Scaling properties of rainfall and desert dust in the Canary Islands

Nonlin. Processes Geophys., 20, 1079–1094, 2013 www.nonlin-processes-geophys.net/20/1079/2013/ doi:10.5194/npg-20-1079-2013 © Author(s) 2013. CC Attribution 3.0 License. Nonlinear Processes in Geophysics Open Access Scaling properties of rainfall and desert dust in the Canary Islands I. Peñate1, J. M. Martín-González2, G. Rodríguez2, and A. Cianca2 1Agencia Estatal de Meteorología, Delegación Territorial en Canarias, C/ Historiador Fernando de Armas, 12, 35017, Las Palmas de Gran Canaria, Spain 2Departamento de Física, Universidad de Las Palmas de Gran Canaria, 35017, Las Palmas de Gran Canaria, Spain Correspondence to: I. Peñate ([email protected]) Received: 20 July 2013 – Revised: 8 October 2013 – Accepted: 23 October 2013 – Published: 9 December 2013 Abstract. 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. 1 Introduction Life on Earth critically depends on freshwater availability. In particular, human life, settlement, and any of their activities are restricted by the existence of such a vital resource. This fact is particularly evident in desert, arid, and semi-arid zones, where prolonged droughts are commonly related to health problems, soil erosion and massive population displacements. Hence, mankind largely depends upon precipitation, the primary mechanism transporting water from the atmosphere to the planet surface, as a part of the water cycle, and a driving agent of many other processes. Consequently, temporal and spatial variability of precipitation are issues of general concern. Thus, positive or negative anomalies in precipitation regimes have severe impacts on freshwater availability for consumption, agriculture, terrain stability, desertification processes, and so on (e.g. Potter and Colman, 2003). Another aspect of huge importance for human life and the environment is the quality of the surrounding air. In this sense, air composition normally includes some fraction of solid material, which generally results from anthropogenic air pollution, biomass burning, or soil erosion by wind. In particular, mineral dust from desert, arid, and semi-arid regions can be eroded and suspended in the air, giving rise to dust storms, also referred to as desert dust outbreaks or intrusions. Dust can be transported by wind over large distances on Earth’s surface and, as a consequence, its effects can be felt in regions far away from the dust sources. Suspended, transported and deposited mineral dust has a broad range of important socioeconomic and environmental implications. In general, dust storms reduce visibility and disrupt daily life and economic activities. Desert aeolian emissions play an important role in regional weather and climate (Sassen et al., 2003). For instance, the impact of dust storms on the Earth–atmosphere radiative system has been studied by some authors (Slingo et al., 2006; Heinold et al., 2007; Kaufman et al., 2002; Sassen et al., 2003). The aerosol effects on precipitation formation and distribution have also been considered (Lynn et al., 2007). Others interesting aspects are that mineral aerosols exert an important influence over the distribution of soil nutrients (Mahowald et al., 2005; Yoon et al., 2007), induce changes in soil characteristics (McTainsh and Strong, 2007) and cause adverse effects on human health (Boreson et al., 2004; Fisher et al., 2000; Goudie, 2009; De Longueville et al., 2010, 2012, 2013). Additionally, large concentrations of aeolian emissions could lead to problems in transport operations (Baddock et al., 2013). Mineral dust deposition on the ocean surface represents an input of micronutrients and, as PublishedbyCopernicusPublicationsonbehalfoftheEuropeanGeosciencesUnion&theAmericanGeophysicalUnion. 1080 I. Peñate et al.: Scaling properties of rainfall and desert dust a consequence, partially controls the productivity of marine ecosystems (Shi et al., 2011). A detailed list of environmental consequences and hazards to human population caused by dust storms, as well as an excellent review of causes and effects of dust storms, can be found in Goudie and Middleton (2006). Previous comments are of particular concern for the Canaries, due to their low pluviometry and proximity of the Sahara, which produces more than half of the yearly global mineral dust (De Longueville et al., 2010). The hydraulic resources directly derived from rainfall in the archipelago are scarce. Hydric conditions have worsened with demographic increase and tourism development, giving rise to the aquifers’ overexploitation (Custodio, 2002), but have been partially alleviated through the construction of reservoirs and by a great development in seawater desalination technology (Veza, 2001). On the other hand, desert dust intrusions are a common phenomenon in the archipelago, which is located along one of the three major Sahara dust pathways and within one of the North Atlantic Ocean surface parcels with higher annual dust deposition rates (Goudie and Middleton, 2001). Furthermore, two source regions of dust (Sahelian and Sahara) related to different atmospheric pathways of the desert mineral dust affect the Canary Islands (Bergametti et al., 1989). The most important aerosol invasions over the area of the Canaries respond to a long-range transport pattern. Aeolian emissions stemming from the Sahara, the largest dust source in the world, can reduce the visibility over the islands to a few kilometres (Díaz et al., 2001). As a consequence, the following impacts on the islands concerning desert dust intrusions have been reported: air traffic managing (Criado and Dorta, 2002), changes in soil properties (Suchodoletz, 2013) and health (Juliá-Serdá et al., 2005; Sánchez-Lerma et al., 2009). In brief, rain events, droughts, and desert dust outbreaks are natural phenomena, related to the atmospheric dynamics, which under some conditions can turn into natural catastrophes (De et al., 2004). Owing to their highly complex nature, these processes are not fully understood and deserve further study. The Canary Islands constitute an isolated spot poorly studied from a climatic point of view (e.g. Puyol, et al., 2002). In this sense, de Lima and de Lima (2009) properly pointed out that precipitation studies on the islands are scarce and based on large temporal scales. Moreover, a recent review (De Logueville et al., 2013) on desert dust impacts on human health stresses the need to carry out studies on Saharan dust impact in western Africa, where dust events are more frequent and intense than anywhere else. Nevertheless, the atmosphere is a highly non-linear and complex dynamical system. Hence, as with many others meteorological phenomena, rainfall is characterised by very complex dynamics exhibiting wide variability over a broad range of time and space scales. Similarly, the presence of desert dust in the atmosphere and its variability depends on an intricate combination of processes and interactions. Turbulent wind action over source areas and favourable synoptic conditions to transport dust to the interest area are some of them (Liu et al., 2004). The turbulent nature of atmospheric flows could play a relevant role in the physical process behind rainfall and desert dust. Some authors have shown that turbulence is related to some features such as solar flare activity (Boffetta et al., 1999). Additionally, rainfall variability and dust storm occurrence are mutually related to complex and not yet well understood mechanisms. Thus, rainfall is one of the most important factors controlling the occurrence of mineral dust erosion from soils. Rainfall in the source area reduces dust erosion, while intense erosion is commonly related to episodes of drought (Prospero and Lamb, 2003). On the other hand, the presence of desert dust in the atmosphere has an effect on rainfall in a still not well known way. Several papers provide no definitive and even contradictory results (e.g. Levin and Cotton, 2009) about these issues. Because of the high complexity of atmospheric processes, conventional statistical methods have proved to be quite inefficient to describe the statistical structure of phenomena such as rainfall over a wide range of scales. However, it has been shown that many complex processes occurring in Earth’s atmosphere exhibit fractal or power law scaling (e.g. Dickman,2004),particularly rainfalloccurrences(Mazzarellaand Diodato, 2002). That is, statistical properties of a given process are similarly related to each other over a wide range of scales. Thus, exploration of invariance properties across scales offers an alternative approach to quantify the variability of rainfall and desert dust emission processes. Considering the need to improve knowledge on the variability of rainfall and desert aerosol outbreaks in the Canary Islands and the intrinsic complexity of these phenomena, the main goal of this study is to contribute to a better understanding of their temporal scaling properties, as well as their spatial variability. Specifically, the study intends to explore the desert dust intrusion intensity and duration, at low atmospheric levels, in terms of the horizontal visibility reduction. The rest of the paper is organised as follows. The next section presents a brief description of topographic and climatic featuresofthe archipelago, as well as the main characteristics of the data sets examined in the study. Data analysis methods used to explore scaling properties in rainfall and desert dust observations are described in Sect. 3. Section 4 contains results derived from the analysis of experimental data and their discussion. Finally, Sect. 5 outlines the main conclusions of the study. 2 Study area and data sets 2.1 Study area The Canary archipelago, constituted by seven inhabited islands (Lanzarote, Fuerteventura, Gran Canaria, Tenerife, Nonlin. Processes Geophys., 20, 1079–1094, 2013 www.nonlin-processes-geophys.net/20/1079/2013/ I. Peñate et al.: Scaling properties of rainfall and desert dust 1081 La Palma, La Gomera, and El Hierro), is a Spanish autonomous community and the outermost region of the European Union. It is located in the Atlantic Ocean, bounded by 27◦370and 29◦300N latitudes and 13◦300and 18◦100W longitudes (Fig. 1). Generated as the result of volcanic activity on the African continental shelf, it forms a chain with a roughly linear arrangement extending about 500km in the longitudinal direction. Its eastern edge lies only 100km from the Saharan coast. The orography and topography of the islands are highly variable, with sharp differences between and within islands. Elevation changes from a maximum height of about 3718ma.s.l., in Tenerife, to elevations rarely above 600m in the eastern islands (Lanzarote and Fuerteventura). La Palma, Gran Canaria, El Hierro and La Gomera, also exhibit high elevations, close to 2400, 1950, 1500, and 1490m, respectively. In general, the islands’ orography is very rugged, except in the flat eastern islands. This densely populated oceanic archipelago has a combination of subtropical, semi-arid and semi-humid conditions (Sperling et al., 2004) with strong orographic, topographic, meteorological and ecological contrasts. Due to their location in the Atlantic subtropical belt and being dominated almost all year by the Azores High, which prevents transient disturbances as Atlantic lows, the typical weather in the Canaries can be considered stable and dry. The islands are exposed to the predominant trade winds, blowing over the Atlantic from the northeast for almost the whole year and driving one of the major coastal upwelling ecosystems in the world along the NW African coast (Fernandopullé, 1976). Their oceanic position, within an area affected by both coastal upwelling and Saharan mineral dust eolian inputs, strongly influences their climate, which is characterised by a low annual thermal oscillation ranging from 18◦C during winter to 24◦C in summer and influenced mainly by cloudiness, altitude and orientation (Font-Tullot, 1956; Martín et al., 2012). The proximity to the Sahara converts the archipelago into a very complex scenario. Between approximately 700 and 1500 m a subsidence inversion is often present. Above the inversion layer, the air is dry and clear. The existence of two astronomical observatories, El Roque de los Muchachos (La Palma) and El Teide (Tenerife), reveals the presence of clear skies with excellent air quality. Below the inversion layer, the presence of a fresh and humid boundary layer explains the marked contrast between the windward side with green valleys in the north and the leeward side of the islands with sandy beaches. Vegetation zones can be classified into humid and semi-arid types (Juan et al., 2000). When prevailing trade winds reach the higher islands, moisture is condensed, bringing cloudiness, humidity and sometimes rain to the northern sectors. Hence, northern locations are generally dull, wet and cloudy, while southern ones are characterised by dry clear days with sunshine. The main feature of the rainfall regime in the Canaries is itsirregularity. The location of the islands,farfrom the belt of low pressures in the medium latitudes, explains the low rate Fig. 1. Geographic location of the Canary Islands and recording stations used in the study. The airport is the only station included for Gran Canaria in this figure, the others are shown in Fig. 2. of precipitation throughout the islands. However, the combined effect of the trade winds and the abrupt relief makes some places of these islands much wetter than the normal pattern at this latitude. The island’s averaged precipitation regimes show a strong seasonality with maximum monthly rainfall during autumn and winter and dry or rainless months in spring and summer. The relief is one of the critical variables controlling the local rainfall distribution. In general, precipitation increases across the archipelago from east to west. Frontal tails associated with surface disturbances affect predominately the western and higher islands, which are much wetter. Conversely, the eastern islands are characterised by dry and stable meteorological conditions almost all year round and are quite arid (García-Herrera et al., 2001, 2003). The key role played by the topographic and orographic complexity of the islands is noteworthy. Predominant trade winds interact with the relief of the islands to generate mesoscale and microscale meteorological phenomena, leading to a large variability of microclimates. As result, the islands show a great biodiversity characterised by a large variety of species classified as tropical, subtropical, arid, semi-arid or Mediterranean (Arteaga et al., 2009; Zachow et al., 2008) and containing a great proportion of endemic ones. Among other important factors, the cold Canary Current is responsible for inducing atmospheric stability and, therefore, reduces the probability of development of subtropical systems and the occurrence of heavy winds or rainfall associated with them. Their almost latitudinal disposition and abrupt topography induce perturbations in the Canary Current and North Atlantic trade wind persistent flow, in which they are immersed. In conclusion, the Canary Islands constitute a unique and highly complex environment to explore space and time properties of processes related to the atmospheric dynamics. www.nonlin-processes-geophys.net/20/1079/2013/ Nonlin. Processes Geophys., 20, 1079–1094, 2013 1082 I. Peñate et al.: Scaling properties of rainfall and desert dust 2.2 Data sets With reference to the previous comments, considerable spatial non-uniform rainfall and desert dust events are common in the study region. Hence, to take into account this spatial heterogeneity, data from various representative measurement points have been used. Rainfall and dust intrusion time series have been extracted from archives provided by Aemet (National Meteorological Service of Spain). Particularly, METeorological Aerodrome Reports (METARs) from three aerodromes of reference have been used. Such reports contain encoded information on atmospheric parameters and are made by trained certified weather observers who review and encode the observations. This procedure is developed following a protocol regulated by the World Meteorological Organization (WMO, 1995), in consort with the International Civil Aviation Organization (ICAO), and using a general global standard format. Data on Saharan dust levels are obtained by using a standard scale of visibility. Sahara dust can be distinguished from other causes by means of several features such as its colour, relative humidity, or visibility reduction. The parameters extracted from METARs to be used in this study are visibility (km), rainfall (mmm−2), wind direction (angular degrees) and wind speed (kmh−1). The visibility is defined as the maximum distance that a black object of suitable dimensions can be seen near the horizon (Wauben, 2003). The observations of visibility used in this study were determined by a human observer using several landmarks. Special attention is paid to this parameter since low visibility could have disastrous impacts on air traffic. A considerable amount of research has looked into the relationship between visibility and aerosol properties or concentration (e.g. Dialmeida, 1986; Ben Mohamed et al., 1992; Bäumer et al., 2008). It is therefore reasonable to use visibility measurements as a proxy to explore desert dust events. A very important advantage provided for this study, in spite of the intrinsic uncertainties of this traditional measurement procedure, is the availability of long-term horizontal visibility observations, from which intensity and duration of dust events can be inferred. As a criterion for this work, a dust event duration has been defined as the number of dusty days, considering a day dusty when during a 24 h period a dust observation with visibility equal to, or lower than, 8km is reported. The intensity of the dust event is estimated by the minor visibility recorded. For the selection of dust events, visibility data were considered only if the METAR included one of the following phenomena: haze (HZ), widespread dust in suspension in the air (DU), drifting dust raised by wind at or near the station at the time of observation (DRDU), dust storm (DS) or blowing dust (BLDU). Moreover, a rainfall event was considered when some of these descriptors were included in the METAR: RA (rain), SHRA (shower), TS (thunder storm) or DZ (drizzle). Aerodromes chosen as reference are those from Gran Canaria (GCLP), Fuerteventura (GCFV) and La Palma (GCLA) (Fig. 1). These weather stations were selected based on availability of long data sets and representativeness. Gran Canaria airport, located at 27.93◦N and 15.39◦W, with an elevation of 24m, an international high density traffic airport operational 24 h a day provides a good quality METARsbased data set. Fuerteventura airport situated at 28.45◦N and 13.86◦W, with an elevation of 26m and placed at the eastern edge of the archipelago, gives appropriate measurements of dust incursions affecting the islands, due to its proximity to the Sahara. Finally, La Palma airport, in the western side, sited at 28.62◦N and 17.76◦W at 33ma.s.l. was also selected being affected by high precipitation when Atlantic lows influence the archipelago. Data acquisition was semi-hourly and only diurnal observations from 06:00 to 21:00UTC were considered. Analysed records cover a period of twenty two years, from January 1989 to December 2010. For La Palma, less observations than in the others airports were available because they were hourly until the end of March 2002 and semi-hourly from the beginning of April 2002 up to date. In addition, to explore the fractal dimension behaviour and regional differences of rainfall, daily data from 28 rain gauges (automatic and manual) for an average period of 42yr, from January 1969 to December 2010, have been analysed. Their locations are depicted in Figs. 1 and 2. These points have been selected on the basis of their geographical position, altitude and orientation, factors that contribute to explaining the observed rainfall regimes. Although time coverage varies between stations, the average recording period is considered suitable for the aims of the study. Nomenclature used to denote each measurement station is described below. The islands are divided into two provinces: Las Palmas (P) and Sta. Cruz de Tenerife (T). The aerodromes of reference are named by the airport codes: G. Canaria A/P (GCLP), Lanzarote A/P (GCRR), Fuerteventura A/P (GCFV), Tenerife north A/P (GCXO), Tenerife south A/P (GCTS), La Palma A/P (GCLA) and El Hierro A/P (GCHI). The highest point is Izaña (T5) with an elevation 2371m. The main part of the rest of the stations considered in this work are sited in Gran Canaria (Fig. 2), the most suitable island for this study because of its relative central position in the archipelago and medium elevations. 2.3 Synoptic conditions: numerical models Synoptic weather conditions favouring dust events over the islands have been detected by using analysis and reanalysis from numeric models over the three aerodromes of reference (Fuerteventura, Gran Canaria, and La Palma). This information covers a period of twenty one years, from January 1989 to December 2009. To detect and classify the more representative dust events, 36 episodes associated with visibility equal to, or lower than, 3km due to haze or dust observations Nonlin. Processes Geophys., 20, 1079–1094, 2013 www.nonlin-processes-geophys.net/20/1079/2013/ I. Peñate et al.: Scaling properties of rainfall and desert dust 1083 Fig. 2. Topographic map and geographic location of measurement stations in Gran Canaria. have been considered. To such end, compositions of geopotential height, wind, temperature and humidity fields in different pressure levels were examined. The final synoptic classification was based essentially on the isobaric configurations favouring dust incursions in low levels. Mesoscale analysis was considered for some particular cases, playing an important role on the prevailing wind direction and contributing to drive dust over the areas of study. Most synoptic charts used come from the ERA 40 reanalysis developed by the ECMWF (European Centre for Medium-Range Weather Forecasts) and included in the Meteorological Archival and Retrieval System (MARS). Additionally, these synoptic data were compared with reanalyses from the National Centre for Environmental Prediction (NCEP) and a counterpart of NOAA’s Earth System Research Laboratory (ESRL), the National Center for Atmospheric Research (NCAR), which is supported by the National Science Foundation (NSF). The comparison between reanalyses from different numerical models showed a high consistency. Inspection of surface analysis charts revealed that the most frequent mechanism that brings dust over the islands corresponds to a system of high pressures in northern Algeria, the western Mediterranean, the Iberian Peninsula and even the northern Azores. This system is often accompanied by a depression in the vicinity of the Canaries, predominately situated in the south or southwest. Such a situation generates southeasterly winds favouring the dust invasion over the archipelago. 2.4 Validation of dust events observations Despite being obtained by trained observers following a standardised procedure, as well as the special attention paid, including strict checking procedures due to its importance for air traffic, visual estimations of visibility entail some degree of subjectivity (Lerner et al., 2004). Two approaches have been applied to reduce uncertainty and improve confidence on visibility measurements derived from METARs. The first approach is based on the comparison of visibility data against in situ column optical depth data, gathered with a Cimel sunphotometer, and the other makes use of reanalysis information. Aerosol optical depth (AOD) data recorded from 2005 to 2010 by an AERONET (AErosol RObotic NETwork) station installed in Sta. Cruz de Tenerife (28.47◦N, 16.24◦W) at an altitude of 52m has been used to validate and improve confidence on dust episodes information encoded in METARs. AOD is a measurement of the dispersion and absorption of the visible light by the particles in a vertical column of the atmosphere. Hence, it provides information on the degree to which aerosols prevent the transmission of light and consequently represents an indicator of the amount of particulated matter in air. Among others authors, Ångström (1929) expressed its wavelength variation as AODλ∼λ−α, where the Ångström exponent, α, is a coefficient related to the aerosol size distribution and represents a measure of the relative abundance of fine to coarse-sized particles. The combined use of the AODλand the Ångström exponent estimated for a given pair of wavelengths, αλ1−λ2, is a useful approach to distinguish aerosols of diverse origin or types (e.g. Holben et al., 2001). Some parameters like AOD=AOD675nm and α=α440−870nm have been used by other authors (e.g. Basart et al., 2009) to characterise atmospheric aerosols in different AERONET sites around the Sahara (Holben, et al., 2001) and to establish some reference to distinguish desert mineral dust from other aerosol types. According to these authors, pure Saharan dust conditions are observed for 0.7<AOD <5, and α < 0.3. Additionally they conclude, by analysing data from Izaña AERONET station (with an elevation of 2371m), that Saharan dust can be represented by the pair AOD>0.15 and α < 0.25. Owing to the difficulty in establishing reliable criteria to classify mineral dust in the area of the Canary Islands from AERONET measurements, only events satisfying the above conditions have been considered in the validation study. Table 1 summarises the most representative dust occurrences recorded in METAR code, including the minor visibility and the dust event duration. The daily maximum value of AOD and the minimum of αfor the record were initially taken into account according to the above-mentioned criterion. In general, selecting the maximum daily value of AOD and minimum of αfor the record, most of the dust www.nonlin-processes-geophys.net/20/1079/2013/ Nonlin. Processes Geophys., 20, 1079–1094, 2013 1084 I. Peñate et al.: Scaling properties of rainfall and desert dust Table 1. Dust episodes encoded in METARs. Duration in hours and minor visibility in km for the Canaries. AOD675nm >0.15 and α440−870nm <0.25 for Sta. Cruz de Tenerife (2005–2010). Episode Most dusty Season Minor Duration AOD α day visibility (h) (km) 7–8 Feb 2006 8 Feb 2006 W 1 0.88 0.2262 0.1632 7–11 Mar 2006 7 Mar 2006 W 5 4.33 0.6848 0.0775 1 Apr 2006 1 Apr 2006 Sp 5 0.13 0.325 0.171 3 Sep 2006 3 Sep 2006 S 1.5 0.68 0.736 0.1075 6 Oct 2006 6 Oct 202006 A 7 0.02 0.904 0.0508 9–12 Nov 2006 11 Nov 2006 A 1 2.50 0.3977 0.0302 20–21 Nov 2006 20 Nov 2006 A 2 1 0.6382 0.1985 11 Jan 2007 11 Jan 2007 W 3 0.12 0.3502 0.1991 10 Mar 2007 10 Mar 2007 W 4 0.30 2.0293 0.1748 20–21 Jan 2008 20 Jan 2008 W 1.8 1.47 0.4968 0.1869 8 Feb 2008 8 Feb 2008 W 2.5 0.43 0.9298 0.1984 3–4 Apr 2008 3 Apr 2008 Sp 2.5 1.35 0.6672 0.1765 25–27 Apr 2008 26 Apr 2008 Sp 2.5 2.03 0.6063 0.2269 27 Jun 2008 27 Jun 2008 S 5 0.17 0.5469 0.2096 17–18 Jan 2010 18 Jan 2010 W 3 0.98 0.1682 0.1551 7 Feb 2010 7 Feb 2010 W 4 0.77 1.0564 0.0357 occurrences and the longest ones were related to a high AOD value and a low value of α. Figure 3 displays the temporal evolution of AOD675nm at Sta. Cruz de Tenerife, the duration of the dust episodes in days and the visibility in km derived from data sets in METAR code in the Canaries from 2005 to 2010 (for visibility and duration only the episodes included in Table 1 are represented). Results point out that at least during the longest dust intrusions observed in surface, a value of AOD characteristic of desert aerosol was also recorded. At a first glance, the analysis of data depicted in Fig. 3 indicates a low relationship between visibility and AOD data. Nevertheless, a proper interpretation of these results must take into account various aspects. Firstly, visibility observations represent horizontal integrations at surface level, whereas AERONET measurements are vertically integrated values at a given surface point. Additionally, the existence of a thermal inversion layer at a level between 1000 and 1500m during the main part of the year divides the trade wind flow into two layers. Dust intrusion events are commonly detected above the marine boundary layer (MBL) (Bergametti et al., 1989) mainly in the SAL (the Saharan air layer) (Karyampudi et al., 1999; Westphal et al., 1988) during early summer to early autumn, while desert dust emissions below this layer are commonly observed during winter and autumn (e.g. AlonsoPérez et al., 2011). Results achieved by examining atmospheric conditions during dust storm occurrences agree with those reported by other studies (e.g. Jankowiak and Tanré, 1992; Chiapello et al., 1995; Alonso-Pérez et al., 2007) which suggest that dust transportation over the NW African Fig. 3. Dust event duration in days (bars), surface visibility in km (circles) for Canaries, and AOD 657nm >0.15 for Sta. Cruz de Tenerife (dots) for the period 2005–2010. coast takes place in wintertime, predominately from December to May. In agreement with these results, dust episodes detected through METARs were also more frequent in winter, which supports the suitability of such observations for the intent of this study. In summary, dust intrusions can occur at high or low levels. AERONET measurements detect both type of events, but METAR data include only low-level events. Consequently, dust events examined in the present study are only those detected in atmospheric lower layers, which are very important due to their influence on human activities. The second approach to validate information on dust episodes encoded in METARs has been based on the use of information on synoptic atmospheric conditions, derived by reanalysis from numerical models. Following the experience Nonlin. Processes Geophys., 20, 1079–1094, 2013 www.nonlin-processes-geophys.net/20/1079/2013/ I. Peñate et al.: Scaling properties of rainfall and desert dust 1085 gained from previous studies (Alonso-Pérez et al., 2011), results from this analysis reveal that, regarding the dust events coming from the low troposphere affecting the islands, the most frequent mechanism corresponds to a system of high pressures in general located in northern Africa. This system is often accompanied by a depression in the vicinity of the Canaries, predominately situated in the south or southwest and relatively close to the western African coast. Such a situation generates southeasterly winds favouring the dust invasion over the archipelago. It is interesting to remark that during winter the Azores High weakens and displaces from its normal position (Díaz et al., 2001), which favours the synoptic scenario mentioned above. Results from the analysis of prevailing winds extracted from METARs when desert dust intrusions affect the islands increase the robustness of visibility surface observations used in this work. Thus, when the presence of such phenomena impliesvisibilitiesequalto,orlower than, 3.5km, a southerly or southeasterly wind pattern prevails and reveals dust emissions stemming from the Sahara. 3 Methodology A time series of a process shows scaling properties if it has the same statistical properties within a considerable range of scales. Exploring the existence of power law frequency statistical behaviour and fractal properties in time series of natural system has shown to be a successful approach to characterise their complexity (Mandelbrot, 1983; Schertzer, 2012). This section introduces the methods used in the present work to examine the scaling properties of rainfall and Saharan dust events in the studied area. 3.1 Power law frequency statistics Scaling invariance is present in a given process if the probability or frequency-size distributions of events (intensity or duration) obeys a power law (PL hereafter) relationship of the type f (x) =Cx−β, where Cis a constant, the value of f (x) is proportional to some power of the input x, and β is the scaling exponent (e.g. White et al., 2008). In a log–log representation, this power law distribution becomes a straight line and the scale exponent, β, is given by its slope. This behaviour occurs for values of the explanatory variable, x, higher than a given threshold, x0, that is, in the tail of the distribution. Phenomena which follow PL distributions are widespread in natural and social disciplines (e.g. Malamud and Turcotte, 2006). An important implication is that a PL is heavy-tailed, which indicates that extreme events occur at a higher frequency more than in other distributions such as the normal or exponential (e.g. Stumpf and Potter, 2012). Apart from this, the detection of a PL pattern in empirical data or in the time interval between them may indicate the presence of either long-range correlations or unusual underlying mechanisms like feedback loops, random network, self-organisation or phase transitions (West et al., 1997; Barabasi and Albert, 1999; Newman et al., 2006). This hypothesis also suggests possible presence of long-range correlations. One important limitation of this tool is the occurrence of the power law behaviour at the tail of the distribution where it is desirable to have the best accuracy (Stumpf and Potter, 2012). The tails of the empirical distributions present the largest fluctuation due to a lower number of observations. As a result of this, the uncertainty of the estimation of the exponent increases. Nevertheless, in this work, our aim is merely to provide a qualitative analysis on the existence of a power law behaviour in the examined phenomena, but not to obtain the exact power law pattern exhibited by the processes. On the other hand, the scaling laws do not always provide the best fit. Alternative distributions to characterise these environmental phenomena are the lognormal (Mitzenmacher, 2003), the stretched exponential (Laherrère and Sornette, 1998) and other truncated PLs (Burroughs and Tebbens, 2001; Tsallis, 2009). In spite of these difficulties, an advantage of the application of PL tools for diagnostic, characterisation and even prediction purposes is its simplicity. Moreover, in recent years, improved statistical tests have provided strong evidence of scaling laws over a substantial, although limited, range of scales (Clauset et al., 2009; Virkar and Clauset, 2012). 3.2 Fractal dimension Non-equilibrium phenomena following power laws verify general scaling relations and are, by definition, self-similar (Schroeder, 1991; Boettcher and Paczuski, 1996). Selfsimilarity is a key concept in the scaling properties exploration because it means that small sections of a time series cannot be distinguished from the whole signal after being properly scaled. That is, self-similar time series have a fractal structure. Thus, knowledge of its fractal dimension provides a way to relate information at different scales (e.g. Malamud and Turcotte, 2006). Many algorithms to estimate the fractal dimension have been proposed, each one with its advantages and drawbacks. The box-counting method is the oldest and more commonly used because it is intuitive and easy to apply (Lovejoy et al., 1987; Olsson et al., 1992, 1993). This technique has been successfully used on different natural processes like earthquakes (Chen et al., 2003), desert storms (Mayer, 1992), floods (Mazzarella and Rapetti, 2004), volcanology (Dubois and Cheminee, 1991), El Niño events (Mazzarella and Giuliacci, 2009), rainfall (Olsson et al., 1992,1993; Izzo et al., 2004; de Lima and de Lima, 2009) and eolian dust deposits on desert alluvial terraces (Pelletier et al., 2007). The method employed in this study to estimate the fractal dimension of dust and rain events is known as the Cantor dust method considered by other authors as a proper framework www.nonlin-processes-geophys.net/20/1079/2013/ Nonlin. Processes Geophys., 20, 1079–1094, 2013 1086 I. Peñate et al.: Scaling properties of rainfall and desert dust for non linear analysis like the fractal behaviour of rainfall occurrence (Mazzarella and Diodato, 2002). It is in fact a box-counting algorithm in which the space of observation represents the total length of the time series and the boxes correspond to the time intervals. The intervals or clusters of dust or rain events are taken as natural point processes (e.g. Mandelbrot, 1983; Turcotte, 1997; Takayasu, 1990). Thus, when applied to a time series, this method is based on dividing the space of observation, the time interval, T, into n non-overlapping segments of characteristic size, s, such that s=T /n for n=2,3,4,..., and computing the number N(s) of intervals of length soccupied by events. If the distribution of events has a fractal structure, then the relationship N(s) =CsDholds. The fractal or box-counting dimension Dfis estimated from the slope Dof the regression line of log(N(s)) on log(s). This parameter, Df=|D|, describes the strength of the rainfall or dust events gathered and can be used as a measure of the nature of the phenomenon, since it quantifies the scale-invariant clustering of the time series (Mazarella, 1998; Mazarella and Diodato, 2002). Clustering increases when Dapproaches 0. So, the smaller fractal dimensions correspond to clusters formed by events that occur sparsely (Izzo et al., 2004). If Dis close to 1, the events are randomly spaced in time. That is, they correspond to a more dense or uniform distribution and not to time clustering. To sum up, the box-counting method uses boxes to cover an object to find the fractal dimension (Olsson et al., 1992, 1993; de Lima and de Lima, 2009). The signal is partitioned into boxes of various sizes and the amount of non-empty squares is counted. A log–log plot of the number of boxes versus the size of the boxes is done. Signal binarisation, i.e. whether a box is occupied or not, implies a limitation of the method. 4 Results and discussion 4.1 Dust outbreak power-law Time series of minimum visibility registered during dust event occurrences over the Canaries, extracted from hourly records from the reference aerodromes (METARs), is shown in Fig. 4a, while the corresponding duration of each event is represented in Fig. 4b. It can be observed that there is no significant correlation between the intensity (reduced visibilities) of the dust intrusions and their durations. That is, prolonged intrusions do not commonly imply higher intensities and vice versa. Scatter plots (not shown) appear randomly when intensity versus duration is represented. Determination coefficients of linear regression are R2=0.09 for Gran Canaria, R2=0.18 for La Palma and R2=0.16 for Fuerteventura. These time series also present a wide interannual variability, which becomes clearer in the bar chart depicted in Fig. 5, in which the height of each bar indicates the number of events recorded during that year. Fig. 4. Visibility (km) (a) and duration (days) (b) of dust events (HZ, DU, DRDU or DS) over the Canaries for the period 1989– 2010 (METARs). The average number of events per year during the 22 yr period (1989–2010) analysed is close to 5 events per year, but clear dispersion around this value is observed with time. At a first glance, values of visibility reduction and duration of events represented in Fig. 4 reveal that, even when variability is notable, dust intrusions have a greater chance of occurring during winter months. This fact is clarified by representing the total number of events recorded during each month for the whole period (see Fig. 5 inset). During the study period, the number of dust intrusions that occurred from April to December is very similar. However, this uniformity disappears during the wintertime, where the frequency of occurrence experiences a noticeable increase peaking in February. Results from the seasonal analysis of dust events affecting low altitudes in the archipelago agree with those derived from the examination of synoptic conditions driving dust intrusions at low atmospheric levels and with previous studies (e.g. Jankowiak and Tanré, 1992; Viana et al., 2002). Figure 6 provides the distributions of dust event duration over the same locations. The frequency of dust occurrences is represented versus the number of consecutive dusty days. The histogram evidently shows that dust events of a short duration are more probable, whereas long events are rare, which may correspond to extreme events. The goodness of fit to a straight line obtained in the log–log representation shown in the inset figure, with R2=0.96 and root mean square error (RMSE)=0.29, reveals the presence of a PL relationship between the frequency of occurrence of dust events and their duration, in which the slope or scale exponent is β= −1.49±0.28. 4.2 Power law of dry periods The duration of intervals between rainy events in Gran Canaria A/P has been analysed by using the long data set Nonlin. Processes Geophys., 20, 1079–1094, 2013 www.nonlin-processes-geophys.net/20/1079/2013/ I. Peñate et al.: Scaling properties of rainfall and desert dust 1087 Fig. 5. Interannual and seasonal (inset figure) variability of dust occurrences over the Canaries during the period 1989–2010 (METARs). derived from METARs, to gain insight on the rainfall time distribution over the archipelago. This station has been selected because of the available long data set and its geographical location. It is important to note that METARs only take into account the occurrence or non-occurrence of rain events but not their intensity. This implies that a light rain is considered as rainfall occurrence in the same way as a heavy one. Hence, dry periods could be even longer than those detected in this study. The number of dry periods as a function of the durations is represented in Fig. 7. It can be observed that the number of dry events decreases sharply for low and moderate durations, but a small number of notably large events are present in the upper tail, with dry periods between rain events reaching durations of about 5months. This fact evidences that the data follow a heavy tail distribution and suggests that they may exhibit a power law behaviour. The log–log plot of the frequency of dry spells versus duration shown in the inset of Fig. 7 reveals the existence of a PL with exponent β= −1.75±0.25 (R2=0.90 and RMSE=0.42). As commented previously, it is remarkable that for very large durations data are scarce and sparse, and therefore this may influence the computed values of the exponent. These results agree with those reported in other studies (e.g. Mazzarella, 1999; Izzo et al., 2004). In general, the presence of long tail distributions is an indicator of the absence of some statistics like the mean or the variance, in particular for values of |β|<2, as those found in this work. When analysing dust and dry spell frequencies presented in this section, such statistics could be interpreted as infinite. This kind of distribution reveals the possibility of natural hazards (Cello and Malamud, 2006) and also suggests the existence of scale-invariant properties underlying critical phenomena Fig. 6. Histogram of dust events duration over the Canaries for the period 1989–2010 from METARs and log–log representation with fitted straight line (inset figure). Fig. 7. Histogram of time intervals (in days) between rain events for Gran Canaria airport, METARs (1989–2010), and log–log representation with fitted straight line (inset figure). (Sornette, 2004). Occurrences of dust and rain events following power laws might point out the existence of selforganised criticality, such as manifested in the high diversity of the climatic, topographic, or botanic features found throughout the archipelago. 4.3 Fractal characteristics Fractal behaviour of the dust occurrence regime has been examined by using time series extracted from METARs. To this end, semi-hourly data from reference aerodromes have been considered. The same approach has been followed to explore fractal characteristics of rainfall events. The fractal www.nonlin-processes-geophys.net/20/1079/2013/ Nonlin. Processes Geophys., 20, 1079–1094, 2013 , -- ' --:::- , u "' "',,,,,, .... --, ' "" '" --- "' 1094 I. Peñate et al.: Scaling properties of rainfall and desert dust 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: http://arxiv.org/abs/1208.3524, 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, doi:10.1126/science.276.5309.122, 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, doi:10.1029/2005J007044, 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. Nonlin. Processes Geophys., 20, 1079–1094, 2013 www.nonlin-processes-geophys.net/20/1079/2013/