Bernard G Barthès
email: bernard.barthes@ird.fr

Jean-Luc Chotte

Infrared spectroscopy approaches support soil organic carbon estimations to evaluate land degradation

Keywords:

Soil organic carbon (SOC) is an acknowledged indicator for land degradation, but conventional determination of SOC remains tedious, especially regarding SOC stock (in kgC m -2 for a given depth layer), which is the product of SOC concentration (gC kg -1 ) by volumetric mass (kg dm -3 ). Diffuse reflectance infrared spectroscopy (DRIS) is a time-and cost-effective approach, which uses calibrations for making predictions. The aim of this paper is to propose an overview of DRIS uses for estimating SOC, thus land degradation. Indeed, many papers have demonstrated the precision of DRIS for quantifying SOC concentration, at different scales. Current development of large soil calibration databases and improvements in spectral data analysis pave the way for ever-wider use of DRIS, which should help solving the soil data crisis, regarding SOC especially. The increasing availability of portable spectrometers allows SOC quantification in the field, which seems particularly promising; but large calibration databases made of soil spectra acquired in the field are difficult to build, while large collections of analyzed soil samples (air dried, 2-mm sieved) already exist. Some recent studies indicate that DRIS can also be used for predicting SOC stock, even from sieved samples, which represents an efficient option because determining the volumetric mass is particularly tedious and an obstacle for exactly specifying the role of soils in the global carbon cycle. In short, DRIS has strong potential for supporting better evaluation of soil and land degradation, and the availability of spectrometers at increasingly affordable prices reinforces this potential.

Introduction

Land degradation represents huge challenge. It consists in the reduction of biological or economic productivity and complexity of agroecosystems as a result from combined pressures, including land use and management practices (UNCDD, 1994). This phenomenon is considered pervasive and systemic, with negative impacts on biodiversity and ecosystem services (IPBES, 2018) and on climate change (IPCC, 2019). The scientific community has provided evidences on the drivers of land degradation [START_REF] Mbow | What four decades of Earth Observation tell us about land degradation in the Sahel?[END_REF][START_REF] Tully | The state of soil degradation in Sub-Saharan Africa: Baselines, trajectories, and solutions[END_REF][START_REF] Sklenicka | Classification of farmland ownership fragmentation as a cause of land degradation: A review on typology, consequences, and remedies[END_REF][START_REF] Safriel | Land Degradation Neutrality (LDN) in drylands and beyondwhere has it come from and where does it go[END_REF] and on means to combat it [START_REF] De Vente | How does the context and design of participatory decision making processes affect their outcomes? Evidence from sustainable land management in global drylands[END_REF][START_REF] Kust | Land Degradation Neutrality: Concept development, practical applications and assessment[END_REF][START_REF] Sanz | Sustainable Land Management contributions to successful land-based climate change adaptation and mitigation[END_REF]Felix et al., 2018;Giger et al., 2018). In September 2018, the General Assembly of the United Nations adopted the Sustainable Development Goals, which, in particular, aim at restoring degraded lands and soils and at achieving a land degradation neutral world by 2030 (Target 15.3;United Nations, 2018). This represents a clear political recognition of the key role of soils and lands to achieve sustainable development. Land Degradation Neutrality (LDN) has been defined as "a state whereby the amount and quality of land resources necessary to support ecosystem functions and services and enhance food security remains stable or increases within specified temporal and spatial scales and ecosystems" (UNCCD, 2016). A scientific conceptual framework has been developed to implement LDN and provide guidance to monitor progress to LDN [START_REF] Cowie | Land in balance: The scientific conceptual framework for Land Degradation Neutrality[END_REF]. For these purposes, degradation is assessed through three indicators as proxies for the capacity of land to deliver ecosystem services: land cover, land productivity, and soil organic carbon (SOC). Indeed, SOC is the main constituent of soil organic matter, which has a long-acknowledged and key role in soil fertility through nutrient release, structure stabilization, improvement in water-holding capacity and soil biodiversity, biodegradation of contaminants, etc. [START_REF] Lal | Influence of soil erosion on carbon dynamics in the World[END_REF]. Moreover, SOC is the largest terrestrial carbon pool, and is thus an important component in the global carbon cycle [START_REF] Lal | Soil and climate[END_REF]. Organic carbon is present in the soil in a wide range of chemical forms: carbohydrates, proteins and protein-derived compounds, lipids, phenols and cyclic nitrogenous compounds, and still unknown compounds [START_REF] Paul | The nature and dynamics of soil organic matter: Plant inputs, microbial transformations, and organic matter stabilization[END_REF]. Analyzing the exact molecular composition of organic matter in soils is hardly feasible due to its complex nature. So SOC has often been separated into fractions having homogenous characteristics [START_REF] Chenu | Methods for studying soil organic matter: Nature, dynamics, spatial accessibility and interactions with minerals[END_REF]: firstly alkali/acid solubility pools (fulvic acids, humic acids and humin); then more functional pools, for instance kinetic pools, having specific turnover rates (labile, stable, resistant), or chemical functional groups (alkyl, O-alkyl, aromatic, carbonyl, etc., determined by nuclear magnetic resonance). Studying such SOC fractions allows deep understanding of SOC composition, dynamics and stability as affected by climate, mineralogy or land use and management. However, studying such SOC fractions is not necessarily the most appropriate level for assessing land degradation, especially when looking at practical indicators. Actually, total SOC is considered by both scientists and farmers a primary indicator of soil quality and health, which itself is considered a primary indicator of sustainable land management [START_REF] Doran | Soil health and global sustainability: translating science into practice[END_REF]. When dealing with land degradation practically, it therefore seems relevant to focus on total SOC (simply denoted SOC hereinafter).

Conventional quantification of SOC requires analyzing SOC concentration, which is generally carried out by Dumas combustion or sulfochromic oxidation, using reagents and producing wastes that are toxic [START_REF] Pansu | Handbook of soil analysis -Mineralogical, organic and inorganic methods[END_REF]. Moreover, SOC concentration (in gC kg -1 ) is not an additive variable, thus quantifying SOC at field, region or country scale involves determining the apparent volumetric mass (or bulk density, D b , in kg dm -3 ), in order to calculate SOC stock (in gC dm -3 , or in kgC m -2 for a given soil layer), which is additive [START_REF] Poeplau | Soil organic carbon stocks are systematically overestimated by misuse of the parameters bulk density and rock fragment content[END_REF]. The determination of D b is generally achieved by drying at 105°C then weighing a known volume of intact soil (with undisturbed structure), which is most often collected using a bevelled cylinder thus requires digging a pit or using a mechanized coring device. Quantifying SOC is thus tedious using conventional approaches, especially for SOC stock.

In recent decades, increasing attention has been paid to diffuse reflectance infrared spectroscopy (DRIS) for characterizing soil properties, SOC concentration especially [START_REF] Dalal | Simultaneous determination of moisture, organic carbon, and total nitrogen by near infrared reflectance spectrophotometry[END_REF][START_REF] Sudduth | Evaluation of reflectance methods for soil organic matter sensing[END_REF][START_REF] Mccarty | Midinfrared and near-infrared diffuse reflectance spectroscopy for soil carbon measurement[END_REF][START_REF] Barthès | Determination of total carbon and nitrogen content in a range of tropical soils using near infrared spectroscopy: influence of replication and sample grinding and drying[END_REF]Bellon-Maurel & McBratney, 2011). Indeed, DRIS is a time-and cost-effective, non-destructive and reproducible approach, with no reagent required and no waste generated; moreover a single spectrum may be used to assess various properties. In its current uses DRIS is based on calibration, using multivariate regression and developed on calibration samples characterized by both spectral data and conventional reference data; then calibration can be applied to predict the property considered on new samples only from their spectrum. Indeed, the property is not measured but predicted, with known uncertainty, quantified using standard error of prediction. As stated by [START_REF] Reeves | Near-versus mid-infrared diffuse reflectance spectroscopy for soil analysis emphasizing carbon and laboratory versus on-site analysis: where are we and what needs to be done?[END_REF], conventional analytical approaches produce small amounts of highly accurate, expensive data, while DRIS produces large amounts of low-cost, fair quality data, with specified uncertainty. In this way, [START_REF] Mcbratney | Spectral soil analysis and inference systems: A powerful combination for solving the soil data crisis[END_REF] considered the combination of DRIS and multivariate statistics an opportunity for solving the soil data crisis. This paper proposes an overview to demonstrate the relevance of DRIS for high-speed and low-cost quantification of SOC concentration and stock. So, given the key role of SOC in soil fertility and in the global carbon cycle, we aim at demonstrating that DRIS represents great opportunity for evaluating the land capacity to deliver ecosystem services.

DRIS quantification of SOC concentration

Physical background and historical outlines

Infrared radiation causes molecular bonds to vibrate, and the vibrations absorb energy at wavelengths that depend on bond strength, on the atoms involved, and on chemical environment [START_REF] Siesler | Basic principles of near-infrared spectroscopy[END_REF]. So when compared with the incident radiation, the radiation reflected by a solid sample is modified in the spectral regions that correspond to energy absorption by the sample. Fundamental vibrations occur in the mid infrared region (4000-400 cm -1 , i.e. 2500-25,000 nm), while their overtones and combinations mostly vibrate in the near infrared region (800-2500 nm), where they overlap (Bellon-Maurel & McBratney, 2011).

Reflected spectra thus display much clearer peaks in the mid than in the near infrared range [START_REF] Stenberg | Visible and near infrared spectroscopy in soil science[END_REF] cf. Figure 1), which explains why the former have long been used for molecule identification, based on visual observation. For instance, the regions around 2750-2670 and 1730-1710 cm -1 have been assigned to saturated aliphatic carboxylic acids, and the region around 1650 cm -1 to amides [START_REF] Socrates | Infrared and Raman characteristics group frequencies: Tables and charts[END_REF][START_REF] Barthès | Studying the physical protection of soil carbon with quantitative infrared spectroscopy[END_REF]. Such peak recognition is hardly possible with near infrared spectra (except for water, cf. Figure 1), though spectral regions could also be assigned to chemical compounds [START_REF] Workman | Practical guide to interpretative near-infrared spectroscopy[END_REF][START_REF] Barthès | Studying the physical protection of soil carbon with quantitative infrared spectroscopy[END_REF]. In general statistical tools are required for analyzing near infrared spectra, hence the more recent applications of this spectral range for analytical purposes. However, absorption is much stronger in the mid than in the near infrared range (cf. Figure 1), according to the vibrations they are associated with (i.e. fundamentals vs. overtones, respectively; Bellon-Maurel & McBratney, 2011). As a consequence, the reflected radiation is stronger in the near infrared, thus requires less sensitive and less costly sensors. This explains the rapid development of quantitative applications of near infrared spectroscopy once computer and data analysis sciences developed, followed, after a while, by their counterparts in the mid infrared range.

Numerous authors have reported the usefulness of DRIS for characterizing SOC concentration based on spectra acquired in laboratory conditions (most often on air dried, 2-mm sieved samples). [START_REF] Bowers | Reflection of radiant energy from soils[END_REF] were the first to demonstrate the qualitative effect of SOC on visible and near infrared reflectance (VNIR) spectra by comparing the same soil sample with and without SOC. Quantification of SOC concentration from NIR spectra was firstly achieved by multiple linear regression, using a few wavelengths, then by principal component regression (PCR) and partial least squares regression (PLSR), which are more sophisticated procedures, based on latent variables (i.e. small numbers of orthogonal variables inferred from large numbers of redundant observed variables, such as infrared spectra, and used for replacing them in regression procedures; [START_REF] Dalal | Simultaneous determination of moisture, organic carbon, and total nitrogen by near infrared reflectance spectrophotometry[END_REF][START_REF] Sudduth | Evaluation of reflectance methods for soil organic matter sensing[END_REF].

Similar PLSR approach was then used for inferring SOC concentration from mid infrared reflectance (MIR) spectra [START_REF] Janik | Characterization and analysis of soils using midinfrared partial least-squares. II. Correlations with some laboratory data[END_REF] Since then, numerous papers have used PLSR to infer SOC concentration from VNIR, NIR or MIR spectra; while some authors used nonlinear regression procedures such as local regressions (predictions made only using spectral neighbours) or data mining approaches like neural networks, boosted regression trees, random forests, etc. [START_REF] Stenberg | Visible and near infrared spectroscopy in soil science[END_REF][START_REF] Ramirez-Lopez | The spectrum-based learner: A new local approach for modeling soil vis-NIR spectra of complex datasets[END_REF][START_REF] Vågen | Mapping of soil properties and land degradation risk in Africa using MODIS reflectance[END_REF]; and others tested spiking, which consists of enriching the calibration database with samples from the target set (Guerrero et al., 2010(Guerrero et al., , 2014)).

Assessing the fit between predictions and observations has often been achieved using R², which is widely known and, to some extent, allows comparison between different studies. However, R² represents proportionality rather than similarity, thus may sometimes result in inappropriate judgement (though this has rarely been the case in the domain considered). The root mean square error (RMSE, often called standard error of prediction) is more specific but not very informative as long as the variable distribution has not been presented; moreover it hardly allows convenient comparisons between studies. The RPD (ratio of performance to deviation) is the ratio of observed standard deviation to RMSE, which integrates information on the variable distribution thus can be used for comparing the predictions of different variables, or different studies. [START_REF] Bellon-Maurel | Critical review of chemometric indicators commonly used for assessing the quality of the prediction of soil attributes by NIR spectroscopy[END_REF] however considered RPD inappropriate for variables that do not have normal distribution, and instead, recommended RPIQ (ratio of performance to interquartile distance, which is the ratio of interquartile distance to RMSE). Nevertheless, RPIQ has not been widely used to date, so RPD has remained useful for comparison between studies, and we have used it hereinafter, along with R². According to [START_REF] Chang | Near-infrared reflectance spectroscopy-principal components regression analyses of soil properties[END_REF], predictions of soil properties were considered accurate when RPD ≥ 2, and acceptable when 1.6 ≤ RPD < 2.0.

Large calibration databases

In their review on SOC quantification by DRIS, Bellon-Maurel & McBratney (2011) insisted on the need for as large and exhaustive calibration databases as possible. Some work had already be done in the VNIR range by [START_REF] Shepherd | Development of reflectance spectral libraries for characterization of soil properties[END_REF] for eastern and southern Africa, by [START_REF] Brown | Global soil characterization with VNIR diffuse reflectance spectroscopy[END_REF] for the USA, and other continents to a lesser extent, and by Viscarra Rossel & Webster (2012) for Australia (Table 1). These studies gathered samples from different experiments, trials and surveys. More systematic spectral databases have then been presented, which aimed at covering areas relevant from geographical or administrative viewpoints. Noticeable work has been carried out in France using the national soil quality monitoring network and its associated bank of soil samples collected regularly over the French metropolitan territory [START_REF] Arrouays | A new initiative in France: a multi-institutional soil quality monitoring network[END_REF], either using the VNIR, NIR or MIR range, and topsoils only or both top-and subsoils (Gogé et al., 2012(Gogé et al., , 2014;;Grinand et al., 2012;[START_REF] Clairotte | National calibration of soil organic carbon concentration using diffuse infrared reflectance spectroscopy[END_REF]; Table 1). Several authors have also worked with the LUCAS (Land use/cover area frame statistical survey; [START_REF] Tóth | The LUCAS topsoil database and derived information on the regional variability of cropland topsoil properties in the European Union[END_REF] VNIR database, which represents the topsoils from 23 European Union countries, more or less densely sampled.

They distinguished cropland, grassland, woodland, other mineral soils and organic soils, possibly used covariables, and either performed data mining approaches [START_REF] Stevens | Prediction of soil organic carbon at the European scale by visible and near infrared reflectance spectroscopy[END_REF] or local PLSR [START_REF] Nocita | Prediction of soil organic carbon content by diffuse reflectance spectroscopy using a local partial least square regression approach[END_REF]. Interestingly, local PLSR yielded better predictions than data mining approaches without covariable, but worse results when using sand as covariable (Table 1); moreover, using geographical coordinates as covariables did not improve the results [START_REF] Nocita | Prediction of soil organic carbon content by diffuse reflectance spectroscopy using a local partial least square regression approach[END_REF]. Other large VNIR calibration databases have been built in China [START_REF] Shi | Prediction of soil organic matter using a spatially constrained local partial least squares regression and the Chinese vis-NIR spectral library[END_REF], who improved predictions when using spectral but also geographical neighbours for calibration) and Australia [START_REF] Lobsey | RS-LOCAL datamines information from spectral libraries to improve local calibrations[END_REF], who performed local calibration with independent validation in Australia but also New Zealand; Table 1). An attempt has even been made to build a global VNIR library, using samples from 92 countries (Viscarra Rossel et al., 2016a). Though the diversity of conventional methods used for analyzing SOC concentration (dry combustion, wet oxidation, loss on ignition, etc.), predictions using a machine learning algorithm with spectral pre-classification were accurate.

Table 1 shows that most studies achieved accurate predictions of SOC concentration using large soil spectral libraries, with R² val and RPD val around 0.8 and > 2 in general, and up to 0.9 and > 3 sometimes, respectively, even using common regression approach (PLSR). When procedures were optimized, in particular the representativeness of calibration samples (e.g. using spectral neighbours) and the spectral range (e.g. MIR for soils from temperate regions, cf. 2.5), standard error of prediction close to standard error of laboratory reference analysis could be achieved (e.g. 2.0 vs. 1.0-1.5 g kg -1 according to [START_REF] Clairotte | National calibration of soil organic carbon concentration using diffuse infrared reflectance spectroscopy[END_REF]Stevens et al., 2013, respectively). In such conditions, DRIS could helpfully be used in SOC estimation and monitoring for LDN planning; but to our knowledge, this has not been the case yet.

Types of soil samples used for spectrum acquisition

Spectrum acquisition in laboratory conditions is generally made on air-dried, 2-mm sieved soil sample, which is the most general soil preparation for laboratory analyses and for longterm sample conservation [START_REF] Pansu | Soil analysis -Sampling, instrumentation, quality control[END_REF]. However, the sample may be further prepared for specific analyses or purposes; for instance SOC analysis by dry combustion is made on finely ground sample (e.g. < 0.2 mm; [START_REF] Pansu | Handbook of soil analysis -Mineralogical, organic and inorganic methods[END_REF]. Studies that compared NIRS predictions made on coarsely vs. finely prepared samples indicated in general that fine grinding (from < 0.2 to < 0.5 mm) resulted in better prediction of SOC concentration than coarse preparation (from < 2 to < 4 mm) in clayey soils but not in coarse-textured soils [START_REF] Dalal | Simultaneous determination of moisture, organic carbon, and total nitrogen by near infrared reflectance spectrophotometry[END_REF]Fystro, 2002;[START_REF] Reeves | The potential of diffuse reflectance spectroscopy for the determination of carbon inventories in soils[END_REF]Russel, 2003;[START_REF] Barthès | Determination of total carbon and nitrogen content in a range of tropical soils using near infrared spectroscopy: influence of replication and sample grinding and drying[END_REF][START_REF] Brunet | Determination of carbon and nitrogen contents in Alfisols, Oxisols and Ultisols from Africa and Brazil using NIRS analysis: effects of sample grinding and set heterogeneity[END_REF]. These contradictory effects have been explained by the size and arrangement of particles, which affect light transmission [START_REF] Chang | Near-infrared reflectance spectroscopy-principal components regression analyses of soil properties[END_REF][START_REF] Barthès | Determination of total carbon and nitrogen content in a range of tropical soils using near infrared spectroscopy: influence of replication and sample grinding and drying[END_REF]. More accurate MIRS prediction of SOC concentration using spectra acquired on 0.2-than on 2-mm samples is a less controversial result, though it has rarely been studied [START_REF] Barthès | Studying the physical protection of soil carbon with quantitative infrared spectroscopy[END_REF].

Actually, to our knowledge, all studies carried out to date in laboratory conditions (except the above-mentioned) have used finely ground samples for MIR spectroscopy (< 0.2 mm and sometimes finer), which indicates there is implicit agreement that MIR requires finely ground samples.

Moreover, several authors reported more accurate VNIRS prediction of SOC concentration on air-dried cores (a few dm in size) or clods (a few cm in size) than on air-dried, 2-mm sieved samples, possibly because higher bulk density in clods or cores would result in higher reflectance [START_REF] Morgan | Simulated in situ characterization of soil organic and inorganic carbon with visible near-infrared diffuse reflectance spectroscopy[END_REF]Fontán et al., 2010). Gras et al. (2014) even achieved more accurate VNIRS prediction of SOC concentration on field-moist than on air-dried clods, probably due to better light transmission. Indeed, increasing moisture reduces the refraction difference between soil particles and pore spaces, thus increases forward light scattering, hence the probability of photon absorption by soil particles [START_REF] Twomey | Reflectance and albedo differences between wet and dry surfaces[END_REF]. Actually, several authors reported similar or better VNIRS performance in field than in laboratory conditions (cf. Table 2), which is counterintuitive a priori because, among other things, field acquisition involves variable soil moisture and the presence of coarse particles (which are removed before reference analyses used for calibration). But field conditions might be beneficial to some respects due to higher sample density, and higher cohesion in moist conditions [START_REF] Stevens | Laboratory, field and airborne spectroscopy for monitoring organic carbon content in agricultural soils[END_REF]Gras et al., 2014). However, [START_REF] Morgan | Simulated in situ characterization of soil organic and inorganic carbon with visible near-infrared diffuse reflectance spectroscopy[END_REF] achieved less accurate VNIRS prediction of SOC concentration on field-moist cores than on air-dried, 2-mm sieved samples, probably because field-moist cores had contrasting moisture contents (sampling had been performed in rather hot conditions with possible storms or irrigation, and at different depths). [START_REF] Veum | Predicting profile soil properties with reflectance spectra via Bayesian covariate-assisted external parameter orthogonalization[END_REF], [START_REF] Allory | Quantification of soil organic carbon stock in urban soils using visible and near infrared reflectance spectroscopy (VNIRS) in situ or in laboratory conditions[END_REF]Hutengs et al. (2019) similarly reported less accurate SOC prediction in field than in laboratory conditions firstly due to variable in-situ soil moisture content: moisture conditions might vary among depth layers (when several were sampled) and/or during long field campaigns (Table 2). In the study reported by [START_REF] Morgan | Simulated in situ characterization of soil organic and inorganic carbon with visible near-infrared diffuse reflectance spectroscopy[END_REF], prediction accuracy ranked as follows: air-dried cores > air-dried 2-mm sieved > field-moist cores. While for Gras et al. ( 2014), also on a range of soils, the rank was: field-moist cores > field-moist clods > air-dried clods > air-dried 2-mm sieved. In that study, field-moist samples had rather homogeneous soil moisture because all had been collected in wet conditions in winter. In laboratory conditions, Stenberg (2010) also observed that VNIRS predictions of SOC concentration were more accurate on standardized rewetted than on airdried samples, all sieved at 2 mm. These results suggest the following trends:

-prediction accuracy increases with sample particle size, from finely ground samples to cores, due to better light transmission; except on ground clayey soils, for which prediction is better on 0.2-than on 2-mm samples, probably due to higher homogeneity and lower diffusivity of finely ground clayey samples; -prediction is better on moist than on dried samples when moisture is homogeneous among samples, due to better light transmission, but this is the opposite when moisture content varies among samples, because varying moisture brings noise to the spectra; thus field spectroscopy would be recommended outside dry periods and rainfall (or irrigation) events; -prediction is better on 2-mm sieved than on coarsely prepared soil samples (clods, etc.) when the soil is rich in coarse particles (> 2 mm), and the difference increases with their proportion.

These trends have to be confirmed with other studies that would compare different sample preparations, moistures and coarse particle contents, on large and diverse sample sets as far as possible.

Spectrum acquisition in laboratory vs. field conditions

As seen above, spectrum acquisition on field moist samples, possibly cores or clods (coarsely crushed cores) may yield accurate predictions. Getting soil spectra directly onsite, in the field, has aroused much interest because this eliminates the need for sample packaging, transport, drying, crushing and sieving, except for calibration purposes. This allows characterizing many samples and improves even more time-and cost-effectiveness [START_REF] Viscarra Rossel | Proximal soil sensing: an effective approach for soil measurements in space and time[END_REF].

However, prediction of soil attributes using spectra acquired in the field most generally requires, to date, calibration with spectrum acquisition in the field, which is more tedious than spectrum acquisition in the lab. This explains why much less applications to soils have been carried out in the field than in the laboratory. Indeed, collections of conventionally analyzed soil samples are available air-dried and sieved (i.e. ready to be scanned), but no such collection of analyzed samples is available with samples as they were in the field. So calibration of field spectra requires specific field campaign and conventional analyses, which is particularly tedious and costly if the calibration database has to be representative of a country.

Nevertheless some work has been done. [START_REF] Sudduth | Soil organic-matter, CEC, and moisture sensing with a portable NIR spectrophotometer[END_REF] were the first to report NIR spectrum acquisition in the field. Then a range of studies reported good predictions of SOC concentration at either local, regional or multi-regional scale, using VNIR spectra acquired in boreholes, on fresh cores, on crushed fresh samples, from the soil surface, from a measurement height of 1 m, or on-line with a spectrometer probe fitted to a subsoiler [START_REF] Mouazen | Effect of wavelength range on the measurement of some selected soil properties using visible-near infrared spectroscopy[END_REF][START_REF] Stevens | Laboratory, field and airborne spectroscopy for monitoring organic carbon content in agricultural soils[END_REF][START_REF] Kusumo | The use of diffuse reflectance spectroscopy for in situ carbon and nitrogen analysis of pastoral soils[END_REF][START_REF] Kusumo | Measuring carbon dynamics in field soils using soil spectral reflectance: prediction of maize root density, soil organic carbon and nitrogen content[END_REF][START_REF] Nocita | Predictions of soil surface and topsoil organic carbon content through the use of laboratory and field spectroscopy in the Albany Thicket Biome of Eastern Cape Province of South Africa[END_REF]Gras et al., 2014;[START_REF] Cambou | Prediction of soil organic carbon stock using visible and near infrared reflectance spectroscopy (VNIRS) in the field[END_REF][START_REF] Nawar | Optimal sample selection for measurement of soil organic carbon using online vis-NIR spectroscopy[END_REF][START_REF] Lal | Soil and climate[END_REF][START_REF] Allory | Quantification of soil organic carbon stock in urban soils using visible and near infrared reflectance spectroscopy (VNIRS) in situ or in laboratory conditions[END_REF]Hutengs et al., 2019;[START_REF] Pei | Improving in-situ estimation of soil profile properties using a multi-sensor probe[END_REF]. Prediction results were often good, but not as good in general as in laboratory conditions (R² = 0.71 to 0.87 and RPD = 1.9 to 2.8 in cross-or external validation; Table 2). However, less accurate in situ VNIR predictions of SOC concentration have sometimes been reported [START_REF] Morgan | Simulated in situ characterization of soil organic and inorganic carbon with visible near-infrared diffuse reflectance spectroscopy[END_REF][START_REF] Veum | Predicting profile soil properties with reflectance spectra via Bayesian covariate-assisted external parameter orthogonalization[END_REF][START_REF] Nawar | On-line vis-NIR spectroscopy prediction of soil organic carbon using machine learning[END_REF]; R² val = 0.64-0.65 and RPD val = 1.5-1.7), and even poor ones (Hutengs et al., 2019; R² val = 0.27 and RPD val = 1.2). This might be due to variable moisture content among samples (cf. 2.3) or insufficient representativeness of calibration samples (e.g. selected at random).

Much less field work has been carried out using MIRS, because transportable MIRS is recent technology. In an exploratory study, Izzauralde et al. (2013) achieved good SOC predictions from MIR spectra of samples collected at different depths in a field, using calibration samples from that field, from another field and from archived samples (R² val = 0.77 and RPD val = 2.1). [START_REF] Ji | Assessment of soil properties in situ using a prototype portable MIR spectrometer in two agricultural fields[END_REF] studied two fields using MIR spectra acquired at 5-cm depth, and achieved good SOC predictions for one field, where the soil was very organic, but poorer ones for the other field, less organic (R² = 0.86 and 0.60 and RPD = 2.6 and 1.6 in cross-validation, respectively). Hutengs et al. ( 2019) studied 90 fields (one sample per field) in a small region and achieved acceptable SOC predictions (R² val = 0.63 and RPD val = 1.7). According to the authors, variable soil moisture content during field campaign (in spring) affected prediction accuracy negatively; but the fact that MIR spectra had been acquired from the soil surface while SOC was analyzed at 0-5 cm depth might also be considered (Table 2).

Developing tools for applying calibrations built in laboratory conditions (on air-dried, 2-mm sieved samples) to spectra acquired in the field (moist, structured, with coarse particles, etc.) represents a great challenge and would have important consequences. Indeed, this would allow applying easy-to-build calibration databases made from archived soil collections to easy-to-get field spectra. Some authors have begun trying to remove the effects of moisture and structure from spectra, by identifying the spectral subspaces they affect then projecting the spectra orthogonally. [START_REF] Minasny | Removing the effect of soil moisture from NIR diffuse reflectance spectra for the prediction of soil organic carbon[END_REF] studied 2-mm sieved samples at different moisture contents and reported that VNIRS prediction accuracy of SOC concentration, instead of being deteriorated for moist samples (R² val decreased from 0.83 for air-dried samples to 0.56 for wet samples, and RPD val decreased by 70%), was similar whatever sample moisture content after spectrum "orthogonalization". Ge et al. ( 2014) studied intact cores and 2-mm sieved samples either air-dried or wet, and observed that VNIRS prediction of SOC concentration using wet cores was improved after orthogonalization (R² val increased from 0.49 to 0.53 and RPD val increased by 30%). This was mainly due to the removing of moisture effect, while the effect of structure was more difficult to address. Such approaches require scanning samples in different moisture and structural conditions, which is tedious, and has been limited to rather small sample sets to date.

Spectral range: (V)NIRS vs. MIRS

Many papers have reported better prediction of SOC concentration using MIR than (V)NIR spectra [START_REF] Reeves | Mid-infrared diffuse reflectance spectroscopy for the quantitative analysis of agricultural soils[END_REF][START_REF] Reeves | The potential of diffuse reflectance spectroscopy for the determination of carbon inventories in soils[END_REF][START_REF] Mccarty | Midinfrared and near-infrared diffuse reflectance spectroscopy for soil carbon measurement[END_REF]McCarty & Reeves, 2006;[START_REF] Viscarra Rossel | Visible, near-infrared, mid-infrared or combined diffuse reflectance spectroscopy for simultaneous assessment of various soil properties[END_REF]Igne et al., 2010;[START_REF] Dong | Determination of soil parameters in apple-growing regions by near-and midinfrared spectroscopy[END_REF][START_REF] Xie | Predicting soil organic carbon and total nitrogen using mid-and near-infrared spectra for Brookston clay loam soil in Southwestern Ontario[END_REF]; but it is worth noting that they concerned temperate regions (except [START_REF] Dong | Determination of soil parameters in apple-growing regions by near-and midinfrared spectroscopy[END_REF], and rather homogeneous soil sample sets in general. The trend was less clear in other studies [START_REF] Madari | Mid-and near-infrared spectroscopic determination of carbon in a diverse set of soils from the Brazilian National Soil Collection[END_REF][START_REF] Yang | Determination of organic carbon and nitrogen in particulate organic matter and particle size fractions of Brookston clay loam soil using infrared spectroscopy[END_REF], while some even reported better NIRS than MIRS predictions [START_REF] Madari | Mid-and near-infrared spectroscopic assessment of soil compositional parameters and structural indices in two Ferralsols[END_REF][START_REF] Ludwig | Use of mid-infrared spectroscopy in the diffuse-reflectance mode for the prediction of the composition of organic matter in soil and litter[END_REF][START_REF] Rabenarivo | Comparing near and mid-infrared reflectance spectroscopy for determining properties of Malagasy soils, using global or LOCAL calibration[END_REF][START_REF] Barthès | Studying the physical protection of soil carbon with quantitative infrared spectroscopy[END_REF]and also Shao & He, 2011, for N concentration), regarding tropical and subtropical regions (except [START_REF] Ludwig | Use of mid-infrared spectroscopy in the diffuse-reflectance mode for the prediction of the composition of organic matter in soil and litter[END_REF] and more diverse sample sets.

The supposedly superior performance of MIRS has been attributed to the richer information it provides (cf. Figure 1): more defined peaks, assigned to fundamental vibrations; while NIR is the range of o+verlapping overtones and combinations [START_REF] Reeves | Near-versus mid-infrared diffuse reflectance spectroscopy for soil analysis emphasizing carbon and laboratory versus on-site analysis: where are we and what needs to be done?[END_REF]Bellon-Maurel & McBratney, 2011). However, in Al and Fe oxide-rich soils (i.e. in particular tropical and subtropical regions), MIR information relating to SOC could be partly masked due to the overlap of regions relating to mineral and organic components (e.g. metal oxides often absorb at 1020-970 and 1100-825 cm -1 while carbohydrates and polysaccharides absorb at 1080-1030 and 1170-950cm -1 , respectively; [START_REF] Rabenarivo | Comparing near and mid-infrared reflectance spectroscopy for determining properties of Malagasy soils, using global or LOCAL calibration[END_REF]. And this would explain better NIRS than MIRS prediction of SOC in tropical and subtropical regions. But this result has to be consolidated with other studies, on large and diverse sample sets as far as possible.

Importantly, [START_REF] Barthès | Studying the physical protection of soil carbon with quantitative infrared spectroscopy[END_REF] reported noticeably poorer MIRS predictions using spectra acquired on 2-than on 0.2-mm samples; thus MIRS requires fine grinding, which is somewhat tedious and contradicts the time-and cost-effectiveness of the approach. In contrast, these authors found little difference in SOC prediction accuracy when NIR spectra were acquired on 2-vs. 0.2-mm samples. This is confirmed by the fact that all cited MIRS applications used finely ground soil (< 0.2 mm or finer), while most cited NIRS applications used more coarsely-prepared soil (< 2 mm in general).

DRIS quantification of SOC stock

Sample SOC stock (gC dm -3 ) is calculated as the product of SOC concentration (gC kg -1 ) and apparent volumetric mass (or bulk density, D b , kg dm -3 ), preferably weighted by the proportion of fine earth (< 2 mm; [START_REF] Poeplau | Soil organic carbon stocks are systematically overestimated by misuse of the parameters bulk density and rock fragment content[END_REF]; and then reported for a given depth layer (kgC m -2 or MgC ha -1 for that depth layer). Some studies have attempted to estimate SOC stock from measurement of D b and DRIS prediction of SOC concentration: [START_REF] Cardinael | Impact of alley cropping agroforestry on stocks, forms and spatial distribution of soil organic carbona case study in a Mediterranean context[END_REF] used VNIR spectra acquired on fieldmoist intact cores, and [START_REF] Baldock | Stocks, composition and vulnerability to loss of soil organic carbon predicted using mid-infrared spectroscopy[END_REF] used MIR spectra acquired on air-dried, 2-mm sieved sample; but these studies presented predictions of SOC concentration, not SOC stock.

Moreover, conventional determination of D b is tedious, as it involves collecting samples of known apparent volume, which requires opening pits or using hydraulic coring machine. Some studies used other approaches to determine D b . [START_REF] Priori | Field-scale mapping of soil carbon stock with limited sampling by coupling gammaray and Vis-NIR spectroscopy[END_REF] studied samples from Sicilian fields, and besides VNIRS prediction of SOC concentration on air-dried, 2-mm sieved samples, they predicted D b using a pedotransfer function that involved measured SOC concentration and texture. These authors achieved R² val = 0.77 and RPD val = 2.1 for SOC stock prediction on fine earth (< 2 mm), which was then corrected for semi-quantitativelyestimated volumetric gravel content. On field-moist intact cores, [START_REF] Lobsey | Sensing of soil bulk density for more accurate carbon accounting[END_REF][START_REF] Viscarra Rossel | Baseline estimates of soil organic carbon by proximal sensing: Comparing design-based, modelassisted and model-based inference[END_REF][START_REF] Safriel | Land Degradation Neutrality (LDN) in drylands and beyondwhere has it come from and where does it go[END_REF] used gamma-ray attenuation for predicting D b , which was corrected for volumetric moisture content using VNIR spectra; and spectra were also used for predicting SOC concentration. However, these authors aimed at evaluating SOC stock at the field level, and did not present comparisons between observed and predicted SOC stocks at the sample or profile level (except Viscarra Rossel et al., 2016b, who predicted SOC stocks at the profile level using kriging in addition to gamma-ray attenuation and VNIRS, which added a layer of uncertainty: in leave-one-out cross-validation, they achieved R² = 0.4-0.5 and RPD = 1.3-1.4). Attempts to directly predict D b using DRIS have rarely been successful: several studies obtained poor predictions (R² val < 0.3 and RPD val < 1.2; [START_REF] Minasny | Using soil knowledge for the evaluation of mid-infrared diffuse reflectance spectroscopy for predicting soil physical and mechanical properties[END_REF][START_REF] Moreira | Near infrared spectroscopy for soil bulk density assessment[END_REF][START_REF] Veum | Estimating soil quality index with VNIR reflectance spectroscopy[END_REF]. Some authors reported good figures of merit (R² val = 0.64-0.81 and RPD val = 1.7-2.2; [START_REF] Askari | Evaluation of soil quality for agricultural production using visible-near-infrared spectroscopy[END_REF][START_REF] Roudier | Prediction of volumetric soil organic carbon from field-moist intact soil cores[END_REF][START_REF] Cambou | Prediction of soil organic carbon stock using visible and near infrared reflectance spectroscopy (VNIRS) in the field[END_REF][START_REF] Pérez-Fernández | Global and local calibrations to predict chemical and physical properties of a national spatial dataset of Scottish soils from their near infrared spectra[END_REF]. But this might sometimes have been due to homogenous soil population [START_REF] Roudier | Prediction of volumetric soil organic carbon from field-moist intact soil cores[END_REF], or conversely to very wide distribution (prediction error being actually larger than in other studies; [START_REF] Pérez-Fernández | Global and local calibrations to predict chemical and physical properties of a national spatial dataset of Scottish soils from their near infrared spectra[END_REF], or to aggregation of sites with poor within-site prediction [START_REF] Cambou | Prediction of soil organic carbon stock using visible and near infrared reflectance spectroscopy (VNIRS) in the field[END_REF].

Actually, in their review Bellon-Maurel & McBratney (2011) recommended direct DRIS prediction of SOC stock, and considered works in that direction should be a priority. And indeed, doing so, some authors have got promising results. [START_REF] Roudier | Prediction of volumetric soil organic carbon from field-moist intact soil cores[END_REF] achieved good predictions of sample SOC stock in one large arable field, using VNIR spectra from fresh intact cores taken with hydraulic coring equipment mounted on a truck (R² val = 0.85 and RPD val = 2.6). [START_REF] Cambou | Prediction of soil organic carbon stock using visible and near infrared reflectance spectroscopy (VNIRS) in the field[END_REF] achieved acceptable prediction of sample SOC stock in two agroforestry fields 250 km apart using VNIR spectra of fresh cores collected using handheld auger (R² val = 0.70 and RPD val = 1.8), which is a much lighter approach thus opens exciting prospects. Cores collected with such manual auger are made of partly disturbed soil material; but the results indicate they nevertheless contain information on structure and SOC stock, which can be extracted from their VNIR spectra. Of course, information on SOC stock is poorer than from intact soil materials, which explains why prediction was less accurate in the latter study than in the former (cores with disturbed vs. undisturbed soil material, respectively); along with the probable fact that the homogeneity of the soil sample set was lower in the latter study than in the former (two agroforestry sites in undulating loess areas 250 km apart vs. one arable site in a sand plain, respectively), which often makes DRIS predictions less accurate [START_REF] Brunet | Determination of carbon and nitrogen contents in Alfisols, Oxisols and Ultisols from Africa and Brazil using NIRS analysis: effects of sample grinding and set heterogeneity[END_REF]. [START_REF] Allory | Quantification of soil organic carbon stock in urban soils using visible and near infrared reflectance spectroscopy (VNIRS) in situ or in laboratory conditions[END_REF] also scanned intact soil material but on pit walls, and achieved good VNIR prediction of sample SOC stock in urban soils of two French cities 800 km apart (R² val = 0.78 and RPD val = 2.2), though marked differences between soils (calcareous or acid soils, under parks or streets). Unexpectedly, these authors achieved noticeably more accurate sample SOC stock prediction from spectra acquired in laboratory conditions (air-dried, 2-mm sieved samples; R² val = 0.89 and RPD val = 3.1), probably due to variable soil moisture during in situ spectrum acquisition.

Accuracy was even improved when SOC stock was considered at the profile level (in kgC m -2 ; R² val = 0.94 and RPD val = 4.4) than at the sample level (in gC dm -3 ), probably because some uncertainties at the sample level could offset each other at a more integrated level.

Conclusions and perspectives

Many studies have evidenced the usefulness of DRIS for quantifying SOC concentration, especially when using large calibration databases (e.g. national spectral databases), with R² up to 0.9 and RPD up to 3.3 in external validation. And it is likely that improvements in spectral data analysis will allow even more accurate predictions, in particular through approaches such as local calibration and spiking. Complementary use of soil expert knowledge could also be fruitful, for instance for calibrations based on soil textural or mineralogical classes, or using covariables easy to obtain (e.g. sand content).

Though more and more portable instruments allow implementation in the field, it may be assumed that most DRIS applications to soils will still long be carried out in laboratory conditions. Indeed, building calibration databases with spectra acquired in the field represents huge work, moreover field spectra may be acquired according to different procedures (on the soil surface, on clods, on cores, on pit walls, etc.) and spectra acquired in different conditions cannot easily be grouped in a common calibration database. In contrast, large calibration databases using soil spectra acquired in laboratory conditions are already available, will very probably become larger, and are often based on one type of soil samples (i.e. air-dried, 2 mm sieved). Developing tools that would allow using calibration databases built in laboratory conditions for making predictions from field spectra is a very exciting perspective; but according to the results achieved to date, such solution will not be operational soon.

As emphasized by Bellon-Maurel & McBratney (2011), direct DRIS prediction of SOC stock represents an efficient option, using spectra acquired in field conditions, or more simply, in laboratory conditions. Indeed, determining SOC stock without having to determine the volumetric mass (except for calibration purposes), in particular without having to tediously collect intact soil cores, represents noticeable progress and should help getting much more extensive information on SOC stocks. Soil organic carbon is the largest carbon pool in terrestrial ecosystems, thus an important component in the global carbon cycle. Moreover, because of its multifunctional role and its sensitivity to land management, SOC is one of the major indicators used for evaluating land degradation neutrality. Therefore providing guidance to help countries to estimate and monitor SOC for LDN planning is a key issue. Where SOC monitoring is necessary to verify LDN achievement, accurate data are needed [START_REF] Chotte | Realising the carbon benefits of sustainable land management practices: Guidelines for estimation of soil organic carbon in the context of land degradation neutrality planning and monitoring[END_REF]. DRIS has strong potential, either considering SOC concentration or stock, for supporting better evaluation of soil and land degradation, and the availability of spectrometers at increasingly affordable prices reinforces this potential. reticulatum) mitigate degradation of tropical soils but do not replenish nutrient exports. Land Degradation & Development, 29, 2694-2706. doi: 10.1002/ldr.3033 Fontán, J.M., Calvache, S., López-Bellido, R.J., & López-Bellido, L. (2010) 110, 168-176. doi: 10.1016/j.chemolab.2011.11.003 Gogé, F., Gomez, C., Jolivet, C., & Joffre, R. (2014). Which strategy is best to predict soil

TABLE 1

Predictions of SOC concentration from large spectral libraries. Scanned samples were 2-mm sieved, air-dried, except for Gogé et al. (2012Gogé et al. ( , 2014)), who used 1-mm sieved, 55°C-dried samples, and Grinand et al. ( 2012) and [START_REF] Clairotte | National calibration of soil organic carbon concentration using diffuse infrared reflectance spectroscopy[END_REF], who used 0.2-mm ground, 40°C-dried samples. Abbreviations and/or brief explanation of regression approaches: PLSR, partial least squares regression; local PLSR, uses spectral neighbours for PLSR; "double local" PLSR, uses spectral and spatial neighbours; LW PLSR, locally weighted PLSR (neighbour contributions depend on their similarity with target samples); spiking, consists of enriching the calibration set with a few target samples; MARS, multivariate adaptive regression spline; RT, regression tree; BRT, boosted RT; Cubist, rule-based RT; SVMR, support vector machine regression

TABLE 2

Predictions of SOC concentration using VNIR or MIR spectra acquired in the field, and when reported, homologous predictions using spectra acquired in laboratory conditions, on 2-mm sieved, air-dried samples (in italics; same sets and regression procedures). All studies performed PLSR (partial least squares regression) except [START_REF] Nawar | On-line vis-NIR spectroscopy prediction of soil organic carbon using machine learning[END_REF], who used random forest. Abbreviations and/or brief explanations of procedures: CV, cross-validation; LOO CV, leave-one-out CV; RD CV, repeated double CV; Ext., external validation with around 30% samples in general, selected either at random or on samples well represented by calibration samples (denoted "repres."; e.g. selecting every third sample after SOC-sorting); spiking, consists of enriching the calibration set with a few target samples MIR 2 mm sieved, dry 0.77 2.0 † Calibration using some archived samples, samples from another site, and 10% samples of the current experiment FIGURE 1 MIR and NIR spectra of SOC-rich and -poor Malagasy topsoil samples that had been 40°C oven-dried and 0.2-mm ground (59 and 5 gC kg -1 , respectively). Abscissas are usually wavenumbers (in cm -1 ) for mid infrared and wavelengths (in nm) for near infrared (2500 nm = 4000 cm -1 ). In the mid infrared, absorbance is stronger and spectra display more informative peaks (near infrared peaks mostly relate to water, e.g. at 1400, 1900 and 2200 nm)

  . Soil carbon measurement in clods and sieved samples in a Mediterranean Vertisol by Visible and Near-Liniger, H., Sauter, C., & Schwilch, G. (2018). Economic benefits and costs of sustainable land management technologies: an analysis of WOCAT's global data. Land Degradation & Development, 29, 962-974. doi: 10.1002/ldr.2429 Gogé, F., Joffre, R., Jolivet, C., Ross, I., & Ranjard, L. (2012). Optimization criteria in sample selection step of local regression for quantitative analysis of large soil NIRS database.

	Infrared	Reflectance	Spectroscopy.	Geoderma,	156,	93-98.	doi:
	10.1016/j.geoderma.2010.02.001
	Fystro, G. (2002). The prediction of C and N content and their potential mineralisation in
	heterogeneous soil samples using Vis-NIR spectroscopy and comparative methods. Plant
	and Soil, 246, 139-149. doi: 10.1023/A:1020612319014
	Ge, Y., Morgan, C.L.S., & Ackerson, J.P. (2014). VisNIR spectra of dried ground soils
	predict properties of soils scanned moist and intact. Geoderma, 221-222, 61-69. doi:
	10.1016/j.geoderma.2014.01.011
	Giger, M., Chemometrics	and	Intelligent	Laboratory	Systems,

properties of a local site from a national Vis-NIR database? Geoderma, 213, 1-9. doi: j.geoderma.2013.07.016 Gras, J.P., Barthès, B.G., Mahaut, B., & Trupin, S. (2014). Best practices for obtaining and processing field visible and near infrared (VNIR) spectra of topsoils. Geoderma, 214-215, 126-134. doi: 10.1016/j.geoderma.2013.09.021 Grinand, C., Barthès, B.G., Brunet, D., Kouakoua, E., Arrouays, D., Jolivet, C., Caria, G., & Bernoux, M. (2012) Prediction of soil organic and inorganic carbon contents at a national scale (France) using mid-infrared reflectance spectroscopy (MIRS). European Journal of Soil Science, 63, 141-151. doi: 10.1111/j.1365-2389.2012.01429.x Guerrero, C., Zornoza, R., Gómez, I., & Mataix-Beneyto, J. (2010). Spiking of NIR regional models using samples from target sites: Effect of model size on prediction accuracy. Geoderma, 158, 66-77. doi: 10.1016/j.geoderma.2009.12.021 Guerrero, C., Stenberg, B., Wetterlind, J., Viscarra Rossel, R.A., Maestre, F.T., Mouazen, A.M., Zornoza, R., Ruiz-Sinoga, J.D., & Kuang, B. (2014). Assessment of soil organic carbon at local scale with spiked NIR calibrations: effects of selection and extra-weighting on the spiking subset. European Journal of Soil Science, 65, 248-263. doi: 10.1111/ejss.12129 Hutengs, C., Seidel, M., Oertel, F., Ludwig, B., & Vohland, M. (2019). In situ and laboratory soil spectroscopy with portable visible-to-near infrared and mid-infrared instruments for the assessment of organic carbon in soils. Geoderma, 355, 113900. doi: geoderma.2019.113900 Igne, B., Reeves, J.B. III, McCarty, G., Hively, W.D., Lund, E., & Hurburgh, C.R. Jr (2010). Evaluation of spectral pretreatments, partial least squares, least squares support vector machines and locally weighted regression for quantitative spectroscopic analysis of soils. Journal of Near Infrared Spectroscopy, 18, 167-176. doi: 10.1255/jnirs.883 IPBES (Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services; 2018). The assessment report on land degradation and restoration. Bonn, Germany: IPBES Secretariat. Retrieved from https://www.ipbes.net/assessment-reports/ldr. IPCC (International Panel on Climate Change; 2019). Climate change and land. IPCC special report on climate change, desertification, land degradation, sustainable land management,


Antoine Bonneau
email: antoine.bonneau@insa-lyon.fr

Fabien Mieyeville

Frédéric Le Mouël

On-device learning for ultra-low-power wireless sensors: evaluating the effects of data subsampling

Keywords: On-Device Learning, Intermittent Learning, Federated Learning

Integrating Artificial Intelligence (AI) into embedded systems is critical for the development of viable Ambient Intelligence (AmI). However, the energy requirements of current AI computations are not compatible with the limited resources of AmI devices and global sustainability goals. To address this issue, we propose using Federated Learning across multiple intermittent embedded systems to distribute data gathering, storage, and load balancing, thus enabling the system to assess and adapt appropriately to the environment. We initially focus on relevant real-world data acquisition to check the minimum data required by a local node in a federation. Our preliminary results demonstrate a direct correlation between signal decimation, a decrease in both training time and energy usage, and a collapsing threshold limit in accuracy.

I. INTRODUCTION

The increasing prevalence of embedded systems has made the environment more intelligent but presents both opportunities and challenges. Ambient Intelligence (AmI) and Artificial Intelligence (AI) are intertwined, as the growing autonomy of AmI devices has spurred the deployment of connected objects that generate large amounts of data suitable for AI. However, current AI computation energy requirements are not suited to the limited resources of AmI devices and global sustainability goals.

Initially, the sensors and actuators do not require significant computing or memory capabilities. Therefore, current solutions for introducing intelligence rely on cloudbased systems. However, such solutions cannot be considered embedded in the environment. As low-end IoT devices become more powerful and energy-efficient, it may be worth considering relocating computations away from the cloud. Edge computing represents a step in this direction, but it still faces limitations that prevent the use of traditional algorithms.

To address this, we propose using Federated Learning (FL). Even though FL is mainly used in scenarios where confidentiality is crucial, this paradigm can also distribute the computational load among sensors, adapt duty cycling to energy availability, and prolong sensors' lifespan. The AmI version of FL requires the ability to synchronize with surrounding devices and distribute the models aggregation among active participants.

Intelligent sensors must prioritize various tasks (e.g., monitoring, learning, inference, communication) and adjust to energy availability. One of these tasks is collecting relevant data. Our primary area of attention is this task, and we have first focused on subsampling incoming data as an effective approach to reduce computational requirements. II. RELATED WORKS Previous works have shown that it is possible to use advanced AI solutions despite the memory constraints of AmI low-end devices. Lin et al. [START_REF] Lin | On-Device Training Under 256KB Memory[END_REF] has successfully fine-tuned a human recognition model on an STM32F746 using less than 256 KB of RAM and 1 MB of Flash. Profentzas et al. [START_REF] Profentzas | MiniLearn: On-Device Learning for Low-Power IoT Devices[END_REF] optimized a pre-trained activity-recognition neural network on an nRF-52840 SoC featuring: a 32-bit ARM Cortex-M4 with FPU at 64 MHz, 256 KB of RAM and 1 MB of Flash.

Lee et al. [START_REF] Lee | Intermittent Learning: On-Device Machine Learning on Intermittently Powered System[END_REF] introduced intermittent learning as a way for energy-harvested computing platforms to perform machine learning tasks effectively and efficiently. Among the frameworks for intermittent learning that later emerged, [START_REF] Bakar | REHASH: A Flexible, Developer Focused, Heuristic Adaptation Platform for Intermittently Powered Computing[END_REF] developed REHASH, a tool helping with the design of adaptative IoT workflow heuristics. They evaluated their work by running activity recognition and greenhouse monitoring applications using an MSP430FR5994 Launchpad.

Another category of work has addressed the energy constraints imposed on intelligent sensors and the distribution of AI calculations in embedded systems. Dai et al. [START_REF] Dai | DisPFL: Towards communication-efficient personalized federated learning via decentralized sparse training[END_REF], with DispFL, have proposed to act on communication costs using personalized FL and decentralized learning. Costa et al. [START_REF] Costa | Train Me If You Can: Decentralized Learning on the Deep Edge[END_REF] designed a framework to enable the deployment of decentralized learning in resource-constrained devices. They evaluated their contribution on a STM32L4R5ZIT6 MCU over some Artificial Neural Network models.

However, to the best of our knowledge, there has been no prior attempt to combine these distinct approaches on lowcapacity and ultra-low-power devices.

III. METHODOLOGY

Different approaches exist to tailor AI models and their life cycles to meet low-energy and high-constraint requirements. Communication is the most energy-intensive task for a lowend device. As we aim to use distributed learning, optimizing exchanges with peers will be necessary. We have to evaluate specialized FL aggregators such as Compressed Sensing or Adaptive Neighbor Matching based ones.

AI being inherently data processing, Data Reduction can alleviate both memory and complexity issues in training and inference. Adaptative Subsampling and Time Series Segmentation exemplify this concept and preserve the relevant properties of the monitored phenomenon.

We selected Data Reduction as our primary area of compromise and measuring the influence of diverse subsampling techniques as our first task in this direction.

IV. EXPERIMENTAL SETUP

We are targeting Structural Health Monitoring (SHM) applications and have begun working with a dataset containing three mechanical physical signals from a vibrating system, built for a previous research [START_REF] Zieliński | Système distribué actif sans fil basse consommation pour l'amortissement des vibrations[END_REF] at the Ampere laboratory. The testbed, illustrated in Figure 1, consists of an aluminum plate with a modal shaker (M20/PA300E from Data Physics) attached near its center, flanked by two piezoelectric patches DuraACT P-876.A15 on either side. A laser vibrometer is used to measure the ground truth of the vibrations. Each dataset comprises recordings of an excitation sweep applied to the vibrating pot from 10 to 500 Hz at a sampling frequency of 1600 Hz. Each recording is represented by a set of timestamps, tension signals from the two piezoelectric sensors, and the vibrometer tension measured at the pot and plate contact point.

V. PRELIMINARY RESULTS

We utilized a classification model based on Fully Convoluted Neural Networks (FCN) [START_REF] Wang | Time series classification from scratch with deep neural networks: A strong baseline[END_REF] to pinpoint the piezoelectric patch of signals' origin. The classifier was trained with signal decimation (pick 1 record every 2, 4, . . . ) applied on the time series data, and the experiment was repeated until the model's accuracy decreased. To compare subsampling influence on the training, we calculated accuracy, timed it, and measured power consumption using a software wattmeter. The experiment was conducted on an HP Precision 5570 laptop using 15 CPUs simultaneously. A linear correlation was observed in Figure 2 between the signal decimation resultant sampling frequency and the decrease in training time and power usage down to a plateau corresponding to the laptop idle energy consumption. The accuracy decreases below 10Hz since there isn't enough data to support effective learning.

VI. FUTURE WORKS

Future works involve comparing this data selection approach with random and variations-aware strategies. We plan to first move the training onto an STM32F302R8 device with a lightweight ML framework and then distribute it over a network.

Our current experiment is limited mainly by its size. We plan to set up a larger modular plate including a movable vibration source, additional piezoelectric patches, and the ability to simulate material changes over short periods.

Following our examination of the Data Reduction trade-offs, we aim to address another challenging FL task. Specifically, we plan to evaluate the costs of different synchronization strategies for distributed learning. This will involve coupling energy models from ns3 to the Flower FL framework and then validating these simulated strategies with our vibrating system.

Dynamic

  Hardware Management is a possible modelagnostic technological lever for performance/energy tradeoffs. Recent MCUs have different operating modes balancing performance and autonomy. ADCs sampling duration can be decreased a the expense of measurement accuracy. Quantization, Pruning, and Encoding are in essence memory related techniques. By simplifying or compressing the AI model's parameters or representations you can squeeze down models to smaller sizes and induce faster computation.

Fig. 1 .

 1 Fig. 1. Experimental vibrating testbed

Fig. 2 .

 2 Fig. 2. Effects of signal decimation on piezoelectric classification