Jorge Assis
email: jorgemfa@gmail.com

Ester Álvares Serrão
email: eserrao@ualg.pt

Nelson Castilho Coelho

Fernando Tempera

Myriam Valero

Filipe Alberto

Ester Álvares Serrão

Nelson Castilho Coelho

Past climate changes and strong oceanographic barriers structured low-latitude genetic relics for the golden kelp Laminaria ochroleuca

Keywords: Northeastern Atlantic Ocean Taxon: Laminaria ochroleuca climate change, range shifts, connectivity, genetic diversity, marine phylogeography, kelp forests

Introduction

The climate fluctuations of the Quaternary strongly influenced the dynamics of marine populations [START_REF] Maggs | Evaluating signatures of glacial refugia for north atlantic benthic marine taxa[END_REF][START_REF] Assis | Climate-driven range shifts explain the distribution of extant gene pools and predict future loss of unique lineages in a marine brown alga[END_REF][START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF][START_REF] Neiva | Climate Oscillations, Range Shifts and Phylogeographic Patterns of North Atlantic Fucaceae[END_REF]. During glacial periods (e.g., Last Glacial Maximum, LGM; ~21,000 yr BP), the higher latitudinal range margins of cold-to warm temperate species often retreated, particularly in the northern hemisphere, due to both sea surface temperatures (North Atlantic winter sea temperatures anomalies amount to ~10 °C; [START_REF] Strandberg | High-resolution regional simulation of last glacial maximum climate in Europe[END_REF] and advance of continental ice sheets (Hewitt, 2004). The restriction of populations to small suitable regions beyond ice margins (i.e., refugia) is frequently hypothesized [START_REF] Provan | Phylogeographic insights into cryptic glacial refugia[END_REF][START_REF] Neiva | Climate Oscillations, Range Shifts and Phylogeographic Patterns of North Atlantic Fucaceae[END_REF] but large low latitude expansions were also likely [START_REF] Kettle | Refugia of marine fish in the northeast Atlantic during the last glacial maximum: Concordant assessment from archaeozoology and palaeotemperature reconstructions[END_REF]Assis et al., 2017a). In contrast, during warmer interglacial periods (e.g., Holocene; ~12,000 yr BP to present time), refugial populations gradually recolonized formerly glaciated regions [START_REF] Maggs | Evaluating signatures of glacial refugia for north atlantic benthic marine taxa[END_REF][START_REF] Provan | Phylogeographic insights into cryptic glacial refugia[END_REF][START_REF] Neiva | Climate Oscillations, Range Shifts and Phylogeographic Patterns of North Atlantic Fucaceae[END_REF], and range contractions might have occurred at lower latitudes [START_REF] Assis | Climate-driven range shifts explain the distribution of extant gene pools and predict future loss of unique lineages in a marine brown alga[END_REF][START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF].

The demographic history of populations can be reflected in the present distribution of genetic diversity. Under extreme climate conditions, populations might have lost genetic diversity if effective sizes decreased drastically, increasing genetic drift [START_REF] Provan | The effects of past, present and future climate change on range-wide genetic diversity in northern North Atlantic marine species[END_REF], bottlenecks and local extinctions. Even more pervasive reductions of diversity could take place during range expansions owing to founder effects at leading edges (Excoffier et al., 2009;Neiva et al., 2012a;[START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF]. Conversely, in regions that kept long-term suitable habitats, persistent populations could accumulate ancient genetic diversity (Hewitt, 2004;[START_REF] Maggs | Evaluating signatures of glacial refugia for north atlantic benthic marine taxa[END_REF][START_REF] Provan | The effects of past, present and future climate change on range-wide genetic diversity in northern North Atlantic marine species[END_REF][START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF][START_REF] Neiva | Climate Oscillations, Range Shifts and Phylogeographic Patterns of North Atlantic Fucaceae[END_REF]. The number and isolation of refugia may have also played an important role in shaping the genetic variation of species [START_REF] Assis | Climate-driven range shifts explain the distribution of extant gene pools and predict future loss of unique lineages in a marine brown alga[END_REF].

The paradigm of range-shifting effects of past climate events might not be sufficient to explain the present patterns of diversity, as it may be changed by widespread contemporary dispersal [START_REF] Silva | Anchovies go north and west without losing diversity: Post-glacial range expansions in a small pelagic fish[END_REF] or local habitat conditions [START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF][START_REF] Lourenço | Upwelling areas as climate change refugia for the distribution and genetic diversity of a marine macroalga[END_REF]. For marine organisms, ocean currents influence relative isolation and connectivity of populations 1 1 1 ., 2017), keeping or diluting the signatures left by past climate changes ., 2017). Dispersal predictions are increasingly compared with genetic estimates, but not along species ranges (e.g., [START_REF] Billot | Current patterns, habitat discontinuities and population genetic structure: The case of the kelp Laminaria digitata in the English channel[END_REF][START_REF] Alberto | Isolation by oceanographic distance explains genetic structure for Macrocystis pyrifera in the Santa Barbara Channel[END_REF][START_REF] Coleman | Connectivity of the Habitat-Forming Kelp, Ecklonia radiata within and among Estuaries and Open Coast[END_REF][START_REF] Buonomo | Habitat continuity and stepping-stone oceanographic distances explain population genetic connectivity of the brown alga Cystoseira amentacea[END_REF]. Species with restricted dispersal generally hold fine-scale genetic differentiation (e.g., seaweeds: Neiva et al., 2012b;[START_REF] Assis | High and Distinct Range-Edge Genetic Diversity despite Local Bottlenecks[END_REF][START_REF] Robuchon | Contrasting genetic diversity patterns in two sister kelp species co-distributed along the coast of Brittany, France[END_REF], while those with larger dispersal probabilities (having larval stages) tend to have variable or little phylogeographic structure (e.g., mussels:

., 2017; pelagic fish: [START_REF] Silva | Anchovies go north and west without losing diversity: Post-glacial range expansions in a small pelagic fish[END_REF], benthic fish: Klein et al., 2016). In benthic marine organisms, depth range shifts, the equivalent to terrestrial elevation shifts, may further permit long-term persistence of ancient gene pools. Populations colonizing deeper colder waters may safeguard diversity during warming periods, regardless of their inherent dispersal ability (Graham et al., 2007;Santelices, 2007a;[START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF]. Likewise, coastal upwelling regions may generate pockets of cryptic refugia preserving regional diversity in the face of climate changes [START_REF] Lourenço | Upwelling areas as climate change refugia for the distribution and genetic diversity of a marine macroalga[END_REF].

Disentangling how past climate changes and dispersal ecology structured the distribution of intraspecific diversity is of much biogeographical and evolutionary relevance, although only a few studies combined both processes et al., 2017). Furthermore, while the role of refugia in poleward expansions is well documented (e.g., [START_REF] Neiva | Climate Oscillations, Range Shifts and Phylogeographic Patterns of North Atlantic Fucaceae[END_REF], range shifts at low latitudes are insufficiently understood. Most importantly, describing the processes shaping endemic genetic lineages is timely, as their persistence might be threatened by climate changes (Provan & Maggs, 2012;Assis et al., 2017a;Wernberg et al., 2018).

A good model to explore the aforementioned topic is the golden kelp Laminaria ochroleuca Bachelot de la Pylaie, 1824. These large brown algae structure marine forests providing many ecosystem functions [START_REF] Araújo | Status, trends and drivers of kelp forests in Europe: an expert assessment[END_REF]. Its niche matches thermal physiological responses (10 to 24ºC; Assis et al., 2017b), a crucial feature to track climate-driven range shifts. Long-range dispersal by this species is likely to occur by rafting and not spore dispersal, as kelp spores have short viability (~1 day; [START_REF] Reed | Dispersal in kelps: factors affecting spore swimming and competency[END_REF][START_REF] Pereira | Temperature effects on gametophyte development of L. Ochroleuca and S. polyschides, kelps with contrasting life histories[END_REF], settling within tens of kilometers maximum (Gaylord et al., 2002). Whole individuals of L. ochroleuca cannot float, but multiple reports of Laminaria rafting [START_REF] Thiel | The ecology of rafting in the marine environment. I. The floating substrata[END_REF] indicate that fragments may become buoyant and/or entangled in other rafts [START_REF] Thiel | The ecology of rafting in the marine environment. I. The floating substrata[END_REF][START_REF] Clarkin | Environment, not characteristics of individual algal rafts, affects composition of rafting invertebrate assemblages in Irish coastal waters[END_REF]. Since reproductive blades may remain viable for long time [START_REF] Thiel | The ecology of rafting in the marine environment. I. The floating substrata[END_REF], dispersal distances may extend to hundreds of kilometers (e.g., Hernández-Carmona et al., 2006). Additionally, a paleoclimatic niche model for this species estimated low latitude persistent populations, some in deep and upwelling settings (Assis et al., 2017a), likely to retain ancient genetic biodiversity [START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF][START_REF] Lourenço | Upwelling areas as climate change refugia for the distribution and genetic diversity of a marine macroalga[END_REF].

In this paper, we ask whether extant rich gene pools of L. ochroleuca can be explained by past climate-driven range shifts, coupled with contemporary dispersal mediated by ocean currents.

We matched persistence predictions of a paleoclimatic model (Assis et al., 2017a) against endemic genetic diversity and potential oceanographic connectivity. We hypothesize that (1) climatic refugia display higher and endemic genetic diversity relative to to more recent populations and that (2) effective long-distance dispersal is rare, restricting the homogenization of populations and isolating important biodiversity hotspots.

Methods

Study area and focal species

The study area comprised the entire distributional range of Laminaria ochroleuca, from Cornwall (50.0N, 5.5W; England) to Sesimbra (38.4N, 9.2W; Portugal), plus isolated regions where it occurs beyond the more continuous range: Alboran Sea, Morocco upwelling spots, seamounts and Azores islands [START_REF] Araújo | Status, trends and drivers of kelp forests in Europe: an expert assessment[END_REF]Assis et al., 2017a). Along continental coastlines, the species is vertically distributed from intertidal pools down to ca. 30 m depth. In the clearer waters of shallow seamounts, islands and the Mediterranean, it can reach 50-80 m depth (e.g., Formigas bank, shallow seamounts off southwestern Iberia, Alboran Sea and Strait of Messina). This is a perennial species with a heteromorphic life cycle alternating between macroscopic sporophytes and microscopic gametophytes.

Genetic diversity and structure

Approximately 30 individuals were sampled haphazardly per site (dependent on abundance and accessibility) for genetic analyses (24 sites; Fig. 1a), by removing a piece (~1 cm 2 ) from the base of the blade. Genomic DNA was extracted using NucleoSpin96 PlantKit II (Macherey-Nagel, Germany). Microsatellite amplification and scoring was performed for 15 polymorphic loci as in [START_REF] Coelho | Characterization of fifteen microsatellite markers for the kelp Laminaria ochroleuca and cross species amplification within the genus[END_REF].

Genetic diversity per site and genetic group (see structure analysis below) was estimated as allelic richness, private alleles and gene diversity (expected heterozygosity). Sample sizes were standardized to the smallest in any population (excluding those ≤10), using 10 4 randomizations.

To test the role of refugia, standardized genetic diversity was determined separately for regions of persistence and post-LGM settlements, identified in Assis et al. (2017a;Fig. 1a). The null expectation for refugia was tested as the proportion of 10 4 randomizations retrieving higher diversity and endemism (i.e., private alleles). F IS and departures from Hardy-Weinberg equilibrium were tested per site with Fstat (Goudet, 1995) under 10 4 randomizations of alleles among individuals, and individuals within sites.

Genetic structure was inferred with Structure [START_REF] Pritchard | Inference of population structure using multilocus genotype data[END_REF] without a priori population assignment and allowing admixture. This analysis was performed for a range of genetic groups, by running the model of correlated allele frequencies with a burn-in time of 2x10 5 repetitions and 10 6 iterations. The number of groups was inferred with the DeltaK criterion (Evanno et al., 2005). An additional level of genetic structure was inferred by running a second analysis within genetic groups. Two sites showing admixture in the first hierarchal run (see results below) were included in the pool of each genetic group to better disentangle genetic structure.

Genetic differentiation was s i d b w si s d ic ps wi h J s 's D This w s used in detriment of F ST because it is more appropriate to compare populations with contrasting levels of genetic diversity (Jost, 2008;Whitlock, 2011;[START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF], as in our case (see results).

Connectivity potential

Simulations of potential connectivity used a biophysical model following [START_REF] Buonomo | Habitat continuity and stepping-stone oceanographic distances explain population genetic connectivity of the brown alga Cystoseira amentacea[END_REF], [START_REF] Klein | High Interannual Variability in Connectivity and Genetic Pool of a Temperate Clingfish Matches Oceanographic Transport Predictions[END_REF] and Cunha et al. (2017), with daily data from the Hybrid Coordinate Ocean Model (HYCOM; [START_REF] Chassignet | The HYCOM (HYbrid Coordinate Ocean Model) data assimilative system[END_REF]. This high-resolution hindcast accurately reproduces key oceanographic processes like fronts, meandering currents, filaments and eddies [START_REF] Chassignet | The HYCOM (HYbrid Coordinate Ocean Model) data assimilative system[END_REF][START_REF] Lett | A Lagrangian tool for modelling ichthyoplankton dynamics[END_REF], and its main limitation lies on the inability to simulate processes at scales below its raw resolution (~7 km at mid-latitudes; Fossette et al., 2012). While this can constrain seascape genetic studies focusing on nearshore processes, it may be neglected at the scales of our genetic sampling.

The simulation comprised the ~5000 km of the study area, gridded to 0.01° spatial resolution (~1 km). Virtual particles were released from each cell, daily from April to September. This period covers the reproductive stages that can potentially fragment and drift, releasing spores after dispersal [START_REF] Thiel | The ecology of rafting in the marine environment. I. The floating substrata[END_REF][START_REF] Clarkin | Environment, not characteristics of individual algal rafts, affects composition of rafting invertebrate assemblages in Irish coastal waters[END_REF] even when rafting for long time [START_REF] Macaya | Presence of sporophylls in floating kelp rafts of Macrocystis spp. (Phaeophyceae) along the Chilean Pacific Coast[END_REF]. Particles were allowed to drift until reaching shore, and their position was determined hourly with bilinear interpolation on the velocity fields of currents [START_REF] Klein | High Interannual Variability in Connectivity and Genetic Pool of a Temperate Clingfish Matches Oceanographic Transport Predictions[END_REF]Cunha et al., 2017). Since real dispersal times of L. ochroleuca are unknown, different simulations were performed with contrasting thresholds of: 1 day, for dispersal by spores, as sporulation lasts 15-18 h [START_REF] Pereira | Temperature effects on gametophyte development of L. Ochroleuca and S. polyschides, kelps with contrasting life histories[END_REF] and spores stop swimming after ~24 h (inferred for Macrocystis pyrifera and Pterygophora californica; [START_REF] Reed | Dispersal in kelps: factors affecting spore swimming and competency[END_REF]; 30 days, considering long-lived rafts, in line with the period estimated for other brown algae [START_REF] Thiel | The ecology of rafting in the marine environment. I. The floating substrata[END_REF][START_REF] Monteiro | Temporal windows of reproductive opportunity rein-force species barriers in a marine broadcast spawning assemblage[END_REF]; 60 days, for longer-lived rafts.

The probability of connectivity was computed by dividing the number of particles released from a given cell i that ended on cell j, by the total number of particles released from cell i.

Oceanographic variability was taken into account by running independent simulations for the most recent 10-year period available in HYCOM (i.e., from 2003 to 2012). A final asymmetrical connectivity matrix was produced by averaging the products of the annual simulations. To consider the hypothesis of year-to-year stepping-stone migration, a network analysis was implemented, in which vertices were the cells and edges the probabilities of transport between them (e.g., [START_REF] Buonomo | Habitat continuity and stepping-stone oceanographic distances explain population genetic connectivity of the brown alga Cystoseira amentacea[END_REF]. Connectivity was estimated as the shortest path between cells, i.e., the one that minimizes the sum of negative log-transformed probabilities across all possible paths (Floyd-W sh 's i h ).

The role of ocean currents was tested with linear regression models fitting genetic differentiation J s 's D) i s probability of stepping-stone connectivity between the sites sampled for genetics. The models considered the dispersal periods of 1, 30 and 60 days. A null model of isolation by distance was built by fitting genetic differentiation against alongshore marine distances. The models were compared using adjusted R-sq s 's c i c ffici and Akaike Information Criteria (AIC).

Network community detection was used to identify the major oceanographic regions of the study area, i.e., those with higher within-region connectivity (e.g., Cunha et al. 2017). Excessive connections with unimportant information in the stepping-stone connectivity matrix were removed until a threshold maximizing the goodness of fit index of Modularity [START_REF] Newman | Modularity and community structure in networks[END_REF]. The leading eigenvector algorithm [START_REF] Newman | Modularity and community structure in networks[END_REF] used the percolated network to assign a unique membership (oceanographic region) to each vertex. The significance of regions was tested by computing the proportion of 10 4 random assignments of memberships retrieving higher Modularity than observed.

1 et al.,
Dispersal simulations and network analyses were implemented in R (R Development Core Team, 2016) with packages: data.table, dismo, doparallel, gstat, igraph, raster and vegan.

Results

Genetic diversity and structure

A total of 262 alleles were found across 649 genotyped specimens. Southern diversity was generally higher, decreasing northwards. Allelic richness (Table 1) was higher in Tarifa (Â > 6) than in all other sites (Â <5). Endemism (i.e., private alleles; Table 1) ranged from very high in southern isolated sites of Formigas and Tarifa to nearly no private diversity in several more northern sites (e.g., h c ). Gene diversity (Table 1), like allelic richness, was highest in Tarifa. Lower diversity and endemism were found in northern sites, and where no standardization was implemented due to low sample size. Significant heterozygote deficit was found in only 1 out of 25 sites (Table 1).

When considering the paleoclimatic model for L. ochroleuca, genetic diversity was higher within refugia (i.e., western Iberia, the Iberian Seamounts, Gibraltar Strait, western Morocco and the Azores; Fig. 1a), accounting for approximately 2-fold higher diversity and 7-fold more private alleles than in regions of post-LGM settlements (i.e., Galicia in northwestern Iberia and western English Channel; Fig. 1a).

The first hierarchal level of Structure analysis revealed (1) a north group including all continental sites from Plymouth southwards to Ericeira and the Iberian Seamounts, (2) a south group including Tarifa, Morocco and the Azores (Formigas), and (3) an admixture zone in Sesimbra and Espichel (Fig. 2). The second level divided the north group in (1) Western English Channel,

(2) Western Iberia and (3) Iberian Seamounts. The south group was divided into four sub-groups corresponding to each site (Fig. 2). The admixture zone grouped with Western Iberia (refer to S1

for DeltaK criterion).

Allelic richness per genetic group (second hierarchical level) was higher in Tarifa, followed by El Jadida, Western Iberia and the Iberian Seamounts (Fig. 2d). Much more private diversity was found in Tarifa (21.2), Formigas and El Jadida. Considering both Moroccan sites, the private diversity of Morocco (16.4) is similar to that in Formigas (16.7). The Western English Channel sh w d h w s div si d d is Fi d) i wis diff i i J s 's D) b w groups was lower between the three northernmost groups, and also between Tarifa and Essaouira (Fig. 2e). Highest differentiation was between Formigas and all groups (Fig. 2).

Connectivity potential

Genetic differentiation was best explained by stepping-stone connectivity considering dispersal up to 30 days (Fig. 3a; p-value: < 0.001; adjusted R 2 : 4 s 's c : -0.798; refer to S3 for additional models). The simulations further showed that although dispersal events may occur over dozens to thousands of kilometers, only 5% go beyond 3.93 km (Fig. 3c). The identification of oceanographic regions for L. ochroleuca retrieved a significant modularity of 0.827 (p-value: < 0.001; Fig. 3b). This analysis identified fifteen regions, eleven of which within the speci s' distribution (Fig. 3b).

Discussion

This study demonstrates that the distribution of population genetic diversity across species ranges can be highly skewed and structured by processes acting at different scales. By combining theoretical modelling with empirical genetic data, we reveal how range shifts of the recent past (ca. 20,000 yr BP) structured regions of long-term persistence at low latitude (warmer) range margins, where higher and unique genetic diversity was retained. Simulating the potential degree of connectivity further allowed estimating well-defined barriers shaped by physical oceanographic transport, which restrict homogenization of extant populations, leaving genetic biodiversity hotspots demographically and genetically isolated.

Past climate changes structuring genetic diversity

The overall genetic diversity distribution of L. ochroleuca corroborated expectations underlying estimated past range shifts. The paleoclimatic niche model identified multiple refugia presently located at lower latitudes. These locations displayed significantly higher genetic diversity and disproportional endemism, when compared to populations estimated to be much younger. As in other species [START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF][START_REF] Neiva | Climate Oscillations, Range Shifts and Phylogeographic Patterns of North Atlantic Fucaceae[END_REF], persisting within refugia might have been central to preserve and accumulate genetic diversity. In contrast, founder effects at the leading edge of post-LGM settlements might have produced successive bottlenecks (Excoffier et al., 2009), reducing diversity of higher latitude populations beyond refugia (i.e., Galicia and western English Channel). Such an extremely skewed pattern of genetic diversity contrasts with that of several other brown algae, which currently display higher diversity in the central region of their distributions [START_REF] Coyer | Post-ice age recolonization and differentiation of Fucus serratus L. (Phaeophyceae; Fucaceae) populations in Northern Europe[END_REF]Hoarau et al., 2007;[START_REF] Assis | Climate-driven range shifts explain the distribution of extant gene pools and predict future loss of unique lineages in a marine brown alga[END_REF][START_REF] Robuchon | Contrasting genetic diversity patterns in two sister kelp species co-distributed along the coast of Brittany, France[END_REF] Remarkably, although the hotspots of endemic diversity for L. ochroleuca occur at the warmer range margins, all are in upwelling coldspots receiving cold nutrient-rich waters (Gibraltar Strait, Morocco, Azores). Offshore seamounts may further retain ancient diversity during warming periods [START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF], as increased light penetration allows deeper (colder) settlements (Graham et al., 2007;Santelices, 2007a;Assis et al., 2017b). The diversity patterns found in the deep populations of the Azores and the Iberian seamounts support the refugial hypothesis, however, the high differentiation of the Azores indicates that this region was colonized much earlier than the separation of all other populations and has remained isolated since then. In Iberian seamounts, fringe environments with steep bathymetric slope (Santelices, 2007b;Assis et al., 2017a) might hypothetically restrict population sizes and promote a large effect of genetic drift, reducing diversity by purging low frequency alleles over time (Young et al., 1996). The isolation of such regions, hundreds of kilometers offshore, may further prevent gene flow from genetically-distinct populations, a process that can further decrease diversity relative to refugium expectations (Hewitt, 2004). Similar population size limitations could have been expected for the small upwelling region of Tarifa and the steep slopes of volcanic islands of the Azores. Yet the high endemic genetic diversity of these two regions indicates that either there have not been major bottlenecks there, or the diversity is still significant but reflects a shifted baseline from an even richer state.

Western Iberia was also predicted as persistent climate refugium, as suggested also by the high private diversity (see Sesimbra, Amorosa, Peniche). However, compared to refugia further south, it has lower diversity. This refugium was the northern range margin during colder periods (like the LGM, Fig. 1b) and is presently the southern range margin of the continuous continental distribution. Thus, it might have experienced genetic drift and bottlenecks owing to reduced population sizes while occurring near niche thresholds (Eckert et al., 2008;[START_REF] Oppliger | Alteration of sexual reproduction and genetic diversity in the kelp species Laminaria digitata at the southern limit of its range[END_REF]. Even when climate conditions in this region approximated niche optimum, priority colonization effects [START_REF] Tellier | The lessonia nigrescens species complex (laminariales, phaeophyceae) shows strict parapatry and complete reproductive isolation in a secondary contact zone[END_REF]Neiva et al., 2012b) and/or strong oceanographic barriers (see discussion below) could have limited gene flow from richer populations. Also, one cannot discard the uncertainty of paleoclimatic models [START_REF] Pearson | Model-based uncertainty in species range prediction[END_REF], which could overrate the refugial potential of some regions. The climate data used for the LGM predictions might underestimate winter cooling of western Iberia [START_REF] Ramstein | How cold was Europe at the Last Glacial Maximum? A synthesis of the progress achieved since the first PMIP model-data comparison[END_REF], rendering local extinctions if temperatures dropped below the 10°C limit (Assis et al., 2017a). However, the genetic data do not support this possibility, given the considerable private diversity of this region, even when each population is considered separately (e.g., Sesimbra, Amorosa and Peniche).

Oceanographic barriers isolating ancient genetic diversity

We discovered that L. ochroleuca has two main genetic groups, which coincide with the regions of persistence over the cold and warm climate maxima (Assis et al., 2017a). Within lineages, further structure was revealed, comprising seven groups. Their significant differentiation indicates low gene flow, not counterbalancing genetic drift and/or mutation.

The simulations of connectivity suggest the possibility of long distance dispersal, up to 30 days.

Despite the expected 1-day kelp spore viability [START_REF] Reed | Dispersal in kelps: factors affecting spore swimming and competency[END_REF], Laminaria are recurrently recorded rafting offshore [START_REF] Thiel | The ecology of rafting in the marine environment. I. The floating substrata[END_REF] and L. ochroleuca crossed the English Channel and reached the Azores in the mid-Atlantic. Paradoxically, despite the possibility of such events, L. ochroleuca and other kelp maintain strong genetic structure (Fraser et al., 2010;Johansson et al., 2015;[START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF], suggesting that long effective dispersal (i.e., resulting in settlement and recruitment) is possible but very rare, in agreement with our simulations, as rafts unable to accomplish connectivity in the first days are typically lost in the open ocean (also demonstrated for other large brown algae; Buonomo et al. 2017). This further agrees with its low expansion potential along the English Channel (5 km/year; [START_REF] Straub | The Dynamic Biogeography of the Anthropocene: The Speed of Recent Range Shifts in Seaweeds. Seaweed Phylogeography[END_REF]. Moreover, priority colonization in well-established populations [START_REF] Tellier | The lessonia nigrescens species complex (laminariales, phaeophyceae) shows strict parapatry and complete reproductive isolation in a secondary contact zone[END_REF]Neiva et al., 2012b) may block effective dispersal by later migrants. Our data show that dispersal over long distances is not common in L. ochroleuca, preventing the homogenization of phylogroups, but must have been crucial for colonization of distant habitats across large water masses (e.g., Iberian seamounts and the Azores) and during post-glacial expansions.

Connectivity simulations identified 11 oceanographic regions within the species range, that largely match the distribution of genetic groups, particularly in lower latitudes (i.e., Iberian Seamounts, Alboran, Morocco and Azores). However, colonization pathways can be hypothesized from our genetic data for the more recent populations in the English Channel and Galicia, both appearing derived from the Iberian refugium. The former could have resulted from a (rare) long-distance dispersal from a population similar to that currently present in Viana do Castelo (less differentiated) towards Brittany, followed by Channel crossing. Founder effects during these events would have shaped the distinct genetic group found in this northern range (Neiva et al., 2012b;[START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF]. Galicia could have been colonized by near shore range expansion, hypothetically starting from a population similar to that observed in Amorosa. There is no evidence of any involvement of the remaining lower latitude populations in northern colonizations. Indeed, expansions by low dispersal species tend to be mediated by few individuals that happen to be located at the leading edge of the expanding front (Hoarau et al., 2007;Excoffier et al., 2009;Neiva et al., 2012a;[START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF].

The temporal scale of range expansions may surpass the contemporary oceanographic processes simulated in the present study, preventing connectivity with distant regions, across large water masses. In particular, our results of ocean transport could not explain migration to the Azores, even for 2 months of potential dispersal (Refer to S4). However, there are several records of cold temperate algae found drifting in the Azores, even though they do not occur there (e.g., Ascophyllum nodosum; [START_REF] Neto | Checklist of the benthic marine macro algae of the Azores[END_REF], which could originate from both sides of the Atlantic with increased dispersal periods [START_REF] Putman | Tracking the long-distance dispersal of marine organisms: sensitivity to ocean model resolution[END_REF]. Also, long-distance events might have occurred more frequently in a past with different oceanographic patterns and glacial coastlines, such as when the LGM sea level dropped -120m (e.g., [START_REF] Peltier | Global glacial isostasy and the surface of the ice-age earth: the ice-5g (vm2) model and grace[END_REF], potentially increasing stepping stone connectivity (Fig. 1b) through habitats that are submerged today [START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF]. Human-mediated transport cannot explain the establishment of such remote populations of L. ochroleuca because these are so genetically distinct that their existence is expected to be much more ancient than the colonization of the Azores by humans. In contrast, colonization by Fucus serratus of Atlantic North America is correlated with historical shipping pathways, but population divergence is still very low [START_REF] Brawley | Historical invasions of the intertidal zone of Atlantic North America associated with distinctive patterns of trade and emigration[END_REF].

Oceanographic barriers may maintain contact zones between parapatric populations, with high but not unique local diversity, due to admixture. This may be the case for the admixture region (Arrábida) between the two main lineages of L. ochroleuca, over an oceanographic barrier in front of the Tagus estuary. Contact zones may also increase regional homozygosity if differentiated gene pools have some reproductive isolation (Wahlund effect). While this was not verified in Arrábida, it could hypothetically explain homozygote excess in São Bartolomeu do Mar, where an oceanographic barrier was identified separating northwest from western Iberian shorelines.

Concluding, our results show key roles of multiple refugia (from past climate changes) in safeguarding most of the species genetic diversity. Simulating connectivity further showed how such biodiversity hotspots are kept isolated by contemporary ocean currents (oceanographic barriers). While the present range of L. ochroleuca shows that long-distance dispersal is possible, our results suggest that these events are rare.

The strong divergence and endemism of low latitude populations, coupled with their strong oceanographic isolation, represent the most remarkable feature of the species phylogeography.

These populations, occurring mostly in deep or upwelled pockets within the warmer range margin, have not contributed to post-LGM expansion. These traits are not unique to L.

ochroleuca (e.g., [START_REF] Neiva | Species distribution models and mitochondrial DNA phylogeography suggest an extensive biogeographical shift in the high-intertidal seaweed Pelvetia canaliculata[END_REF]Johansson et al., 2015;[START_REF] Assis | Deep reefs are climatic refugia for genetic diversity of marine forests[END_REF] and render a disproportionate evolutionary significance to marine forest refugia populations. Their hypothetical future loss could dramatically reduce genetic diversity and compromise adaptive potential (Hampe & Petit, 2005;Provan & Maggs, 2012;Wernberg et al., 2018), also causing ecosystem changes in overall richness and biomass of associated species (Hoegh-Guldberg & Bruno, 2010).

The general agreement between paleoclimatic models and observed genetic diversity suggests broad niche conservatism, implying low plasticity and adaptive potential on a wide scale. Low latitude refugial regions are in risk of disappearing, even when associated with upwelling (Gibraltar and Morocco for L. ochroleuca; Assis et al., 2017a). This might not be compensated by reported and predicted poleward expansions [START_REF] Smale | The rise of Laminaria ochroleuca in the Western English Channel (UK) and comparisons with its competitor and assemblage dominant Laminaria hyperborea[END_REF]Assis et al., 2017a) because we showed here that low-latitude biodiversity hotspots are not involved in high latitude expansions. In contrast, detrimental climate effects are not expected for the deep refugia of the Iberian seamounts and Azores Islands (Assis et al., 2017a) representing safer sites for ancient diversity than cold upwelling spots. However, currently no empirical evidence distinguishes the different refugial roles provided by both environments.

FiguresFigure 1 .

 1 Figures

  Figure 1. (panel a) Current distribution of Laminaria ochroleuca (black line; inferred by Assis et

Figure 2 .

 2 Figure 2. (panel a) Sampled sites with colors depicting genetic subdivision inferred with

Figure 3 .

 3 Figure 3. (panel a) Linear regression of genetic differentiation against probability of connectivity

Table 1 .

 1 Site number (#) and name, depth (m), sample size (n), standardized allelic richness (Â), 407 private alleles (PÂ) d xp c d h z si H ) † i dic s s d diz i d 408 small sample), and F IS multilocus estimates (* indicates significant deviations from Hardy-409

	410	Weinberg with Bonferroni correction).
		#	Site	Depth	n	Â	PÂ	He	FIS
		1 Plymouth	0	27	2.19±0.12	0.17±0.38 0.18	-0.02
		2 Port Blanc	0	29	2.03±0.06	0.49±0.50 0.26	-0.12
		3 Brignogan-Plages	0	4	1 †	1.01±0.17 0.29	0.25
		4 Lorient	0	15	2.33±0.00	1.97±0.85 0.27	0.07
		5 A Coruña	0	25	3.33±0.20	1.80±0.97 0.35	0.02
		6 Barrañán	0	4	†	0.27±0.45 0.34	-0.09
		7 Laxe	0	11	2.95±0.00	1.87±0.85 0.38	0.03
		8 Camariñas	0	30	3.91±0.13	2.83±1.11 0.31	0.02
		9 Viana do Castelo	0	38	3.33±0.16	1.49±0.99 0.33	0.06
		10 Amorosa	0	51	4.58±0.21	3.18±1.54 0.42	0.01
		11 S. Bartolomeu do Mar	0	39	2.10±0.10	0.94±0.64 0.28	0.31*
		12 Peniche	0	22	4.52±0.18	3.07±1.15 0.50	0.03
		13 Ribeira de Ilhas	0	3	1 9 †	1.00±0.00 0.49	0.34
		14 Ericeira	10	6	†	0 0.24	0.37
		15 Camões seamount	40	7	†	2.11±0.62 0.42	0.04
		16 Espichel	10	11	2.16±0.00	1.44±0.58 0.32	0.03
		17 Sesimbra	10	27	4.49±0.22	4.60±1.52 0.41	0.12
		18 Ormonde seamount	50	46	3.30±0.22	0.73±0.64 0.35	0.04
		19 Gorringe seamount	50	48	3.28±0.20	2.96±1.83 0.34	0.11
		20 Gettysburg seamount	50	68	3.60±0.28	2.15±1.24 0.34	0.02
		21 Tarifa (Gibraltar Strait)	20	52	6.38±0.33	10.19±2.14 0.53	-0.01
		22 El Jadida	0	31	4.71±0.21	8.75±1.96 0.48	0.09
		23 Essaouira	0	32	3.38±0.13	5.71±1.72 0.32	0.08
	411	24 Formigas (Azores)	50	23	3.63±0.18	11.14±1.87 0.35	0.01
	412
	413

Acknowledgements

This study was supported by a Pew Marine Fellowship (USA) and the Foundation for Science and Technology (FCT) of Portugal through postdoctoral fellowship SFRH/BPD/111003/2015 and programs CCMAR/Multi/04326/2013, UID/MAR/04292/2013, PTDC/MAR-EST/6053/2014 (GENEKELP), and BIODIVERSA/004/2015 (MARFOR). IMAR-DOP/UAz is R&D Unit no. 531 also funded by FCT through PEst-OE/EEI/LA0009/2011-2014 (OE,

Data accessibility

Microsatellite data are permanently available at https://doi.org/10.6084/m9.figshare.6275387.v2.

Biosketch

Jorge Assis is a post-doctoral researcher at CCMAR. His research is mainly focused on the evolutionary consequences arising from climate changes and the drivers mediating gene flow in marine populations.

Supplementary information

S1. Estimation of the number of genetic groups for the first and second hierarchical levels of Structure analyses.

S2. Analysis of Molecular Variance and pairwise differentiation levels between sites.

S3. Supplementary results for the simulations of potential dispersal.


M Lagha

M Bensebti

Weather Radar signals with Alpha Stable Distributions

This work, treats about a modeling of the weather precipitation echoes detected by a weather pulse Doppler radar. The methods used for the simulation of the Doppler spectrum, and I & Q signals representing the precipitations radar echoes, is based on a macroscopic models, i.e. random processes with assigned spectra. We propose global model, with a power spectrum having a range of statistical distributions ranging between Cauchy and Gauss called alpha-stable model. The results obtained shows that this new model represents correctly the Doppler spectrum of precipitations.

I. INTRODUCTION

The computer simulation is mainly used for the generation and the analysis of the weather radar signals for low cost offered by simulations, [START_REF] Doviak | Doppler radar and weather observation[END_REF], [START_REF] Galati | Computer simulation of weather radar signals[END_REF], [START_REF] Bringi | Polarimetric Doppler Weather Radar: Principles and Applications[END_REF].

The signals received at the weather radar's are a compound of a very great number of various particles of air (hydrometeors), or irregularities of the refraction index of the air, [START_REF] Lagha | Performances comparison of pulse-pair and 2-step prediction algorithms for the Doppler spectrum[END_REF], [START_REF] Skolnik | Radar Handbook[END_REF], [START_REF] Doviak | Doppler radar and weather observation[END_REF], [START_REF] Bringi | Polarimetric Doppler Weather Radar: Principles and Applications[END_REF]. In this fact these echoes are supposed to be modeled as a random process and where their power spectral density will obey to the Normal statistical distribution (Gaussian Law). This assumption is justified by the central limit theorem, [START_REF] Papoulis | Probability, Random Variables, and Stochastic Processes[END_REF].

In addition, we can find sometimes that this Gaussian model is not adequate [START_REF] Keeler | Signal Processing for Atmospheric Radars in Meteorology[END_REF], to represent of the spectral irregularities and also called spikes, which occur during the detection of weather echoes at low altitudes, from where we are interested to suggest the model of alpha stable distributions, for the representation of the Doppler spectrum of severe weather perturbations (winds, gusts of wind,…), and then to generate and simulate the radar signals I and Q.

The aim of this paper is to propose a global model which resolves the problem of the spectral spikes. In the second part a theoretical background about alpha stable distributions is done, in the third part a routine generation of the I and Q radar data is discussed. Results and comments about the results obtained are presented in the fourth part.

II. THEORETICAL BACKGROUND

We introduce in this section the use of alpha stable distribution S α S, to model the radar echoes. The most aim of the introduction of this range of statistical distributions called α-stable law, for the modeling and the representation of the Doppler spectrum and signals I and Q of the precipitation radar echoes and/or of a severe weather perturbation, is that to have a good representation of a spectrum sullied with stationery echoes in the presence of the ground clutter effect, and the representation of multimodal aspects of the Doppler spectrum. This problem of spectral irregularities is mentioned by R.J. Keeler in the reference [START_REF] Keeler | Signal Processing for Atmospheric Radars in Meteorology[END_REF].

The range of the alpha stable distributions is defined as a direct generalization of the Gaussian law [START_REF] Ilow | Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers[END_REF], [START_REF] Nikias | Signal Processing with Alpha-Stable Distributions and Applications[END_REF], [START_REF] Tsihrintzis | Performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha-stable process[END_REF], [START_REF] Tsihrintzis | Fast estimation of the parameters of alpha-stable impulsive interference[END_REF], it includes in fact the Gaussian distribution density as particular case (α=2). The principal characteristic of a stable function (non Gaussian) with probability density function pdf, is that its spectrum are broader than those of the Gaussian density. It is one of the principal reasons for which the α-stable law (Levy laws) is considered adapted to model useful signals and noises with impulsive nature, and processes with heavy tail [START_REF] Nikias | Signal Processing with Alpha-Stable Distributions and Applications[END_REF], [START_REF] Tsihrintzis | Performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha-stable process[END_REF]. This law defined by its characteristic function pdf, and given as:

) w . w . j . exp( ) w ( F α γ - δ = (1)
The parameters, α, γ and δ describes completely a stable distribution. The characteristics parameter α (alpha) acts directly, over the width of the probability density function (pdf), and on impulsiveness of the alpha stable process S α S. The parameter α can take values in the interval [0,2], a smaller value implies broader extents and heavy tails, and for α=2 (Gaussian case) the spectral width is narrow. The dispersion parameter γ (γ >0) plays a part similar to the variance and refers to the width distribution. When α=2 (Gaussian case) the variance is equal to 2γ. The dispersion parameter δ is comparable with the mean of the distribution, where δ can take values in the interval ]-∞, +∞ [, [START_REF] Ilow | Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers[END_REF], [START_REF] Nikias | Signal Processing with Alpha-Stable Distributions and Applications[END_REF].

The theoretical justification of the use of the α-stable distributions as a basic tool of statistical modeling comes from the generalized central limit theorem [START_REF] Papoulis | Probability, Random Variables, and Stochastic Processes[END_REF]. This theorem stipulates that the sum of independent random variables identically distributed (i.i.d) with or without variance converges towards a stable distribution, [START_REF] Nikias | Signal Processing with Alpha-Stable Distributions and Applications[END_REF], [START_REF] Tsihrintzis | Performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha-stable process[END_REF], [START_REF] Tsihrintzis | Fast estimation of the parameters of alpha-stable impulsive interference[END_REF].

If a signal or a noise observed can be regarded as result of a great number of identically distributed independent variables, then the generalized central limit theorem suggests that a stable model can be well adapted to model it, [START_REF] Papoulis | Probability, Random Variables, and Stochastic Processes[END_REF].

But, an expression with compact form does not exist for the stable probability density function, except for the particular distributions Gaussian (α=2) and of Cauchy (α=1). In this fact to model the power spectrum of the weather precipitation, we can use a linear interpolation between the Gaussian distribution and that of Cauchy for α ranging between 0 and 2, and it is shown, [START_REF] Nikias | Signal Processing with Alpha-Stable Distributions and Applications[END_REF], [START_REF] Tsihrintzis | Fast estimation of the parameters of alpha-stable impulsive interference[END_REF], that the probability density pdf of these range distributions is given by the equation as: -

) x ( f . p ) x ( f ). p 1 ( ) x ( f ˆ2 1 + - = α (2)
Where, the parameter p lies between 0 and 1, for α ranging between 0 and 2 (0≤ α ≤2). f 2 (x), f 1 (x) are respectively the probability densities functions of the Gaussian and Cauchy distributions.

From [START_REF] Nikias | Signal Processing with Alpha-Stable Distributions and Applications[END_REF], we can use the approximation

) ( g P α = : 3147 . 0 0355 . 0 3484 . 0 ) ( g 2 - α - α = α (3-a) or 25 . 1 ) 1 ( p - α = (3-b)
Thus for our case of study, i.e. the modeling of the weather radar echo characterizing a severe perturbation and/or a precipitation, the probability density function of the weather Doppler spectrum is given by ( 2).

With:

-

( ) ( ) [ ] ( ) (
)

2 1 1 / 1 . / 1 ) ( θ π - + = x x f , Cauchy distribution with ( θ , x ), parameters. - ( ) ( 2 2 2 2 / ) ( exp 2 / 1 ) ( σ μ σ π - - = x x f
), Gaussian distribution with the parameters ( σ μ, ), where µ is the variance and is the width.

σ

The equation (2) represents the numerical interpolation of the α-stable distribution (Levy laws), for the parameter α ranging between 0 and 2.

Thus by replacing the parameter α=1 in the equation (3-b), we obtains (p=0) and this will induce a distribution of Cauchy on the equation ( 2), well after elimination of the second term by its multiplication by the term (p=0). In the same manner by replacing α=2, in the equation (3-b) we obtains (p=1), which will imply the elimination of the first term (that of Cauchy) and thus there will be a Gaussian distribution in the equation [START_REF] Doviak | Doppler radar and weather observation[END_REF]. For the values α ranging between 0 and 2 (0≤α≤2), there will be Doppler spectra with It is well noted that there is a visible effect of the noise on the Doppler power spectrum of the weather perturbation. This noise is materialized by secondary peaks power (spikes). These secondary peaks with impulsive nature, are all the more numerous for low values of the parameter α (α < 2), which are adequate for the modeling of the radar echoes drowned in a background noise and particularly at low altitude.

Let us note that the rate of the background noise is much more important at low altitudes, and in particular when the antenna sweeps nearing the ground, it can come from the reflections of the ground, or of the vehicles circulating in the agglomeration covered by the pulsed weather Doppler radar's [START_REF] Doviak | Doppler radar and weather observation[END_REF], [START_REF] Keeler | Signal Processing for Atmospheric Radars in Meteorology[END_REF].

In practice these secondary peaks power (spikes) characterized by almost null velocities can harm the quality of the estimations made on the Doppler spectrum, which makes necessary the use of adaptive filters in order to eliminate them from the spectral contents of the radar echoes, [START_REF] Keeler | Signal Processing for Atmospheric Radars in Meteorology[END_REF].

III. DATA'S GENERATION

Work Hypothesis

It is shown [START_REF] Skolnik | Radar Handbook[END_REF], [START_REF] Doviak | Doppler radar and weather observation[END_REF], [START_REF] Keeler | Signal Processing for Atmospheric Radars in Meteorology[END_REF], [START_REF] Ilow | Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers[END_REF], [START_REF] Nikias | Signal Processing with Alpha-Stable Distributions and Applications[END_REF], [START_REF] Bringi | Polarimetric Doppler Weather Radar: Principles and Applications[END_REF] that the received signal of the weather targets is well represented by a random process with Gaussian (Normal) distributions. But, nevertheless some authors in this field mention that the impulsive character of the noises and same of the useful signals, are not well represented by this model. We propose a global model having statistical distributions ranging between the Gaussian law and Cauchy law according to the prevalence of the noise see figure 4. 1) The number of reflections in the illuminated volume by the emitted impulse radar is large (>10 6 );

2) The illuminated volume by impulse is large compared with the transmitted wavelength;

3) The volume of impulse is filled with reflections, causing all of the random phases ranging between 0 and 2π;

4) The particles are moving the ones compared to the others. This movement is due to turbulence created by weather precipitations, and at their velocities which are also variable.

The superposition of the dispersed electric fields of such great number of particles (each one with random phase) gives place, by the central limit theorem limit, a signal with stable statistics (alpha stable law) [START_REF] Keeler | Signal Processing for Atmospheric Radars in Meteorology[END_REF], [START_REF] Tsihrintzis | Fast estimation of the parameters of alpha-stable impulsive interference[END_REF].

Since the particles are moving the ones compared to the others, there is also a Doppler diffusion, often indicated under the name of dissension of the Doppler spectrum or also of Doppler frequency.

We should produce the radar signals I and Q. The variables entry for our routine should include the signal noise ratio (SNR), radial velocity V r , a number data points (samples of data) ndata, ambiguous velocity V a , the parameter α and the spectral width σ v , and the power of the emitted signal PP as well as the radar reflectivity dBz. The output data must be Doppler velocities, the Doppler spectrum and signals I and Q (time series).

IV. RESULTS AND COMMENTS

In this part we highlight the simulations results in the form of graphs. Initially we discuss the effect of each entry parameter on the Doppler spectrum velocities and on signals I and Q. the graphs will represent at the same time disturbed and non disturbed Doppler spectrum, and the time series I and Q. Then in the second time we comment the results and the incidence of each parameter entry on the Doppler spectra and signals I and Q generated during simulations.

The effect of the Signal Noise Ratio SNR on the Doppler spectrum and signals I & Q:

SNR=1dB (fig. 5

and fig.6)

It is noted that there are too many ripples on the Doppler spectrum (peak with 3.10 5 w), and the two signals I and Q overlap, i.e. that we cannot distinguish them at sight of eye. This is obvious, because the useful signal merges with the noise signal (SNR=1), from where the bad distinction enters the two signals, see figure 5. In practice this can occur when the useful signals radar and the interfering signals are of the same level, [START_REF] Doviak | Doppler radar and weather observation[END_REF].

SNR=10dB

A level of noise of 10 dB, means that the signal has a level higher than the noise of ten times.

It is noted that there is less of ripples than the preceding case, and we distinguishes a quite apparent peak power on the Doppler spectrum disturbed from speeds to a magnitude of 2,8.10 5 w. And signals I and Q do not overlap see figure 6.

The effect of the number of data samples ndata on the Doppler spectrum and signals I and Q ; (fig.7 and 8)

We can say that starting from 256 points we will have the same properties if one increases further this number (i.e. symmetry repetition), as we can see it on figures 7 and 8. This number is given in power of 2 (ndata=2 n ).

The number of points has a direct relation with the time and the distance cells on which the echoes are reflected. Thus to have a good simulation of the physical phenomenon and good resolutions of the radar signals I and Q and Doppler spectra correspondents to take a significant time as much, i.e..256T S =256(1/2000)=0.1280, [START_REF] Zrniç | Simulation of weatherlike Doppler spectra and signals[END_REF], [START_REF] Galati | Computer simulation of weather radar signals[END_REF].

Therefore, the number of samples of data ndata for a cell distance, does not affect in any manner the properties of the Doppler spectrum, except if the weather phenomenon is spread out over several seconds. In this case, it is necessary to increase the number of points (in power of 2), [START_REF] Galati | Computer simulation of weather radar signals[END_REF].

But, to exploit the data from air traffic radar's (airport radar's), we must take the number of data lower than 64, or lower than 32 samples [START_REF] Galati | Computer simulation of weather radar signals[END_REF]. The peak power of the emitted signal has a direct influence on the amplitude of the received Doppler spectrum. Thus if the peak power increases, the amplitude of the spectrum increases and the reverse is true, as we can see it on figures 9 and 10. This is also explained, by a dilemma which exists between a higher or lower power of emitted radar signals; Because to be able to emit a signal with higher power, this one will require an expensive and cumbersome material, and to have a weak power signal can harm the quality of detection of precipitation's, and this is due to the attenuation's caused by the fixed obstacles (ground clutter), [START_REF] Skolnik | Radar Handbook[END_REF], [START_REF] Keeler | Signal Processing for Atmospheric Radars in Meteorology[END_REF].

The effect of the peak power of the emitted signal on the

The presence of a peak power on the received Doppler spectrum, means the presence of weather perturbation, and this same peak corresponds to the perturbation velocity that we can read directly on the velocities axis of the Doppler spectrum.

If figure10 is considered, we can see well the existence of a peak power of Doppler spectrum, which represents a weather perturbation with a velocity of 10 m/s.

The effect of the spectral width (m/s) (σ v ) on the Doppler spectrum and signals I and Q:

σ v =0.25 m/s Doppler velocities, lie between (5 and 15 m/s), see figure 11.

σ v =10 m/s
Doppler speeds lie between (-10 and 30 m/s), see figure 12.

We can say that, σ v has a direct influence on the width of the Doppler spectrum, [START_REF] Doviak | Doppler radar and weather observation[END_REF], and [START_REF] Keeler | Signal Processing for Atmospheric Radars in Meteorology[END_REF]. Thus if we wants to have a broader spectrum σ v increases and this means that we will take in account a larger number of weather precipitation's phenomenon. And if we want to reduce the width of the weather spectrum, i.e. to select the range of the perturbations to be detected, we reverse the operation, i.e. and we reduces σ v . This parameter (m/s) plays a very important part for the modeling of the Doppler spectra characterizing the weather perturbations; it means an average deviation of the Doppler velocities variations, [START_REF] Skolnik | Radar Handbook[END_REF], [START_REF] Doviak | Doppler radar and weather observation[END_REF], [START_REF] Keeler | Signal Processing for Atmospheric Radars in Meteorology[END_REF].

V. CONCLUSION

In this paper we have discussed a model simulation of weather radar signals of precipitation's, was described. In order to have a good simulation of the ground clutter effects on the Doppler spectrum, we have proposed the alpha stable distribution which proves to be adequate, with the representation of the spectral spikes. The distribution proposed is adequate and can also represent the Doppler spectrum of the weather perturbation even with a reduced number of sequences (lower than 64 points), which is used in the air traffic control radar's [START_REF] Galati | Computer simulation of weather radar signals[END_REF].

  intermediate distributions. The modeling of the Doppler spectrum of the radar signals I and Q representing the radar echoes of a weather precipitation at low altitude, by the Levy law for various values of the parameter, α, is illustrated in the figures 1, 2 and 3.

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. Power spectrum of the weather echoes and the I, Q radar signals for α =1

Fig. 4 .

 4 Fig. 4. Weather Doppler spectrum, received Power according to the Doppler mean velocity

  Doppler spectrum and signals I/Q: (fig 9. and 10)

Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 9 .Fig. 10 .Fig. 11 .Fig. 12 .

 56789101112 Fig. 5. Effect of the SNR on the Doppler spectrum and I, Q signals (SNR=1)