales. 2009. The transition to strong convection. Journal of Atmospheric Science.
Neelin, D., O. Peters, J. Lin, K. Hales y C. Holloway. 2008. Rethinking convective quasi-equilibrium: observational constraints for stochastic convective schemes in climate models. Philosophical Transactions of the Royal Society A, 366: 2579– 2602.
Newman, M. 2005. Power laws, Pareto distributions and Zipf’s law. Contemporary Physics, 46(1).
Olami, Z., H. J. Feder y K. Christensen. 1992. Selforganized criticallity in a continuous, nonconservative cellular automaton modeling earthquakes. Phys. Rev. Lett., 68: 1464–1247.
Palacios, E. y S. Serrano. 2011. Validación de los Modelos de Cambio Climático hidrostáticos y no hidrostáticos sobre la climatología de Ecuador en las variables de precipitación y temperaturas extremas. La Granja, 13.
Palacios, E., S. Serrano y P. Núñez. 2009. Estudio de la climatología ecuatorial andina con métodos numéricos: pronósticos de tiempo, validaciones y recosntrucción de la atmósfera. La Granja, 10.
Paltridge, G. 1975. Global dynamics and climate: a system of minimum entropy exchange. Quart. J. Roy. Meteorol. Soc., 101: 475–484.
Parsons, D. B., K. Yoneyama y J. Redelsperger. 2000. The evolution of the tropical western Pacific ocean-atmosphere system following the arrival of a dry intrusion. Meteorological Society, 126: 517–548.
Peixoto, J., A. Oort, M. de Almeida y A. Tome. 1991. Entropy budget of atmosphere. Journal Geophys. Res., 96: 10981–10988.
Peters, O. y K. Christensen. 2002. Rain: Relaxations in the sky. Physical Review E.
Peters, O., C. Hertlein y K. Christensen. 2002. Complexity view of rainfall. Physical Review Letters, 88(1).
Peters, O. y D. Neelin. 2006a. Critical phenomena in atmospheric precipitation-Supplementary Information. nature physics.
Peters, O. y J. D. Neelin. 2006b. Critical phenomena in atmospheric precipitation. Nature physics, 2: 393–396.
Privman, V., P. Hohenberg y Aharony. 1991. A. in Phase Transitions and Critical Phenomena. Academic, New York, 14: 1–134.
Pruessner, G. y O. Peters. 2006. Self-organized criticality and absorbing states: Lessons from the Ising model. Physical Review E, 73(025106).
Puyeyo, S. 2011. Self organised criticality and the response of wildland fires to climate change. Climatic Change, 82: 131–161.
Ramirez, R. 2000. Autocriticalidad de los incendios forestales. Tesis Doctoral, Universidad Nacional de Estudios a Distancia.
Raup, M. D. 1986. Bilogical extinction in earth history. Science, 251: 1530–1532.
Reynoso, C. 2007. Complejidad y el Caos: Una exploración antropológica. Universidad de Buenos Aires.
Roopun, Kramer, Carracedo, Kaiser, Davies, Traub, Kopell y Whittington. 2008. Temporal interactions between cortical rhythms. Front. Neurosci., 2: 145–154.
Sekar, I. 2007. Realization of soc behavior in a dc glow discharge plasma. Physics Letters A, 360: 717–721.
Sethna, J. 2010. Entropy, order parameters and Complexity. Clarendon, Oxford.
Steward, I. 1997. Does God play dice? Penguin Books.
Turcotte, D. L. 1985. Collapse of loaded fractal trees. Nature, 313: 671.
Wolf, B., D. Marks, E. Amital, D. Silberstein, B. Fisher, A. Tokay, J. Wang y L. Pippitt. 2005. Ground Validation for de Tropical Rainfall Measuring Mission (TRMM). American Meteorological Society.
Wolff, D. B., D. Marks, E. Amitai, D. Silberstein, B. Fisher, A. Tokay, J. Wang y J. Pippitt. 2004. Ground Validation for the Tropical Rainfall Measuring Mission (TRMM). American Meteorological Society.
Xu, K. y K. Emanuel. 1989. Is the tropical atmosphere conditionally unstable? . Monthly Weather Review, 117: 1471–1479.
a
Yeomans, J. 1992. Statistical Mechanics of Phase Transitions. Clarendon, Oxford.
Zhang, G., U. Tirnakli, L. Wang y T. Chen. 2011. Self organized criticality in a modified Olami-FederChristensen model. The European Physical Journal B, 82: 83–89.
Zhang, Y. y S. Klein. 2010. Mechanisms Affecting the Transition from Shallow to Deep Convection over Land: Inferences from Observations of the Diurnal Cycle Collected at the ARM Southern Great Plains Site. Journal of atmospheric sciences.