Michel Bonnard

Bruno Boury
email: bruno.boury@umontpellier.fr.

Isabelle Parrot
email: isabelle.parrot-smietana@umontpellier.fr.orcid

A Critical Analysis of Sustainable Solutions

Keywords: Key Insights, Tools, and Future Prospects on Oyster Shell End-of-Life:

HAL is

critical description of valuable routes including processing methods when necessary.

2.1. Potential Applications of NOS. Before any treatment, shells are generally decontaminated of organic substances and salts by radiation, thermal treatment, brushing or oxidation with soaking solutions (NaOH, NaOCl, H 2 O 2 , . . .). In most cases, shells are roughly crushed to reduce storage and transport volumes. Milling gives a uniform and easy-to-use powder, allowing to increase the roughness and the available specific surface area for chemical and physical transformations. [START_REF] Tsai | Microstructural Characterization of Calcite-Based Powder Materials Prepared by Planetary Ball Milling[END_REF] The mother of pearl (the inner layer of Pteriidae shells) is highly prized especially for body art and fashion purposes. In this case, the animal is specifically farmed for its shell and pearl, it only requires a surface treatment followed by shaping.

2.1.1. Food and Cosmetic Industries. NOS powder is a relevant source of calcium, offering real value for food, nutraceutical, or cosmetic purposes. Traditional Chinese medicine praises the health benefits of what is commonly known as Concha ostrea in Latin (Mu-li in Mandarin). The recent edition of the Chinese Pharmacopeia lists NOS powders of different species; C. gigas is the major source of this material, and CaCO 3 the major effective constituent. [START_REF] Yang | Chemical Profiles and Identification of Key Compound Caffeine in Marine-Derived Traditional Chinese Medicine Ostreae Concha[END_REF][START_REF] Li | Traditional Chinese Medicine for Parkinson's Disease: A Review of Chinese Literature[END_REF] Another review summarizing cosmetics in Roman antiquity referred to oyster shell powder as an ingredient for smoothing skin due to the potential local burning effect of lime. [START_REF] Olson | Cosmetics in Roman Antiquity: Substance, Remedy, Poison[END_REF] NOS powder is a potential natural and organic alternative for synthetic phosphate in pork-based products and has attracted substantial interest. [START_REF] Cho | Egg Shell and Oyster Shell Powder as Alternatives for Synthetic Phosphate: Effects on the Quality of Cooked Ground Pork Products[END_REF][START_REF] Cho | Effects of Calcium Powder Mixtures and Binding Ingredients as Substitutes for Synthetic Phosphate on the Quality Properties of Ground Pork Products[END_REF] With a clean label, this calcium source acts as a real additive for food and health products [START_REF] Kim | The Effect of Oyster Shell Powder on the Extension of the Shelf Life of Tofu[END_REF][START_REF] Shono | Reducing Effect of Feeding Powdered Nacre of Pinctada Maxima on the Visceral Fat of Rats[END_REF] or animal feeding. [START_REF] Guinotte | Effects of Particle Size and Origin of Calcium Sources on Eggshell Quality and Bone Mineralization in Egg Laying Hens[END_REF][START_REF] Ahmad | Alternative Feeding Regimen of Calcium Source and Phosphorus Level for Better Eggshell Quality in Commercial Layers[END_REF][START_REF] Wang | Influence of Particle Size and Calcium Source on Production Performance, Egg Quality, and Bone Parameters in Laying Ducks[END_REF][START_REF] Anwar | Effect of Calcium Source and Particle Size on the True Ileal Digestibility and Total Tract Retention of Calcium in Broiler Chickens[END_REF] Different oyster shell powders are commercially available for their benefit effects against bone-related deficiencies. For the development of such products, the granulometry of the oyster shell powder and its association with other elements have a direct influence on the bioavailability and solubility of calcium as was observed on ovariectomized and albino rats by oral administration. [START_REF] Ahmed | Evaluation of Food Products Fortified with Oyster Shell for the Prevention and Treatment of Osteoporosis[END_REF][START_REF] Lee | Highly Bioavailable Nanocalcium from Oyster Shell for Preventing Osteoporosis in Rats[END_REF] The oral uptake of Mg-, Fe-, Cu-, and Zn-rich mollusk shell powder carries health benefits, however, the high bioaccumulation ability of oyster shell, higher than that of eggshells, suggests that traces of toxic heavy metals may often be present or can lead to adverse effect by oral or dermal route. [START_REF] Palaniappan | Oyster Shell Calcium Induced Parotid Swelling[END_REF] Therefore, caution and safety-oriented approaches are recommended for food, animal feeding or other human uses. To protect humans from exposure and consumption, different organizations have specified allowable levels of heavy metals. An evaluation of NOS powders of P. margaritifera from French Polynesia revealed that calcium constitutes 40% of the total weight of the shell. If we consider a human intake of 2.5 g per day, the levels of hazardous metals such as Cd, As, Hg, and Pb are lower than the maximum levels authorized by food committees. [START_REF] Chang | Element Concentrations in Shell of Pinctada Margaritifera from French Polynesia and Evaluation for Using as a Food Supplement[END_REF] 2.1.2. Medical Uses. Nacre produced by the Pinctada genus, have been considered as a prime candidate for bone tissue bioengineering applications, as this biomaterial is compatible with bone tissues and has high mechanical properties. [START_REF] Zhang | a Natural, Multi-Use, and Timely Biomaterial for Bone Graft Substitution[END_REF] Based on in vitro and in vivo studies, nacre is described as a natural, biocompatible, and biodegradable biomaterial with osteoinductive, osteointegrative, and osteoconductive properties and is therefore extensively studied for its bone substitution capacity. One of the first historical instances of the use of nacre in bone tissue bioengineering was observed in 1931 in the lower jawbone of a Mayan individual (Figure 2). [START_REF] Green | Evolving Marine Biomimetics for Regenerative Dentistry[END_REF] Later, major breakthroughs have been made by the group of Prof. Lopez in the field of bone graft substitution by nacre of Pinctada spp. shells, as highlighted by Westbroek and Marin. 32 This work includes in vivo and in vitro studies with various nacre preparations, such as nacre powder mixed with blood, nacre chips, and nacre prostheses; [START_REF] Zhang | a Natural, Multi-Use, and Timely Biomaterial for Bone Graft Substitution[END_REF] alginate hydrogels including nacre powder have also been investigated. [START_REF] Flausse | Osteogenic Differentiation of Human Bone Marrow Mesenchymal Stem Cells in Hydrogel Containing Nacre Powder[END_REF] In contrast, only one study has focused on the osteogenic capacity [START_REF] Atlan | Interface between Bone and Nacre Implants in Sheep[END_REF] of Ostreida shells. [START_REF] Coringa | Bone Substitute Made from a Brazilian Oyster Shell Functions as a Fast Stimulator for Bone-Forming Cells in an Animal Model[END_REF] This study is attractive since it shows the potential use of NOS for bone tissue bioengineering, not only restricted to nacre from Pinctada shells. With the advance of material science, this field of research is in constant progress. The development of functionalized and specific composites with various shapes constitutes one of the main challenges. Promising perspectives were recently obtained with the design of hydroxyapatite nanoparticles coated on substrates of nacre from P. maxima shell, [START_REF] Brundavanam | Synthesis of a Bone like Composite Material Derived from Waste Pearl Oyster Shells for Potential Bone Tissue Bioengineering Applications[END_REF] with composite of calcium sulfate and oyster shell [START_REF] Shen | Engineering Scaffolds Integrated with Calcium Sulfate and Oyster Shell for Enhanced Bone Tissue Regeneration[END_REF] or with scaffold composites of dried oyster shell powder and poly(L-lactide). [START_REF] Didekhani | Electrospun Composite PLLA/Oyster Shell Scaffold Enhances Proliferation and Osteogenic Differentiation of Stem Cells[END_REF] Moreover, the use of innovative technologies for the development and production of personalized bone-like implant, with controlled porosity and shape starts to be used in research laboratories. A good example is the use of fused deposition modeling technology recently applied to design scaffolds of NOS powder dispersed in a polycaprolactone matrix with a positive osteogenic activity when tested in vitro on osteoblast-like cells. [START_REF] Luo | 3D Printed Porous Polycaprolactone/Oyster Shell Powder (PCL/OSP) Scaffolds for Bone Tissue Engineering[END_REF] By combining new technologies with material science and biology, these studies show the outstanding properties of NOS for use in bone grafting. It would be interesting to evaluate the osteogenic performances of NOS compared to others more accessible and less expensive natural composites. Other potential medical uses stay underexplored despite the presence of few preliminary studies in the literature. For example, the stimulation of skin fibroblasts by nacre powder implanted between dermis and hypodermis in rats was observed by Lopez et al. (2000), [START_REF] Lopez | Stimulation of Rat Cutaneous Fibroblasts and Their Synthetic Activity by Implants of Powdered Nacre (Mother of Pearl)[END_REF] as well as the anticarcinogenic potential of C. gigas shell powder when administered to mice with induced tongue tumors. [START_REF] Chen | Inhibition of 4NQO-Induced Oral Carcinogenesis by Dietary Oyster Shell Calcium[END_REF] 2.1.3. Pollutant Remediation. Soil Quality Improvement. The pKb of hydrogen carbonate (6.6) has led to consider NOS as an efficient base to neutralize the acidity of soil in different environments, natural or polluted. [START_REF] Moon | Amelioration of Acidic Soil Using Various Renewable Waste Resources[END_REF] Treatment of acidic soil with pulverized NOS causes neutralization but also a beneficial increase in Ca 2+ , Mg 2+ , K + , and Na + and the stabilization of heavy metals that are less exchangeable upon lixiviation (SI Table S2). Surface adsorption is a possible explanation, in addition to the formation of poorly soluble metal hydroxides or metal carbonates. The specific sorption of metal cations by the CaCO 3 mineral phases distributed in oyster shells (aragonite and calcite) plays an important role in surface adsorption. [START_REF] Du | Biosorption of Divalent Pb, Cd and Zn on Aragonite and Calcite Mollusk Shells[END_REF] Such decontamination or stabilization is also dependent on the pH, aerobic conditions, ion composition, and counterion but in general, the efficiency of NOS to stabilize soil has been established. Some studies mentioned a putative role of chitin occurring in the organic matrix and the possible coordination of heavy metal cations. Although not enriched in carbon, NOS powder can be a source of carbon for plant growth; the presence of residual NaCl is apparently not injurious in most cases. [START_REF] Lee | Effects of Oyster Shell on Soil Chemical and Biological Properties and Cabbage Productivity as a Liming Materials[END_REF] Combining NOS and biochar or biopolymer improves soil fertility, carbon sequestration, and worm activity. [START_REF] Awad | Carbon and Nitrogen Mineralization and Enzyme Activities in Soil Aggregate-Size Classes: Effects of Biochar, Oyster Shells, and Polymers[END_REF][START_REF] Kwon | Development of Vermicast from Sludge and Powdered Oyster Shell[END_REF] Given the overuse of fertilizers, especially in agriculture, and the resulting deterioration in water quality, NOS powders were found to be effective in phosphorus removal and are applicable as a beneficial media in artificial wetland systems. [START_REF] Seo | Phosphorus Retention Capacity of Filter Media for Estimating the Longevity of Constructed Wetland[END_REF][START_REF] Park | Phosphorus Adsorption Characteristics of Oyster Shells and Alum Sludge and Their Application for Nutrient Control in Constructed Wetland System[END_REF] Water Treatment. Living oysters are well-known for their capacity to reduce eutrophication in natural water, [START_REF] Bricker | Role of Shellfish Aquaculture in the Reduction of Eutrophication in an Urban Estuary[END_REF] as well as metals cations, plastic particles, and other chemicals in some cases. [START_REF] Liu | Facilitated Bioaccumulation of Cadmium and Copper in the Oyster Crassostrea Hongkongensis Solely Exposed to Zinc[END_REF][START_REF] Tan | Modeling the Toxicokinetics of Multiple Metals in the Oyster Crassostrea Hongkongensis in a Dynamic Estuarine Environment[END_REF][START_REF] Cole | Ingestion of Nanoplastics and Microplastics by Pacific Oyster Larvae[END_REF][START_REF] Jeon | Bioaccumulation of Perfluorochemicals in Pacific Oyster under Different Salinity Gradients[END_REF] Although, high efficiency is not always achieved, the list of pollutants that can be potentially removed by NOS is summarized in SI Table S3, including anions, cations, organics such as antibiotics, [START_REF] Huang | Removal of Antibiotics and Resistance Genes from Swine Wastewater Using Vertical Flow Constructed Wetlands: Effect of Hydraulic Flow Direction and Substrate Type[END_REF] neurotoxins, [START_REF] Melegari | Preliminary Assessment of the Performance of Oyster Shells and Chitin Materials as Adsorbents in the Removal of Saxitoxin in Aqueous Solutions[END_REF] and nitrogen. [START_REF] Shih | The Effect of Water Purification by Oyster Shell Contact Bed[END_REF] Two major phenomena can explain the ability of NOS to remove such pollutants: first, the ionic interaction between ions and the surface of the NOS; and second, the precipitation on the NOS surface of insoluble salts resulting from the presence of carbonate, calcium, and hydroxyl. Unfortunately, many experimental parameters are not systematically reported which limits comparability. The shell structure and its microstructures are parameters that can drive the ability of NOS to adsorb pollutants as it was shown for the different adsorption behaviors between the prismatic and nacreous layers. [START_REF] Wu | Adsorption of Copper to Different Biogenic Oyster Shell Structures[END_REF] The organic matrix may also participate in the complexation of cations and can explain why removal is more efficient with NOS than with calcined NOS.

Thanks to its porous structure and its buffering properties, NOS in collaboration with microorganisms is also relevant in eco-friendly remediation of wastewater achievable in packedbed bioreactors. [START_REF] Yokogawa | Development of Porous Materials as Carriers Immobilizing a Microorganism for Water Purification Prepared by Using Waste Materials[END_REF][START_REF] Moon | Initial Alkalinity Requirement and Effect of Alkalinity Sources in Sulfur-Based Autotrophic Denitrification Barrier System[END_REF][START_REF] Sengupta | Autotrophic Biological Denitrification for Complete Removal of Nitrogen from Septic System Wastewater[END_REF][START_REF] Sahu | Biological Perchlorate Reduction in Packed Bed Reactors Using Elemental Sulfur[END_REF][START_REF] Yam | A Preliminary Investigation of Wastewater Treatment Efficiency and Economic Cost of Subsurface Flow Oyster-Shell-Bedded Constructed Wetland Systems[END_REF][START_REF] Feng | Production of Unburned Calcium Silicon Filter Material (UCSFM) from Oyster Shell and Its Performance Investigation in an A/O Integrated Biological Aerated Filter Reactor (A/O-BAF)[END_REF][START_REF] Jung | Feasibility Test of Waste Oyster Shell Powder for Water Treatment[END_REF][START_REF] Tong | Effect of Oyster Shell Medium and Organic Substrate on the Performance of a Particulate Pyrite Autotrophic Denitrification (PPAD) Process[END_REF][START_REF] Wang | Fe 0 /C-Bentonite Alginate Beads and Oyster Shell Fixed-Bed Column Combined Process to Continuously Remove N-Acetyl-p-Aminophenol in Persulfate System[END_REF] In general oyster shells served a 3-fold purpose: as a biofilm carrier, a source of organic carbon, and as a basifying agent. [START_REF] Tong | Effect of Oyster Shell Medium and Organic Substrate on the Performance of a Particulate Pyrite Autotrophic Denitrification (PPAD) Process[END_REF][START_REF] Njoyim | Coupling Gliding Discharge Treatment and Catalysis by Oyster Shell Powder for Pollution Abatement of Surface Waters[END_REF][START_REF] Chiou | Using Oyster-Shell Foamed Bricks to Neutralize the Acidity of Recycled Rainwater[END_REF] Research conducted in this field has also been developed at the pilot-plant scale using oyster shells mixed with inorganic minerals like zeolite for phosphorus and nitrogen removal [START_REF] Jung | A Novel Approach to an Advanced Tertiary Wastewater Treatment: Combination of a Membrane Bioreactor and an Oyster-Zeolite Column[END_REF] or for the growth of biofilms. [START_REF] Luo | Waste Oyster Shell as a Kind of Active Filler to Treat the Combined Wastewater at an Estuary[END_REF] NOS is efficient to remove a wide range of pollutants from wastewater at various processing scale, it would be interesting to evaluate its sorption capacity toward highly hazardous pollutants. NOS could also be a relevant fixing support in aquaculture as it is the case for the development of C. gigas larvae in hatchery [START_REF] Nestlerode | Settlement and Survival of the Oyster Crassostrea Virginica on Created Oyster Reef Habitats in Chesapeake Bay[END_REF] or wastewater treatment.

Dechlorination of Waste. This is certainly not the most appealing route for recycling oyster shells, but surely a useful and simple application. When mixed with polyvinyl chloride (PVC), NOS neutralizes harmful HCl resulting from PVC incineration with an efficiency similar to commercially available calcium carbonate and with CaCl 2 as byproducts. [START_REF] Tongamp | Simultaneous Treatment of PVC and Oyster-Shell Wastes by Mechanochemical Means[END_REF][START_REF] Tongamp | Relation between Mechanochemical Dechlorination Rate of Polyvinyl Chloride and Mill Power Consumption[END_REF] 2.1.4. Material Synthesis. Composites. Recent researches demonstrate that NOS can be used as filler in polymers such as polyethylene. [START_REF] Yao | Surface Free Energy and Mechanical Performance of LDPE/CBF Composites Containing Toxic-Metal Free Filler[END_REF] Although performances are limited, the thermal decomposition of NOS at high temperature generates CO 2 that is relevant for retarding the thermal decomposition of the polymer. Composites made of NOS and polyethylene, polypropylene, natural rubber, or asphalt present remarkable mechanical and thermal stability. [START_REF] Chong | Fire-Retardant Plastic Material from Oyster-Shell Powder and Recycled Polyethylene[END_REF][START_REF] Shah | Development of Biowaste Encapsulated Polypropylene Composites: Thermal, Optical, Dielectric, Flame Retardant, Mechanical, and Morphological Properties[END_REF][START_REF] Shah | The Influence of Particle Size and Surface Treatment of Filler on the Properties of Oyster Shell Powder Filled Polypropylene Composites[END_REF][START_REF] Li | Effect of Oyster Shell Powder Loading on the Mechanical and Thermal Properties of Natural Rubber/Oyster Shell Composites[END_REF][START_REF] Nciri | Potential of Waste Oyster Shells as a Novel Biofiller for Hot-Mix Asphalt[END_REF] The granulometry of NOS powder and the mediation of interfacial weak interactions revealed to be crucial points for the development of such composites. These studies show that NOS is a cheap, natural, and easy to work substitute of common fillers in polymeric industry.

Foaming Agent. Due to the production of CO 2 resulting from the decomposition of calcite at T > 550 °C, NOS has been used as a foaming agent for the preparation of vitrocrystalline foam. The best results were obtained with 91% glass bottles and 9 wt % oyster foams fired at 900 °C, demonstrating characteristics and properties similar to (or better than) those of analogous commercial products such as glass and alumina foams. [START_REF] Teixeira | Vitrocrystalline Foams Produced from Glass and Oyster Shell Wastes[END_REF] Templates in Material Science. In this field, the general approach is the replication of natural organs leading to materials biomimicking natural structures. Since it is easily removed by acidic treatment, NOS is an interesting option as sacrificial template for such morphological mimicry. Careful attention should be paid to the shell structure selected as the template and the targeted application. For example, the design of folded SiO 2 requires a shell substrate made of chalky and foliated structures only occurring in Ostreidae shells. [START_REF] Lee | New Approach for Fabrication of Folded-Structure SiO 2 Using Oyster Shell[END_REF] Another example is the pyrolysis of powdered NOS with layered structure mixed with soft pitch to prepare porous carbon anodes in lithium ion batteries. [START_REF] Gao | Hierarchical Porous Carbon Sheets Derived from Biomass Containing an Activation Agent and In-Built Template for Lithium Ion Batteries[END_REF] However, materials are not performant enough to be an attractive way of recycling.

Support for Catalysts in Organic Chemistry. The use of NOS as support of catalysts is a growing field of research with high potential. Heterogeneous catalyst was formulated with powders of CuBr and NOS with higher efficacy than a mixture of CuBr and CaCO 3 . [START_REF] Xiong | Eco-Efficient, Green, and Scalable Synthesis of 1,2,3-Triazoles Catalyzed by Cu(I) Catalyst on Waste Oyster Shell Powders[END_REF] The authors hypothesized an important chelating role of chitin and proteins constituting the organic matrix of NOS for [Cu]-active species. The good chemical stability and reusability (at least eight times) of the [NOS-CuBr] composite are among the attractive points of this approach. Among other recent attractive data, NOS powder has been found to be useful as a support for MgO, Al 2 O 3 , CaCO 3 , and zeolite (ZSM-5) to catalyze gas produced by the pyrolysis of waste tires. [START_REF] Kordoghli | Novel Catalytic Systems for Waste Tires Pyrolysis: Optimization of Gas Fraction[END_REF] Despite the novelty of the approach, the latter is limited by the necessity to avoid any contaminant from the shell that would disturb the catalytic activity.

Relevant Original Source of Calcium, Calcium Carbonate, and Sodium. The most general way of recycling seashell waste is the use as aggregates for the formulation of concrete that could easily be established in aquaculture where concrete is used as a growing support. The important points being the granulometry of NOS and other minerals entering in the formulation. [START_REF] Mo | Recycling of Seashell Waste in Concrete: A Review[END_REF][START_REF] Eziefula | Properties of Seashell Aggregate Concrete: A Review[END_REF] Despite the relative simplicity for the implementation of this type of material, their long-term durability is not well-known. Such applications are not innovative but still relevant for a large-scale recycling of NOS.

The use of NOS instead of ores as source of CaCO 3 can also be innovative for the production of advanced materials such as aragonite needles, [START_REF] Ramakrishna | Synthesis of Aragonite-Precipitated Calcium Carbonate from Oyster Shell Waste via a Carbonation Process and Its Applications[END_REF] high-purity calcite submicrometern powder [START_REF] Lu | Scalable Recycling of Oyster Shells into High Purity Calcite Powders by the Mechanochemical and Hydrothermal Treatments[END_REF] and CaSO 4 :2H 2 O powder or whiskers. [START_REF] Zhao | Synthesis of Calcium Sulfate Hemihydrate Whiskers Using Oyster Shells[END_REF] In this field the hydroxyapatite is the paramount example of a highdemanded Ca 2+ -containing material (eq 1), and NOS was found useful for its synthesis with different morphologies and specific surface areas depending on the conditions of the hydrothermal process (Figure 3). (1)

In an innovative approach, NOS was used for the preparation of 1D nanostructured single-crystalline Na 2 Ti 6 O 13 and Na 2 W 4 O 13 with lower processing temperature and higher yield than with chemical mixtures (Figure 4). [START_REF] Lee | Growth of Single-Crystalline Sodium Titanate and Sodium Tungstate One-Dimensional Nanostructures: Bio-Inspired Approach Using Oyster Shell[END_REF] 2.2. Potential Applications of CNOS. Calcination of NOS leads to the so-called calcined natural oyster shell (CNOS), a potential multiuse raw material. This is usually performed on mixed batches of shells with unreliable traceability and poor consideration of the composition and structural differences among oyster species. This is a limit to the recycling of shells, especially when targeting specific synthesis of advanced materials. Calcination of NOS starts with water loss and decomposition of the organic matrix at temperatures of approximately 200-400 °C, leading to a weight loss of 2-4%. [START_REF] Soisuwan | The Characteristics of Green Calcium Oxide Derived from Aquatic Materials[END_REF] In the case of aragonite-rich shells like P. margaritifera, a thermal structural phase transition from aragonite to calcite occurs between 280 and 500 °C. [START_REF] Bourrat | Nacre Biocrystal Thermal Behaviour[END_REF][START_REF] Wardecki | Internal Pressure in Annealed Biogenic Aragonite[END_REF] At higher temperatures, the decomposition of calcite leads to the eco-valuable production of calcium oxide, which is concomitant with the release of carbon dioxide between 550 and 800 °C (weight loss of 40-45%) but calcite can still be present up to 900 °C (eq 2). 95

→ + Δ = CaCO CaO CO DH 178kJ/mol 3(s) (s) 2(g) (2)
In light of the energy required, thermal treatment of NOS should be considered only for attractive applications. An innovative microwave calcination treatment was recently applied to oyster shell powder with quasi-complete decomposition obtained at 900 W (2.45 GHz; 20 min). [START_REF] Huang | Microwave Calcination of Waste Oyster Shells for CO 2 Capture[END_REF] Considering the time and energy required, microwave calcination is an attractive method. NOS powder can also be decomposed with high-voltage electric current under a reduced oxygen concentration at approximately 800 °C. [START_REF] Fujita | Active Absorbable Algal Calcium (AAA Ca): New Japanese Technology for Osteoporosis and Calcium Paradox Disease[END_REF][START_REF] Fujita | Intestinal Absorption of Oyster Shell Electrolysate[END_REF] Known as active absorbable calcium (AACa) or oyster shell electrolysate (OSE), this powder is mainly composed of lamellar CaO structure. [START_REF] Fujita | Active Absorbable Algal Calcium (AAA Ca): New Japanese Technology for Osteoporosis and Calcium Paradox Disease[END_REF][START_REF] Fujita | Effect of Calcium Supplementation as Oyster Shell Heated in Vacuo on Metabolism and Survival of Rats[END_REF] However, the description of the preparation of AACa suffers from a lack of scientific criteria of repeatability. 2.2.1. Medical Uses. The research group of Fujita extensively studied the effect of preparations of CNOS in the prevention and treatment of calcium metabolism-related diseases. Their review on osteoporosis summarizes the contributions of AACa and active absorbable algal calcium (AAACa). 100 Compared to CaCO 3 , AACa is described as a readily absorbable form of calcium, [START_REF] Fujita | Intestinal Absorption of Oyster Shell Electrolysate[END_REF] favorable for the treatment of osteoporosis by oral route 101,102 as well as AAACa, which is a mixture of AACa with an extract of the seaweed Cystophyllum f usiforme. [103][104][105] AAACa was suggested to be the most efficient ingredient at preventing osteoporosis 106 with positive analgesic effect on joint pain. 107 More surprisingly, supplementation with AAACa has been reported to prevent light, sound, and emotional stress resulting from neuromuscular instability. 108 Among these various studies, no adverse effects have been observed.

This substantial work displays interesting effects of CNOS toward the prevention of osteoporosis. Combining CNOS with other active ingredients could be an innovative approach for the development of nutraceuticals as it was recently shown for the treatment of inflammatory bowel disease on mice by oral administration of zeolite-CNOS mixture. 109 The development of such products has to be evaluated in comparison with NOSbased products given the low sustainability of NOS calcination. S4). [START_REF] Moon | Amelioration of Acidic Soil Using Various Renewable Waste Resources[END_REF] Further comparative researches are needed to evaluate the relevance of CNOS compared to NOS.

Water Treatment. CNOS generally removes cationic pollutants more effectively than NOS as described for Cd(II) (SI Table S4). 110,111 The higher the temperature of calcination, the better is the efficiency of CNOS. This observation is directly related to the large increase in the specific surface area of the material upon calcination. 112 This phenomenon can also be explained by the formation of insoluble metal hydroxides by adsorption of the metal on the surface of CNOS. Unlike NOS, CNOS was applied to remove and recover other chemicals such as boron, 113 free fatty acids and iodine from the bleaching process of palm kernel oil, 114 and pathogen like E. coli. 115 Gas Treatment. The basic character of CNOS is welladapted to remove pollutants such as SO 2 , SO 3 , H 2 S, and NO x in dry or wet processes as well as CO 2 sequestration. [116][117][118] Obviously, this strategy is relevant only if the cyclability of the process allows higher CO 2 sequestration than CO 2 generation due to calcination. 119 2.2.3. Material Synthesis. Standard Reagent. Different studies support that NOS-derived CaO powder can be used as a standard chemical reagent and can be classified in the reactive class R4. 120 Dissolution of CNOS leads to a Ca(OH) 2 solution/suspension that is useful for the preparation of hydroxyapatite, 121 unfired fly ash bricks, 122 mortar, 123 or nanomaterials like Ca(OH) 2 hydoxide nanoplates (Figure 5). 124 Hydroxyapatite can also be obtained by direct solventfree ball-milling and calcination, 125,126 an interesting way to produce chemicals with higher added value than NOS.

In the field of nanotechnology, nanomaterials are easily accessible by reacting CNOS with K(MnO 4 ) to form nanostructured Mn/Ca mixed-oxides decorated with Mn 3 O 4 nanoparticles that have potentially high adsorption capacities for Pb(II) and Eu(III). 127 Silicate nanofibers prepared hydrothermally with CNOS (Figure 6) are efficient porous absorbent of metal cations, such as Cu(II), Cr(VI), 128 and anion such as phosphates. 129 In the same application field, calcium silicate wollastonite and pseudowollastonite were obtained at 1100-1200 °C by mixing NOS and waste float glass from building demolition. This work represents an additional step toward the synthesis of advanced materials made from 100% waste. 130 Catalyst and Support for Catalysts. CNOS is potentially attractive for catalysis or cocatalysis in processes that require basic media, a typical case being the transesterification of soybean oil. [131][132][133][134][135] Very recently, CNOS nanoparticles were employed as a catalyst for the preparation of 1,8-dioxooctahydroxanthenes via the one-pot condensation of 5,5dimethylcyclohexane-1,3-dione or dimedone with various aldehydes under solvent-free conditions. 136 Chemical stability and reusability of CNOS catalyst are among parameters to be investigated.

Filler in the Synthesis of Polymer. Applications of CNOS in this area are limited, CNOS powder was reported as a filler in a polypropylene polymer. 137 Thermal and mechanical properties of this material are comparable to those obtained with commercial CaCO 3 , thus questioning the relevance of NOS calcination.

2.2.4. Antibacterial Agent. The antibacterial activity of NOS calcined under ohmic heating was evaluated against E. coli, Salmonella, and Listeria monocytogenes inoculated on the surface of tomatoes. 138 CNOS had an efficient antimicrobial activity, higher than that of a preparation with 200 ppm chlorine and distilled water. The antibacterial activity is certainly attributed to the basicity of the preparation due to the hydration of CaO. 139 This emerging application shows that CNOS is a potential antibacterial agent of interest as a substitute of synthetic commercial chemicals or in the polymer industry where antibacterial polypropylene/CNOS composites were recently investigated. 140 2.3. Potential Applications of Biomolecules Extracted from the Organic Matrix. Frequently described as a set of macro-and low-molecular-weight biomolecules, the organic matrix is actually an extremely complex material whose exact composition, assembly, and mechanism of action are not fully defined at the molecular level. The organic matrix can be classified into sets of biomolecules based on their extraction process and solubility, that is, the water-soluble matrix (WSM), ethanol-soluble matrix (ESM), acid-soluble matrix (ASM), acid-insoluble matrix (AIM), EDTA-soluble matrix (ED-TASM), EDTA-insoluble matrix (EDTAIM), and fat-soluble matrix (FSM).

The nature of AIM (sometimes called conchiolin) has been shown to be proteinaceous and constitutes more than 90% of the organic matrix. 141 ASM and AIM can be obtained after dissolution with acids followed by several separation steps. 141,142 Calcium-chelating agents, such as EDTA, are also employed at neutral pH. A general protocol was proposed by the research group of Marin which was described to minimize the degradation of proteins and avoids the formation of aggregates. 143,144 In the nacre of P. maxima shell, the extraction yields of ASM and AIM are 1.20 and 0.17 wt %, respectively. 145 WSM extraction from nacre was originally applied and patented by the research group of Prof. Lopez. The extraction method does not allow recovery of molecules strongly bound to the mineral phase but is directly compatible with biological purposes such as in vitro and in vivo trials. The achievable extraction yield varies from approximately 0.2 to 5 wt %. 146,147 A method was recently developed to extract and fractionate ESM from the nacre of P. margaritifera; 148 to the best of our knowledge, the molecular characterization of ESM has not yet been investigated. In addition, extraction yield has not been reported.

Among these extracts, WSM is the most studied, but has almost exclusively been investigated for its osteogenic activity. The different potential applications of these extracts are summarized in the following subsections.

2.3.1. Water-Soluble Matrix (WSM). Bone Tissue Bioengineering. The osteogenic activity of WSM originally extracted from the powdered nacre of P. maxima shell (50-150 μm) was highlighted by the research group of Prof. Lopez. 149 WSM was revealed to be osteoinductive, enhancing in vitro bone cells differentiation and cellular osteogenic markers. Osteogenic activity studies of WSM were extended to P. f ucata and P. martensii nacre. As an example, this academic research has been developed in the form of cosmetic and nutraceutical ingredients by the French company StanSea. To the best of our knowledge, no in vivo or in vitro studies have been published on the osteogenic activity of WSM extracted from Pteria and Ostreida oyster shells, whereas the presence of WSM in the shell of C. gigas is well-known. 150 Only a few studies have described the relationship between WSM proteins of Ostreida shells and osteogenic activity. 151,152 To confirm this assumption, in vitro trials are further required.

Other Biological Activities: Antioxidant Activity, Anti-Inflammatory Activity, and Dermal Fibroblast Regulation. The antioxidant activity of WSM extracted from the nacreous layer of P. f ucata shell was investigated in terms of its capacity to scavenge free radicals (DPPH and ABTS tests), to inhibit lipid peroxidation and to reduce damage in human keratinocyte cells after inducing oxidative stress. 153 The authors showed that WSM can scavenge free radicals in a dose-dependent manner, reducing the effect of oxidative stress in human keratinocytes.

WSM was also tested in vitro for its anti-inflammatory and antioxidant activities on mouse macrophages. 154 WSM suppresses or decreases pro-inflammatory factors linked to pro-inflammatory cytokine inhibition and exhibits antioxidant activity. Unfortunately, information on the oyster species used in this study was not presented.

For a different purpose, Latire et al. (2017) described the fact that WSM extracted from C. gigas shell can favor the catabolic activities of human dermal fibroblasts in vitro. 150 In comparison with the numerous osteo-benefits attributed to WSM, these are the only examples found in the literature highlighting other biological properties, and therefore the field is still highly open.

Ethanol-Soluble Matrix (ESM). Brion et al. (2015)

originally described the osteogenic effect of ESM from the nacre of P. margaritifera. 155,156 This topic was further investigated in vitro by the stimulation of mouse preosteoblasts and human osteoarthritis osteoblasts with ionic fractions of ESM. 148 This study reveals clues about the cationic nature of the osteogenic compounds found in the nacre of oyster shells. Comparative osteogenic and scalability studies between ESM and WSM are required knowing that the process by which ESM is obtain does not require a freeze-drying step as it is the case for WSM extraction.

2.3.3. Acid-Soluble Matrix (ASM). Prevention of Cognitive Diseases. Recently, ASM extracted from the nacreous layer of P. f ucata shells was tested in vivo against scopolamine-induced memory impairment in Wistar rats and ICR mice. 157 In both cases, ASM improved memory and cognitive impairments, suggesting that ASM can affect brain function by protecting against the dysfunction of glutamate neurotransmission. This mechanism was supported by the examination of the known genes associated with memory.

Free Radical Scavenging. A purple organic substance precipitated from a solution of ASM was capable of scavenging hydroxyl and superoxide radicals. 158 With an extraction rate of approximately 2.49 wt %, this extract could be of great commercial interest, especially for food, nutraceutical, or cosmetic products. Unfortunately, the article lacks sufficient experimental details to allow easy reproduction of the protocol.

Dermal Fibroblast Regulation. Latire et al. ( 2017) recently described the regulatory activities of ASM on the metabolism of dermal fibroblasts in vitro. 150 This pioneer work was performed with ASM obtained from the shell of C. gigas.

Material Synthesis. Adding supersaturated CaCO 3 solution to ASM extracted from the nacreous layer of P. margaritifera shell produces nanostructured CaCO 3 crystals whose morphology depends on the concentration of ASM. 159 A protein isolated from the ASM of the nacre from P. f ucata shell was employed to induce the formation of aragonite and calcite crystals. 160 Such innovative results open new pathways for the synthesis of inorganic phases.

2.3.4. Acid-Insoluble Matrix (AIM). Natural Multifunctional Biopolymer. Chitin (poly 2-acetamido-2-deoxy-β-Dglucose) is a nontoxic, biodegradable, and biocompatible biopolymer of considerable interest for the pharmaceutical, cosmetic, biochemical, agricultural, and food industries. This biopolymer was identified for the first time in the AIM of the prismatic layer of P. fucata. 161 Recently, extraction of chitin was reported from undefined raw oyster shell species, 162 but the reported content of chitin extracted from the shell (69 wt %) is inconsistent with all other reported mass fractions of the organic matrix in the oyster shell.

Material Synthesis. In the design field of crystal growth, a promising application describes the preparation of macromesoporous TiO 2 . 163 TiO 2 nanoparticles were grown onto AIM macrotemplate by sol-gel. The resulting anatase showed interesting photocatalytic activity, especially for samples calcined at 450 °C. However, the chemistry by which AIM and TiO 2 nanoparticles interact is not described. This study shows the prime importance of the shell structure for such material synthesis.

2.3.5. EDTA-Soluble Matrix (EDTASM). The only application found in the literature regarding the use of EDTASM concerns material synthesis. Calcite and aragonite crystals were selectively prepared with the help of EDTASM proteins extracted from specific microstructures of C. gigas shells. 164,165 2.3.6. EDTA-Insoluble Matrix (EDTAIM). A single article relates the use of the proteinaceous fraction of EDTAIM to induce aragonite crystals formation in saturated CaCO 3 solution with the addition of Mg 2+ . 166 It is important to note that the aragonite crystals do not grow either without Mg 2+ or with individual components of the fraction.

2.3.7. Fat-Soluble Matrix (FSM). Perhaps more unexpected, lipids are part of the shell organic matrix. The research group of Prof. Lopez highlighted the fact that FSM extracted by maceration of nacre with a mixture of methanol and chloroform can promote the restoration of the stratum corneum in vitro. 167 2.3.8. Shell color related compounds. A potential application is never mentioned in reviews on the topic: the use of pigments and dyes extracted from the oyster shell. Shell color generally varies from dark-red to brown, and sometimes golden or even pink (Figure 7). In the current industrial context, synthetic pigments and dyes tend to be substituted by natural equivalents, especially in health products. One key challenge to be resolved lies in the identification of compounds at the origin of shell coloration and thus their selective extraction. The presence of melanin extracted in black C. gigas shell is a hypothesis but has not yet been convincingly established. 168 To date, no biomolecules have been associated with shell coloration other than black excepted for the presence of fluorescent porphyrins in the shells of Pinctada and Pteria genius. [169][170][171] This innovative recycling of oyster shell is still at the level of fundamental research and lacks of substantial and exhaustive works.

CRITICAL ANALYSIS

The economic viability of any recycling process depends on two essential parameters: the cost and the logistic to collect the shell on one hand, and the added-value of the product resulting from the recycling on the other hand. The generation of pollutants, emissions, or new waste must be minimized in an environmentally friendly philosophy; however, this might be acceptable if the added value of the final product can cover the expense of the treatment in eco-friendly conditions.

So far, oyster shells collection remains to be organized since it is actually considered as a diffuse pollution (consumers, factories, and farms). Recently, de Alvarenga et al. (2012) examined the LCA of oyster shell waste according two scenarios: (i) the direct deposit of shells in a landfill or (ii) the implementation of a simple process to produce CNOS powder (<20 μm). 174 They concluded in favor of the chalk production process. Although this option is strongly dependent on the distance between the source point and the shell-processing facility. Figure 8 gives an overview of possible application fields for the recycling of waste oyster shells.

As raw material, NOS is useful for basic applications requiring simple and low-cost processing technologies at largescale such as animal feeding (SI Table S5).

In economic terms, these applications do not bring high added-value but they allow the distribution of large quantities of NOS with adapted performances. For the other highly documented applications of water and soils depollution, the use of NOS is performant and cheap, but probably requires standardization of the manufactured product. It also raises the question of the elimination of the resulting contaminated NOS. An alternative remaining to be explored would be to consider the presence of metals at the surface of NOS as a possible catalyst. This would be similar to what has been successfully developed by the team of C. Grison using metalhyperaccumulating plants to produce metal oxide catalyst. 175 The use of NOS in building materials or as filler in composites represents an interesting option with more addedvalue but probably requires here again a standardization of materials. Besides, the durability of these materials remains limited, still relatively unknown, [START_REF] Mo | Recycling of Seashell Waste in Concrete: A Review[END_REF] not fully studied, and hardly documented.

Other applications with higher economic potential concern NOS and CNOS in material and health fields. NOS as a source of calcium in food requires simple treatments without altering its quality, in line with consumer's expectations. The major limit lies in human safety directly related to heavy metals and hazardous chemicals content as a consequence of the possible bioaccumulation of toxins in the shell. As an excipient or source of calcium in pharmaceutical products, NOS has to be declared and requires to be produced following GMP guidelines. Besides, the real economic advantage of NOS compared to other CaCO 3 sources is not always obvious. The answer may probably be driven by a significant shift in mindsets and ways of working. This is actually the case in the cosmetic industry, where the naturalness of ingredients is highly marketed. As a cosmetic ingredient, NOS powder has a real interest, especially for its soft abrasive properties (skin softpeeler), making it a potential substitute for plastic microbeads used in cosmetics. This expanding market meets a growing demand for natural, safe, and effective ingredients. This may be reinforced if further research demonstrates additional biological activities of NOS, especially of the organic matrix.

Among the applications with high economic value, the use of NOS in bone grafting seems to be a promising route but requires deeper knowledge about long-term biocompatibility and stability.

Concerning materials chemistry, NOS is an interesting template of advanced material or support for catalysts as evidenced by the increasing number of publications on this subject. However, the scalability and the repeatability of these applications remains linked to the collection, selection and standardization of the shell.

The unsustainability of NOS calcination in oven questions the relevance of CNOS, especially since these applications are frequently similar to those with NOS. Few applications reported better performances of CNOS compared to NOS but do not seem high enough to justify the calcination cost and the carbon dioxide emission. Thus, calcination in oven has to be considered only for applications where the required performance level is not achievable with NOS. In this instance, the development of sustainable calcination processes is needed such as fast microwave calcination, [START_REF] Huang | Microwave Calcination of Waste Oyster Shells for CO 2 Capture[END_REF] or solar oven combined with carbon dioxide sequestration.

Biomolecules of the organic matrix (SI Table S6) are perhaps the best candidates for applications with high value, being entirely competitive with chemical sources of calcium carbonate. The high performance of these biomolecules compensate for the low scalability of the extraction process. WSM as a cosmetic and nutraceutical ingredient commercialized by StanSea is a good example. This research area is still highly open both for the identification of new biological activities for health applications and for the synthesis of innovative advanced materials. The future development of these applications depends on the progress made in the characterization of these extracts, in particular their composition and mechanisms of action. The difficulty relies on low yields and does not solve the problem of recycling calcium carbonate wastes, which should be handled together.

PERSPECTIVES AND OUTLOOK

The globalization of oyster farming generates short-term profits for local economic actors, but the massive production of shells starts to raise ecological questions. In this context, several studies disclose promising recycling applications from low to high value. The economics of recycling is dominated by the balance between the cost of collection/decontamination/ processing and the added value of the product and its use. This can change due to the great consideration of environmental issues by consumers and their demand for a natural product. From depollution of soil and water to bone tissue reconstruction and production of nanomaterials, oyster shell has plenty to offer for chemists. To effectively treat the recycling and recovery of this byproduct, diverse issues need to be addressed, especially those related to the variability of composition and microstructures of the shell. Some other aspects still need to be better explored, such as parts of the shell, including pigments and the organic matrix, that still lack detailed characterization but can lead to new valuations.

Figure 1 .

 1 Figure 1. Phylogeny of oyster species.

Figure 2 .

 2 Figure 2. Examples of nacre bone substitute. (A) Incisors of the lower jawbone replaced by nacre.[START_REF] Green | Evolving Marine Biomimetics for Regenerative Dentistry[END_REF] (B) Solid nacre (N) implanted in the femur of sheep after 10 months.[START_REF] Atlan | Interface between Bone and Nacre Implants in Sheep[END_REF]

Figure 3 .

 3 Figure 3. SEM image of hydroxyapatite produced by hydrothermal processing of NOS at 200 °C for 92 h.89

Figure 4 .

 4 Figure 4. TEM images of Na 2 Ti 6 O 13 nanorods prepared with NOS.[START_REF] Lee | Growth of Single-Crystalline Sodium Titanate and Sodium Tungstate One-Dimensional Nanostructures: Bio-Inspired Approach Using Oyster Shell[END_REF]

Figure 5 .

 5 Figure 5. Ca(OH) 2 nanoplates prepared from CNOS according to Khan et al. (2018).124

Figure 6 .

 6 Figure 6. Calcium silicate prepared with CNOS. Reproduced with permission from Ref.128 Copyright 2015 The Physical Chemistry Chemical Physics Owner Societies.

Figure 7 .

 7 Figure 7. C. gigas oyster shells with six coloration types. (A) Whole white shell, (B) whole black shell, (C) whole golden shell, (D) partially colored shell. 172 (E) Pink oyster from the French oyster farming Tarbouriech (Thau, France).173

Figure 8 .

 8 Figure 8. Application fields of waste oyster shell described in this review.

  [START_REF] Lemos | Hydroxyapatite Nano-Powders Produced Hydrothermally from Nacreous Material[END_REF][START_REF] Terasaka | Ability of Hydroxyapatite Synthesized from Waste Oyster Shells to Remove Fluoride Ions[END_REF]

	10CaCO 3	+	6(NH ) HPO 42 4	+	2H O 2	→	Ca (PO ) (OH) 1 0 4 6 2	+	6
	(NH ) CO 4 2 3	+	4H CO 2 3

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

We acknowledge TARBOURIECH-MEDITHAU for PhD financial support and the PILE-CIFRE program of the Reǵion Occitanie/Pyreńeés-Mediterraneé.


Styc Quentin

Lagacherie Philippe

Philippe Lagacherie

Uncertainty assessment of soil available water capacity using error propagation: a test in Languedoc-Roussillon

Keywords: soil available water capacity, digital soil mapping, uncertainty, error propagation SAWC: soil available water capacity, DSM: digital soil mapping, AWC: available water capacity, AWCE: elementary available water capacity, ST: soil thickness, MSOD: maximal soil observation depth, PTF: pedotransfer function

Soil available water capacity (SAWC) is a key soil indicator that plays a major role in many ecosystem services, such as food production, irrigation management, soil drought, flood control, and climate and gas regulation. Digital soil mapping (DSM) can be used to obtain needed SAWC maps. However, SAWC differs from the usual soil properties considered in DSM in that it involves several soil properties determined at several soil layers. Therefore, a specific approach is required to obtain SAWC maps and the associated uncertainty predictions.

The objective of this study was to build a SAWC mapping approach that could predict SAWC values at three maximum rooting depths (60, 100 and 200 cm) and their associated prediction uncertainties.

The approach was tested in the Languedoc-Roussillon region (southern France). Elementary available water capacities of each layers (in cm.cm -1 ) and soil layer thicknesses were first mapped separately at 0-30, 30-60, 60-100 and 100-200 cm and then aggregated to estimate the SAWCs at the three mentioned maximum rooting depths. SAWC uncertainty was estimated with an error propagation model that used a first-order Taylor analysis. This analysis considered the mapping errors of each involved property, which were estimated by the quantile regression forest algorithm. We tested different error propagation models that

Introduction

Soil available water capacity (SAWC) refers to the capacity of soils to store water for plants (Veihmayer and Hendrickson, 1927). SAWC is a key soil indicator that plays a major role in many ecosystem services, such as food production, irrigation management, soil drought, flood control, and climate and gas regulation. It is therefore a fundamental parameter that has been used in land evaluations and recently in soil ecosystem service assessments [START_REF] Dominati | A soil change-based methodology for the quantification and valuation of ecosystem services from agro-ecosystems: a case study of pastoral agriculture in New Zealand[END_REF]. Currently, SAWC is operationally computed in the literature as follows [START_REF] Cousin | Influence of rock fragments on the water retention and water percolation in a calcareous soil[END_REF]:

(1) = ℎ * * 100 - 100 * - ( 1
)
where SAWC is the soil available water capacity (cm), ℎ = the thickness of the ith horizon (cm), = the bulk density of the ith horizon (g.cm -3 ), = the coarse fragment content of the ith horizon (% volumetric), and and are the soil water contents at field capacity (FC) (i.e., the soil water content that remains in the soil after water has drained due to gravitational force) and at permanent wilting point (PWP) (i.e., the soil water retained so strongly that it is no longer available for plant roots, so plants wither and cannot recover their turgidity) of the ith horizon (cm 3 .cm -3 ), respectively.

To meet the need to map the SAWC, digital soil mapping [START_REF] Mcbratney | On digital soil mapping[END_REF] can be considered an adequate approach since it provides the best solution for synergizing all data on the soils and its drivers that can be available in a given region, regardless of its size. [START_REF] Styc | What is the Best Inference Trajectory for Mapping Soil Functions: An Example of Mapping Soil Available Water Capacity over Languedoc Roussillon (France)[END_REF] proposed a modified equation for calculating SAWC (Eq. 2) to make it more easily mappable. The modifications consisted in i) replacing the difficult-to-measure FC and PWP inputs by pedotransfer functions that only involved available primary soil properties that are more current in the soil databases and ii) harmonizing the mapping inputs across sites by replacing the horizons defined by variable depth intervals by soil layers defined by fixed depth intervals.

( (2)

where ! is the thickness of the soil layers fixed by the soil depth interval, is the coarse fragment content of the ith horizon (% volumetric), + … + 89 3 … 3 are the coefficients of the pedotransfer functions used to calculate the volumetric water contents at the field capacity and permanent wilting point respectively, --… -are the values of the primary soil properties used as inputs for the pedotransfer functions (most often textural fractions) and

/ 01
and / 454 are the errors of the pedotransfer functions used for estimating Field capacity and Permanent wilting point respectively. Equation 2shows that the SAWC determination involved several primary soil properties determined at several soil layers, which created methodological questions that have not been addressed by the classical DSM framework.

First, there is no consensus about the inference trajectory selected for predicting SAWC. In the DSM literature, there were i) studies that calculate first AWC at the observed sites prior using these sites for calibrating a mapping function [START_REF] Vanderlinden | Soil water-holding capacity assessment in terms of the average annual water balance in southern Spain[END_REF][START_REF] Poggio | Soil available water capacity interpolation and spatial uncertainty modelling at multiple geographical extents[END_REF][START_REF] Hong | Predicting and mapping soil available water capacity in Korea[END_REF] and ii) studies that mapped the AWC components first and then combined the mapping outputs to obtain an estimate of AWC [START_REF] Ugbaje | Functional digital soil mapping for the prediction of available water capacity in Nigeria using legacy data[END_REF][START_REF] Leenaars | Mapping rootable depth and root zone plant-available water holding capacity of the soil of sub-Saharan Africa[END_REF][START_REF] Román Dobarco | Pedotransfer functions for predicting available water capacity in French soils, their applicability domain and associated uncertainty[END_REF]. However, a comparison of 18 inference trajectories that combined different AWC calculations from the primary soil properties, soil layer aggregation and mapping [START_REF] Styc | What is the Best Inference Trajectory for Mapping Soil Functions: An Example of Mapping Soil Available Water Capacity over Languedoc Roussillon (France)[END_REF] showed significant differences in SAWC prediction accuracies, and none of the two inference trajectories cited above were optimal. The best inference trajectory was an intermediate trajectory that, before mapping, calculated the AWC for four soil layers.

Another methodological question was the ex-ante uncertainty assessment of the SAWC mapping output. In the classical DSM framework, the different models can provide a local estimate of the uncertainty of the predicted values of the target soil properties [START_REF] Heuvelink | Uncertainty quantification of GlobalSoilMap products, GlobalSoilMap: basis of the global spatial soil information system[END_REF][START_REF] Vaysse | Using quantile regression forest to estimate uncertainty of digital soil mapping products[END_REF]. Obtaining a similar estimate for the SAWC map requires an error propagation model that combines the different errors associated with the mapping of each layer of the soil properties involved in the SAWC calculation. Román [START_REF] Dobarco | Uncertainty assessment of GlobalSoilMap soil available water capacity products: A French case study[END_REF] used a first-order Taylor analysis to propagate mapping errors and pedotransfer function errors to the final SAWC predictions. They showed that the mapping of the SAWC components (soil texture and coarse fragment) was the main source of SAWC mapping uncertainty. However, the soil thickness mapping errors were not considered in their analysis, although Algayer et al. (2019) demonstrated that soil thickness can be the most critical component in the SAWC estimation. Furthermore, the error propagation model proposed by [START_REF] Román Dobarco | Pedotransfer functions for predicting available water capacity in French soils, their applicability domain and associated uncertainty[END_REF] neglected the error correlations between the SAWC components, which assumed that these errors were independent of each other, which has not been demonstrated.

The objective of this study was to build a SAWC mapping approach with the best possible inference strategy that could predict all SAWC values for three maximum rooting depths (60, 100 and 200 cm) and their associated prediction uncertainties while taking into account all SAWC component mapping errors and their correlations. The approach was tested in the former Languedoc-Roussillon region (Southern France).

The Study Case

Study area

This study was carried out in the former Languedoc-Roussillon French administrative region, which is now part of the new Occitanie region (Figure 1). Located in southern France, the former region covers 27,236 km² of land that stretches from the Mediterranean Sea to the Pyrenees and Massif Central mountains. The region includes a wide-ranging diversity of climates, geologies, and landscapes that lead to a large pedodiversity, with 18 WRB major soil groups, which represent 75% of all soil groups in Europe, being included in this study area. Further details can be found in Vaysse andLagacherie (2015, 2017).

Figure 1. Location of the study area (in color)

Soil profiles with observed SAWC components

In this study, we used a legacy dataset of 2024 measured soil profiles from Vaysse andLagacherie (2015, 2017). SAWC for the different soil profiles were harmonized for providing AWC component values at the fixed soil layers that were considered for SAWC mapping (0-30 cm, 30-60 cm, 60-100 cm and 100-200 cm) (see explanation further on section 3.3.). For that, each AWC components were estimated at these layers from the initial soil horizons using mass conservation cubic splines [START_REF] Bishop | Modeling soil attribute depth functions with equal-area quadratic smoothing splines[END_REF]. For each considered soil layer, we selected the profiles at which all AWC components (soil texture, coarse fragments and soil layer thicknesses) were fully documented (see details below). This resulted in a reduction of the number of soil profiles for mapping each layer (Table 1).

Documenting soil layer thicknesses

The soil layer thicknesses (SLT) were documented by considering the following rules :

• If the lower limit of the soil layer (LL) was less than both the maximum soil observation depth (MSOD) of the soil profiles and the upper depth of a lithic or paralithic contact (UDPLC), then SLT was equal to the difference between its fixed lower and upper limits (e.g. the SLT of 30-60 cm soil layer is 30 cm)

• Else if LL was less than MSOD but greater than UDPLC, SLT was equal to the difference between UDPLC and LL (e.g. the SLT of the 30-60 cm layer with a lithic contact appearing at 50 cm is 20 cm)

• Else if LL was greater than MSOP, the SLT could not be determined, which lead to remove the soil layer from the input soil dataset.

Pedotransfer functions

In this study, we used the national-level pedotransfer functions (PTFs) developed by Román [START_REF] Dobarco | Uncertainty assessment of GlobalSoilMap soil available water capacity products: A French case study[END_REF] because our case study was in the domain of applicability of these PTFs, which ensured the best possible performances (Roman [START_REF] Dobarco | Uncertainty assessment of GlobalSoilMap soil available water capacity products: A French case study[END_REF]. The volumetric soil water contents at field capacity (Eq. 3) and permanent wilting point (Eq. 4).

These PTFs used clay and sand contents (%) as the predictive variables, which were calculated as follows:

(3) : ; = 0.278 + 2.45 10 where : ; and : F are the volumetric water contents at field capacity and permanent wilting point, respectively.

Soil covariates

The employed DSM process, which relies on the scorpan model [START_REF] Mcbratney | On digital soil mapping[END_REF], used the quantitative relationships between the target soil properties and available spatial variables related with soil, which are also called the "soil covariates".

The soil covariates of this study area were selected by [START_REF] Vaysse | Evaluating Digital Soil Mapping approaches for mapping GlobalSoilMap soil properties from legacy data in Languedoc-Roussillon (France)[END_REF] following two criteria: i) they could be derived from freely available geo-datasets for at least the French national level, and ii) they had a logical and process-based relationship with soil properties according to the literature. The soil covariates (table 1) accounted for the impact of topography, climate, organisms, and parent material. The regional-scale map (1:250,000) that delinated the major landscape types across the region was also considered as a soil covariate.

All the soil covariates were computed at the nodes of the 90 m x 90 m grid of the SRTM Digital Elevation model, which corresponded also to the resolution of the predicted SAWC map. More details can be found in the descriptions of several applications of DSM to the region (Vaysse andLagacherie, 2015, 2017;[START_REF] Styc | What is the Best Inference Trajectory for Mapping Soil Functions: An Example of Mapping Soil Available Water Capacity over Languedoc Roussillon (France)[END_REF]. [START_REF] Breiman | Random forests[END_REF] are an ensemble learning method for both classification and regression. A forest, which is an ensemble of randomized decision trees, is built and trained based on a bootstrap approach. Individual trees are built using the principle of recursive partitioning. "The feature space is recursively split into regions containing observations with similar response value" [START_REF] Strobl | An introduction to recursive partitioning: rationale, application, and characteristics of classification and regression trees, bagging, and random forests[END_REF]. The predictions of the individual trees are finally averaged to give one single prediction.

Mapping model: the quantile regression forest

In this study, we use one of the most commonly used algorithms in DSM studies, namely, the quantile regression forest algorithm (QRF; [START_REF] Meinshausen | Quantile regression forests[END_REF], which is an extension of Breiman's random forests (RF; 2001). For the regression, RF provides an ensemble prediction based on n regression trees. For every tree, the algorithm integrates random features by randomly selecting a subset of features to be split. While RF provides solely the conditional mean, QRF supplies the whole conditional distribution of the target variable by keeping all observations at the terminal nodes and can infer estimates for the conditional quantiles [START_REF] Meinshausen | Quantile regression forests[END_REF]. More details on QRF can be found in [START_REF] Meinshausen | Quantile regression forests[END_REF].

QRF was run with the ranger package, which is a fast implementation of Breiman's random forest and Meinshausen's quantile regression forest (Wright and Ziegler, 2015).

Inference trajectories

Since SAWC is a soil indicator that involves several soil properties determined at several soil layers, it can be estimated following various possible inference following the order with which the three different steps, i.e., "combining primary soil properties", "aggregating soil layers across depths" and "mapping" are executed to provide the targeted output [START_REF] Styc | What is the Best Inference Trajectory for Mapping Soil Functions: An Example of Mapping Soil Available Water Capacity over Languedoc Roussillon (France)[END_REF]. Styc and Lagacherie (2019) tested a total of 18 inference trajectories for throughout Languedoc-Roussillon that were performed to obtain the most appropriate SAWC map. From this study, we considered the best performing inference trajectory, i.e., we computed first AWC in four layers (0-30, 30-60, 60-100 and 100-200 cm) obtained by merging the three first layers defined in the GlobalSoilmap specifications [START_REF] Arrouays | The GlobalSoilMap project specifications[END_REF], mapped them and then aggregating the maps of the four soil layers to obtain the final SAWC maps. To account for the different possible rooting depths across the different crops, these aggregations were performed over three different maximal rooting depth (60 cm, 100 cm, 200 cm).

However, we modified the inference trajectory (Figure 2) by mapping, the soil thickness and the elementary available water capacity ( I ) separately for each layer. AWCE represent the water retention capacity for one centimeter of soil (in cm.cm -1 ) and is defined as follows:

(5)

I = " ##$%& ' ## ( * )*∑ + , --, , + /2 -*

Set of locations

Maps SAWC Maps

Aggregating soil layers

Combining soil properties M a p p i n g

The rationale of this modification was to separately map two soil properties that exhibited very low correlations, meaning that their variations could result from different landscape drivers that could be imperfectly considered by a single mapping model.

Uncertainty analysis using error propagation modeling

Following Román [START_REF] Dobarco | Uncertainty assessment of GlobalSoilMap soil available water capacity products: A French case study[END_REF], the error propagation was modeled using first-order

Taylor expansion to calculate the variance of the SAWC predictions. This variance was considered a proxy of the prediction uncertainty of the target variable [START_REF] Heuvelink | Propagation of errors in spatial modelling with GIS Int[END_REF].

This method relies on the approximation of the estimates obtained for the soil property (i.e., the available water capacity). Let Y be an estimation of a given soil property as follows (Eq. 6):

J = K L (6)
where K is a continuously differentiable function from ℝ into ℝ and z is the vector of the n input variable of f. The approximation of f uses a series centered on the mean values of the n input variables μ = Oμ , μ Q , … , μ R S [START_REF] Heuvelink | Propagation of errors in spatial modelling with GIS Int[END_REF]. The variance of Y = f(z) is calculated with the following formula (Eq. 7):

(7)

T U Q ≈ ∑ " WX Y WZ ' ( Q TL Q + 2 ∑ ∑ " WX Y WZ ' ( " WX Y WZ [ ( TL L \ \ \] ]\ (7)
where T U Q is the variance of Y, L and L \ are the soil input variables, TL L \ is the covariation of the L and L \ errors from the ^ and _ variables, TL is the standard deviation of L and

WX Y WZ ' and WX Y WZ [
are the partial derivatives of f(z) around μ. TL is estimated by the standard deviations of the conditional distributions provided by QRF at each predicted location [START_REF] Meinshausen | Quantile regression forests[END_REF].

Then, the estimate of the variance can be used to compute the limits of the confidence interval. Assuming a normal distribution, the limits of the confidence interval can be computed as follows (Eq. 8):

` = D a b ± 1.645 T U e b ( 8
)
where ` is the interval limits of the prediction, D a b the mean of the distribution, T U f the standard deviation and 1.645 is the Student's coefficient for a 90% confidence interval estimation.

Error propagation was performed using the propagate R package [START_REF] Spiess | Propagate: Propagation of Uncertainty. R package version 1[END_REF].

The experiment

In this study, we considered two sources of uncertainty: i) the mapping error of both SAWC components, i.e., the soil thickness and the AWCE, and ii) the error of the AWC of every soil layer.

The tested options of error propagation

To evaluate the importance of the correlations of the AWC components errors for the quantification of SAWC uncertainty, four options of error propagation were considered according to whether are considered: i) the error correlations between the predicted properties involved in the determination of AWC at each soil layer, i.e. AWC and soil layer thickness (denoted further SP) ii) the error correlations between the predicted AWC at different soil layers (denoted further SL), iii) both of these correlations (denoted further SP.SL) or iv) none of these correlations (denoted further NONE).

To compute the error correlations, we considered the residuals calculated by the K-fold cross validation (see next section).

Additionally, we derived the SAWC predictions according to three different fixed maximum soil depth, i.e. 200 cm, 100 cm and 60 cm. The rationale was to determine if the predictions for the deepest layers (60-100 cm and 100-200 cm) played a beneficial or nonbeneficial roles in the SAWC predictions.

Evaluation protocol

The performance of the SAWC DSM was evaluated by k-fold cross validation. This evaluation procedure consisted of randomly dividing the data into k subsets. Then, the holdout method was repeated k times such that one of the k subsets was used as the validation set in each repetition, while the other k-1 subsets were merged to form the calibration set. Following this procedure, every data point was included in a calibration set k-1 times. In this study, we selected k = 10; to increase the robustness of the evaluation, the 10-fold cross-validation was iterated 20 times. The k-fold cross-validation was performed using cvTools [START_REF] Alfons | cvTools: Cross-Validation Tools for Regression Models[END_REF] that was used to define the folds.

To evaluate the prediction performances, we used classic performance indicators, e.g., the mean square error skill score (SSMSE, [START_REF] Nussbaum | Evaluation of digital soil mapping approaches with large sets of environmental covariates[END_REF], which has the same interpretation as the percentage of variance explained by the model, the root mean square error (RMSE) and the bias.

Furthermore, we evaluated the estimation of the prediction uncertainty using the prediction interval coverage probability (PICP, Eq. 9) [START_REF] Shrestha | Machine learning approaches for estimation of prediction interval for the model output[END_REF], which was computed as follows:

(8) -` -= ghi9 -< D < k- 9 × 100 (9)
where 9 is the total number of observations in the validation set, and the numerator counts if the observation D fits within the prediction limits prior to estimation by the error propagation method. For a 90% confidence level, which is usually chosen in DSM studies [START_REF] Arrouays | The GlobalSoilMap project specifications[END_REF], the uncertainty is optimally predicted when the PICP value is close to 90%.

In addition to PICP, we verified that the largest errors were at locations having the largest widths of estimated prediction intervals. For that, the population of validation sites was split into four quartiles of predicted interval widths and four RMSEs were computed separately for each quartile.

Results

Basic statistics

Soil input distributions

In Figure 3, we present the distributions of the soil thickness and the elementary available water capacity across the set of soil profiles that was used as input of the mapping model.

The soil thickness ranged from 5 to 200 cm (i.e., the maximum soil observation depth was fixed at 200 cm), with the average ST at 89 cm, which was close to the median value (90 cm).

The most common ST in the dataset was 120 cm soil thickness. Then, the distribution dropped dramatically, showing that deep soils were less represented than shallow soils. The shape of the distribution was far from normal, although the skewness and kurtosis tests indicated a normal distribution. The AWCE for the 0-30 cm and 30-60 cm soil layers were nearly normally distributed, with peaks at 0.09 and 0.10, respectively. The AWCE for the 60-100 cm and 100-200 cm soil layers differed from the shallowest layers by the shapes of their distributions, which were bimodal (two distribution peaks located at 0.03 cm/cm and at 0.11 cm/cm). While the skewness test indicated that the distributions of the AWCE values of every soil layer were approximatively symmetric, the excess kurtosis test showed that the distributions were less peaked and presented less extreme values than a normal distribution. The correlations between the errors from AWCE and soil thickness (table 3) were very low whatever the considered soil layer and even non-significant for layers 0-30 cm and 60-100 cm. It may reveal that the mapping models of these soil properties were very different by weighing very differently the used soil covariates. 4 shows the correlation of the AWC errors between soil layers. The AWC errors of the soil layers were correlated, especially for the consecutive soil layers, and the correlations decreased for deeper layers, which may denote large similarities between mapping models of consecutive soil layers. It is worth noting that all error correlations between the soil layers were significant and generally higher than the error correlations between the primary soil properties. 7, we present the uncertainty evaluation of the predictions averaged with their standard deviations using the PICP. The PICP values ranged from 71% to 91%; the PICP values were closer to optimal (i.e., 90%) when the correlation of the errors between the soil layers was considered regardless of whether the correlation of errors between the soil properties were considered during error propagation. It is worth noting that when the correlation of the errors between the soil layers was not accounted for, the PICP dropped dramatically to values ranging between 71 and 81%, which led to an underestimation of the SAWC uncertainty. Table 8 shows the differences in the prediction performances (RMSE) for the different quartiles in the 90% confidence interval width using the error propagation model for SL (i.e., the one that considered the correlation of the error between soil layers only) for SAWC predicted at 200 cm. The RMSE calculated separately for each quartile tended to increase from the predicted confidence interval with the smallest width to the largest confidence interval (from 3.12 cm to 5.51 cm). Therefore, as expected, the uncertainty predicted by the model was related to the uncertainty observed through the validation protocol. Similar trends were observed for SAWC predictions at 100 and 60 cm. According to the previously presented results (cf. Table 7), there was no clear difference in performance in the SAWC predictions of 60, 100 or 200 cm, so we chose to present the SAWC map for the maximum soil thickness of 200 cm.

The SAWC map (Figure 5) was mainly divided in two regions of contrasting soil thickness that corresponded to different lithologies and reliefs. The low predicted values of SAWC (shown in red) were predominant in the mountainous crystalline rocks of the Pyrenees and the Massif Central mountains, which were located in the south and northwest of the region, respectively, and on the hard limestone plateaus (the Causses). The high predicted values of the SAWC (in blue color) were located in the hills and plains of the soft marine and fluviatile sediments located near the seaside and in a narrow channel in the west of the region.

However, more subtle differences in the predicted SAWC could be observed within the two regions. In the sedimentary area, a gradient was observed from high predicted SAWCs in the alluvium valleys, which had deep soil with low coarse fragment contents, to low predicted SAWCs in the stony soils of the old alluvial terraces (e.g., Nîmes Costières, which is in a red circle in Figure 5) the soils on tertiary sediment ("molasse") hillsides showed intermediate values. The mountainous crystalline rock areas and the Causses also showed identifiable differences in the predicted SAWCs (dark blue circle in Figure 5) that could be explained by the soil map and DEM derivative covariates (e.g., Multi Resolution Valley Bottom Flatness index, Multi Resolution Ridge Top Flatness index and slope). Similar situations were encountered in the Causses (light blue circles in Figure 5).

Discussion

Evaluation protocol

The evaluation protocol that was applied in this study consisted of a 10-fold cross validation approach with 20 repetitions, with the reference data being the soil profiles at punctual sites with the observed properties (textural fractions, coarse fragments and soil thickness) used to produce a local estimation of the SAWC using the pedotransfer functions. This protocol ensured both, an evaluation of the SAWC predictions from independent samples and a comprehensive consideration of the mapping errors of all SAWC components. To our knowledge, this is the first time that these two conditions were fulfilled in an evaluation protocol dealing with the SAWC, which makes the comparisons with previous papers dealing with SAWC (e.g. [START_REF] Poggio | Soil available water capacity interpolation and spatial uncertainty modelling at multiple geographical extents[END_REF][START_REF] Hong | Predicting and mapping soil available water capacity in Korea[END_REF][START_REF] Leenaars | Mapping rootable depth and root zone plant-available water holding capacity of the soil of sub-Saharan Africa[END_REF] difficult.

However, our evaluation protocol had two main limitations. First, the evaluation sites were not characterized by the real SAWC measurements, and the fine earth water retention was estimated with the pedotransfer functions. This did not allow us to account for the PTF errors, as Román [START_REF] Dobarco | Uncertainty assessment of GlobalSoilMap soil available water capacity products: A French case study[END_REF] did in their study. However, these authors showed that PTF errors played a minor role in comparison with the mapping errors of the SAWC components.

This should be even more true with the addition of the ST mapping errors in the evaluation protocol in comparison with the protocol of Román [START_REF] Dobarco | Uncertainty assessment of GlobalSoilMap soil available water capacity products: A French case study[END_REF]. Furthermore, the introduction of the PTF error in our error propagation models following the technique proposed by Román [START_REF] Dobarco | Uncertainty assessment of GlobalSoilMap soil available water capacity products: A French case study[END_REF] did not modify the ex-ante uncertainty evaluation of the SAWC paper (result not shown in this paper). However, a full evaluation of the SAWC mapping would be preferable, which means investing in costly field and laboratory measurements or finding accurate and inexpensive proxies for the SAWC [START_REF] Coulouma | Carbon isotope discrimination as a surrogate for soil available water capacity in rainfed areas: A study in the Languedoc vineyard plain[END_REF].

A second limitation of our evaluation protocol was that SAWC mapping was evaluated at the site level, which was not representative of the decision-making units of the end-user and represents the worst case scenario for assessing the soil property prediction quality. Ideally, the evaluation should be performed for areal units [START_REF] Bishop | Validation of digital soil maps at different spatial supports[END_REF], which would produce more realistic results that would be in accordance with the visual evaluation of the map (see further). However, evaluating the SAWC from the areal units would require data collection that cannot be reasonably envisaged. Consistency checking involving data available at larger spatial support and closely related with AWC could be an alternative [START_REF] Vanderlinden | Soil water-holding capacity assessment in terms of the average annual water balance in southern Spain[END_REF]

Error propagation model

Following Román [START_REF] Dobarco | Uncertainty assessment of GlobalSoilMap soil available water capacity products: A French case study[END_REF], an error propagation model using a first-order Taylor expansion was developed for the ex-ante estimation of SAWC mapping uncertainty. This model was, to some extent, more complete than the one developed by Román [START_REF] Dobarco | Uncertainty assessment of GlobalSoilMap soil available water capacity products: A French case study[END_REF] in that it considered the error in the soil thickness maps and the correlations between the error in the SAWC component maps that were not considered in Román [START_REF] Dobarco | Uncertainty assessment of GlobalSoilMap soil available water capacity products: A French case study[END_REF]. This model was obtained by selecting an inference trajectory that included separate mapping of the soil layer thicknesses, which allowed easy application of the first-order Taylor expansion. The results revealed that the consideration of the error correlations had an impact on the final result if they reached a given level, which was the case for the error correlations between the soil layer maps (Table 4). The results showed that the ex-ante estimation of uncertainty was only slightly biased (differences with nominal values of 90% less than 1 for two out of three SAWC maps), which corresponded to much smaller uncertainty estimation biases than those obtained by Román [START_REF] Dobarco | Uncertainty assessment of GlobalSoilMap soil available water capacity products: A French case study[END_REF]. We also verified that the RMSE obtained from the validation protocol was closely related to the predicted uncertainty (Figure 4), which, to our knowledge, has not yet been verified. We note, however, that the error propagation model built in this study did not consider the PTF errors. This error could be easily added by following the procedure proposed by Román [START_REF] Dobarco | Uncertainty assessment of GlobalSoilMap soil available water capacity products: A French case study[END_REF].

General performances of the SAWC predictions

Although the SAWC map of the Languedoc-Roussillon region exhibited expected and pedologically sound soil patterns, poor results were obtained from the evaluation protocol (Table 6). This was likely related to the difficulty of mapping the two most critical components of the SAWC, namely, the coarse fragments and the soil layer thicknesses (Table 5). As observed by [START_REF] Vaysse | Evaluating Digital Soil Mapping approaches for mapping GlobalSoilMap soil properties from legacy data in Languedoc-Roussillon (France)[END_REF], the soil thickness and coarse fragments were characterized by a pre-eminence of short-scale variations that could not be captured by a DSM model using a so sparse soil spatial sampling according to the soil layer depths (Table 1). A denser spatial sampling is therefore necessary in this situation. Furthermore, the coarse fragment data were obtained from visual observations of the soil profile, which carry a greater uncertainty than the ones of other soil properties that are measured in a laboratory. More accurate field protocols for measuring the proportion of coarse fragments (Algayer et al, 2019) are required to improve this situation.

It is also important to notice that biases were important components of the SAWC prediction errors (between 15 and 30% as shown on table 6), which generated an overall SAWC overestimation. This overestimation can be related with the important positive biases observed for the predictions of the thicknesses of the three first soil layers (table 5). Such biases should be caused by the difficulties of the Random Forest algorithm to deal with the important subset of locations having null soil layer thicknesses. Dealing with zero-inflated input datasets of regression models is a well-known problem in ecology [START_REF] Martin | Zero tolerance ecology : improving ecological inference by modelling the source of zero observations[END_REF].

Specific regression approaches adapted to zero-inflated datasets [START_REF] Savage | Predicting relative species composition within mixed conifer forest pixels using zero-in fl ated models and Landsat imagery[END_REF] should be applied to mitigate this problem.

Conversely, the last soil layer exhibited a negative bias (table 5) that can be related with the unbalanced distribution of soil thicknesses in the set of sampling locations (figure 3). Indeed, a very small proportion of deep soils were sampled because of the low maximum observation depths (only 15% of the soil profiles had maximum observation depths greater than 120 cm).

This too small proportion generated the underestimation of the deepest soil layers thicknesses since, the random forest algorithm is known to behave like an interpolator and to smooth the outliers [START_REF] Song | Bias correction for Random Forest in regression using residual rotation[END_REF]. A more balanced sampling of the ST across the study region is therefore necessary.

Conclusions

• We developed a DSM model that mapped the SAWC values and provided an ex ante local estimation of the prediction uncertainty. For the first time, this uncertainty model took into account all SAWC component mapping errors for all soil layers.

• The results showed weak performances of the SAWC predictions, although the final map exhibited pedologically sound spatial patterns of predicted SAWC. This paradoxical result could be caused by the inadequate spatial support at which the evaluations were conducted (punctual one).

7.

Figure 3 .

 3 Figure 3. Distributions of the observed SAWC components at sampling locations ; a) soil thickness, b) elementary available water capacity of the 0-30 cm soil layer, c) elementary available water capacity of the 30-60 cm soil layer, d) elementary available water capacity of the 60-100 cm soil layer and e) elementary available water capacity of the 100-200 cm soil layer (in color) 4.1.2. Correlation of error between the AWCE and the soil thickness

Figure 5 .

 5 Figure 5. Predicted soil available water capacity (SAWC) map of Languedoc-Roussillon (in color). 4.4.4. Spatial distribution of the SAWC prediction uncertainty

Figure 6 .

 6 Figure 6. Uncertainty map presented by the classes estimated from the quartiles of the validation distribution (in color)

Table 1 . Number of soil profiles for each soil layer

 1

	Soil layer depths (cm)	Number of profiles
	0-30	1464
	30-60	1323
	60-100	1064
	100-200	822

Table 2 . The soil covariates 173

 2

					Soil
	Variables	Abbreviation	Resolution/Scale Source	forming	Type 2
					factor 1
	Topography
	Elevation	ELEV	90 m	SRTM	r	Q
	Multiresolution Valley Bottom Flatness MRVBF	90 m	SRTM	r	Q
	Slope	SLOPE	90 m	SRTM	r	Q
	Topographic Wetness Index	TWI	90 m	SRTM	r	Q
	Plan Curvature	PLANCURV	90 m	SRTM	r	Q
	Profile Curvature	PROCURV	90 m	SRTM	r	Q
	Multiresolution Ridge Top Flatness	MRRTF	90 m	SRTM	r	Q
	Topographic Position Index	TPI	90 m	SRTM	r	Q
	Geology
				Geological
	Hardness	HARDNESS	90 m	map/soil	p	C
				profile
				Geological
	Texture	TEXTURE	90 m	map/soil	p	C
				profile
				Geological
	Mineralogy	MINERALOGY	90 m	map/soil	p	C
				profile
	Climate
	Martonne Index	MARTONNE	90 m	WorldClim c	Q
	Emberger Index	EMBERGER	90 m	WorldClim c	Q
	Maximum Temperature	TMAX	90 m	WorldClim c	Q
	Minimum Temperature	TMIN	90 m	WorldClim c	Q
	Precipitation	PRECIPITATION 90 m	WorldClim c	Q
	Organisms
	Land Use	LANDUSE	30 m	Landsat 7 o	C
	Soil
	Soil Map	SOILMAP	1:250 000	RRP	s	C

Conceptual diagram of SAWC digital soil mapping with an example of inference trajectory including the new level of soil property combination, elementary available water capacity (AWCE) and soil layer thickness (modified from Styc and Lagacherie, 2019) (in color)

				∑ + , --, ,	+ /26	(5)
		Profiles
	Aggregated layers (1,2,3
	& 4,5,6) 2 layers
	Aggregated layers (1,2,3
	& 4,5)	3 layers
	Aggregated layers (1,2,3)
	4 layers
	Aggregated layers (1,2)
	5 layers
	6 layers Figure 2. Single soil layers	PP	AWC E + SLT	AWC i

Table 3 . Correlation of the error between the elementary available water capacity (AWCE) and the soil layer thickness

 3

	Soil properties
			AWCE
	Depth intervals (cm)	0-30	30-60 60-100 100-200
	0-30	0.01 ns	-	-	-
	30-60	-	0.09 **	-	-
	Soil layer thickness
	60-100	-	-	0.02 ns	-
	100-200	-	-	-	-0.13 *

ns : not significant (p-value ˃ 0.05); * : p-value ≤ 0.05; ** : p-value ≤ 0.01; *** : p-value ≤ 0.001 4.1.3. Correlation of the errors between soil layers Table

Table 4 . Correlation of the available water capacity (AWC) error between the soil layers

 4 , we present the performances of the SAWC component predictions. While the SSMSE values of both the clay and sand contents increased in depth, SSMSE of both the coarse fragment content and soil thickness showed very low performances (e.g., the SSMSE was close to 0%) as well low RMSE and bias values. The performances of the AWCE indicated a weak SSMSE that ranged from 6 to 14% of explained variance.

	Soil property	Depth intervals (cm)
	AWC	0-30	30-60	60-100
	30-60	0.67 ***	-	-
	60-100	0.42 ***	0.63 ***	-
	100-200	0.16 **	0.24 ***	0.36 ***
	AWC: available water capacity
	4.2. SAWC component prediction performances
	In Table 5

Table 5 . Prediction performances of soil available water capacity (SAWC) components: Mean values (standard deviations) over 20 iterations of SSMSE (mean square error skill score) RMSE (root mean square error) and bias.

 5 We present in Table6the performances of the SAWC predictions obtained by aggregating the predictions of AWCE and soil thickness of the four aggregated soil layers till the selected maximum rooting depths (60 cm, 100 cm or 200 cm).SAWC was poorly predicted regardless of the maximum rooting depth considered. The variance explained by the model reached 12-13%. Positive bias values (between 0.51 and 0.97 cm) denoted an overall overestimation of SAWC.

	Soil properties	Unit	Depth interval (cm)	SSMSE	RMSE	Bias
	Clay	(% mass)	0-30	0.16 (0.007) 10 (0.05)	-2 (0.04)
			30-60	0.20 (0.006) 11 (0.06)	-2 (0.04)
			60-100	0.26 (0.008) 12 (0.07)	-2 (0.09)
			100-200	0.27 (0.011) 12 (0.11)	-2 (0.13)
	Sand	(% mass)	0-30	0.29 (0.005) 15 (0.09)	1 (0.08)
			30-60	0.29 (0.006) 18 (0.07)	0 (0.07)
			60-100	0.33 (0.008) 16 (0.11)	0 (0.12)
			100-200	0.32 (0.009) 17 (0.23)	-1 (0.18)
	Coarse fragments (% vol)	0-30	0.07 (0.008) 20 (0.09)	-4 (0.21)
			30-60	0.09 (0.01)	26 (0.15)	-4 (0.12)
			60-100	0.07 (0.013) 29 (0.21)	-3 (0.12)
			100-200	0.03 (0.013) 30 (0.21)	-3 (0.14)
	AWCE	(cm.cm -1 )	0-30	0.12 (0.007) 0.03 (0.0001) 0 (0.0001)
			30-60	0.14 (0.007) 0.03 (0.0001) 0 (0.0001)

Table 6 . Performances of the soil available water capacity (SAWC) predictions : Mean values (standard deviations) over 20 iterations of SSMSE (mean square error skill score) RMSE (root mean square error) and bias.

 6

	Maximum rooting depth (cm)	SS MSE	RMSE (cm)	Bias (cm)
	60	0.13 (0.008)	1.86 (0.008)	0.51 (0.006)
	100	0.12 (0.007)	3.29 (0.013)	0.97 (0.013)
	200	0.12 (0.007)	4.2 (0.018)	0.66 (0.017)
	4.3. Uncertainty in the SAWC mapping prediction performances
	In Table

Table 7 . Uncertainty prediction evaluation: Mean values (standard deviations) over 20 iterations of PICP (prediction interval coverage probability) with different options for error propagation: considering the error correlation between both soil properties and soil layers (SP.SL), solely the soil layer error correlation (SL), solely the soil property error correlation (SP) or no correlation (NONE).

 7

	Maximum rooting depth (cm)		PICP (%)
			Options for error propagation
		SP.SL	SL	SP	NONE
	60	89 (0.46)	88 (0.40)	81 (0.53)	80 (0.59)
	100	88 (0.40)	87 (0.40)	71 (0.59)	71 (0.51)
	200	91 (0.28)	91 (0.34)	75 (0.53)	75 (0.48)

Table 8 . RMSEs for the quartiles of prediction interval widths.

 8

	Maximum rooting depth (cm)	Predicted uncertainty (cm)	RMSE (cm)
	60	< 5.81	1.67
		5.81 -6.23	1.86
		6.23 -6.67	1.95
		> 6.67	1.96
	100	<9.45	2.64
		9.45 -10.39	3.04
		10.39 -11.23	3.38
		> 11.23	3.96

: SCORPAN factors (s=soil property, c = climate, o = organisms, r = relief, p=parent material)

: Q = quantitative, C = categorical SRTM = Shuttle Radar Topography Mission; RRP = Référentiel Régional Pédologique.

The method

Acknowledgments This research was granted by the French National Research Institute for Agriculture, food and environment (INRAE), the French Research and Technology Agency (ANRT) and BRL Exploitation. Philippe Lagacherie is a collaborator of the GLADSOILMAP Consortium supported by the LE STUDIUM Loire Valley Institute for Advanced Research Studies 8.