Christian Piedallu
email: christian.piedallu@agroparistech.fr

Eloise Pedersoli

Emeline Chaste

François Morneau

Ingrid Seynave

Jean-Claude Gegout

Jean-Claude Gégout

Optimal resolution of soil properties maps varies according to their geographical extent and location

Keywords: Resolution, scale, soil properties, digital soil mapping, environmental predictors, map accuracy. pH

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

Introduction

Soils provide important services including water, carbon, nutrient storage or water filtering, and represent ecological support for vegetation, with implications on biodiversity, food and biomass production. Accurate knowledge of the soil chemical, physical and biological properties is important to improve research and practices in environmental management. The challenge is to understand their horizontal and vertical spatial variations, that can be substantial even on short distances [START_REF] Wilding | Spatial Variability: A Pedologist's Viewpoint 1[END_REF]. For example, surface pH variation ranged between 7.2 and 10.1 across a 41,000-ha area in Iran [START_REF] Pahlavan-Rad | Spatial variability of soil texture fractions and pH in a flood plain (case study from eastern Iran)[END_REF]. At a more local scale, significant changes in texture and soil thickness were observed in an experimental 567 m² plot in Italy by [START_REF] Buttafuoco | Studying the spatial structure evolution of soil water content using multivariate geostatistics[END_REF]. Different pedogenic factors and landscape processes linked to lithology, topography, hydrology and weathering operate at varying intensities according to the location, leading to possible multi-scale variation across a same area [START_REF] Stolt | Soil-Landscape Relationships in Virginia: I. Soil Variability and Parent Material Uniformity[END_REF]. [START_REF] Liu | Spatial multi-scale variability of soil nutrients in relation to environmental factors in a typical agricultural region, Eastern China[END_REF] observed short-range variation driven by topography and long-range changes driven by parent materials in eastern China. In a context of increased demand for spatial data, identifying these sources of spatial variability and representing their variation at the relevant scale is crucial for agricultural and forest management, land use planning, and natural resource conservation.

Digital soil mapping (DSM) has considerably developed since the 1990s following increased spatial data availability and the development of data processing techniques and tools [START_REF] Lagacherie | Digital Soil Mapping: An Introductory Perspective[END_REF][START_REF] Mcbratney | On digital soil mapping[END_REF]. It employs empirical correlations between field observations and digital environmental data often available through geographic information systems (GIS) layers (i.e. the environmental covariates) to create digital maps [START_REF] Mcbratney | On digital soil mapping[END_REF]. DSM techniques are based on the factors of soil formation (climate, organisms, relief, parent material and time -clorpt, [START_REF] Jenny | Factors of soil formation: A system of quantitative pedology[END_REF]. They provide a comprehensive digital framework describing the empirical relationships between maps of environmental covariates related to the soil class or properties, that represent proxies of the signatures left on the landscape by the factors and processes of soil formation. The most commonly used are topographic information based on digital elevation models (DEM), existing soil maps, climate parameters, sometimes complemented by remote sensing images or other existing soil maps according to data availability [START_REF] Nussbaum | Evaluation of digital soil mapping approaches with large sets of environmental covariates[END_REF]. The accuracy of these digital soil maps varies according to the number, the distribution and the accuracy of the observations used for calibration, the nature and the quality of the environmental covariates used for prediction, the model structure, and the mapping procedure [START_REF] Scull | Predictive soil mapping: a review[END_REF].

Numerous studies have demonstrated the importance of scale in DSM [START_REF] Roecker | Scale Effects on Terrain Attribute Calculation and Their Use as Environmental Covariates for Digital Soil Mapping[END_REF], and the need to further investigate it [START_REF] Cavazzi | Are fine resolution digital elevation models always the best choice in digital soil mapping?[END_REF][START_REF] Moore | Soil Attribute Prediction Using Terrain Analysis[END_REF]. The notion of scale includes the measurement scale and the modelling scale, and is characterized by three concepts: i) the extent is represented by the area covered by the dataset or the map, ii) spacing is the distance between samples, which corresponds to the resolution or cell size for gridded datasets, and iii) the spatial support refers to the area covered by each sample [START_REF] Western | On the spatial scaling of soil moisture[END_REF][START_REF] Wiens | Spatial scaling in ecology[END_REF]. A change of scale means a change in extent, spacing, or spatial support [START_REF] Dungan | A balanced view of scale in spatial statistical analysis[END_REF]. For a given geographical extent, the resolution of digital soil maps is usually determined by the resolution of available environmental covariates, not according to the spatial variation of soil properties. The increasing availability of high-resolution DEM and remote sensing images have made much finer resolution possible, even across large areas. For example, the GlobalSoilMaps consortium has made fine-resolution maps available (nearly from 100 m.) for many countries [START_REF] Mulder | GlobalSoilMap France: Highresolution spatial modelling the soils of France up to two meter depth[END_REF]. It is commonly believed that fine spatial resolution provides more accurate information, because calculating maps at too large resolution can mask fine-scale variation and alter their performance. Calculating maps at too fine resolution can also be inefficient to improve accuracy if the raw dataset and the methods do not capture local-scale variability [START_REF] Cavazzi | Are fine resolution digital elevation models always the best choice in digital soil mapping?[END_REF], and can generate noise that impairs data accuracy [START_REF] Roecker | Scale Effects on Terrain Attribute Calculation and Their Use as Environmental Covariates for Digital Soil Mapping[END_REF]. The optimal cell size should correspond to an area with little variation of the studied property value [START_REF] Florinsky | Determination of grid size for digital terrain modelling in landscape investigations -exemplifed by soil moisture distribution at a micro-scale[END_REF][START_REF] Hengl | Finding the right pixel size[END_REF]. These questions of resolution and geographical extent are strongly linked, and refer to the geographers' "modifiable areal unit problem" (MAUP) [START_REF] Openshaw | The modifiable areal unitproblem[END_REF]. The MAUP states that for the same area, a change in the shape or the size of the units often leads to different results. The MAUP includes two components: the "scale problem", which relates to the change in spatial resolution through the level of aggregation of pixels, and the "zoning problem", concerning the changes in the boundaries. It was demonstrated that MAUP effects can lead to meaningless results [START_REF] Jelinski | The modifiable areal unit problem and implications for landscape ecology[END_REF].

Different spatial resolution levels can be compared in many ways, including directly recording data at different resolutions (for remote sensing mainly), transforming raw data from plots or polygons into raster data at different resolutions, or upscaling raster datasets by coarsening spatial resolution [START_REF] Gottschalk | Influence of grain size on species-habitat models[END_REF]. Existing studies mainly concern the effect of environmental factors calculated for a same extent at different spatial resolutions, to predict species distribution [START_REF] Guisan | Sensitivity of predictive species distribution models to change in grain size[END_REF], to elaborate hydrological models [START_REF] Dixon | Resample or not?! Effects of resolution of DEMs in watershed modeling[END_REF], or relevant remote sensing data [START_REF] Stow | Reducing the effects of misregistration on pixel-level change detection[END_REF]. Most of them focus on the DEM resolution effect [START_REF] Chow | Effects of lidar post-spacing and DEM resolution to mean slope estimation[END_REF][START_REF] Gao | Resolution and accuracy of terrain representation by grid DEMs at a micro-scale[END_REF], but also sometimes on the mapping of soil properties [START_REF] Guo | Exploring the Influence of Spatial Resolution on the Digital Mapping of Soil Organic Carbon by Airborne Hyperspectral VNIR Imaging[END_REF][START_REF] Florinsky | Determination of grid size for digital terrain modelling in landscape investigations -exemplifed by soil moisture distribution at a micro-scale[END_REF][START_REF] Maynard | Scale-dependency of LiDAR derived terrain attributes in quantitative soil-landscape modeling: Effects of grid resolution vs. neighborhood extent[END_REF][START_REF] Sena | Analysis of terrain attributes in different spatial resolutions for digital soil mapping application in southeastern Brazil[END_REF][START_REF] Thompson | Digital elevation model resolution: effects on terrain attribute calculation and quantitative soil-landscape modeling[END_REF]. They show a significant effect of cell size on predictions [START_REF] Usery | Geospatial data resampling and resolution effects on watershed modeling: A case study using the agricultural non-point source pollution model[END_REF][START_REF] Wu | An evaluation of grid size uncertainty in empirical soil loss modeling with digital elevation models[END_REF], and globally an increase of performance with decreasing resolution [START_REF] Guo | Exploring the Influence of Spatial Resolution on the Digital Mapping of Soil Organic Carbon by Airborne Hyperspectral VNIR Imaging[END_REF][START_REF] Lassueur | Very high resolution digital elevation models: Do they improve models of plant species distribution?[END_REF][START_REF] Zhang | Digital elevation model grid size, landscape representation, and hydrologic simulations[END_REF]. Other studies also suggest no effect of resolution, or better performance of coarser resolution [START_REF] Costa | Digital elevation model quality on digital soil mapping prediction accuracy[END_REF][START_REF] Kim | Soil Phosphorus and Nitrogen Predictions Across Spatial Escalating Scales in an Aquatic Ecosystem Using Remote Sensing Images[END_REF][START_REF] Roecker | Scale Effects on Terrain Attribute Calculation and Their Use as Environmental Covariates for Digital Soil Mapping[END_REF]. An effect of pixel aggregation from small size to coarse resolution showed both improved and decreased digital map accuracy [START_REF] Carmel | Aggregation as a Means of Increasing Thematic Map Accuracy[END_REF][START_REF] Mccloy | Optimizing image resolution to maximize the accuracy of hard classification[END_REF]. These different results illustrate that decreasing cell size does not always describe more detailed information [START_REF] Samuel-Rosa | Do more detailed environmental covariates deliver more accurate soil maps?[END_REF]. They suggest that fine spatial resolution could be more accurate only if the fine-scale variables can better describe the drivers of soil forming processes. This research work aims to evaluate how spatial resolution can impact the accuracy of soil properties maps, by studying a large range of ecological conditions and different geographical extents. We focused on two soil properties among those most commonly used in ecological studies -the pH and the C/N ratio -recognized for their interest in explaining plant distribution and growth [START_REF] Beauregard | Beyond a Climate-Centric View of Plant Distribution: Edaphic Variables Add Value to Distribution Models[END_REF][START_REF] Seynave | Picea abies site index prediction by environmental factors and understorey vegetation: a two-scale approach based on survey databases[END_REF]. Using a large number of plots with pH and C/N values estimated from bioindication from field observations collected in forests, and a dataset of environmental variables mapped at eight spatial resolution levels, we addressed the following four questions:

-Question 1: how does the resolution of the candidate environmental predictors influence the model calibration? We compared the composition and performances of models elaborated with predictors calculated at different resolutions; -Question 2: how the predictor's spatial resolution influence map accuracy? We compared the performance of the same model mapped with predictors at increasing spatial resolution; -Question 3: does aggregation of the fine-resolution maps of soil properties at different coarser resolution levels improve accuracy? The pH and C/N maps calculated at the finest spatial resolution were aggregated at coarser resolution, and their performances were compared with those of the maps directly built from the environmental predictors calculated at different cell sizes (Question 2); -Question 4: do the performances of the maps calculated at different spatial resolution vary according to their location and extent? We compared the performances of the maps calculated for questions 2 and 3 for different geographical extents.

Methods

To evaluate the optimal resolution of maps, defined as the resolution leading to the highest accuracy for a fixed geographical extent, pH and C/N bioindicator values were modeled with candidate variables describing topography, geology, climate and stand type calculated for eight different spatial resolution levels (Figure 1). The models were first compared (Question 1). Then, the model calibrated with the most local information was directly mapped at the eight resolution levels, and the performances of the maps were compared (Question 2). Finally, these maps were compared with those elaborated by aggregating the 50-m pH and C/N maps at coarser resolution (Question 3). All the calculations were validated with an independent dataset. Because we hypothesized that results could differ according to the studied area, map performances were compared for different geographical extents of four different sizes (the whole studied area, divided in 100*100 km, 50*50 km, and 25*25 km squares).

Study site

The study area encompassed a 91,364 km² area in the north-east of France where plains are dominant, surrounded by four mountain ranges (Jura, Massif Central, Ardennes and Vosges), and crossed by one calcareous plateau (Figure 2A). The average elevation is close to 300 meters; it reaches 1,493 m in the Jura mountains and 1,424 m in the Vosges mountains (Figure 2B). The Vosges mountains, the Ardennes and the Massif Central are composed of a wide variety of Paleozoic rocks like granites, gneiss, schists, or volcanic -mainly acidic -rocks (Figure 2C). The calcareous plateau and the Jura Mountains are mainly made of limestone, with rich soils. The sedimentary basins contain limestones, marls, clays or sandstones (Champagne, central plain), or alluvial sediment made of sand or gravel (Alsace).

Topography combined with oceanic and semi-continental influences lead to a wide gradient of climates, and occasional abrupt changes at short distances. Annual rainfall ranges from 500 mm in Alsace to 2,000 mm in the Vosges and Jura mountains, while mean annual temperatures range between 9°C and 11°C [START_REF] Cachan | Etude bioclimatique du massif vosgien[END_REF][START_REF] Canellas | Les normales climatiques spatialisées Aurelhy 1981-2010: températures et précipitations[END_REF]. The driest areas are found in Champagne, the south of the central plain, and Alsace (Figure 2D). Soil and climate variability lead to a gradient of vegetation, with mainly broadleaved species (oak, beech) in plains and coniferous species (silver fir, spruce) in the mountains, often in a mixture with beech (Figure 2E). [START_REF] Piedallu | Soil water balance performs better than climatic water variables in tree species distribution modelling[END_REF] summarizes climate conditions, with low values in dry areas vs. high values in wet ones.

Bioindication of pH and C/N on NFI plots

We used floristic surveys from 40,663 temporary plots recorded between 1984 and 2017 by the French National Institute of Geographic and Forest Information (IGN) and stored in the National Forest Inventory (NFI) database [START_REF] Drapier | La base de données écologiques de l'IFN. The NFI's ecological data base[END_REF] to predict pH and C/N values using bioindication [START_REF] Ellenberg | Zeigerwerte von Pflanzen in Mitteleuropa[END_REF]. This inventory was realized with a similar sampling density for all the forested areas, by administrative units between 1984 and 2005, and on a regular mesh shift each year encompassing the whole of France since 2005 (about 7000 plots per year). The floristic survey was realized on a circular plot on a 700 m² area. Indicator values (IVs) were calibrated for the most common forest plant species in France using the Ecoplant database [START_REF] Gegout | EcoPlant: A forest site database linking floristic data with soil and climate variables[END_REF], which contains both floristic surveys and soil analyses for the same locations. For each of the most common forest species, IVs provide the highest probability to observe the species along different ecological gradients [START_REF] Gegout | Prediction of forest soil nutrient status using vegetation[END_REF]. For each of the 40,663 plots, we obtained bioindicated pH and C/N values for the soil surface layer by averaging the IV values of the plants present in the floristic survey. At large scales, the validation of these values with independent datasets yielded R² values of 0.45 and 0.41, and RMSEs of 0.47 and 3.8 for pH and C/N, respectively [START_REF] Gegout | Prediction of forest soil nutrient status using vegetation[END_REF]. Because prediction is less accurate when few species are present, pH and C/N were not estimated when less than five species with IVs were surveyed. We obtained 37,958 plots with pH estimations and 37,737 with C/N estimations, collected with a density near of 1.10 plot per km² in forested areas. pH values ranged between 3 and 8, and C/N values between 10 and 35 (See Appendix A for plot location, Appendix B for the observed spatial distribution of pH and C/N, and Appendix C for the range of pH and C/N values). Values from the plots were autocorrelated up to 110 km for pH and 96 km for C/N (Appendix D).

Explanatory environmental variables

A set of 25 potential explanatory environmental variables was identified from the literature [START_REF] Mcbratney | On digital soil mapping[END_REF][START_REF] Scull | Predictive soil mapping: a review[END_REF], describing topography, geology, climate and stand type (Table 1). Because gravity plays a role in water and nutrient transport, topography is described as an important driver of the redistribution of soil properties along slopes. For the whole studied area, we used the 50-m resolution digital elevation model (DEM) from the IGN to calculate topographic indices2 . Elevation (DEM), slope, shape of the soil surface (concave, convex, curved), sine and cosine of aspect (sinaspect and cosaspect), and relative distance or elevation between ridges and talwegs (reldist/relalt) characterized the position in the landscape (Table 1). Flow accumulation (flac) and topographic wetness index (TWI) quantified the topographic drivers of hydrological processes.

Because parent materials provide nutrients to the soil, a simplified geological map based on the 1:50000 vector maps of the Bureau de Recherches Géologiques et Minières (BRGM) was calculated over the whole study area (Geol). The original maps, which contain data about bedrocks and most of the time superficial units, were homogenized by the BRGM for each French "département" (administrative unit). We concatenated the sixteen departmental maps describing the study area. The 130,164 polygons and 2,841 different units were homogenized and simplified according to the chemical characteristics of the units to obtain 16 simplified units (Appendix E).

Monthly mean temperature (TM) and rainfall (R) were modeled and mapped for the whole of France at 50 m resolution for the 1961-1990 period (Table 1), using variables describing distances to the sea, vegetation, and topography [START_REF] Piedallu | Soil water balance performs better than climatic water variables in tree species distribution modelling[END_REF]. Two hundred and thirty-seven Météo France weather stations were used for temperature calibration and 432 for rainfall calibration. The data were validated using annual values from independent weather stations. Ninety-three percent of the variance was explained for temperature, and 78% for rainfall. Climatic water balance (CWB) was calculated as the difference between rainfall and potential evapotranspiration [START_REF] Piedallu | Soil water balance performs better than climatic water variables in tree species distribution modelling[END_REF]. Monthly mean data were averaged for temperature and cumulated for rainfall and CWB for each season: winter (wi, December to February), spring (sp, March to May), summer (su, June to August) and autumn (au, September to November). Finally, an IGN vector map representing stand composition (BD Forêt3 ) for units greater than 0.5ha was used to characterize the stand types of the forested areas (Stand). The 22 initial units were simplified into five stand types: coniferous, broadleaved, mixed, tree-less forest, and others.

The 25 predictors were calculated and mapped for the whole area at eight spatial resolution levels: 50, 100, 250, 500, 1,000, 8,000, 16,000 and 50,000 m. We studied a large range of resolutions to detect if predictive ability could decrease beyond a specific threshold. All the variables initially existed in 50 m resolution grids, except Geol and Stand that were in vector format and were rasterized. For these last two predictors, the pixel value was attributed for each of the eight spatial resolution levels according to the polygon unit with the greatest area in the cell. The raster layers were calculated at the coarser resolution by averaging the cells from the 50-m resolution maps.

Category

Variable

Effect of the resolution of variables on model calibration

To evaluate the influence of the resolution of the candidate variables on model calibration (Question 1), we calibrated the pH and C/N models with the set of the 25 environmental variables (Table 1) calculated for the eight resolution levels. Each model was calibrated independently using multiple linear regression. The explanatory variables were selected one by one. At each step, the variable best explaining the variance was selected, provided that it was statistically significant (P value < 0.001). To ensure a selection of relevant responses according to current knowledge, we allowed a pH decrease or a C/N increase with altitude or slope increase, on convex areas or near the ridges with low Flac and TWI values, on northern or eastern slopes, in cold areas, and with high R or CWB values. At each step, variables were discarded if they were correlated with another previously selected variable (Pearson's r > 0.7). The model ended if the R² increase was less than 0.001. For each model, the relative importance of each variable contribution was calculated with the relaimpo package [START_REF] Gromping | Relative importance for linear regression in R: The package relaimpo[END_REF]. We used the averaging over ordering method (lmg) that provides the R 2 contribution averaged over orderings among regressors, identified as one of the most relevant ones (Lindeman et al., 1980). Then, the model compositions and performances were compared at the eight resolution levels.

Effect of spatial resolution on model mapping

Once the models were calibrated, we evaluated how the resolution of the maps describing the selected variables influenced the accuracy of the maps of soil properties (Question 2). To only consider the effect of the predictor's resolution on accuracy, we used the same model (those previously calibrated with the most local information, 50 m) to map pH and C/N with the predictors calculated at the eight spatial resolution levels. Because pixel aggregation can improve map performance (Carmel, 2004), we also used the finest-resolution pH and C/N maps (50 m) and averaged their cell values to the coarser resolution levels (Question 3). For different coarser resolutions, we compared the performances of the maps obtained by aggregation with those of the maps directly built from the environmental predictors with the same validation dataset.

Because map performance can vary according to the geographical extent [START_REF] Openshaw | The modifiable areal unitproblem[END_REF], we compared the performance of all the pH and C/N maps elaborated at the eight spatial resolution levels at different geographical extents: the whole studied area, and 100*100 km, 50*50 km, and 25*25 km squares (Question 4). For these last three extents, the study area was split into squares that contained a subset of plots. For the whole area and each square that contain more than 100 plots, maps values (Appendix A and B) were compared to an independent subset of plot estimations and the differences in performances were mapped. For the eight resolution levels and the four geographical extents, global performances were compared, by averaging the performances of all the 100*100 km, 50*50 km, and 25*25 km squares.

Comparison of model and map performances

Four metrics were used to evaluate model performance following calibration at different resolution levels: R², root mean squared error (RMSE), mean absolute error (MAE), and mean bias error (MBE). R² assesses the proportion of explained variance, but does not inform about the difference between predicted and estimated values. RMSE and MAE are two of the most common metrics used to evaluate model prediction error in units of the variable of interest; RMSE gives a more important weight to large errors (Willmott & Matsuura, 2005)

: = 1 [ - ]² = 1 [| -|] = 1 [ - ]
Where n is the number of recordings, j y is the observed value, and j y ˆ is the predicted value.

Due to a large number of calculations and the difficulties in representing all the results, we only used R² and MAE to evaluate map performance (Questions 2, 3 and 4) for the whole area and for each 100*100 km, 50*50 km and 25*25 km square. The metrics were estimated with an independent dataset both for model calibration and map accuracy evaluation. The model and maps were set up with 80% of the randomly selected plots, and predictions were validated with the remaining 20%. Performances were calculated by averaging values from 100 iterations.

Results

Similar variables but decreasing performances when calibrating models with data at increasing spatial resolution

Two to 6 variables were selected to calibrate each model for the eight resolution levels, with responses in line with current knowledge (Appendix F). Although 25 candidate variables were evaluated, most of the selected ones were similar for the different resolution levels (Table 2). The maximum R² values were about 0.65 and 0.54 for pH and C/N, and the minimum MAEs were 0.48 and 2.25, respectively. A large part of the variance (> 60%) was explained by geology for both pH and C/N. Climate also explained the variance of pH (except when the models were calibrated with the variables at coarse resolution), with stand type and topography to a lesser extent. For C/N, stand type performed better than topography and climate (Table 2-B). We showed a slight decrease of the variance explained by geology at resolution levels < 1km, compensated by an increase of the variance explained by stand type (for pH) and topography (for C/N) (Appendix G). At coarser resolution, the importance of stand type and climate decreased while the importance of topography increased. R², RMSE and MAE were comparable when the resolution of the input variables ranged between 50 m and 1 km, and strongly decreased at coarser resolution. The best performances were reached for input variables at 250 m resolution for pH. For C/N, they were reached at 250 m resolution according to R² and 50 m according to RMSE and MAE (Table 2

Lower accuracy when digital maps larger than 1 km resolution

We used the equation calibrated with the most local data (i.e. at 50 m resolution, Appendix F), to map pH and C/N with the sets of variables calculated at the eight spatial resolution levels (Figure 3). Logically, both for pH and C/N, the more reduced the geographical extent, the lower the R² value (Figure 4). MAE decreased with geographical extent, except for predictions taking the whole area into account. Performances varied according to location, with both for pH and C/N globally better R² but higher MAE on the Vosges mountains, and lower R² but also lower MAE in calcareous plateaux and Jura mountains (Appendix H and Figure 1 for the location of ecological units).

Using variables with different spatial resolution levels had a limited impact on map accuracy, whatever the extent up to 1 km cell size, and then map performance dropped significantly at coarser resolution levels (Figure 4). The highest R² and lowest MAE were consistently obtained in 250 m resolution maps for pH. For C/N, the highest R² were obtained at 50 or 100 m resolution, and the lowest MAEs were found between 250 m and 1 km resolution (Figure 4). Beyond these mean performances, significant spatial variability was highlighted (Figure 5). Fine-resolution maps globally performed better in the Vosges mountains, in the north of the Jura mountains and the south of the central plain (see Figure 1 for the location of ecological units). Great discrepancies were found for C/N, whether R² or MAE was used (Figure 5). When we compared the performances of the 50 m and 1 km spatial resolution maps, fine resolution mainly improved map performances in the Vosges mountains, with a greater effect on R² than on MAE and on C/N than on pH (Appendix I). The maximum increase of R² at 50 m resolution comparatively to 1 km resolution was + 0.15 for pH and + 0.21 for C/N at the 25km*25km scale. and4). For each square, performances were calculated between the maps calculated at different spatial resolution and an independent subset of plots. White areas, no performance calculated because the number of plots was lower than 100.

Spatial aggregation improves map quality

We compared the performances of the maps calculated by directly using the variables at different spatial resolution levels with the maps calculated by aggregating the 50-m pH or C/N maps at coarser resolution (Figure 6). For large resolution (≥ 500m), the maps consistently performed better when they were calculated by aggregation. The highest R² and lowest MAE were reached at 1 km resolution, whatever the geographical extent (Appendix J). Although aggregation improved the performance of the 1 km maps, some of the maps at smaller resolution levels remained more accurate locally, mainly when considering R² and C/N , and in the Vosges mountains (Appendix K and L).

Fine-resolution maps better describe local variability when geographical extents are smaller

Because optimal resolution can vary according to the size of the geographical extent (Figure 5), we compared the performance of the maps calculated at different resolution levels for the studied geographical extents (table 3). We compared the 50 m and 1 km resolution maps because the previous analysis had shown that performance significantly decreased above 1 km cell size. For the maps directly calculated at different resolutions, 50 m resolution maps showed on average a higher R² and lower MAE than 1 km resolution maps for the 25*25 km extent compared to the whole area (Appendix M for average performances, Appendices I, and L for the maps). The efficiency of the 50 m resolutions maps increased compared to the coarser resolution maps as the extent decreased. The better performance of the 50 m maps was mainly observed when focusing on R² rather than on MAE, and was better for C/N than for pH (Table 3). The 50 m resolution maps had higher R² than the 1 km resolution maps for 59 and 80 % of the squares in the 25*25 km extent for pH and C/N, respectively. The percentage of the squares for which the 50 m resolution maps performed better than the 1 km resolution maps decreased when they were calculated with aggregation: 48 and 41 % of the squares had a higher R² than at 1 km resolution for pH and C/N, respectively, for the 25*25 km extent.

Discussion

Using bioindication to optimize the calibration dataset

Although the question of resolution has been extensively studied for terrain attributes [START_REF] Deng | DEM resolution dependencies of terrain attributes across a landscape[END_REF], and despite the increasing number of digital maps of soil properties calculated at finer and finer spatial resolution [START_REF] Dai | A review of the global soil property maps for Earth system models[END_REF], the question remains about the impact of scale on DSM performance. Using bioindication allowed to calibrate and validate models and maps with a large dataset based on floristic surveys carried out at high sampling density. Bioindication has long been used in ecology [START_REF] Ellenberg | Zeigerwerte von Pflanzen in Mitteleuropa[END_REF] and has proved efficient to represent local variation of soil properties [START_REF] Coudun | Soil nutritional factors improve models of plant species distribution: an illustration with Acer campestre (L.) in France[END_REF][START_REF] Simon | A framework for the predictive mapping of forest soil properties in mountain areas[END_REF]. Its main weaknesses are linked to greater uncertainty compared to measurements, whose intensity can vary along the gradient of variables [START_REF] Gegout | Prediction of forest soil nutrient status using vegetation[END_REF]. For example, bioindicated pH does not discriminate values from acidic soils as precisely as it discriminates values from neutral or alkaline soils [START_REF] Riofrio-Dillon | Toward a recovery time: forest herbs insight related to anthropogenic acidification[END_REF]. A comparison with measurements should allow to quantify if these differences could have an impact on the map's performances calculated at different scales. Thanks to the large dataset used, various ecological conditions have been investigated. A large amount of pH and C/N variance was explained by our models, allowing us to study how resolution influences model and map performances for a large range of environmental conditions and different geographical extents.

Resolution had a limited influence on predictor selection

In our models, the resolution had little influence on variable selection but influenced the proportion of variance they explain. Whatever the resolution, simplified geology was the most efficient predictor, and represented 63 to 75% of explained pH and C/N variances, respectively. It was complemented by stand type, climate and topography. Different studies reported the most commonly used predictors are terrain attributes, while the parent material was used in only less than 10% and 25 % of DSM studies according to the reviews by [START_REF] Grunwald | Multi-criteria characterization of recent digital soil mapping and modeling approaches[END_REF] and [START_REF] Mcbratney | On digital soil mapping[END_REF], respectively. The importance of the parent material has been highlighted in different studies carried out in Europe [START_REF] Simon | A framework for the predictive mapping of forest soil properties in mountain areas[END_REF] or in China [START_REF] Wiesmeier | Digital mapping of soil organic matter stocks using Random Forest modeling in a semi-arid steppe ecosystem[END_REF]. We demonstrated geology can be a good surrogate in the absence of soil maps. Its efficiency in our models can be explained by the large variety of units of different chemical characteristics. The absence of quaternary deposits on some maps and the difficulty in summarizing a great variety of substrates, mainly in mountainous areas, constitute the main obstacles to the use of geology. Stand type and climate also contributed significantly to our models, and showed relevant responses according to current knowledge. The negative effect of coniferous species on the pH reflected the soil acidification by coniferous tree species already observed in experimental studies [START_REF] Augusto | Impact of tree species on forest soil acidification[END_REF]. The pH increase and C/N decrease with temperature and water stress are in agreement with experimental studies showing better N mineralization under warm temperature and a low water content [START_REF] Cassman | Nitrogen mineralization as affected by soil moisture, temperature, and depth[END_REF]. In a context where topography is often showed to be the most efficient predictor, we highlighted the important role of parent material, stand type and climate variables in DSM studies. This comparison was based on explanatory variables all calculated at the same resolution, but some authors found better results when considering predictors at different resolution levels [START_REF] Miller | Impact of multi-scale predictor selection for modeling soil properties[END_REF]. Therefore, further investigations should be carried out to evaluate the optimal resolution of each soil property predictor taken independently.

Resolution strongly influences map accuracy

The optimal resolution of maps of soil properties is complex to determine because different categories of factors interplay [START_REF] Mcbratney | On digital soil mapping[END_REF], while biophysical processes can operate at different spatial scales [START_REF] Deng | DEM resolution dependencies of terrain attributes across a landscape[END_REF][START_REF] Phillips | The role of spatial scale in geomorphic systems[END_REF]. Map cell size is often determined subjectively to match with the finest data available, or by expert knowledge [START_REF] Deng | DEM resolution dependencies of terrain attributes across a landscape[END_REF]. [START_REF] Florinsky | Determination of grid size for digital terrain modelling in landscape investigations -exemplifed by soil moisture distribution at a micro-scale[END_REF] proposed a framework to identify optimal map cell size by correlating topographic variables derived from a DEM calculated at different resolution levels with landscape properties. We adapted this approach to compare the performances of models and maps of soil properties. Although average performances can mask great discrepancies, we determined that the average optimal resolution, i.e., the largest cell size before performance decreases, was 1 km cell size. Performances for pH and C/N were on average comparable at resolution levels ranging between 50 m and 1 km, and strongly decreased at coarser resolution. We expected a global improvement of accuracy with decreasing cell size because important variations in soil pH can be observed on short distances [START_REF] Laslett | Comparison of several spatial prediction methods for soil pH[END_REF], and smoothed variables can mask fine-scale variations [START_REF] Chow | Effects of lidar post-spacing and DEM resolution to mean slope estimation[END_REF][START_REF] Gao | Resolution and accuracy of terrain representation by grid DEMs at a micro-scale[END_REF]. Our result can reflect the local spatial relationships between soil properties and the underlying pedogenic factors that operate at a specific range of spatial scales [START_REF] Maynard | Scale-dependency of LiDAR derived terrain attributes in quantitative soil-landscape modeling: Effects of grid resolution vs. neighborhood extent[END_REF][START_REF] Samuel-Rosa | Do more detailed environmental covariates deliver more accurate soil maps?[END_REF]. A value below which increased resolution does not seem to impact performance has already been reported for terrain parameters [START_REF] Zhang | Digital elevation model grid size, landscape representation, and hydrologic simulations[END_REF]. The scale invariance that we globally observed below 1 km resolution, already observed with fine-resolution predictors [START_REF] Pradervand | Very high resolution environmental predictors in species distribution models: Moving beyond topography? Progress in Physical Geography[END_REF], can also suggest that the study design failed to completely capture the spatial variability of soil properties when variations were low. This result can be influenced by the bioindication of pH and C/N values, that increased uncertainty compared to laboratory analyses, and probably smoothed out spatial variability in areas with little changes. Better performance of the fine-resolution maps can be expected using measured pH and C/N values.

Different spatial supports were used in this study: point support collected on a 700 m² plot for soil data, used for model and map calibration and validation, and cells of different surfaces from the digital maps. The support size should be relevant to describe the natural variability of the soil properties: if the support of the soil data is too large compared to the process scale, variability can be averaged [START_REF] Western | On the spatial scaling of soil moisture[END_REF]. The use of bioindication increases the support size comparatively to soil analysis classically collected from a single point at the plot center. Complementary studies should investigate the small-scale variability of pH and C/N in heterogeneous areas to evaluate the optimal support size. The difference in support size between digital maps and the validation dataset probably underestimates the map performances, and the validation of digital maps at the point support probably performs worse than larger spatial units [START_REF] Bishop | Validation of digital soil maps at different spatial supports[END_REF].

Optimal resolution matched point density -around one plot per km² in our calibration dataset, potentially contributing to the scale invariance below 1 km resolution. Sampling density is known to have a strong influence [START_REF] Loiseau | Density of soil observations in digital soil mapping: A study in the Mayenne region, France[END_REF]: increasing it globally improves the accuracy of prediction [START_REF] Guo | Exploring the Sensitivity of Sampling Density in Digital Mapping of Soil Organic Carbon and Its Application in Soil Sampling[END_REF]. On the other hand, the 1 km threshold beyond which accuracy decreases is an average value that hides important local differences. This does not advocate for a global effect of the sampling density on our results. For example, in some heterogeneous areas, map accuracy strongly decreased both for pH and C/N above 50 m resolution (R² was up to 0.15 and 0.11 higher for the 50 m resolution maps than for the 1 km resolution maps for pH and C/N maps, respectively; see appendix I), while sampling density remained the same. We suggest further studies to better understand how the sampling scheme can influence the results, by comparing optimal resolution with models calibrated at various sampling densities. We recommend such comparisons of maps with different cell sizes with an independent dataset of field observations to reach an optimal resolution.

Using cell aggregation improves the performances of predictive maps

We observed better performances when upscaling finer pH or C/N resolution maps rather than calibrating them at coarser resolution. Data aggregation results are controversial across studies. In some cases, coarsening spatial resolution by aggregating cell size causes a loss of information that increases uncertainties. For example, [START_REF] Maharjan | Effects of input data aggregation on simulated crop yields in temperate and Mediterranean climates[END_REF] showed that aggregating climatic and soil data led to a greater error when simulating crop yields, in agreement with other studies and despite the use of diverse models, crops, production conditions, and variables [START_REF] Zhao | Effect of weather data aggregation on regional crop simulation for different crops, production conditions, and response variables[END_REF]. On the other hand, several studies demonstrated the interest of cell aggregation, mainly for the classification of remote sensing images (Carmel, 2004;[START_REF] Townshend | The impact of misregistration on change detection[END_REF]. As in our study, they showed better accuracy when aggregating pixels up to the object size, followed by a decrease when the pixel was bigger [START_REF] Mccloy | Optimizing image resolution to maximize the accuracy of hard classification[END_REF][START_REF] Woodcock | The factor of scale in remote sensing[END_REF].

The gain in performance we observed with aggregation can be attributed to the qualitative predictors available through vector maps. When a vector map was rasterized at different cell sizes, the pixel value was attributed according to the polygon unit that occupied the greatest area in the cell, and information about minority units was lost. On the contrary, cell aggregation after pH or C/N mapping at fine spatial resolution allowed for unbiased calculations that considered all the existing units proportionally to their geographical extent. The two vector datasets we used (Geol and Stand type) explained a large part of the variance in our models, so that performance was improved by aggregation. On the contrary, the quantitative predictors initially available through raster maps at 50 m resolution were calculated at coarser resolution using aggregation. This method probably contributes to improve the performance of the maps directly calculated at a coarser resolution than 50 m, and could contribute to explain the global scale invariance observed below 1 km resolution. Aggregation efficiency can vary according to the upscaling method [START_REF] Dai | A review of the global soil property maps for Earth system models[END_REF], and this effect could be evaluated in further studies. Therefore, data aggregation can be an efficient tool to improve map accuracy, and its use should be evaluated in DSM studies.

4.5 Environmental characteristics and geographical extent have a strong impact on optimal map resolution Beyond the average performances showing a scale invariance below 1 km resolution, important differences were recorded according to the location and the size of the geographical extent. Fineresolution maps performed better in heterogeneous areas, while the coarse resolution was more efficient in homogeneous ones. As already reported by other studies [START_REF] Liu | Spatial multi-scale variability of soil nutrients in relation to environmental factors in a typical agricultural region, Eastern China[END_REF], multi-scale variation can be observed depending on the different environmental characteristics. In our case, geology and climate varied at a regional scale, but also more locally in mountainous areas. Acidic units were mainly grouped in a few specific regions (see paleozoic rocks in Figure 2-C), but significant shortdistance variation can occur locally. Climate gradients also operated at a large scale (Figure 2-D), but were influenced locally by topographic gradients [START_REF] Piedallu | Efficient assessment of topographic solar radiation to improve plant distribution models[END_REF]. This probably explains why fine-resolution maps performed better in the Vosges mountains because they better described these strong local changes in an area showing highly diverse chemical characteristics among parent materials [START_REF] Nedeltcheva | Influence of granite mineralogy, rainfall, vegetation and relief on stream water chemistry (Vosges Mountains, north-eastern France)[END_REF] and a great diversity of climates, topographies, and stand types [START_REF] Cachan | Etude bioclimatique du massif vosgien[END_REF]. On the contrary, in homogeneous areas, coarse cells probably improve the prediction by smoothing out local uncertainties. Similar findings have been reported for topographic variables calculated with DEMs, with a better performance at coarse resolution in flat areas and at fine resolution in morphologically varied areas [START_REF] Cavazzi | Are fine resolution digital elevation models always the best choice in digital soil mapping?[END_REF][START_REF] Thompson | Digital elevation model resolution: effects on terrain attribute calculation and quantitative soil-landscape modeling[END_REF]. Our results suggest that different spatial resolution could be used according to the environmental characteristics of the areas to be studied.

The size of the studied geographic space influences the results because the range of soil properties globally decreases with decreasing extents [START_REF] Grunwald | Digital Soil Mapping and Modeling at Continental Scales: Finding Solutions for Global Issues[END_REF]. The performance of the fineresolution maps was clearly improved compared to coarser resolution when the size of the study area decreased. For reduced extents, the 50 m maps were most of the time more efficient than the 1 km maps to explain pH or C/N variations because they exhibited a higher variance that better described local spatial variability than coarser resolution did. Their ability to describe local variability is an important advantage for managers or policymakers, who often need to extract data about a specific extent from maps calibrated and validated over broad areas. Further investigations should be carried out to evaluate if the performance of fine-resolution maps keeps increasing relatively to coarseresolution maps when geographical extents are further decreased. These results argue for the calculation of fine-resolution maps in heterogeneous landscapes and for local use. On the other hand, coarse data do not dramatically degrade map quality and could be used when they are the sole data available, particularly for homogeneous areas or regional studies. Multi-scale validation of the map performances should provide a more comprehensive evaluation of their quality according to the intended use.

Conclusion

The need for relevant digital data about soil properties has increased in recent years in link with the need to manage the consequences of human actions on environmental changes. Two pitfalls have to be avoided: too coarse resolution that leads to less precision, and too fine resolution that makes users believe in false precision. We observed that optimal map resolution varied according to soil properties, local environmental characteristics, and geographical extent. In a context where digital maps of soil properties are calculated at finer and finer resolution, we did not show an altogether linear improvement of accuracy as resolution grew finer. However, we did observe a significant effect of cell size on performances, with a range of suitable resolution levels before an abrupt loss of performance at coarser resolution. The finest spatial resolution proved to be of interest as it significantly improved accuracy in heterogeneous areas, with rising performances as the geographical extent decreased. Moreover, fine-resolution maps allowed for cell aggregation, which showed promising results. In a context where the benefits of digital maps are highly dependent on their accuracy, we highlighted the importance of identifying the best resolution to provide land managers and policymakers with relevant maps available for a broad range of geographical extents.

Figure 1 :

 1 Figure 1: Synthetic presentation of the methods used to answer the four questions addressed in the paper (Q1, Q2, Q3, and Q4).

Figure 2 :

 2 Figure 2: Simplified maps of the studied area: A, ecological units (based on Sylvoecoregions 1 ); B, geology; C, elevation (m.); D, vegetation category; E, annual average 1961-1990 climatic water balance (the difference between rainfall and potential evapotranspiration, in mm.). The climatic water balance[START_REF] Piedallu | Soil water balance performs better than climatic water variables in tree species distribution modelling[END_REF] summarizes climate conditions, with low values in dry areas vs. high values in wet ones.

Figure 3 :

 3 Figure 3: Examples of pH and C/N maps calibrated using the model with the most local data and mapped with explanatory variables at 50-m, 1-km, 8-km and 50-km spatial resolution levels.

Figure 4 :Figure 5 :

 45 Figure 4: Performance (R² and MAE) of pH and C/N maps calculated at the eight different spatial resolution levels (50 m to 50 km) for different geographical extents (Question 2). For the 100, 50, and 25 km extents, values were averaged from the different squares.

Figure 6 :

 6 Figure 6: Performances (R² and MAE) of pH and C/N maps calculated by directly using the variables at the eight different spatial resolution levels for the whole studied area or by aggregating the 50 m pH and C/N maps at coarser resolution levels (Question 3).

Table 1 :

 1 Ecological variables used to model pH and C/N, units and references. wi= winter, sp= spring, su= summer, au= autumn.

	name	Definition

Table 2 :

 2 ). Selected variables and performances of the models for eight spatial resolution levels A) for pH and B) for C/N (Question 1). The numbers provided for each selected variable indicate the part of explained variance they added to the model (in %). RMSE, MAE and MBE were expressed in pH or C/N units. The highest performances are highlighted in grey. See Table1for explanations about the names of the variables.

	A) PH CATEGORY VARIABLE 50 M 100 M 250 M 500 M 1 KM 8 KM 16 KM 50 KM
		Geology	Geol	74	74	72	70	69	72	73	75
		Stand type	Stand	9	8	15	16	17	1	6
		Climate	TMwi	13	13	8
			CWBsu				7	6	20	12
	VARIABLES	Topography Slope	3	4	4	6	7			25
			Flac	1	1	1	1	1	7
			TWI							8
			Sinaspect							1
			R²	0.64	0.64	0.65	0.65	0.64	0.56	0.52	0.40
			RMSE	0.65	0.64	0.64	0.64	0.64	0.71	0.74	0.83
	PERFORMANCES	MAE	0.48	0.48	0.48	0.48	0.48	0.53	0.56	0.64
			MBE					0.00
	B) C/N CATEGORY VARIABLE 50 M 100 M 250 M 500 M 1 KM 8 KM 16 KM 50 KM
		Geology	Geol	70	70	69	67	66	63	66	76
		Stand type	Stand	18	18	18	18	18	8	9
		Climate	TMsu	6	6	5	5	4
			CWBsu						14
	VARIABLES	Topography Curv	1	1
			Slope	4	5	7	9	11	15	22	24
			RELalt	1		1	1	1
			Convex							3

Table 3 :

 3 Percentage of the squares where the 50 m resolution maps performed better than the 1 km resolution maps, for the 25*25, 50*50 and 100*100 km extents, for pH and C/N calculated directly using the variables at different resolution or by aggregating the 50 m maps (Question 4, see Appendices G and J for the maps).

		Extent	25*25 km 50*50 km	100*100 km
		n	132	46	17
		pH	59	57	35
	R²	CN	80	76	71
		pH aggregated	37	17	0
		CN aggregated	61	48	35
		pH	48	41	35
	MAE	C/N	41	41	35
		pH aggregated	23	17	24
		C/N aggregated	26	22	24

https://inventaire-forestier.ign.fr/IMG/pdf/IF_SER_web.pdf

https://geoservices.ign.fr/ressources_documentaires/Espace_documentaire/MODELES_3D/BDALTIV2/SE_BDAL TI.pdf

https://inventaire-forestier.ign.fr/spip.php?article646

Acknowledgements

This study was funded through the Rescale project by the Regional Council of Grand-Est ("Region Grand-Est") and the "Direction de l'Agriculture et de la Forêt (DRAF) "Grand-Est. We thank Eric Karcher and Margaux Lebecque, Anne Sophie Simon, Laurence Benini, Budiman Minasny and the two anonymous reviewers for their help.

Appendices

Appendix A: Location of the 37,958 plots from the National Forest Inventory used for model calibration (black dots), and delineation of the four geographical extents: the whole studied area, 100*100 km, 50*50 km, and 25*25 km squares (squares with less than 100 plots does not appear and were not used in the analysis). No performance was calculated when the number of plots in a cell was lower than 100. For each square, performances were calculated between the maps calculated at different spatial resolution and an independent subset of plots.

Appendix L: Difference of performance (R² and MAEs) between the aggregated maps of pH and C/N at 50 m and 1 km resolution for the different geographical extents (Questions 3 and 4). Positive values highlight better performance of 50 m maps while negative values highlight better performance of 1 km maps. No performance was calculated when the number of plots in a cell was lower than 100. For each square, performances were calculated between the maps calculated at different spatial resolution and an independent subset of plots.


Siavash Bakhtiarnia

Saeed Sheibani
email: ssheibani@ut.ac.ir

Pascal Briois

Eric Aubry

Mohammad Arab

Pour Yazdi

Ag-Doped BiVO4 Thin Films Deposited by Reactive Magnetron Sputtering as Visible Light Photocatalysts

Keywords: Photocatalyst, BiVO4, Thin film, Sputtering, Rhodamine B

In this study, the Ag-doped monoclinic BiVO4 thin films were synthesized with a reactive magnetron sputtering technique and a post-annealing treatment. The X-ray diffraction and scanning electron microscopic analysis exhibited the formation of silver vanadate and metallic silver phase with various quantities depending on Ag loading. The photocatalytic experiments established the importance of Ag distribution in photoactivity enhancement since the heterojunctions between the phases are responsible for the charge separation. It was also proved that Ag-doping improves the photoactivity of monoclinic BiVO4 at neutral pH by favoring the chromophore cleavage pathway in the photodegradation mechanism, which is a significant advantage over the pristine BiVO4 being optimal at acidic pH.

Introduction

In recent years, bismuth vanadate in monoclinic scheelite structure (m-BiVO4) has received an enormous amount of attention from the material scientific community thanks to its beneficial properties e.g. stability, non-toxicity, cheap production, optical absorption in the visible region, and the ability to decontaminate organic pollutions [START_REF] Samsudin | Epigrammatic progress and perspective on the photocatalytic properties of BiVO4-based photocatalyst in photocatalytic water treatment technology: A review[END_REF][START_REF] Malathi | A review on BiVO4 photocatalyst: Activity enhancement methods for solar photocatalytic applications[END_REF]. These properties enabled engineers to design procedures advancing photocatalytic processes using clean solar energy. There have been numerous attempts in synthesizing m-BiVO4 through liquid-phase chemical routes, including solgel [START_REF] Yin | One step fabrication of C-doped BiVO4 with hierarchical structures for a high-performance photocatalyst under visible light irradiation[END_REF], hydrothermal [START_REF] Geng | Synthesis of Co doped BiVO4 with enhanced visiblelight photocatalytic activities[END_REF], co-precipitation [START_REF] Huo | Visible-light photocatalytic degradation of glyphosate over BiVO4 prepared by different co-precipitation methods[END_REF][START_REF]Synthesis and photocatalytic performances of BiVO4 by ammonia co-precipitation process -ScienceDirect[END_REF] that produce powder form, bringing certain downsides like recyclability, reusability, and using toxic chemicals, while the physical vapor deposition methods gained much less attention, particularly sputtering technique. Not only does it have advantages like clean low-cost products, and a high deposition rate [START_REF] Sarkar | Optical constants, dispersion energy parameters and dielectric properties of ultra-smooth nanocrystalline BiVO4 thin films prepared by rfmagnetron sputtering[END_REF], but they are also able to produce thin films that solve the recyclability problem making the entire photocatalytic water treatment more practical and economically viable. Magnetron sputtering technique has been widely used for high throughput stable and uniform productions in the industry [START_REF] Sarkar | Optical constants, dispersion energy parameters and dielectric properties of ultra-smooth nanocrystalline BiVO4 thin films prepared by rfmagnetron sputtering[END_REF], while few studies can be found in the literature utilizing this technique to synthesize BiVO4 thin films.

Although there are a significant number of advantages in m-BiVO4 thin films, it contains a few downsides like low charge mobility and electron recombination that should be overcome [START_REF] Ge | Novel visible-light-driven Pt/BiVO4 photocatalyst for efficient degradation of methyl orange[END_REF].

Doping and creating heterojunctions are the procedures that have been proved effective in solving the mentioned problems through charge separation preventing the photogenerated electrons to recombine [START_REF] Sun | NiO nanosheet/TiO2 nanorod-constructed p-n heterostructures for improved photocatalytic activity[END_REF][START_REF] Ismail | Mesostructured pt/tio 2 nanocomposites as highly active photocatalysts for the photooxidation of dichloroacetic acid[END_REF]. Many elements were examined to enhance the photocatalytic properties of m-BiVO4 e.g. Co [START_REF] Geng | Synthesis of Co doped BiVO4 with enhanced visiblelight photocatalytic activities[END_REF], Cu [START_REF] Wang | Effects of Cu dopants on the structures and photocatalytic performance of cocoon-like Cu-BiVO4 prepared via ethylene glycol solvothermal method[END_REF], Ag [START_REF] Zhang | Preparation of Ag doped BiVO4 film and its enhanced photoelectrocatalytic (PEC) ability of phenol degradation under visible light[END_REF], Mo [START_REF] Chen | Mo-Doped BiVO 4 Photoanodes Synthesized by Reactive Sputtering[END_REF], Se [START_REF] Ullah | Structural and electronic properties of oxygen defective and Se-doped p-type BiVO4(001) thin film for the applications of photocatalysis[END_REF], Fe [START_REF] Regmi | Visible-light-induced Fedoped BiVO4 photocatalyst for contaminated water treatment[END_REF], Mo [START_REF] Yin | High porosity Mo doped BiVO4 film by vanadium re-substitution for efficient photoelectrochemical water splitting[END_REF]. Amongst the dopant elements, silver shows promising prospects. Numerous researches have already stated the silver doping effectiveness in charge separation and narrowing the bandgap of TiO2 [START_REF] Abbad | Effect of silver doping on the photocatalytic activity of TiO2 nanopowders synthesized by the sol-gel route[END_REF]. It has also been employed to enhance BiVO4. Wang et al. synthesized Ag + /Ag/BiVO4 composite fibers and observed a redshift in the absorption spectrum and superior photocatalytic activity compared to the pristine BiVO4 [START_REF] Wang | Facile synthesis of hollow and porous Ag+/Ag/BiVO4 composite fibers with enhanced visible-light photocatalytic performance[END_REF]. Xue et al. argued that Ag incorporation and formation of silver vanadate through a hydrothermal synthesis, affect the morphology and the heterojunction between the phases acts as a charge separator preventing the electron recombination, thus improving the photocatalytic properties of pure BiVO4 [START_REF] Xue | The effects of Ag doping on crystalline structure and photocatalytic properties of BiVO4[END_REF]. Although many authors have also reported similar results utilizing various methods [START_REF] Zhou | Synthesis of visible-light sensitive M-BiVO4 (M = Ag, Co, and Ni) for the photocatalytic degradation of organic pollutants[END_REF][START_REF] Li | Synthesis of Ag/BiVO 4 /rGO composite with enhanced photocatalytic degradation of triclosan[END_REF][START_REF] Zhang | Synthesis and characterization of Ag/BiVO 4 composite photocatalyst[END_REF][START_REF] Xu | One-pot solvothermal preparation and enhanced photocatalytic activity of metallic silver and graphene co-doped BiVO 4 ternary systems[END_REF], to the best of our knowledge, there is no research on silver doping of BiVO4 thin films using the sputtering technique.

This study aims to evaluate the effects of silver doping with various loadings on the photocatalytic activity enhancement of m-BiVO4 by producing Ag/BiVO4 thin films through a reactive magnetron sputtering technique on different substrates and experimenting with their photocatalytic potential in photodegradation of organic dyes at acidic and neutral pH. The structural, optical, and microscopic analysis give significant insights to the basic understanding of sputtered deposition of Ag-doped BiVO4 thin films behavior for catalytic applications. The results were also compared with those of the pristine m-BiVO4 thin films produced by reactive magnetron sputtering conducted by our team in previous research.

Experimental procedure

Thin film deposition

The deposition of BiVO4 thin films was done by reactive DC magnetron sputtering technique using Bi, V, and Ag metallic targets (Ø 50 mm × 3 mm, purity 99.9 at. %) in argon-oxygen gas mixtures. A 90 L cylinder Alcatel 604 SCM (CIT Alcatel, Annecy, France) was used as the sputtering reactor vacuumed below 10 -4 Pa via a turbo-molecular-pump. The chamber employs four circular planar with water-cooled magnetron sputtering sources while the rotating substrate holder is parallel to the cathodes at 60 mm. The Bi and V cathodes were powered with a pulsed DC advanced energy dual generator and the silver doping was performed employing an Ag target supplied by a DC generator. The coating chemical compositions were controlled via adjusting the discharge power for the targets. The gas flow rates were adjusted with Brooks flowmeters and the sputtering pressure was measured with an MKS Baratron gauge. The specifications for the reactor used in reactive magnetron sputtering are presented elsewhere [START_REF] Yazdi | Influence of the annealing conditions on the structure of BaCe1-xYxO3-α coatings elaborated by DC magnetron sputtering at room temperature[END_REF]. Glass, monocrystal silicon, and fused silica (76 ×26 × 1 mm 3 ) were mainly used as the substrates for measuring the film optical, structural, and photocatalytic properties. Before each sputtering process, the substrates were washed with alcohol and soap and then rinsed with water and placed on the substrate holder at a distance of 50 mm from the axis, which the substrate rotates. The deposition was performed at room temperature (no external heatings) and the sputtering pressure is controlled by the Ar flow rate. The parameters concerning the sputtering process are presented in Table 1.

Characterization

X-ray characterization was performed by Bragg-Brentano XRD configuration using a BRUKER D8 focus diffractometer (Bruker AXS, Karlsruhe, Germany) with a cobalt X-ray tube (Co Kα1+α2 radiations λα1 = 0.178897 nm and λα2 = 0.179278 nm) and equipped with a LynxEye linear detector for structural analysis of the samples. The diffraction patterns were collected under airflow at a scan rate (2θ) of 0.1 degrees per second. The thickness of the thin films was measured using a step method with an Altysurf profilometer (Altisurf 500), manufactured by Altimet, equipped with a tungsten micro force inductive probe allowing an accuracy of about 20 nm. The calibration of the experimental device was realized with a reference sample number 787569 accredited by the CETIM organization prior to each measurement. For the morphology assessment, the top surface microscopic observations and the brittle-fracture cross-sections of the coatings as well as the determination of the film thickness were performed by a JEOL JSM 7800F

FESEM. The chemical composition was analyzed by energy-dispersive X-ray spectroscopy (EDS, Bruker Nano, Berlin, Germany). The samples were carbon-coated prior to measurement to achieve sufficient electronic conductivity. The Bi and V atomic percentages are exclusively determined within the precision of the EDS measurements (the relative error is about 1 %) as EDS does not allow a precise estimation of the oxygen content in the films.

Photocatalytic performance measurement

The photocatalytic activity of the thin films was assessed through photodegradation of Rhodamine-B (RhB) solution (50 ml) with an initial concentration of 5 mg l -1 at acidic and neutral pH during 7 hours of illumination in the visible range by a xenon light source (150 W, Lot-Oriel) equipped with a UV-cutoff filter (λ > 400 nm) in a handmade setup. Hydrochloric was used to adjust the pH. The samples were fixed at a distance of 15 cm from the light source which emits constantly at 15 mW m -2 while placed in a water bath in order to keep the solution cool at room temperature (25 ˚C). The thin-film samples were placed in the solution 30 min prior to irradiation to reach the adsorption-desorption equilibrium. A 3 ml sample of the solution was collected every hour to determine its concentration by measuring the absorbance at 554 nm corresponding to the maximum wavelength using a spectrophotometer (Libra S12-UV-visible (200-999 nm) -BIOCHROM). The kinetics of the photodegradation behaves based on the Langmuir-Hinshelwood model and described as follows (Eq. ( 1)) [START_REF] Kumar | Langmuir-Hinshelwood kinetics -A theoretical study[END_REF].

ln ! ! ! = k′t (1)
Here, C0 is the initial concentration, t is the time of irradiation in visible light, C is the concentration of the solution at t, and kʹ is the rate constant. The rate constant (kʹ) is achieved via plotting ln (C0/C) as a function of t, whose slope corresponds to kʹ.

Results and discussion

Fig. 1 shows the correlation between the Ag atomic compositions of the thin films measured by the EDS, and the power discharge applied to the Ag target. The power discharges respecting Bi and V are kept in the range to achieve the stoichiometric ratio of 1. It is well known that the sputtering yield of Ag is very high, so with a minimum amount of power discharge (1w), the atomic percentage in the films exceeds 14% and continues to grow exponentially. To achieve lower amounts of Ag in the thin films, a various number of grids have been used to prevent the Ag atoms to reach the substrate. This might not be a desirable method since it may well have an unpredictable influence on the morphology. The exponential trend may be ascribed to the change in the spatial distribution of the plasma becoming more direct, which amounts to a higher diffusion of Ag particles to the substrate surface. was continued by the addition of Ag up to at. 40 % except for the sample with 24 at. % Ag content that seems to enjoy the Ag in its metallic form (≈ 12 %) which its characteristic peak is observable at 2θ = 45 ˚.As the Ag at. % content of the thin films increases, the percentage of BiVO4 decreases, indicating that vanadium forms a more thermodynamically favorable compound with Ag, leaving the bismuth to form Bi2O3 (≈ 1-14 %). In the sample with 40 at. % of Ag, the intensity of the peaks corresponding to m-BiVO4 was significantly decreased compared to those of the silver vanadates which indicates that the silver vanadate now consists of the majority of phases (≈ 57 % as opposed to 16 % for m-BiVO4).

Although some researchers reported the emergence of the tetragonal phase by introducing Ag [START_REF] Xue | The effects of Ag doping on crystalline structure and photocatalytic properties of BiVO4[END_REF], this phenomenon was not observed here. The sample with 28 at. % of Ag behaved closely to the sample with 21 at. % except for the shape of silver vanadate which can be characterized as interconnected islands. It is also apparent that in the sample with 24 at. % of Ag, the small particles of silver oxide and silver vanadate were distributed uniformly over the surface which is ideal for photocatalytic applications as opposed to the thin films with 21 and 28 at. % of Ag where the silver is accumulated forming a slab-like The pristine sample shows an absorption edge near 520 nm while this value for the samples with Ag content is lower. The bandgaps of the thin films were obtained by extrapolation of the linear part of the (αhν) n which is shown in Fig. 5 (b). Here n is equal to 2 assuming that BiVO4 is a direct bandgap semiconductor. The bandgap value for the pristine sample is estimated at 2.45 eV while for the Ag content samples this value is around 2.5 eV except for the sample with 24 at. % which is significantly lower (1.65 eV). The reason for the higher bandgap value of the Ag content sample might be the formation of silver vanadate (Eg = 2.7 eV) which promotes a higher value of bandgap.

This also agrees with the lower bandgap value for the sample with 24 Ag at. %, since the Ag2V4O7 (silver vanadate) phase was less observed in this sample. Although the amount of Ag can have a significant impact on optical properties, it is not the only factor. The morphology, porosity, and structure should also be factored in to have a precise assessment. The highest photocatalytic performances were performed by the samples with 24 and 40 at. % of Ag that managed to photodegrade the RhB solution by 41 % and 44 % after 7 h of visible illumination, respectively. The other Ag-doped samples functioned at the 20-26 % range, which was slightly higher than that of the pristine sample (18 %). This proves the photoactivity enhancement of silver-doped BiVO4 thin films. One can also conclude that over 24 % of Ag loading the enhancement stop improving. This lack of improvement by Ag loading is also observed from 8 to 21 at. % that can be ascribed to the poor distribution of silver over the surface by formation of oversize slab-like shape silver vanadate that results in low phase interface and limits the charge separation. This agrees with the previous microscopic observation in Fig. 3 and4, which showed the best phase distribution concerning the sample with 24 at. % of Ag which has the highest photocatalytic activity. deposited on monocrystal silicon exhibited higher activity due to a change in morphology and light absorption efficiency, while apparently, the silver doping overshadows the effect of substrate nature. This argument is also valid for the pH effect which was proved to be dependant, showing higher activity in acidic pH with no shift in the spectra over time, while in neutral pH due to the deethylation pathway, a blue shift was observed and a reduction in photocatalytic potential. Here we can also observe that the silver-doped sample did not undergo the deethylation pathway, thus no blue-shift is seen. Therefore it is concluded that the photodegradation pathway of RhB by silverdoped BiVO4 in both acidic and neutral pH is favored towards chromophore cleavage. So not only silver doping enhanced photoactivity through charge separation and electron mobility, but it also improved its photocatalytic activity in neutral pH independent of substrate nature, which is an important advantage for an economic design in the industry.

Conclusion

In this research, Ag-doped monoclinic BiVO4 thin films were successfully deposited on fused silica and monocrystal silicon substrates using reactive magnetron sputtering technique and a postannealing treatment for 2 h at 450 ˚C. The structural and microscopic analysis showed the formation of a silver vanadate phase as well as a metallic silver phase. The photodegradation of RhB solution as photocatalytic experiment proved the photoactivity enhancement by silver doping, and it was optimal when a sufficient distribution of silver is achieved. The sample with a 24 at. % of Ag managed to photodegrade the RhB solution by 41 % under 7 h of visible illumination. It was also established that the morphology and photoactivity enhancement of Ag-doped BiVO4 thin films are independent of the substrate nature, unlike the pristine BiVO4. In addition, it was proved that Ag-doped BiVO4 thin-film photocatalysts are optimal in RhB photodegradation at neutral pH, as opposed to the pristine BiVO4 that showed the highest photocatalytic activity potential in acidic pH.

Fig. 1 .Fig. 2 (

 12 Fig. 1. (a) The atomic composition of Ag in the thin-film samples as a function of power

Fig. 2 (

 2 Fig. 2 (a) the diffractograms of thin films with various Ag at. %. (b) the diffractograms in the

Fig. 3

 3 Fig. 3 depicts the top surface and brittle-fracture cross-sections of FESEM observations samples

Fig. 3 FESEM

 3 Fig. 3 FESEM observations of the top surface and brittle-fracture cross-sections of thin-film

Fig. 4 Fig. 5 (

 45 Fig. 4 Mapping observations of the thin-film samples with Ag content of (a) 8, (b) 21, (c) 24, (d)

Fig. 5 (

 5 Fig. 5 (a) the transmission spectra of the thin-film samples with different Ag content. (b)

Fig. 6 (

 6 Fig. 6 (a) exhibits the photodegradation of RhB solution at pH = 3 by BiVO4 thin films doped

Fig. 6 (

 6 Fig. 6 (a) photodegradation of RhB by silver-doped BiVO4 thin-film photocatalysts. (b) the rate

Fig. 7 (

 7 Fig. 7 (a) represents the photocatalytic degradation of RhB at different pH using thin-film

Fig. 7 (

 7 Fig. 7 (a) RhB photodegradation at different pH by the photocatalyst deposited on fused silica

Fig 8 (

 8 Fig 8 (a) SEM top-surface and cross-section micrograms of the thin-film with 24 at. % of Ag

Table 1 .

 1 The sputtering parameters for the deposition of thin films.

	Ar

flow rate (sccm) 200 Targets Bi V Ag O2 flow rate (sccm) 20 Intensity (A)

				0.07 → 0.09 0.64 → 0.66 0.004 → 0.014
	Total pressure (Pa)	4.5 Power (W)	9 → 11	247 → 255	1 → 4
	Runtime (h)	3.5 Frequency (kHz)	70	50	-
	Drawing distance (mm)	60	Toff (µs)	4	4	-

Acknowledgments

The authors would like to acknowledge the supports of this study by the Iran National Science Foundation (project No: 98001285) and Pays de Montbéliard Agglomération.

Conflict of interest

The authors declare that they have no conflict of interest.