Wissem Inoubli

Sabeur Aridhi

Haithem Mezni

Mondher Maddouri

Engelbert Mephu Nguifo

A Comparative Study on Streaming Frameworks for Big Data

Recently, increasingly large amounts of data are generated from a variety of sources. Existing data processing technologies are not suitable to cope with the huge amounts of generated data. Yet, many research works focus on streaming in Big Data, a task referring to the processing of massive volumes of structured/unstructured streaming data. Recently proposed streaming frameworks for Big Data applications help to store, analyze and process the continuously captured data. In this paper, we discuss the challenges of Big Data and we survey existing streaming frameworks for Big Data. We also present an experimental evaluation and a comparative study of the most popular streaming platforms.

Introduction

In recent decades, increasingly large amounts of data are generated from a variety of sources. The size of generated data per day on the Internet has already exceeded two exabytes [START_REF] Gandomi | Beyond the hype: Big data concepts, methods, and analytics[END_REF]. Stream processing problems lead to several research questions such as [START_REF] Alexandrov | The stratosphere platform for big data analytics[END_REF] how to design scalable environments, (2) how to provide fault tolerance and (3) how to design efficient solutions. In this context, stream processing frameworks are mainly designed to process the huge amount of data streams and to make on-the-fly decisions. With the rise of big data, various organizations have started to employ stream frameworks to solve major emerging big data problems related to smart ecosystems, healthcare services, social media, etc. For example, in smart cities, various sensors such as GPS, weather conditions devices, public transportation smart cards and traffic cameras are installed on diverse regions (e.g, water lines, utility poles, buses, trains, traffic lights) [START_REF] Soomro | Towards provisioning of real-time smart city services using clouds[END_REF]. From these sensors, very large quantities of data are collected. To understand such volume of data, it is important to reveal hidden and valuable information from the big stream/storage of data. Social media is another representative data source for big data that requires real-time processing and results [START_REF] Vlassopoulos | Dynamic graph management for streaming social media analytics[END_REF]. In fact, a huge volume of data is instantly and continuously generated from a wide range of Internet applications and Web sites. Examples include online mobile photo and video sharing services (e.g, Instagram, Youtube, Flickr), social networks (e.g. Facebook, Twitter), business-oriented networks (e.g. LinkedIn), etc. The adoption of in-stream frameworks that offer iterative processing and learning capabilities allows to effectively perform specific tasks such as social network analysis, links prediction, etc. Given the importance of the above discussed real-world scenarios, finding the relevant framework for the big/high stream-oriented applications becomes a challenging problem.

Several systems have been proposed in the literature. In this paper, we present a comparative study of popular stream processing frameworks according to their key features. The studied frameworks have been chosen based on their number of contributors. Our contributions are summarized as follows:

• We present four popular streaming frameworks for big data, their architecture and their internal behavior. • We compare the presented frameworks according to their key features.

• We evaluate the performance of the presented frameworks in terms of resources consumption.

This paper is organized as follows. In Section 2, we present some well-known stream frameworks for big data. Section 3 is devoted to the comparison of the discussed frameworks. In Section 4, an experimental evaluation of the presented stream processing frameworks is provided.

Stream processing frameworks for big data

Several streaming frameworks for big data have been proposed to allow real-time largescale stream processing. This section sheds the light on the most popular big data stream processing frameworks and provides a comparison study of them according to their main features.

Apache Spark

Apache Spark [START_REF] Spark | Apache spark: Lightning-fast cluster computing[END_REF] is a powerful processing framework that provides an ease of use tool for efficient analytics of heterogeneous data. It was originally developed at UC Berkeley in 2009 [START_REF] Zaharia | Spark: Cluster computing with working sets[END_REF] . Spark has several advantages compared to other big data frameworks like Hadoop MapReduce [START_REF] Dean | Mapreduce: simplified data processing on large clusters[END_REF] and Storm [START_REF] Toshniwal | Storm@ twitter[END_REF]. A key concept of Spark is Resilient Distributed Datasets (RDDs). An RDD is basically an immutable collection of objects spread across a Spark cluster. In Spark, there are two types of operations on RDDs: (1) transformations and (2) actions. Transformations consist in the creation of new RDDs from existing ones using functions like map, filter, union and join. Actions consist of final result of RDD computations. Spark Streaming is a Spark library that enables scalable and high-throughput stream processing of live data streams.

Apache Storm

Storm [START_REF] Toshniwal | Storm@ twitter[END_REF] is an open source framework for processing large structured and unstructured data in real time. Storm is a fault tolerant framework that is suitable for real time data analysis, machine learning, sequential and iterative computation. A Storm program is represented by a directed acyclic graphs (DAG). The edges of the program DAG represent data transfer. The nodes of the DAG are divided into two types: spouts and bolts. The spouts (or entry points) of a Storm program represent the data sources. The bolts represent the functions to be performed on the data. Note that Storm distributes bolts across multiple nodes to process the data in parallel. Storm is based on two daemons called Nimbus (in master node) and a supervisor for each slave node. Nimbus supervises the slave nodes and assigns tasks to them. If it detects a node failure in the cluster, it reassigns the task to another node. Each supervisor controls the execution of its tasks (affected by the nimbus). It can stop or start the spots following the instructions of Nimbus. Each topology submitted to Storm cluster is divided into several tasks.

Apache Flink

Flink [START_REF] Flink | Scalable batch and stream data processing[END_REF] is an open source framework for processing data in both real time mode and batch mode. It provides several benefits such as fault-tolerant and large scale computation. The programming model of Flink is similar to MapReduce [START_REF] Dean | Mapreduce: simplified data processing on large clusters[END_REF] . By contrast to MapReduce, Flink offers additional high level functions such as join, filter and aggregation. Flink allows iterative processing and real time computation on stream data collected by different tools such as Flume [START_REF] Chambers | Flumejava: easy, efficient data-parallel pipelines[END_REF] and Kafka [START_REF] Garg | Apache Kafka[END_REF]. It offers several APIs on a more abstract level allowing the user to launch distributed computation in a transparent and easy way.

Apache Samza

Apache Samza [START_REF] Samza | Linkedin's real-time stream processing framework[END_REF] is an open source distributed processing framework created by Linkedin to solve various kinds of stream processing requirements such as tracking data, service logging of data, and data ingestion pipelines for real time services. Since then, it was adopted and deployed in several projects. Samza is designed to handle large messages and to provide file system persistence for them. It uses Apache Kafka as a distributed broker for messaging, and Hadoop YARN for distributed resource allocation and scheduling. YARN resource manager daemon is adopted by Samza to provide fault tolerance, processor isolation, security, and resource management in the cluster. Samza is based on three layers. The first one is devoted to streaming data and uses Apache Kafka to transit the data flow. The second layer is based on YARN resource manager to handle the distributed execution of Samza processing and to manage CPU and memory usage across a multi-tenant cluster of machines. The processing capabilities are available in the third layer which represents the Samza core and provides API for creating and running stream tasks in the cluster [START_REF] Samza | Linkedin's real-time stream processing framework[END_REF]. In this layer, several abstract classes can be implemented by the user to perform specific processing tasks. These abstract classes are implemented with a MapReduce Framework to ensure the distributed processing.

Comparison of stream processing frameworks

In this section, the frameworks presented above are compared according to several features (see Table 1) including: data format, types of data sources, programming model, cluster manager, supported programming languages, latency and messaging capacities.

We notice that Spark importance lies in its in-memory features and micro-batch processing capabilities, especially in iterative and incremental processing [START_REF] Bajaber | Big data 2.0 processing systems: Taxonomy and open challenges[END_REF]. Although Spark is known to be the fastest framework due to the concept of RDD, it remains characterized by its low throughput compared to other frameworks, while its micro-batch concept could guarantee the fault tolerance. Flink shares similarities and characteristics with Spark. It offers good processing performance when dealing with complex big data structures such as graphs. Although there exist other solutions for large-scale graph processing, Flink and Spark are enriched with specific APIs and tools for machine learning, predictive analysis and graph stream analysis [START_REF] Alexandrov | The stratosphere platform for big data analytics[END_REF] [START_REF] Zaharia | Spark: Cluster computing with working sets[END_REF]. In contrast, resource allocation in Storm is ensured in a dynamic and transparent way. While existing stream processing frameworks implement their own message transport protocol, Samza jobs use a set of named Kafka topics as input/output. Although the low-level one-message-at-a-time model offers some flexibility to Samza, it presents limitations regarding the frequency of produced errors and the automatic optimization. When a broker node fails, the messages located in the file system will be lost and cannot be recovered.

Experiments

In this section, we first present our experimental environment and protocol. Then, we discuss the obtained results. More detailed experiments could be found in [START_REF] Inoubli | An experimental survey on big data frameworks[END_REF].

Experimental environment and protocol

All the experiments were performed in a real cluster called GALACTICA 1 . The cluster is composed of 10 machines operating with Linux Ubuntu 16.04. Each machine is equipped with a 4 CPU, 8GB of main memory and 500 GB of local storage. For our tests, we used Flink 1.3.2, Spark 1.6.0, Samza 0.10.3 and Storm 1.1.1. All the studied frameworks have been deployed with YARN as a cluster manager. For our experimental protocol, we used Twitter4J API 2 to stream tweets that contain the "Big Data" word in real time. Every tweet consists of a JSON file with a set of attributes such as tweet creation date, tweet identifier and user informations. Our experimental protocol consists on executing an Extract, Transform and Load (ETL) routine that (1) extracts tweets using Kafka in order to ensure the same streaming rate while evaluating the studied frameworks, (2) transforms the tweets by keeping only attributes like tweet identifier, tweet content, date, geocoordinate and user informations, and (3) loads the transformed tweets to ElasticSearch. In this work, we studied: (1) the number of messages processed by each framework in a given period, (2) the impact of the size of the message on the number of processed messages, and (3) the resources consumption of the studied frameworks.

Experimental results

Figure 1 shows that Flink, Samza and Storm have better processing rates compared to Spark. This can be explained by the latency feature. In fact, the latency of Spark about seconds while it is about subseconds in the case of Flink, Samza and Storm (see Table 1). In the next experiment, we changed the sizes of the processed messages. We used 5 tweets per message (around 500 KB per message). The results presented in Figure 2 show that Samza and Flink are very efficient compared to Spark, especially for large messages.

CPU consumption

As shown in Figure 3, Flink CPU consumption is low compared to Spark, Samza and Storm. Flink exploits about 10% of the available CPU, whereas Storm CPU usage varies between 15% and 18%. However, Flink may provide better results than Storm when CPU resources are more exploited. In the literature, Flink is designed to process large messages, unlike Storm which is only able to deal with small messages (e.g., messages coming from sensors). Unlike Flink, Samza and Storm, Spark collects events' data every second and performs processing task after that. Hence, more than one message is processed, which explains the high CPU usage of Spark. Because of Flink's pipeline nature, each message is associated to a thread and consumed at each window time. Consequently, this low volume of processed data does not affect the CPU resource usage. Samza exploits about 55% of the available CPU because it is based on the concept of virtual cores and each job or partition is assigned to a number of virtual cores. In fact, it deploys several threads (one for each partition), which explains the intensive CPU usage by Samza compared to the other frameworks.

RAM consumption

Figure 4 shows the cost of event stream processing in terms of RAM consumption. Figure 4 shows the cost of event stream processing in terms of RAM consumption. Spark reached 6 GB (75% of the available resources) due to its in-memory behavior and its ability to perform in micro-batch (process a group of messages at a time). Flink, Samza and Storm did not exceed 5 GB (around 61% of the available RAM) as their stream mode behavior consists in processing only single messages. Regarding Spark, the number of processed messages is small.

Bandwidth resource usage

As shown in Figure 6, the amount of data exchanged per second varies between 375 KB/s and 385 KB/s in the case of Flink, and varies between 387 KB/s and 390 KB/s in the case of Storm. It is about 400 Mb/s in the case of Samza. This amount is high compared to Spark as its bandwidth usage did not exceed 220 KB/s. This is due to the reduced frequency of serialization and migration operations between the cluster nodes, as Spark processes a group of messages at each operation. Consequently, the amount of exchanged data is reduced, while Storm, Samza and Flink are designed for the stream processing.

Conclusion

With the increasing amount of data generated by billions of devices over the world, stream processing becomes a key requirement of big data frameworks. The main goal of the present work is to study and experimentally evaluate the most popular frameworks for large-scale stream data processing. Spark, Storm, Flink and Samza were presented and categorized according to their main features. We also evaluated the performance of the presented frameworks in terms of resource consumption. We mention that this work is a part of our previously published paper [START_REF] Inoubli | An experimental survey on big data frameworks[END_REF]. In this work, we focus on the evaluation of streaming frameworks for Big Data. We mainly added a categorization of the studied frameworks based on specific features of stream processing systems. In the future, we will address the velocity of data processing by conducting more experiments on the frequency and the size of incoming events data.

Figure 1 .

 1 Figure 1. Impact of the window time on the number of processed events (100 KB per message)

Figure 2 .

 2 Figure 2. Impact of the window time on the number of processed events (500 KB per message)

Figure 6 .

 6 Figure 4. RAM consumption

Table 1 . Comparison of popular stream processing frameworks

 1

			Spark		Storm		Flink	Samza
	Data format		DStream		Tuples		DataStream	Message
	Data sources		HDFS,	DBMS,	Spoots		HDFS,	kafka
			and Kafka				DBMS, and
							Kafka
	Programming	Transformation	Bolts		Actions	Mapreduce
	model		and action				functions	Job
							(map,groupby,..)
	Programming	Java, Scala and	Java		Java	java
	languages		Python
	Cluster manager Hadoop YARN,	Zookeeper	Hadoop	YARN
			Apache Mesos			YARN,
							Apache
							Mesos
	Latency		Few seconds	Sub-second	Sub-second	Sub-second
	Messaging		Exactly once	At least once Exactly once Exactly once
	Machine learning	SparkMLLIB	Compatible	FlinkML	Compatible
	compatibility				with		with
					SAMOA	SAMOA
					API		API
	Elasticity		Yes		Yes		No	No
	Sliding	win-	time based		time based	time based	time based
	dows/Windowing			and	count	and	count
					based		based
	Auto-		On demand	Pipelined	Pipelined	On demand
	parallelization			processing	processing
	Streaming query SparkSQL		No		No	Yes (Samza-
							SQL API)
	Data Partitioning Yes		No		No	Yes
	API		Declaratif		Copositionnel Declartaif	Copositionnel
	Data transport	RPC		RPC		RPC	Kafka

https://galactica.isima.fr

Acknowledgements

This research was partially supported by the General Direction of Scientific Research in Tunisia (DGRST).


Both of which were found to be linked with adherence to CB (Swami et al., 2014; Marchlewska et al., 2017) Limitations: only one type of CB measure, self-reported outcome, no proper laboratory conditions, no replication study among general population samples.

Perspectives: two pre-registered replication studies among the general population with both absurdist text/painting primes and a measure of education level as a moderator.

Results

were meta-analyzed. A linear mixed-model was computed with the following equation: CB ~1 + (1 | Study) + (1 | Gender) + Age + Education + Type + Threat + Education*Threat + Type*Threat. (AIC = 1973.9, r² marginal = .16, r² conditional = .21).

Interaction effect between Education and Threat, F (2, 909) = 5.11; p = .006 with a main, positive effect of threat found only among the general population sample t(909) = -2.32, p = .021, d = .30.

Florent Varet 13 , Jaïs Troian 12 , Alexis Akinyemi 14 & Éric Bonetto 1 1 LPS, Aix-Marseille Univ., 13100 Aix-en-Provence, France. 2 Centre PsyClé, Aix-Marseille Univ., 13100 Aix-en-Provence, France.

3 IFSTTAR-TS2-LMA, 13300, Salon-de-Provence, France. 4 LAPPS, Univ. Paris Nanterre, UPL, 92001, Nanterre, France.

We conducted conceptual replications of Proulx, Heine & Vohs (2010, Study 2). The Magritte Effect :

Results

No straightforward effect of meaning threat was found across studies. It seems that education level plays a moderating role upon meaning-threat regulation through adherence to CB.

Figure 2 .Figure 1 .

 21 Figure 2. Priming stimuli from study 5. Left = control; Right = Threat

Figure 3 .

 3 Figure 3. Mean GCBS scores across studies as a function of sample education level and threat conditions. Education: 0 = General population, 1 =WEIRD, 2 = STEM workers. Threat: 0 = Control, 1 = Meaning-threat. * p < .05.

  This might be due to psychological differences between WEIRD and non-WEIRD populations (see Heinrich, Heine & Norezayan, 2010) regarding:  Cognitive abilities (e.g. analytical reasoning)  Epistemic motivations (e.g. need for closure) Introduction Hypothesis Discussion Note. Number between brackets represent SDs. * p < .05, **p < .01.

The Magritte Effect: Adherence to Conspiracy Beliefs as Fluid Compensation after a Meaning-Threat ?

	hal-01835514
	Experimental design	Measures
	1) Prime,	CB measure: 'General
	2) PANAS,	Conspiracist Beliefs' scale'
	3) Distractor Task,	(GCBS; 15 items; 5-points likert;
	4) CB measure.	Brotherton, French, & Pickering,
		2013)

Florent Varet, Jaïs Troian, Alexis Akinyemi, Eric Bonetto To cite this version: Florent Varet, Jaïs Troian, Alexis Akinyemi, Eric Bonetto. The Magritte Effect: Adherence to Conspiracy Beliefs as Fluid Compensation after a Meaning-Threat ?. Society for Personality and Social Psychology Annual Convention (SPSP 2018), Mar 2018, Atlanta, GA, United States. , SPSP 2018, Society for Personality and Social Psychology Annual Convention, 2018, 10.13140/RG.2.2.32942.41281.

Table 1 .

 1 Sample characteristics, methodology and effect size of differences in GCBS scores based on t-test comparisons across studies (N = 925)

	Adherence to Conspiracy Beliefs as Fluid Compensation
	after a Meaning-Threat ?

However, no research has yet investigated the effects of basic meaning threats upon adherence to CB.


Keywords: Syntaxe, sémantique, surdité, langues sourdes, langue orale Summary Syntax, semantics, deafness, Deaf Languages, oral speech

Dans les années 1990, des études en syntaxe et sémantique chez des enfants sourds profonds dont les seuils auditifs avec prothèse se situaient en dehors de la zone conversationnelle ont permis de poser l'hypothèse des langues sourdes. Les prothèses actuelles et les implants cochléaires apportent désormais de meilleurs gains auditifs. Il est donc nécessaire d'établir si l'hypothèse des langues sourdes est toujours valable. Les caractéristiques syntaxiques et sémantiques de données orales recueillies auprès de 6 enfants et adolescents francophones et de 6 enfants et adolescents anglophones sourds profonds oralistes ayant au moins 7 ans d'utilisation de leur implant ont donc été analysées et comparées à des données similaires recueillies auprès de 4 enfants et adolescents francophones et de 4 enfants et adolescents anglophones sourds profonds oralistes. Certains schémas des langues sourdes restent présents et de nouveaux aspects linguistiques émergent, tels que les commentaires métalinguistiques, les emplois métaphoriques, l'humour et les énoncés complexes. Le maintien de schémas propres aux langues sourdes pourrait s'expliquer par le déficit de perception auditive des premiers mois de vie qui pourrait entraîner le développement de représentations cognitives spécifiques chez les sourds profonds, en particulier pour l'espace et le temps, et ce en dépit d'un apport linguistique ultérieur important en quantité et en variété.

Introduction

In the field of deaf studies, Charrow's hypothesis on Deaf English (1974[START_REF] Charrow | A psycholinguistic analysis of Deaf English[END_REF] initiated a stimulating new approach to syntactic and semantic analyses of the profoundly deaf subjects' productions. Indeed, instead of considering that the deaf make errors in reference to Standard English, Charrow suggested that they actually use "a variety of non-Standard English" with rules of its own: Deaf English. Charrow's hypothesis was extended as further research evidenced the rules of "Deaf writing" [START_REF] Lacerte | La langue des signes québécoise (LSQ) et le français : difficultés à l'écrit chez la personne sourde[END_REF], of "Deaf French" [START_REF] Dubuisson | L'enseignement de la langue maternelle aux déficients auditifs[END_REF] from written and spoken data, and more generally of "Deaf Languages" (Vincent- Durroux, 1990Durroux, & 1992) ) from the comparative study of spoken data in French and English. The subjects involved in these studies did not necessarily know sign languages. The surveys were undertaken at a time when the profoundly deaf benefited from hearing aids which did not bring aided thresholds into the range of conversation level across the speech frequencies, and profound deafness could therefore be considered as causing specific cognitive patterns with consequences on the productions of the deaf. Time and space are greatly implied in the patterns of Deaf Languages, which can be summarized in those terms: determiner, subject and tense are not necessarily repeated when these items would have been similar in subsequent utterances; many prepositions are missing (especially in the expression of time, space and type); spatial patterns are almost the only way to set up the discourse theme; determiners and subjects in nominal and verbal phrases respectively are greatly autonomous: the analysis of repetitions and spontaneous corrections confirms the loose structure of syntagms in Deaf Languages ; almost no complex sentences, no humor, no metaphor, no metalinguistic comments are observed.

Presently, aided thresholds may come within the range of conversation level across the speech frequencies with typical aided thresholds of 30 decibel (dB) thanks to hearing aids or implant systems in eligible subjects (Inscoe [START_REF] Ramirez | Expressive spoken language development in deaf children with cochlear implants who are beginning formal education. Deafness and Education International[END_REF]. In these conditions, the speech productions of the deaf can be expected to be close or similar to standard productions. Studies have been carried out on implanted subjects to evaluate benefits for patients in terms of perception and intelligibility (Miyamoto, Kirk, Svirsky & Sehgal, 1999), and to evaluate the influence of communication mode and duration of implant use on perception and intelligibility (O'Donoghue, 1999;[START_REF] Geers | Effects of communication mode on skills of long-term cochlear implant users[END_REF]. Other studies consider lexical progress (Ouellet, Le Normand & Cohen, 2001) or syntactic progress (Vieu et al. 1998). No research combining syntax and semantics across two languages has been carried out with implanted subjects. Yet, in the early months, as long as no hearing aid is provided, profound deafness may still affect the deaf subjects' perception of their environment, from the linguistic point of view, but also from the cognitive point of view, since the fundamental notions of time and space have been shown to be related and to be conceived mainly through the sense of hearing (Lafon, 1985;Vinter, 1991Vinter, & 2000)).

The purpose of this research is therefore to assess if profound deafness in present conditions still has the consequences previously described on language itself. Data from implanted Frenchspeaking and English-speaking deaf teenagers are considered in order to evaluate if the description in terms of Deaf Languages still applies.

The data

Oral data were gathered in 1988 1 and in 2006 from English-speaking and French-speaking subjects 1 The first set of data (1988) was collected for the author's doctoral dissertation (Université de Sherbrooke, Québec, Canada), and was supported by a grant from the Entraide Universitaire Mondiale du Canada from 1987 to 1990. The author wishes to thank the children and teenagers who participated in the research, as well as their with pre-lingual deafness. They did not have sign languages in their environment. The 1988 subjects had classical hearing-aids which did not bring aided thresholds into the range of conversation level across the speech frequencies. The 2006 subjects had been implanted and had typical aided thresholds through the implant system of 30 dB across the speech frequencies and a profound loss in the other ear as they had been unilaterally implanted; they all had at least 7 years of implant use. The number and age of the subjects are summarized in Table 1.

In the 1988 study, the age of the subjects was determined following the results of Bochner & Albertini (1988) on the absence of significant progress after pre-adolescent years. In the 2006 study, the reported benefits of implants were taken into account: more subjects were recorded, as well as a sub-group of younger subjects. A control subject was recorded in each language.

The same protocol (Vincent-Durroux, 1990& 1992) was used to collect the two sets of data. The instructions were given in the oral and written modes. The subjects knew they were being recorded with an audiotape. The tasks were aimed at the production of various types of speech.

Descriptive speech was elicited through the descriptions of a picture and of the subject's home; narrative speech was elicited thanks to a sequence of pictures and through the report of a birthday party; argumentative speech was obtained as the subject reacted to an interdiction.

The data were transcribed according to Level 2 of the Network of European Reference Corpora (NERC), thus using orthographic representations and indicating turns of speech and a few nonverbal elements such as laughter. The transcriptions were divided into Communication Units or C-Units (Loban, 1976, p.105). The quantitative description of the data is presented in Table 2.

Results

parents and speech therapists.

Remaining patterns of Deaf English

Remaining patterns of Deaf Languages still are to be found in the 2006 data, along the same lines as in the earlier data (Vincent-Durroux, 1990& 1992); they involve tenses, determiners and prepositions, and can be observed equally in the French corpus and the English corpus.

Tenses

In Deaf Languages, the past tense which appears at the beginning of the sentence is not necessarily maintained in the rest of it. It still is the case in the 2006 data (in italics, verbs with no past tense marker):

(1) the children seemed quite happy and seem to enjoy this little trip with the frog seeing all these animals in different colours [LS138]2 (2) and there was a robot who is standing on the shelf [AX97]

(3) and it was very hot because it is in June 19 th [AM85] (4) il y avait le petit chat qui dort sur le lit [SM32] (5) et après quand il était dehors il y a il y a des il y a des plein de jouets [SM79]

The same pattern is also to be found in series of speech units in the 2006 data, especially in narrative discourse, as shown by the following examples:

(6) we went to Lake Districts which is up in North and I had a really good time but it was very cold hum (...) we were in groups with our teacher and we get to do different activities a day and we do like evening activities [LS69-75] (7) et ils ont découvert une vache verte qui lisait le journal un cheval qui dessine des carottes un chien qui dessine des petits bonhommes des formes des formes un garçon qui comprenait rien une poule bleue un canard à rayures gris blanc une autre poule bleue une vache qui est à l'extérieur de la ferme un mouton rose qui joue à à saute-mouton avec le chat une poule qui fait un un gâteau avec une fermière [AG38]

Determiners

In Deaf Languages, the repetition of the determiner is almost systematically avoided when unchanged, especially in lists such as:

(8) one person saw the boy and girl and woman [dd146] (9) there's a clerk and shelf [sb72] (10) pour mettre des serviettes débarbouillettes [jd95] (11) y'a des machines pour hacher la viande, puis aussi machine pour presser des oranges, puis le grille-pain grille-pain, puis cafetière pour chauffer [na61] The same pattern still is to be found in the 2006 data, but only in a few occurrences, such as:

(12) and when the pink hippo and cat were playing a dance the e-the green elephant and cow and pink horse and and red lion were talking together [AM106] (13) y'a deux chambres mon bureau et bureau d'ordinateur [CT23] Another specific aspect in the use of determiners by deaf subjects was described by [START_REF] Ivemey | The written language of young English deaf children[END_REF], and confirmed by the 1988 data: the determiner is more often omitted with a noun in object position whereas it is usually there in subject or thematic positions (Vincent- Durroux, 1990Durroux, & 1992)). This is also to be found in the 2006 survey: in the English data, the determiner is omitted 25 times but only once in subject position where it belongs to a list: The analysis of the use of prepositions by deaf subjects is of great interest since prepositions are based on spatial relationships for a great number of them (Groussier, 1997, p. 222). The use of prepositions is a good indicator of the subjects' modes of representation of space, but also of their representations of time and type, which are both cognitively related to space. From that point of view, the study of prepositions in our data can be considered as complementary to the analysis of tenses (2.1.1) and determiners (2.1.2.), which deal more specifically with time and space, respectively.

Prepositions may be omitted in Deaf English, especially when they would have referred to space, All 2006 subjects use modals in English, with several occurrences each, whereas few occurrences of modals were found in the 1988 data.

There is also the reinforcement of narrative patterns in narrative tasks, with the building up of a narrative frame and the resorting to imaginary explanations, with for example fictional names given to the characters in the pictures:

(67) once upon a time a a boy and a girl woke up in a bedroom and they went on the computer straight away when they turned the computer on a great big pink frog came out [BL97-99] (68) Atrick and Tedjin were playing on the computer they didn't notice that the toy robot has grown up bigger when they played on the computer this fr-frog jumped out of the computer in the paint the frog took them into the computer of the land of animals they saw all sorts of strange animals [AM93-96] (69) dans la chambre des deux petits gar-des petits enfants Mimi et Arnaud jouent sagement dans sur leur ordinateur ils jouent à une grenouille qui saute mais les parents aimeraient bien que ils rangent leur chambre ils voient la grenouille sauter sauter sauter et d'un coup la grenouille sort de l'ordinateur [CT100-14] (70) alors Vincent et sa soeur sont sortis de leur lit un bon matin vers neuf heures pour pour jouer un peu s-pour jouer un petit peu sur l'ordinateur ils se mettent ils se mettent ils ouvrent le jeu de zoo safari zoo pour créer un nouveau univers avec des animaux des fermes et tout ça euh ils y créaient des animaux fantastiques de couleurs de rouge bleu vert tout ça et pouf tout à coup une grenouille rose sort de l'écran et les et les entraîne dans l'ordinateur ils se retrouvent dans le monde dans le monde fantastique disons qu'ils ont créé Finally, when the subjects had to describe their home, the protocol allowed the use of drawing.

The subjects never resorted to drawing in 2006 whereas it was systematic in 1988. This may be due to the fact that the 2006 subjects feel more confident in their language skills.

Discussion

The results presented here suggest that the Deaf Languages hypothesis cannot be discarded: it still applies similarly to English and French, showing that profound deafness may still affect the faculty of language. Yet emerging elements exhibit the symbolic function of language and hint at greater linguistic mastery. The results can be discussed in terms of (a) cognitive patterns and (b) possible influence of the greater amount and variety of input.

Cognitive patterns

The sense of hearing is central in the perception of time, successiveness and space. The results

show that there is a specific way of using verb tenses in sequences by the deaf. This typical pattern of Deaf Languages is also described in sign languages (Lacerte, 1993, p.147). These facts may hint at specific cognitive patterns developed by the deaf.

The same conclusion can be drawn from the point of view of space patterns, when comparing the results on prepositions with the description of Sign Languages. As already mentioned, time and space are related to each other and to auditory perception. Type is also related to space, as types and sub-types are referred to in terms of spatial hierarchy (sub-types) and in terms of inclusion.

Time, space, and therefore type are likely to be dealt with in specific ways by all deaf subjects. The These results hint at specific cognitive patterns developed by the deaf, whatever their prosthetic device and auditory gains. This may be due to the lack of perception in the earlier months when they do not have hearing devices. Even if our study bears on profound deafness, it is interesting to put our results in perspective with studies on subjects with less severe hearing impairment. For example, [START_REF] Delage | Language development and mild-to-moderate hearing loss: Does language normalize with age?[END_REF] show that even with mild-to-moderate hearing loss, language does not seem to normalize at adolescence.

Influence of a greater amount and variety of input

On the other hand, the results show emerging patterns that hint at linguistic mastery: in these patterns, the language is obviously used as a symbolic mode of representation, rather than as a code; this may be related to the fact that more linguistic input is available for the deaf. The situations of communication for the deaf with aided thresholds within the range of conversation are no longer restricted, neither in quantity nor in variety. The deaf no longer have to rely almost only on specific situations, such as speech therapy, to improve their language. They can also rely on natural everyday situations with their peers, which involves playing with the language; when prosthetic gains were really small, the mother tongue had to be taught, a situation which led to a stilted use of language. Indeed, contrary to their peers twenty years ago who answered "walk on the pavement" when asked what they were going to do after school (H. Viau, personal communication), implanted deaf teenagers now show their ability to interpret "after" in a nonfigurative way when they provide that kind of answer:

(73) la piscine, le golf, le vélo [CT140]

Conclusion

It may be difficult to modify the cognitive patterns developed by the deaf, especially if they date back to the earlier months. Yet the greater amount and variety of linguistic input that the deaf may now benefit from is an asset to further elaborate their linguistic competence with the help of the people in their environment; in this case, it is necessary for the latter to be are aware of the patterns of Deaf Languages since these features may not be easily noticed in the present speech of the deaf as they do not appear in great quantity. The emerging aspects described here (e.g. metalinguistic comments, metaphoric use, humor, complex sentences) may also be developed by the deaf with the help of their environment.

(

  14) well the the orange and the orange horse and orange sheep were dancing together [AM108] In the French data, there are 27 occurrences but only 6 in subject position, although not necessarily in lists, as shown by the following examples: (15) euh les zèbres et les girafes les hippopotames les crocodiles des des des éléphants ours blancs euh ils dansent [MR85] (16) euh hippopotame il danse avec le chat et aussi le zèbre avec un mouton [MR93] The other cases occur in object position, such as: (17) hum it's got school nearby [LS9] (18) and a cow was reading newspaper [EB103] (19) then I saw wee tiny monkey on a monkey [BL90] (20) and then I saw baby ostrich [BL91] (21) we had birthday cake [SR31] (22) il donne nourriture au singe et au grenouille [SM84] (23) euh pour faire sport dans la maison [CM36] 2.1.3. Prepositions

  use of prepositions has been described in detail by de Vriendt & Rasquinet for the Belgian Sign Language (BSL). The missing prepositions in the 1988 & 2006 data would almost never have been signed in BSL (Vincent-Durroux, 2008), with proportions unchanged between the two sets of data: out of the 38 cases in the 1988 data, 35 would not have been signed in BSL and two of them would have been signed erratically, and out of the 17 cases in the 2006 data, 15 would not have been signed in BSL and two of them would have been signed erratically.

  time, or type. Prepositions are omitted in the 2006 data when referring to time (examples 24-25),

	Languages emerge, such as meta-linguistic comments, metaphoric use, humor, and complex (66) je pourrais ramener des tas et des tas de photos (…) et puis des repas italiens
	[AG55]
	sentences.
	2.2.1. Meta-linguistic comments
	Meta-linguistic comments are based on the capacity of the subject to consider linguistic
	productions as referents, on the choice of which comments can be made. They are found in the
	2006 data when the utterer is (a) trying to be more precise or explicit (examples 33-34); (b)
	unsatisfied with previous productions (examples 35-36); (c) showing concern for the acceptability
	of what has been said (examples 37-38); (d) commenting on the co-utterer's discourse, especially
	to space (examples 26-29), and to type (examples 30-32). For each example, the most likely with the BE -ING form (example 39); (e) taking up the former predicative relation with DO, an
	preposition appears between brackets: image of that predicative relation (examples 40-42):
	(24) hum last birthday party I had camping [AX48]
	hum [for my] last birthday party I had camping
	(25) et mon anniversaire c'est la fin du mois [TM103]
	et mon anniversaire c'est [à] la fin du mois
	(26) it is left side [sb13]
	it is [on the] left side
	(27) and the garage [ms57]
	and [in] the garage
	(28) ils rentrent leur lit [MR98]	understand what
	ils rentrent [dans] leur lit it means]
	(29) tu vas un peu droite [MR5] (40) did we have a birthday cake I think we did [AM87-88]
	tu vas un peu [à] droite (41) [interviewer: I don't think you have enough] [i.e. money]
	I do have enough, honestly [BL139]
	(30) we had pizza take-away [SR32] (42) we don't have a shower or we have a s-we do have a shower but we want to have a
	we had pizza [to] take-away separate shower from the bath [EB20-22]
	(31) it's like a game Cluedo [EB55]
	it's like a game [of] Cluedo 2.2.2. Metaphoric use
	(32) c'est le bowling Montpellier [SM49]
	c'est le bowling [de] Montpellier Metaphors are based on the capacity of the subject to deal with abstraction, since both the referent
	2.2. Emerging linguistic aspects and the comparative markers are absent (V. Rey, personal communication); when we say "John is
	It is remarkable that in the 2006 survey, some linguistic aspects which are absent from Deaf a lion", there is neither lion in the situation nor comparative form in the sentence. The following

(33) in the living-room no I mean a dining-room [AX23] (34) il y a comme un meuble où dessus il y deux médicaments dans un plateau sur un plateau je veux dire [TM70] (35) I can't really explain it [BL6] (36) un petit garçon qui est sous le lit enfin disons sous la couette [CM50] (37) the monkey fuck our back window thing and they jumped on top and we used the sweepers for weapons to get them off oh come on [BL85-88] (38) on voit que le cheval le lion qui rigolent bien qui rient bien [CM141] (39) I understand what you're saying [LS165] [ = when you say (…) I

Initials in capital letters refer to the 2006 subjects; initials in small letters refer to the 1988 subjects.

Humor often involves criticism on situations or speech productions and therefore some distance is necessary. Such distance implies the use of language as an abstract representation. A tinge of humor is found in the 2006 data with:

(53) I was hoping there'd be a big present on the table which was a big present hum I got an i-pod speakers [LS89-90] (54) en avion c'est quoi le prix Internet prix avion pour l'Italie ouai 875 euros euh ouai bon on verra bien hein [GP113-119] (55) il y a pas de tour à exploser là-bas t'inquiète ah non ouai il y a Pise In example (53), there is a play on the word big: subject LS was away from home on her birthday and expected to find a big present to make up for her absence. As her parents are listening to her, she acknowledges that she may have been disappointed by the size of the present but not by its value. In example (54) subject GP mimics the search of a price on the Internet in order to convince his mother to let him go to Italy. Unfortunately he gives a very expensive price and acknowledges his mistake by saying euh ouai and by changing his plans by saying on verra bien hein. In example (55), humor is built on the ridiculous comparison between the Twin Towers and the Tower of Pisa.

Complex sentences

The specificity of sentences with subordinate clauses, or complex sentences, is that they include a marker (that, which, or que, qui, dont …) which represents the element(s) that would have appeared in both clauses had they been independent. For example, in:

(56) we went to Lake Districts which is up in North [LS69] which represents Lake Districts in the relative clause. As such, it is an abstract image; its use in discourse can be considered as a sign of linguistic mastery (Dubuisson & Emirkanian, 1981-82).

Whereas there were very few complex sentences in the earlier data, the 2006 data show a great number of standard complex sentences, such as:

(57) we have a store-room quite a s-small room where we put put our books and stuff  we don't need [EB16] (58) il y a le calendrier qui est caché par les lumières [SM42] In the 2006 data, only 8 utterances in English and 3 utterances in French can be considered as illformed, such as: Vincent-Durroux L., & Dubuisson C. (1989). Quantité, qualité et variété de la production linguistique chez de jeunes déficients auditifs profonds. Revue de l'Association Québécoise de Linguistique Théorique et Appliquée, 8, 3-4, 347-359. Vincent-Durroux L. (1990). Problèmes d'acquisition du langage par les adolescents déficients auditifs profonds oralistes, en français et en anglais. Unpublished doctoral dissertation, Université de Sherbrooke, Sherbrooke, Canada. Vincent-Durroux L., & Viau H. (1990). Quelques mesures du comportement de jeunes déficients auditifs oralistes. Rééducation Orthophonique, 28, 162, 147-158. Vincent-Durroux L. (1990). La langue orale des sourds profonds oralistes. Etude comparative


K R M Adeline Ab

X Briottet

X Ceamanos

T Dartigalongue

J.-P Gastellu-Etchegorry

ICARE-VEG: A 3D PHYSICS-BASED ATMOSPHERIC CORRECTION METHOD 1 FOR TREE SHADOWS IN URBAN AREAS 2 3

Keywords: atmospheric correction, 14 radiative transfer, 15 hyperspectral, 16

Many applications dedicated to urban areas (e.g. land cover mapping and biophysical 23

Infrared Region (V-NIR: 0.4-1.0µm) with hyperspectral airborne data at 0.8m resolution on 43 three ground materials types, grass, asphalt and water. Results show that (i) ICARE-VEG 44 improves the mean absolute error in retrieved reflectances compared to ICARE in tree 45 shadows by a multiplicative factor ranging between 4.2 and 18.8, and (ii) reduces the spectral 46 bias in reflectance from visible to NIR (due to light transmission through the tree crown) by a 47 multiplicative factor between 1.0 and 1.4 in terms of spectral angle mapper performance. 48 ICARE-VEG opens the way to a complete interpretation of remote sensing images (sunlit, 49 shade cast by both buildings and trees) and the derivation of scientific value-added products 50 over all the entire image without the preliminary step of shadow masking. 51

52

. Although sufficient 70 for coarse classification of urban material types, it is unsatisfactory for the intra-class 71 variability quantification and the retrieval of physico-chemical properties of surface materials, 72 which requires the accurate spectral reflectance of each material. The second category of de-73 shadowing methods uses atmospheric correction codes to convert at-sensor radiance into 74 reflectance units. They are physics-based methods which correct the radiometrical bias 75 occurring in shaded pixels by considering atmospheric conditions and sometimes the scene 76 3D topography (e.g. Digital Surface Model -DSM or a vector model). To our knowledge, 77 only a few atmospheric correction codes are adapted to urban environments: the semi-78 empirical model of Chen et al., 2013, ICARE (Inversion Code for urban Areas Reflectance 79 Extraction, Lachérade et al., 2008) and ATCOR-4 (Atmospheric/topographic correction for 80 airborne imagery, Richter and Schläpfer, 2002). However, only the two last codes can achieve 81 an exact calculation of the 3D radiative terms to retrieve surface reflectance. 82

properties estimation) using high spatial resolution remote sensing images require the use of 24 3D atmospheric correction methods, able to model complex light interactions within urban 25 topography such as buildings and trees. Currently, one major drawback of these methods is 26 their lack in modelling the radiative signature of trees (e.g. the light transmitted through the 27 tree crown), which leads to an over-estimation of ground reflectance at tree shadows. No 28 study has been carried out to take into account both optical and structural properties of trees in 29 the correction provided by these methods. The aim of this work is to improve an existing 3D 30 atmospheric correction method, ICARE (Inversion Code for urban Areas Reflectance

Introduction 53 54

The potential of hyperspectral remote sensing imagery with high spatial resolution in 55 the reflective domain 0.4-2.5µm has long been studied to increase the characterization of 56 surface materials for ecosystem monitoring [START_REF] Wulder | High spatial resolution remotely 993 sensed data for ecosystem characterization[END_REF], and particularly for urban 57 environments [START_REF] Jensen | Remote sensing of urban/suburban infrastructure and 898 socioeconomic attributes[END_REF][START_REF] Small | Spectral dimensionality and scale of urban radiance[END_REF][START_REF] Puissant | Les images à très haute résolution spatiale: une source 938 d'information géographique en milieu urbain ? état des lieux et perspectives[END_REF], such as for 58 vegetation biodiversity assessment [START_REF] Alonzo | Urban tree species mapping using hyperspectral 827 and lidar data fusion[END_REF], road traffic monitoring (Rosenbaum 59 et al., 2010) and land cover classification [START_REF] Roessner | Automated differentiation of urban 949 surfaces based on airborne hyperspectral imagery[END_REF]. For urban applications, one 60 major limitation comes from the complex topography of urban landscapes combined with low 61 solar elevation, which induces many shaded pixels in aerial and satellite images at high spatial 62 resolution. In image processing, shaded region areas are often neglected, with shadows 63 classified as a material class [START_REF] Dell'acqua | Urban land cover mapping using hyperspectral 868 and multispectral vhr sensors: spatial versus spectral resolution[END_REF][START_REF] Yuan | Mapping impervious surface area using high resolution imagery: 996 A comparison of object-based and per pixel classification[END_REF] or used to 64 retrieve the dimensions of nearby buildings [START_REF] Liow | Use of shadows for extracting buildings in aerial 914 images[END_REF]. 65 ATCOR-4 is currently the most used atmospheric correction code by the scientific 83 community that has been tested for a large panel of hyperspectral airborne sensors over the 84 spectral range 0.4-2.5µm. For a flat terrain composed of lambertian materials (i.e. 85 corresponding to an isotropic light reflection), ATCOR-4 performance achieves an error in 86 the retrieved reflectance of 0.02 and 0.04 for an initial reflectance of less than 0.10 and 0.40, 87 respectively (Rese ATCOR-4 User Guide; [START_REF] Richter | Geo-atmospheric processing of airborne imaging 945 spectrometry data.part 2: Atmospheric/topographic correction[END_REF]. For a rugged terrain, 88 ATCOR-4 performance is not quantified since it strongly depends on the DSM accuracy and 89 the registration between the image and the DSM (Rese ATCOR-4 User Guide ;Schläpfer et 90 al., 2000). An improved version of ATCOR named BREFCOR is able to correct the effects of 91 bidirectional reflectance distribution function of materials [START_REF] Schläpfer | Operational BRDF Effects Correction for 974 Wide-Field-of-View Optical Scanners (BREFCOR)[END_REF]. ICARE is a 92 3D atmospheric correction method dedicated to urban areas with lambertian materials. It was 93 initially developed to process airborne multispectral images acquired by the PELICAN image 94 system (Duffaut and Deliot, 2005) with spectral bandwidth of 30nm at a spatial resolution of 95 20cm, and with limited spatial extent. Its performance showed a maximum peak to peak 96 accuracy of 0.04 in the retrieved reflectance for eight spectral bands from 420 to 917nm and 97 for pixels located in shadows cast by buildings [START_REF] Lachérade | Icare: A 909 physically-based model to correct atmospheric and geometric effects from high spatial and 910 spectral remote sensing images over 3d urban areas[END_REF]. Currently, ICARE is 98 being improved to process hyperspectral images. The improved method named ICARE-HS 4 (ICARE using HyperSpectral imagery) was tested with airborne HySpex hyperspectral data 100 with 160 spectral bands in the Visible-Near Infrared (V-NIR: 0.4-1.0µm) at a spatial 101 resolution of 80cm [START_REF] Ceamanos | Using 3D information 844 for atmospheric correction of airborne hyperspectral images of urban areas[END_REF]. The performance of this new ICARE version was 102 not quantitatively validated. 103 Atmospheric correction codes succeed in modeling opaque objects governed by 104 absorption and reflection processes (e.g. buildings). However, the main issue lies in the lack 105 of modeling of transmittance processes resulting from semi-transparent and transparent 106 surfaces (e.g. trees and windows). For trees, ATCOR-4 and ICARE neglect the fraction of the 107 incident solar radiation that is transmitted through tree crown, thus generating a bias in the 108 retrieved reflectance in tree shadows [START_REF] Adeline | Material reflectance retrieval in shadow due 820 to urban vegetation from 3D lidar data and hyperspectral airborne imagery[END_REF][START_REF] Schläpfer | Correction Of Shadowing In Imaging 970 Spectroscopy Data By Quantification Of The Proportion Of Diffuse Illumination[END_REF]Damm et al, 109 2015). Actually, the under-estimation of total irradiance in the shade produces an over-110 estimation of retrieved reflectance, which is higher in the NIR bands than in the visible with a 111 transition close to the red-edge [START_REF] Adeline | Material reflectance retrieval in shadow due 820 to urban vegetation from 3D lidar data and hyperspectral airborne imagery[END_REF][START_REF] Damm | Impact of varying irradiance on vegetation indices and chlorophyll fluorescence derived 862 from spectroscopy data[END_REF]. With ICARE, 112 [START_REF] Adeline | Material reflectance retrieval in shadow due 820 to urban vegetation from 3D lidar data and hyperspectral airborne imagery[END_REF] showed that the retrieved reflectance in tree shadows compared to their 113 counterpart in sunlit areas for the same material type (asphalt and grass) gave mean root mean 114 square error values up to 0.09. With ATCOR-4, [START_REF] Damm | Impact of varying irradiance on vegetation indices and chlorophyll fluorescence derived 862 from spectroscopy data[END_REF] showed that an inaccurate 115 estimation of irradiance can lead to a difference in tree shadows in NDVI values (Normalized 116 Difference Vegetation Index; Rouse, 1974) up to 13% and in PRI values (Photochemical 117 Reflectance Index; [START_REF] Gamon | A narrow-waveband spectral index that tracks diurnal 884 changes in photosynthetic efficiency[END_REF] up to 32% for some test scenarios over grass. One of 118 the required steps to solve this issue is to carry out a sensitivity analysis in order to know 119 which tree canopy parameters, both spectral (e.g. optical properties of leaves and wood) and 120 structural (e.g. leaf area index, leaf angular distribution, clumping, tree dimensions) have the 121 most impact on light transmission through the tree crown. To our best knowledge, such an 122 analysis has not been performed yet for radiative transfer budget estimation. 123

The objective of this work is to improve the existing 3D atmospheric correction code 124 ICARE to cope with the presence of trees. The new version is further named ICARE-VEG 125 (ICARE with VEGetation). It is based on the building of a physics-based correction factor to 126 apply to ICARE's outputs in order to provide a better estimation of surface reflectance in tree 127 shadows. The challenge is to define a general correction baseline adapted to any urban trees 128 and requiring a small number of relevant variables to study. To this end, ICARE-VEG relies 129 on the decoupling between a spectral reference correction based on a "reference tree model" 130 with fixed geometrical dimensions, and a spatial correction accounting for the real dimensions 131 of the tree processed in the image. The spectral reference correction is built from the results of 132 a sensitivity analysis based on a design of experiments to derive the most important factors 133 contributing to light transmission through the tree crown. The spatial correction factor is 134 computed from the tree dimensions and the location of the pixel within the tree shadow. At 135 last, ICARE-VEG only considers deciduous trees with green healthy leaves and surfaces with 136 a lambertian spectral behaviour. 137

This paper is organized as follows. Section 2 introduces the physical principles of 138 radiative transfer modeling for ICARE-VEG. Section 3 describes each step implemented in 139 ICARE-VEG. Section 4 presents the airborne and field data used for validation. Finally, the 140 performance of ICARE-VEG for surface reflectance retrieval in tree shadows is presented in 141 section 5. Conclusion and perspectives are given in section 6. 142 143

Physical modeling for ICARE-VEG 144 145

For a given wavelength λ in the optical domain 0.4-2.5μm, the surface reflectance ρ of 146 a target is derived from the direct upwelling radiance coming from the target and 147 reaching a given pixel of the sensor detector matrix, the total downwelling irradiance 148 received at ground, and the upwelling direct atmospheric transmission (Fig. 1; Lachérade 149 et al., 2008) , is the sum of the direct radiance, , the environment radiance due to the 162 atmospheric light scattering, , and the atmospheric radiance (the so-called path radiance), 163 (Fig. 1). Also, the total irradiance, , is the sum of the direct solar irradiance, , the 164 atmospheric diffuse solar irradiance, , the irradiance due to scattering by the surrounding 165 environment,

, and the earth-atmosphere coupling irradiance, (Fig. 1). 166 167 ICARE (noted IC) considers that surfaces have lambertian reflectances and the 168 viewing direction is Nadir. The surface spectral bidirectional reflectance for any pixel P at the 169 wavelength is simply named . ICARE analytically determines the surface reflectance 170 for a pixel A in a sunlit region (Fig. 1a , must be considered in addition to (Fig. 1c). 182

The term can be split into , the light directly transmitted without interactions with 183 the tree elements, and , the light that is transmitted after at least one scattering with 184 crown elements, either leaves or woody stems (Fig. 1c). Consequently, Eq. 3 needs to be 185 modified for a pixel C in tree shadow with a more accurate estimation of total irradiance 186 The factor depends on the wavelength , and the solid angle under which the tree 199 crown that casts the shadow is seen from any pixel C in the shadow. The analytical 200 determination of is not straightforward due to both the spectral and spatial dependence of 201 the ratio . Here, the main assumption is that the spectral and spatial response of 202 can be linearly decorrelated. Thus, is decomposed as follows: 203 204 with (6) 205 206 is the mean spectral response of according to a "reference tree model" with 207 fixed geometric dimensions.

received
is further called the reference correction factor. It is 208 associated with a reference solid angle . is the solid angle at the location of the pixel 209 C for the real geometrical dimensions of the tree in the scene. 210 211

ICARE-VEG method implementation 212 213

The semi-automatic ICARE-VEG correction code is structured as depicted in Fig. 2. 214

The original ICARE code is executed as a preliminary step (section 3.1). Individual trees and 215 their associated shadows are then identified to perform a tree-specific local correction for each 216 pixel in tree shadow (sections 3.2 and 3.3). The physics-based correction factor (section 3.4) 217 is divided into the determination of the reference correction factor (section 3.4.1) and the 218 solid angles, and (section 3.4.2). is evaluated in 3 steps. They rely on a 219 "reference tree model" with fixed geometrical dimensions to study how is impacted by 220 tree crown biophysical and structural variables, and other external variables. For that purpose, 221 the DART 3D radiative transfer code is used to simulate light interactions within a tree crown 222 (Discrete Anisotropic Radiative Transfer;[START_REF] Gastellu-Etchegorry | Modeling radiative 887 transfer in heterogeneous 3-d vegetation canopies[END_REF]. The results are 223 stored in a look-up table and a sensitivity analysis aims at defining the major variables 224 required to assess (section 3.4.1.1). Then, these major variables are derived from the 225 processed image (section 3.4.1.2) and they are used to empirically compute thanks to 226 statistical multivariate strategies (section 3.4.1.3). At last, ICARE-VEG correction provides 227 an improved reflectance retrieval for the pixels in tree shadows, while pixels in the sun and in 228 the shadow of buildings are not updated from ICARE outputs (section 3.5). 229 [START_REF] Lachérade | Icare: A 909 physically-based model to correct atmospheric and geometric effects from high spatial and 910 spectral remote sensing images over 3d urban areas[END_REF] requires 3 inputs: an at-sensor image expressed in 237 spectral radiance unit, a DSM and the geometry conditions (e.g. flight altitude, sensor spatial 238 and spectral characteristics, sun and viewing angles) and the atmospheric conditions. 239 Atmospheric radiative components are computed with the radiative transfer code 6SV 240 [START_REF] Vermote | Second Simulation 985 of the Satellite Signal in the Solar Spectrum, 6S: An Overview[END_REF]. The output is an image of spectral surface reflectance. 241 2014) is used to delineate the tree 265 crowns. In short, the method detects local maxima in the DSM from the high vegetation mask, 266 attributes a tree label to each treetop, and then performs a gradient descent technique to give a 267 tree label to all pixels in the high vegetation mask. This step provides a tree label mask. 268

To avoid the detection of several treetops for the same tree, an adjacency condition 269 sets the minimum distance between two treetops. This distance, expressed in a number of 270 pixels, essentially depends on the image spatial resolution. The tree label mask is refined with 271 two other criteria. The first removes trees with very small crowns, using a minimum number 272 of pixels per tree label. The second one eliminates tree crowns that are partially in the shade 273 of other trees or buildings. For that, it uses a maximum percentage of shaded pixels for a tree 274 crown. 275 276

Tree shadow detection 277 278

The identification of tree shadows is twofold: detection of all the shadows in the image 279 and assignation of tree labels for tree shadows pixels (Fig. 4). thresholding following the first valley detection method of [START_REF] Nagao | Region extraction and shape analysis in aerial 921 photographs[END_REF]. This method 292 has shown good performance for high spatial resolution aerial images (Adeline et al, 2013a). 293

A morphological closing filter is applied in order to spatially homogenize the tree shadows 294 possibly containing many penumbra areas. 295

Second, the detection of tree shaded pixels is achieved by framing each individual tree 296 shadow with a rectangular box with vertices (Fig. 5a). The edge of 297 this box represents the tree crown diameter, which is the segment intersecting the treetop in 298 the direction perpendicular to the sun azimuth angle . The orientation of the adjacent edges 299 of the box, namely and , is driven by while their length is dependent on the 300 tree shadow length (Fig. 5a) following sun ray parallel projection to the ground (Rosskopf 301 et al., 2017). This length L is actually computed from the knowledge of the ground sampling 302 applied, consisting in gradually scanning the box area and looking for pixels that belong to the 314 global shadow mask but do not fall into the labeled pixels of the tree label mask. Each 315 13 detected tree shaded pixel is assigned to the corresponding tree label to build a tree shadow 316 label mask. 317

In case of overlapping tree shadows, the highest tree is assumed predominant over the 318 others. Also, a shaded region cannot be associated with more than one tree. And a refinement 319 step is applied to remove small tree shadows based on a criterion counting the number of 320 pixels belonging to each tree label. 321 322

Correction factor determination 323 324

The correction factor is the product between the reference correction factor 325 (section 3.4.1) and a ratio of viewing solid angles (section 3.4.2; Eq. 6). 326 327

Reference correction factor 328 329

A regression model is built using a design of experiments based on a "reference tree 330 model" for further empirical computation of . 331 332

Design of experiments with DART and sensitivity analysis 333 334

A simple scenario was considered in the form of an isolated tree on a flat ground, for 335 urban mid-latitude conditions and considering a viewing direction at Nadir (Fig. 6). Table 1 336 gives the DART input parameters that describe the scene and the "reference tree model" 337 [START_REF] Gastellu-Etchegorry | Modeling radiative 887 transfer in heterogeneous 3-d vegetation canopies[END_REF]. The latter has fixed arbitrary dimensions, an ellipsoid 338 crown, and a trunk outside and inside the crown with a cylindrical and conical shape, 339 respectively. The DART spatial discretization scheme was set to 0.4m (i.e. spatial resolution 340 of the output image). 341 In agreement with previous studies characterizing the canopy reflectance (Weiss et al., 351 2000;[START_REF] Combal | Retrieval of canopy biophysical variables from bidirectional 857 reflectance -using prior information to solve the ill-posed inverse problem[END_REF] or the tree crown transmittance [START_REF] Sampson | Influence of canopy architecture on light penetration in 963 lodgepole pine (Pinuscontorta var. latifolia) forests[END_REF], seven 352 variables of interest X are selected to study the variations of : tree Leaf Area Index that is 353 the product between Leaf Area Index of the scene and the vegetation cover of the scene (for 354 simplicity referred in this paper as LAI; [START_REF] Norman | Radiative transfer in an array of canopies[END_REF], Average Leaf Angle 355 (ALA) defined for an ellipsoidal angle distribution [START_REF] Campbell | Derivation of an angle density function for canopies with ellipsoidal leaf 841 angle distributions[END_REF], percentage of holes in 356 the tree crown (POROSITY) approximating somehow the clumping effect, Leaf Optical 357 Properties (LOP), ground reflectance (GROUND), sun zenith angle (SUN) and atmospheric 358 visibility (VISI). Each variable is tuned between 2 and 10 values according to its sensitivity. 359

The ground and trunk optical properties come from the DART spectral database while the leaf 360 optical properties come from the ANGERS03 spectral database [START_REF] Jacquemoud | ANGERS leaf optical properties 895 database[END_REF]. 361

The ground surface is assumed to be asphalt or grass (Fig. 7). Three representative urban tree 362 species were chosen: liquidambar "liquidambar styraciflua", for its mean leaf optical 363 properties, and oak "quercus palustris" and poplar "populus alba", for their extreme optical 364 properties (Fig. 7). 365 366 16 367 Fig. 7. Optical properties of scene components: two ground types (asphalt and grass) and 368 trunk (left), leaves for the "reference tree model" (right: reflectances are in solid lines and 369 transmittances are in dashed lines). 370 371 A full factorial design was carried out to study the impact of each independent variable 372 X, individually or in interactions with the others, on the variations of (Droesbeke et al., 373 1997). DART simulated a total of 3240 scenarios, corresponding to top-of-canopy 374 hyperspectral images with 110 spectral bands. It provided the radiative quantities required to 375 compute per ground pixel in tree shadow. Mean values of were stored in a look-up-376 table and used to perform a global sensitivity analysis to find out the major variables X' for 377 determining

. A variance analysis (ANOVA) with a linear relationship between and 378 the variables X was performed to compute a sensitivity index noted . This is the ratio "sum 379 of squares values accounting for the single and combined effects of the variables on the 380 variance of " over "total sum of square values" [START_REF] Monod | Working with Dynamic Crop Models -Chapter 3 917 39 Uncertainty and sensitivity analysis for crop models[END_REF]Olejnik and Algina, 381 2003). SUN and LAI are the major variables X' because they give the highest values of (cf. 382 Appendix A). SUN being usually known (e.g. from date, time and location), the issue is to 383 estimate the LAI, which is therefore discussed below. 384 385

Tree LAI estimation 386 387

Tree LAI can be estimated through the use of spectral vegetation indices from which 388 NDVI is the most used [START_REF] Colombo | Retrieval of leaf area index in 852 different vegetation types using high resolution satellite data[END_REF][START_REF] Jensen | Estimating Urban Leaf Area Index (LAI) of 901 Individual Trees with Hyperspectral Data[END_REF]). An empirical LAI-NDVI 389 relationship is built based on a Beer-Lambert exponential regression model with 3 coefficients 390 [START_REF] Baret | Potentials and limits of vegetation indices for lai and apar 830 assessment[END_REF] The training data is provided by the design of experiments. For each DART scenario 398 with a fixed LAI value, the NDVI is computed as the mean over a mask of 6×6 pixel grid 399 centred at the canopy treetop. Then for each scenario out of the total of 324 run with DART, 400 10 pairs of LAI and NDVI are available. However, the estimation of the coefficients of the 401 regression model in Eq.9 depends on the 6 remaining variables of X from the design of 402 experiments (ALA, POROSITY, LOP, GROUND, SUN, VISI). Except when SUN = 60° 403 (high solar incidence angle leading to odd fits), performance of the built regression models 404 gave coefficients of determination > 0.87 and root mean square errors < 0.37 in the 405 estimated LAI. 406 Then, regression models are applied in the NDVI image and the NDVI value for each 407 tree is computed as a mean over a 3×3 pixel grid centred at the treetop (grid size can be 408 chosen manually). In practice, due to the difficulty to have a priori knowledge about the 409 variable values (ALA, POROSITY, LOP, GROUND, SUN, VISI) for each tree, they are 410 arbitrarily fixed to their average values : ALA = 57° (close to the common spherical 411 distribution), POROSITY = 0% (uniform leaf spatial distribution), LOP = liquidambar, 412 GROUND = asphalt, SUN = 45° and VISI = 23km (good visibility). 413 414

Multivariate regression analysis 415 416

From the previously determined major variables X' (i.e. SUN and LAI), a multivariate 417 linear regression model is built to estimate the reference correction factor by using a 418 stepwise strategy in order to decrease the number of terms in the regression expression 419 [START_REF] Burnham | Multimodel inference understanding aic and bic in 838 model selection[END_REF]. A second degree polynomial expression with first order 420 interactions between X' (LAI, SUN) is chosen at first. After some tests, the following reduced 421 equation was chosen for all spectral bands: 422 423 424 with (10) 425 426

The 9 regression coefficients were bootstrapped over 1000 samples and their mean 427 values were the coefficients of the final expression in Eq. 10. The confidence intervals for the 428 bootstrap fit of Eq. 10 were: 0.87 ≤ ≤ 0.93 and 5.3% ≤ ≤ 8.3% (n = 2592). The 429 estimated corresponds to the ratio between and (Eq. 6). For instance for a sun 430 zenith angle of 55°, its values reach more than 40%, and have a monotonous increase towards 431 NIR bands for very low LAI values (LAI ≤ 1; Fig. 8).

is mainly dominated by the 432 contribution of due to few light interactions with tree crown elements (Eq.4). The more 433 the LAI increases, the more values have a curvature at red-edge position between 700nm 434 and 800nm. This emphasizes the contribution of in addition to in . As a 435 matter of fact, this spectrally-dependant feature of is consistent with the leaves optical 436 property features (Fig. 7). Hence with the strong light multiple scattering within the tree 437 crown, values account less than 10% for very high LAI values (LAI ≥ 5; Fig. 8). 438 Once the reference correction factor is estimated for each tree, a pixel-based 446 spatial correction factor is needed to account for the real dimensions of the tree compared to 447 the one used as a "reference tree model" in the design of experiments with DART. In a real 448 scene, each point in the shade views a specific part of the tree; the closer the shaded point is to 449 the tree position, and the larger the occultation is. This occultation is represented by the solid 450 angle under which the tree crown is seen. For simplicity, each tree crown is modelled as an 451 elliptic shape (Fig. 5b). However, the mathematical expression of is not straightforward and 452 is further detailed in Appendix B. Then, the spatial correction factor is the ratio of for the 453 real tree in the image over for DART "reference tree model" (see Eq. 6). Ω values 454 usually ranges between 0 and π in steradian unit. equals to 0.4sr. 455 456 3.5. Tree shadow reflectance correction 457 458 20 ICARE-VEG corrects the ICARE reflectance of any pixels in a tree shadow by a 459 specific factor (see Eq. 6). Other pixels are not corrected. In order to compare ICARE and 460 ICARE-VEG performances, the Mean Absolute Error (MAE) in retrieved reflectance in tree 461 shadows, i.e.

, is compared with ground truth measurements when they are available, or 462 ICARE sunlit retrieved reflectance of the same material type over another area, i.e.

, 463 such as: 464 465 ( 11) 466

with N the number of spectral bands. 467 468

The threshold for best MAE accuracy is set to 0.04 according to the performance of 469 ICARE [START_REF] Lachérade | Icare: A 909 physically-based model to correct atmospheric and geometric effects from high spatial and 910 spectral remote sensing images over 3d urban areas[END_REF]. A second metric is used, the spectral angle mapper (SAM; 470 [START_REF] Kruse | The Spectral Image Processing System (SIPS) -Interactive visualization 906 and analysis of Imaging Spectrometer data[END_REF], to inform about the spectral distortions in the retrieved reflectance. It is a 471 similarity spectral index independent of illumination and shadowing conditions. It requires 472 computing the spectral angle α between the reference reflectance, i.e.

, and the 473 retrieved reflectance, i.e.

: 474

(12) 476 477

The lower α value is, the more similar the spectral shape is between the reference and 478 ICARE-VEG retrieved reflectances. 479 Airborne hyperspectral images were acquired with the push-broom sensor HySpex-490 VNIR1600 (NorskElektroOptikk) with 160 bands in the spectral range 0.4-1µm and a spectral 491 resolution of 3.7nm. For further analysis, 22 spectral bands are kept after removing low 492 instrumental signal-to-noise ratio and water vapour atmospheric windows, and after spectral 493 aggregation at 18nm to be compatible with ICARE running with 6SV code. The acquisitions 494 were at Nadir with a ground spatial resolution of 0.8 m. In addition, a DSM was derived by 495 multi-stereoscopic acquisitions from a panchromatic camera with a horizontal accuracy of 496 0.12 m (Pierrot-Deseilligny and Paparoditis, 2006). The aerial images were manually 497 georeferenced based on the DSM. More than 20 ground control points were selected with the 498 use of the ENVI software and the precision accuracy was inferior to the pixel size. At last, the 499 images were radiometrically corrected with in-lab sensor calibration coefficients. 500 Three images were studied and extracted, namely image U1, U2 and U3 (Fig. 9). They 501 corresponded respectively to an acquisition time of 12h40UTC for U1 and U2, and 502 11h30UTC for U3, with a solar zenith and azimuth angles of respectively (57.2°; 198.1°) for 503 U1 and U2, and (55.5°; 177.5°) for U3. They induced large shadows on aerial images 504 specifically in urban areas. The image U1 contains 27% of shaded pixels, 34% for U2, and 505 finally 30% for U3. The images U1 and U2 are located on a sports centre, and are largely 506 For tree shadow detection, the minimum number of pixels for a tree shadow was set to 565 100. From the original images in Fig. 11a, results of intensity images and histogram 566 thresholding are shown in Fig. 10b and10d, leading to the global shadow masks shown in 567 Fig. 11c, and finally to the tree label shadow masks in Fig. 11d. Usually urban scenes contain 568 a high percentage of shadows, which makes easier the thresholding on the intensity image 569 based on a bimodal histogram. However, dark materials in sunlit regions and bright materials 570 in shaded regions may be falsely detected as shadows (Adeline et al., 2013a). To address 571 these problems, the thresholding method of [START_REF] Nagao | Region extraction and shape analysis in aerial 921 photographs[END_REF] is used to remove water bodies 572 (canal detected in U3 without shadow detection: Fig. 11c) and the morphological closing filter 573 homogenizes shaded regions (white road lines and cars, U3: Fig. 11c). In the tree label 574 shadow masks, the method visually performs well for trees in rows and less for clustered trees 575 such as observed before. In some cases, the tree shadow is truncated or under-detected due to 576 a local less accurate DSM horizontal and vertical description (tree in row at bottom-left in U3 577 and the clustered tree at middle-left in U1: Fig. 11d). 578 For LAI estimation, the application of the LAI-NDVI regression model to the images 590 shows the diversity of low estimated LAI values during the start of the fall season (Fig. 12). 591 Without ground truth measurements, no validation can be performed. But on visual 592 examination and by knowledge about the study site, qualitative comparison from one LAI to 593 another seems correct if LAI values are not extreme (LAI close to 0 or superior to 4). Their 594 values range is 0.77-2.35m 2 .m -2 for U1, 0.63-2.06m 2 .m -2 for U2 and 0.61-2.21m 2 .m -2 for U3. 595

Improvements can be investigated in the future by adding the contribution of textural indices 596 or geostatistical information in cases of heterogeneous and patchy spectral information over 597 tree crowns [START_REF] Colombo | Retrieval of leaf area index in 852 different vegetation types using high resolution satellite data[END_REF]. 598

Finally for tree viewing solid angle estimation, Ω is computed for every pixel in each 599 tree shadow. Its mean value is 0.16sr for U1 and U2, and 0.18sr for U3 (Fig. 12). For instance 600 for the long cast shadow at the bottom right in U1, Ω values range between 2.0sr for the pixel 601 the closest to the trunk and 0.36sr for the pixel the furthest to the trunk. 602

Spectral analysis and comparison between ICARE and ICARE-VEG 608 609

The improvement of ICARE-VEG over ICARE in tree shaded regions is analyzed for 610 3 types of materials, namely grass (high variable reflectance), asphalt (intermediate flat 611 reflectance), and water (very low reflectance), respectively for 2 trees with different LAI 612 values (Fig. 13). Performances are assessed with the computation of the metrics, MAE and 613 SAM (Eq. 12, Table 2), and by observing the spectral variability in the retrieved reflectance 614 (Fig. 14). The results show that: 615 616 (i) the mean reflectance of ICARE in the tree shade is always overestimated compared 617 to its counterpart in the sun. This is strengthened if the material in the shade has a high 618 reflectance (i.e. grass compared to asphalt) and if the LAI is small (since the tree crown 619 transmittance increases; Fig. 13). The MAE for ICARE in the tree shade is at least 4 times 620 higher than the one with ICARE in the sun when compared to the ground truth (Table 2), 621 (ii) ICARE retrieved reflectance in the tree shade is distorted from visible to NIR 622 bands, with a spectral increase starting at the red-edge position (particularly more visible for 623 grass). This observation is in line with the previous comments on (Fig. 12). ICARE-VEG 624 correction attenuates this spectral distortion: SAM values are better by a multiplicative factor 625 between 1.0 and 1.4 compared to ICARE (Table 2), 626 (iii) ICARE-VEG retrieves lower reflectance values than ICARE, and have a better 627 accuracy due to the correction brought by : its MAE decreases by a multiplicative 628 factor between 2 and 4.5 when considering ground truth as a reference, and by a 629 multiplicative factor between 4.2 and 18.8 when considering ICARE in the sun as a reference 630 (Table 2). ICARE-VEG correction is spectrally-dependent; it is less notable in the visible 631 range but becomes important in the NIR where ICARE can achieve non physical reflectance 632 values higher than 1 (e.g. grass; Fig. 13a and13b), 633 (iv) The spectral dispersion in ICARE retrieved reflectances increases from sunlit to 634 shaded regions (Fig. 14). This may be due to penumbra and tree clumping effects impacting 635 the spatial homogeneity of the tree shadow at ground. Globally, ICARE-VEG correction 636 reduces this dispersion but not at the same order of magnitude of what ICARE in the sun 637 does, 638 (v) The correction applied to water is the most challenging because of its very low 639 reflectance, smaller than the 4% threshold in MAE selected as the desired accuracy for 640 atmospheric correction models (Fig. 13). However, ICARE-VEG correction is promising 641 since the order of magnitude in retrieved reflectances is correct as well as its global spectral 642 shape, 643 (iv) The spectral differences between ICARE-VEG results and ground truth may be 644 explained by the fact that ground truth has been measured close to tree shadow but in the 645 sunny part, which induces spectral intra-class variability issue, and factor brings a mean 646 correction over the tree shadow, which cannot account for all local variations in tree shadow, 647 especially when LAI is low. 648 At last, ICARE and ICARE-VEG are compared for all pixels belonging to the tree 649 shadow label mask (U1: 5048 pixels, U2: 3843 pixels, U3: 4034 pixels). In the NIR band at 650 800nm, the decrease in the mean ICARE-VEG retrieved reflectance compared to ICARE is 651 43.3% for U1, 54.5% for U2 and 36.7% for U3. In the red band at 670nm, this decrease is 652 36.4% for U1, 51.8% for U2 and 40.1% for U3. At 800nm, ICARE reflectance is larger than 1 653 for 5.9%, 3.6% and 0.3% of pixels for U1, U2 and U3, respectively. ICARE-VEG reduces 654 this percentage of pixels to 4.1%, 2.9% and 0.1%, respectively. 655 656 657 Fig. 13. ICARE reflectances in the sun ("IC_sun") and both ICARE and ICARE-VEG 658 reflectances in the shade ("IC_sh" and "ICV_sh") for 3 ground materials (grass: first column, 659 29 asphalt: second column, and water: third column) and for 2 different LAI values (high: first 660 row and low: second row). In-situ measurements are also shown when available ("GT" : 661 Ground Truth). 662 663 Table 2. ICARE and ICARE-VEG performance (MAE : Mean Absolute Error expressed in 664 percentage of reflectance unit, and SAM : Spectral Angle Mapper expressed in radian unit) 665 for scenarios from a to f (please refer to Fig. 13). Reference reflectance is in-situ 666 measurements or ICARE in the sun. ICARE in the sun ("IC_sun") and both ICARE and ICARE-VEG in the shade ("IC_sh" and 673 "ICV_sh" respectively) for scenarios from a to f (please refer to Fig. 13). 674 675 6. Conclusions 676 677 ICARE-VEG improves ICARE 3D atmospheric correction in order to correct retrieved 678 surface reflectances in presence of tree shadows. It includes image-based techniques such as 679 tree crown delineation and tree shadow detection, and then the application of a spectral and 680 geometrical physics-based correction factor in tree shadow pixels following each tree crown 681 characteristics. Since this issue is relatively new, the strategy was based on a complex 682 exploratory methodology by using the DART 3D canopy radiative transfer model, and heads 683 towards the development of a semi-automatic method. ICARE-VEG only considers deciduous 684 trees with green healthy leaves and surfaces with a lambertian spectral behaviour. 685

The application of ICARE-VEG on VNIR hyperspectral high spatial resolution data 686 and the comparison between ICARE and ICARE-VEG clearly stress that a large inaccuracy 687 occurs if tree crown transmission is neglected. Globally, results were encouraging and showed 688 that (i) neglecting the transmitted irradiance demonstrates an over-estimation in retrieved 689 reflectances, the higher the material reflectance is and the lower the tree LAI is, (ii) this bias 690 increases from visible to NIR at the red-edge position, which is due to the additive 691 contribution of the diffuse over the direct transmitted irradiance in the total transmitted 692 irradiance received at tree shadow; ICARE-VEG attenuated this spectral distortion by a 693 multiplicative factor between 1.0 and 1.4 by means of spectral angle mapper performance, 694 (iii) ICARE-VEG improves the mean absolute error in retrieved reflectances compared to 695 ICARE in tree shadows by a multiplicative factor ranging between 4.2 and 18.8 for some test 696 cases (taking ICARE in the sun as reference), and (iv) for a given wavelength, the spectral 697 variability in the retrieved reflectances increases from sunlit to shaded regions due to 698 penumbra and tree clumping effects, which makes difficult for the ICARE-VEG correction to 699 exactly reduce at the same order of magnitude of what ICARE does in sunlit regions. 700

These results highlight the complexity to model physical natural processes with finer 701 spatial resolutions. The difficulty relies on the high number of sources of variability to cope 702 with, among them, the spectral and spatial dimensions for the tree shadow correction, the 703 intra-class variability for a given material, and the intrinsic characteristics of urban areas 704 [START_REF] Small | Spectral dimensionality and scale of urban radiance[END_REF]. 705 Future work includes the validation of ICARE-VEG in the Short Wave Infrared 706 Region (SWIR: 1.0-2.5µm), the replacement of 6SV atmospheric code with MODTRAN 707 (MODerate resolution atmospheric TRANsmission; [START_REF] Berk | 834 MODTRAN4 radiative transfer modeling for atmospheric correction[END_REF] in ICARE-HS, and the 708 comparison of 3D atmospheric codes in urban areas between the fusion of ICARE-VEG and 709 ICARE-HS and ATCOR-4. Moreover, a better analysis of the direct and diffuse transmitted 710 irradiance terms in presence of a tree crown is planned to better understand the possible 711 sources of errors and improvements of values showed few spectral dependence except locally on 742 the red-edge with around 10% maximum variation (data not shown). In one side for the full 743 LAI range (0.5 ≤ LAI ≤ 8) and by order of importance, LAI and SUN contribute the most to 744 variance, then VISI, the interactions (mainly dominated by ALA with SUN), ALA, 745 POROSITY, and at last no contribution for LOP and GROUND. These two last variables 746 might interfere in the radiative budget (i.e.

) at a second level compared to LAI and SUN 747 since the contribution of the direct light is predominant over the diffuse light within the 748 canopy. On the other side, by considering LAI ranges, the more LAI increases, the more the 749 influence of LAI and VISI is reduced for the increasing benefit of SUN, ALA, the interactions 750 (e.g. ALA with SUN) and POROSITY. Indeed, increasing tree clumping and both sun zenith 751 angle and leaf orientation gets more transparency in a very closed canopy (i.e. high LAI). 752 Finally, LAI and SUN are selected as X' variables to estimate . 753 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q IC_sun IC_sh ICV_sh IC_sun IC_sh ICV_sh c) LAI = 1.34 q q q q q q q q q q IC_sun IC_sh ICV_sh e) LAI = 1.57 q q q q q q q q q q IC_sun IC_sh ICV_sh 0.00 b) LAI = 1.14 q q q q q q q q q q IC_sun IC_sh ICV_sh 0.0 0.2 0.4 0.6 0.8 reflectance at 670nm d) LAI = 1.16 q q q q q q q q q q q q IC_sun IC_sh ICV_sh 0.00 q q q q q q q q q q q q q q q q q q IC_sun IC_sh ICV_sh 0.0 0.5 1.0 1.5 2.0 2.5 3.0 grass reflectance at 800nm a) LAI = 1.36 q q q q q q q q q q q q IC_sun IC_sh ICV_sh 0.00 0.10 0.20 0.30 asphalt reflectance at 800nm IC_sun IC_sh ICV_sh c) LAI = 1.34 q q q q q q q q q q q q q q q q IC_sun IC_sh ICV_sh -0.15 -0.10 -0.05 0.00 0.05 water reflectance at 800nm e) LAI = 1.57 q q q q IC_sun IC_sh ICV_sh 0.0 0.5 1.0 1.5 2.0 2.5 3.0 reflectance at 800nm b) LAI = 1.14 q q q q q q q IC_sun IC_sh ICV_sh 0.0 0.2 0.4 0.6 0.8 1.0 1.2 reflectance at 800nm d) LAI = 1.16 q q q q q q q q q q IC_sun IC_sh ICV_sh -0.15 -0.10 -0.05 0.00 0.05 reflectance at 800nm f) LAI = 0.97

  Taxonomy of the radiative transfer components for ICARE (IC) and ICARE-VEG 155 (ICV) for an urban scene and for a target a) in the sun, b) in a building shadow and c) in a topography inducing downwelling and upwelling multiple reflections on 160 surrounding surface elements, and to local atmospheric multiple scattering. The total at-sensor 161 radiance,

  for is only valid for shadows cast by opaque 180 surface materials such as buildings. In shaded regions cast by trees, however, the incoming 181 light transmitted through tree crowns,

  ICARE-VEG method workflow (3.1 existing ICARE method, from 3.2 to 3.5 new 232 developments presented in this paper, highlighted by bold boxes). 233 234 3.1. Atmospheric correction by ICARE 235 236 ICARE

(

  segmentations are performed for delineating the individual 245 tree crowns: detection of tree clusters, and separation of individual tree crowns in each cluster 246 of vegetation are extracted in the image by computing the NDVI with the 252 red band at 670nm and the NIR band at 800nm. The histogram of the NDVI image is 253 thresholded with the bimodal technique of Otsu (1979) to create a binary vegetation mask. 254 Then, a refinement step uses the DSM to separate high vegetation (e.g. trees) and low 255 vegetation (e.g. grass). The histogram of the DSM image is classified with a user-defined 256 threshold based on the minimum tree height the user wants to consider. The overlap between 257 the resulting DSM mask and the vegetation mask generates the high tree vegetation mask (i.e. 258 tree clusters location). 259 Afterwards, individual tree crowns are delineated within each tree cluster. Zheng et al., 260 2016 give a relevant review of long studied techniques in the literature. The most used 261 technique is rasted-based using extrapolation, interpolation and smoothing procedures for 262 treetop detection and crown segmentation. First, the DSM mask is smoothed with a Gaussian 263 filter in order to flatten the strong irregularities on top of tree canopies. Second, a region 264 growing segmentation based on the method of Iovan et al. (

  Flowchart of the individual tree shadow detection. 283 284 First, the shadow mask is created using an intensity image (noted I) computed from 285 the combination of four radiance (R) spectral images (B: 470nm, G: 550nm, R: shadow binary mask is derived from this intensity image by histogram 291

  distance (GSD), the sun zenith angle ( ), and the tree height ( Geometric configurations with an isolated tree for a) tree shadow framing and b) solid 309 angle computation from a point C in tree shadow and for a tree crown modelled as an 310 ellipsoid (for the annotations see Appendix B). 311 312 Once the dimensions of the rectangular box are known, a region growing technique is 313

  . "Reference tree model" building from the DART interface. 344 345 Table 1. DART settings for the design of experiments (the abbreviations of the variables of 346 interest are given in brackets and in bold) x,y,z [m x m x m] For a zenith angle <60°: 22.8 x 22.8 x 14.0 For a zenith angle = 60°: 30.8 x 30.8 x 14.0 Voxel size in x,y,z [m x m x m] 0.4 x 0.4 x 0.4 Ground reflectance (GROUND) Asphalt and grass (cf. Fig.7) Isolated tree Tree height [m]/ tree crown height [m] 14.2 / 9.4 Tree crown ellipsoid axis in x,y [m x m] 6 x 6 Trunk diameter below crown [m] 0.4Tree leaf area index [m 2 .m -2 ] (LAI) 0.5 -1 -1.5 -2 -2.5 -3 -3.5 optical properties (LOP) Liquidambar, oak and poplar (cf.

Fig. 7 )a

 7 Fig.7) a Spectral bands inside atmospheric water vapour windows are not considered 348 b FHWM: Full-Half-Width-Maximum 349 350

  was validated by using the data collected on October 24 th 2012 over 483 Toulouse, France, from the UMBRA campaign (Urban Material characterization in the sun 484 and shade of Built-up structures and trees and their Retrieval from Airborne image 485 acquisitions over two French cities;Adeline et al., 2013b). 486 487 4.1. Airborne hyperspectral data 488 489 21

  dominated by vegetated areas, both well maintained grass lawns and isolated trees, with 507 sports infrastructures. They are characteristics of open areas whereas image U3 is oppositely 508 representative of dense urban areas with high buildings and tree rows alongside the "RGB composite images used in this study associated with their greyscale DSM and 513 their location on a Google Earth image over Toulouse, France. 514 5154.2. Field measurements and atmospheric conditions 516 517Road asphalt and grass surface reflectance were measured over the spectral range 518 0.35-1.0µm at 3nm spectral resolution and 1nm spectral sampling interval with a portable 519 ASD (Analytical Spectral Devices Inc., Boulder, CO, USA) spectroradiometer and a 520 reflectance plate Spectralon® of known reflectance. The integrated water vapor content and 521 the aerosol type and abundance were measured with a microwave radiometer and a is applied on the three images described in section 4. Results are 527 discussed for each processing step, then ICARE-VEG performance is compared with those of 528 ICARE in tree shadows and with ground truth. 529 530

  Fig. 10.a) NDVI images, b) intensity images, c) NDVI histograms and d) intensity histograms 581 (black dots indicates thresholds values). 582 583

  . LAI estimated from the LAI-NDVI regression model (first row) and tree viewing 605 solid angles computed in each tree shadow (second row; treetops are indicated in red dots). 606 607

  Figure1 Click here to download Figure: Fig1.pdf

  Figure14aClick here to download Figure: Fig14a.pdf

Figure14b

  Figure14bClick here to download Figure: Fig14b.pdf

Figure

  Figure Click here to download Figure: Fig2_revised.pdf

Extraction), to account for trees in its new version, ICARE-VEG (ICARE with VEGetation).

Present address : CNRM, Météo-France/CNRS, 31057 Toulouse, France *

Acknowledgements

ANOVA is applied on a second degree polynomial expression with first order interactions 726 between the inputs X={LAI, ALA, POROSITY, LOP, GROUND, SUN, VISI} and the output 727 . For each spectral band, the regression fit between X and gives: R 2 > 0.98 and p-728 value < 1%. The sensitivity index is computed for 4 ranges of LAI from the results of 729 ANOVA: full LAI range (0.5-8), low LAI (0.5-2), medium LAI (2-3.5) and high . 730 for the contribution of the variable in the variance of computed over the spectral domain 734 for different LAI ranges and based on ANOVA results. Each single variable represents its 735 main effect (coefficient of the variable taken alone and squared except for the qualitative 736 variables: LOP, GROUND, VISI); the interaction effect is the sum of all combinations 737

Results are shown in

Appendix B 755 756

The solid angle viewing a surface situated in the upper space from any point is usually 757 defined by: 758 34 759 (B.1) 760 761 θ denotes the elevation angle (which is not the standard notation in spherical 762 coordinate system), and φ the azimuth angle (anticlockwise from South direction, e.g. X axis). 763 is the partial angle of the object for a given θ and is set to 0 764 when the object is out of reach for a given direction ( . However, here the tree crown is 765 assumed to have an ellipsoid shape (Essery et al., 2008; Fig. 5), hence expression is 766 not trivial to determine and to integrate since it depends on θ variations. 767

Let's consider a given point C(0,0,0) situated in the tree shadow. C is the centre of the 768 Cartesian coordinates system. The coordinates of the base of the trunk T are (x 0 ,y 0 ,0), the total 769 tree height is , the trunk height , the tree crown has a diameter of 770 and is modelled by an ellipsoid with a revolution symmetry in Z axis: 771 the trunk (i.e. ). By reporting Eq. B.6 and Eq. B.5 in Eq. B.1, the integration will be solved 802 numerically by using the Riemann integral, further validated with a Monte Carlo method. 803 will be set to 0 when the tree is out of reach, i.e. for values of θ leading to , 804 where the arcos function is not defined. 805 806