NPG Nonlinear Processes in Geophysics NPG Nonlin. Processes Geophys. 1607-7946 Copernicus Publications Göttingen, Germany 10.5194/npg-20-1079-2013 Scaling properties of rainfall and desert dust in the Canary Islands Peñate I. 1 Martín-González J. M. 2 Rodríguez G. 2 Cianca A. 2 Agencia Estatal de Meteorología, Delegación Territorial en Canarias, C/ Historiador Fernando de Armas, 12, 35017, Las Palmas de Gran Canaria, Spain Departamento de Física, Universidad de Las Palmas de Gran Canaria, 35017, Las Palmas de Gran Canaria, Spain 09 12 2013 20 6 1079 1094 Copyright: © 2013 I. Peñate et al. 2013 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://npg.copernicus.org/articles/20/1079/2013/npg-20-1079-2013.html The full text article is available as a PDF file from https://npg.copernicus.org/articles/20/1079/2013/npg-20-1079-2013.pdf

Precipitation and desert dust event occurrence time series measured in the Canary Islands region are examined with the primary intention of exploring their scaling characteristics as well as their spatial variability in terms of the island's topography and geographical orientation. In particular, the desert dust intrusion regime in the islands is studied in terms of its relationship with visibility. Analysis of dust and rainfall events over the archipelago exhibits distributions in time that obey power laws. Results show that the rain process presents a high clustering and irregular pattern on short timescales and a more scattered structure for long ones. In contrast, dustiness presents a more uniform and dense structure and, consequently, a more persistent behaviour on short timescales. It was observed that the fractal dimension of rainfall events shows an important spatial variability, which increases with altitude, as well as towards northern latitudes and western longitudes.

 References Alonso-Pérez, S., Cuevas, E., Querol, X., Viana, M., and Guerra, J. C.: Impact of the Saharan dust outbreaks on the ambient levels of total suspended particle (TSP) in the Marine Boundary Layer (MBL) of the Subtropical Eastern North Atlantic Ocean, Atmos. Environ., 41/40, 9468–9480, <a href="http://dx.doi.org/10.1016/j.atmosenv.2007.08.049">https://doi.org/10.1016/j.atmosenv.2007.08.049</a>, 2007. Alonso-Pérez, S., Cuevas, E., Pérez, C., Querol, X., Baldasano, J. M., Draxler, R., and Bustos, J. J.: Trend changes of African air mass intrusions in the marine boundary layer over the subtropical eastern North Atlantic region in winter, Tellus B, 63, 255–265, <a href="http://dx.doi.org/10.1111/j.1600-0889.2010.00524.x">https://doi.org/10.1111/j.1600-0889.2010.00524.x</a>, 2011. Ångström, A.: On the Atmospheric Transmission of Sun Radiation and on Dust in the Air, Geogr. Ann., 11, 156–166, 1929. Arteaga, M. A., Delgado, J. D., Otto, R., Fernández-Palacios, J. M., and Arévalo, J. R.: How do alien plants distribute along roads on oceanic islands? A case study in Tenerife, Canary Islands, Biol. Invasions, 11, 1071–1086, 2009. Baddock, M. C., Strong, C., Murray, P., and McTainsh, G.: Aeolian dust as a transport hazard, Atmos. Environ., 17, 7–14, 2013. Barabási, A. L. and Albert, R.: Emergence of scaling in random networks, Science, 286, 509–512, 1999. Basart, S., Pérez, C., Cuevas, E., Baldasano, J. M., and Gobbi, G. P.: Aerosol characterization in Northern Africa, Northeastern Atlantic, Mediterranean Basin and Middle East from direct-sun AERONET observations, Atmos. Chem. Phys., 9, 8265–8282, <a href="http://dx.doi.org/10.5194/acp-9-8265-2009">https://doi.org/10.5194/acp-9-8265-2009</a>, 2009. Bäumer, D., Vogel, B., Versick, S., Rinke, R., Möhler, O., and Schnaiter, M.: Relationship of visibility, aerosol optical thickness and aerosol size distribution in an ageing air mass over South-West Germany, Atmos. Environ., 42, 989–998, 2008. Ben Mohamed, A., Frangi, J. P., Fontan, J., and Druilhet, A.: Spatial and temporal variations of atmospheric turbidity and related parameters in Niger, J. Appl. Meteorol., 31, 1286–129, 1992. Bergametti, G., Gomes, L., Coudé-Gaussen, G. , Rognon, P., and Le Coustumer, M.-N.: African dust observed over Canary Islands: Source-regions identification and transport pattern for some summer situations, J. Geophys. Res., 94, 14855–14864, <a href="http://dx.doi.org/10.1029/JD094iD12p14855">https://doi.org/10.1029/JD094iD12p14855</a>, 1989. Boettcher, S. and Paczuski, M.: Ultrametricity and memory in a solvable model of self-organized criticality, Phys. Rev. E, 54, 1082–1095, 1996. Boffetta, G., Carbone, V., Giuliani, P., Veltri, P., and Vulpiani, A.: Power laws in solar flares: Self-organized criticality or turbulence?, Phys. Rev. Lett., 83, 4662–4665, <a href="http://dx.doi.org/10.1103/PhysRevLett.83.4662">http://dx.doi.org/10.1103/PhysRevLett.83.4662</a>,1999. Boreson, J., Diller, A. M., and Peccia, J.: Correlating bioaerosol load with PM2.5 and PM10cf concentrations: a comparison between natural desert and urban-fringe aerosols, Atmos. Environ., 38, 6029–6041, <a href="http://dx.doi.org/10.1016/j.atmosenv.2004.06.040">https://doi.org/10.1016/j.atmosenv.2004.06.040</a>, 2004. Burroughs, S. M. and Tebbens, S. F.: Upper-Truncated Power Laws in Natural Systems, Pure Appl. Geophys., 158, 741–757, 2001. Cello, G. and Malamud, B. D.: Fractal analysis for natural hazards, Geological Society Publishing House, London, 2006. Chen, Y.-C., Sung, Q.-C., Yu, T. T., and Sun, R. J.: Earthquake time series analysis by Cantor set model in Taiwan, Terr. Atmos. Ocean. Sci., 14, 85–98, 2003. Chiapello, I., Bergametti, G., Gomes, L., Chatenet, B., Dulac, F., Pimenta, J., and Suares, E. S.: An additional low layer transport of Sahelian and Saharan dust over the north-eastern Tropical Atlantic, Geophys. Res. Lett., 22, 3191–3194, 1995. Clauset, A., Shalizi, C. R., and Newman, M. E. J.: Power-law distributions in empirical data, SIAM Rev., 51, 661–703, 2009. Criado, C. and Dorta, P.: An unusual "blood rain" over the Canary Islands (Spain). The Storm of January 1999, J. Arid Environ., 55, 765–783, 2002. Custodio, E.: Aquifer overexploitation: What does it mean?, Hydrogeol. J., 10, 254–277, 2002. De, U. S., Khole, M., and Dandekar, M. M.: Natural Hazards Associated with Meteorological Extreme Events, Nat. Hazards, 31, 487–497, 2004. de Lima, M. I. P. and de Lima, J. L. M. P.: Investigating the multifractality of point precipitation in the Madeira archipelago, Nonlin. Processes Geophys., 16, 299–311, <a href="http://dx.doi.org/10.5194/npg-16-299-2009">https://doi.org/10.5194/npg-16-299-2009</a>, 2009. De Longueville, F., Hountondji, Y. C., Henry, S., and Ozer, P.: What do we know about effects of desert dust on air quality and human health in West Africa compared to other regions?, Sci. Total Environ., 409, 1–8, 2010. De Longueville, F., Hountondjib, Y. C., Ozer, P., Marticorenad, B., Chatenetde, B., and Henrya, S.: Saharan Dust Impacts on Air Quality: What Are the Potential Health Risks in West Africa?, Hum. Ecol. Risk Assess., 19, 1595–1617, <a href="http://dx.doi.org/10.1080/10807039.2012.716684">https://doi.org/10.1080/10807039.2012.716684</a>, 2012. De Longueville, F., Ozer, P., Doumbia, S., and Henry, S.: Desert dust impacts on human health: an alarming worldwide reality and a need for studies in West Africa, Int. J. Biometeorol., 57, 1–19, 2013. Dialmeida, G. A.: A model for Saharan Dust Transport, J. Clim. Appl. Meteorol., 25, 903–916, 1986. Díaz, J. P., Expósito, F. J., Torres, C. J., Herrera, F., Prospero, J. M., and Romero, M. C.: Radiative properties of aerosols in Saharan dust outbreaks using ground-based and satellite date: Applications to radiative forcing, J. Geophys. Res., 106, 18403–18416, <a href="http://dx.doi.org/10.1029/2001JD900020">https://doi.org/10.1029/2001JD900020</a>, 2001. Dickman, R.: Fractal rain distributions and chaotic advection, Braz. J. Phys., 34, 337–346, 2004. Dubois, J. and Cheminee, J. L.: Fractal analysis of eruptive activity of some basaltic volcanoes, J. Volcanol. Geoth. Res., 45, 197–208, 1991. Fernandopullé, D.: Climatic characteristics of the Canary Islands, in: Biogeography and Ecology in the Canary Islands, Springer Netherlands, 30, 185–206, 1976. Fisher, M. C., Koenig, G. L., White, T. J., and Taylor, J. W.: Pathogenic Clones versus Environmentally Driven Population Increase: Analysis of an Epidemic of the Human Fungal Pathogen Coccidiodes immitis, J. Clin. Microbiol., 38, 807–813, 2000. Font Tullot, I.: El tiempo atmosférico en las islas Canarias, Servicio Meteorológico Nacional, Sección de Predicción, 1956 (in Spanish). García-Herrera, R., Puyol, D. G., Martín, E. H., Presa, L. G., and Rodriguez, P. R.: Influence of the North Atlantic Oscillation on the Canary Islands Pecipitation, J. Climate, 14, 3889–3903, 2001. García-Herrera, R., Gallego, D., Hernández, E., Gimeno, L., Ribera, P., and Calvo, N.: Precipitation trends in the Canary Islands, Int. J. Climatol., 23, 235–241, <a href="http://dx.doi.org/10.1002/joc.870">https://doi.org/10.1002/joc.870</a>, 2003. Goudie, A. S.: Dust storms: Recent developments, J. Environ. Manage., 90, 89–94, 2009. Goudie, A. S. and Middleton, N. J.: Saharan dust storms: nature and consequences, Earth Sci. Rev., 56, 179–204, 2001. Goudie, A. S. and Middleton, N.: Desert dust in the global system, edited by: Czeschlik, D., Springer Berling Heidelberg New York, Heidelberg, 2006. Heinold, B., Helmert, J., Hellmuth, O., Wolke, R., Ansmann, A., Marticorena, B., Laurent, B., and Tegen, I.: Regional modelling of Saharan dust events using LM-MUSCAT:Model description and case studies, J. Geophys. Res., 112, D11204, <a href="http://dx.doi.org/10.1029/2006JD007443">https://doi.org/10.1029/2006JD007443</a>, 2007. Holben, B. N., Tanré, D., Smirnov, A., Eck, T. F., Slutsker, I., Abuhassan, N., Newcomb, W. W., Schafer, J. S., Chatenet, B., Lavenu, F., Kaufman, Y. J., Vande Castle, J., Setzer, A., Markham, B., Clark, D., Frouin, R., Halthore, R., Karneli, A., O'Neill, N. T., Pietras, C., Pinker, R. T., Voss, K., and Zibordi, G.: An emerging ground-based aerosol climatology: Aerosol optical depth from AERONET, J. Geophys. Res., 106, 12067–12097, 2001. Izzo, M., Aucelli, P. P. C., and Mazzarella, A.: Recent changes in rainfalland air temperature at Agnone (Molise – Central Italy), Ann. Geophys.-Italy, 47, 1689–1698, <a href="http://dx.doi.org/10.4401/ag-3368">https://doi.org/10.4401/ag-3368</a>, 2004. Jankowiak, I. and Tanré, D.: Satellite climatology of Saharan dust outbreaks: Method and preliminary results, J. Climate, 5, 646–656, 1992. Juan, C., Emerson, B. C., Oromí, P., and Hewitt, G. M.: Colonization and diversification: towards a phylogeographic synthesis for the Canary Islands, Trends Ecol. Evol., 15, 104–109, <a href="http://dx.doi.org/10.1016/j.bbr.2011.03.031">https://doi.org/10.1016/j.bbr.2011.03.031</a>, 2000. Julià-Serdà, G., Cabrera, P., Acosta, O., Martín, P., Batista, J., Álamo, F., Rodríguez de Castro, F., and Antó, J. M.: High prevalence of asthma symptoms in the Canary Islands: climatic influence?, J. Asthma, 42, 507–511, 2005. Karyampudi, V. M., Palm, S. P., Reagen, J. A., Fang, H., Grant, W. B., Hoff, R. M., Moulin, C., Pierce, H. F., Torres, O., Browell, E. V., and Melfi, S. H.: Validation of the Saharan dust plume conceptual model using Lidar, Meteosat, and ECMWF data, B. Am. Meteorol. Soc., 80, 1045–1076, 1999. Kaufman, Y. J., Tanré, D., and Boucher, O.: A satellite view of aerosols in the climate system, Nature, 419, 215–223, 2002. Laherrère, J. and Sornette, D.: Stretched exponential distributions in Nature and Economy: "fat tails" with characteristic scales, Eur. Phys. J. B, 2, 525–539, 1998. Lerner, J. A., Westphal, D., and Reid, J.: Quality controlled surface visibility observations used to validate predicted surface aerosol concentration for southwest Asia, 20th Conference on Weather Analysis and Forecasting/16th Conference on Numerical Weather Prediction, Seattle, WA, 10–15 January 2004. Levin, Z. and Cotton, W. R. (Eds.): Aerosol pollution impact on precipitation: a scientific review, Springer, Springer Science+Business Media B.V., Netherlands, 2009. Liu, X., Yin, Z. Y., Zhang, X., and Yang, X.: Analyses of the spring dust storm frequency of northern China in relation to antecedent and concurrent wind, precipitation, vegetation, and soil moisture conditions, J. Geophys. Res., 109, D16210, <a href="http://dx.doi.org/10.1029/2004JD004615">https://doi.org/10.1029/2004JD004615</a>, 2004. Lovejoy, S., Schertzer, D., and Tsonis, A. A.: Functional box-counting and multiple elliptical dimensions in rain, Science, 235, 1036–1038, 1987. Lynn, B., Khain, A., Rosenfeld, D., and Woodley, W. L.: Effects of aerosols on precipitation from orographic clouds, J. Geophys. Res., 112, D10225, <a href="http://dx.doi.org/10.1029/2006JD007537">https://doi.org/10.1029/2006JD007537</a>, 2007. Mahowald, N. M., Baker, A. R., Bergametti, G., Brooks, N., Duce, R. A., Jickells, T. D., Kubilay, N., Prospero, J. M., and Tegen, I.: Atmospheric global dust cycle and iron inputs to the ocean, Global Biogeochem. Cy., 19, GB4025, <a href="http://dx.doi.org/10.1029/2004GB002402">https://doi.org/10.1029/2004GB002402</a>, 2005. Malamud, B. D. and Turcotte, D. L.: The applicability of power-law frequency statistics to floods, J. Hydrol., 322, 168–180, 2006. Mandelbrot, B. B.: The fractal geometry of nature, W. H. Freeman and Co., New York, USA, 1983. Martín, J. L., Bethencourt, J., and Cuevas, E.: Assessment of global warming on the island of Tenerife, Canary Islands (Spain). Trends in minimum, maximum and mean temperatures since 1944, Climatic Change, 114, 343–355, 2012. Mayer, L.: Fractal characteristics of desert storm sequences and implications for geomorphic studies, Geomorphology, 5, 167–183, 1992. Mazzarella, A.: Multifractal dynamic rainfall processes in Italy, Theor. Appl. Climatol., 63, 73–78, 1999. Mazzarella, A. and Diodato, N.: The alluvial events in the last two centuries at Sarno, southern Italy: their classification and time-power law occurrence, Theor. Appl. Climatol., 72, 75–84, 2002. Mazzarella, A. and Giuliacci, A.: The El Niño events: their classification and scale-invariance laws, Ann. Geophys.-Italy, 52, 517–522, 2009. Mazzarella, A. and Rapetti, F.: Scale-invariance in the recurrence interval of extreme floods: an application to the Upper Po River valley (Northern Italy), J. Hydrol., 288, 264–271, 2004. McTainsh, G. and Strong, C.: The role of aeolian dust in ecosystems, Geomorphology, 89, 39–54, 2007. Mitzenmacher, M.: A Brief History of Generative Models for Power Law and Lognormal Distributions, Internet Mathematics, 1, 226–251, <a href="http://dx.doi.org/10.1080/15427951.2004.10129088">https://doi.org/10.1080/15427951.2004.10129088</a>, 2003. Newman, M. E. J., Barabási, A.-L., and Watts, D. J.: The Structure and Dynamics of Networks, Princeton University Press, Princeton, New Jersey, 2006. Olsson, J., Niemczynowicz, J., Berndtsson, R., and Larson, M.: An analysis of the rainfall time structure by box-counting – some practical applications, J. Hydrol., 137, 261–277, 1992. Olsson, J., Niemczynowicz, J., and Berndtsson R.: Fractal Analysis of High-Resolution Rainfall Time Series, J. Geophys. Res., 98, 23265–23274, 1993. Pelletier, J. D.: Cantor set model of eolian dust deposits on desert alluvial fan terraces, Geology, 35, 439–442, 2007. Potter, T. D. and Colman, B. R. (Eds.): Handbook of weather, climate, and water: Atmospheric chemistry, hydrology, and societal impacts, Wiley-Interscience, Michigan, USA, 2003. Prospero, J. M. and Lamb, J. P.: African droughts and dust transport to the Caribbean: Climate change and implications, Science, 302, 1024–1027, 2003. Puyol, D. G., Herrera, R. G., Martín, E. H., Presa, L. G., and Rodríguez, P.: Major influences on precipitation in the Canary Islands, Climatic Change: Implications for the Hydrological Cycle and for Water Management, Adv. Glob. Change Res., 10, 57–73, 2002. Sánchez-Lerma, B., Morales-Chirivella, F. J., Peñuelas, I., Blanco Guerra, C., Mesa Lugo, F., Aguinaga-Ontoso, I., and Guillén-Grima, F.: High prevalence of asthma and allergic diseases in children aged 6 to 7 years from the Canary Islands: the International Study of Asthma and Allergies in Childhood, J. Invest. Allerg. Clin., 19, 383–390, 2009. Sassen, K., DeMott, P. J., Prospero, J. M., and Poellot, M. R.: Saharan dust storms and indirect aerosol effects on clouds: CRYSTAL-FACE results, Geophys. Res. Lett., 30, 1633, <a href="http://dx.doi.org/10.1029/2003GL017371">https://doi.org/10.1029/2003GL017371</a>, 2003. Schertzer, D., Tchiguirinskaia, I., Lovejoy, S., and Tuck, A. F.: Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply, Atmos. Chem. Phys., 12, 327–336, <a href="http://dx.doi.org/10.5194/acp-12-327-2012">https://doi.org/10.5194/acp-12-327-2012</a>, 2012. Schroeder, M.: Fractals, chaos, power laws: Minutes from an infinite paradise, W. H. Freeman Co., New York, USA, 1991. Shi, Z. B., Woodhouse, M. T., Carslaw, K. S., Krom, M. D., Mann, G. W., Baker, A. R., Savov, I., Fones, G. R., Brooks, B., Drake, N., Jickells, T. D., and Benning, L. G.: Minor effect of physical size sorting on iron solubility of transported mineral dust, Atmos. Chem. Phys., 11, 8459–8469, <a href="http://dx.doi.org/10.5194/acp-11-8459-2011">https://doi.org/10.5194/acp-11-8459-2011</a>, 2011. Slingo, A., Ackerman, T. P., Allan, R. P., Kassianov, E. I., McFarlane, S. A., Robinson, G. J., Barnard, J. C., Miller, M. A., Harries, J. E., Russell, J. E., and Dewitte, S.: Observation of the impact of a major Saharan dust storm on the atmospheric radiation balance, Geophys. Res. Lett., 33, L24817, <a href="http://dx.doi.org/10.1029/2006GL027869">https://doi.org/10.1029/2006GL027869</a>, 2006. Smalley, R. F., Chatelain, J. L. Turcotte, D. L., and Prévot, R.: A fractal approach to the clustering of earthquakes: applications to the seismicity of the New Hebrides, B. Seismol. Soc. Am., 77, 1368–1381, 1987. Sornette, D.: Critical phenomena in natural sciences: Chaos, fractals, self-organization, and disorder: Concepts and tools, 2nd Edn., Springer Series in Synergetics, Springer-Verlag, Heidelberg, 2004. Sperling, F. N., Washington, R., and Whittaker, R. J.: Future climatic change of the subtropical North Atlantic: implications for the cloud forests of Tenerife, Climatic Change, 65, 103–123, 2004. Stumpf, M. P. H. and Porter, M. A.: Critical truths about power laws, Science, 335, 665–666, <a href="http://dx.doi.org/10.1126/science.1216142">https://doi.org/10.1126/science.1216142</a>, 2012. Suchodoletz, H., Glaser, B., Thrippleton, T., Broder, T., Zang, U., Eigenmann, R., Kopp, B., Reichert, M., and Ludwig, Z.: The influence of Saharan dust deposits on La Palma soil properties (Canary Islands, Spain), Catena, 103, 44–52, 2013. Takayasu, H.: Fractals in the Physical Science, Manchester University Press, New York, 1990. Tsallis, C.: Introduction to nonextensive statistical mechanics: Approaching a complex world, Springer, New York, 2009. Turcotte, D. L.: Fractals and chaos in geology and geophysics, Cambridge University Press, New York, 1997. Veza, J. M.: Desalination in the Canary Islands: an update, Desalination, 133, 259–270, 2001. Viana, M., Querol, X., Alastuey, A., Cuevas, E., and Rodríguez, S.: Influence of African dust on the levels of atmospheric particulates in the Canary Islands air quality monitoring network, Atmos. Environ., 36, 5861–5875, 2002. Virkar, Y. and Clauset, A.: Power-law distributions in binned empirical data, pre-print, available at: <a href="http://arxiv.org/abs/1208.3524">http://arxiv.org/abs/1208.3524</a>, last access: 26 February 2013, 2012. Wauben, W. M.: Comparison of Visibility Measurements with Routine Visual Observations in The Netherlands, in: 3rd International Conference on Experiences with Automatic Weather Stations, Torremolinos, Spain, 2003. West, G. B., Brown, J. H., and Enquist, B. J.: A general model for the origin of allometric scaling laws in biology, Science, 276, 122–126, <a href="http://dx.doi.org/10.1126/science.276.5309.122">https://doi.org/10.1126/science.276.5309.122</a>, 1997. Westphal, D. L., Toon, O. B., and Carlson, T. N.: A case study of mobilization and transport of Saharan dust, J. Atmos. Sci., 45, 2145–2175, 1988. White, E. P., Enquist, B. J., and Green, J. L.: On estimating the exponent of power-law frequency distributions, Ecology, 89, 905–912, 2008. WMO (World Meteorological Organization): Manual on Codes, Suppl. 6 (VIII.2007), WMO, Geneva, Switzerland, 1995. Yoon, Y. J., Ceburnis, D., Cavalli, F., Jourdan, O., Putaud, J. P., Facchini, M. C., Decesari, S., Fuzzi, S., Sellegri, K., Jennings, S. G., and O'Dowd, C. D.: Seasonal characteristics of the physicochemical properties of North Atlantic marine atmospheric aerosols, J. Geophys. Res., 112, D4206, <a href="http://dx.doi.org/10.1029/2005J007044">https://doi.org/10.1029/2005J007044</a>, 2007. Zachow, C., Berg, C., Müller, H., Meincke, R., Komon-Zelazowska, M., Druzhinina, I. S., Kubicek, C. P., and Berg, G.: Fungal biodiversity in the soils/rhizospheres of Tenerife (Canary Islands): Relationship to vegetation zones and environmental factors, ISME J., 3, 79–92, 2008.