María Del

Pilar Salas-Zárate

Rafael Valencia-García

Estanislao López-López

Nathalie Aussenac-Gilles

Ángela Almela

Giner Alor-Hernández

A study on LIWC categories for opinion mining in Spanish reviews

Keywords: Sentiment analysis, opinion mining, natural language processing with LIWC, machine learning

With the exponential growth of social media i.e. blogs and social networks, organizations and individual persons are increasingly using the number of reviews of these media for decision making about a product or service. Opinion mining detects whether the emotions of an opinion expressed by a user on Web platforms in natural language, is positive or negative. This paper presents extensive experiments to study the effectiveness of the classification of Spanish opinions in five categories: highly positive, highly negative, positive, negative and neutral, using the combination of the psychological and linguistic features of LIWC. LIWC is a text analysis software that enables the extraction of different psychological and linguistic features from natural language text. For this study, two corpora have been used, one about movies and one about technological products. Furthermore, we have conducted a comparative assessment of the performance of various classification techniques: J48, SMO and BayesNet, using precision, recall and F-measure metrics. All in all, findings have revealed that the positive and negative categories provide better results than the other categories. Finally, experiments on both corpora indicated that SMO produces better results than BayesNet and J48 algorithms, obtaining an F-measure of 90.4% and 87.2% in each domain.

Introduction

their clients' expectations and needs, clients' feelings

Related Work

LIWC

Evaluation and Results

6.1.

Table 1 .

 1 Comparison of proposals for sentiment classification.

	Proposal	Computational learning	Linguistic resources	Domain	Language
	[4]	Yes (SVM(Support Vector	Ngrams, TF-IDF ( Term	Movies, books,	English
		Machines))	frequency -Inverse document	cars, cookware,
			frequency), BO (Binary	hotels, music,
			Occurrence) and TO (Term	cameras, phones
			Occurrence)	and computers
	[5]	Yes (SVM and	Bag-of-words model	Movies, GPS, books	English
		ANN(Artificial Neural		and cameras
		Network))
	[6]	Yes (NB (Naïve Bayes), ME	Ngrams and TF-IDF	Movie, books,	English
		(maximum entropy) and		DVDs, Electronics
		SVM)		and Kitchen.
	[7]	Yes (NB, SVM and ME)	Sentiment dictionary	Books, DVDs,	English
				electronics and
				Kitchen.
	[8]	No	Sentiment	Movies	English
			dictionary(SentiwordNet) and
			ontologies
	[9]	Yes (SVM)	Ngrams, TF and TF-IDF	Twitter (movies)	English
	[10]	Yes (SVM, NB and ME)	SentiwordNet	Twitter (politics,	English
				business,
				economics)
	[11]	Yes (NN(Neural	BPN (back-propagation neural	Movie, MP3 and	English and Chinese
		Network))	network) and SO	Blog
			indexes.
	[12]	Yes (SVM)	Ngrams and TFIDF-C	Hotels and	Chinese
				products
	[13]	Yes (SVM)	Sentiment dictionary(S-HAL)	News	Chinese
	[14]	No	Sentiment dictionary (SentiRank) Products	Chinese
	[15]	Yes (ANN and SVM)	Ngrams	Movie	Chinese
	[16]	No	BLEL: the Bing Liu English	Movie	Spanish and English
			Lexicon

Table 2 .

 2 LIWC

	categories
	1. Linguistic processes	Word count, total pronouns, articles, prepositions, numbers, negations
	2. Psychological Processes	Affective process, positive emotions, negative emotion, cognitive process, perceptual
		process
	3. Relativity	Time, space, motion
	4. Personal concerns	Occupation, leisure activity, money/financial issues, religion, death and dying
	4. Data Sets

Table 3 .

 3 Machine learning methods Classifier Description J48 J48 was developed by Ross Quinlan. It is an open source Java implementation of the C4.5 algorithm in the Weka data mining tool. The algorithm uses an advanced technique to induce decision trees for classification and uses reduced-error pruning. The purpose of classifying data with decision tree is to discover if it contains wellseparated classes of items that can be interpreted meaningfully [25] BayesNet Bayesian networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs imply the existence of direct causal dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. Such a network can be used to represent the deep causal knowledge of an agent or a domain expert and turns into a computational architecture if the links are used not merely for storing factual knowledge, but also for directing and activating the data flow in the computations which manipulate this knowledge [26]. SMO Sequential minimal optimization (SMO) was developed by John Platt in 1998. SMO is an improved training algorithm for SVMs. Like other SVM training algorithms, SMO breaks down a large QP (quadratic programming) problem into a series of smaller QP problems. Unlike other algorithms, SMO utilizes the smallest possible QP problems, which are solved quickly and analytically, generally improving its scaling and computation time significantly [27].

Table 4 .

 4 Products with two categories (positive and negative).

		J48			BayesNet			SMO
		P	R	F1	P	R	F1	P	R	F1
	1	0.739	0.741	0.74	0.799	0.797	0.797	0.843	0.843	0.843
	2	0.799	0.8	0.799	0.833	0.833	0.833	0.823	0.822	0.822
	3	0.733	0.735	0.73	0.781	0.782	0.781	0.796	0.795	0.795
	4	0.742	0.741	0.741	0.76	0.761	0.761	0.755	0.755	0.755
	1_2	0.803	0.804	0.803	0.885	0.881	0.882	0.887	0.887	0.886
	1_3	0.75	0.752	0.751	0.819	0.818	0.819	0.832	0.833	0.832
	1_4	0.771	0.771	0.771	0.813	0.811	0.812	0.832	0.833	0.832
	2_3	0.819	0.82	0.819	0.879	0.878	0.878	0.863	0.863	0.863
	2_4	0.808	0.809	0.809	0.854	0.852	0.853	0.845	0.845	0.844
	3_4	0.737	0.737	0.737	0.811	0.811	0.811	0.817	0.818	0.817
	1_2_3	0.816	0.816	0.816	0.889	0.885	0.886	0.881	0.881	0.881
	1_2_4	0.821	0.822	0.82	0.87	0.865	0.867	0.879	0.879	0.879
	1_3_4	0.803	0.804	0.802	0.828	0.827	0.828	0.837	0.838	0.837
	2_3_4	0.805	0.806	0.804	0.878	0.874	0.875	0.866	0.867	0.867
	1_2_3_4	0.83	0.831	0.83	0.878	0.874	0.875	0.904	0.905	0.904

Table 5 .

 5 Products with three categories (positive-neutral-negative).

		J48			BayesNet			SMO
		P	R	F1	P	R	F1	P	R	F1
	1	0.677	0.687	0.682	0.697	0.687	0.692	0.743	0.745	0.744
	2	0.671	0.669	0.670	0.703	0.709	0.706	0.713	0.732	0.722
	3	0.605	0.634	0.619	0.597	0.645	0.620	0.585	0.678	0.628
	4	0.614	0.622	0.618	0.614	0.66	0.636	0.561	0.649	0.602
	1_2	0.705	0.704	0.704	0.769	0.753	0.761	0.772	0.782	0.777
	1_3	0.736	0.747	0.741	0.775	0.777	0.776	0.714	0.707	0.710
	1_4	0.672	0.68	0.676	0.717	0.71	0.713	0.717	0.727	0.722
	2_3	0.693	0.706	0.699	0.745	0.75	0.747	0.732	0.75	0.741
	2_4	0.667	0.675	0.671	0.739	0.742	0.740	0.73	0.744	0.737
	3_4	0.652	0.658	0.655	0.661	0.695	0.678	0.716	0.713	0.714
	1_2_3	0.677	0.678	0.677	0.763	0.748	0.755	0.776	0.785	0.780
	1_2_4	0.698	0.704	0.701	0.774	0.759	0.766	0.769	0.78	0.774
	1_3_4	0.665	0.672	0.668	0.727	0.719	0.723	0.738	0.748	0.743
	2_3_4	0.688	0.692	0.690	0.759	0.759	0.759	0.753	0.771	0.762
	1_2_3_4	0.678	0.686	0.682	0.766	0.753	0.759	0.774	0.786	0.780

Funding


Email: dominique.cahard@univ-rouen.fr

Compounds featuring the SF5 motif stand out through their remarkable chemical properties that include outstanding chemical and thermal stability, hydrolytic stability, high lipophilicity and hydrophobicity, low polarizability, high-density, low boiling point, and low surface tension as well as potentially great biological activity. 17,18,19 Before 2002, the production of pentafluorosulfanyl compounds with the aid of SF5Cl relied on the use of excessive temperatures, high-pressure autoclaves, photochemical procedures, hazardous reactants to end up with low or variable yields together with the generation of toxic side-products. In 2002, the use of triethylborane (Et3B) as a catalytic initiator for the free radical chain addition of SF5Cl to alkenes and alkynes provided a major breakthrough. 11,20 This is currently the method of choice for pentafluorosulfanylation serving as starting point for several synthetic applications.

Preparative Methods

A method of producing SF5Cl without the use of SF4 includes admixing potassium fluoride, sulfur powder, chlorine and bromine (possibly acting as a solvent) at room temperature for two weeks (eq 14). 21

Reactions with C=C bonds

Addition to Unfunctionalized Alkenes.

Transannular cyclization of 3,7-dimethylenebicyclo[3.3.1]nonane has been developed for the synthesis of SF5-substituted noradamantane. The reaction proceeds without initiation in low yield, but light irradiation improves greatly the yield and selectivity (eq 15). Transannular cyclization of norbornadiene works equally well and SF5-nortricyclanes were obtained as a 2.7:1 isomeric product ratio (eq 16). In contrast, reaction of SF5Cl with cis,cis-1,5-cyclooctadiene didn't yield transannulation, but gave as major product the addition of SF5Cl to only one double bond of the diene. Use of triethylborane as radical initiator improved slightly the yield, but no transannulation was observed (eq 17). 22 The addition of SF5Cl to benzobarralene followed by a sequence of base-promoted HCl elimination / naphthalene formation gave access to 2-pentafluorosulfanylnaphthalene (eq 18). 23 A route to pentafluorosulfanylbenzene (C6H5SF5) was developed through addition of SF5Cl to cyclohexene, followed by HCl elimination, dibromination with N-bromosuccinimide and dehydrobromination under basic conditions to afford the desired C6H5SF5 in 68% overall yield (eq 19). 24 The two halogen atoms required for the dehydrohalogenation step can be initially present on the cyclohexene (eq 20). The synthesis of conjugated 1,3-dienes substituted with a terminal SF5 was performed from terminal olefins. Comparative radical addition of SF5Cl to olefins under UV irradiation or with a catalytic amount of triethylborane showed that the second method gave higher yields. Elimination of HCl under basic conditions afforded the SF5-substituted mono-olefins. Then, reaction with bromine led selectively to allylic bromination and consecutive elimination of HBr under basic conditions provided access to SF5-substituted 1,3-dienes (eq 21). [START_REF] Ponomarenko | Synthesis[END_REF] Using the Et3B-initiation approach, SF5Cl was added to ethylene and 1,1-difluoroethylene for the preparation of monomers intended for radical polymerization and production of original SF5containing copolymers (eq 22). 27 Unactivated alkenes with a distant functional group react almost identically to simple olefins; however, the distant function could participate in a subsequent reaction. The Et3B-mediated addition of SF5Cl to mono-substituted alkenes proved to be tolerant to the presence of an -

+ SF 5 Cl Et 3 B (0.1 equiv) hexane, -30 °C to rt SF 5 Cl i) t-BuOK, Et 2 O ii) NBS iii) t-
F F i) SF 5 Cl, Et 3 B, CH 2 Cl 2 -60 to -30 °C, 3 h ii) KOH, H 2 O, iPrOH, reflux, 2 h F F F 5 S F 5 S 51% 28% (22)
carboxylic acid function, which then served for the cyclization into γ-butyrolactone in the presence of silver triflate and triethylamine (eq 23).

28

Addition to Allylic Alcohols and derivatives.

Primary allylic and homoallylic alcohols were subjected to the photo-induced radical addition of SF5Cl to the C=C bond followed by dehydrochlorination with potassium hydroxide (eq 24). 29,30 The resulting primary alcohols were further transformed (Cl, N3, SCN) or oxidized to higher oxidation state functional groups (aldehyde, acid, ester, nitrile) and engaged, for example, as dienophiles in Diels-Alder cycloadditions.

Secondary allylic alcohols reacted similarly and afforded -SF5 enones after an oxidation step (eq 25). 31 The same intermediate treated with KOH and then dehydrated gave 1pentafluorosulfanylbuta-1,3-diene. 32 Allyl ethers are also suitable substrates for SF5Cl addition. The trans addition of SF5Cl to 7oxanorbornene derivatives afforded exclusively the endo addition of the SF5 moiety caused by the steric bulk of SF5 (eq 26). The elimination step mediated by lithium hydroxide proceeded smoothly but depends on the lateral substituents. Using the low temperature Et3B initiated free radical chain procedure, SF5Cl underwent addition to 7-oxabicyclo[2.2.1]hept-5-ene-2-carbonitrile to give two regioisomeric adducts as precursor of the pentafluorosulfanylfurans via a retro-Diels-Alder approach (eq 27). 34 The Et3B-mediated radical addition of SF5Cl was initially reported in hexane and latter in dichloromethane at -40 °C. It was later showed that the chloropentafluorosulfanylation of ((allyloxy)methyl)benzene tolerated many solvents such as toluene, ethyl acetate, THF, acetone, methanol, acetonitrile, acetic acid or even water . In contrast, DMF and DMSO completely inhibit the SF5 addition. Noteworthy, the temperature seems to remain the main limitation since the highest yields were obtained at -40 °C (eq 28). 35 Similarly to (homo)allylic alcohols and allyl ethers, the addition of SF5Cl to allylic esters under standard radical conditions worked efficiently (eq 29). SF5-Containing allylic alcohols can then be obtained by elimination/deprotection with KOH. Consecutive oxidation with CrO3 affords β-SF5 acrylic acid (eq 29), 36 while oxidation with PCC yields β-SF5 enal. Addition to N-Allylamides. The addition of SF5Cl to N-allylbenzamides under standard conditions was employed in the first step towards 5-[(pentafluorosulfanyl)methyl]-2-oxazolines (eq 30). The subsequent cyclization in the presence of silver triflate proceeded through chlorine substitution rather than leading to elimination products typically obtained with the aid of various bases. 39 Additions to Enol Ethers.

α-SF5 Substituted aldehydes can be synthesized by radical addition of SF5Cl to enol ethers in the presence of Et3B followed by acidic hydrolysis. The chloropentafluorosulfanyl intermediates were typically 9:1 diastereomeric mixtures (eq 31). 40 High purity of enol ethers proved to be crucial to reach satisfactory yields. α-SF5 Aldehydes were further transformed into α-SF5-substituted aldimines and used in cycloaddition reactions.

Addition of SF5Cl to phenyl trifluorovinyl ether was performed in the presence of a catalytic amount of benzoyl peroxide (BPO) at 110 °C; then, treatment with sulfuric acid at the same temperature afforded the pentafluorosulfanyldifluoroacetic acid (eq 32). The latter can be converted to the corresponding acyl chloride in reaction with PCl5 for reactions with various nucleophiles (alcohols, amines, Grignard reagents). 41 Ph The first addition of SF5Cl to vinyl acetate was performed under thermal conditions in an ironnickel-molybdenum pressure reactor (eq 33). 42 The resulting adduct was used to access α-SF5

methyl ester by forming an acetal in hot methanol and then oxidation with m-CPBA (eq 33). 43 The SF5 addition was improved thanks to the use of triethylborane as radical initiator (eq 34) whereas

the conversion into methyl ester followed basically the same process. 44 A modified strategy was later proposed that include a reduction into primary alcohol, oxidation to the acid and esterification. 45 The preparation of -SF5 ketones was achieved by reaction of SF5Cl with enol acetates such as isopropenyl acetate at 100 °C for 1 h in a Ni-Fe-Mo alloy at autogenous pressure. 42 More conveniently, the enol acetate of acetophenone reacts with SF5Cl and Et3B in hexane at -30 °C (eq 35). [START_REF] Welch | The Research Foundation of State University of New[END_REF] Additions to ,-Unsaturated Esters.

Methyl acrylate (also methyl methacrylate) reacted with the SF5 radical generated from SF5Cl under thermal conditions in an autoclave at 120 °C (Eq 36). Addition to Allyl Silanes.

Addition of SF5 to allyl silanes required 4 to 7 equivalents of SF5Cl to reach full conversions; then, HCl elimination with the aid of KOH gave the corresponding (E)-3-SF5 allyl silanes in high yields, except in the case of the volatile trimethylallylsilane (eq 37). 36

Addition to Allene.

A single case of addition of SF5Cl to allene mediated by triethylborane gave access to (2-chloro-2-propen-1-yl) pentafluorosulfur (eq 38). 44

Additions to Alkynes

Aryl-, hetaryl-, and alkyl-acetylenes react with SF5Cl in the presence of triethylborane at -40 °C to give regioselectively the corresponding pentafluorosulfanyl alkenyl chlorides. Aryls featuring electron-donating substituents afforded higher yields. Dehydrochlorination was then achieved with lithium hydroxide in DMSO to produce the SF5-substituted alkynes, which utility as building blocks was demonstrated in many 1,3-dipolar cycloadditions for the synthesis of SF5-isoxazole and -isoxazolines (eq 39), 49 with azomethine ylides generated in situ from aziridine esters for the synthesis of SF5-dihydropyrroles and SF5-pyrroles (eq 40), 50

SF5-pyrroles (eq 41) 51 , and with thiocarbonyl ylide obtained from chloromethyl trimethylsilylmethyl sulfide to provide 3-pentafluorosulfanyl-4-(3'-thienyl)thiophene (eq 41). SF5-Substituted alkynes were also subjected to Diels-Alder reactions or a sequence Diels-Alder / retro-Diels-Alder reactions for the synthesis of SF5-bicyclo[2.2.1]hepta-2,5-diene derivatives and SF5-furans, respectively (eq 42). 53,34 Hydration of SF5-alkynes has been delineated. The study revealed that SF5 acts as an efficient directing group in gold-catalyzed regioselective hydration of SF5-alkynes with the aid of (JohnPhos)AuCl (eq 43). 54 Toward the synthesis of liquid crystals, the radical addition of SF5Cl onto alkynes (alkenes also reacted but less efficiently) followed by standard elimination with LiOH/DMSO combination gave SF5-acetylene structures (eq 44). The compounds showed low birefringences (Δn), but high dielectric anisotropies (Δε) wich are interesting properties for polar liquid crystals. 55 Vincent

  Université de Haute-Alsace, Université de Strasbourg, CNRS, LIMA, UMR 7042, Mulhouse Normandie Université, CNRS, UMR 6014 COBRA, Mont Saint Aignan,

  BuOK, Et 2 O

										SF 5
										(19)
										68% (overall yield)
	Cl						Et 3 B cat.	F 5 S	Cl	EtONa, EtOH	SF	5
						CH	2 Cl	2 , -20 °C, 18 h		rt, 15 min
	+		SF	5 Cl
										(20)
	Cl								Cl	Cl
										96%	79%
								Cl
										i) Br	2 (1.2 equiv)
								SF		SF	SF
	SF	5 Cl (1.5 equiv)		5	K	2 CO	3 (5 equiv)	5	pentane, rt, 12 h	5
										(21)
	(a) UV irradiation hexane, rt, 6-8 h		(a): 84 %	DMF, 50-55 °C, 10 h	78%	ii) K DMF, 55 °C, 10 h 2 CO 3 (5 equiv),	82%
	(b) EtB	3 (10 mol %)
	CH	2 Cl	2 , -30 °C, 2-6 h		(b): 95%

  52

				SF 5 Cl (1.2 equiv) Et 3 B (0.1 equiv)		SF 5	LiOH, H 2 O	(39)
			hexanes, -30 to -40 °C, 1 h		DMSO, rt, 2 h
							Cl	SF 5
							50%	88%
							O -	OMe	N	OH
							Ph	N +	Ph	Cl
							THF, rt, 16 h	NEt 3 , THF, rt, 36 h
							O	N Ph	OMe	O	N	Ph
							SF 5	SF 5
							65%	55%
							SF
							5
				SF	5 Cl (1.2 equiv)
	Ph			Et 3 B (0.1 equiv)	Ph	LiOH, H	2 O	Ph
							(40)
		hexanes, -30 to -40 °C, 1 h		DMSO, rt, 2 h
							Cl	SF
							5
							43% (over two steps)
		CO	2 Me		Ph	Ph
					F 5 S		F 5 S
		N
		t-Bu					DDQ
					N	CO	2 Me	CO	2 Me	60% (over two steps)
							N
		xylene, 135 °C	t-Bu		t-Bu
							S
							TMS	N	OMe	F 5 S
							SF
							5
							Bz
							96%
							i) TFA (0.2 equiv)
							N
		i) SF hexanes, -30 to -40 °C, 1 h 5 Cl (1.2 equiv), Et 3 B (0.1 equiv)		CH	2 Cl ii) DDQ 2 , reflux, 24 h	Bz	(41)
	S	ii) LiOH, H	2 O, DMSO, rt, 2 h	S	S
							TMS	S	Cl
							F 5 S
							i) TBAF, THF
							43%
							ii) SO	2 Cl	2, CH	2 Cl	2
							S


Anne-Laure Tiberi-Wadier
email: laure.tiberi-wadier@cerema.fr

Nicole Goutal

Sophie Ricci

Philippe Sergent

Maxime Taillardat

François Bouttier

Céline Monteil

Strategies for hydrologic ensemble generation and calibration: On the merits of using model-based predictors

Keywords: Ensemble Prediction System, Global Sensitivity Analysis, Hydrologic Ensemble Forecast, Quantile Regression Forest, MORDOR-TS, Odet catchment

Introduction

In spite of the great efforts that have been put into land surface models coupled to hydrologic models, deterministic simulation and forecast of streamflow remains limited mostly due to the stochastic nature of precipitation and the complexity of meteorological and hydrologic processes. Thus an ensemble approach is favored; it provides a probabilistic hydrologic forecast needed by decision support systems dealing with risk-based stakes in real-time (low and high flow) as well as by water resources management actors (hydropower production, irrigation, navigation, tourism). Forcing hydraulic models with forecasted hydrologic inflow allows to extend forecast lead time at stations where security and production are at stake. Before use for application, the performance of the ensemble forecast should be assessed [START_REF] Jolliffe | Forecast verification: a practitioner's guide in atmospheric science[END_REF] in terms of reliability and resolution, with respect to observations. The reliability refers to the statistical consistency between the ensemble and the observations. The resolution describes the ability of the ensemble to discriminate situations leading or not to an event.

Hydrometeorological uncertainties

The objective of ensemble forecasts is to cover and represent the uncertainties existing in the prediction chain. Numerous and various sources of uncertainties along the hydrometeorological simulation chain lead to uncertainty in discharge simulation and forecast. Three main sources of hydrometeorological uncertainties are acknowledged in the literature [START_REF] Bourgin | Comment quantifier l'incertitude prédictive en modélisation hydrologique ? : Travail exploratoire sur un grand échantillon de bassins versants[END_REF][START_REF] Zappa | Superposition of three sources of uncertainties in operational flood forecasting chains[END_REF][START_REF] Thiboult | Accounting for three sources of uncertainty in ensemble hydrological forecasting[END_REF][START_REF] Demargne | The Science of NOAA's Operational Hydrologic Ensemble Forecast Service[END_REF]: atmospheric forcing observation and prediction, hydrologic model initial condition, hydrologic model structure and parameters. According to the classification proposed by [START_REF] Krzysztofowicz | Bayesian theory of probabilistic forecasting via deterministic hydrologic model[END_REF], atmospheric forcing is referred to as input uncertainty, whereas the other sources are referred to as hydrologic uncertainties.

On the one hand, input uncertainty, i.e meteorological uncertainty, can be accounted for by an Ensemble Prediction System (EPS), which accounts for uncertainties in initial conditions and model physics in Numerical Weather Prediction (NWP) models. The most straightforward technique to issue Hydrologic Ensemble Forecasts (HEF) is to use EPS as input for a hydrologic model, thus producing an ensemble of discharges. Numerous studies and operational applications have been conducted on this topic [START_REF] Cloke | Ensemble flood forecasting: A review[END_REF], [START_REF] Pappenberger | Hydrological Ensemble Prediction Systems Around the Globe[END_REF]). On the other hand, hydrologic uncertainty is also taken into account to issue HEF considering model parameters uncertainties [START_REF] Dietrich | Assessing uncertainties in flood forecasts for decision making: prototype of an operational flood management system integrating ensemble predictions[END_REF] or using a multi-model approach [START_REF] Hopson | A 1-10-Day Ensemble Forecasting Scheme for the Major River Basins of Bangladesh: Forecasting Severe Floods of 2003-07*[END_REF][START_REF] Velázquez | Can a multimodel approach improve hydrological ensemble forecasting? A study on 29 French catchments using 16 hydrological model structures[END_REF][START_REF] Thiboult | Accounting for three sources of uncertainty in ensemble hydrological forecasting[END_REF][START_REF] Bellier | Prévisions hydrologiques probabilistes dans un cadre multivarié: quels outils pour assurer fiabilité et cohérence spatio-temporelle?[END_REF]. Since 2004, research, operational and user communities gathered around the HEPEX initiative (Hydrologic Ensemble Prediction EXperiment, www.hepex.org), which aims at advancing the science and practice of hydrological ensemble prediction and demonstrating their utiliy in decision making [START_REF] Thielen | Aims, challenges and progress of the Hydrological Ensemble Prediction Experiment (HEPEX) following the third HEPEX workshop held in Stresa 27 to 29[END_REF][START_REF] Schaake | Summary of recommendations of the first workshop on Postprocessing and Downscaling Atmospheric Forecasts for Hydrologic Applications held at Météo-France[END_REF].

Uncertainty quantification for Hydrologic Ensemble Forecasts (HEF) generation

The performance of the raw hydrologic ensemble is linked to how the different sources of uncertainties are accounted for in the ensemble generation. The HEF system should be built taking into account major sources of uncertainties (both atmospheric and hydrologic) with associated ranges of uncertainty. To that end, identifying and ranking sources of uncertainty is necessary. Given assumptions on uncertain parameters, this can be achieved with a sensitivity analysis (SA).

A review of SA methods is available in [START_REF] Iooss | A Review on Global Sensitivity Analysis Methods[END_REF].

Global Sensitivity Analysis (GSA) (Saltelli, 2008) allows to quantify the contribution of model inputs to its outputs. It implies the integration of an ensemble of simulations from which sensitivity indices are computed; for instance Sobol indices based on variance-based methods [START_REF] Efron | The Jackknife Estimate of Variance[END_REF]. GSA is widely applied in hydrology. In [START_REF] Emery | Temporal Variance-Based Sensitivity Analysis of the River-Routing Component of the Large-Scale Hydrological Model ISBA-TRIP: Application on the Amazon Basin[END_REF], a GSA is achieved in order to highlight the key parameters impacting the river-routing scheme Total Runoff Integrating Pathways (TRIP) that simulates river water height and discharge on the Amazon catchment. [START_REF] Garambois | Characterization of process-oriented hydrologic model behavior with temporal sensitivity analysis for flash floods in Mediterranean catchments[END_REF] analyzed MARINE hydrologic model sensitivity during flash-floods. In [START_REF] Michon | Stratégie de calage du modèle hydrologique semi-distribué MORDOR-SD[END_REF], a GSA on the Kling-Gupta Efficiency (KGE, [START_REF] Gupta | Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling[END_REF]) of the MORDOR-TS hydrologic model was carried out on several French catchments.

Statistical calibration of ensembles

Ensemble approaches aim at representing the uncertainty along a simulation chain. However, the total uncertainty is rarely fully covered and raw EPS are known to be underdispersive and biased [START_REF] Hamill | Verification of Eta-RSM Short-Range Ensemble Forecasts[END_REF][START_REF] Schaake | Summary of recommendations of the first workshop on Postprocessing and Downscaling Atmospheric Forecasts for Hydrologic Applications held at Météo-France[END_REF]. A post-processing step on the ensemble precipitation forecast (post-processing with respect to meteorology, pre-processing with respect to hydrology) should thus be achieved before using them as input for rainfallrunoff models and issuing HEF. Similarly, HEF should be post-processed to account for uncertainty in EPS as well as in hydrologic model parameters. The improvement of EPSs' and HEFs' reliability and resolution relies on a statistical post-processing, named ensemble calibration.

Statistical ensemble calibration is an active field of research in meteorology and hydrology. It exploits the relation between the past previsions and their corresponding observations [START_REF] Wilks | Univariate ensemble post-processing[END_REF] to correct the forecast. Parametric and non-parametric calibration methods are reported in the literature. Parametric methods rely on an a priori assumption for the output data distribution which parameters are identified by the calibration algorithm. In contrast, nonparametric methods are data-based only. [START_REF] Wilks | Univariate ensemble post-processing[END_REF] describes the state of the art of statistical postprocessing of meteorological ensemble forecasts. A review of statistical ensemble calibration methods used in the field of hydrology is available in [START_REF] Li | A review on statistical postprocessing methods for hydrometeorological ensemble forecasting[END_REF].

Two widely used parametric methods are Ensemble Model Output Statistics (EMOS that is a regression method) [START_REF] Gneiting | Calibrated Probabilistic Forecasting Using Ensemble Model Output Statistics and Minimum CRPS Estimation[END_REF] and the Bayesian Model Averaging method (BMA that is an ensemble dressing method) [START_REF] Raftery | Using Bayesian Model Averaging to Calibrate Forecast Ensembles[END_REF]. Both EMOS and BMA provide the entire predictive distribution for the output variable. In the field of EPS calibration, EMOS technique was used in [START_REF] Taillardat | Calibrated Ensemble Forecasts Using Quantile Regression Forests and Ensemble Model Output Statistics[END_REF][START_REF] Taillardat | Forest-Based and Semiparametric Methods for the Postprocessing of Rainfall Ensemble Forecasting[END_REF]; [START_REF] Bellier | Prévisions hydrologiques probabilistes dans un cadre multivarié: quels outils pour assurer fiabilité et cohérence spatio-temporelle?[END_REF] for calibration of temperature and precipitation ensemble forecast. In the field of ensemble streamflow calibration, EMOS was used in [START_REF] Bellier | Prévisions hydrologiques probabilistes dans un cadre multivarié: quels outils pour assurer fiabilité et cohérence spatio-temporelle?[END_REF]; [START_REF] Hemri | Multivariate postprocessing techniques for probabilistic hydrological forecasting[END_REF], and BMA was used in [START_REF] Duan | Multi-model ensemble hydrologic prediction using Bayesian model averaging[END_REF].

Popular non-parametric methods are: rank histogram recalibration [START_REF] Hamill | Verification of Eta-RSM Short-Range Ensemble Forecasts[END_REF], quantile regression [START_REF] Bremnes | Probabilistic wind power forecasts using local quantile regression[END_REF], individual ensemblemember adjustments [START_REF] Van Schaeybroeck | Ensemble post-processing using member-by-member approaches: theoretical aspects[END_REF] or statistical learning methods, also called machine learning methods [START_REF] Hastie | The elements of statistical learning[END_REF].

While non-parametric methods require very large training data sets, they are flexible, data-adaptive, and adapted to non-linearities in the input-output relation [START_REF] Wilks | Univariate ensemble post-processing[END_REF]. The non-parametric Quantile Regression Forest (QRF) method proposed by [START_REF] Meinshausen | Quantile Regression Forests[END_REF] is a statistical learning approach. QRF provides an estimation of desired quantiles for the output data, but not the entire distribution, as opposed to EMOS or BMA.

Scope of the paper

The objective of this paper is the implementation and assessment of an HEF system for small to medium size catchments taking into account hydrologic model parameters' uncertainty. The first part of the study is dedicated to the analysis and classification of uncertainties in the distributed MORDOR-TS model [START_REF] Garçon | Prévision opérationnelle des apports de la Durance à Serre-Ponçon à l'aide du modèle MORDOR. Bilan de l'année 1994-1995[END_REF][START_REF] Garavaglia | Impact of model structure on flow simulation and hydrological realism: from a lumped to a semi-distributed approach[END_REF][START_REF] Rouhier | Impact of mesoscale spatial variability of climatic inputs and parameters on the hydrological response[END_REF] with GSA in order to identify the most significant sources of uncertainties to take into account into the ensemble generation. The GSA is carried out with respect to uncertainty in hydrologic model parameters and EPS using forecasted precipitation provided by Arome Ensemble Prediction System1 [START_REF] Seity | The AROME-France Convective-Scale Operational Model[END_REF][START_REF] Bouttier | Impact of Stochastic Physics in a Convection-Permitting Ensemble[END_REF][START_REF] Raynaud | Comparison of initial perturbation methods for ensemble prediction at convective scale[END_REF][START_REF] Bouttier | Sensitivity of the AROME ensemble to initial and surface perturbations during HyMeX[END_REF], when available.

The second part of the study is dedicated to the HEF generation and en-semble calibration. Different strategies are compared : a model-based approach where the raw ensemble comes from ensemble hydrologic simulation is implemented, then two approaches are implemented with QRF ensemble calibration method, with different predictors. The MORDOR-TS model [START_REF] Garçon | Prévision opérationnelle des apports de la Durance à Serre-Ponçon à l'aide du modèle MORDOR. Bilan de l'année 1994-1995[END_REF][START_REF] Garavaglia | Impact of model structure on flow simulation and hydrological realism: from a lumped to a semi-distributed approach[END_REF][START_REF] Rouhier | Impact of mesoscale spatial variability of climatic inputs and parameters on the hydrological response[END_REF] dedicated to water resource management is implemented on each sub-catchment of the Odet catchment. MORDOR-TS is a spatialized and continuous conceptual rainfall-runoff hydrologic model that connects the mesh cells according to the hydrographic network. At each time step, the production is calculated for each cell and then routed to simulation points on the mesh. The structure of the production module is presented in Fig. 3 and MORDOR-TS's hydrologic parameters are described in Tab. 2. The production module takes spatially distributed precipitation (P) and temperature (T) as input data and adjusts the water balance through two coefficients c p and k min . This latter parameter is involved in the calculation of the actual evapostranspiration AET .

The production module is then composed of six conceptual reservoirs; two for ice and snow (not active here), and four others: a superficial reservoir U of capacity U max , an intermediate reservoir L of capacity L max of which filling level is driven by the parameter ev L , an evaporating reservoir Z of capacity Z max and a deep reservoir N of which filling level is driven by the parameter lk N . Three fluxes components are transfered from the production module to the routing module: area runoff Q s , subarea runoff Q v and base runoff Q b . The parameter k r determines the ratio of the water feeding reservoir N and the subarea runoff.

The routing module propagates the water production of each cell into the hydrographic network. The transfer function is based on the 1D diffusive wave model, with celerity Cel and diffusion Dif f coefficients independent from the runoff [START_REF] Hayami | On The Propagation Of Flood Waves[END_REF]. � Rain data: The ANTILOPE rainfall product is a combination of radar and gauge rainfall data from Météo-France [START_REF] Champeaux | Les mesures de précipitations et l'estimation des lames d'eau à Météo-France : état de l'art et perspectives[END_REF]. The grid resolution is 1 km.

� Temperature data: Surface temperature is extracted from SAFRAN reanalysis [START_REF] Vidal | A 50-year high-resolution atmospheric reanalysis over France with the Safran system[END_REF]. The grid resolution is 8 km.

Forecasted data

AromeEPS-RR1 ensemble rain forecast product is used to describe uncertainty in rainfall for the GSA. As this product is available over a limited period only, the deterministic Expert-RR3 rain forecast product is used by debault, in particular for the generation and the ensemble-calibration of the HEF.

AromeEPS-RR1. AromeEPS-RR1 uses the regional atmospheric model AROME described in [START_REF] Seity | The AROME-France Convective-Scale Operational Model[END_REF] with ensemble perturbations documented in [START_REF] Bouttier | Impact of Stochastic Physics in a Convection-Permitting Ensemble[END_REF]; [START_REF] Raynaud | Comparison of initial perturbation methods for ensemble prediction at convective scale[END_REF]; [START_REF] Bouttier | Sensitivity of the AROME ensemble to initial and surface perturbations during HyMeX[END_REF], accounting for uncertainties in initial conditions, boundary conditions, surface conditions and the model physics. Its large scale boundary conditions are provided by the global PEARP ensemble [START_REF] Descamps | PEARP, the Météo-France short-range ensemble prediction system[END_REF]. AromeEPS-RR1

ensemble is composed of 12 equiprobable members and covers a 1800x1700km

2 Western European domain that encompasses the Odet catchment with a horizontal grid at 2.5 km resolution. AromeEPS-RR1 is operational since the end of 2016. A limited period of 112 days in early 2016 was made available a posteriori for this study in order to cover former rain events on the Odet catchment.

It provides a daily forecast at 21:00 UTC, with hourly output over a 45-hour forecast range.

Expert-RR3. Expert-RR3 3 is a 3-hours deterministic rainfall accumulation forecast specified by human experts on the basis of numerical forecasts from atmospheric models, with a 72 hours forecast range. These data are used operationally for flood forecasting in the French governmental services and available over 2011-2014 for this study.

3 RR3 provide a forecast of 3-hour rainfall cumul, with a maximum lead-time of 72 hours, updated every 15 minutes 3. Methods

Global Sensitivity Analysis (GSA)

In the present study, the GSA stands in the computation of Sobol' indices [START_REF] Sobol | Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[END_REF], with the assumption that the input aleatory variables are independant. Sobol' indices apportion the variance of the output Y = f (X) with

X = (X 1 , X 2 , ..., X k )
, to the variation of different inputs X 1 , ..., X k on their uncertainty domain. With the assumption that the variance of Y is finite and the input variables are independant, the Hoeffing decomposition [START_REF] Hoeffding | A Class of Statistics with Asymptotically Normal Distribution[END_REF] leads to the definition of the Sobol'indices :

1 = � i S i + � i � j>i S i,j + ... + S 1,2,3,...,k (1)
where

� S i = Vi V (Y ) is the first order Sobol index of X i and represents the normal- ized elementary contribution of X i to V(Y), � S i,j = Vi,j V (Y )
is the second order Sobol index of X i and X j and represent the normalized contribution due to interactions between X i et X j to V(Y), and so on.

The total Sobol' index S Ti , gathering all contributions related to X i is then defined as

S Ti = S i + � j� =i S i,j + � j� =i,k� =i,j<k S i,j,k + ... + S 1,2,3,...,k = � l∈�i S l (2)
where �i are all the subsets of {1, ..., k} including i.

Sobol' indices thus measure the influence of the different independant imputs X 1 , X 2 , ..., X k and their interactions on the output Y = f (X). The more sensitive the model response is to an input parameter, the larger its associated Sobol index. Usually only first and total Sobol indices are computed. The first order indices are useful for factor prioritization (FP) and provides the parameter(s) that most significantly control(s) the most the output variance, whereas the total order indices are hepfull in factor fixing (FF), to determine which parameters can be fixed without consequences on the output (Saltelli, 2008). In practice, the estimation of Sobol' indices is generally achieved with a stochastic estimation using an ensemble of model output realizations [START_REF] Saltelli | How to avoid a perfunctory sensitivity analysis[END_REF]. The computation of Sobol' indices is here achieved using the python modules OpenTURNS (http://openturns.org/) and OT-Batman (T. Roy et al., 2018).

Quantile Regression Forest (QRF)

Non parametric regression with QRF method. The Quantile Regression Forest (QRF) method [START_REF] Meinshausen | Quantile Regression Forests[END_REF]) technique is detailed in Zamo et al.

(2014); [START_REF] Taillardat | Forest-Based and Semiparametric Methods for the Postprocessing of Rainfall Ensemble Forecasting[END_REF]. The principle of the method is the aggregation of meteorological or hydrological situations according to their forecasts, with the assumption that close forecasts predictors lead to close observations. In that way, this method can be linked to the analog method [START_REF] Hamill | Probabilistic Quantitative Precipitation Forecasts Based on Reforecast Analogs: Theory and Application[END_REF][START_REF] Zalachori | Statistical processing of forecasts for hydrological ensemble prediction: a com-60 parative study of different bias correction strategies[END_REF][START_REF] Delle Monache | Probabilistic Weather Prediction with an Analog Ensemble[END_REF]. QRF is a non-parameric and non-linear regression, which consists in building random forests from binary decision trees given a set of predictors [START_REF] Breiman | Random Forests[END_REF]. Contrary to random forests that approximate the conditional mean, QRF estimates the full conditional distribution of the response variable.

Chosing the predictors. A wide range of predictors are available for the QRF method. They can obviously stem from the ensemble forecast : statistics (ensemble mean, variance or percentiles) of the variable to calibrate or other variables within the ensemble, as well as other characteristics of the forecast, such as the time or day (providing a modality instead of a value). Predictors can also be described from real observation of the forecasted variable. The choice of the predictors represents a key element in the implementation of the QRF calibration method. In the following, a learning sample is formed by chosing a set of predictors and picking the associated observations.

Building a binary decision tree. A binary decision tree is built by iteratively splitting the learning sample into two groups. For a quantitative predictor, the split is done according to a threshold, while for a qualitative predictor, the split is done according to the modality. The predictor and the splitting criteria are chosen to minimize the variability of the associated observations in the resulting two groups. Each resulting group is then itself split in two following the same algorithm, until a stopping criterion is reached (for example a minimum number of data in the sub-groups, or an insufficient decrease of variance). Each final group is called leaf and contains a set of observations, also called predictand.

The splitting algorithm is illustrated in Fig. 4 with two predictors p1 and p2 ranging between 0 to 1. In this example, the tree has three leaves with associated observations (rain or discharge for our purpose). Building a forest. [START_REF] Breiman | Bagging predictors[END_REF] proposes to improve the robustness of the prediction issued from a decision tree by selecting different learning samples to build several trees and form a forest. Since this approach would require a large amount of data, usually not available in practice, bootstrap sampling is often used. Randomly choosing a subset of predictors for each split of each tree, as suggested by [START_REF] Breiman | Random Forests[END_REF], enhances the independence of the trees and consequently forms a random forest. [START_REF] Matheson | Scoring Rules for Continuous Probability Distributions[END_REF], [START_REF] Hersbach | Decomposition of the Continuous Ranked Probability Score for Ensemble Prediction Systems[END_REF], [START_REF] Gneiting | Strictly Proper Scoring Rules, Prediction, and Estimation[END_REF]) assesses reliability and resolution simultaneously.

It is negatively oriented: the lower the better. The Rank Histogram [START_REF] Talagrand | Evaluation of probabilistic prediction systems[END_REF], [START_REF] Hamill | Verification of Eta-RSM Short-Range Ensemble Forecasts[END_REF], [START_REF] Anderson | A Method for Producing and Evaluating Probabilistic Forecasts from Ensemble Model Integrations[END_REF]) is useful to assess reliability only. A reliable ensemble implies that each rank is filled with the same probability, so the rank histogram is flat.

�.� 2 = � � � � K+1 � i=1 (f i - 1 K + 1 ) 2 (3)
where f i represents the frequency of observations in the ith rank. For a perfectly 311 reliable ensemble system, �.� 2 is equal to zero. The second part of the study is dedicated to the HEF generation and calibration over a three-year (2011-2014) period over which there was significant hydrological events. Only uncertainty in hydrologic parameters is considered since the AromeEPS-RR1 product is not available over this period. The raw HEF ensemble is then calibrated with the QRF method. � The GSA-hydro is carried out over two periods. It requires the integration of an ensemble of hydrology simulations over the period P GSA-hydro that is either P GSA-Arome or a sub period of P HEF (12/23/2013-12/26/2013).

The deterministic atmospheric forcing is provided by ANTILOPE for both periods.

� The raw HEF generation is achieved using atmopsheric forcing from the Météo-France Expert-RR3 deterministic forecast (as AromeEPS-RR1 is not available) over P HEF (09/01/2011-06/01/2014). HEF ensemble streamflows are calibrated with QRF against Banque Hydro streamflow observations, using ANTILOPE observations, Expert-RR3 rain forecast and Banque Hydro streamflow observations as predictors.

In both GSAs and HEF, hydrology simulations start from a spin-up forced by ANTILOPE and SAFRAN observed data.

GSAs for MORDOR-TS model

The GSA-Arome and GSA-hydro for streamflow on the Odet catchment are carried out with respect to the forecasted runoff at the outlet of each of the subcatchments Tréodet, Kerjean and Ty-Planche. Both GSA take into account uncertainties that relate to a set of 10 parameters for MORDOR-TS (Sect. 4.2.1). GSA-Arome (Sect. 4.2.2) is performed for each lead-time with a cycled procedure and takes also into account uncertainties that relate to rain forcing, considering an integer that represents the index within the 12-member

P HEF Observed data rainfall ANTILOPE X X X X temperature SAFRAN X X X streamflow BanqueHydro X Forecasted data rainfall AromeEPS-RR1 X X rainfall Expert-RR3 X
calibrated AromeEPS-RR1 ensemble, drawn from a uniform distribution U [START_REF] Li | A review on statistical postprocessing methods for hydrometeorological ensemble forecasting[END_REF]12] .

In , ANTILOPE deterministic rain is used to force all model runs within the ensemble while hydrologic parameters vary.

Hydrologic parameters' distributions

The 10 MORDOR-TS parameters are drawn from uniform distributions with For each subcatchment, the predictors are the percentiles 10, 50 and 90 of the raw AromeEPS-RR1 hourly rainfall, surface humidity, surface temperature and the moment of the day of the lead-time (morning, afternoon, evening, night).

V
The evaluation of the calibration is achieved with a leave-one out method: each element of the training sample is alternatively used for validation, while the other are used for learning. This AromeEPS-RR1 calibration strategy relies on the fact that the error in rainfall intensity is homogeneous over a small catchment, and that it only depends on the moment of the day. The loss of predictability as the lead time increases is assumed to be negligible. It is also assumed that the rainfall intensity data are non correlated over time. This assumption would not be valid for temperature or streamflow. For rainfall, a 6h correlation is suspected and could be taken into account to improve the robustness of the calibration, especially if used to calibrate new data.

GSA-Arome. The GSA-Arome study is carried out in an operational framework with hourly updated AromeEPS-RR1 forecast. For that purpose, the ensemble is built as shown in Fig. 6(a) over a spin-up, a re-analysis and a forecast period.

GSA-hydro implementation

The GSA-hydro study uses the observed rainfall ANTILOPE as input for every member, thus the notion of lead-time is no longer relevant. Each member is initiated with a 1-year spin-up, then integrated over P GSA-hydro using its associated set of hydrologic parameters as illustrated in Fig. 7. To ensure the convergence of the Sobol' indices estimation, the GSA-hydro Sobol indices are computed hourly over 154000 MORDOR-TS simulations.

Generation and ensemble-calibration of the HEF

It was not possible to apply the QRF calibration on the ensemble of streamflows from the MORDOR-TS simulations that were used for the GSA-Arome over P GSA-Arome . Indeed, this period is too short, the learning sample for the QRF method is thus too small, especially given that it should be further reduced to account for temporal correlation of streamflow. Another ensemble was thus generated, over a longer period P HEF (2011-2014) over which significant hydrological events occured, but without considering uncertainty related to the rainfall since the AromeEPS-RR1 product was not available over this period.

Expert-RR3 deterministic forecast rain was used to generate the raw HEF. The HEF generation and calibration is achieved with a hydrologic ensemble of 99 members. The raw HEF is generated in an operational framework with hourly updated RR3 forecast. For that purpose, the ensemble is built as shown in Fig. 8(a), similarly to that for GSA-Arome over a spin-up, a re-analysis and a forecast period, except that the deterministic forecast Expert-RR3 is used in place of AromeEPS-RR1. This is cycled hourly as the RR3 forecast rain product is updated several times per hour. Only the predominant parameters that were previously identified by the GSA are taken into account for the ensemble generation of raw HEF. The forecasts are calibrated and evaluated against observations over 27 months, from October 2011 to June 2014, excluding summer months (July, August and September). A cross-validation method is used: each month of the calibration period is alternatively used for validation, while the 26 other months are used for learning. It should be noted that data over a 10-day period before and after the validation month was removed from the learning sample to avoid auto-correlation between learning and validation data. the QRF method use no information from the hydrologic simulations. Strictly speaking, this is not a calibration strategy as the raw ensemble is not used;

QRF is used to generate calibrated quantiles of an observed variable. This leads to the ensemble denoted as QRF-nothydro quantiles. In the combined model-observation approach, predictors for QRF calibration uses the mean and standard deviation of the raw ensemble. The resulting ensemble is denoted as QRF-hydro quantiles. After applying the Ensemble Copula Coupling (ECC) method to reorder the calibrated QRF-hydro quantiles, the Trajectory Smoothing (TS) procedure was finally applied, leading to QRF-hydro-TS ensemble.

The impact of smoothing the reconstructed hydrologic time-series from QRF quantiles is here investigated in the prospect of using the hydrologic ensemble as input for hydraulic simulation. It should be noted that the ECC method can not be applied on QRF-nothydro quantiles, since it requires the availability of the raw ensemble as dependence template. (N b = 24 hours -lead-time)

F rain mm forecasted rain over the catchment between X X the current time and the lead-time volume and peak flow [START_REF] Hemri | Multivariate postprocessing techniques for probabilistic hydrological forecasting[END_REF]. Following conclusions from Bellier et al. ( 2017) and [START_REF] Gneiting | Comparing Density Forecasts Using Thresholdand Quantile-Weighted Scoring Rules[END_REF], the HEF is assessed with a forecast-based stratification for CRPS and RH computation, focusing on the (f orecast, observation) pairs for which the maximum of the ensemble is beyond the 90 th percentile of the associated observation (hourly, cumulated or maximum measured streamflow), computed for heavy rainfall. is thus mostly dominated by c p and rain that both control the water balance of the model. Rainfall mostly matters for lead-times that are greater than the concentration time of the catchment. This implies that the construction of HEF for short lead times can be achieved only taking into account uncertainties that relate to hydrology. To a lesser extent, at the beginning of the event, the streamflow is influenced by the capacity of the reservoir L max (red curve) that directly feeds the runoff. The importance of L max decreases before the end of the event; indeed, when the reservoir is full, the overflow directly feeds the runoff and its capacity no longer has impact on the simulated streamflow. For 6-hour lead-time, the wave celerity Cel (dark purple curve) has noticeable importance when the streamflow gradient is strong (both in increase and decrease phases).

Results

5

The runoff coefficient k r (light orange curve) has noticeable importance at the peak of the event (and beyond). Indeed, when reservoir Z is full, part of the excess amount of water k r × out Z directly feeds the runoff. Finally, simulated streamflow is not sensitive to the two parameters k min and Dif f over the three For the 2016 event, GSA-hydro (Fig. 12(a)) and GSA-Arome (Fig. 11(a)) at short lead time, for which uncertainty in rainfall is not significant, show similar results. This allows to rely on GSA analysis when rainfall uncertainty is neglected for HEF construction at short forecast lead time. Moreover, GSAhydro over P GSA-Arome (Fig. 12(a)) and P HEF (Fig. 12(b)) show similar results since these two events correspond to similar weather conditions. This allows to further the study with HEF construction over P HEF . Finally, as previously stated over the three catchments, the two parameters k min and Dif f have very low Sobol' indices meaning that these two parameters have thus no impact on the simulated runoff. These parameters were thus fixed to their hydrologic calibration value for HEF generation in the following while the other parameters are drawn from uniform distribution described in Tab. 4.

Calibration of the HEF

Ensemble reliability and resolution are assessed with univariate and global RH and CRPS metrics computed over streamflow. Fig. 13 shows rank his- The raw ensemble is biased and underdispersive over all three catchments, tors are used for the three catchments. For the three catchments, the CRPS computed for maximum streamflow is minimized when trajectory smoothing is applied. To conclude, ensemble calibration with hydrology related predictors globally improves reliability and CRPS values for both maximum and cumulated streamflow and TS procedure brings a slight additional improvement for the maximum streamflow.

����� ����� ����� ����� ����� ���� ��� ��� ��� ��� ��� ��� ��� � � � � � � � � � � � � � � �� �� �� �� �� �� �� �� � � � � � � � � � � � � (

Importance of the QRF predictors

The a priori choice of the predictors is a key element in the QRF calibration.

The a posteriori usefulness of the predictors is assessed as the loss in the meansquared error of the whole forest if the predictor is randomly permuted without replacement: the values of the given predictor is a random sample of the original values. The predictor is of great (little) importance if the mean-squared error does (not) significantly increase when the predictor is randomly permuted. the lead-time exceeds the catchment concentration time (about 15 hours for Tréodet), the cumulated forecasted rain since the beginning of the run F rain , is the most important predictor, before Q 0 . It also predominates the impact of the measured rain M rain , meaning that the measured rainfall before the run has less importance than forecasted rainfall between the current time and the lead-time.

For the short and long lead-times, the raw ensemble mean and the standard deviation (M ean and Sigma) have moderate influence (with a sligth predominance of M ean over Sigma). This is consistent with the fact that the QRFnothydro ensemble, which has not been built with these predictors, presents comparatively less favourable performances than the QRF-hydro ensemble. It should finally be noted that the importance of the different predictors tend to homogenise as the lead-time increases, and the interquartile range tends to decrease.

Discussion and perspectives

In this study, the hydrometeorological chain was investigated with an ensemble approach at a catchment scale, with the aim of issuing a statistically This strategy paves the way for an operational HEF system. A straightforward perspective is to apply this study over a period for which AromeEPS-RR1 is available, hydrological events occured, and that is long enough for QRF calibration to be applied on streamflows. This would allow to fully consider sources of uncertainty, especially those that relate to precipitation. Taking into account a larger variation of the corrective rain factor in MORDOR-TS jointly to using EPS could also be considered. This methodology could a priori be applied and assessed to other catchments for consistency check. The choice of predictors may be catchment dependant. For instance, the predictors M rain and F rain are closely related to the concentration time of the catchment: the period (in hours) over which the mean of measured or forecasted rain is computed may be adjusted, hence reduced for catchments that are subject to flash floods. The predictor Month may also be more significant as it allows to discriminate autumn flash floods from other events.

Finally, the hydrometeorological simulation chain could be extended to hydraulics, using forecasted calibrated streamflows as inputs to a hydraulic model to provide Hydraulics Ensemble Forecast. GSA on discretized water level and discharge in the river would be carried out with respect to rain-, hydrology-and hydraulic-related sources of uncertainty, now also considering uncertain friction and river bathymetry. Major sources uncertainties in the meteo-hydro-hydraulic chain could then be corrected in real time with assimilation of observed water level relying on the multi-physics ensemble simulation system.

Figure 1

 1 Figure 1 summarizes the general process flow of the study. The two main objectives of the study correspond to the grey boxes.

Figure 1 :

 1 Figure 1: General process flow of the study.

Figure 2 :

 2 Figure 2: Odet catchment

Figure 3 :

 3 Figure 3: Structure of the MORDOR-TS model over the Odet catchment. Adapted from Rouhier et al. (2017)

Figure 4 :

 4 Figure 4: Illustration of binary decision tree with 2 predictors p1 and p2.

1 .

 1 General ensemble workflowThe first part of the study consists in a Global Sensitivity Analysis (GSA) applied to the distributed MORDOR-TS model, taking into account (i) uncertainties in rainfall and hydrologic model parameters (GSA-Arome), or(ii) only uncertainty in hydrologic model parameters (GSA-hydro). This last GSA without uncertainty in rainfall aims at assessing the consistency of the results when a deterministic rainfall (ANTILOPE) is taken into account in place of an EPS (AromeEPS-RR1). The implementations of the two GSAs are described in Sect. 4.2. It should be noted that the use of AromeEPS-RR1 for GSA-Arome is preceded by a QRF ensemble-calibration step. These two GSAs studies validate the methodology used for HEF generation in the second part of the study: hypothesis on the choice of uncertain variables, associated statistical distributions and related hyper parameters.

Figure 5 :

 5 Figure 5: Configurations for GSA-Arome, GSA-hydro and raw HEF

  min and V max extreme values, shown in Tab 4 and determined from a set of 2-year of hydrologic calibrations. The lower bound (respectively upper bound) of the uniform distribution is chosen as the minimum (respectively maximum) of the values reached in the different hydrologic calibrations (Sect. 2.1.2).

  Each ensemble member is associated to a realisation of the set of hydrologic parameters and of AromeEPS-RR1. Each hydrologic simulation is run over a 1-year spin-up and a 1-hour re-analysis with ANTILOPE rainfall, then run over a 45-hour forecast AromeEPS-RR1 rainfall. This is cycled hourly as the rain product is updated hourly. The GSA-Arome indices are computed hourly for the 45 lead times over the N cycled simulations (Fig.6(b)). Here, to ensure the convergence of the Sobol' indices estimation, the GSA-Arome study is achieved with an ensemble of 192000 MORDOR-TS simulations.

Figure 7 :

 7 Figure 6: Cycled runs for GSA-Arome

Figure 8 :

 8 Figure 8: Cycled runs for HEF

Figure 9 :

 9 Figure 9: Strategies for Hydrologic Ensemble Forecast generation. Data used for hydrologic model integration as well as QRF predictors are shown. The resulting four HEFs or ensemble of quantiles are indicated in colored boxes.

. 1 .

 1 GSAs for MORDOR-TS model 5.1.1. Calibration of AromeEPS-RR1 As shown in Fig. 10, ensemble calibration improves AromeEPS-RR1 with smaller mean CRPS value and flatter rank histograms than that of the raw ensemble (0.119 and 0.1351 respectively for the CRPS). The �.� 2 norm for the QRF rank histogram (1.11 * 10 -2 ) is smaller than that of the raw ensemble (3.58 * 10 -2 ). The calibrated AromeEPS-RR1 data are thus more consistent with observations than before calibration, and thus can be used as input of GSA-Arome.

Figure 10 :(

 10 Figure 10: Rank histogram and CRPS for the raw and calibrated AromeEPS-RR1 ensemble.

  The streamflow probability density functions represented over time for GSA-Arome are displayed in 11(b) and 11(d) for 6-hour and 21-hour lead times respectively, with time on the x-axis. The observed discharge is plotted in blue, the determinisitic reference simulation with parameters issued from the hydrologic calibration presented in Section 2.1.2 is plotted in red and the MORDOR-TS ensemble mean and mean plus or minus standard deviation are plotted in black (solid and dotted lines). The reference simulation clearly underestimates the flood peak (except for the Kerjean catchment). The ensemble probability density function underestimates the flood peak since the measured streamflow is closer to the upper dotted black line in Fig. 11 (ensemble mean + standard deviation) than to the mean curve; neither the perturbation of the hydrologic model parameters nor that of the rain scenario allows to overcome this effect. 5.1.3. Consistency between GSA-Arome and GSA-hydro results GSA-hydro was carried out over the subperiod of P GSA-Arome (01/26/2016-01/30/2016) and over a subperiod of P HEF (12/23/2013-12/26/2013) and associated Sobol' indices are shown in Fig. 12 at Tréodet. Results at Kerjean and Ty-Planche can be found in Fig. 19 and 20 as supplementary material in section 7.

Figure 12 :

 12 Figure 12: First order Sobol' indices without uncertainty on rain input for the events 01/26/2016-01/30/2016 (12(a)) and 12/23/2013-12/26/2013 (12(b)) at Tréodet catchment

  Figure 13: Rank histograms for raw HEF, QRF-hydro quantiles, QRF-nothydro quantiles and QRF-hydro-TS HEF for 6-hours and 21-hours lead-times for Treodet. The associated CRPS is given at the top of the panel.

Figure 14 :

 14 Figure 14: Time-varying CRPS for raw HEF, QRF-hydro quantiles, QRF-nothydro quantiles and QRF-hydro-TS HEF over lead-time for Tréodet, Kerjean and Ty-Planche.

Fig. 16

 16 Fig.16displays the log-importance of the QRF-hydro predictors for 2-hour and 16-hour lead-times for Tréodet. Since the QRF calibration is achieved with a cross-validation approach, a forest is built for each of the 27 months of P HEF , and the importance of each predictor is thus computed over each of the 27 forests. For short lead-times, the most important predictor is the measured streamflow Q 0 ; that is consistent with the fact that hourly streamflows are strongly correlated in time. The second most important predictor is the gradient of the measured streamflow GradQ 0 that accounts for the flow dynamics. When the lead-time increases, rain-related predictors become predominant. When

Figure 16 :

 16 Figure 16: Log-importance of QRF-hydro predictors for the 2-hour and 16-hour lead-times at Tréodet. The box-plot is built for the measure of importance over 27 forests. The box extends from the lower to upper quartile values of the data, with a line at the median. The whiskers extend from the box to show the range of the data.

coherent

  Hydrological Ensemble Forecast (HEF) for up to 24 hours for the Odet cathment in France. The predominance of uncertainty sources is assessed with a global sensitivity analysis, first taking into account uncertainty in rain using AromeEPS-RR1, then only focusing on hydrological parameters from MORDOR-TS model. Predominant parameters were identified and taken into account in the HEF generation.Because of the lack of AromeEPS-RR1 availability, the HEF is generated without taking into account uncertainty in rain forecast. However, it should be pointed out that for smaller lead-times than the concentration time of the catchments, the conclusions of this study are expected to be similar, as demonstrated by the comparative GSA without uncertainty in rainfall: the Sobol index associated to the rain is negligible at 6-hour lead-time. It was shown that the raw hydrological ensemble is underdispersive and underestimates observed streamflows, especially large values. The model-based-only approach is thus not sufficient to generate well-calibrated ensembles. The QRF calibration strategy is also applied for quantiles generation, with two different approaches: an observation-based-only approach, where the hydrologic model is not used and a combined model-observation approach where both observed and simulated information from the raw ensemble are used as predictors. The merits of the QRF calibration are assessed with reliability and resolution metrics computed for time-varying, cumulated and maximal streamflow. This article demonstrates, on the Odet catchment, that forest-based techniques, often used for the calibration of EPS, are also suitable for hydrologic ensemble calibration. QRF calibration provides an improvement of the reliability and CRPS values over the three studied sub-catchments. It was shown that better forecast skills are obtained when hydrology-related predictors are used. This highlights that the choice of the predictors is of great importance for the QRF calibration strategy to be successful. Moreover, it also shows that statistically learning from observation fails to substitute for solving partial derivative equations when it comes to representing and forecasting the dynamics of the catchment. It should also be kept in mind that the reconstruction step following QRF-calibration requires the availability of the raw HEF in the Ensemble Copula Coupling method. The reconstructed HEF should finally be smoothed out before use as input for a hydraulic simulation with a hydrometeorological chain. The reliability of the smoothed ensemble is slightly deteriorated for hourly streamflow, but CRPS and global skills are mainly improved.

  Figure 17: First order Sobol' indices and associated hydrographs for the event between 01/26/2016 and 01/30/2016 at Kerjean catchment for GSA-Arome. A vertical section of Fig(b) and Fig(d) displays the probability density function at the given date, according to the legend shown in (f). The results are shown for 6-hour ((a) and (b)) and 21-hour ((c) and (d)) lead-times.

7. 3 .

 3 Figure 23: Rank histograms for the cumulated and the maximum streamflows over the 24 hours lead-time for the four ensembles for Kerjean catchment. The associated CRPS is given at the top of the panel.

Table 1 :

 1 Characteristics of the Tréodet, Kerjean, Ty-Planche sub-catchments

	Sub-catchment	Tréodet Kerjean	Ty-Planche
	Elevation of the source	175 m	200 m	100 m
	Total river length (km)	37	21	23
	Catchment area (km 2 )	205	107	179
	Mean flow (m 3 /s)	4.8	2.27	3.79
	10-year flow (m 3 /s)	55	19	39
	50-year flow (m 3 /s)	75	25	53
	Highest flow recorded 12-2000 (m 3 /s)	110	46.6	81
	Second highest flow recorded 12-2013 (m 3 /s)	91.5	17.6	42.7
	Mean rainfall (mm/yr)	743	672	671
	2.1.2. The MORDOR-TS distributed conceptual rainfall-runoff model

Table 2 :

 2 Description of the parameters of MORDOR-TS hydrologic model

	Parameter	Unit	Description	Module
	cp	-	Precipitation multiplicative correction factor	Water balance
	k min	-	Maximum seasonal crop coefficient
	Umax	mm	Maximum capacity of the root zone U	Runoff production
	Lmax	mm	Maximum capacity of the hillslope zone L
	ev L	-	Outflow exponent of storage L
	Zmax	mm	Maximum capacity of the capillarity storage Z
	kr	-	Runoff coefficient
	lk N	mm.h -1	Outflow coefficient of storage N
	Cel	m.s -1	Wave celerity	Routing module
	Dif f	m 2 .s -1	Wave diffusion
	The hydrologic calibration 2 of the 10 previously described parameters of
	MORDOR-TS (Tab. 2) is achieved after a one-year spinup, using Banque Hy-
	dro streamflow observations, ANTILOPE rainfall and SAFRAN surface tem-
	perature forcing described in Sect. 2.2. The hydrologic calibration is carried out
	with respect to a multi-objective function using the caRamel genetic algorithm
	(Le Moine et al., 2015; Monteil et al., 2019). The multi-objective function gath-
	ers three scores : (i) Nash-Sutcliffe Efficiency (NSE, Nash and Sutcliffe (1970))
	over the entire time serie, (ii) NSE over the inter-annual daily regime and (iii)
	NSE over the empirical cumulative distribution.
	The hydrologic calibration is first achieved over a 6-year period (01/01/2007-
	12/31/2013) and validated over the period 01/01/2014-05/31/2017. Over the
	validation period, scores values are of the same order of magnitude as over the
	calibration period, which validates the hydrologic calibration. In the following,
	the deterministic simulation with calibrated hydrologic parameters is referred to

  How to use QRF to calibrate a new ensemble forecast ?. In operational mode, when a new ensemble forecast is available for calibration, its associated predictors are computed and run through each tree of the previously constructed forest. The terminal leaf predictand values are used to estimate the predictive CDF and quantiles of the calibrated forecast.Merits and limitation of the QRF method. It should be noted that no a priori assumption is made on the distribution of the variable to calibrate neither before nor after calibration. Also, since the terminal leaves are composed of observa-

	Ensemble evaluation metrics. Various tools are available to evaluate proba-
	bilistic forecasts and are well described in the literature. In this study, two
	widely used verification measures for ensemble forecast are used. The Continu-
	ous Ranked Probability Score

tions, the ensemble calibration is bound to output physically consistent values (for example, no negative amount of precipitation). The associated drawback is that by construction, the predicted CDF is unable to predict values outside of the observation range within the learning sample. This may be limiting when dealing with extreme values but may be overcome when working with anomalies or fitting a parametric function to the CDF

[START_REF] Taillardat | Forest-Based and Semiparametric Methods for the Postprocessing of Rainfall Ensemble Forecasting[END_REF]

. It should finally be noted that one of the main drawback of QRF method stands in the need of a large data set.

Reconstuction of the calibrated members. In the following, the Ensemble Copula Coupling (ECC,

[START_REF] Schefzik | Uncertainty Quantification in Complex Simulation Models Using Ensemble Copula Coupling[END_REF]

) method is used to reorder the postprocessed quantiles to recreate time-series, but this method yields unrealistic jumps when applied to HEF streamflows. The Trajectory Smoothing (TS) procedure proposed by

[START_REF] Bellier | Prévisions hydrologiques probabilistes dans un cadre multivarié: quels outils pour assurer fiabilité et cohérence spatio-temporelle?[END_REF]

was thus applied to preserve temporal correlation consistency, in the perspective of using the ensemble of reconstructed streamflow time series as forcing to hydraulic ensemble simulations. It should be noted that, as opposed to Ensemble Copula Coupling, the Trajectory Smoothing procedure modifies the post-processed ensemble.

Table 3 :

 3 Data for the GSA and QRF calibration of rainfall and streamflow

	QRF	QRF

Table 4 :

 4 Extreme values for MORDOR-TS model parameters' uniform PDFs AromeEPS-RR1 ensemble is calibrated with the QRF method before its use in GSA-Arome. In order to increase the volume of data available for AromeEPS-RR1 ensemble calibration over the limited period P GSA-Arome in 2016, the calibration is carried out without discriminating the lead-times. The ensemble gathers all AROME cells within a subcatchment (63, 36 and 51 for Tréodet, Kerjean and Ty-Planche respectively); thus forming a new ensemble with (12*number of cells) members. The size of the learning sample is 45 (lead-times) ×112 (days). The ensemble is calibrated against the ANTILOPE observations, averaged over the whole subcatchment.

	Paramètre	Tréodet	Tréodet	Kerjean	Kerjean	Ty-Planche	Ty-Planche
		min	max	min	max	min	max
	cp (-)	0.98	1.21	0.97	1.13	0.99	1.18
	k min (-)	0.18	1.11	0.14	1.03	0.32	0.79
	Umax (mm)	75	196	30	111	39	116
	Lmax (mm)	64	153	30	493	74	298
	ev L (-)	3.95	4.00	1.50	3.98	3.38	4.00
	Zmax (mm)	47	138	77	256	72	482
	kr (-)	0.10	0.28	0.10	0.41	0.10	0.30
	lk N (mm.h -1 )	-5.8	-5.2	-6.2	-5.5	-5.7	-5.4
	Cel (km.h -1 )	0.44	0.56	0.45	1.10	0.50	0.55
	Dif f (km 2 .h -1 )	1	659	1	5000	329	731

Table 5 :

 5 Choice of predictors for QRF-hydro and QRF-nothydro HEF calibration strategies.

	Name	Unit	Description	QRF-hydro	QRF-nothydro
	Mean	m 3 /s	mean of raw ensemble streamflows	X
	Sigma	m 3 /s	standard deviation of raw ensemble streamflows	X
	Month		month of the validation time	X	X
	Period		period of validation time (0 am -6 am, 6 am -12 am,	X	X
			0 pm -6 pm, 6 pm -12 pm)
	Q 0	m 3 /s	measured streamflow at the current time	X	X
	GradQ 0	m 3	gradient of the measured streamflow at the current time	X	X
			measured rain over the catchment during
	M rain	mm	the N b past hours of re-analysis	X	X

Table 6 :

 6 Time-averaged �.� 2 RHs norm over lead-times ranging from 1 to 24 hours for raw HEF, QRF-hydro quantiles, QRF-nothydro quantiles and QRF-hydro-TS HEF, for Tréodet,

	Kerjean and Ty-Planche.
	10 -2 �.� 2	10 -2 �.� 2	10 -2 �.� 2	10 -2 �.� 2
	Catchment	raw	QRF-hydro	QRF-nothydro QRF-hydro-TS
	Tréodet	25.8	1.8	3.3	4.5
	Kerjean	15.8	1.8	2.8	4.0
	Ty-Planche	9.3	1.9	3.6	3.1

Table 7 :

 7 Time-averaged �.� 2 RHs norm for cumulated and maximum streamflow cumulated over 24 lead-times for the four ensemble for Tréodet, Kerjean and Ty-Planche catchments.

			10 -2 �.� 2	10 -2 �.� 2	10 -2 �.� 2	10 -2 �.� 2
		Catchment	raw	QRF-hydro	QRF-nothydro QRF-hydro-TS
		Tréodet	17.1	9.4	8.8	9.4
	Cumulated Stramflow	Kerjean	13.3	6.9	11.1	6.9
		Ty-Planche	9.1	6.8	9.5	6.8
		Tréodet	20.5	8.6	6.0	3.3
	Maximum streamflow	Kerjean	16.8	6.6	4.8	3.9
		Ty-Planche	20.1	4.0	3.6	6.7

This product, denoted by AromeEPS-RR1 in the following, provides a forecast of 1-hour rainfall cumul, with a maximum lead-time of 45 hours, updated every day.

In this paper, the term calibration refers either to the calibration of the parameters of the hydrologic model MORDOR-TS or to the statistical ensemble calibration with the Quantile Regression Forest (QRf) method. To avoid confusion, the calibration of the hydrologic parameters is always denoted as hydrologic calibration. The statistical calibration with QRF is denoted as ensemble calibration when necessary.

Acknowledgements. The authors greatfuly thank the French national service for flood forecasting (SCHAPI) for supporting this study, EDF-DTG for providing MORDOR-TS hydrologic model as well as Rémy Garçon and Matthtieu Le Lay for their active support on the model, Fabrice Zaoui (EDF R&D) for developping the Python API interface to MORDOR-TS and Charles Perrin and Julie Viatgé (INRAE) for fruitful discusions on the GRP hydrologic model. The authors also acknowledge the Pôle de Calcul et de Données Marines (PCDM) for providing DATARMOR storage and computational resources (http://www.ifremer.fr/pcdm).

Supplementary material


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pH-responsive mesoporous silica drug delivery system, its biocompatibility and co-adsorption/co-release of 5-Fluorouracil and Naproxen

Eva Beňová, Virginie Hornebecq, Vladimír Zeleňák, Veronika Huntošová, Miroslav Almáši, Mariana Máčajová, David Bergé-Lefranc

To cite this version:

Eva Beňová, Virginie Hornebecq, Vladimír Zeleňák, Veronika Huntošová, Miroslav Almáši, et al.. pH-responsive mesoporous silica drug delivery system, its biocompatibility and coadsorption/co-release of 5-Fluorouracil and Naproxen. Applied Surface Science, 2021Science, , 561, pp.150011. 10.1016Science, /j.apsusc.2021.150011.150011. hal-03518568v2

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