Simone Vincenzi
email: simon.vincenz@gmail.com

Alain Crivelli

Dušan Jeseňsek

Ellen Campbell

John Garza

Simone Vincenzi1

Alain J Crivelli3

| Dušan

Ellen Campbell1

John C Garza1

Effects of species invasion on population dynamics, vital rates and life histories of the native species

Keywords: demography, growth, marble trout, pedigree reconstruction, rainbow trout, random-effects models

come

INTRODUCTION

The invasion of native communities by alien species is one of the major threats to the stability of ecosystem processes and the persistence of endemic species [START_REF] Simon | Impacts of freshwater invaders at different levels of ecological organisation, with emphasis on salmonids and ecosystem consequences[END_REF]. Although they are one of the biggest challenges conservation biologists are facing [START_REF] Allendorf | Introduction: Population biology, evolution, and control of invasive species[END_REF], invasions occurring in natural environments also provide the opportunity to study how vital rates change and life histories (the timing of key events in an organism's lifetime) evolve in competing species, a central topic of ecology and evolutionary biology [START_REF] Sakai | The population biology of invasive species[END_REF]. In the case of long-lived and mobile organisms, insights from laboratory or small-scale experiments are of limited value, since spatial constraints may force species to interact at unnaturally small scales [START_REF] Korsu | Invasion of north European streams by brook trout: Hostile takeover or pre-adapted habitat niche segregation?[END_REF], the effects of the invasion on the native communities may be appreciated only after a few generations, and the size and direction of the effects may change with changes in the environment [START_REF] Carroll | Natives adapting to invasive species: Ecology, genes, and the sustainability of conservation[END_REF].

The study of biological invasions has mostly focused on understanding the mechanism by which non-native species successfully invade new regions. In particular, the focus has been on the environmental (e.g., climate, [START_REF] Jiménez | Extreme climatic events change the dynamics and invasibility of semi-arid annual plant communities[END_REF] or ecological (e.g., unoccupied niches, [START_REF] Olden | Life-history strategies predict fish invasions and extirpations in the Colorado River Basin[END_REF] conditions facilitating or hampering establishment and spread of the invading species, the life history traits that are associated with invasion success [START_REF] Capellini | The role of life history traits in mammalian invasion success[END_REF], and the adoption of life history strategies by the colonist population that differ from those of the source population [START_REF] Amundsen | Invader population speeds up life history during colonization[END_REF]. On the other hand, few studies have investigated the overall effects of invasion on the native species, such as effects on its diet, growth, survival, reproduction, life histories and population dynamics [START_REF] Peterson | Population ecology of an invasion: Effects of brook trout on native cutthroat trout[END_REF].

For life histories, it has often been found that fast life histories increase invasion success [START_REF] Ruesink | Global analysis of factors affecting the outcome of fresh water fish introductions[END_REF] and that colonists adopt life histories that are faster than those of the source population (i.e., pioneer life histories), since younger age at reproduction and higher reproductive effort may facilitate rapid population growth and spatial expansion when the invading population is small (after the introduction) and throughout the invasion process (establishment and spread) [START_REF] Burton | Trade-offs and the evolution of life-histories during range expansion[END_REF][START_REF] Kurz | Shifts in life-history traits of two introduced populations of threespine stickleback[END_REF]. Similarly, fast life histories in the invaded population may help avoid the invasion of the alien species or limit their abundance. For instance, [START_REF] Jones | Life history influences the vulnerability of New Zealand galaxiids to invasive salmonids[END_REF] found that native galaxiid species (small freshwater fish living in the Southern Hemisphere) in New Zealand cooccurred with alien salmonids only when possessing fast life histories. In contrast, galaxiid species with slow life histories were excluded from salmonid-invaded reaches even when salmonid densities were low.

Native species may also respond adaptively to biological invasions [START_REF] Carroll | Natives adapting to invasive species: Ecology, genes, and the sustainability of conservation[END_REF][START_REF] Strauss | Evolutionary responses of natives to introduced species: What do introductions tell us about natural communities?[END_REF], but testing the hypothesis of adoption of faster life histories by the invaded population as an adaptive response to the invasion-either through adaptive genetic differentiation or phenotypic plasticity-is intrinsically challenging. Variation in extrinsic (e.g., weather, predators and food availability) and intrinsic (e.g., population density) habitat factors determines a large part of intra-specific differences in life histories, behavior and physiology of organisms [START_REF] Southwood | Habitat, the templet for ecological strategies?[END_REF]. As habitats differ geographically and temporally, the distribution of vital rates, life histories and phenotypic traits are expected to vary in space and time [START_REF] Linhart | Evolutionary significance of local differentiation in plants[END_REF]. It follows that the variation in life histories among invaded and non-invaded populations-or before and after the invasion within the same population-may just reflect genetic adaptations or plastic responses to spatial or temporal variation of the environment and not to the presence of a competitor occupying a similar ecological niche [START_REF] Strauss | Evolutionary responses of natives to introduced species: What do introductions tell us about natural communities?[END_REF]. In addition, individual heterogeneity in life history traits complicates teasing apart the effects of individual variation from those of habitat variation and the presence of competing species [START_REF] Vincenzi | Tradeoffs between accuracy and interpretability in von Bertalanffy random-effects models of growth[END_REF][START_REF] Vincenzi | Determining individual variation in growth and its implication for life-history and population processes using the empirical Bayes method[END_REF].

In this work, we combine a fine-grained, long-term, tagrecapture dataset with powerful statistical and modelling methods that take into account individual and temporal heterogeneity in vital rates to estimate differences in individual growth, survival, reproduction, life histories and population dynamics between individuals of a native species living in allopatry or competing with an invasive species, using a model system marble trout Salmo marmoratus (native species) and rainbow trout Oncorhynchus mykiss (non-native species) living in Western Slovenian streams. Salmonids have often been used as model systems in ecology and evolutionary biology, due to their vast geographic distribution, their ecological and life history variability, and their strong genetic and plastic responses to habitat and climate variation [START_REF] Elliott | Quantitative ecology and the brown trout[END_REF][START_REF] Garcia De Leaniz | A critical review of adaptive genetic variation in Atlantic salmon: Implications for conservation[END_REF][START_REF] Jonsson | Ecology of Atlantic salmon and brown trout: Habitat as a template for life histories[END_REF][START_REF] Stearns | Evolution illuminated: Salmon and their relatives[END_REF].

Marble trout is endemic to rivers tributary to the upper Adriatic Sea and persists in pure form in the Alps of Western Slovenia and parts of Northern Italy [START_REF] Sušnik | Population genetic SNP analysis of marble and brown trout in a hybridization zone of the Adriatic watershed in Slovenia[END_REF][START_REF] Vincenzi | Within and among-population variation in vital rates and population dynamics in a variable environment[END_REF]. Two of the eight remaining genetically pure populations of marble trout in Western Slovenia are in the Idrijca River, where an impassable waterfall separates fish in Upper Idrijca from a closely related group in Lower Idrijca [START_REF] Fumagalli | Extreme genetic differentiation among the remnant populations of marble trout (Salmo marmoratus) in Slovenia[END_REF]. Marble trout in Lower Idrijca co-exist with non-native rainbow trout, which were introduced in the 1960s and have been established since then, but they are absent in Upper Idrijca [START_REF] Stankovic | Rainbow trout in Europe: Introduction, naturalization, and impacts[END_REF]. Given the high similarity of Lower and Upper Idrijca habitats (Vincenzi, Mangel, et al., 2016), this unintended treatment-control experiment allows the study of variation in vital rates, life histories and population dynamics of the native species when competing with an invasive species of the same taxonomic Family.

In models of competition-colonization tradeoff, when two species occupying similar niches meet the better competitor excludes the other [START_REF] Cadotte | Competition-colonization trade-offs and disturbance effects at multiple scales[END_REF]. On the other hand, evolutionary models of community assembly often assume that coexistence of competing species results from the operation of resource partitioning mechanisms [START_REF] Macarthur | The limiting similarity, convergence, and divergence of coexisting species[END_REF]. [START_REF] Musseau | Dietary niche expansion and niche shift in native marble trout (Salmo marmoratus) living in sympatry with introduced rainbow trout (Oncorhynchus mykiss)[END_REF] found only minor overlap between trophic niches of rainbow and marble trout in Lower Idrijca and between trophic niches of marble trout living in Lower Idrijca and in Upper Idrijca. Although rainbow trout is known to take food from other Salmonids, the niche shift of marble trout when occurring in sympatry with rainbow trout in Lower Idrijca was not caused by a niche replacement of marble trout by rainbow trout. [START_REF] Musseau | Dietary niche expansion and niche shift in native marble trout (Salmo marmoratus) living in sympatry with introduced rainbow trout (Oncorhynchus mykiss)[END_REF] also found that marble trout in Upper and Lower Idrijca occupy a high trophic position (3.5 in Upper to 3.9 in Lower Idrijca), which confirms observations of piscivory and cannibalism in other marble trout populations. Marble trout in Lower Idrijca showed higher δ 13C than marble trout in Upper Idrijca, which is likely to be caused by the inclusion of rainbow trout as additional prey in the diet of marble trout [START_REF] Musseau | Dietary niche expansion and niche shift in native marble trout (Salmo marmoratus) living in sympatry with introduced rainbow trout (Oncorhynchus mykiss)[END_REF]. Marble and rainbow trout living in sympatry are thus competitors for food and space, and we expect effects of this interspecific competition on vital rates, life histories and population dynamics of marble trout living in sympatry with rainbow trout, such as faster growth, earlier reproduction, lower survival and lower population densities in marble trout living in Lower Idrijca (sympatry) than in Upper Idrijca (allopatry).

However, the absence of replicates does not allow for strong inference (sensu [START_REF] Platt | Strong inference[END_REF] on the causes of variation in vital rates, life histories and population dynamics; therefore we use the results of the study not to test, but to generate hypotheses on the ultimate and proximate causes of the observed variation. Specifically, we used tag-recapture and genetic data (>2,500 unique marble and rainbow trout were sampled and genotyped) to reconstruct pedigrees and estimate age of parents, model survival using tag-recapture analysis, and model growth using random-effects models that explicitly take into account individual heterogeneity. The overarching data and modelling approach allowed us to test for population synchrony, and estimate differences in population dynamics, proportion of younger parents, individual growth trajectories, and survival between marble trout living in allopatry and in sympatry with rainbow trout. We then discuss the observed variation in life histories in the light of ecological and life history theory.

MATERIAL AND METHODS

Study area and species description

The Idrijca catchment is pristine and there is neither poaching nor angling in the study area. Marble trout is the only fish species living in Upper Idrijca. Within the Lower (LIdri) and Upper (UIdri) Idrijca study areas, there are no physical barriers impairing upstream or downstream movement of marble and rainbow trout; however, both species are territorial and their lifetime movement is typically limited (Vincenzi, Mangel, et al., 2016). Mean daily water temperatures in LIdri and UIdri over years 2006 to 2013 were 8.1 0.2 and 7.7 0.2 C, respectively (Vincenzi, Mangel, et al., 2016). There is ample spawning habitat in both Lower and Upper Idrijca. Detailed description of the biology and ecology of marble trout can be found in Vincenzi, Mangel, et al. (2016). Marble trout populations are highly genetically differentiated [START_REF] Fumagalli | Extreme genetic differentiation among the remnant populations of marble trout (Salmo marmoratus) in Slovenia[END_REF], persist at low population densities (approximately 600 and 1,250 ha-1 for fish older than young-of-year), are at high risk of extinction due to hybridization with non-native brown trout (Salmo trutta) and the occurrence of extreme events such as flash floods, debris flows and landslides [START_REF] Vincenzi | Potential factors controlling the population viability of newly introduced endangered marble trout populations[END_REF]Vincenzi, Mangel, et al., 2016;[START_REF] Vincenzi | The genetic and life-history consequences of extreme climate events[END_REF]. Brown and marblebrown trout hybrids living in the hybridization zone cannot move into either Lower or Upper Idrijca due to the presence of waterfalls that prevent the upstream movement of fish.

Rainbow trout is a north Pacific species [START_REF] Gall | The rainbow trout[END_REF] that was introduced in the Adriatic basin of Slovenia in the early 20th century and established self-sustaining stream-resident populations there [START_REF] Stankovic | Rainbow trout in Europe: Introduction, naturalization, and impacts[END_REF]. Rainbow trout were stocked in the headwaters of the Idrijca River (Upper Idrijca) only once, in 1962. Rainbow trout in the Adriatic basin of Slovenia typically start spawning at age 1 (D. Jeseňsek and A.J. Crivelli, unpublished data).

Sampling

We sampled the rainbow and marble trout populations of LIdri and UIdri bi-annually in June and September of each year from June 2004 to September 2015 for a total of 24 sampling occasions. Fish were captured by electrofishing and total length (L) and weight (W) recorded to the nearest millimetre and gram. If captured fish had L > 115 mm, and had not been previously tagged or had lost a previously applied tag, they received a Carlin tag [START_REF] Carlin | Tagging of salmon smolts in the river lagan[END_REF] and age was determined by reading scales. Fish are aged as 0+ in the first calendar year of life, 1+ in the second year and so on. Subyearlings of both rainbow and marble trout are smaller than 115 mm in June and September, so fish were tagged when at least age 1+. The adipose fin was also removed from all fish captured for the first time (starting at age 0+ in September), including those not tagged due to small size at age 1+. Therefore, fish with an intact adipose fin were not sampled during previous sampling occasions at age 0+ or 1+. Males and females of marble and rainbow trout are morphologically indistinguishable in either June or September; sex was thus assigned in the laboratory using molecular techniques [START_REF] Yano | The sexually dimorphic on the Ychromosome gene (sdY) is a conserved male-specific Y-chromosome sequence in many salmonids[END_REF].

Single-nucleotide polymorphism genotyping

DNA was extracted from dried fin clips using the DNeasy 96 filter-based nucleic acid extraction system on a BioRobot 3,000 (Qiagen, Inc., Hilden, Germany), following the manufacturer's protocols. Extracted DNA was diluted 2:1 with distilled water and used for polymerase chain reaction amplification of 96 population-specific single-nucleotide polymorphisms (SNPs). SNPs were assayed with 96.96 Dynamic Array integrated fluidic circuits (IFCs) for Genotyping on an EP1 (EndPoint Reader 1) instrument (Fluidigm, Inc.,), using the manufacturer's recommended protocols. Genotypes were called using SNP Genotyping Analysis software (Fluidigm, Inc., South San Francisco, US). Two people called all genotypes independently, and discrepancies in the scores were resolved either by consensus, by re-genotyping, or by deletion of that genotype from the data set. A proportion of individuals were genotyped more than once (e.g., in case of tag loss or when the fish was <115 mm, and later at tagging), as determined by observed identical genetic profiles and compatible age and length data, and one of the samples was excluded from the analyses. Matching genotypes of individuals with different physical tags is a method of "genetic tagging" that allows reconstruction of the life histories of individuals after tag loss. Mean SD minor allele frequency (MAF) of the SNPs was 0.27 0.13 for LIdri_MT (95 polymorphic SNPs, Supporting Information Table S1), 0.27 0.14 for UIdri_MT (95 SNPs, Supporting Informa-tion Table S2) and 0.26 0.14 for LIdri_RT (83 SNPs, Supporting Information Table S3). Such MAFs with nearly 100 SNPs are sufficient for parent pair/offspring trio reconstruction with high accuracy [START_REF] Anderson | The power of single-nucleotide polymor phisms for large-scale parentage inference[END_REF]. The final dataset included 1,129 marble trout living in LIdri (LIdri_MT), 610 marble trout living in UIdri (UIdri_MT) and 291 rainbow trout living in LIdri (LIdri_RT) that were identified either as offspring or potential parents.

Statistical analyses and hypotheses tested

We first estimated density of age-classes and then tested for (a) recruitment-driven population dynamics, (b) population synchrony and (c) temporal differences in population densities between the three populations. Then, we reconstructed pedigrees in each population and fitted models of growth and survival to estimate differences in (d) lifetime growth trajectories, (e) probability of survival and (f ) proportion of young parents between LIdri_MT, LIdri_RT and UIdri_MT.

Estimation of population density

We estimated the density of 0+ fish only in September, since marble trout normally emerge a few days before the June sampling and rainbow trout emerge in July. We estimated the density of 0+ fish and fish older than 0+ using a twopass removal protocol [START_REF] Carle | A new method for estimating population size from removal data[END_REF] and the R (R Development Core Team, 2014) package FSA [START_REF] Ogle | FSA: Fisheries Stock Analysis[END_REF]. Total stream surface of the monitored area (1,084 and 1,663 m2 for LIdri and UIdri, respectively) was used for the estimation of fish density (in fish ha-1 ). Previous studies (Vincenzi, Mangel, et al., 2016) have found that population dynamics of other marble trout populations living in Western Slovenian streams are driven by recruitment. Following Vincenzi, Mangel, et al. (2016), we tested for recruitmentdriven population dynamics in LIdri_MT, LIdri_RT and UIdri_MT by estimating cross-correlations between density of 0+ fish (D0+) in September (recruitment) and density of older than 0+ fish (D>0+) 1 year later within each population. We also tested for synchrony of population dynamics ("Moran effect," Ranta, Kaitala, Lindström, & Helle, 1997) of LIdri_MT and LIdri_RT, and LIdri_MT and UIdri_MT. Statistical significance was set at the 0.05 level 2.6

Pedigree reconstruction and age at spawning

We used a two-step conservative approach for reconstructing pedigrees in the marble and rainbow trout populations [START_REF] Vincenzi | The genetic and life-history consequences of extreme climate events[END_REF], using the software SNPPIT [START_REF] Anderson | Large-scale parentage inference with SNPs: An efficient algorithm for statistical confidence of parent pair allocations[END_REF] and FRANz [START_REF] Riester | FRANz: Reconstruction of wild multi-generation pedigrees[END_REF]. SNPPIT is tailored for identification of mother-father parent pairs in single generations and does not perform single-parent assignments. FRANz can also infer single parents and can be used to infer parentage in multiple generations. Known parent-offspring relationships can be used by FRANz to estimate genotyping error rate. Marble trout genotypes were analysed with SNPPIT to identify parentpair/offspring trios with a false discovery rate threshold of 0.05, and these trios were then used in FRANz as known relationships to identify single parent-offspring pairs and additional parent-pair/offspring trios. Further details on pedigree reconstruction are in Text 1 in Supporting Information Appendix S3.

Marble trout in UIdri and LIdri spawn from midNovember to mid-December. Therefore, for example, the eggs of cohort 2011 were fertilized in November-December of 2010 and newborn emerged in June 2011. Rainbow trout in Lower Idrijca spawn in April and offspring emerge in July of the same year (T. W. Lee and A. J. Crivelli, unpublished data). Marble trout are iteroparous. Age at first reproduction varies within and among marble trout populations; pedigree reconstruction in other populations found that marble trout spawn typically at age 3+ and older, with fewer fish spawning at age 1+ and 2+ [START_REF] Meldgaard | Hybridization mechanisms between the endangered marble trout (Salmo marmoratus) and the brown trout (Salmo trutta) as revealed by instream experiments[END_REF][START_REF] Vincenzi | The genetic and life-history consequences of extreme climate events[END_REF].

We used a χ2 test of equality of proportions to test for differences in the proportion of younger parents between LIdri_MT and UIdri_MT. Since the distribution of age at spawning is skewed and potentially biased by some old parents, we only considered parents aged 1+ and 2+ (young parents), and 3+ and 4+ (old parents).

Growth and body size

To characterize size-at-age and growth trajectories, we modelled variation in lifetime growth trajectories of marble and rainbow trout living in LIdri_MT, LIdri_RT and UIdri_MT taking into account within-population individual heterogeneity in growth.

The standard von bertalanffy growth function (vBGF;[START_REF] Von Bertalanffy | Quantitative laws in metabolism and growth[END_REF]) is where L∞ is the asymptotic size, k is a coefficient of growth (in time-1) and t0 is the (hypothetical) age at which length is equal to 0. However, to accurately estimate overall, group-specific or individual growth trajectories, we need to take into account individual variation in growth; otherwise, the average trajectory can be substantially pulled up or down by a few long-living fast or slow growers [START_REF] Vincenzi | Determining individual variation in growth and its implication for life-history and population processes using the empirical Bayes method[END_REF].

We used the formulation of the vBGF specific for longitudinal data of [START_REF] Vincenzi | Determining individual variation in growth and its implication for life-history and population processes using the empirical Bayes method[END_REF], in which L∞ and k may be allowed to be a function of shared predictors and individual random effects. In the estimation procedure, we used a log-link function for k and L∞, since both parameters must be non-negative. We set.

where u~N(0, 1) and v~N(0, 1) are the standardized individual random effects, α 1

(1) and β 1 (1) are group effects (e.g., sex, 1 1 yearof-birth cohort, population and species), σ u and σ v are the standard deviations of the statistical distributions of the random effects and the other parameters are defined as in Equation ( 1).

We thus assume that the observed length of individual i in group j at age t is Where ε ij is normally distributed with mean 0 and variance σ 2 ε

Since the growth model operates on an annual time scale and more data on tagged fish were generally available in September of each year, we used September data for modelling lifetime growth trajectories. In order to test for differences in growth trajectories, we included three potential categorical predictors (α1 and β1 in Equation 2) of k and L∞: (a) Species (MT and RT), (b) Population (Lidri_MT, UIdri_MT, LIdri_RT), (c) Cohort. We also tested whether there were large differences in vBGF population-specific models when estimating parameters separately for each population using a standard non-linear regression routine with no random effects (nls function in R) or when using models in Equations ( 2) and (3).

Survival

Our goal was to estimate variation in survival among populations and to investigate the effects of presence of rainbow trout on survival, time (sampling occasion or season) and successful reproduction.

Two probabilities can be estimated from a capture history matrix:φ, the probability of apparent survival (defined "apparent" as it includes permanent emigration from the study area), and p, the probability that an individual is captured when alive [START_REF] Thomson | Modeling demographic processes in marked populations[END_REF]. We used the Cormack-Jolly-Seber (CJS) model as a starting point for the analyses [START_REF] Thomson | Modeling demographic processes in marked populations[END_REF]. We tested the goodness-of-fit of the CJS model with the program Release. The global model (i.e., the model with the maximum parameterization) was a good starting point to model survival and capture probabilities. All other survival models tested were simplified versions of this global starting model, with the potential addition of covariates. From the global model, recapture probability was modelled first. The recapture model with the lowest akaike information criterion (AIC) was then used to model survival probabilities.

We modelled the seasonal effect (Season) as a simplification of full-time variation, by dividing the year into two periods: June to September (Summer), and the time period between September and June (Winter). As the length of the two intervals (Summer and Winter) was different (3 months and 9 months), we estimated probability of survival on a common annual scale. Previous work has found no or minor effects of population density, water temperature, body size or sex on survival in marble trout (Vincenzi, Mangel, et al., 2016).

Since only trout with L > 115 mm (aged at least 1 +) were tagged, capture histories were generated only for those fish. We first used data for all three populations to estimate the overall differences in survival probabilities among them using population (LIdri_MT, LIdri_RT, UIdri_MT) and sampling occasion or season as predictors of survival. Then, in order to obtain a finer-grained estimation of variation in survival in marble trout, we excluded LIdri_RT from the dataset and modelled survival only in LIdri_MT and UIdri_MT, also in this case using population (LIdri_MT, UIdri_MT) and sampling occasion or season as predictors of survival.

Next, we used a subset of the tag-recapture data set (fish born after the start of tagging, i.e., ≥2004, and only females) for the two marble trout populations to test for costs of reproduction. Spawning successfully (i.e., at least one offspring assigned to the parent) was modelled as a timevarying predictor (Spawn_temp: 1 for the September to June sampling period in which spawning occurred and 0 otherwise). The hypothesis tested is of a lower survival probability of female parents in the months following reproduction in LIdri_MT than in UIdri_MT due to higher costs of reproduction. Models tested included a population component (constant or LIdri_MT/UIdri_MT), a time component (sampling occasion or season) and a spawning component (constant or Spawn_temp).

For each model, we tested additive and multiplicative interactions among predictors. Models were considered to provide the same fit to data when ΔAIC between models was <2 [START_REF] Burnham | Model selection and multimodel inference: A practical information-theoretic approach[END_REF]. We carried out the analysis of survival using the package marked [START_REF] Laake | Marked: An R package for maximum-likelihood and MCMC analysis of capture-recapture data[END_REF] for R (R Development Core Team, 2014) (Genotype data: https://dx.doi.org/10.6084/m9.figshare.4244252.v2; Tag-recapture data: https://dx.doi. org/10.6084/m9.figshare.4244249.v2).

RESULTS

A paired t test found significantly higher population density in September of fish older than 0+ in UIdri_MT than in LIdri_MT (p = 0.01, average difference approximately 250 individual ha-1) and a density of 0+ fish significantly higher in LIdri_MT than in UIdri_MT (p < 0.01, average difference approximately 500 individual ha-1) (Figure 1a). LIdri_RT older than 0 + were found at much lower densities than LIdri_MT (p < 0.01, average difference approximately 550 individual ha-1), but densities of 0 + were not significantly different between LIdri_RT and LIdri_MT (p = 0.06) (Figure 1b).

There were significant cross-correlations with a lag of 1 year between the density of 0+ and fish older than 0+ for both LIdri_MT (r = 0.65) and UIdri_MT (r = 0.61), which suggest that recruitment (i.e., density of 0+ in September at year t) was driving variation in density of fish older than juveniles. In contrast, the 1-year lagged correlation between the density of 0+ and fish older than 0+ for LIdri_RT was not significant. Densities of LIdri_MT and LIdri_RT older than 0+ were cross-correlated with no lag (r = 0.77), while densities of 0+ were cross-correlated with no lag only when excluding an outlier (year 2012, r = 0.60). The densities of both 0 + and older than 0 + fish of the two marble trout populations were not significantly cross-correlated; however, when excluding the outliers 2007 (for 0+) and 2008 (for older than 0+) (which identify the same process, since the 2007 high recruitment in UIdri_MT led to the high density of fish older than 0+ 1 year later, Figure 1), the two time series were significantly correlated with no lag (0+: r = 0.63, > 0+: r = 0.62).

Some old, big marble trout were found in LIdri (Figure 2), probably due to a large pool there that allowed their survival. vBGF models fitted with no random effects show how the estimated average growth trajectories can be heavily biased by a few long-lived, bigger-at-age marble trout living in Upper and Lower Idrijca (Supporting Information Figure S1), thus making necessary the adoption of models with individual random effects. Random-effects models with Species and Population as predictors of vBGF parameters provided the same fit to data (ΔAIC < 2). Both average growth trajectories and confidence intervals of LIdri_MT and UIdri_MT almost completely overlapped, while on average rainbow trout grew faster and remained bigger-at-age throughout their lifetimes than marble trout in either population (Figure 2).

The best model of survival probabilities had survival varying with sampling occasion and population, with survival probabilities consistently higher in UIdri_MT than in LIdri_MT and LIdri_RT (Table 1, Figure 3). When including only marble trout populations, the best models had survival varying with population and sampling occasion (Table 1). The addition of Spawn_temp did not improve model fit after accounting for population and sampling occasion (Table 1). We were able to confidently assign to parent pairs or single parents 36% of genotyped individuals for UIdri_MT, 45% for LIdri_MT and 25% for LIdri_RT (Supporting Information Figure S2). Individuals continued to spawn throughout their lifetime (Supporting Information Figure S3). The proportion of younger parents was higher in LIdri_MT than in UIdri_MT (χ2 = 4.98, p = 0.02), while no difference in proportion of younger parents was found between LIdri_MT and LIdri_RT (χ2 = 0.002, p = 0.96) (Figure 4). Similar results were obtained when considering only 1+ as young parents.

Discussion

The population dynamics of the two marble trout populations and of rainbow trout were overall synchronous. We found higher prevalence of younger parents, higher mortality and lower density of individuals older than 0 + in marble trout living in sympatry with rainbow trout than in marble trout living in allopatry. In contrast, there were no differences in the average growth trajectories between the two marble trout populations. We discuss the observed variation in population dynamics, vital rates and life histories between he two marble trout populations, the pieces of missing infor mation that will improve our understanding of its proximate and ultimate causes, and how the observed variation is con sistent with the predictions of life history theory.

Population dynamics and reproduction

Supported by [START_REF] Musseau | Dietary niche expansion and niche shift in native marble trout (Salmo marmoratus) living in sympatry with introduced rainbow trout (Oncorhynchus mykiss)[END_REF] hypothesis on the likely inclusion of rainbow trout as additional prey in the diet of marble trout living in Lower Idrijca, our hypothesis is that predatory pressure on rainbow trout juveniles by marble trout older than 1+ caused both the low density of rainbow trout older than 0+ and the lack of cross-correlation between recruitment and density of older fish in rainbow trout. DNAbased faecal dietary analysis [START_REF] Valentini | DNA barcoding for ecolo gists[END_REF] will help us test this hypothesis.

Overall, the population dynamics of marble trout in Upper and Lower Idrijca and of marble and rainbow trout in Lower Idrijca were synchronous, which points to common environmental determinants of temporal variation in vital rates ("Moran effect"). Vincenzi, Mangel, et al. (2016) showed that variation in water temperature alone-over sampling occasions or early in life-did not explain much variation in either survival or growth in marble trout living in Western Slovenian streams, including the Idrijca populations. In addition, Vincenzi, Mangel, et al. (2016) found strong cohort effects on survival and growth in almost all marble trout populations living in Western Slovenia, which suggest that a combination of environmental factors (e.g., food, water flow and temperature) experienced early in life is driving a large part of the variation in vital rates in marble and rainbow trout living in Idrijca. An analysis of spatio-temporal patterns of fluctuation of 57 brown trout populations across France found that the degree of synchrony among sites for the 0+ fish was significantly related to the degree of hydrological synchrony, in particular synchronous high flows across rivers and streams during the emergence period [START_REF] Cattaneo | Synchrony in brown trout, Salmo trutta, population dynamics: A "Moran effect" on early-life stages[END_REF]. Future measurement of water flows in Upper and Lower Idrijca with probes or meters and estimation of temporal variation of food-web components would provide a clearer picture of the environmental determinants of synchronous population dynamics. At each sampling occasion, density of juvenile marble trout in allopatry was much lower than that of marble trout in sympatry. The lower density of juveniles in allopatry was due to reproduction occurring mostly in a small tributary of Upper Idrijca located upstream of the two monitored stream stretches; the time passing between emergence of new-borns and sampling in September was not long enough to allow for the arrival of 0+ in the monitored stream stretches. It follows that estimated recruitment was only a small fraction of real recruitment.

Survival

One of the central tenets of life history theory is the expected tradeoff between survival and reproduction. Vincenzi, Mangel, et al. (2016) hypothesized that lower average survival in marble trout populations exhibiting faster individual growth was caused by the cost of reproduction: faster growth early in life can lead to younger age at sexual maturity when gonadal development is size dependent [START_REF] Alm | Connection between maturity, size and age in fishes[END_REF][START_REF] Craig | Aging in fish[END_REF][START_REF] Jonsson | Effects of temperature and food quality on age and size at maturity in ectotherms: An experimental test with Atlantic salmon[END_REF] and then cause higher mortality of spawners due to energetic limitations [START_REF] Berg | Energetics and survival of virgin and repeat spawning brown trout (Salmo trutta)[END_REF]. In marble trout living in Upper and Lower Idrijca, we did not find evidence of lower survival probabilities for female parents in the sampling interval (September to June) following spawning. However, most marble trout females spawn each year after becoming sexually mature and the cost of reproduction should not be limited to only those females that reproduced successfully. Thus, even if present, higher costs of reproduction in marble trout living in Lower Idrijca may be difficult to detect using parents as a proxy for spawners. Another hypothesis to explain lower survival of marble trout in sympatry with rainbow trout is more intense competition for hiding places; although the total density of fish in Upper and Lower Idrijca is similar, rainbow trout are bigger than marble trout and this may be due to their more aggressive and/or territorial behavior, with negative effects on marble trout survival rates.

Age at spawning, growth and life histories

We found that marble trout in sympatry had a higher proportion of young parents than marble trout living in allopatry, and the same proportion of young parents as sympatric rainbow trout. Along with lower survival, higher proportion of young parents points to faster life histories in sympatric than in allopatric marble trout.

It has often been found that fast life histories increase invasion success [START_REF] Ruesink | Global analysis of factors affecting the outcome of fresh water fish introductions[END_REF] and that colonists adopt life histories that are faster than those of the source population (i.e., pioneer life histories). Similarly, fast life histories in the invaded population may help avoid the invasion of the alien species or limit their abundance. Theoretical and empirical studies have found that fitness is highly sensitive to variation in age at first reproduction [START_REF] Fay | Variation in the age of first reproduction: Different strategies or individual quality?[END_REF]. Age at reproduction varies greatly withinand among populations of the same species, and life history theory predicts a tradeoff between growth and reproduction [START_REF] Roff | Life-history evolution[END_REF][START_REF] Stearns | The evolution of life histories[END_REF]: organisms with a slower pace of life allocate more energy to growth throughout their life and reproduce at older ages, since fecundity and other reproductive traits, such as the ability to secure mates, often increase with size.

However, growth of fish results from the interaction of resource acquisition, availability and allocation (Vincenzi, Crivelli, et al., 2016), along with other factors such as temperature, water flow and length of growing season [START_REF] Crozier | Interact ing effects of density and temperature on body size in multiple populations of Chinook salmon[END_REF]. According to life history theory, when there is a minimum size for gonadal development, organisms adopting faster life histories should grow faster and then plateau in size after sexual maturity due to allocation of energy to reproduction at the expense of growth. However, despite the presence of a competitor and the shift in diet, marble trout living in sympatry with rainbow trout did not grow differently than marble trout in allopatry, which shows that the acceleration of reproduction may occur without variation in growth.

Phenotypic shifts over contemporary time scales can result from phenotypic plasticity or selection acting on standing genetic variation, and they are most likely a result of a combination of these factors [START_REF] Hendry | Whither adaptation?[END_REF]. Reproductive traits are heritable [START_REF] Carlson | A review of quantitative genetic components of fitness in salmonids: Implications adaptation to future change[END_REF], and can thus respond adaptively to changes in the fitness landscape. In marble trout living in streams affected by flash floods causing massive mortalities, [START_REF] Vincenzi | The genetic and life-history consequences of extreme climate events[END_REF] found that fish born after the flash floods had younger mean age at reproduction than fish born before the flash flood. [START_REF] Vincenzi | The genetic and life-history consequences of extreme climate events[END_REF] hypothesized that younger age at reproduction after the flash floods was due to a combination of faster growth due to lower population density and fewer older fish competing for mates. In the case of Idrijca, the age-structure of marble trout in Lower and Upper Idrijca and their fish densities are similar, and average growth trajectories are basically the same; thus other adaptive or plastic processes causing a higher prevalence of younger parents in marble trout living in Lower Idrijca may be at work. Currently on-going common garden experiments will help elucidate the proximal causes of faster life histories in marble trout living in Lower Idrijca.

FIGURE 1

 1 FIGURE 1 (a) Density over time of LIdri_MT and UIdri_MT aged 0+ (dashed line) and older than 0+ (solid line) in September. (b) Density over time of LIdri_MT and LIdri_RT aged 0+ (dashed line) and older than 0+ (solid line) in September

FIGURE 3

 3 FIGURE 3 Best model of apparent survival when including all three populations, with survival varying by population and sampling occasion (i.e., ϕ[Population + Time]). Vertical bars are 95% confidence intervals

TABLE 1

 1 Five best models of probability of apparent survival ϕ for all three populations (LIdri_MT, UIdri_MT and LIdri_RT), only the two marble trout populations, and only females for the two marble trout

	Note : The symbol * denotes interaction.
	AIC, akaike information criterion; npar, number of parameters of the
	survival model; Time, the interval between two consecutive sampling
	occasions; Season, categorical variable for Summer (June to September)
	and Winter (September to June); Spawn_temp, categorical variable for
	females spawning successfully (1) or not (0).

ACKNOWLEDGMENT

We thank the employees and members of the Tolmin Angling Association (Slovenia) for carrying out fieldwork since 1993. This study has been funded by MAVA Foundation.

Author Contributions

S.V., A.J.C. and J.C.G. conceived the ideas and designed methodology; A.J.C. and D.J. collected the data; S.V. and E.C. analysed the data; S.V., J.C.G. and A.J.C. led the writing of the manuscript. All authors contributed critically to the drafts and gave final approval for publication.

SUPPORTING INFORMATION

Additional supporting information may be found online in the Supporting Information section at the end of the article.


Alain Ledoux

Marie Décultot

Marie-Christine Fournier-Salauen

Lionel Estel

Lionel Estel Carboxylation

Carboxylation of alcohol for CO2 valorisation: thermodynamic and kinetic study

teaching and research institutions in France or abroad, or from public or private research centers.

Studied Reaction

Carboxylation of diols and alcohols to obtain cyclic and linear carbonates with the use of cerium oxide catalyst.

Applications of carbonates:

Synthesis of the main products:

CO 2 H 2 O + + 2 CH 3 OH méthanol dimethyl carbonate CeO 2 CO 2 H 2 O + + CeO 2 propylene carbonate 1,2-propanediol

o+

  Considering global warming effect on earth, the diminution of CO 2 emissions becomes imperative.o A new chemistry of CO 2 is developing to face up to the rarefaction of fossil resources.o The valorization of CO 2 using bio-based products creates a true circular economy by using CO 2 as a source of carbon to produce value-added products.Development and optimisation of a process which associate CO 2 from flue gas stream and bio-based reactants to synthesize a value-added product.

o

  Fuel additive to reduce SOx and NOx emissions Low toxic solvent materials for polycarbonates Study of the solubility of CO 2 1 M. Honda et al. J. Catal., vol. 318, pp. 95-107, 2014, M. Honda et al. ACS Catal., vol. 4, no. 6, pp. 1893-1896, 2014 ; 2 Gui et al. J. Chem. Eng. Data 56, 2420-2429Study of the reaction of carboxylation of alcohols and diols with CO 2 to produce carbonates: study of dehydration systems. o Measure of the solubility of CO in methanol, ethanol, 1,2-propanediol and glycerol. o Objective : Development of a sustainable process which associate CO 2 and a bio-based reagent to produce value-added chemical products The solubility is proportional to the pressure of CO 2 for ethanol, methanol, 1,2propanediol and glycerol. Results are in good agreement with the literature 2 . dehydrating systems to shift the equilibrium toward the formation of carbonates Use of a dehydrating reagent Use of a molecular sieve Use of a pervaporation system


domain: spi phys

text:
S Salgado

L Poutier

X Briottet

S Mathieu

Validation of an empirical method for thin cirrus correction with Sentinel-2 data

Keywords: Cirrus, cloud, correction, validation, atmosphere, cirrus removal Area [0.4 -0.7 µm] [0.7-0.86 µm] SWIR Ci0 Ci1 Ci2 Ci3

Most satellite images are polluted by the presence of semi-transparent clouds, called cirrus, returning them unusable. Gao and Li (2017) have developed an empirical method for the correction of thin cirrus for Landsat-8, allowing to return to a clear sky apparent reflectance. Validated qualitatively, we propose here a quantitative validation method using Sentinel-2 data by comparing the corrected image with a clear sky reference image. Their method shows good results on dark surfaces, like water, with an apparent reflectance found close to 0.02. On the other hand, it becomes less accurate for thicker cirrus and on more reflective surfaces. In addition, the data analysis shows that pixels located in the shadow of the cirrus are over-corrected. The downward path should therefore be taken into account when correcting the signal.

INTRODUCTION

Atmospheric correction is today well controlled under clear-sky conditions. Unfortunately, an average of 2/3 of the Earth are covered by clouds and at the scale of an observed scene of a few tens or even hundreds of km², they can cover the sky entirely, reducing drastically the amount of usable data acquired by an optical sensor from space. Among the different types of clouds, the most widespread are cirrus clouds, with an average coverage of around 30% [START_REF] Stubenrauch | Cloud Properties and Their Seasonal and Diurnal Variability from TOVS Path-B[END_REF] Cirrus are semi-transparent clouds, allowing us to see the underlying surface. Thus, there is a real interest to achieve an atmospheric correction in the presence of such clouds if their optical thickness is not too thick. These clouds, composed with ice crystals of different sizes and shapes depending on their position in the cloud, are located in the troposphere at altitudes above 8 km. As most of the water-vapor is located below this altitude, Gao and al. 2 (1993) showed, with AVIRIS hyperspectral instrument's data, that the exploitation of strong water-vapor absorption bands, like 1.38 µm or 1.88 µm, allowed cirrus detection. The 1.38µm band was then integrated into various sensors: MODIS (Terra (1999) and Aqua (2002)), then VIIRS (Suomi-NPP, 2011), OLI (Landsat-8, 2013) and MSI (Sentinel-2, 2015). However, this detection method has limitations: dry atmosphere, high altitude or strong albedo surface and high water clouds [START_REF] Ben-Dor | A precaution regarding cirrus cloud detection from airborne imaging spectrometer data using the 1.38/am Water vapor band[END_REF] . Gao and al. proposed then an empirical method to correct thin cirrus, based on the utilization of the 1.38µm band. The method was initially limited to the [0.4-1.0 µm] region [START_REF] Gao | Correction of thin cirrus path radiance in the 0.4-1.0 µm spectral region using the sensitive 1.38 µm cirrus detecting channel[END_REF] , then, extended to the SWIR for Landsat-8 [START_REF] Gao | Removal of thin cirrus scattering effects in Landsat 8 OLI images using the cirrus detecting channel[END_REF] , in 2017.

Gao and al. method (1998) is today used in several processing chains, and has shown qualitatively its effectiveness in removing cirrus effects. In this paper, a quantitative validation of 2017'method is proposed.

The next section of this paper describes Gao and al. method, as well as the method and data used for validation. The 3rd part reports the results and finally, the method is discussed in the 4 th section.

MATERIEL AND METHOD

Cirrus detection

Gao and al. [START_REF] Gao | Cirrus cloud detection from airborne imaging spectrometer data using the 1.38 µm water vapor band[END_REF] shows that the 1.38µm saturated water vapor absorption band allowed cirrus detection. Indeed in this band, the only signal reaching the sensor comes from the scattering in the upper cirrus cloud, all the signal coming from below being totally absorbed by the water vapor. This led Richter and al. [START_REF] Richter | Atmospheric and Topographic Correction (ATCOR Theoretical Background Document)[END_REF] to propose a cirrus classification. This classification is based on thresholds in the apparent reflectance of the cirrus band (1.38 µm) as shown below:

• The 𝜌𝜌 * ( 1.38 µ𝑚𝑚 ) = 0.04 separates semi-transparent cirrus from optically thick cirrus. These thresholds are used in the following for the analysis of the results.

Cirrus correction: Gao and al. method

Empirical model

Gao and al. [START_REF] Ben-Dor | A precaution regarding cirrus cloud detection from airborne imaging spectrometer data using the 1.38/am Water vapor band[END_REF] (1998) proposed a first empirical method for the correction of thin cirrus. This method is limited to the [0.4-1.0 µm] region where cirrus optical properties can be assumed spectrally flat. Beyond 1.0 µm, absorption effects modify the spectral signature.

The Earth-atmosphere system is modeled by 2 plan and parallel layers: a virtual surface (including the surface and all the atmosphere -water-vapor, water clouds, aerosols) and a layer of cirrus clouds.

Using the classic formula of 6S [START_REF] Vermote | Second Simulation of a Satellite Signal in the Solar Spectrum -Vector (6SV)[END_REF] and applying it to the cirrus layer, the measured apparent reflectance is written:

𝜌𝜌 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 * (𝜆𝜆) = 𝜌𝜌 𝑐𝑐 * (𝜆𝜆) + 𝑇𝑇 𝑐𝑐 𝜌𝜌 * (𝜆𝜆). 1 1-𝑆𝑆 𝑐𝑐 𝜌𝜌 * (𝜆𝜆) , (1)
with ρ* c the apparent reflectance of the cirrus cloud, T c the total transmission (diffuse + direct, up and down) through the cirrus, ρ* the apparent reflectance of the virtual, and S c the spherical albedo of the cirrus. From this equation some simplification are made : the coupling term is simplified, assuming S c is weak ( < 0.2) and, total absorption being negligible for thin cirrus, the transmission is put equal to unity and, the apparent reflectance of the cirrus in the domain 0.4-1.0 µm is proportional to the signal at 1.38 µm :

𝜌𝜌 𝑐𝑐 * ( 𝜆𝜆 ) = 𝜌𝜌 𝑐𝑐 * (1.38 µ𝑚𝑚) 𝐾𝐾 𝑎𝑎 , (0.4 < λ < 1.0 µm) (2)
The K a coefficient accounting for the residual water vapor absorption in the 1.38 band. The reflectance corrected from the presence of thin cirrus then expresses as:

𝜌𝜌 * (𝜆𝜆) = 𝜌𝜌 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 * (𝜆𝜆) - 𝜌𝜌 𝑐𝑐 * ( 1.38 µm ) 𝐾𝐾 𝑎𝑎 , (0.4 < λ < 1.0 µm) (3)
In 2017 Gao and Li 5 extended the method to the SWIR, for Landsat-8 (11 bands, from 0.4 to 12.5 µm), by modifying the formula 3 considering not just one coefficient K a , but a K a depending on the wavelength:

𝜌𝜌 * (𝜆𝜆) = 𝜌𝜌 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 * (𝜆𝜆) - 𝜌𝜌 𝑐𝑐 * ( 1.38 µm ) 𝐾𝐾 𝑎𝑎 (𝜆𝜆) (4)

Estimation of K a coefficient

The coefficients K a (λ) are estimated by a scatterplot between the 1.38 µm band and the band λ (Fig. 1). These coefficients depend on the scene, the cirrus, and on solar and view angles. The linear regression slope is obtained with the Gao and al. method 8 , which consist in, for each bins in the cirrus apparent reflectance, taking the closest points to the minimum value of the apparent reflectance in the band λ. They also suggest a piecewise-linear line with x slopes. But as the number of slopes and the threshold on ρ * ( 1.38 µm ) depend on the image and the band, it is difficult to set it manually.

Figure 1: Example of a linear correlation between the 1.24 and 1.38 μm bands for an AVIRIS image (Gao et al., 1998). On the left, the graph corresponds to a homogeneous surface image containing only cirrus type clouds. On the right, the pixels around the dotted line are the fine cirrus pixels. The points to the right of the line correspond to the cumulus. The same type of graph is obtained when correlating any λ and 1.38 μm bands.

Data and validation method

To validate the method, couples of Sentinel-2 images were used. Sentinel-2 is a series of 2 Earth observation satellites (S2A (2015) and S2B (2017)) from ESA (European Space Agency) developed for the Copernicus program. These satellites are equipped with a MSI multispectral imager using the pushbroom technique and having 13 bands from visible to SWIR with spatial resolution of 10, 20 and 60 meters. They are taken in Level-1C product (Top of Atmosphere radiance).

Thanks to the instrument high revisit, two acquisitions, one under clear sky conditions and the second with cirrus clouds, can be found in a short period time (less than 5 days) so that the ground scene can be assumed invariant and the solar angles almost identical. Then, on each pair of images, areas of interest were carefully selected. Once the cirrus image is corrected by the method previously described, it is compared with the corresponding clear sky image. For this, on each selected area the RMS difference is calculated between the corrected image and the clear sky reference, for each band, and according to the class of cirrus. Each downloaded Sentinel-2 granule has been cut to reduce computational time. 5 couples of images fulfilling the conditions were found: 2 couples of water images and 3 containing mixed surfaces of sea and continental surface (Table 1).

RESULTS

Cirrus detection

The ATCOR cirrus classification is applied on the different selected images. Fig. 2 shows an illustration of this classification for the La Crau site. The different thicknesses of cirrus appear well distinct and contrails are also detected.

Cirrus correction

Fig. 4(a). shows how the presence of cirrus affects the apparent reflectance for pixels of water, inducing a positive offset, whatever the wavelength. The curve after application of Gao and Li method fit very well the clear sky curve, showing an offset corrected for this pixel. Then, for each studied area, the RMS difference is calculated in each band and each class of cirrus according to the ATCOR classification. In the table 2 below, an average value per band group of the RMS values of each band is presented. The bands were grouped into 3 groups: those before the red-edge, those of the NIR and those of the SWIR.

Table 2: RM S error for each studied area, and for each group of band and class of cirrus. In red region with high RM S values.

On water, results show that the reflectance error is generally found to be less than 0.02, for all bands and even for the thickest cirrus. However, for images of the Black Sea and La Crau, larger values are observed. The common feature between these two images is the presence of contrails. In the Black Sea case, these values are due to the K a coefficients. Indeed, Fig. 3 shows that the pixels used for the calculation of K a (λ) correspond to the contrails pixels (in red in the Fig) .  The green and blue groups correspond to the cirrus and exhibit a different slope. Only the contrails are well corrected while cirrus were under-corrected. On the image of La Crau region, the pixels used for calculating the K a coefficients correspond to cirrus above the water, but here the contrails pixels "sign" and do not just cause any offset (Fig. 4.(b)) therefore, after correction, the spectrum found is not consistent with water signature.

Once the correction on the water analyzed, the study was done on continental surfaces. Forests are dark and therefore present an apparent reflectance in clear sky which remains weak. This case is similar to that of water, except above the red-edge. By the bye, it's in this region where the RMS values are a little larger and raise up to 0.021. On the rest of the spectrum, RMS values remain less than 0.01.

The La Crau plain, on the other hand, has higher apparent reflectance values in clear sky, especially in the red-edge and SWIR regions where the values are higher than 0.2. It is in these same 2 regions that high RMS values (> 0.03) are found after correction. In the visible, thicker cirrus are also poorly corrected.

Globally, Gao's method delivers consistent results and finds apparent reflectance values within 0.02. The thicker the cirrus is, the less accurate the correction will be. Similarly, larger uncertainties are obtained with highly reflective surfaces. K a (λ) estimation seems to play a major role in the accuracy of the correction.

DISCUSSION

Estimation of the Ka coefficient

The formula 4, as the Black Sea example, shows that the accuracy of the correction depends largely on the quality of K a (λ) estimation. Depending on the situation, the estimation is more or less simple. When scatterplots are usually in the shape of the left Fig. 1 for water images with an easy slope to estimate, the presence of contrails modifies the scatterplot and "falsifies" the correction (Fig. 3).

A test on this image has been done. 3 slopes were calculated, corresponding to the 3 groups of Fig. 3, and the pixels of each group were corrected with the corresponding K a . Fig. 5 shows the results of RMS with the use of a single K a for all the pixels (a) and with the use of coefficients depending on the pixel (here 3 different K a (λ)) (b). The correction is improved for thin cirrus and we are left with similar cases to other images. For thicker cirrus, the RMS is higher but it is possible that they were not well selected and thus corrected with the wrong value of K a (λ). Without contrails, the image would have been well corrected. Furthermore, for more complex images with several types of surfaces, the scatter plot may be different depending on the bands and surfaces present, and the estimation of K a (λ) becomes more complex. Let's take the example of scatterplot between the bands 1.38 and 0.78 µm of the S2 La Crau image below (Fig. 6.(a)). If we calculate the slope using all the points of the left envelope, the slope will have a value of 0.395. Moreover, if we do not exclude the points circled in Fig. 6.(a), the calculation of the slope also differs with a value of 0.369. If now we decide to set a threshold manually, at 𝜌𝜌 * ( 1.38 µ𝑚𝑚 ) = 0.05 where the cirrus are starting to get very thick, and calculate the slope only up to this value, we get a slope of 0.835. Fig. 6.(b) shows the RMS as a function of the wavelength, calculated for every cirrus on La Crau plain, with these 3 different estimation of the coefficients K a (λ). This show that a different value of K a (λ) can completely change the accuracy. For this image, and others, the result is better when the threshold is fixed (orange curve), particularly in the NIR bands, where the RMS is less than 0.02 instead of 0.05.

Limitation

The image above La Crau site raised many questions. Some pixels of La Crau region were over-corrected. Looking closer, it was found that in some cases, in the 0.7-0.9 μm region, the signal of the cirrus image is lower than that of the clear sky image. We found that this case correspond, most of the time, to the cirrus shadow as we can see in the figure 7 were patterns are found.

Figure 7: 2 zooms on the image of the Crau, showing the different classes of cirrus and, in black, the pixels where the apparent reflectance in the band 8A in the presence of cirrus is lower than that in clear sky. Red arrows show that it seems to match the shadows of the cirrus.

Gao and Li model only corrects the rising path. However, the downward path has a significant impact on the signal, especially for surfaces of strong apparent reflectance. These observations led to simulations, with COMANCHE 9 , to understand how the presence of cirrus in the downward path modifies the apparent reflectance and then propose an improvement of the correction.

14 cirrus are simulated in the conditions of the Sentinel-2 image of La Crau, and 3 possible situations are studied (Fig. 8): An homogeneous cirrus covering the entire scene, an homogeneous cirrus only in the downward path and an homogeneous cirrus only on the upwelling path.

We focus here on the 0.8µm wavelength, where we noticed the problems. The analysis of the difference between the signal in presence of cirrus and the signal in clear sky show different results according to the situation. When we see clear sky on the image, the received signal may be lower than the actual signal if a cirrus is present on the downward path, especially if the surface has a strong reflectance and if the cirrus on the down path is optically thick. This can cause errors up to 0.06 on the signal before the correction. When the cirrus is only on the rising path, there is mainly an increase on the apparent reflectance. But when the cirrus is thin and the surface has a strong reflectance there is an inversion, and the signal is reduced. The last case is a combination of the 2 other. It would be necessary to be able to identify these different situations in the image in order to apply the appropriate correction.

CONCLUSION

The method of thin cirrus correction of Gao and Li extended to the SWIR applied on Sentinel-2 data globally shows good results. On dark surfaces such as water or forest, the apparent reflectance in clear sky is found to 0.02. But on more reflective surfaces, such as La Crau plain, results are worse, especially in the NIR bands, where the RMS values are greater than 0.03.

  Clear sky (Ci0) : 𝜌𝜌 * ( 1.38 µ𝑚𝑚 ) ∈ [0 -0.01[ • Semi-transparent thin cirrus (Ci1) : 𝜌𝜌 * ( 1.38 µ𝑚𝑚 ) ∈ [0.01 -0.015[ • Semi-transparent medium cirrus (Ci2) : 𝜌𝜌 * ( 1.38 µ𝑚𝑚 ) ∈ [0.015 -0.025[ • Semi-transparent thick cirrus (Ci3) : 𝜌𝜌 * ( 1.38 µ𝑚𝑚 ) ∈ [0.025 -0.04[ • Optically thick thin cirrus (Ci4) : 𝜌𝜌 * ( 1.38 µ𝑚𝑚 ) ∈ [0.04 -0.05[ • Optically thick medium (Ci5) : 𝜌𝜌 * ( 1.38 µ𝑚𝑚 ) ≥ 0.05

Figure 2 :

 2 Figure 2: Left: RGB S2 image of La Crau region. Right: Classification of the cirrus with threshold in the apparent reflectance at 1.38µm

Figure 3 :Figure 4 :

 34 Figure 3: (a) Scatterplot of the 1.38µm band with the 0.66µm band with the different groups in color. (b) The Sentinel-2 image in the 1.38µm band with the color pixels of the associated groups. (c) RGB image

Figure 5 :

 5 Figure 5: RM SE function of the thickness of the cirrus, for each band. (a): when applying Gao and al 2017 method. (b): Gao and al. 2017 method with different coefficients K a .

Figure 6 :

 6 Figure 6: (a): Scatterplot between the apparent reflectance at 1.38 µm and at 0.78 µm for the S2 image over the La Crau region.(b): RM S as a function of the wavelength, calculated for all cirrus, for 3 different corrections, for the La Crau plain. In red, with a K a (λ) calculated with all the pixel of the left envelope of the scatterplot; in green, with a K a (λ) calculated after filtering point; in orange, with a K a (λ) calculated only up to ρ*(1.38µm) = 0.05.

Figure 8 :

 8 Figure 8: Left: Different case of simulations. Right: Difference between the apparent reflectance in presence of cirrus and in clear sky as a function of the surface reflectance, for the case of simulation corresponding, at λ = 0.8µm

Table 1 :

 1 Characteristics of selected sentinel-2

images S2 tile Region Studied area Sky Satellite Date + UTC time Solar zenithal angle Solar azimuthal angle Zenithal angle of view Azimuthal angle of view

	T17TLL	Huron Lake (Canada)	Water	Clear sky Cirrus	S2B S2B	08/23/2018 -16h18 08/26/2018 -16h28	36.8° 37.0°	153.5° 158.2°	8.3° 6.4°	105° 284.5°
				Clear sky	S2B	10/28/2018 -8h20	56.1°	166.4°	6.0°	105.2°
	T37TOG	Black Sea	Water
				Cirrus	S2B	10/31/2018 -8h30	56.7°	169.5°	8.9°	286.0°
	T31TFJ	La Crau (France)	Water La Crau plain	Clear sky Cirrus	S2B S2A	07/29/2018 -10h30 08/03/2018 -10h30	28.8° 29.9°	145.0° 146.2°	7.2° 7.1°	106.5° 105.5°
			Water	Clear sky	S2A	09/11/2018 -10h56	41.8°	160.3°	2.9°	196.6°
	T30TXQ	Landes (France)
			Pine forest	Cirrus	S2B	09/16/2018 -10h56	43.5°	161.6°	2.8°	193.6°
			Water	Clear sky	S2A	10/25/2017 -11h33	54°	168.7°	9.0°	287.3°
	T29TNF	Portugal
			Forest	Cirrus	S2A	10/22/2017 -11h21	53.4°	165.3°	6.0°	103.8°

The model is limited by several things. First, K a (λ) estimation plays a fundamental role in the accuracy of the correction. The latter can sometimes be distorted by the presence of contrails. Then, the model only corrects the rising path here. However, the analysis of the images show that for some pixels, the apparent reflectance in the presence of cirrus is lower than that in clear sky, causing an over-correction when applying the formula. This weaker reflectance appears to be caused by the presence of a cirrus on the descending path (sun-ground). This is supported by the various simulations. Knowing how to separate the pixels in the cirrus 'shadow from the others, with the help of the single cirrus image, would make it possible to apply two different corrections and to improve the accuracy of the correction.