J P Corella

G Benito

A P Monteoliva

J Sigro

M Calle

B L Valero-Garcés

V Stefanova

E Rico

A-C Favre

B Wilhelm

A 1400-years flood frequency reconstruction for the Basque Country (N Spain): Integrating geological, historical and instrumental datasets

Keywords: Paleofloods, Lake, Historical floods, Late Holocene, Multi-archive integration

Highlights

 First multi-proxy flood reconstruction in Northern Spain covering 1400 years  Integration of recent instrumental data (rainfall and water discharge), historical documents and geological reconstructions provides a regional, high-resolution time series of cold-season floods  Higher flood frequency during periods of Rapid Climate Change (RCC) 2

INTRODUCTION

Recent global warming seems to have directly affected timing and magnitude of European floods (Blöschl et al., 2017;2019). However, the long-term impact of climate change on flooding and its regional variability is difficult to assess, mainly due to the geographically sparse flood records from catchments with natural flow regime and the shortness of instrumental datasets (Blöschl et al., 2020;[START_REF] Hall | Understanding flood regime changes in Europe: A state of the art assessment[END_REF]. In addition, there is not yet a clear understanding of flood trends in small catchments where the expected increase in local convective storms [START_REF] Ban | Heavy precipitation in a changing climate: Does short-term summer precipitation increase faster[END_REF] may have a larger impact on flood frequency and magnitude than global changes in atmospheric patterns (Blöschl et al., 2019).

Geological, botanical and historical archives of past flooding events (i.e. paleofloods) overcome the limitations derived from the scarcity of instrumental information. They extend our knowledge of past flood occurrence beyond the instrumental record and also provide information where gauged data are absent [START_REF] Wilhelm | Interpreting historical, botanical, and geological[END_REF]. Among paleoflood archives, lake sediments are particularly valuable paleohydrological records due to its temporal continuity and the good preservation of flood layers [START_REF] Gilli | Lake Sediments as Archives of Recurrence Rates and Intensities of Past Flood Events[END_REF][START_REF] Schillereff | Flood stratigraphies in lake sediments: A review[END_REF][START_REF] Wilhelm | Recent advances in paleoflood hydrology: From new archives to data compilation and analysis[END_REF]2019). On the other hand, documentary flood archives fill the gap between instrumental and paleoflood records providing a wealth of spatio-temporal paleohydrological information including precise flood dates, number of affected watersheds and/or the socio-economic impacts (Benito et al., 2005a). Nevertheless, the integration of historical and paleoflood records at the local and regional scale is complex due to the comparison of nonhomogeneous data with various uncertainties (e.g. geochronological, record completeness), coming from heterogeneous watersheds, among other factors (Schulte et al., 2019). Thus, a detailed and critical assessment of the different flood archives should be made to adequately integrate the different sources of information.

In the Iberian Peninsula, floods are considered as the most damaging natural hazard in social and economic terms [START_REF] Ferrer | Las inundaciones en España: impacto económico y gestión del riesgo, Riesgos naturales[END_REF]. In Spain, more than 20 floods per 10,000 km 2 were registered between 1980 and 2015 accounting for 652 casualties (EEA, 2016) and annual average losses > 100 million Euros [START_REF] Barredo | Assessing trends in insured losses from floods in Spain 1971-2008[END_REF]. The Basque Country (Northern Spain) is one of the most vulnerable Spanish regions. Flood risk in this mountainous region is related to northern and western atmospheric flows leading to intense rain, that together with the concentration of socio-economic activities at valley bottoms, result in a high flood exposure and vulnerability. The costliest flood in Spain´s recent history (i.e. the August 1983 flood in the Nervión River) resulted in 34 fatalities and >620 million euros economic losses [START_REF] Barredo | Assessing trends in insured losses from floods in Spain 1971-2008[END_REF]Piserra et al., 2005).

Unfortunately, the instrumental flood record in the Basque Country is limited to the last decades, which makes difficult to disentangle the flood response to climate variability and other forcings such as land use and vegetation changes.

In Spain, annual to decadal scale flood frequency changes have been obtained from karstic lakes in the Southern central Pyrenees (Corella et al., 2016;2014b;2019) and the Iberian Range [START_REF] Barreiro-Lostres | Erosion in Mediterranean mountain landscapes during the last millennium: a quantitative approach based on lake sediment sequences (Iberian Range, Spain)[END_REF][START_REF] Moreno | Flood response to rainfall variability during the last 2000 years inferred from the Taravilla Lake record (Central Iberian Range, Spain)[END_REF]. These karstic lakes are excellent systems to reconstruct past flood variability due to the high sedimentation rates and sensitivity of the relatively small watersheds to flooding events [START_REF] Valero-Garcés | Lacustrine carbonates of Iberian Karst Lakes: Sources, processes and depositional environments[END_REF]. All these paleoflood series document events under Mediterranean influence. The determinant role of large atmospheric modes of climate variability in lake-watershed dynamics -particularly North Atlantic Oscillation (NAO) and Western Mediterranean Oscillation (WeMO) -has been assessed in several sites from the Central System (Corella et al.,2016;Hernandez et al., 2015Hernandez et al., ., 2018;;[START_REF] Sánchez-López | Climate reconstruction for the last two millennia in central Iberia: The role of East Atlantic (EA), North Atlantic Oscillation (NAO) and their interplay over the Iberian Peninsula[END_REF]. Flood variability at millennial scale has also been identified in Sanabría Lake sedimentary sequence (NW Iberian Peninsula) and related to changes in NAO-like patterns and vegetation cover during the Holocene (Jambrina-Enríquez et al., 2017). In this study, we reconstruct the first high-resolution lacustrine paleoflood record for the last 1400 years in a region under Atlantic influence in the Iberian Peninsula based on the sedimentary record of Lake Caicedo Yuso-Arreo (hereafter Lake Arreo), the only deep natural lake in the Basque Country. The wealth of instrumental and documentary data from the lake and its catchment, the multiproxy characterization of the flood layers and the known vegetation history of the watershed allow us to assess the long-term interplays between large-scale climate variability, land use, vegetation changes and flood frequency patterns. The results are compared with compiled documentary archives of catastrophic floods occurring in rivers from Northern Spain (Basque Country and Western Ebro basin) to assess the centennial-scale flood variability in Northern Spain.

STUDY SITE

Geographical and geological context

Lake Arreo is located in the northwestern limit of the Ebro Basin (Basque Country, Northern Spain) (42º 46´ N, 2º 59´ W; 655 m a.s.l.) (Fig. 1). The lake is located on the southwestern edge of the Añana saline diapir. The Lake Arreo watershed (491.5 ha) lies on Triassic gypsiferous and mudstone formations (Keuper facies). Hypovolcanic ophite rocks are cropping out forming scarps associated to an ENE-WSW fault at the northern shore of the lake [START_REF] Martín-Rubio | Factors affecting the distribution of recent lacustrine ostracoda from the Caicedo de Yuso-Arreo Lake (Western Ebro Basin, Spain)[END_REF]. The origin of the lake is attributed to interstratal evaporite dissolution and subsequent subsidence. 2.2 Lake´s morphology and hydrology Lake Arreo (6.57 ha, 24 m maximum depth) has a funnel-shaped morphology, with an almost circular perimeter and bounded to the north by a steep scarp (Fig. 1d and2a).

Before 1993, the lake was meromictic with a chemocline between 12 and 16 meters deep that delimited an anoxic monimolimnion of more saline water in the deep zone (Corella et al., 2011a;[START_REF] Chicote | Limnología y Ecología microbiana de un lago kárstico evaporítico: El lago de Arreo (Norte de España)[END_REF][START_REF] González-Mozo | Limnological characterization of an evporite karstic lake in Spain (lake Arreo)[END_REF][START_REF] Rico | Batimetría y análisis morfométrico del lago de Arreo (N. España)[END_REF]. However, the synergetic effect of lower rainfall during the last two decades and intensive water extraction in the lake brought the meromictic conditions to an end (Corella et al., 2011a).

Thus, Lake Arreo is currently monomictic -holomictic, with a strong summer thermal stratification and anoxic conditions in the hypolimnion, and a mixed period during autumn-winter.

A temporary stream (Arroyo de lago) drains the eastern area of the watershed providing water and sediments to the lake during flood events (Fig. 1c). The hydrological balance is controlled by surface and groundwater inputs and by an outlet in the southwestern shore that controls the maximum lake level. Regional authorities have conducted a monitoring program since early 1990s including water chemistry, biology and limnological parameters showing that lake level fluctuates less than 1 m during the annual cycle (www.uragentzia.euskadi.eus). Only two extraordinary lake level drops (> 2 m) have been documented during the last 30 years due to illegal water extraction in 1995 and 2002 (Corella et al., 2011a).

2.3 Land use and vegetation in the watershed Catchment land cover (Fig. 1b) consists on crops and pastures in the lowlands (38% of the total area), while the higher elevation areas are occupied by sub-humid mountain trees

Climate

The regional climate is of Atlantic-Mediterranean transitional type. The coldest and warmest months have average temperatures of 4.7º C (January) and 19.8º C (July). Mean annual rainfall in the area is 670 mm. November is the wettest month with a mean rainfall of 82.5 mm. Extreme one-day rainfall events (EREd) (> 70 mm) usually associated with convective storms mainly occur in summer (JJA) (with the highest intensities). A second period of EREd occurs during the cold season (October-April) but with lower precipitation intensity. Precipitation during the cold season for the period 1961-2010 yr CE is positively correlated with Western Mediterranean Oscillation (WeMO, 76.5% of the cases) [START_REF] Ríos-Cornejo | Links between teleconnection patterns and precipitation in Spain[END_REF]. A positive WeMO phase often brings northern air flow to the Spanish northern coast, carrying wet air and abundant precipitation in the inner reliefs [START_REF] Ríos-Cornejo | Links between teleconnection patterns and precipitation in Spain[END_REF].

METHODS

Fieldwork: bathymetric, mapping and coring surveys

A hydroacoustic survey was carried out using a 200 kHz split-beam transducer and echo sounder (Biosonics DT-X) synchronized to a Differential Global Positioning System (DGPS). A digital bathymetric model was obtained by kriging interpolation showing a similar morphology than the first bathymetric map carried out by [START_REF] Rico | Batimetría y análisis morfométrico del lago de Arreo (N. España)[END_REF] although improving the spatial resolution. Lake shoreline was adapted from [START_REF] Rico | Batimetría y análisis morfométrico del lago de Arreo (N. España)[END_REF]. Detailed imaging of lake floor was obtained by a SSS survey (high resolution Sonarbeam-150A, 400-1250 kHz), combined with continuous geo-referenced videorecording for ground-truthing, using by an Intova Connex Action Camera featuring a waterproof housing and tethered to an underwater control cable for operation, powering, and monitoring at the surface. The video settings are Full HD 1080p at 30 fps. The submerged vegetation mapping was carried out using an unsupervised classification method implemented in SonarWiz acquisition and post-processing Software from Cheasepake Technology [START_REF] Ecohydros | Caracterización de la vegetación acuática del lago caicedo yuso-arreo 2015. Situación de partida para evaluar las acciones del proyecto life-TREMEDAL[END_REF]. Sediment cores ARR04-1A1K (679 cmlong) and ARR04-1B-1K (503 cm-long) were retrieved in May 2004 at 24 and 23.2 m water depth, respectively) using a Kullenberg coring platform from the University of Minnesota (USA) (Fig. 1). A short UWITEC gravity core (ARR08-1A-1U) was retrieved in 2008.

Event layers' characterization

Sediment cores were split lengthwise and imaged with a DMT core scanner. Physical properties (density and magnetic susceptibility) of sediment cores were measured at a 5 mm resolution with a Geotek multi-sensor core logger (MSCL). Identification of discrete detrital layers (>5 mm thick) punctuating the sedimentary sequence were carried out i) by direct visual observations of sediment cores and smear slides and ii) by detailed inspection of thin sections. Lake clastic layers are deposited by direct runoff from the watershed related to major flooding episodes and/or by mass movement from slope failures as seen in other lake records (Corella et al., 2014a,b;[START_REF] Czymzik | A 450 year record of spring-summer flood layers in annually laminated sediments from Lake Ammersee (southern Germany)[END_REF][START_REF] Kremer | Origin of turbidites in deep Lake Geneva (France-Switzerland) since the last 1500 years[END_REF][START_REF] Moernaut | Lacustrine turbidites as a tool for quantitative earthquake reconstruction: New evidence for a variable rupture mode in south central Chile[END_REF][START_REF] Noren | Millennial-scale storminess variability in the northeast United States during the Holocene epoch[END_REF]Santos-Gonzalez et al., 2021;[START_REF] Wilhelm | 1400 years of extreme precipitation patterns over the Mediterranean French Alps and possible forcing mechanisms[END_REF][START_REF] Wilhelm | Recent advances in paleoflood hydrology: From new archives to data compilation and analysis[END_REF]Wilhelm et al., 2016). Discerning the triggers of each single clastic layer is required to avoid over-or underestimations in the frequency of either floods and/or massmovements. For this purpose, thin sections with dimensions of 120 mm × 35 mm were prepared after freeze-drying and impregnation with epoxy resin (Araldite) under vacuum conditions following (Brauer and Casanova, 2001). Thin-section inspection allowed us to characterize internal structure, texture and compositional features of detrital microfacies, and lastly identifying the process trigger.

Mineralogical and geochemical compositions of clastic layers were carried out in the core ARR04-1A-1K providing compositional information of clastic layers.

Mineralogical analyses (X-ray diffraction, XRD) were carried out in selected clastic facies using an automatic X-ray diffractometer SIEMENS-D500, Cu-Kα, 40 kV, 30 mA and graphite monochromator (Corella et al., 2013) (Fig 2c). Total (TC), organic (TOC) and inorganic (TIC) carbon, as well as Total Sulphur (TS), were analyzed using a LECO 144DR elemental analyzer. Total nitrogen (TN) was analyzed using a VARIO MAX CN elemental analyzer (Corella et al., 2011a;2013) (Fig. 2c). The base sublayers of 44 detrital layers were analyzed for grain size determination. Grain size distributions were measured on between 12 and 19 layers of each event type. Grain size of all fractions ranging from 3.9 µm to 217 mm was analyzed by Coulter laser grain sizer after destruction of organic matter with 10 % H2O2 at 80 ºC, stirred 24 h to facilitate particle dispersion and subjected to ultrasound during the analyses.

The flood record was reconstructed only in sediment core ARR04-1A-1K (Fig 2c )    because i) the geochemical, mineralogical and dating analyses used to characterized the event layers were performed in this core and ii) it is closer to the Arroyo del Lago river mouth. We consider that this core, is representative of the depositional dynamics in the distal basin given i) the reduced area of the profundal sub-basin (Fig 2a), and ii) the similar facies variability and sedimentation rates in distal cores previously reported in [START_REF] Corella | A 2500-year multi-proxy reconstruction of climate change and human activities in northern Spain: The Lake Arreo record[END_REF].

Age-depth model

The original depth-age model, published in Corella et al. (2011a[START_REF] Corella | A 2500-year multi-proxy reconstruction of climate change and human activities in northern Spain: The Lake Arreo record[END_REF] was based on varve counting, 137 Cs radiometric dating for the uppermost 52 cm and 5 radiocarbon dates (2 more dates were rejected because of stratigraphic reversal), and it was constructed using the mixed regression method of [START_REF] Heegaard | Relationships between calibrated ages and depth in stratigraphical sequences: an estimation procedure by mixed-effect regression[END_REF]. Here we revise the age model using Bacon software for Bayesian age modeling in R (Blaauw and Christen, 2011). All dates were included in the model, including the two obvious outliers at 510.5 cm and 570 cm (Fig. S1, Table S1). Because Bacon assumes stratigraphic ordering of dates and a linear sedimentation process, it rejects age models that violate these assumptions, so the presence of an outlier date affects model uncertainty but not the maximum likelihood estimates for the age model. For the upper part of the core the onset of Pinus radiata in the palynological sequence dated at 1870 yr CE was added as an additional chronological tie point. The age model output from Bacon is based on the probability density function for each calibrated radiocarbon age and a prior estimate of the mean sedimentation rate throughout the core set at 2 cm/ yr, and section length of the piece-wise-calculated spline, set to 20 cm (thick=20). According to the model, the 6.78 m composite depth sedimentary sequence covers the period 620-2008 CE.

Precipitation and water discharge instrumental datasets

Characterization of the precipitation patterns over the lake basin was carried out using a composition of the climatic series of precipitation corresponding to two open-access AEMET stations (Spanish meteorological service). The 9087 (Vitoria/Aeródromo) and 9091O (Foronda/Txokiza) meteorological stations, (~24 km from the lake), have been combined for the periods 1943[START_REF] Iñiguez Herrero | Timing of deglaciation and postglacial environmental dynamics in NW Iberia: the Sanabria Lake record[END_REF]CE and 1980-2019 CE respectively in order to get a continuous daily precipitation record. The quality of the data has been ensured following protocol control that checked possible erroneous data and guarantees the homogeneity of the series (Brunet et al., 2008) and was carried out using RClimDex-extraqc (freely available at http://www.c3.urv.cat/softdata.php along with the user manual (Aguilar, 2010)). Dataset homogeneity has also been tested with the ACMANT software [START_REF] Domonkos | Homogenization of precipitation time series with ACMANT[END_REF], also available at http://www.c3.urv.cat/softdata.php), using precipitation series from six nearby stations as reference. The daily water discharge series was obtained from a gauge station installed a few meters upstream the river mouth entering Lake Arreo (Fig. 1c). Hydrological data are based on continuous monitoring of flow and lake level by the Basque Water Agency (www.uragentzia.euskadi.eus) for the period 2001-2020. Calibration of the sedimentary record and the hydrological dataset was not possible due to i) the lack of sediment for the period 2008-2020 yr CE due to poor recovery of the top sediments; ii) the poor sediment preservation of the upper sediments in Lake Arreo for the period 1990-2008 due to the presence of two disrupting event layers related to documented slope failures in 1993 and 2002 respectively. Until data sets are available for a calibration, the reconstructed paleoflood archive should be interpreted with caution in quantitative terms.

Documentary flood data

Regional documentary flood data include Basque rivers and the western part of the Ebro basin, namely the catchment draining the uppermost 150 km of the Ebro River (Fig. 1a).

Historical flood datasets were obtained from: (1) written documents, scientific and technical reports, local history books and non-systematic compilations by historians such as the works by [START_REF] Font | Historia del Clima en España. Cambios Climáticos y sus Causas[END_REF][START_REF] Fontana-Tarrats | Historia del Clima en Cataluña[END_REF][START_REF] Masachs | El Régimen de los Ríos Peninsulares[END_REF]; (2) published historical flood compilations (e.g. [START_REF] Barriendos | Study of historical flood events on Spanish rivers using documentary data[END_REF]Benito et al., 1996), and (3) available datasets, namely the National Catalogue of Historical floods (Protección Civil, 2014), which completed flood records and damages over the 20 th century. Archival flood information provides direct (e.g. flood date, duration, inundation extent) or indirect (e.g., economic damage and repair works) data of individual flooding [START_REF] Barriendos | Climatic and social factors behind the Spanish Mediterranean flood event chronologies from documentary sources (14th-20th centuries)[END_REF]Brázdil et al., 2006). Reported floods correspond to overbank inundation in urban areas (streets, bridge, mills) and overflow to agricultural fields. Floods are classified in terms of severity impact [START_REF] Barriendos | Secular climatic oscillations as indicated by catastrophic floods in the Spanish Mediterranean coastal area (14th-19th centuries)[END_REF] as catastrophic (channel overflow with major damage) and extraordinary (channel overflow with some damage).

The Basque rivers dataset comprises 144 units of information on floods from 18 rivers, which corresponds to 86 flood events over the period 1400-2011 yr CE (Table S2). Some flood events have been reported in multiple locations particularly in recent times when documentary data is abundant, which support the assumption to infer past regional flood conditions from point sources. The Ebro River basin dataset (1330-2010 yr CE) contains 188 entries from 23 rivers, and 161 flood events (Table S3).

RESULTS AND DISCUSSION

Lake Arreo morphometric analyses and depositional environments

The bathymetric analyses, video-recording and aquatic vegetation mapping carried out in Lake Arreo (Fig. 2) have revealed a complex morphometry with four distinctive depositional and ecological subsystems: 1) A hygrophyte vegetation belt mostly developed in the eastern and southern flat area over 39,000 m 2 . This area can be largely flooded when there is an increase in the water discharge of Arroyo de Lago stream. Communities of helophytes (mainly Phragmites australis) dominate in the eastern area at the river mouth (13,212 m 2 ) and the larger extension of the outer southern rim (25,791 m 2 ).

Cladium mariscus and Schoenoplectus lacustris are colonizing the southern area occupying 10,676 and 640 m 2 respectively (Fig. 2b). The surface area covered by these plant communities has been stable during the last years due to the protection protocols implemented by the regional government since this site was included in the "Nature 2000 Network -Special Areas of Conservation (ZEC)" (ES2110007).

Palynological studies of lake sediment cores have revealed that this vegetation belt has been present for the last 1400 years and the changes in its composition and surface area have been strongly related to variations in the lake level and land uses (Corella et al., 2011a;2013).

2) A palustrine area (shallow waters), mainly in the southern and western areas (18,000 m 2 , 35% of the lake area, 0-3 m depth with slopes <20º), with lake waters mixed throughout the year. This area is covered with remains of helophytes and submerged macrophytes coated with biogenic carbonates (Fig. 2b). Indeed, the sedimentary record shows high rates of biogenic carbonate precipitation in this sub-environment (~1 cm/year) mainly associated with Chara macrophyte incrustations [START_REF] Martín-Rubio | Factors affecting the distribution of recent lacustrine ostracoda from the Caicedo de Yuso-Arreo Lake (Western Ebro Basin, Spain)[END_REF][START_REF] Corella | A 2500-year multi-proxy reconstruction of climate change and human activities in northern Spain: The Lake Arreo record[END_REF]. Currently submerged vegetation has been strongly reduced by the collateral effects of invasive species [START_REF] Haubrock | Control and eradication efforts of aquatic alien fish species in Lake Caicedo Yuso-Arreo[END_REF].

3) A step talus >3 m deep with slopes > 20º dominated by sediment transport and with limited deposition. The southern and western talus has a rocky substratum and presence of abundant submerged dead tree trunks. Slopes are particularly steep in the northern margin where echo-sounding and video recording have showed numerous mass-wasting deposits. Scarp-failure deposits in the northern littoral areas of the lake were already described by [START_REF] Martínez-Torres | Batimetría y propuesta de cartografía geológica del Lago de Arreo (Diapiro de Salinas de Añana, Álava)[END_REF]. 4) A deep basin covering a flat area at 24 m depth. Finely laminated sediments are preserved in the deep basin favored by the anoxic conditions prevailing during most of the annual cycle that impeded bioturbation activities in the lake bottom (Corella et al., 2011a[START_REF] Corella | A 2500-year multi-proxy reconstruction of climate change and human activities in northern Spain: The Lake Arreo record[END_REF]. These laminated sediments mostly consist on alternating gypsum-rich rhythmites and biogenic varves punctuated by mm to cm thick event layers; similar laminated successions have been described in other Iberian karstic lakes (Corella et al., 2011b;[START_REF] References Aguilar | Manual de uso de RSNHT.R (software de homogenización del Center for Climate Change[END_REF][START_REF] Martín-Puertas | The Iberian-Roman Humid Period (2600-1600 cal yr BP) in the Zoñar Lake varve record (Andalucía, southern Spain)[END_REF]Trapote et al., 2018b).

Deep basin lithostratigraphical units

The sediment sequences in both cores ARR04-1A-1K and ARR04-1B-1K in the distal deep basin show alternating finely laminated endogenic calcite-rich and gypsum-rich facies punctuated with event layers. [START_REF] Corella | A 2500-year multi-proxy reconstruction of climate change and human activities in northern Spain: The Lake Arreo record[END_REF]

Event layers in Lake Arreo

Lake Arreo sedimentary sequence in the distal basin includes 142 event layers (Figs. 2,3 and 5). The sedimentological, textural and geochemical analyses of the layers provide insight into the depositional processes operating in the lake during the last 1400 years and tools to ascribe them to turbidite and flood events.

Mass-movement turbidites

Event layers deposited as Mass-movement turbidites (MMT) have been identified in the distal cores based on sedimentological, textural and compositional features. Sixteen MMT layers have been identified. They consist on centimetre-thick detrital layers with a sandy, non-graded coarse basal sub-layer and an erosive basal surface, followed by finer sediments with several fining upward pulses (Fig. 3c). The thick and homogeneous basal sub-layer as well as the multiple coarse grain-size pulses occurring during individual events found in Lake Arreo´s MMTs are all common features of mass-movement-induced gravity flows [START_REF] Gorsline | Seismically triggered turbidites in small margin basins: Alfonso Basin, Western Gulf of California and Santa Monica Basin, California Borderland[END_REF][START_REF] Mulder | The physical character of subaqueous sedimentary density flows and their deposits[END_REF][START_REF] Mulder | Marine hyperpycnal flows: initiation, behavior and related deposits. A review[END_REF]Wirth et al., 2011). These individual flood laminae are the thickest observed in the sedimentary sequence ranging between 1 and 26 cm (mean thickness of 6.9 cm). Grainsize of MMT bases minimal and maximum values ranges between 17 and 217 µm (mean = 91.4 µm) (Fig. 5). MMT in Lake Arreo are mostly composed of siliciclastic material with abundant plagioclase, quartz and pyroxene crystals. Reworked hydrophyte fragments and/or littoral carbonates are also frequent. MMT show very high Magnetic Susceptibility (MS) values, while TIC and TOC values are very low, ranging respectively from 0.1-0.2 and 0.4-0.8 % wt. The carbon-nitrogen ratio is high (C/N= 12.8-17.4).

The abundant plagioclase and pyroxene crystals as well as the high MS values in the MMT deposits point out to the ophitic body from the northern cliff (with significant presence of ferromagnetic minerals) as the main source of the slope failures. Indeed, scarp-failure deposits in the northern littoral areas of the lake were described by [START_REF] Martínez-Torres | Batimetría y propuesta de cartografía geológica del Lago de Arreo (Diapiro de Salinas de Añana, Álava)[END_REF]. Nevertheless, the presence of reworked carbonates and hydrophytes in the MMTs also demonstrate that they incorporate sediment from the southeastern littoral platform with high carbonate production and hydrophytes communities.

According to the age model, the two most recent MMTs in Lake Arreo sequence occurred in 2002 and 1995, and they have been attributed to documented slope failures related to the 1995 and 2002 triggered by 2 and 4.7 m lake level drops due to illegal water extraction (Corella et al., 2011a). These lake level drops would have increased shear stress and strain as well as decrease pore water pressure in slope sediments, leading to scarp failure. Nevertheless, such lake level changes are not expected to occur under natural lake 16 dynamics (0.5-0.7 m variability; Fig. 6). Thus, the fourteen MMT occurring before the instrumental and observational period were likely caused by other mechanisms such as rapid sediment loading, earthquakes, underwater seepage or slope undercutting and oversteepening (Fig. 3c) as seen in other lacustrine and marine settings [START_REF] Girardclos | The 1996 AD delta collapse and large turbidite in Lake Brienz[END_REF][START_REF] Hampton | Submarine landslides[END_REF][START_REF] Locat | Submarine landslides: advances and challenges[END_REF][START_REF] Strasser | Quantifying subaqueous slope stability during seismic shaking: Lake Lucerne as model for ocean margins[END_REF][START_REF] Sultan | Triggering mechanisms of slope instability processes and sediment failures on continental margins: a geotechnical approach[END_REF]. Local or regional earthquakes could be a likely trigger of some of these MMTs since the northern margin of Lake Arreo is bounded by an ENE-WSW fault [START_REF] Martín-Rubio | Factors affecting the distribution of recent lacustrine ostracoda from the Caicedo de Yuso-Arreo Lake (Western Ebro Basin, Spain)[END_REF]) that could be reactivated during seismic shaking.

Flood layers

In Lake Arreo, two types of flood layers have been identified based on different textural characteristics (Fig. 3a andb).

Fine detrital layers (FDL)

FDL consist on mm to cm-thick blackish, non-graded fine silt layers mainly composed of clay minerals (>80%) with minor contributions of terrestrial and aquatic organic matter (i.e. planktonic diatoms). Thin basal coarse-silt sublayers sometimes occur without any clear micro-erosion features (Fig. 3a). Elemental geochemistry shows TIC and TOC values ranging between 0.1-0.3 % and 0.8-1.8 % wt (C/N = 10-10.5). Textural analyses of the basal part of the flood layers show a grain size range from 3.9 to 19.2 µm (min and max values respectively, mean = 8.1 µm) (Fig. 5). 76 FDL have been identified with maximum and mean thicknesses ranging between 9.1 and 2.4 cm, respectively. The non-graded structure of the fine material and the lack of micro-erosion features suggest low-density currents as the depositional process for these layers. In these conditions, the sediment plumes from the currents are not sufficiently dense to pervade the thermocline formed by the permanent water stratification so that suspended matter is distributed within the lake basin through overflows and/or interflows (Wilhelm et al., 2015). The thin silty basal sublayer (mean grain-size of 8.1 µm, Fig. 5) and the faintly grading towards finer clayish material on top of the layers suggest the differential settling of suspended particles according to their grain size.

Coarse detrital layers (CDL)

CDL are characterized by mm to cm-thick greyish graded layers with a thin coarse sublayer and a well-developed fining upwards bed (Fig. 3b). They are mostly composed by quartz and carbonate-rich silty mud with abundant clay minerals (60%), plagioclase (20%) and gypsum (5%). Micro-erosion and irregular basal surfaces as well as plant remains, and reworked littoral carbonates are also present in the basal sub-layer. They display relatively high MS and density values. TIC and TOC values are low ranging between 0.4-0.5% wt and 1.1-2.3 % wt, respectively, while C/N values ranges from 9.5 to 15.1 (terrestrial origin). Fifty CDL have been identified in the sequence with maximum and mean thickness of CDL layers varies between 7.2 and 2 cm respectively. The basal parts of the CDL layers have grain-size ranging from 6.3 to 86.2 µm (mean = 37.2 µm) (Fig. 4). Grain-size of the thinnest CDL might appear similar to the one of FDL. This may, however, result from the limited sampling resolution (≥5 mm minimum) that makes not possible to sample only the mm-scale basal layer. Deposition of CDLs are interpreted to occur when major flooding episodes trigger high-energy density currents, penetrating through the lake stratification as underflows as previously described in stratified lakes elsewhere (Corella et al., 2014a;[START_REF] Giovanoli | Horizontal transport and sedimentation by interflows and turbidity currents in Lake Geneva[END_REF][START_REF] Sturm | Turbidites and varves in Lake Brienz (Switzerland): deposition of clastic detritus by density currents[END_REF]Wilhelm et al., 2015). The higher grain-size of CDL layers might reflect higher flood magnitudes since grain-size may be a proxy for flow energy and discharge [START_REF] Lapointe | 1750 years of large rainfall events inferred from particle size at East Lake, Cape Bounty, Melville Island, Canada[END_REF][START_REF] Schillereff | Hydrological thresholds and basin control over paleoflood records in lakes[END_REF][START_REF] Wilhelm | 1400 years of extreme precipitation patterns over the Mediterranean French Alps and possible forcing mechanisms[END_REF]2013).

Influence of climate variability and land use on FDL and CDL deposition

Lake Arreo paleoflood record should be carefully interpreted in terms of reconstructing past hydroclimate since sediment supply may vary as the result of a complex interplay between natural and anthropogenic processes. Flood layers in Lake Arreo (both FDL and CDL) remained low during the High and Late Middle Ages (10-15 th centuries) concomitant with the most intense land use in the watershed reflected by the elevated pollen anthropogenic indicators in Lake Arreo sediments and during the late MCA and beginning of the LIA (Fig. 5). On the other hand, more frequent deposition of flood layers occurred during periods of forest recovery and reduced anthropogenic pressure in the watershed (the 8 th century and some intervals during the last five centuries) suggesting that flood layers are closely controlled by hydroclimate variability. Thus, heavier rainfall triggering high-magnitude floods would probably lead to CDL deposition while moderate events would result in FDL layers.

Nevertheless, we cannot rule out the role of human pressure on the watershed on run-off generation. We observe a major increase in FDL frequency during the 18 th century coinciding with a peak in Sporormiella dung spores a proxy for grazing activities [START_REF] Etienne | Influences of sampled environments and livestock number on Sporormiella abundances in modern samples sediments in French Alps[END_REF][START_REF] Montoya | Grazing activities in the southern central Pyrenees during the last millennium as deduced from the non-pollen palynomorphs (NPP) record of Lake Montcortès[END_REF]Trapote et al., 2018a). FDL layers also increased during the 1960s concomitant with a smallholding concentration process that affected the vegetation belt around the lake and the sediment availability in the watershed [START_REF] Corella | Climate and human impact on a meromictic lake during the last 6,000 years (Montcortès Lake, Central Pyrenees, Spain)[END_REF]. Thus, flood layer occurrence depends on the interplay between heavy rainfall variability and human impact at catchment scale, which is in agreement with observations from other Iberian karstic lakes [START_REF] Barreiro-Lostres | Erosion in Mediterranean mountain landscapes during the last millennium: a quantitative approach based on lake sediment sequences (Iberian Range, Spain)[END_REF][START_REF] Corella | A millennium-long perspective of flood-related seasonal sediment yield in Mediterranean watersheds[END_REF]. based Lake level reconstruction from Lake Arreo (from [START_REF] Corella | A 2500-year multi-proxy reconstruction of climate change and human activities in northern Spain: The Lake Arreo record[END_REF]. Blue and green horizontal bars represent periods with increase in CDL and FDL frequencies respectively.

Flood record in the Lake Arreo watershed

Instrumental data can bring information about the hydro-meteorological processes generating floods and, thereby, about the type of flooding recorded in historical and geological archives. Flood generation in Lake Arreo watershed was analyzed by comparing daily water discharge with precipitation over the period 2001-2020 yr CE.

Annual floods do not always correspond to the maximum daily precipitation, pointing to the combination with other hydro-meteorological processes and/or catchment conditions.

Daily discharge data reveal that extreme floods mostly occur in winter (DJF) and spring (MAM), while the most severe annual maximum daily heavy rainfall events occur in summer (Fig. 6). Interestingly, direct runoff during summer heavy rainfalls, characterized by high intensity and short duration, is limited due to high infiltration capacity and permeability of soils (infiltration coefficient ~0.4) developed on ophyte/diabase bedrock (cambisols and regosols) [START_REF] Iñiguez Herrero | Timing of deglaciation and postglacial environmental dynamics in NW Iberia: the Sanabria Lake record[END_REF]. Only saline soils and lithosols developed on clayish material (16% in surface area) are producing hortonian flows during summer rainfalls. On the other hand, water discharge measurements at the gauge station reveal that 75% of the largest floods can be explained by heavy rainfall episodes (>20 mm/day) preceded by long rainfall episodes (accumulated rainfall >80 mm in 6-13 days).

Thus, both heavy rainfall and high antecedent moisture conditions (i.e. saturated soils) are needed to trigger floods in the Lake Arreo watershed. Thus, CDL layers of Lake Arreo sequence are interpreted as high energy flood events occurring during the cold season (Oct-May). The record spans since the onset of the Middle Ages (Fig. 7) with moderate increase in the frequencies between 720-780 CE, 850-900 CE, 1480-1540 CE, 1720-1740 CE and the largest increase in frequencies occurring between 1830-1880CE and 1950-1990 CE. Water inflows to the lake correlates well with lake level variability. Thus, the water table can increase between 0.5 and 0.7 m during periods of maximum river discharge, while lake level regularly decreases from 0.2 to 0.3 m during summer droughts (Fig. 6).

A relation between flood variability/sediment delivery and lake level changes is further observed in the longer term. Thus, lower flood frequency during the Middle Ages coincided with lower lake levels (Fig. 5), coherent with lower rainfall and run-off. On the other hand, the highest flood frequency occurred during the last five centuries in agreement with the highest lake level and a shift from a brackish lake to a meromictic lake with reduced salinity in Lake Arreo (Fig. 5) [START_REF] Corella | A 2500-year multi-proxy reconstruction of climate change and human activities in northern Spain: The Lake Arreo record[END_REF].

Historical floods of the western Ebro Basin and the Basque Country

The compiled historical flood datasets from rivers of the Western Ebro Basin and the Basque Country reports a total of 200 historical floods since 1330 CE. The level of flood risk perception by the riverine population was relatively high due to frequent damages triggered by the Ebro River overflows into major villages. Typically, documentary flood registers describe economic impacts caused by flood water inundation (mostly in urban areas), and social disruption as consequence of damages in irrigation canals, roads and bridges. The analysis of regional documentary data indicates flood-rich and flood-poor periods over the last 700 years. High flood frequency in rivers from Western Ebro basin occurred between 1625-1670, 1830-1850, 1900-1940 and 1950-1980 yr CE while Basque rivers show high flood frequency between 1580-1600, 1820-1840, 1860-1880, 1910-1930and 1970-2010 yr CE (Fig. 7, Tables S1 andS2). In contrast, periods between 1410-1530 and 1610-1690 CE and between 1300-1580 yr CE were characterized by few reported floods in the Basque rivers and Western Ebro basin respectively.

Comparison between historical and paleoflood records

In the Iberian Peninsula, compiling historical flood information at a regional scale results in a mixed population of flood types due to the spatial diversity of flood-producing hydrometeorological conditions, and variety of geomorphology, catchment size and vegetation cover. Thus, multi-archive, regional flood reconstructions should be carried out with care.

The historical flood records of the Ebro basin headwaters and the Basque rivers show a regular increase of floods towards modern times (Fig. 7), which may result from i) increase in reported floods during the last centuries and ii) an increasing vulnerability/exposure of population associated to demographic growth since second half of the 19 th century. As a result, flood frequency during the Pre-Industrial Period is most likely underestimated as highlighted when comparing with the paleoflood record from Lake Arreo (Fig. 7).

As instrumental data and documentary evidence show, the Arreo record is mostly a cold-season flood archive. Thus, we have decoupled the flood seasonality from the historical flood archives to provide an adequate comparison with the lacustrine records (Fig. 7). The Lake Arreo and Basque rivers cold-season flood time series variability shows a higher agreement suggesting a similar hydroclimate driver. Winter rainfalls in the Basque Country mainly result from atmospheric fronts coming from the north and northwest, a pattern clearly different from central and eastern Iberian Peninsula, more strongly influenced by Mediterranean dynamics (Capel, 1981;[START_REF] Esteban-Parra | Spatial and temporal patterns of precipitation in Spain for the period 1880-1992[END_REF][START_REF] Serrano | Monthly modes of variation of precipitation over the Iberian Peninsula[END_REF]. The evolution pattern of extreme one-day precipitation events (EPEd) that cause major winter floods in the Basque Country also follows this same behavior (Benito et al., 1996b). The relief also plays a major role because the Cantabrian Mountains, parallel to the coast, forces the air masses to ascend (orographic forcing), producing EPEd on the windward side (northern slopes), very close to the location of Lake Arreo. When air masses reach the southern slopes, they are drier and warmer because of the rain shadow effect, and for this reason, the Ebro Valley is isolated from the winter Atlantic moisture fluxes [START_REF] Beguería | Annual and seasonal mapping of peak intensity, magnitude and duration of extreme precipitation events across a climatic gradient, northeast Spain[END_REF]. This behavior has been verified for precipitation events above the 90 th percentile in autumn and spring, mainly associated with two specific synoptic situations (Fernandez-Montes, 2014). One, a steep gradient between the Azores High and much lower pressure in the Western Mediterranean and Northern Africa, significantly conducive to a strong North flow converging over the northern mountain chains and promoting the ascent of air and precipitation in north-facing slopes at high altitude. Another, the Azores anticyclone in the Atlantic and low pressure extended in Central Europe with a through over the Western Mediterranean, driving a humid northern-westerly flow to Northern Iberia. This SLP configuration produces extreme precipitation in the north/northwest facing slopes and rain-shadow effect leeward of Cantabrian, Iberian and Pyrenees Mountains. Atmospheric synoptic situations driving the largest cold season water discharge in Lake Arreo correspond to these atmospheric reorganization patterns (Fig. S2). Therefore, the agreement between historical floods series of the Basque rivers and the reconstructed paleoflood series of Lake Arreo stream suggests that the lacustrine record represent a long-term, regional hydroclimatic proxy of floods induced by winter Atlantic atmospheric flows. S1 andS2);. All curves represent the 31 yr running average. Main climatic and historical periods are also indicated.

Flood variability during the last 1400 years in Northern Spain.

Combining instrumental, historical and geological flood records is a valuable approach to understand the flood evolution at a regional scale since each archive contains complementary hydrological information [START_REF] Wilhelm | Interpreting historical, botanical, and geological[END_REF]. The Arreo multi-archive dataset provides a reconstruction of cold-season flood variability since the 7 th century for Northern Spain.

Low flood frequency was recorded up to 7 th century (Fig. 7), corresponding to the end of the Migration period, characterized by a strong hydrological deficit in the Mediterranean and scarce paleoflood events in both fluvial and lacustrine archives in the Iberian Peninsula (Benito et al., 2015b;Corella et al., 2016;[START_REF] Currás | Climate change and human impact in central Spain during Roman times: High-resolution multi-proxy analysis of a tufa lake record (Somolinos, 1280 m asl)[END_REF].

Overlapping this period, central Spain lake records suggest warm temperatures and arid conditions and low flood frequency [START_REF] Sánchez-López | Climate reconstruction for the last two millennia in central Iberia: The role of East Atlantic (EA), North Atlantic Oscillation (NAO) and their interplay over the Iberian Peninsula[END_REF]. Similar reduced flood frequency and lower lake levels during this period have been also reported in the southern and western European Alps [START_REF] Magny | Holocene climate variability as reflected by mid-European lakelevel fluctuations and its probable impact on prehistoric human settlements[END_REF][START_REF] Sabatier | 6-kyr record of flood frequency and intensity in the western Mediterranean Alps-Interplay of solar and temperature forcing[END_REF][START_REF] Schulte | A 2600 year history of floods in the Bernese Alps, Switzerland: frequencies, mechanisms and climate forcing[END_REF][START_REF] Gilli | Lake Sediments as Archives of Recurrence Rates and Intensities of Past Flood Events[END_REF]. Flood frequency variability remained low during the Middle Ages except for two periods during the 8 th and the late 9 th centuries (Fig. 7) that corresponds to i) the termination of the Dark Ages Cold Period (DACP; 460-775 CE), a cold and humid episode in Europe [START_REF] Helama | Dark Ages Cold Period: A literature review and directions for future research[END_REF] and ii) the transition to the Medieval Climate Anomaly (MCA; 900-1300 CE). Lower flood frequency reconstructed in Lake Arreo during the MCA is concomitant with the warmer and more arid conditions reconstructed in the Iberian Peninsula during this period [START_REF] Moreno | The Medieval Climate Anomaly in the Iberian Peninsula reconstructed from marine and lake records[END_REF]Sanchez-Lopez et al., 2016). Increased aridity might have increased sediment availability in the watersheds that could be easily eroded and re-mobilized during moderate rainfall events as documented in other Iberian lakes (i.e. Cimera lake (Sanchez-Lopez et al., 2016)). Nevertheless, we infer the opposite pattern in Lake Arreo with more floods occurring during the LIA, characterized by colder and more humid conditions in NE Spain [START_REF] Morellón | A multi-proxy perspective on millennium-long climate variability in the Southern Pyrenees[END_REF][START_REF] Oliva | The little ice age in Iberian mountains[END_REF]. This is coherent with our hydrological interpretation of floodgenerating mechanisms needing preconditioning humid (i.e. saturated) conditions in the watershed´ soils to trigger large floods.

The last five centuries stand out as the period with the largest flood variability of the last 1400 years in agreement with historical floods from Northern Spain, fluvial paleoflood records of Iberian rivers (Benito et al., 2015) (Fig. 7) and paleoflood records from lakes of the Iberian Range [START_REF] Moreno | Flood response to rainfall variability during the last 2000 years inferred from the Taravilla Lake record (Central Iberian Range, Spain)[END_REF]. And abrupt increase in FDL frequency occurred during the 17 th and the 18 th centuries while higher CDL frequencies have intermittently occurred since the early 17 th century (Fig. 7). A marked abrupt increase in floods in the mid-19 th century occurred in both paleoflood records and historical floods from Basque rivers (Fig. 7). Interestingly, the highest increase in flood frequency before the onset of the current global warming coincides with the termination of well-known cold and humid periods (i.e. DACP and LIA). Increased flood frequency during intervals of rapid climate changes has also been described in European flood records from fluvial archives (Benito et al., 2015a;[START_REF] Macklin | Past hydrological events reflected in the Holocene fluvial record of Europe[END_REF] suggesting changes in atmospheric circulation patterns resulting in increased hydroclimate instabilities [START_REF] Knox | Sensitivity of modern and Holocene floods to climate change[END_REF].

The second largest increase in flood frequency recorded in both lacustrine and documentary archives occurred during the second half of the 20 th century (Fig. 7). This period coincides with the Great Acceleration (1950 CE-Present day) and the intensification of the global warming. Several studies suggest changes in the characteristics of precipitation in the study region throughout the 20 th century with i) an increase in the number of days of intense or very intense precipitation in summer and winter; ii) a general increase in the number of rainy days throughout the year and iii) an increase in rainfall above the 90 th and 98 th percentiles in the study area [START_REF] Gallego | Trends in frequency indices of daily precipitation over the Iberian Peninsula during the last century[END_REF][START_REF] Moberg | Indices for daily temperature and precipitation extremes in Europe analyzed for the period 1901-2000[END_REF]). An increase in flood magnitude and frequency of floods in Atlantic basins between 1960-1980 CE and a subsequent decrease in peak discharge of extraordinary floods has also been reported by a comprehensive assessment endorsed by the Spanish Ministry of Environment (Benito et al., 2005b) which agrees well with our multi-archive reconstruction from the Basque Country. Flood events in Northern Spain increased over the last decades of the 20 th century characterized by warming conditions and dry anomalies in Iberia (Brunet et al., 2007;Coll et al., 2017). Such weather conditions are an indication of higher frequency of persistent anomalous atmospheric circulations associated to warm sea surface temperature anomaly in the Northern Atlantic Ocean [START_REF] Ballesteros-Cánovas | On the extraordinary winter flood episode over the North Atlantic Basin in 1936[END_REF]Blöschl et al., 2020). At the European scale, documentary gauged flood records showed a similar increase in flood frequency since 1960 under warm climate (Blöschl et al., 2019).

Our research demonstrates a high sensitivity of flooding to climate variability over the last 1400 years, in particular during periods of climate transition including the current global warming. Whereas most flood projections under different climate change scenarios uses a top-bottom down approach sometimes not adapted to local conditions, paleoflood hydrology provides a local approach to better understand long-term flood hydrology and thus improve our adaptation capacity to future flood hazard and risk analysis.

CONCLUSIONS

The integration of instrumental, historical and paleoflood datasets as well as the comparison with other available paleohydrological records have allowed us i) to depict the large spatio-temporal heterogeneity of extreme floods in Northern Spain and; ii) to highlight the complexity of comparing different flood archives. This study also exemplifies the need to carefully interpreted paleoflood and historical records before establishing comparisons between the different sources of paleohydrological information.

The exceptional morpho-sedimentary and catchment conditions of Lake Arreo  CDLs were generated by high-magnitude floods mainly controlled by regional hydroclimate.

Instrumental data indicate that floods in Lake Arreo are generated during the cold season by heavy rainfall events after several days of continuous Atlantic frontal rainfalls, leading to soil moisture saturation as a catchment precondition for flood generation.

Historical data suggest that the Lake Arreo flood record represent regional, long-term changes in flood occurrence, given the similarities with changes in winter floods in the Basque Country over the last centuries. Thus, the lacustrine flood layers archive has been interpreted as a reconstruction of cold-season flood variability in the region. The highest flood frequencies occurred between the 8-9 th centuries and during the last 500 years.

Long-term paleoflood records demonstrated a high sensitivity of flooding to anomalous atmospheric circulation patterns occurring during climate transitions. It also provides a robust and viable approach to improve our understanding future changes on flood hazards to enhance climate change adaptation. Medioambiente, Madrid, pp. 507-527. Benito, G., Macklin, M.G., Panin, A., Rossato, S., Fontana, A., Jones, A.F., Machado, M.J., Matlakhova, E., Mozzi, P., Zielhofer, C., 2015a. Recurring flood distribution patterns related to short-term Holocene climatic variability. Scientific Reports 5, 16398. Benito, G., Macklin, M.G., Zielhofer, C., Jones, A.F., Machado, M.J., 2015b. Holocene flooding and climate change in the Mediterranean. CATENA 130, 13-33. Benito, G., Machado, M.J., Pérez-González, A., 1996a. Climate change and flood sensitivity in Spain, In: Branson, J., Brown, A.G., Gregory, K.J. (Eds.), Global continental changes: the context of paleohydrology. The Geological Society of London, London, pp. 85-98. Benito, G., Machado, M.J., Pérez-González, A., 1996b. Climate change and flood sensitivity in Spain. Geological Society, London, Special Publications 115, 85-98. Benito, G., Ouarda, T., Bárdossy, A., 2005b. Applications of palaeoflood hydrology and historical data in flood risk analysis. evidence to aid preparations for future floods. Wiley Interdisciplinary Reviews: Water 6, e1318. Wilhelm, B., Nomade, J., Crouzet, C., Litty, C., Sabatier, P., Belle, S., Rolland, Y., Revel, M., Courboulex, F., Arnaud, F., 2016. Quantified sensitivity of small lake sediments to record historic earthquakes: Implications for paleoseismology. Journal of Geophysical Research: Earth Surface 121, 2-16. Wilhelm, B., Sabatier, P., Arnaud, F., 2015. Is a regional flood signal reproducible from lake sediments? Sedimentology 62, 1103-1117. Wirth, S.B., Gilli, A., Simonneau, A., Ariztegui, D., Vannière, B., Glur, L., Chapron, E., Magny, M., Anselmetti, F.S., 2013. A 2000-year long seasonal record of floods in the southern European Alps. Geophysical Research Letters, n/a-n/a. Wirth, S.B., Girardclos, S., Rellstab, C., Anselmetti, F.S., 2011. The sedimentary response to a pioneer geo-engineering project: Tracking the Kander River deviation in the sediments of Lake Thun (Switzerland). Sedimentology 58, 1737Sedimentology 58, -1761. .

Preliminary assessment of impacts in Spain by Climate Change Ministerio de

(

  mainly Quercus faginea and Pinus sylvestris on the north-facing slope) and evergreen oaks (Quercus ilex) on drier south-facing exposures. Shrublands occupies 15 % of the total area mostly composed of Juniperus communis, Aphyllantes monspeliensis, Lavandula latifolia and Thymus vulgaris. The lake is surrounded by a broad palustrine vegetation belt, with Scirpus lacustris communities in the deeper areas, and reed beds with Phragmites australis, Typha latifolia, Typha angustifolia, Sparganium erectum, etc in the shallower ones. In the east and south-east parts those reed beds are replaced by communities of Cladium maríscus with Scirpus marítimus, Juncus acutus and Puccinellia fasciculata, species linked to brackish environments. Characteristic elements of the vegetation developed on drier soil are Carex spp., Althaea officínalis and Epilobium 6 hírsutum. The submerged and floated leaf aquatics are presented by Chara hispida var. hispida, Chara hispida var. major, Myriophyllum verticillatum, Polygonum amphibium, Potamogeton coloratus, P. lucens, P. pectinatus, P. pusillus, Ranunculus trichophyllus, Utricularia australis and Zannichellia pedunculata.

Fig. 1 :

 1 Fig. 1: a) Location of the studied area. Blue and green dotted lines represent the study areas with historical river floods in the Spanish Northern and Ebro basins. Red dot indicates the location of Lake Arreo; b) Aerial photograph of Lake Arreo watershed; c) Digital Elevation Model (DEM) of Lake Arreo watershed and location of the gauging station in Arroyo del lago stream; d) Bathymetric map of Lake Arreo and location of the coring sites.

  Fig 2) punctuated by event layers, and two -units 4 (CE 900-1300) and 2 (CE 1615-1965) -consist of alternating calcite-rich laminites and event layers.

Fig. 2 :

 2 Fig. 2: a) 3-D bathymetric map showing the main depositional environments described in the text; b) Vegetation map of the main helophythic communities; c) core image, sedimentary sedimentological column, magnetic susceptibility, Total Organic Carbon (TOC), Total Inorganic Carbon (TIC), carbon-nitrogen ratio (C/N) and mineralogical proxies (from Corella et al. 2013). Maximum TOC and C/N values indicated by the blue star are 21,8 % and 70,7 respectively. Core images and lithostratigraphic units from ARR04-1A1K sediment core are also shown.

Fig. 3 :

 3 Fig. 3: Polarized microscope photos of the three types of event layers identified in Lake Arreo and sketches of their respective deduced depositional models. A) Fine Detrital Layer (FDL); B) Coarse Detrital Layer (CDL); C) Mass Movement Turbidites (MMT). White vertical lines represent the event layer thickness.

Fig. 4 :

 4 Fig. 4: Ternary plot showing the textural composition of the basal parts of analyzed flood and mass-movement layers.

Fig. 5 :

 5 Fig. 5: From left to right: Flood frequency variability (green FDL; blue: CDL); Main palynological indicators of land use and vegetation changes: AP -arboreal pollen (trees and shrubs); Cultivated taxa -Triticum/Avena, Secale, Cerealia, Cannabis-type, and Polygonum aviculare-type; Ruderals -Artemisia, Chenopodiaceae, Plantago major, P. media, and Urtica; Meadows and pastures -Aster-type, Cirsium, Chichorioideae, Apiaceae, Heracleum, Campanula-type, Filipendula, Potentilla, Gallium-type, Lathyrus, Trifolium-type, Lotus-type, Ranunculaceae, Ranunculus acris-type, Hypericum, Lotus-type, Rumex acetosa, R. acetosella, Plantago lanceolata. Hydrophytes -Potamogetom, Utricularia, Myriophyllum, Lemna; Diatom-

Fig. 6 :

 6 Fig. 6: Daily water discharge recorded on Lake's Arreo inflow compared with (from top to bottom); accumulated precipitation during extreme precipitation events (EPE) and consecutive days before EPE; Monthly daily maximum precipitation; daily lake level variability; (Precipitation data obtained from meteorological station at Vitoria airport)

Fig. 7 :

 7 Fig. 7: From left to right: CDL (blue) and FDL (green) flood layer frequency variability (horizontal blue bands represent periods with increased CDL flood frequency); Paleoflood occurrence probability in Mediterranean (pink) and Atlantic (grey) rivers (Benito et al., 2015); Cold-season (Oct-May) normalized historical floods from Basque rivers and Western Ebro basin tributaries (from TablesS1 and S2);. All curves represent the 31 yr running average. Main climatic

  makes it an ideal setting to record and preserve long-term paleoflood information in the Basque Country (Northern Spain). A total of 126 flood layers were identified over the last 1500 years. A subsequent textural and geochemical characterization of clastic lake sediments classified 50 layers as coarse detrital laminae (CDL) and 76 fine detrital laminae (FDL). The paleoflood record was completed with daily gauged flow records at the lake major stream for the 2001-2020 CE period and documentary flood records from the Basque Rivers (1400-2000 CE) and Ebro headwater tributaries(1300( -2000 CE) CE). The multiproxy analyses of event layers indicates that:  FDL were generated by moderate-magnitude floods, caused by an interplay between hydroclimate and land use.

Table 1 :

 1 Mean characteristics of the different event layers identified in Lake Arreo

	Event layer type	Nº layers	Layer thickness	Grain-size	TIC (%)	TOC (%)	C/N	Magnetic susceptibility (MS)	Mineralogy	Sedimentological features	Depositional processes
	Mass-movement turbidites (MMT)	16	1-26 cm	17-217 µm (91.4 µm)	0.1-0.2	0.4-0.8	12.8-17.4	Very high	Plagioclase, quartz and pyroxene crystals. Frequent calcite reworked) (littoral,	Sandy, basal contact graded coarse non-basal sub-layer with several fining upward pulses. Erosive	Mass-movement-induced gravity flows
										Non-graded fine	Flood-
	Fine detrital layer (FDL)	76	2.4-9.1 cm	3.9-19.2 µm (8.1 µm)	0.1-0.3	0.8-1.8	10-10.5	Moderately high	Dominant clay minerals (>80%)	silt Occasional thin layers. basal coarse-silt sublayers. Non-erosive basal	related low-density currents. Overflows and/or
										contact		interflows
									Quartz and	Graded	silty	Flood-
	Coarse detrital layer (CDL)	50	2-7.2 cm	6.3 -86.2 µm (37.2 µm)	0.4-0.5	1.1-2.3	9.5-15.1	High	carbonates with abundant clay minerals	layers with a thin coarse sub-layer. Fining upwards texture. Micro-erosive basal	related high-energy density currents. Underflow
									(>60%).	contact.		events

ACKNOWLEDGEMENTS

This work was financed by the MSCA project FLOODARC (H2020-MSCA-IF-2017, grant nº 796752) funded by the European Union (MSCA-IF-EF-ST funding scheme).

Additional support has been obtained by the Spanish Ministry of Science, Innovation and Universities (MICINN) projects LIMNOCAL (CGL 2006-13327.C04-01/CLI), MEDLANT (CGL2016-76215-R), MEROMONT (CGL2017-85682-R) and EPHIMED (CGL2017-86839-C3-1-R) (co-financed with European FEDER funds). The Basque Water Agency facilitated access to its hydrological data.

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Brunet, M., Jones, P.D., Sigró, J., Saladié, Ó., Aguilar, E., Moberg, A., Della-Marta, P.M., Lister, D., Walther, A., López, D., 2007. Temporal and spatial temperature variability and change over Spain during 1850-2005. Journal of Geophysical Research: Atmospheres 112. Brunet, M., Saladié, O., Jones, P., Sigró, J., Aguilar, E., Moberg, A., Lister, D., Walther, A., Almarza, C., 2008. A case-study/guidance on the development of long-term daily adjusted temperature datasets. World Meteorological Organization WCDMP-66/ WMO-TD-1425, Geneva. Capel, J., 1981. Los climas de España. Oikos-Tau, Barcelona. Coll, J.R., Aguilar, E., Ashcroft, L., 2017. Drought variability and change across the Iberian Peninsula. Theoretical and Applied Climatology 130, 901-916. Corella, J., Valero-Garcés, B., Vicente-Serrano, S., Brauer, A., Benito, G., 2016. On the frequency, seasonality and atmospheric drivers of Late Holocene heavy rainfall in Western Mediterranean. Scientific Reports. Corella, J.P., Amrani, A., Sigró, J., Morellón, M., Rico, E., Valero-Garcés, B., 2011a. Recent evolution of Lake Arreo, northern Spain: influences of land use change and climate. Journal of Paleolimnology 46, 469-485. Corella, J.P., Arantegui, A., Loizeau, J.L., DelSontro, T., le Dantec, N., Stark, N., Anselmetti, F.S., Girardclos, S., 2014a. Sediment dynamics in the subaquatic channel of the Rhone delta (Lake Geneva, France/Switzerland). Aquatic Sciences 76,[73][74][75][76][77][78][79][80][81][82][83][84][85][86][87]


Felienne Hermans
email: f.f.j.hermans@tudelft.nl

Tijs Van

Copy-Paste Tracking: Fixing Spreadsheets Without Breaking Them

Spreadsheets are the most popular live programming environments, but they are also notoriously fault-prone. One reason for this is that users actively rely on copy-paste to make up for the lack of abstraction mechanisms. Adding abstraction however, introduces indirection and thus cognitive distance. In this paper we propose an alternative: copy-paste tracking. Tracking copies that spreadsheet users make, allows them to directly edit copy-pasted formulas, but instead of changing only a single instance, the changes will be propagated to all formulas copied from the same source. As a result, spreadsheet users will enjoy the benefits of abstraction without its drawbacks.

Introduction

Spreadsheet systems can easily be considered the most successful form of programming. Winston [START_REF] Winston | Executive Education Opportunities[END_REF] estimates that 90% of all analysts in industry perform calculations in spreadsheets. Spreadsheet users perform a range of diverse tasks with spreadsheets, from inventory administration to educational applications and from scientific modeling to financial systems. The financial business is a domain where spreadsheets are especially prevailing. Panko [START_REF] Panko | Facing the Problem of Spreadsheet Errors[END_REF] estimates that 95% of U.S. firms, and 80% in Europe, use spreadsheets in some form for financial reporting.

Researchers have argued that the liveness characteristics of spreadsheets have contributed to the widespread success of spreadsheets [START_REF] Hermans | Analyzing and Visualizing Spreadsheets[END_REF]) and we know from interviews with users that liveness is important to them. They often start building a spreadsheet with the end goal in mind, and manipulate the formulas until they obtain the result they want.

The liveness characteristics of spreadsheets can be divided in two categories:

• Direct manipulation: instead of editing a separate plan or program to achieve some result, the spreadsheet user edits the "thing itself": there is almost no distinction between the actual data and the "code" of a spreadsheet. This feature addresses the "gulf of execution" which exists between the user's goal, and the steps that are required to achieve that goal [START_REF] Norman | User Centered System Design: New Perspectives on Human-Computer Interaction[END_REF]).

• Immediate feedback: after a change to the spreadsheet data or formulas, the user can immediately observe the effect of the edit. This feature bridges the "gulf of evaluation" which exists between performing an action and receiving feedback on the success of that action [START_REF] Norman | User Centered System Design: New Perspectives on Human-Computer Interaction[END_REF].

Despite these attractive features for end-users, spreadsheets are well-known to be extremely fault-prone [START_REF] Panko | Facing the Problem of Spreadsheet Errors[END_REF].

There are numerous horror stories known in which organizations lost money or credibility because of spreadsheet mistakes. TransAlta for example lost US $24 Million in 2003 because of a copy-paste error in a spreadsheet (Pryor).

More recently, the Federal Reserve made a copy-paste error in their consumer credit statement which, although they did not make an official statement about the impact, could have led to a difference of US $4 billion (Durden). These stories, while single instances of copy-paste problems in spreadsheets do, give credibility to the hypothesis that copy-paste errors in spreadsheets can greatly impact spreadsheet quality.

This copy-pasting as in the stories above is not always done by mistake. Rather, we see spreadsheet users using copy-pasting as a deliberate technique. This is understandable, as standard spreadsheets do not support any form of data schema or meta model, so there is no way in which a new worksheet in a spreadsheet could inherit or reuse the model of an existing worksheet. Copy-paste is then often used to compensate for for the lack of code abstractions [START_REF] Hermans | Data Clone Detection and Visualization in Spreadsheets[END_REF]. Finally, when faced with spreadsheets they do not know, users are often afraid to modify existing formulas, thus copy-paste them and add new functionality [START_REF] Hermans | Data Clone Detection and Visualization in Spreadsheets[END_REF]) creating many versions of similar formulas, of which the origin can no longer be determined.

Existing research improving spreadsheets has focused on extending spreadsheets with abstraction mechanisms. An example of this is the work of Engels et al. , who have developed a system called ClassSheets [START_REF] Engels | ClassSheets: Automatic Generation of Spreadsheet Applications from Object-Oriented Specifications[END_REF] with which the structure of a spreadsheet can be described separately. The actual spreadsheet can then be guaranteed to conform to the meta description. Another direction is enriching spreadsheets with user-defined functions (UDFs) [START_REF] Jones | A User-Centred Approach to Functions in Excel[END_REF]. In this case, spreadsheets users can factor out common computations into separate cells, and refer to them from elsewhere in the spreadsheet.

Although these features improve the reliability of spreadsheet use, they have one important drawback, namely, that they break the "direct manipulation" aspect of spreadsheets. In a sense, separate meta models, or user defined abstractions, create distance between the actual user's artifact (data + formulas), and its computational behaviour. Instead of just looking at the cells, the user now has to inspect at least two places: the cells containing the data and the separate definitions of the abstractions (meta model or user defined functions).

In this paper we propose XanaSheet, a spreadsheet system that features an alternative method to manage abstraction, without diminishing directness. XanaSheet employs origin tracking techniques to maintain a live connection between source and destination of copy-paste actions. Whenever a copied formula is edited, the modifications are transformed and replayed on the original and all other copies. Instead of introducing another level of indirection using abstraction, XanaSheet allows users to edit classes of formulas, all at once. In a sense, the abstraction, or user defined function, is there, but it never becomes explicit. By retaining ease of use, this technique has the potential to eliminate a large class of copy-paste errors, without compromising the direct manipulation aspect that make spreadsheets so attractive.

Copy-Paste Tracking in Action

Figure 1: Maintaining consistency among clones of formulas through copy-paste tracking Figure 1 shows an example user interaction with a spreadsheet containing student grades. In the first step the sheet contains just the Lab and Exam grades of three students, and a formula for computing the average of the two grades in D2. In the second step, the formula in cell D2 is copied to D3 and D4. D3 and D4 are clones of D2, and this relation is maintained by the system as an origin relation (visualized using the arrow). In the third step, the clone in D4 is modified to apply rounding to the computed average. Unlike in normal spreadsheets, however, this is not the end of the story and XanaSheet will reconcile the original formula of D2 and the other clone in D3 with the changes in D4.

A way to understand what is happening here, is to see spreadsheet formulas as materialized or unfolded abstractions. The abstraction in Fig. 1 is function average(x,y) for computing the average of two grades. In ordinary programming such a function could, for instance, be mapped over a list of pairs of grades to obtain a list of averages, like map(average, zip(Lab, Exam)). In the spreadsheet of Fig. 1, however, the abstraction average does not really exist, but is represented collectively by the set of all its inlined applications, e.g.

[(Lab[ ]+Exam[ ])/ 2, (Lab[1]+Exam[1])/2, (Lab[2]+Exam[2])/2].
In a sense, each application is a clone of the same implicit prototype, with parameters filled in with concrete data references. The tracking relation induced by copy-paste actions, identifies which clones belong to the same equivalence class. Therefore, editing one clone triggers updating the clones which belong to the same class.

In some cases it might actually not be desired to maintain the origin links between source and destination of copy-paste actions. XanaSheet supports these situations by providing a special "Paste and Detach" action which severs the copy from its original (similar to "Past and Match Style" common in many text editing systems). The example also assumes that when a user edits a formula she always intends to edit the whole class of clones. However, the system allows the user to edit only this copy, or all copies at once (similar to changing "Recurring events" in calendar applications).

Semantics of Copy-Paste Tracking

The previous section introduced copy-paste tracking from the perspective of the user. In this section we describe our considerations regarding the implementation. We have implemented an executable semantics of copy-paste tracking for simulating interactive editing sessions with a spreadsheet. The code can be found online here: https: //github.com/Felienne/LiveSpreadsheets/tree/master/XanaSheet. We are currently working on an interactive prototype of XanaSheet.

A spreadsheet is a rectangular grid of cells where each cell is identified by its address, which are pairs An consisting of a column letter A and a row index n. User actions always operate on one of more of these addresses. The origin relation between cells is then modeled as a binary relation between such addresses. For instance, the relation Org " txD3, D2y, xD4, D2yu captures the origin relation visualized in Figure 1 (2). In this case, the relation states that the formulas in cell D3 and cell D4 are copied from cell D2.

Without loss of generality we assume users only use relative cell referencing in formulas. That is, a cell reference consists of relative row and column offsets starting from the current cell [START_REF] Sestoft | A Spreadsheet Core Implementation in C#[END_REF]. For instance, the reference to B2 in Fig. 1 (1) is a relative cell reference, is represented as C-2R ("two columns left, same row"). Relative cell referencing allows formulas to be moved around across the grid without having to adjust explicit column names or row indices.

Interacting with the spreadsheet not only updates the sheet itself, but also maintains the origin relation. We describe the effect of the most relevant edit operations on a cell c:

• Entering a formula: If c does not participate in any origin relation, it is is simply updated with the new formula, and the origin relation is updated with xc, cy to model the fact that a new formula is its own origin. As a result, the origin relation is always reflexively closed. Otherwise, c has an origin, say c 1 , and the cells that need to be updated are tc 2 | xc 2 , c 1 y P Orgu. By definition, this includes cell c, and, by reflexivity of Org, the source cell c 1 as well. .

• Copying cell c to c 1 : The contents of c is copied to c 1 . If the contents is a formula, the origin relation needs to be updated as well. First, if c 1 has an existing origin, the corresponding pair is removed from the relation. Then the relation is extended based on the current copy operation: if c has an origin c 2 , add xc 1 , c 2 y, else add xc 1 , cy. The check for the origin of c ensures that the origin relation is always transitively closed.

• Inserting/removing a row or column: after updating the sheet, the origin relation is adjusted so that cell addresses refer to their new locations. For instance, when inserting a row at position i, the row components of all the cell addresses on rows ě i in the origin relation needs to be shifted one down. In the case of removal, all pairs in the origin relation that contain coordinates on the removed row or column are removed.

• Entering data: cell c is updated with the new data. All pairs containing c, either as source or target, are removed from the origin relation.

Note that copying a cell c to c 1 removes the origin entries of c 1 (if any). An alternative design could interpret copying a formula as a modification of the destination cell, and thus update all cells in the class of c 1 . In that case all such cells would get c as their new origin.

Although in this section we have just discussed copy-paste tracking for formulas, the same model can be applied equally well to copy-pasting of data. In that case, the origin relation helps against inadvertently duplicating input data. An interesting special case is the "paste as value" operation. Instead of copying a formula, this operation copies the computed value, thus completely disconnecting the destination cell from its source. Tracking such copy-paste actions would probably not be very useful: editing the pasted value would incur computing the inverse of the original formula, and updating the input data accordingly!

Related Work

Copy-paste tracking is a simple technique that is inspired by similar concepts in domains as diverse as term rewriting, hypertext, clone detection, prototypical inheritance , and view maintenance. Below we briefly summarize representative related work in those areas.

Origin tracking: Copy-paste tracking is directly inspired by origin tracking [START_REF] Deursen | Origin Tracking[END_REF]. In general, origin tracking tries to establish a relation between the input and output of some computational process, such as a compiler, or program transformation. Origin tracking, however, has numerous other applications in visualization, debugging, and traceability. An application most similar to our work is presented in [START_REF] Inostroza | Tracing Program Transformations with String Origins[END_REF], where origin tracking is used to implement editable regions on generated code.

Transclusion: Ted Nelson's concept of transclusion [START_REF] Nelson | Complex Information Processing: A File Structure for the Complex, the Changing and the Indeterminate[END_REF]) is a form of "reference by inclusion" where transcluded data is presented through a "live" view: whenever the transcluded content is updated, the views are updated as well.

Our origin relation provides a similar hyper-linking between cells. But unlike in the case of transclusion, the relation is bidirectional: changes to the original are propagated forward, but changes to copies (references) are also propagated backwards (and then forwards again). A similar concept is used in Subtext, where copying is the primary mechanism for abstraction [START_REF] Edwards | Subtext: Uncovering the Simplicity of Programming[END_REF].

Clone tracking in software: Godfrey and Tu [START_REF] Godfrey | Tracking Structural Evolution Using Origin Analysis[END_REF] proposed a method called origin analysis which is a related to both clone detection and the above described origin tracking, but aims at deciding if a program entity was newly introduced or whether it if it should more accurately be viewed as a renamed, moved, or otherwise changed version of an previously existing entity. This laid the ground for a tool called CloneTracker that "can automatically track clones as the code evolves, notify developers of modifications to clone regions, and support simultaneous editing of clone regions." (Duala-Ekoko and Robillard 2007).

Prototype-based inheritance: Lieberman introduced prototypes to implement shared behaviour in object-oriented programming [START_REF] Lieberman | Using Prototypical Objects to Implement Shared Behavior in Object-Oriented Systems[END_REF]). In prototype-based languages, objects are created by cloning and existing object. The cloned object then inherits features (methods, slots) from its prototype. The parent relation between objects is similar to our origin relation. However, we are not aware of any related work using this relation to propagate changes to clones back to their parents.

Bidirectional transformation: one way to look at copy-paste tracking is to see copies as views on the original formula similar to views in database systems. In particular, the copies are updateable views [START_REF] Bancilhon | Update Semantics of Relational Views[END_REF]. Different manifestations of the view update problem have received considerable attention recently in the context of lenses (J. N. [START_REF] Foster | Combinators for Bidirectional Tree Transformations: A Linguistic Approach to the View-Update Problem[END_REF]) and bidirectional transformation [START_REF] Czarnecki | Bidirectional Transformations: A Cross-Discipline Perspective[END_REF]). In the context of user interfaces these concepts were pioneered by Meertens under the header of "constraint maintenance" [START_REF] Meertens | Designing Constraint Maintainers for User Interaction[END_REF]. In a certain sense, copy-paste tracking supports a very basic class of constraint maintenance where clones are simply synchronized to be equal.

Conclusion

Spreadsheet systems are the most popular live programming environments. They adhere to the powerful direct manipulation style of simultaneously editing data and code. Nevertheless, spreadsheets are known to be extremely fault-prone, mainly because users have to use copy-paste instead of user defined abstractions. Existing research has tried to improve spreadsheets by introducing abstractions such as meta models or user defined functions, but this compromises the direct manipulation aspect that makes spreadsheets so attractive in the first place.

In this paper we propose XanaSheet: copy-paste tracking as way to both have our cake and eat it too. Instead of introducing another level of indirection, copy-paste tracking supports editing classes of formulas originating at the same source, all at once. As a result, we get the benefits of abstraction (reuse, sharing, "single-point-of-change"), without the incurring the burden of cognitive distance.

Outlook Duplication of knowledge is ubiquitous is computing. Copy-paste tracking can be generalized to a broader scope by seeing it as an example of abstractions that are presented to the user in a materialized, expanded, unrolled, referenced, or instantiated state. The relation between such views and the original is often many-to-one and the views are often read only. Copy-paste tracking could provide a model to make such user views of abstractions editable. Thus, copy-paste tracking in its most general form supports direct manipulation in interactive systems and allows users to maintain abstractions through their multiple concretizations. We conclude by providing a tentative list of examples where similar ideas could be applied:

"Copy" (many) "Source" (one)


Quentin Dariol

Sébastien Le Nours

Sébastien Pillement

Ralf Stemmer

Kim Grüttner

Domenik Helms

Sébastien

A Measurement-based Performance Evaluation Framework for Neural Networks on MPSoCs

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INSTITUT D'ÉLECTRONIQUE ET DE TÉLÉCOMMUNICATIONS DE RENNES

CONTEXT -OBJECTIVE

Quentin DARIOL, Sébastien LE NOURS, Sébastien PILLEMENT (IETR), Ralf STEMMER, Kim GRÜTTNER, Domenik HELMS (OFFIS e. V.)

Email: quentin.dariol@etu.univ-nantes.fr ❖ Case study ➢ Elementary multi-layer perceptrons (such as MNIST use-case) captured using LibFANN [START_REF] Nissen | Implementation of a Fast Artificial Neural Network library (FANN)[END_REF] and modeled in Synchronous Dataflow Graph (SDFG), ➢ Model of Architecture (MoA) consisting of a shared memory and several tiles composed of one processing element with local memory.

Fig 2 .Fig 3 .Fig 1 .

 231 Fig 2. Workflow proposed for performance prediction of neural networks on MPSoC

in timing prediction for neural networks executed on MPSoC➢

  Hard to predict variability of execution time due to dependency to input data and contention on shared resources, ➢ Required exploration of partitioning and mapping/scheduling of neural network for efficient implementation.

	❖

❖ Difficulty

Current limitations of existing real-time analysis methods for neural networks ➢

  Most approaches focus on systematic implementations to measure execution time while exploring mapping/schedulings, and few high level models have been proposed to predict execution time while taking variability inducing phenomena in consideration. ➢ Variability on parallel software execution can be captured by probabilistic model.

CONTRIBUTION

❖ Evaluation workflow ➢ Update for neural network applications of our previous workflow for timing prediction for MPSoC tested on video processing applications

[START_REF] Stemmer | Towards Probabilistic Timing Analysis for SDFGs on Tile Based Heterogeneous MPSoCs[END_REF]

[2]. ➢ Performance prediction performed by scalable probabilistic models annotated via measured timings, obtained through implementation on FPGA, ➢ Exploration of several mapping/schedulings optimizing timing and energy for considered application.

A Measurement-based Performance Evaluation Framework for Neural Networks on MPSoCs