Cynthia Palmieri-Thiers

Stéphane Canaan

Virginie Brunini

Vannina Lorenzi

Félix Tomi

Jean-Luc Desseyn

Ulrike Garscha

Ernst H Oliw

Liliane Berti

Jacques Maury
email: maury@univ-corse.fr

A lipoxygenase with dual positional specificity is expressed in olives (Olea europaea

Keywords: lipoxygenase, olive, development, ripening, aroma

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

Note:

The nucleotide sequence reported is in the GenBank database under the accession number EU678670

Introduction

Lipoxygenases (LOX, EC 1.13.11.12) are non-heme iron-containing fatty acid dioxygenases found in eukaryotes and in a few prokaryotes [START_REF] Grechkin | Recent developments in biochemistry of the plant lipoxygenase pathway[END_REF][START_REF] Vidal-Mas | Cloning and expression of a lipoxygenase from Pseudomonas aeruginosa 42A2[END_REF][START_REF] Koeduka | Cloning and lipoxygenase genes from a cyanobacterium, Nostoc punctiforme, and its expression in Escherichia coli[END_REF]. LOXs catalyse the regioand stereo-specific dioxygenation of polyunsatured fatty acids (PUFAs) with a cis,cis-1,4pentadiene structure [START_REF] Grechkin | Recent developments in biochemistry of the plant lipoxygenase pathway[END_REF][START_REF] Vidal-Mas | Cloning and expression of a lipoxygenase from Pseudomonas aeruginosa 42A2[END_REF][START_REF] Koeduka | Cloning and lipoxygenase genes from a cyanobacterium, Nostoc punctiforme, and its expression in Escherichia coli[END_REF][START_REF] Porta | Plant lipoxygenase. Physiological and molecular features[END_REF]. Based on the positional specificity of the dioxygen insertion using linoleic acid as a substrate, plant LOX isoenzymes are grouped into 9-LOX and 13-LOX types [START_REF] Feussner | The Lipoxygenase pathway[END_REF]. However, a few non-traditional plant LOXs can oxygenate at C-9 and C-13 positions and produce both 9-hydroperoxy and 13-hydroperoxy positional isomers.

Hydroperoxidation products derived from LOX activity are subsequently metabolized into compounds such as jasmonic acid, methyl jasmonate, volatile aldehydes, and conjugated dienoic acids. These compounds are involved in seed germination, plant growth and development, senescence, and in the plant defence response to wounding and both insect and pathogen attack [START_REF] Siedow | Plant lipoxygenase: structure and function[END_REF][START_REF] Blée | Phytooxylipins and plant defence reactions[END_REF]. Plants express numerous LOX isoforms that can be distinguished by their expression pattern, subcellular location and substrate specificity [START_REF] Feussner | The Lipoxygenase pathway[END_REF][START_REF] Siedow | Plant lipoxygenase: structure and function[END_REF]. However, physiological functions of specific LOX isozymes are not all elucidated.

LOXs are also a great interest in food science because hydroperoxides and free radicals resulting from LOX activity can exert deleterious effects on nutritionally important compounds such as essential PUFAs. LOXs also have a role in the production of volatiles molecules that can positively or negatively influence the flavour and aroma in many plant products [START_REF] Robinson | Lipoxygenases and the quality of foods[END_REF].

In olive fruit, the LOX pathway is responsible for the production of desirable organoleptic properties that differentiate virgin olive oil from other vegetable oils. Angerosa et al. [START_REF] Angerosa | Virgin olive oil volatile compounds from lipoxygenase pathway and characterization of some Italian cultivars[END_REF] and more recently Dhifi et al. [START_REF] Dhifi | Virgin olie oil aroma: characterization of some Tunisian cultivars[END_REF] have reported that the qualitative and quantitative composition of the olive oil aroma is tightly dependent on the enzymatic store involved in the LOX pathway which is linked to fruit ripening. Thus, Donaire et al. [START_REF] Donaire | Lipid biosynthesis, oxydative enzyme activities and cellular changes in growing olive fruits[END_REF] and Salas et al. [START_REF] Salas | Lipoxygenase activity in olive (Olea europaea) fruit[END_REF] have reported a low LOX activity in green olives harvested at the initial developmental stages which decreased thereafter. Recently, the existence of several olive LOX isoforms was reported: a LOX isoform was purified from mature olives (black) harvested at the late developmental stage, which produced exclusively 13-hydroperoxides of linoleic and linolenic acids [START_REF] Lorenzi | Purification, product characterization and kinetic properties of lipoxygenase from olive fruit (Olea europaea L.)[END_REF]; two LOX isoforms, with different thermal stabilities, were detected in immature olives (green) of the early developmental stage, which might be involved in the formation of the volatile compounds of the olive oil aroma [START_REF] Luaces | Thermal stability of lipoxygenase and hydroperoxide lyase from olive fruit and repercussion on olive oil aroma biosynthesis[END_REF]. Besides these isoforms, there is likely an uncharacterized isoform responsible for 9-hydroperoxides produced by olive LOX crude extract [START_REF] Olias | Aroma of virgin olive oil: biogenesis of the green odor notes[END_REF].

As LOX enzymes likely influence the organoleptic features of olive oil and in order to better understand the implication of individual LOX isoforms, we looked for new LOX enzymes. Here we report for the first time the cloning and the biochemical characterization of an olive fruit LOX isoform that is expressed at the late developmental stage and that oxygenates linoleic acid at C-9 and C-13 positions in a 2:1 ratio.

Materials and methods

Plant material

Olives (Olea europaea L., Leccino variety) were randomly picked up every two weeks from 8 to 32 weeks after flowering (WAF) from the experimental field of the INRA-CIRAD (Corsica, France). The olives were stoned, the pulp was immediately frozen in liquid nitrogen and stored at -80°C until used.

RNA extraction and Northern blot analysis

Total RNA was extracted from olive pulp as described by Hernández et al. [START_REF] Hernández | Molecular cloning and characterization of genes encoding two microsomal oleate desaturases (FAD2) from olive[END_REF]. Ten micrograms of total RNA were fractionated on a 1% formaldehyde gel according to Sambrook et al. [START_REF] Sambrook | Molecular cloning. A laboratory manual[END_REF] and transferred to Hybond N membrane (Amersham). Two O. europaea LOX probes, the LOX probe1 (775 bp long, Fig. 1) and the LOX probe2 (RT-PCR product 4, wich is 663 bp long, containing the 3' -UTR of the cDNA clone, Fig. 1) were radiolabeled with [α-32 P]dCTP (Perking Elmer) using the random primed DNA labelling kit (Roche) and subsequently used for Northern blot analysis.

DNA extraction and Southern blot analysis

Genomic DNA was extracted from fresh young leaves of the Leccino variety using the method described by Saghai-Maroof et al. [START_REF] Saghai-Maroof | Ribosomal DNA spacer-length polymorphisms in barley: mendelian inheritance, chromosomal location, and population dynamics[END_REF] with some modifications [START_REF] Bronzini De Caraffa | Mitochondrial DNA variation and RAPD mark oleasters, olive and feral olive from Western and Eastern Mediterranean[END_REF].

Genomic DNA (about 10 µg) was cleaved with BamHI, EcoRI or XhoI restriction enzymes, fractionated on 1% agarose gel and transferred to Hybond N membrane (Amersham).

Hybridizations were carried out using radiolabeled O. europaea LOX probes (the LOX probe1 and LOX probe2) according to Sambrook et al. [START_REF] Sambrook | Molecular cloning. A laboratory manual[END_REF].

Reverse transcription (RT) PCR analysis

Reverse transcription was performed using up to 5 µg of total RNA extracted from mature olives (30 WAF, black stage), oligo(dT) 18 primer and the PowerScript reverse transcriptase (Clontech) according to the manufacturer's instructions. The first stand cDNA was used as template in PCR experiments with degenerated (Lox(1+3)a: 5'-ccntaygcngyngaygg, Lox(1,2)bis: 5'-aarttnacngcngcrtg, Lox(1+3)b: 5'-acngayganganttygc, Lox1c: 5'ggnacngtngtnatgatg, where y = c or t, r = a or g, n = a,t,g or c) and/or specific (Loxc: 5'agtagtcctgtacccatg, Loxg: 5'-cctgccaacatctctctcgcgaat, Loxa: 5'-ggagaactagtcgactcc) primers designed from conserved amino acid sequences of known plant LOXs and during the present study, respectively. The primer combinations Lox(1+3)a/Lox(1,2)bis, Lox(1+3)b/Loxc, Lox1c/Loxg and Loxa/oligo(dT) were used to amplify the RT-PCR product1, RT-PCR product2, RT-PCR product3 and RT-PCR product4, respectively (Fig. 1). The PCR conditions were as follows: 94°C 2 min (1 cycle); 94°C 30s, T M (depending of the primer sequences) 1 min, 72°C 3 min (30 cycles); 72°C 7 min (1 cycle).

5' Rapid amplification of cDNA ends (RACE) procedures

The 3' /5' RACE 2 nd Generation kit (Roche) was used to synthesize first-strand cDNA from total RNA (2 µg) of mature olives (30 WAF, black stage) with the specific primer Loxj: 5'caggatcgccattgatggaac in accordance with the manufacturer' s instructions. Five microliters of poly(dA)-tailed first-strand cDNA were used as template in PCR reaction with a nested specific primer Loxl: 5'-gagctgcagagacaccttttggcc and the oligo(dT)-anchor primer. The PCR conditions were as follows: 94°C 3 min, 43°C 2 min, 72°C 2 min (1 cycle); 94°C 30s, 65°C 1 min, 72°C 2 min (20 cycles); 94°C 30s, 43°C 1 min, 72°C 2 min (25 cycles); 72°C 7 min (1 cycle). A 1 µL sample of the primary amplification product was further amplified by a second PCR reaction with the nested specific primer Loxm: 5'-actcatgaactcgatcaagaa and the PCR anchor primer. The PCR conditions were as follows: 94°C 3 min (1 cycle); 94°C 30s, 65°C 30s, 72°C 30s (10 cycles); 94°C 30s, 60°C 30s, 72°C 30s (30 cycles); 72°C 7 min (1 cycle).

Cloning of amplification products

Reverse transcription PCR (RT-PCR) and RACE-PCR products were separated by electrophoresis, stained with ethidium bromide, excised and purified with the GFX Gel Band purification kit (Amersham) and cloned into the pGEM-T (Promega) or the pCR4-TOPO (Invitrogen) vector.

DNA sequencing

Sequencing was performed by MWG Biotech (Germany) and Genome express (France).

Cloning of olive LOX cDNA for expression in E. coli

Full-length LOX cDNA was obtained by RT-PCR using the specific primers Loxsens: 5'gagatgctgagccatatagtcgag and Loxantisens: 5'-gcttcagattgacacactgttg designed on the basis of the LOX cDNA sequence. PCR was performed with 1.25 units of Pfu DNA polymerase (Promega) in a 50 µL reaction mix containing 1 µg of cDNA template and 1 µM of each primer. The amplification was performed using the following conditions: 95°C 30s, 50°C 2 min, 72°C 4 min (1 cycle); 95°C 30s, 55°C 2 min, 72°C 4 min (30 cycles); 72°C 10 min (1 cycle).

The PCR product was purified and cloned into the pMOS-Blue blunt ended vector (Amersham). The insert of the resulting clone, termed pMOS-LOX, was sequenced on both strands. A PCR strategy using pMOS-LOX as template was used to clone the olive LOX cDNA into the pQE-30 expression vector (Qiagen), introducing an N-terminal His tag. The SphILoxsens:

5'-acatgcatgctgagccatatagtcgaggc and KpnILoxantisens: 5'-cggggtacctcagattgacacactgtt specific primers containing unique SphI and KpnI restriction sites were used to introduce a SphI site upstream the ATG start codon and a KpnI site at the 3' end.

The PCR product was cloned in the SphI-KpnI oriented direction into pQE-30 vector. The recombinant construct (pQE30-LOX) was used to transform M15 E. coli cells. Part of the plasmid was sequenced to confirm the correct frame.

Expression and purification of the recombinant olive LOX

Five liters of culture medium (Luria broth medium supplemented with 100 µg.mL -1 ampicillin and 25 µg.mL -1 kanamycin) were inoculated with the overnight culture of the M15 E. coli transformed with pQE30-LOX and incubated at 37°C until the cell density had increased to A 600 0.6. Then IPTG (1mM final concentration) was added and the culture incubated at 15°C for a further 24 h. The culture was centrifuged 20 min at 7000 x g, the pellet resuspended in 250 mL of lysis buffer (50 mM sodium phosphate buffer pH 8 containing 0.25 mg.mL -1 lysozyme, 1mM benzamidine, 5mM MgCl 2 , 0.01 mg.mL -1 of DNase I, 500 mM NaCl and 0.1% Triton X-100) and the cell lysis was performed by freezing and thawing twice. After centrifugation at 25,000 x g for 15 min, the supernatant (soluble protein fraction) was loaded onto Ni-NTA (Qiagen) column (2 mL bed volume) pre-equilibrated with buffer A (50 mM sodium phosphate buffer pH 8 containing 500 mM NaCl). Most of the E. coli proteins elute in the flow through, and once the A 280 of the effluent returned to baseline, the bound proteins were eluted with a linear imidazole gradient of 5-250 mM in buffer A. Fractions enriched in LOX activity were pooled, concentrated and subjected to gel filtration on a Hiload 26/60 Superdex 200 (Amersham Biosciences) prep grade pre-equilibrated with 50 mM sodium phosphate buffer pH 6 containing 500 mM NaCl. Fractions showing LOX activity and containing pure protein on SDS-PAGE were pooled and concentrated by using an Amicon Ultra-15 membrane with a molecular weight cutoff of 30,000 (Millipore). The concentrated protein sample (11.7 mL at 0.358 mg.mL -1 ) was stored at -80°C until used.

Determination of protein concentration

Protein concentration was determined spectroscopically for the pure recombinant olive LOX using an A 280 extinction coefficient ( ) of 144,090 M -1 .cm -1 that was calculated from the tyrosine and tryptophan content [START_REF] Edelhoch | Spectroscopic determination of tryptophan and tyrosine in proteins[END_REF][START_REF] Gill | Calculation of protein extinction coefficients from amino acid sequence data[END_REF] of the deduced amino acid sequence. Protein concentration in other samples was determined by the Bradford method using bovine serum albumine as standard [START_REF] Bradford | A rapid and sensitive for the quantitation of microgram quantitites of protein utilizing the principle of protein-dye binding[END_REF].

SDS-polyacrylamide gel electrophoresis (SDS-PAGE) and immunoblotting

SDS-PAGE was performed using 12% polyacrylamide gels. The proteins were stained with Coomassie brilliant blue R-250 or transferred onto nitrocellulose (Bio-rad). Blots were blocked overnight using 3% BSA and were probed with the monoclonal peroxidaseconjugated anti-His antibody (Sigma) at 1:4,000. The peroxidase was revealed using 1.3 mM

Preparation of LOX crude extracts

The frozen pulp of the olives was blended into a fine powder. One gram of frozen pulp powder was resuspended in 10 times their mass of 50 mM phosphate buffer at pH 6 containing 1 mM phenylmethylsulfonyl fluoride (PMSF) by homogenization during 2 minutes at 8,000 rpm with an Ultra-Turrax T25 (IKA. Labortechnik). The resulting homogenate was then filtered onto 4 layers of cheeseclothes and centrifuged for 10 min at 200 x g. The resulting supernatant was subsequently assayed for lipoxygenase activity.

LOX activity and substrate specificity

LOX activity was determined by continuously monitoring the formation of conjugated dienes at 235 nm [START_REF] Axelrod | Lipoxygenase from soybeans: EC 1.13.11.12 Linoleate:oxygen oxidoreductase[END_REF]. The linoleic acid substrate was prepared as described by Anthon and Barret [START_REF] Anthon | Thermal inactivation of lipoxygenase and hydroperoxytrienoic acid lyase in tomatoes[END_REF]. Enzymatic assays were performed at saturating oxygen concentration. The standard assay mixture consisted in 1 mL of 50 mM phosphate buffer (pH 6.0) and the appropriate amount of enzyme extract (5-10 µL). Reactions were started by the addition of 0.25 mM of linoleic acid. One unit of LOX activity is defined as the amount of enzyme catalysing the formation of 1 µmol of hydroperoxide per minute at 25°C.

The kinetic parameters have been determined from a Michaelis-Menten plot over a range of substrate concentrations (linoleic and linolenic acids) between 75 and 375 µM.

Propyl gallate (0-6.6 µM) and nordihydroguaiaretic acid (NDGA) (0-33 µM) were used for the inhibition experiments.

Synthesis and analysis of LOX products

Hydroperoxide of linoleic acid was synthesized according to Vick and Zimmerman [START_REF] Vick | Pathways of fatty acid hydroperoxide metabolism in spinach leaf chloroplasts[END_REF] with adaptations. Purified recombinant olive LOX (90 Units), 5.36 mM of linoleic acid, and 11 mM NaOH were added to 50 mM sodium phosphate buffer (pH 6.0) containing 3 mM of CaCl 2 , previously oxygenated at 4°C. After 30 min, under gentle oxygenation, the reaction was stopped by acidification. Hydroperoxides were extracted with 3 x 30 mL of diethyl ether and washed with 2 x 30 mL of water. Solvent was removed and replaced by CDCl 3 for NMR experimentation. The yield of hydroperoxide evaluated by 13 C-NMR was 25%.

Identification of LOX products was performed as described by Lorenzi et al. [START_REF] Lorenzi | Purification, product characterization and kinetic properties of lipoxygenase from olive fruit (Olea europaea L.)[END_REF] using a Bruker 400 Avance Fourier Transform spectrometer operating at a 100.623 MHz for 13 C, equipped with a 5 mm probe, in deuteriochloroform, with all shifts referred to internal tetramethylsilane (TMS). 13 C-NMR spectra were obtained with the following acquisition parameters : pulse width 45° (4µs), acquisition time 2.73 s for 128K data table with a spectral width of 25 000 Hz (250 ppm), digital resolution = 0.183 Hz per point. 13 C-NMR chemical shift of hydroperoxides extracted was compared to values obtained by Lorenzi et al. [START_REF] Lorenzi | Purification, product characterization and kinetic properties of lipoxygenase from olive fruit (Olea europaea L.)[END_REF] with soybean commercial LOX on esterified 9-and 13-hydroperoxides of linoleic acid: Enantiomer composition analysis was carried out by chiral-phase HPLC with on-line MS/MS [START_REF] Schneider | Enantiomeric separation of hydroxy and hydroperoxy eicosanoids by chiral column chromatography[END_REF]. The hydroperoxides were reduced by triphenylphosphine, separated by chiral phase-HPLC on a column with amylose tris(3,5-dimethylphenylcarbonate) coated on silica gel (Reprosil Chiral-AM; 10 µm; 250 mm x 2 mm; Dr. Maisch) and eluted with ethanol/hexan/acetic acid, 95/5/0.02 (0.15 mL.min -1 ). The effluent was mixed in a tee with isopropanol/water, 3/2 at 0.1 mL.min -1 and the products were detected by MS/MS analysis of carboxylate anions. The capillary temperature was 315ºC, the spray voltage was 4.5 kV, and prostaglandin F 1 was utilized for tuning. Mass spectrometry experiments were performed on a linear ion-trap (LIT) mass spectrometer using Xcalibur as operating system (LTQ, ThermoFisher). Electrospray ionization was conducted and negative ions were detected.

Results

LOX cDNA isolation and characterization

We isolated a full length cDNA by a combined strategy using RT-PCR and RACE-PCR on total RNA extracted from black olives harvested at 30 weeks after flowering (WAF)

and oligonucleotides designed on the basis of the sequence of known plant LOXs and during this study (Fig. 1). The olive LOX cDNA (GenBank accession number: EU678670) harboured an open reading frame (ORF) of 2592 bp encoding a presumptive translation product of 864 amino acid residues. The product with a calculated molecular mass of 98.4

kDa and a pI of 5.95 is likely confined to the cytosol, because it contained neither consensus targeting nor retention signals for any organelles (pSORT programm; http://psort.ims.utokyo.ac.jp). The ORF is flanked by a 5'-unstranslated (UTR) sequence that is at least 99nucleotides (nt) and a 157-nt 3'-UTR containing a canonical polyadenylation signal (Fig. 1).

The alignment of the deduced amino acid sequence with other LOX sequences using

ClustalW program shows that the olive LOX contained the two functional domains typical of LOXs: the smaller N-terminal region (position 1-164) forming a β-barrel structure, known to mediate binding of lipid body LOX to liposomes and lipid bodies [START_REF] May | The N-terminal beta-barrel structure of lipid body lipoxygenase mediates its binding to liposomes and lipid bodies[END_REF], and the larger Cterminal region (position 165-864) including the catalytic site [START_REF] Boyington | Structure of soybean lipoxygenase-I[END_REF].

FASTA analysis of the deduced amino acid sequence revealed that olive LOX shared the highest degree of identity towards hazelnut LOX (77.3% identity, [START_REF] Santino | Biochemical and molecular characterization of hazelnut (Corylus avellana) seed lipoxygenases[END_REF]) tobacco LOX1 (76.3% identity, [START_REF] Veronesi | Nucleotide sequence of an elicitor-induced tobacco lipoxygenase cDNA (PGR95-009)[END_REF]) and almond LOX (75.5% identity, [START_REF] Mita | Molecular cloning and biochemical characterization of a lipoxygenase in almond (Prunus dulcis) seed[END_REF]).

Several highly conserved regions were identified: the domains likely to be important for the substrate binding (position 364-378) and the oxygen binding (position 710-723), the C-terminal GIPNSVSI domain, as well as the residues (H525, H530, H716, N720 and I864) involved in the iron binding (Fig. 1).

The regio-specificity in plant LOXs are usually determined by the motif R/TF, R/TH, R/CF or R/SF for 13-LOX and R/TV for 9-LOX [START_REF] Feussner | The Lipoxygenase pathway[END_REF]. Olive LOX contained a threonine-valine motif (R/TV at positions 733/582-583; Fig. 1) suggesting that this enzyme is a 9-LOX.

Genomic polymorphism of the Lox gene

To determine the number of the olive Lox genes, we carried out Southern blot analysis using the two LOX cDNA probes. We perform an alignment of olive LOX cDNA nucleic sequence using the ClustalW program with the genomic Lox sequence of Solanum tuberosum (accession number U24232). We predicted that the LOX probe1 spans the exon 2 to exon 4 and contains one EcoRI site in the exon 2 and 4, and one BamHI site in the exon 3 (Fig. 2A).

The LOX probe2 which could be included in the exon 9 contains one EcoRI site (Fig. 2A).

The LOX probe1 and LOX probe2 contain no XhoI site, and a unique XhoI site present in the olive LOX cDNA is located just in 5' of the LOX probe2.

The resulting pattern of hybridization with the LOX probe2 (Fig. 2B) consisted of a single band, at 0.7 kb and 6.1 kb in length, with the EcoRI and BamHI digestions, respectively, and two bands, at 9.3 kb and 7.5 kb in length, with the XhoI digestion. These results suggest the presence of one Lox gene copy with a XhoI polymorphism. The hybridization pattern obtained with the LOX probe1 showed two bands, at 1.3 kb and 0.75 kb in length, with the EcoRI digestion, two bands, at 12.6 kb and 6.1 kb in length, with the BamHI digestion, and three bands at 16.9 kb, 11.3 kb and 8.9 kb in length, with the XhoI digestion. The number of DNA fragments detected for the EcoRI and BamHI digestions is in agreement with a single copy of our Lox gene. Altogether these results showed an XhoI polymorphism for this gene.

Biochemical characterization of recombinant olive LOX

Expression of the olive LOX was induced by 1 mM IPTG and low temperature (15°C) incubation to prevent inclusion body formation. Protein extracts of E. coli harbouring the pQE30-LOX vector showed a specific LOX activity (0.9 U.mg -1 protein) with linoleic acid as substrate, and no LOX activity using the empty vector. These results indicate that olive LOX cDNA encoded a functional enzyme. The recombinant enzyme was purified by affinity chromatography using Nickel chelated column followed by Superdex 200 gel filtration chromatography. The specific activity reached 23.4 U.mg -1 protein with linoleic acid as substrate and a 26-fold purification was achevied. We have obtained 4.18 mg of recombinant protein from five liters of culture medium. Purified recombinant olive LOX appeared as a unique band at 98 kDa in both Coomassie brilliant blue stained SDS-PAGE and immunoblot, in good agreement with the predicted molecular mass (Fig. 3).

The enzymatic activity was analyzed at different pH values (pH 4-9) and we found that recombinant olive LOX has an optimum pH of about 6. The kinetics parameters were investigated using linoleic and linolenic acids as substrates (Table 1). The recombinant olive LOX showed a lower K m for linoleic acid (174.94 µM) than for linolenic acid (343.66 µM).

The estimates of k cat /K m for linoleic acid hydroperoxidation (0.28 s -1 .µM -1 ) and for linolenic acid hydroperoxidation (0.14 s -1 .µM -1 ) suggested that the catalytic efficiency of the recombinant olive LOX was significantly higher for linoleic acid hydroperoxidation than for linolenic acid hydroperoxidation. Inhibition studies were performed with LOX inhibitors such as propyl gallate and NDGA [START_REF] Fornaroli | Purification of a plasma membrane-bound lipoxygenase from soybean cotyledons[END_REF]. The inhibition kinetics analysed by Lineweaver-Burk plots showed that propyl gallate was a competitive inhibitor, and a K i value of 1.88 µM was graphically determined using secondary plots. NDGA inhibition was non competitive with a K i value of 4.09 µM.

In order to determine the regio-specificity of the recombinant olive LOX, we analyzed by 13 C-NMR the reaction products obtained using linoleic acid as substrate. We clearly observed that 9-hydroperoxy octadecadienoic acid ( ) with a ratio about 2:1 (Fig. 4).

The stereo chemistry of 9-and 13-HPODE was analyzed by chiral-phase HPLC after reduction to the corresponding alcohols. 9-HPODE and 13-HPODE were formed in a 2:1 ratio (data not shown) and were predominantly in the 9S and 13R configuration (Fig. 5), indicating that they derived from the activity of a specific enzyme.

LOX expression and enzymatic activity during olive fruit development

We identified the developmental stages on the basis of the olive colour: green stage (harvested from 8 to 16 WAF), turning stage (harvested at 18 WAF) and black stage (harvested from 20 to 32 WAF). The enzymatic activity was preliminarily analyzed at different pH values (pH 4-9) on the olives harvested every two weeks and we found that the olive LOX activity has an optimum pH of about 6 whatever the stage of development. LOX activity was detected in all olive developmental and ripening stages from green small fruits (8 WAF) to black or senescent fruits (32 WAF, Fig. 6A). An increase of the LOX activity was observed at the end of the green stage and the turning stage of the olives, and the maximum (783 nmol.min -1 .mg -1 of proteins) was reached at the black stage.

LOX expression was monitored by Northern analysis using the LOX probe1. An hybridization signal of the expected size for LOX RNA (2.9 kb) was observed in olives harvested from 22 WAF to 32 WAF, with a strong signal for the olives at 32 WAF (Fig. 6B).

A faint signal was observed in olive at 24 WAF which can be explained by a smaller quantity of RNA loaded (Fig. 6B,6C). No hybridization was observed in olives of the green stage, of the turning stage or in the first sample of the black stage (20 WAF). A similar hybridization pattern was observed with the LOX probe2 (data not shown).

Discussion

Using a RT-PCR and RACE-PCR combined approach on total RNA isolated from black olives harvested at 30 WAF, we have isolated and characterized, for the first time, an olive cDNA encoding a LOX isoform. We have shown that this olive LOX is probably encoded by a unique copy of the gene. Amino acid sequence analysis of this olive LOX has shown that the polypeptide contains all of the domains and amino acid residues known to be important for LOX activity. A classification of plant LOXs based on the presence of the chloroplastic transit peptide was introduced by Shibata et al. [33]. The members of the socalled type-2 LOX exhibit this N-terminal extension in contrast to those reassembled in the type-1 LOX subfamily. Our olive LOX isoform, which is likely a cytoplasmic isoform, can be classified among the type-1 LOXs. Plant LOXs are also classified into 9-and 13-LOXs with respect to the position at which the oxygenation of linoleic acid occurs. The primary determinant for regio-specificity was defined by the R/TF, R/TH, R/SF or R/CF motif for 13-LOX and by the R/TV motif for the 9-LOX [START_REF] Feussner | The Lipoxygenase pathway[END_REF]. A special role of an Arg residue at the bottom of the substrate-binding pocket was suggested by its highly conserved occurrence in all plant LOXs and by mutagenesis studies [START_REF] Liavonchanka | Lipoxygenases: Occurrence, functions and catalysis[END_REF][START_REF] Hornung | Conversion of cucumber linoleate 13lipoxygenase to a 9-lipoxygenating species by site-directed mutagenesis[END_REF]. In plant 13-LOXs, the His or Phe residue would mask the positive charge of the Arg and would hamper the interaction with the linoleate carboxylate. Thus, the linoleate would penetrate in the active site by its methyl end, and the C-13 oxidation would occur. In contrast, for the plant 9-LOXs, the replacement of the His or Phe residue by the less space-filling Val residue would allow an inverse orientation of the linoleate in the active site what would favour the C-9 oxidation [START_REF] Feussner | The Lipoxygenase pathway[END_REF]. However, some plant LOXs produce both 9-and 13-hydroperoxide isomers, and thus do not follow the predictive model of regio-specificity [START_REF] Hughes | Probing a novel potato lipoxygenase with dual positional specificity reveals primary determinants of substrate binding and requirement for a surface hydrophobic loop and has implications for the role of lipoxygenases in the tuber[END_REF][START_REF] Hughes | Mutagenesis and modelling of linoleate-bonding to pea seed lipoxygenase[END_REF]. According to the R/TV motif found in the recombinant olive LOX, the 9-LOX activity would be predicted. Surprisingly, as shown by 13 C-NMR and HPLC-MS analysis, both 9-and 13-hydroperoxide of linoleic acid, predominantly in the 9S and 13R configuration, were produced in a 2:1 ratio by the recombinant olive LOX. Thus, this enzyme displayed a dual positional specificity and would be defined as olive 9/13-LOX. The LOX specificity has implications for hydroperoxides metabolism. Indeed, 9-and 13hydroperoxides of linoleic and linolenic acids can be converted into volatile aldehydes by hydroperoxide lyase(s), whereas 13-hydroperoxide of linolenic acid can be converted into jasmonic acid cyclic precursors by allene oxide synthase. The dual positional specificity of the 9/13-LOX suggests that it is able to synthesize compounds that play roles in both developmental process and defence response [START_REF] Siedow | Plant lipoxygenase: structure and function[END_REF].

During the development of olives, the LOX activity shows an increase at the end of the green stage and the turning stage to reach a maximum at black stage. Donaire et al. [START_REF] Donaire | Lipid biosynthesis, oxydative enzyme activities and cellular changes in growing olive fruits[END_REF] and Salas et al. [START_REF] Salas | Lipoxygenase activity in olive (Olea europaea) fruit[END_REF] have previously reported a LOX activity at early stages of the olive development. Here, we report that although the LOX activity is detected at early stages of the olive development, this activity is lower than the activity observed in olives of the black stage.

These results are not surprising since LOXs are associated with plant senescence and fruit ripening. Indeed, LOXs have long been associated with membrane deterioration in plant tissues through peroxidation of PUFAs, and such dysfunction has been seen as a key process in senescence, resulting in loss of compartmentation and cell breakdown [START_REF] Thompson | The molecular basis for membrane deterioration during senescence[END_REF][START_REF] Rogiers | Maturation and ripening of fruit of Amelanchier alnifolia Nutt. are accompanied by increasing oxidative stress[END_REF]. Moreover LOX activity has been shown to increase in conjunction with ripening processes such as loss firmness in kiwifruit [START_REF] Chen | Lipoxygenase in relation to the ripening and softening of Actinidia fruit[END_REF][START_REF] Zhang | The role of salicylic acid in postharvest ripening of kiwifruit[END_REF] and peach fruit [START_REF] Wu | Involvement of lipoxygenase in the postharvest ripening of peach fruit[END_REF].

As shown by the Northern analysis, the 9/13-LOX is specifically expressed in olives of the black stage from the 22 WAF to the 32 WAF. Another LOX enzyme was recently purified from black olives and characterized as a 13-LOX [START_REF] Lorenzi | Purification, product characterization and kinetic properties of lipoxygenase from olive fruit (Olea europaea L.)[END_REF] indicating that at least two LOX differing in their regio-specificity are expressed in olives of the black stage. Both, 9/13-LOX and 13-LOX showed a preference towards linoleic acid (with a K m =174.94 µM and 82.44 µM respectively) than linolenic acid (with a K m =343.66 µM and 306.26 µM respectively), and the K m values suggested that the fatty acid pocket of 13-LOX had a significantly higher affinity for linoleic acid than 9/13-LOX. However, the catalytic efficiency of 9/13-LOX for linoleate hydroperoxidation was higher than that of 13-LOX. Luaces et al. [START_REF] Luaces | Thermal stability of lipoxygenase and hydroperoxide lyase from olive fruit and repercussion on olive oil aroma biosynthesis[END_REF] reported recently two LOX isoforms (a thermo-labile and a thermo-resistant isoforms) from green olives of the early developmental stage which might be involved in the biosynthesis of the olive oil aroma. Our 13-LOX [START_REF] Lorenzi | Purification, product characterization and kinetic properties of lipoxygenase from olive fruit (Olea europaea L.)[END_REF] and the thermo-resistant LOX could correspond to only one and even isoform since they displayed an activation energy in the same range (125.50 kJ.mol -1 and 148.82 kJ.mol -1 respectively). Although our 9/13-LOX displays an activation energy of 82.37 kJ.mol -1 , which is close to that of the thermo-labile LOX (83.39 kJ.mol -1 ) reported by Luaces et al. [START_REF] Luaces | Thermal stability of lipoxygenase and hydroperoxide lyase from olive fruit and repercussion on olive oil aroma biosynthesis[END_REF], they correspond to two Lox genes since our 9/13-LOX is not expressed in green olives. The expression of different LOXs during their development could explain the LOX activity detected throughout the development process.

Multiple isoforms of LOX have been found in a wide range of plants [START_REF] Feussner | The Lipoxygenase pathway[END_REF]. In tomato, for example, at least five Lox genes have been reported: TomloxA expression declines during tomato fruit ripening, and TomloxB expression is present in mature green fruit and enhanced by ethylene [START_REF] Griffiths | Ethylene and developmental signals regulate expression of lipoxygenase genes during tomato fruit ripening[END_REF]; TomloxC is detectable in the onset of ripening and has been identified as a specific isoform involved in synthesis of fruit flavour compounds [START_REF] Chen | Identification of a specific isoform of tomato lipoxygenase (TomloxC) involved in the generation of fatty acid-derived flavor compounds[END_REF]; TomloxD shows low expression levels in fruit, but is rapidly and transiently induced by wounding [START_REF] Heitz | A gene encoding a chloroplast-targeted lipoxygenase in tomato leaves is transiently induced by wounding, systemin, and methyl jasmonate[END_REF], and TomloxE transcripts are present at the breaker and post-breaker stages of fruit ripening [START_REF] Chen | Identification of a specific isoform of tomato lipoxygenase (TomloxC) involved in the generation of fatty acid-derived flavor compounds[END_REF].

More recently, six Lox genes were identified and cloned from a kiwifruit EST (expressed sequence tag) database [START_REF] Zhang | Differential expression within the LOX gene family in ripening kiwifruit[END_REF]. The results showed that the six genes were differentially regulated during kiwifruit ripening and senescence, forming two groups, one active in ripening and responsive to ethylene and the other more constitutively expressed. To date, the physiological role of the olive 9/13-LOX is still unknown, but its expression pattern suggests that it is associated with the ripening and senescence processes. Moreover, as it is expressed in olives of black stage, its contribution to the biosynthesis of the olive oil aroma cannot be ruled out.

The identification of LOX, expressed in the fruit and more widely in the plant, with tissue-specific regulation during development or in response to abiotic and biotics elicitors of stress, and their characterization as recombinant proteins, should prove to be a useful approach to interpret the role of LOXs in plant biology, and in olive in particular in the elaboration of the olive oil aroma.

LEGEND TO FIGURES

  13 C-NMR (100 MHz, CDCl 3 ) 134.03 (9-OOH, C-12), 133.86 (13-OOH, C-11), 131.31 (13-OOH,C-11), 131.14 (9-OOH, C-11), 130.00 (9-OOH, C-10), 129.91 (13-OOH, C-12), 127.56 (13-OOH, C-9), 127,38 (9-OOH, C-13), 86.82 (13-OOH, C-13), 86.72 (9-OOH, C-9) 31.75 (13-OOH, C-16), 31.51 (9-OOH, C-16), 27.92 (9-OOH, C-14), 27.70 (13-OOH, C-8), 25.21 (9-OOH, C-7), 24.97 (13-OOH, C15).

Fig. 1 .

 1 Fig. 1. Compiled full-length olive LOX cDNA sequence and deduced amino acid sequence.

Fig. 2 .

 2 Fig. 2. Southern hybridization of olive leaves genomic DNA of Leccino variety with

Fig. 3 .

 3 Fig. 3. SDS-PAGE (12% acrylamide) of olive LOX at various steps of the purification. The

Fig. 4 .

 4 Fig. 4. Expanded plot of 13 C-NMR spectrum of products obtained by incubating linoleic acid

Fig. 5 Fig. 6 .

 56 Fig. 5 Chiral-phase HPLC-MS/MS analysis of metabolites formed from linoleic acid by recombinant olive LOX. Top trace, separation of the enantiomers of 9-hydroxy octadecadienoic acid and MS/MS analysis (m/z 295 full scan ) with monitoring m/z 171. Bottom trace, separation of the enantiomers of 13-hydroxy octadecadienoic acid and MS/MS analysis (m/z 295 full scan ) with monitoring m/z 195.

  Fig. 1

  Fig. 3

Acknowledgments

This work has been supported by the "Collectivité Territoriale de Corse", Interreg IIIA and Knut and Alice Wallenberg Foundation (KAW 2004.0123). The authors thank Delphine Fontaine (U837-Lille) for her technical help.

Values represent the mean of 3 independent replicates ± standard deviation.


Thomas Viard
email: viard@gocad.org

Guillaume Caumon

Bruno Lévy

Adjacent versus coincident representations of geospatial uncertainty: Which promote better decisions? $

Keywords: Uncertainty visualization, user study, perception, transparency

3D geological models commonly built to manage natural resources are much affected by uncertainty because most of the subsurface is inaccessible to direct observation. Appropriate ways to intuitively visualize uncertainties are therefore critical to draw appropriate decisions. However, empirical assessments of uncertainty visualization for decision making are currently limited to two-dimensional map data, while most geological entities are either surfaces embedded in a 3D space or volumes. This paper first reviews a typical example of decision making under uncertainty, where uncertainty visualization methods can actually make a difference. This issue is illustrated on a real Middle East oil and gas reservoir, looking for the optimal location of a new appraisal well. In a second step, we propose a user study that goes beyond traditional 2D map data, using 2.5D pressure data for the purposes of well design. Our experiments study the quality of adjacent versus coincident representations of spatial uncertainty as compared to the presentation of data without uncertainty; the representations' quality is assessed in terms of decision accuracy. Our study was conducted within a group of 123 graduate students specialized in geology.

Introduction

Spatial uncertainty is present at multiple levels in subsurface studies, from structural interpretation to dynamic flow simulation. In geological modeling, a significant endeavor has been made to sample this uncertainty by producing several possible 3D geological realizations instead of one best -and probably flawed -deterministic model (e.g., [START_REF] Arpat | Conditional simulation with patterns[END_REF][START_REF] Chambers | Practical geostatistics -an armchair overview for petroleum reservoir engineers[END_REF][START_REF] Deutsch | Fluvsim: a program for object-based stochastic modeling of fluvial depositional systems[END_REF][START_REF] Hu | Gradual deformation and iterative calibration of gaussian-related stochastic models[END_REF]. Visualizing such a population of 3D model realizations is paramount for some applications such as assessing risks of water table contamination due to anthropic pollution, studying mechanical rock properties prior to the construction of large buildings (e.g., arch-gravity dams), or targeting of new drillholes to produce/discover natural resources in potentially high-pay areas. While a large body of work proposes methods to visualize spatial uncertainty, we need to improve our understanding on how uncertainty is perceived and how it affects human decisions [START_REF] Harrower | Representing uncertainty: Does it help people make better decisions?[END_REF]). An increasing number of studies address this issue (e.g., [START_REF] Evans | Dynamic display of spatial data-reliability: does it benefit the map user?[END_REF][START_REF] Leitner | Guidelines for the display of attribute certainty[END_REF][START_REF] Edwards | Visualizing data certainty: A case study using graduated circle maps[END_REF][START_REF] Aerts | Testing popular visualization techniques for representing model uncertainty[END_REF][START_REF] Deitrick | The influence of uncertainty visualization on decision making: An empirical evaluation[END_REF]; however, these experiments are currently limited to two-dimensional data (e.g. chloropleth maps) and disregard 2.5D and 3D data that are routinely used in geological applications.

Contributions

This work discusses the applications of two different visualization methods for geological issues, i.e., adjacent versus coincident representations of geospatial uncertainty, and evaluates their relative merits through an empirical user study. In this paper:

1. We review a taxonomy of the multiple concepts encapsulated in the term "uncertainty" (Section 2.1), and discuss which strategies have been adopted so far to represent these concepts in a meaningful way (Section 2.2). We further review studies about the effects of uncertainty visualization on decision making (Section 2.3); 2. We present an example of uncertainty visualization method (Section 3) with its use for a geological issue where uncertainty visualization can add value to decision making, i.e., the quest for the optimal location of a new appraisal well in a hydrocarbon reservoir (Section 4). This issue is illustrated on a real middle-east oil and gas field. The source code and executables can be freely downloaded at our website; 3. 123 graduate students in geoscience participated in a formal study to evaluate adjacent versus coincident uncertainty representations of 2.5D pressure data. The protocol of our study is presented in Section 5, and results and implications are discussed in Section 6.

Background

Preliminary notions

What is uncertainty? Uncertainty is a complex, multi-faceted concept that can affect different parameters of a study for different reasons. Most authors agree to see uncertainty as a metadata representing a lack of knowledge about a model or a piece of information, but they encompass this characteristic into several different notions such as error, accuracy, precision, completeness, volume support, etc. Some authors even consider uncertainty as a component of a broader concept, termed "data imperfection" according to [START_REF] Gershon | Visualization of an imperfect world[END_REF].

Past research has proposed several formalizations of the notions related to uncertainty. The US Geological Survey (USGS) propose a Spatial Data Transfer Standard (SDTS) in which they include notions of positional accuracy, attribute accuracy, logical consistency, completeness and lineage (USGS, 1977). [START_REF] Thomson | A typology for visualizing uncertainty[END_REF] extend the SDTS with a typology of uncertainty that also integrates the concepts of currency, credibility, subjectivity and interrelatedness (see Table 1 for a description of their typology) -the appropriateness of their typology, revised after [START_REF] Maceachren | Visualizing Geospatial Information Uncertainty: What We Know and What We Need to Know[END_REF], has been empirically assessed and refined by Roth (2009a) in the context of floodplain mapping under uncertainty. After discussions with experts involved in various scientific domains, [START_REF] Skeels | Revealing uncertainty for information visualization[END_REF] propose a hierarchical typology of uncertainty, with measure precision on the lowest level, completeness on the middle level and inferences on the highest level; they find that notions of credibility and disagreement are transversal to these three levels.

Uncertainty quantification. Even if uncertainty were a clearly defined concept, the problem of its characterization would stand still. Several impediments limit uncertainty characterization [START_REF] Buttenfield | Representing data quality[END_REF]; for example, one participant interviewed by [START_REF] Skeels | Revealing uncertainty for information visualization[END_REF] highlighted that he may not be aware of the presence of uncertainty (which he called unknown unknows). Being aware of the presence of uncertainty is often not enough -in many scientific applications, there is a need to know the amount of uncertainty associated to the data. This is frequently related to the notion of error; however, the error compares a measured value to the actual value, which is often unknown (termed as known unknows in [START_REF] Skeels | Revealing uncertainty for information visualization[END_REF], i.e. uncertainty you are aware of, but that can not be measured). [START_REF] Bertin | Semiology of Graphics[END_REF][START_REF] Maceachren | Visualizing uncertain information[END_REF] and [START_REF] Mcgranaghan | A cartographic view of spatial data quality[END_REF].

Visual variable Description

Uncertainty visualization

Theoretical framework

In uncertainty visualization, data are at least bivariate -consisting of a primary attribute and its associated uncertainty degree -and may be multivariate if either primary data or uncertainty are not defined as scalar values; such a high data-dimensionality calls for appropriate visualization methods [START_REF] Rheingans | Perceptual principles for effective visualizations[END_REF]. A wide variety of visualization algorithms have been used to depict local uncertainty together with the value of interest in various fields, including GIS, meteorology, oceanography or medical research [START_REF] Griethe | The visualization of uncertain data: Methods and problems[END_REF][START_REF] Pang | Visualizing uncertainty in natural hazards[END_REF][START_REF] Johnson | A next step: Visualizing errors and uncertainty[END_REF][START_REF] Pang | Approaches to uncertainty visualization[END_REF][START_REF] Maceachren | Visualizing uncertain information[END_REF]. Some of these research include adjacent representations of uncertainty, i.e., uncertainty map being displayed separately from the primary data, but most of them focus on coincident representations of uncertainty, i.e., representations where uncertainty is integrated into the same display as the primary data [START_REF] Maceachren | Visualizing georeferenced data: representing reliability of health statistics[END_REF]. Based on the work of [START_REF] Shortridge | Stimulus processing models from psychology: can we use them in cartography?[END_REF], [START_REF] Maceachren | How maps work[END_REF] further distinguishes between coincident integral representations of uncertainty, which directly alter the display of the primary data, and coincident separable representations of uncertainty, which allow for selective attention to either variable. [START_REF] Zuk | Theoretical analysis of uncertainty visualization[END_REF] evaluate the quality of several uncertainty visualization methods based on the perception criteria developed by [START_REF] Bertin | Semiology of Graphics[END_REF], [START_REF] Tufte | The Visual Display of Quantitative Information[END_REF] and [START_REF] Ware | Information Visualization: Perception for Design[END_REF]. They notably work upon Bertin's visual variables, which are location, size, value, grain, color, orientation and shape (Table 2). MacEachren (1992) adds an eighth visual variable which he calls focus. He proposes different ways of manipulating focus through contour crispness, fill clarity, fog and resolution. [START_REF] Mcgranaghan | A cartographic view of spatial data quality[END_REF] further expands this set of perceptual variables with the notion of realism, which is a significant concern in computer graphics. Some other authors apply criteria from the perception community to assess the quality of visualization methods -for example, the uncertainty display should not obscure the display of the primary variable; also, visualization should use preattentive processing1 to be understood at a glance [START_REF] Healey | High-speed visual estimation using preattentive processing[END_REF][START_REF] Tory | Human factors in visualization research[END_REF][START_REF] Ware | Information Visualization: Perception for Design[END_REF].

Dedicated visualization methods

This section provides a quick review of some existing uncertainty visualization methods. It is not intended as a comprehensive state of the art, but rather as a set of examples of different separable versus integral methods.

Visually separable methods. [START_REF] Cedilnik | Procedural annotation of uncertain information[END_REF] overlay distorted wire-frame lines to the visualization as an annotation of the uncertainty degree (Figure 1,a). Their work can be seen as a variation of [START_REF] Wright | Map Makers Are Human: Comments on the Subjective in Maps[END_REF], who suggests changing the value and grain of contour lines to display contour uncertainty. Using lines results in little of the primary data hidden by the uncertainty display. Another method is the use of patterns, typically with a variable grain or intensity (Figure 1,b), as done by [START_REF] Interrante | Harnessing natural textures for multivariate visualization[END_REF] along maps, [START_REF] Rhodes | Uncertainty visualization methods in isosurface rendering[END_REF] along isosurfaces [START_REF] Djurcilov | Volume rendering data with uncertainty information[END_REF] as a post-processing step of a volume rendering algorithm. Their approaches subdivide uncertainty space into a set of smaller ranges, each of which is assigned a different pattern. This results in a categorization of uncertainty levels.

Visually integral methods. MacEachren (1992) uses focus in geographical information systems (GIS), e.g., by changing the fill clarity of land-cover patterns based on their uncertainty degree (Figure 1,c). [START_REF] Kosara | Semantic depth of field[END_REF] extend this notion to what they call semantic depth of field (SDOF). While classical image processing blurs objects based on their depth of field, SDOF blurs objects according to their relevance. Unlike most highlighting methods [START_REF] Robinson | Highlighting techniques to support geovisualization[END_REF], this de-emphasizes irrelevant objects in order to put the focus on the most important ones. Animation methods. Animation methods use time to convey a sense of uncertainty. 2 Fisher (1993) introduces an animation method to convey a sense of uncertainty in soil maps; he selects patches at random map locations through time and re-evaluates the patch type based on the local soil types distribution. Srivastava (1994a) proposes animation to display a sequence of possible models, using a modified p-field algorithm. The frames of this animation can be ordered according to a relevant objective function (Srivastava, 1994b). [START_REF] Ehlschlaeger | Visualizing spatial data uncertainty using animation[END_REF] improve the interpolation schemes between keyframes as in the gradual deformation algorithm [START_REF] Hu | Gradual deformation and iterative calibration of gaussian-related stochastic models[END_REF]. This preserves the spatial variability of Gaussian random fields in interpolated frames. [START_REF] Davis | Modelling and visualizing multiple spatial uncertainties[END_REF] create a patch-based animation of slope stability data. They especially focus on the integration of several sources of uncertainty such as soil type, soil characteristics or elevation values, using fuzzy logic and Monte-Carlo sampling methods. [START_REF] Dooley | Visualizing method-produced uncertainty in isometric mapping[END_REF] propose an animated visualization of plant hardiness zone maps, in which they consider uncertainties due to the data sampling density and to the selected interpolation method. Their approach results in maps being displayed sequentially.

Decision making under uncertainty

Representation of spatial uncertainty has little interest if it does not affect the way people think about their problems to improve their decisions [START_REF] Deitrick | The influence of uncertainty visualization on decision making: An empirical evaluation[END_REF]. Improvements can relate to accuracy, decision speed and confidence in the results [START_REF] Harrower | Representing uncertainty: Does it help people make better decisions?[END_REF]. Uncertainty was initially believed to clutter data display, because of the burden introduced by additional information [START_REF] Mcgranaghan | A cartographic view of spatial data quality[END_REF]. However, studies performed by [START_REF] Leitner | Guidelines for the display of attribute certainty[END_REF] and [START_REF] Aerts | Testing popular visualization techniques for representing model uncertainty[END_REF] conclude that embedding primary map data with uncertainty tends to actually clarify the display. Their results are consistent with the findings of [START_REF] Evans | Dynamic display of spatial data-reliability: does it benefit the map user?[END_REF] and [START_REF] Edwards | Visualizing data certainty: A case study using graduated circle maps[END_REF], whose studies showed that users perform better with integrated uncertainty displays than with separate maps. [START_REF] Sanyal | A User Study to Compare Four Uncertainty Visualization Methods for 1D and 2D Datasets[END_REF] also found that uncertainty perception is not uniform, i.e., that the perception of low uncertainty locations differs from the perception of high uncertainty locations. Most of the experiments discuss the effects of user expertise on decision-making under uncertainty. There is no clear consensus in the literature whether the level of expertise may bias decision-making under uncertainty; results from [START_REF] Kobus | Effects of experience and uncertainty during dynamic decision making[END_REF] and [START_REF] Hope | Testing the effects of thematic uncertainty on spatial decision-making[END_REF] suggest that participants' expertise influences their decisions, whereas [START_REF] Evans | Dynamic display of spatial data-reliability: does it benefit the map user?[END_REF] and [START_REF] Aerts | Testing popular visualization techniques for representing model uncertainty[END_REF] find either little or no significant difference between novices and experts. Roth (2009b) argues that these contradictory findings may come from the task complexity -the more complex, the greater the influence of the participant's expertise. An increasing number of studies focus on the effects of uncertainty visualization for decision-making, but most experiments have been performed with two-dimensional data, resulting in poor knowledge about perception of 2.5D/3D data that are widely used in geology. This work aims at bridging the gaps that exist with such higher dimensional data.

Uncertainty visualization design

Our tests on participants and our case study were performed using an implementation of the uncertainty visualization method based on pattern transparency, as described below. Whereas a full-featured software with 3D support has been implemented in a commercial geomodeling software, we provide an open-source package containing the source code, binaries and a technical documentation of our GPU-accelerated implementation at http: //www.gocad.org/www/research/freesoftware.php.

Uncertainty visualization using pattern transparency. In our experiments, we use transparency to convey a sense of uncertainty, by compositing both the value and the color visual variables [START_REF] Zuk | Theoretical analysis of uncertainty visualization[END_REF]. We blend a predefined pattern to the color-coded data, with a blending ratio expressed as a function of uncertainty. This results in the pattern being visible at some interesting areas; for our problem, we chose to make the pattern visible at high uncertainty areas to bring the attention of participants to these locations, because [START_REF] Sanyal | A User Study to Compare Four Uncertainty Visualization Methods for 1D and 2D Datasets[END_REF] suggests that uncertainty perception is non-uniform. The blending ratio can be seen as a measure of the pattern intensity, noted I(u) where u corresponds to some local scalar uncertainty measure. For every single pixel, the blending results in a final RGB color C f calculated as:

C f = (1 -α p • I(u)) •C i + α p • I(u) •C p (1)
where C i is the RGB color before applying the pattern, C p is the RGB color of the pattern and α p is the pattern opacity at the current pixel.

Pattern definition. Our pattern-based uncertainty visualization method is a variation of [START_REF] Rhodes | Uncertainty visualization methods in isosurface rendering[END_REF], for our pattern uses transparency with continuous uncertainty values rather than density with discrete uncertainty levels. Hence, the method removes the burden of defining a discrete set of patterns, i.e., any relevant 2D pattern can be used in our implementation. We have tested several types of pattern empirically, e.g., fabric, grid, circles, chessboard, etc. We generally use "fabric" patterns because they reproduce natural textures [START_REF] Interrante | Harnessing natural textures for multivariate visualization[END_REF] that make the pattern easy to recognize for most users. However, our tests were performed with participants experienced in geomodeling.

We therefore used a grid pattern in the user study, which is similar to grid wire-frames that participants were familiar with.

Control on the interference. The degree of interference between the pattern and the background color-coded property can be tuned by replacing α p in color equation ( 1) with α p = ω • α p , where ω ∈ [0, 1] is a constant user-defined value.

If ω is close to 0, the pattern should be hardly visible even at locations of maximum intensity I(u), whereas it should be clearly visible if ω is close to 1 (Figure 2). In our experiments, we use an ω value of 0.8 to prevent the pattern from being over-perceived in the display. Perception quality. We chose pattern-based uncertainty visualization over other existing methods because of its high quality in terms of perception:

ω = 0 ω = 0.2 ω = 0.4 ω = 0.6 ω = 0.8 ω = 1
• Interferences -Pattern-based uncertainty visualization has the advantage of being perceptually separable from the primary geological property; furthermore, the choice of adapted patterns minimizes the hidden areas of the model, which is likely to result in lower interferences with the underlying color-coded data.

• Intuitive display -Transparency has proven to be highly connected to the notion of uncertainty, resulting in an intuitive sign-vehicle for uncertainty [START_REF] Griethe | The visualization of uncertain data: Methods and problems[END_REF][START_REF] Grigoryan | Point-based probabilistic surfaces to show surface uncertainty[END_REF][START_REF] Johnson | A next step: Visualizing errors and uncertainty[END_REF][START_REF] Maceachren | Visualizing uncertain information[END_REF].

• Preattentivity -Because blending the pattern affects the value of the image, the local levels of uncertainty are likely to be processed preattentively.

Uncertainty visualization in geology: an example scenario

Since geoscientists typically face various types of uncertainty, uncertainty visualization algorithms can be valuable in many different issues. In this section, we review one specific issue that frequently happens in the oil and gas industry -i.e., the quest for the optimal location of a new appraisal well [START_REF] Lafont | Pers. com. Jaca field trip, Total[END_REF] -in order to provide a typical example of decision-making in geosciences. Appraisal wells primarily aim at gathering information about an unknown area of the subsurface, and are typically drilled at the early steps of the assessment of a reservoir. This example is illustrated on the Nan1 reservoir. 3 We first describe the geological context of the Nan1 field (Section 4.1) and the uncertainty characterization workflow (Section 4.2), before discussing the well locations which are geologically relevant (Section 4.3).

The Nan1 field

Nan1 is a Middle East onshore oil and gas field, covering approximately twenty square kilometers. Oil is accumulated in a structural trap made of low permeability faults and folded strata. The reservoir is located in two stratigraphic formations, named B and W. The B formation was formed in a channeled deltaic environment. It shows a lot of sand bodies stacked on each other, with a good potential in oil and gas content. The B formation is quite homogeneous due to the high density of sand bodies (Figure 3), resulting in a low spatial uncertainty degree on the location of sand-rich areas. The W formation was formed in a fluvial environment. The density of sand bodies is much less favorable and lateral heterogeneity is significant. There is thus a higher uncertainty degree on the location of reservoir rocks. The W formation is estimated to contain between 10 and 20% of the oil in place. A better estimation of the net-to-gross is therefore a worthy challenge, and may help improving the oil production.

Uncertainty characterization

In this study, we focus on the W formation because its evaluation is very sensitive to spatial uncertainty. Because the W formation was deposited in a clastic fluvial environment, we model the facies with the Fluvsim object-based stochastic method [START_REF] Deutsch | Fluvsim: a program for object-based stochastic modeling of fluvial depositional systems[END_REF], which reproduces the geometry of complex channelizing sand bodies [START_REF] Journel | Stochastic modelling of a fluvial reservoir: a comparative review of algorithms[END_REF]. We represent two different facies, the channels and the flood plain. These sedimentary bodies are conditioned to the observations collected along three existing appraisal wells, and honor analog geological observations (sinuosity, height, width, etc.).

For each rock type simulation, we then simulate the petrophysical properties using statistics inferred from core samples. The floodplain porosity is considered constant, but the channels show a higher variability and are therefore simulated using a stochastic algorithm. In this study, we use sequential Gaussian simulation conditioned to well data. The number of realizations is a trade-off between the accuracy of the uncertainty sampling and the CPU cost of the realizations' generation and storage. In this example, we set the cursor to one hundred realizations. After the generation of the set of realizations, it is possible to compute some uncertainty metrics at every single spatial location of the model. We use a normalized standard deviation metric on the set of porosity realizations.

Optimal well location

Appraisal well criteria. To bring as much value as possible, an appraisal well should ideally reach high-pay areas with a high uncertainty. These requirements conflict with each other, since a high-pay area with high uncertainty could actually turn out to be a low-pay area when drilled. Hence, geoscientists have to decide between drilling in an area with a high uncertainty degree where most is unknown, which is typically valuable at the early steps of reservoir characterization, or drilling in an expectedly high-pay zone with moderate uncertainty, which is often preferred when the reservoir is about to enter the production phase. Our visualization methods may be valuable for both approaches, as both require to know about the local uncertainty degree. The Nan1 reservoir shows complex and highly non-linear structures, such as channels, faults and folds. Only three appraisal wells were drilled so far, which is clearly not sufficient to highlight the properties of the reservoir. Minimizing reservoir uncertainty is thus more valuable than minimizing the risk of drilling in a low-pay area at this step.

Reservoir engineers may be interested in a better estimation of the hydrocarbon reserves, typically by finding the oil-water contact. To avoid future overcosts, they may also consider conversion of appraisal wells later in the development of the field, which requires specific care about the placement of the well. For instance, a water-injection well should be placed so that water could sweep oil toward a production well, which means that there should not be any low-permeability zone in-between. Special attention must be paid to faults, which can act either as drains or seals, and to the elevation of the reservoir top. Injectors should also be located at the boundaries of high-pay areas, so that no oil is lost being swept in areas without production wells.

Uncertainty visualization. We applied our pattern-based uncertainty visualization (Section 3) to a layer of the Nan1 field (Figure 4) in order to determine the location of a new appraisal well. Note that for a truly optimal well location, this study should be performed on all of the layers of the reservoir. Using the criteria defined earlier, we were able to define two possible well locations in the Nan1 model. Location A is on the boundary of an area with reasonably high expected porosity, so that the appraisal well may finally be converted into a water-injector. This location is quite deep, however, which means there is a high risk to miss the oil-saturated zone. Location B has a higher position, and is therefore more likely to reach hydrocarbons. Its expected porosity is high, so that the appraisal well could be converted into a producing well on further developments. It may nevertheless be affected by the southern fault permeability, i.e., turning it into a producer would result in low hydrocarbon production if the fault has a sealing effect.

Discussion

On this simple example, uncertainty visualization algorithms were used to support the choice of a new appraisal well location, as they could carry information about the porosity and its associated uncertainty at once. Secondary objectives of the appraisal well should however still be assessed by an expert geologist, as the location of the well is not solely based on the degree of uncertainty. Furthermore, the benefits of uncertainty visualization are not limited to data exploration: uncertainty visualization should also be seen as a way to communicate results to a non-expert audience, in a clear and intuitive manner.

Methodology

This section describes our methodology during the user study design. It is organized around two main axes: (i) the protocol of the user study (Section 5.1) and (ii) the methods used for the analysis of the answers (Section 5.2). Results are discussed in Section 6.

Protocol

Our user study was designed to determine whether uncertainty visualization tools affect decision-making, and if they do, to determine whether adjacent or coincident displays perform better than the other.

Participants

Our study involved 123 participants with a background in geology, including one domain expert, 5 PhD students from the CRPG-CNRS laboratory and 117 MSc students from the Ecole Nationale Supérieure de Géologie. The domain expert was a professional of the oil and gas industry; his level of expertise can be considered as excellent. The 5 PhD students had a variety of different backgrounds; their level of expertise in over-pressured reservoirs ranges from fair to good. The 117 MSc students were involved in geological thematics, but could not be considered as domain experts at this step of their training; their level of expertise ranges from low to fair. Note that participants were selected for logistical reasons rather than because of their expertise.

Model and technical background

The Cloudspin model. The study used a pressure data set generated in the Cloudspin reservoir. 4 The Cloudspin reservoir is an oil and gas field, whose expected production results were simulated with 27 flow simulations -the low number of simulations is due to the large CPU power requirements of flow simulations. As the local pressure around the production well is lower than the reservoir pressure, the hydrocarbons passively flow toward the production well. However, the simulations were performed with several realizations of permeability and various Pressure-Volume-Temperature tables as input parameters. As the viscosity of the hydrocarbons and the rocks permeability varies, so will the local speed of the hydrocarbons' flow, resulting in different reservoir production outcomes. Uncertainty was sampled using all simulated pressure fields taken at a specific time-step of the simulation, then quantified with a normalized standard deviation metric (also termed variation coefficient). The area of high uncertainty highlights the possible boundaries of the depleted area at this time-step.

Pressure in well design. In this user study, participants were required to consider the development of water-injection wells. The goal of such wells is to sweep oil toward the production well, resulting in improved production results. However, the possible local overpressure must be studied prior to drilling a new well, so that the well head counterbalances overpressure at any time. Incorrect estimation of the overpressure may result in a blow up of the well head, putting human lives at risk and destroying costly equipment.

User study description

We split the participants into three groups. All participants were asked the same questions, but were provided with different pictures of the reservoir depending on the group to which they belonged (Figure 5), as suggested in [START_REF] Deitrick | The influence of uncertainty visualization on decision making: An empirical evaluation[END_REF]. The first group was given pressure data only, the second group pressure and uncertainty data displayed separately, and the third group pressure and uncertainty data in a single display using our pattern transparency visualization method. The images were taken in the same conditions for all three groups; all were given short written explanations about the geological background and the risks associated to incorrect overpressure estimation (Section 5.1.2). All materials were provided as colored paper prints; we ensured that images were printed with high quality and that colors were correctly approximated by the printer.

Question design. Because all participants were asked the same questions, we assume that any statistical difference in the answers between the groups would come from the data that were provided. To be valid, this assumption requires that (i) all groups have participants with comparable skills and (ii) a significant amount of answers is collected for each group, so that the statistics are not biased by random behaviors. To meet these requirements, (i) we designed a question meant to compare the groups abilities and (ii) we tried to reach as many participants as possible and assigned them to either group with equal probability, so that the groups were approximately the same size.

Description and goal of the questions. Participants were asked three different questions with increasing complexity. In the first question, participants were asked to indicate in which area of the reservoir pressure was the highest, given three possible choices -east, center or west of the reservoir main panel. This question was intended as a simple map reading test, in order to assess and compare the groups' abilities. The second question required participants to compare well locations A and B in terms of worst possible overpressure. Location A showed higher pressure than location B, but associated uncertainty was lower. We designed this question to study how uncertainty could affect decision in binary choices, and whether the way uncertainty is presented could influence decisions. In the third question, participants were asked to rank well locations D, E, F, G and H from lowest to highest possible overpressure. The goal of this question is quite similar to question 2, but involves much more qualitative decision making, as quantifying the worst possible pressure for each of the five wells may be difficult to achieve in a limited amount of time.

Analysis

The analysis of the answers was performed using different statistical tools. The summary of the tools we used is listed below on a question-per-question basis. Question 1. Question 1 was analyzed using a simple percentage of correct vs. incorrect answers. Although this method does not allow for advanced statistical testing of the distribution of the answers, the large number of correct answers made more sophisticated testing methods useless (Section 6).

Question 2. The results of question 2 were analyzed with the Wilcoxon signed-rank test [START_REF] Wilcoxon | Individual comparisons by ranking methods[END_REF], which was chosen because it does not assume any type of distribution for the answers (non-parametric test). The Wilcoxon test compares two sets of samples, assuming that they come from the same distribution (H0 hypothesis).

We then compute the conditional probability p i-j of the answers of groups i and j under H0. If p i-j is below a threshold α, the H0 hypothesis is rejected, i.e. we make the choice to consider that groups i and j have statistically different answers. We compared the answers of groups 1, 2 and 3 with a threshold α of 0.01.

Question 3. For the analysis of question 3, we have computed the error between the answer and the actual order. This error is computed as the sum of the errors for each well, as detailed in equation ( 2). It can be seen as the total pressure mismatch between the answer and the actual maximum possible pressure of the reservoir, i.e. the error acts as a measure of the perception mismatch.

E = ∑ i∈Ω ∑ j∈Ω, j i
0 if wells i and j are correctly ordered Abs(P i -P j ) otherwise ( 2)

where E is the error, Ω is the set of well locations [well 1 = D, well 2 = E, well 3 = F, well 4 = G, well 5 = H] and P i is the maximum possible pressure at well i.

The average error of a group allows to determine whether the selected visualization method improves or clutters perception. Furthermore, we applied the Wilcoxon signed-rank test to the distribution of the errors, in order to highlight common answer patterns between groups.

Results and discussion

Interpretation of the results

This section provides detailed description of the results we obtained and their implications for each question.

Question 1

Results. Within the 123 participants to the study, more than 96% answered correctly to the first question. We analyzed the correct answer rates for each group; results are reported in Table 3. Participants with incorrect answers were all MSc students.

Interpretation. The large majority of the participants were able to read the data they were provided with. We found that all three groups had an equivalent ability to read the pressure map, which guarantees that our group assignment process did not introduce any bias in terms of map-reading skills. The four participants with incorrect answers were discarded in questions 2 and 3 for additional safety.

Question 2

Results. Distribution of the answers in question 2 were compared using statistical hypothesis testing; answer rates are reported in Figure 6, and probabilities that answers are sampled from similar distributions under the H0 hypothesis are reported in Table 4. We found that groups 2 and 3 have statistically similar answers, while group 1 differs from both group 2 and group 3.

Interpretation. Group 1 had no information about the local uncertainty, while groups 2 and 3 were provided with uncertainty maps. Hence, we interpret these results as the effects of uncertainty on decision-making. This conclusion is similar to the studies performed by [START_REF] Leitner | Guidelines for the display of attribute certainty[END_REF] and [START_REF] Deitrick | The influence of uncertainty visualization on decision making: An empirical evaluation[END_REF]. Note that all groups have the same level of accuracy for that question since wells A and B have very similar worst possible pressures, i.e., 10.50 bars for well A and 10.42 bars for well B.

The way uncertainty is presented has no clear effect on the answers of this question. We believe this is connected to the question complexity; indeed, it is quite easy to quantify pressure and uncertainty at only two well locations, no matter whether uncertainty is presented jointly or separately.

Question 3

Results. The results of question 3 are reported in Table 5; they show that group 1 was closer to the actual pressure ordering than group 3, who in turn performed better than group 2. The Wilcoxon test showed that answers of groups 1 and 3 have similar distribution patterns under the H0 hypothesis, while answers of group 2 differ from the two other groups (Table 6). Interpretation. The average error results suggest that a visualization which integrates a joint display of uncertainty is clearer than two separate visualizations for data and uncertainty for qualitative choices, but that it still occludes part of the primary information present in the map. However, looking at the confidence interval about the average error for groups 1 and 3, we found a non-empty intersection, i.e. both groups may actually be at the same level of perception quality. This hypothesis was checked using the Wilcoxon signed-rank test; we found that answers of groups 1 and 3 had similar distribution patterns under the H0 hypothesis, i.e., that they are actually sampled from the same initial distribution. This result implies that the average error difference between groups 1 and 3 may actually be an artifact, possibly coming from a heterogeneous sampling of the participants, but more likely coming from random behaviors. This suggests that the joint display of uncertainty presented in this paper has the same level of clarity than the map by itself, i.e., that this joint display of uncertainty does not clutter the perception. Conversely, the average error obtained for group 2 suggests that a separate display of the data and the uncertainty obscures perception when compared to the other methods; the Wilcoxon test confirms that group 2 does not share common distribution patterns with any other group.

Groups compared p(similar distributions | H0) Conclusion

Discussion

While the setup of the user study allowed us to answer some of the questions we were investigating, some technical, material or organizational issues prevented us from gathering some interesting pieces of information. This part discusses the limitations of our methodology.

Decision-making speed. Our study was practically distributed as a paper form that could be filled in a limited amount of time. Unfortunately, those conditions did not allow us to measure the time participants took on each question, since the form was distributed to large groups of participants at once. We were only able to limit the total amount of time available to answer all the questions. Time measures would have allowed statistical testing of the decision-making speed between groups, which could have been seen as a first approximation of the intuitiveness of each approach.

Participants' representativity. More than 95% of the parcipants were MSc students; hence, the population used in our experiment clearly suffered from a lack of domain experts. According to Roth (2009b) the task complexity strenghens the influence of the participant's expertise. Our experiments involved well targeting, which is indeed a challenging task. Hence, it is reasonable to expect a bias in the results of our user study, even though the limited number of experts does not allow statistical testing of this hypothesis.

Statistical relevance. In our experiments, participants were evenly distributed into three groups who were asked the same set of three questions, each group having access to a different visualization method. This methodology avoids learning bias, but limits the number of questions that can be tested, hence decreases the statistical relevance of the study. We could have provided the three visualization methods in a random order to each participant, which would have increased our pool of answers while minimizing the effects of learning bias.

Groups compared p(similar distributions | H0) Conclusion

Conclusion

This paper aimed at answering the following questions: Does uncertainty visualization influence decision making? Since this question has already received a positive answer in the literature, we see this test as a cross-check of the consistency of our study, rather than as a new result. The second question of our study revealed different answer patterns whether participants were aware of uncertainty or not, which suggests that uncertainty visualization does have an influence on decision making; hence, our results agree with the findings of previous studies.

Is there a difference in terms of decision-making accuracy between coincident and adjacent displays of spatial uncertainty? Our study resulted in contradictory findings about the influence of the way uncertainty is displayed: our second question resulted in similar results for adjacent and coincident displays, while our third question highlighted significant differences between the two methods. We interpret these different results as a consequence of the increasing complexity of the tasks participants had to perform; the second question was simple enough to be carried out with adjacent displays, while the third question involved complex multi-location assessments, for which adjacent maps introduced a perceptual and cognitive overload [START_REF] Harrower | Representing uncertainty: Does it help people make better decisions?[END_REF]. This suggests that the way uncertainty is presented actually influences user perception; hence, visualizations dedicated to real-world applications should aim at using compact representations of the information in order to minimize cognitive burdens for the users. Does uncertainty visualization act to clarify or to clutter the display of uncertain data? The third question studied the accuracy of the answers with respect to the actual value presented on the display; it has shown that data presented without uncertainty and coincident displays of uncertainty shared the same answer patterns and were close to the best decision, i.e., that uncertainty visualization can present a large amount of information in compact displays without obscuring the important structures in the data. This assertion has to be contrasted with the results of adjacent uncertainty displays, where decisions were much less accurate. This once again points out that only careful design of uncertainty visualizations, with minimal burden on the user, can actually add value to the decisions.

Is the perception of 2.5D/3D data different from the perception of 2D map data in presence of uncertainty? The results of our study are generally consistent with the previous research on this topic, e.g., [START_REF] Leitner | Guidelines for the display of attribute certainty[END_REF] and [START_REF] Deitrick | The influence of uncertainty visualization on decision making: An empirical evaluation[END_REF], which suggests there is little difference in the perception of 2.5D data as compared to traditional map data. However, our experiments did not include any testing of actual 3D data. Exploration of 3D data substantially differs from exploration of 2D/2.5D data, because it typically involves more user interactions, e.g., moving the view point, zooming some particular areas or changing the lights. While such interactions increase the complexity of the logistics of user study design, they may influence the way uncertainty is perceived in the data. Furthermore, results from [START_REF] Sanyal | A User Study to Compare Four Uncertainty Visualization Methods for 1D and 2D Datasets[END_REF] show that it was significantly harder for users to assess uncertainty on 2D data than on 1D data; a similar ascending complexity can thus be expected when jumping from 2D/2.5D data to 3D data. Hence, we consider that the question of user perception on volumes is open; understanding how 3D uncertainties can be seen is a fundamental issue that still needs to be answered in order to produce efficient uncertainty visualizations for geological applications, but also for other scientific domains such as medical research, meteorology or oceanography.

to improve this paper.

Figure 1 :

 1 Figure 1: Visualizations of facies uncertainty on a channel dataset. (a) Uncertainty visualization with procedural annotation lines. The line width denotes of the local uncertainty degree. (b) Pattern-based uncertainty visualization with variable intensity. High-intensity areas have higher facies uncertainty. (c) Fill-clarity uncertainty visualization. Blurred patterns indicate high facies uncertainty. (d) Color-coded facies uncertainty map. For figures (a), (b) and (c), yellow denotes sandy areas and blue denotes shaly areas.

Figure 2 :

 2 Figure 2: Average porosity map on a stratigraphic layer, blended with "fabric" pattern with several values of ω. Top: whole layer without pattern. Bottom: zooms with different values of ω.

Figure 3 :

 3 Figure 3: Two sections of a synthetic geological model showing stacked paleo-channels with different channel densities. Left: the low channel density results in significant facies heterogeneity as in the W formation. Right: the high channel density results in an almost homogeneously sandy medium as in the B formation.

Figure 4 :

 4 Figure 4: Visualization of a faulted geological layer of the Nan1 field showing both the average porosity (color) and its associated uncertainty (pattern intensity). Areas where pattern is visible have high uncertainty degree. The paths of the first appraisal wells are represented as red lines, with a derrick glyph showing their head location. The gray translucent planes correspond to important faults which split the model into several compartments (minor fault planes are not represented). Locations A and B are two possible candidates for the drilling of a new appraisal well, assessed using local uncertainty behavior and domain-dependent knowledge (possible well reconversion in the production phase).

Figure 5 :

 5 Figure 5: Pictures of the Cloudspin reservoir provided with the user study. Top left: average pressure map (available to groups 1 and 2). Top right: uncertainty map (available to group 2). Bottom: average pressure map with uncertainty (available to group 3).

Table 2 :

 2 Visual variables proposed by

Table 3 :

 3 Correct answer rate in question 1.

	Group Correct answer rate Answer count Incorrect answer count
	Group 1		95.1%			41			2
	Group 2		95.0%			40			2
	Group 3		100.0%			42			0
	Group 1
	Group 2										Well A
											Well B
	Group 3
	0%	10%	20%	30%	40%	50%	60%	70%	80%	90%	100%
				Figure 6: Answer rates for question 2.

Table 5 :

 5 Average perception mismatch for each group in question 3.

	Group Average mismatch	Deviation
	Group 1	0.59 Kbars	+/-0.23 Kbars
	Group 2	2.60 Kbars	+/-0.31 Kbars
	Group 3	1.00 Kbars	+/-0.35 Kbars

Table 6 :

 6 Comparison between the distribution of the answers in question 3.

Preattentive processing is a perception mechanism inherent to our visual system that allows humans to perceive some features of a scene very quickly (less than

200ms according to[START_REF] Healey | High-speed visual estimation using preattentive processing[END_REF], which is the time required for eye movement) and without any need to focus on the scene.

Note that although animation is an integral method sensus-stricto, as the uncertainty display is fully integrated into the display of the primary data, we treat animation methods separately because they typically do not need any explicit measure of uncertainty.

Courtesy of Total. For confidentiality reasons, all names and scales related to the reservoir have been modified.

Data courtesy of Schlumberger and model courtesy of Paradigm.

Acknowledgments

We want to express our acknowledgment to all the participants of the user study, and to Irina Panfilova for her useful pieces of advice when designing the user study. We also thank the anonymous reviewers for their suggestions We thank Total for providing the Nan1 model used in the case study, and Paradigm for providing the Cloudspin uncertainty model used in the user study -many thanks to Alexandre Hugot and Emmanuel Gringarten for their work and explanations on the Cloudspin model. We also acknowledge Paradigm for providing the Gocad software and developer API. This research is part of a PhD thesis funded by the Gocad consortium. All the members of the consortium are hereby acknowledged for their support. This is CRPG-CNRS contribution n°2044.