How to measure, report and verify soil carbon change to realize the potential of soil carbon sequestration for atmospheric greenhouse gas removal

Abstract There is growing international interest in better managing soils to increase soil organic carbon (SOC) content to contribute to climate change mitigation, to enhance resilience to climate change and to underpin food security, through initiatives such as international ‘4p1000’ initiative and the FAO's Global assessment of SOC sequestration potential (GSOCseq) programme. Since SOC content of soils cannot be easily measured, a key barrier to implementing programmes to increase SOC at large scale, is the need for credible and reliable measurement/monitoring, reporting and verification (MRV) platforms, both for national reporting and for emissions trading. Without such platforms, investments could be considered risky. In this paper, we review methods and challenges of measuring SOC change directly in soils, before examining some recent novel developments that show promise for quantifying SOC. We describe how repeat soil surveys are used to estimate changes in SOC over time, and how long‐term experiments and space‐for‐time substitution sites can serve as sources of knowledge and can be used to test models, and as potential benchmark sites in global frameworks to estimate SOC change. We briefly consider models that can be used to simulate and project change in SOC and examine the MRV platforms for SOC change already in use in various countries/regions. In the final section, we bring together the various components described in this review, to describe a new vision for a global framework for MRV of SOC change, to support national and international initiatives seeking to effect change in the way we manage our soils.

stocks, inherent spatial and temporal variability and slow soil C gains make the detection of short-term changes (e.g. 3-5 years) in SOC stocks and the design of reliable, cost-effective and easy to apply MRV platforms challenging (Post, Izaurralde, Mann, & Bliss, 1999). Smith et al. (2012) described a framework, building on available models, data sets and knowledge, to quantify the impacts of land use and management change on soil carbon. That paper concluded by presenting a future vision for a global framework to assess soil carbon change, based on a combination of mathematical models, spatial data to drive the models, short-and long-term data to evaluate the models, and a network of benchmarking sites to verify estimated changes. Here, we review the new knowledge since then, and further develop this vision in the light of the need to provide credible and robust MRV capabilities to support the growing International and National initiatives to increase SOC, such as the International '4p1000' initiative (Chabbi et al., 2017;Rumpel et al., 2018Rumpel et al., , 2019. We focus on methods to measure and/or estimate SOC change, but these measurement/estimation methods also form the basis of how changes in SOC can be monitored and reported at plot to national (and even global) scales, and how reported changes could be verified.
We begin by reviewing the methods and challenges of measuring SOC change directly in soils (Section 2), before examining some recent developments that show promise for quantifying SOC stocks (and therefore change) using flux measurements, non-destructive field-based spectroscopic methods and the possibility in future of estimating SOC change through earth observation/remote sensing (Section 3). We then review how repeat soil surveys are used to estimate territorial changes in SOC over time (Section 4), and how longterm experiments and space-for-time substitution sites can serve as sources of knowledge and can be used to testing models, and as potential benchmark sites in global platforms to estimate SOC change (Section 5). Section 6 summarizes recent reviews on models available for simulating and predicting change in SOC, after which Section 7 describes MRV platforms for SOC change already in use in various countries/regions. We finish the review (Section 8) by describing a new vision for a global framework for MRV of SOC change to support national and international initiatives. measurements. This approach traditionally involves the quantification of (a) fine earth (<2 mm) and coarse mineral (>2 mm) fractions of the soil; (b) organic carbon (OC) concentration (%) of the fine earth fraction; and (c) soil bulk density or fine earth mass (FAO, 2019a). In some instances, such as grasslands or forest soils, it may be of interest to quantify and account for the coarse fraction of belowground OC (FAO, 2019a). The challenge remains to accurately estimate the rock content of sampled soils, which can significantly affect soil bulk density (Page-Dumroese, Jurgensen, Brown, & Mroz, 1999;Poeplau, Vos, & Don, 2017;Throop, Archer, Monger, & Waltman, 2012).
Changes in management that influence carbon content also affect the bulk density of the soil (Haynes & Naidu, 1998), and thereby the amount of soil that is sampled within a given sampling depth. It is therefore recommended to use an 'equivalent mass basis' approach when comparing SOC stocks across land uses and different management regimes (Ellert & Bettany, 1995;Upson, Burgess, & Morison, 2016;Wendt & Hauser, 2013).
Direct measurements also rely on appropriate study designs and sampling protocols to deal with high spatial variability of SOC stocks (Minasny et al., 2017). To reduce potential sources of error in SOC stock estimation and minimize the minimum detectable difference (i.e. the smallest difference in SOC stock that can be detected as statistically significant between two sampling periods; FAO, 2019a), a large number of soil samples is often required (Garten & Wullschleger, 1999;Vanguelova et al., 2016). Sufficient sampling depth is a crucial factor for properly evaluating changes in soil C content (IPCC recommends a minimum depth of 30 cm). Several long-term agronomy experiments suffer from an increase in ploughing depth during more recent decades, as agricultural machinery became more powerful.
Insufficient information on historical sampling depth can also add uncertainty to the results.
Several methods for increasing soil C content require deeper sampling for confirming the expected effect. The positive effect of no-till on soil C content measured in the surface soil may not be apparent when measuring to 60 cm depth (Angers & Eriksen-Hamel, 2008;Blanco-Canqui & Lal, 2008). Crops with deep root phenotypes are considered a promising method to increase C sequestration in soils (Paustian et al., 2016), though demonstrating their effect requires deep soil sampling. Deeper soil sampling (100 cm) is recommended (FAO, 2019a), but often requires specific machinery and is costly.
Costs associated with collecting, processing and storing soil samples and C content measurements using, for example, common dry combustion methods (Nelson & Sommers, 1996) can make largescale direct measurements of soil SOC stocks prohibitively expensive. It was estimated that to detect meaningful changes in soil C stocks across forest ecosystems in Finland (i.e. 3,000 plots at the national scale) might cost 4 million Euro for one sampling campaign (e.g. baseline measurement from 1 year) and then again for the following sampling interval (e.g. 10 years later; Mäkipää, Häkkinen, Muukkonen, & Peltoniemi, 2008). Thus, there is the need to evaluate these costs against the value of soil C sequestered (Mäkipää et al., 2008;Smith, 2004b) and search for trade-offs between costs involved and alternative SOC estimation methods including different modelling approaches.
A combination of direct measurements (at the plot scale) and modelling (at larger spatial scales) can greatly help defining the efficacy of different land management practices in enhancing soil C sequestration and has been used for estimating soil C change in national GHG inventory platforms (e.g. VandenBygaart et al., 2008). It is, therefore, crucial to evaluate the cost-effectiveness of measuring and sequestering C across different land uses and socio-economic conditions (Alexander, Paustian, Smith, & Moran, 2015).

| Inferring SOC stock changes from flux measurements
An alternative to repeated measurements is to draw up a full carbon budget. This indirect approach accounts for the initial uptake of carbon through photosynthesis (gross primary production), its subsequent partial losses through respiration (soil, plant and litter) to give net ecosystem exchange (NEE) or net ecosystem production and further C inputs (organic fertilization) and outputs (harvest) to and from the system (see Smith, Lanigan, et al., 2010;Soussana, Tallec, & Blanfort, 2010). The measurements of the net balance of C fluxes exchanged (i.e. estimating NEE) can be achieved by chamber measurements or by the eddy covariance (EC) method (e.g. Baldocchi, 2003).
During recent decades, estimates of C sequestration from flux measurements have been reported to be comparatively uncertain due to (a) necessary assumptions associated with data processing (e.g. footprint, spectral corrections, i.e. Aubinet, Vesala, & Papale, 2012); the fact that (b) this method is a point-in-space measurement; and (c) net changes in soil C pools are relatively small compared to C stored in biomass and litter when measured over short time periods (i.e.

<5 years).
Despite this, recent developments in instrumentation (analyser performance and set-ups, e.g. Rebmann et al., 2018), data acquisition and processing (i.e. data loggers, software, QA/QC checks) have greatly improved the reliability of estimates (e.g. Fratini & Mauder, 2014). Furthermore, harmonized networks of long-term observation sites, created to provide access to standardized data and to quantify the effectiveness of carbon sequestration and/or GHG emission at European (Integrated Carbon Observation System, ICOS;Franz et al., 2018) and global scale (FLUXNET global network, e.g. Baldocchi, Housen, & Reichstein, 2018; Figure 1), have greatly reduced uncertainties in flux and supplementary measurements. Moreover, ongoing analyses on peculiarities of flux measurement likely to increase uncertainties in flux measurements, such as integration of (moving) point sources, that is, grazing animals (Felber, Münger, Neftel, & Ammann, 2015;Gourlez de la Motte et al., 2019), ditches (Nugent, Strachan, Strack, Roulet, & Rochefort, 2018) and fallow periods, have been studied thoroughly and have allowed routine data analyses to be updated (e.g. Sabbatini et al., 2018).
Concerning the comparison between C sequestration determined via the EC technique (i.e. full C balance) and soil C stock changes, some studies have shown poor agreement , but a number of studies have shown comparable estimates, when applied for time frames >10 year and with soil data including at least both top and medium soil depths (i.e. 0-60 cm; e.g. grassland: Leifeld, Ammann, Neftel, & Fuhrer, 2011;Skinner & Dell, 2014;Stahl et al., 2017;cropland: Emmel et al., 2018;Hoffmann et al., 2017;forest: Ferster, Trofymow, Coops, Chen, & Black, 2015). Coupling of EC with soil C stock change studies has become a favoured approach to understand both short-and long-term effects of principal drivers (e.g. management, climate) on ecosystem functioning (i.e. Eugster & Merbold, 2015), in natura measurement and modelling approaches (e.g. Beer et al., 2010;Besnard et al., 2018;Williams et al., 2009).

| Spectral methods for measuring SOC stocks
New spectral methods for measuring SOC concentration and stocks are rapidly becoming available for direct point measurements in field and in the lab, but also for measurement of patterns at larger scales across landscapes and regions. Each comes with a specific associated accuracy and cost (Bellon-Maurel & McBratney, 2011;England & Viscarra Rossel, 2018;Nayak et al., 2019). A smart combination of these and more traditional methods can either bring down costs (Nocita et al., 2015), provide more exhaustive spatial patterns of SOC stocks (Aitkenhead, 2017;Rosero-Vlasova, Vlassova, Pérez-Cabello, Montorio, & Nadal-Romero, 2019) or provide indications for change in stocks Zhao, Ye, Li, Yu, & Mcclellan, 2016).
The methods for measuring SOC concentration mainly rely on the reflectance of light on soil in the infrared region. The organic bonds and minerals in the soil absorb light at specific wavelengths, resulting is a soil content-specific absorbance or reflectance spectrum. This spectrum is measured with high level of spectral detail (hyperspectral, often in the lab) or limited level of detail in wider bands (multispectral, often from satellites or cheaper field instruments). Using a statistical model based on a spectral library, the soil carbon percentage can be predicted from spectral measurements of the unknown samples.
The spectral library is derived from samples on which soil properties have been determined by traditional laboratory methods, such as dry combustion, alongside reflectance measurements. Relevant wavelengths for soil and SOC are mainly in the mid-(4,000-600 cm −1 ) and the near-or short-wave infrared region (2,000-2,500 nm). Other key soil properties can also be simultaneously determined if present in the spectral libraries, including fractions of OC and vulnerability of soil carbon to loss (Baldock, Beare, Curtin, & Hawke, 2018;Baldock, Hawke, Sanderman, & Macdonald, 2013), soil texture, pH and others (Stenberg, Viscarra Rossel, Mouazen, & Wetterlind, 2010), which can be used to inform modelling approaches. Partial least squares regression (PLSR) is a statistical method that is currently most widely used to predict soil properties from spectra. These machine learning approaches (e.g. Cubist, Random Forests, Support Vector [regression] Machines and others) are rapidly developing, and new techniques are becoming available, currently referred to as deep learning (Padarian, Minasny, & Mcbratney, 2019) and memory based learning (Dangal, Sanderman, Wills, & Ramirez-Lopez, 2019;Ramirez-Lopez et al., 2013). These techniques, such as locally weighted PLSR, use local calibrations based on spectrally similar subsets of a spectral library. This will likely lead to considerable improvement, reducing the prediction errors. This does not resolve the inherent laboratory measurement uncertainties associated with both reference and spectral data.
Standardization of reference laboratory methods, spectral measurements and soil data exchange to some extent negates these issues, and they are addressed in several international co-operations, one of which is Pillar 5 of the Global Soil Partnership (GSP, 2017).
If standardization and calibration transfer challenges can be solved, combining spectral libraries can provide a vast data resource for not only local but also more regional and global SOC analyses (England & Viscarra Rossel, 2018;Viscarra Rossel, Behrens, et al., 2016;Viscarra Rossel, Brus, Lobsey, Shi, & Mclachlan, 2016).
Sample preparation is very simple (dry, sieve to <2 mm, fine grind (Soil Survey Staff, 2014) and after a library is built, the measurements are fast and inexpensive, and can assess all of the listed properties at the same time (Nocita et al., 2015).
These spectral libraries can also be used to calibrate field spectrometers, although accuracy will often be lower, mostly due to moisture and surface roughness of the soil. Higher cost in situ systems are available for both NIR and MIR (Dhawale et al., 2015;Hutengs, Ludwig, Jung, Eisele, & Vohland, 2018). Alternatives are cheap in-field NIR spectrometers for point measurements (Tang, Jones, & Minasny, 2019) which tend to have low(er) accuracies due to hardware constraints and which may have bias. On-the-go systems with 2-5 wavelengths are on the market as well as penetrometers with visible and near-infrared reflectance spectroscopy (VNIR), which also provide a measure for penetration resistance or compacted soil (Ackerson, Morgan, & Ge, 2017;Al-Asadi & Mouazen, 2018;Poggio, Brown, & Bricklemyer, 2017;Wetterlind, Piikki, Stenberg, & Söderström, 2015). A final possibility is a core sampler which measures the extracted soil core in field with VNIR and active gamma radiation for (total) bulk density ).
An important property for calculating SOC stocks is soil bulk density which is difficult to measure accurately in field (Bellon-Maurel & McBratney, 2011). A method used in a number of set-ups is gamma attenuation. This can be measured on the extracted soil core (England & Viscarra Rossel, 2018; or directly in the soil (Jacobs, Eelkema, Limburg, & Winterwerp, 2009). With this technique, the attenuation by matter of gamma radiation originating from a small radioactive source is measured over a known volume between source and detector. The matter in this case consists of both soil and moisture. The volume is simulated using Monte Carlo simulations. This provides a measure of dry bulk density after correction for moisture content as measured for instance with a time domain reflectometry (Jacobs et al., 2009) or VNIR .
The benefit of these techniques is the possibility to acquire more samples and/or more in-field measurements, allowing a user to address the potential of carbon sequestration of the soil adequately. Some of these techniques are most suitable for describing the spatial distribution of soil carbon, while others are suitable for quantitative estimates or monitoring (in time, allowing the impacts of management on soil carbon to be detected). Choices can be made based on cost and required accuracy of the purpose (value of information or decision analysis).
At larger scales, remote sensing offers added possibilities. This can either be by relating UAV, airplane or satellite data directly to soil properties, or by inferring changes in SOC by vegetation changes, or by using remote imagery as a covariate in digital soil mapping of SOC.
Direct interpretation can be performed on hyperspectral imagery in combination with spectral libraries for direct quantification of bare soil patterns (top 1 cm; Gomez, Lagacherie, & Bacha, 2012;Jaber, Lant, & Al-Qinna, 2011), or by using multivariate imagery for mapping bare soil patterns as indication of SOC or soil class differences either using raw or enhanced imagery such as by multi-temporal composites (Gallo et al., 2018;Rogge et al., 2018).
Changes in vegetation patterns visible in remote imagery can be used to detect (changes in) land use and thus infer soil properties and SOC change. Analysis of land-use change, net primary productivity and SOC stocks are instrumental for identifying hotspots of SOC sequestration potential (Caspari, Lynden, & Bai, 2015;van der Esch et al., 2017).
The third option is to use satellite imagery products as covariates in digital soil mapping, where the relation between soil properties and satellite information is used to predict SOC maps at various depths using point observations and satellite imagery products McBratney, Mendonça Santos, & Minasny, 2003;.
That said, a combination of remote and in situ or point data will remain necessary to derive high resolution and accurate SOC maps.
Apart from the limited penetration depth (top 1 cm while a soil profile would be desirable), this is also due to the fact that in many regions, bare soil is never visible, or areas are too often covered in clouds. At the same time, the high temporal frequency and high spatial resolution of remote imagery offer an unprecedented possibility to study and monitor space-time dynamics of SOC change if used in combination with (long-term) monitoring stations (Chabrillat et al., 2019).

| REPE ATED SOIL SURVE YS-NATIONAL / SUB NATIONAL
Repeat soil sampling programmes have been conducted in a number of countries, such as England and Wales (Bellamy, Loveland, Bradley, Lark, & Kirk, 2005;Kirkby et al., 2005), Denmark (Heidmann, Christensen, & Olesen, 2002;, Belgium (Sleutel, Neve, & Hofman, 2003) and New Zealand (Schipper et al., 2014-see below). These rely on resampling of previously sampled locations after varying periods. Advantages are that repeat sampling schemes measure actual soil carbon contents over large spatial scales and over long periods (Bellamy et al., 2005), but the main disadvantage is that land-use change and land management between sampling periods are mostly unknown, making attribution of any observed changes in soil carbon to specific drivers (such as management or climate change) very difficult . In some cases, records of land use and management have been available allowing the effect of management changes to be assessed for better verification of modelling approaches to quantifying SOC stock changes .
Resampling of soil survey sites originally sampled in the 1970s-1990s in New Zealand has played an important role in identifying changes in soil carbon stocks in grazed pastures . The difficulty with these historical resampling efforts was that sites were not chosen with national survey purposes in mind, so their representativeness was questionable. Additionally, sampling efforts were not carried out uniformly over space and time, so resampling was potentially confounded by the effects of soil type, climate and other factors. However, these data have been central to development and subsequent implementation of more robust sampling designs of grazed lands. Alongside, resampling of site impacts of management practices on carbon stock has been explored through the sampling of adjacent long-term management practices (e.g. Barnett, Schipper, Taylor, Balks, & Mudge, 2014;Mudge et al., 2017).
In the case of Europe, differences exist in the availability of soil surveys among countries. As highlighted in the final report of the ENVASSO project, soil monitoring networks are much denser in northern and eastern European countries compared with countries located in the southern part of the continent . For example, countries such as France, Sweden or Poland maintain systematic soil monitoring systems at national level with different density of monitoring sites and sampling frequencies.
In the case of France, different soil monitoring system levels exist which operates to either forest and non-forest areas. The Soil Quality Monitoring Network was created 20 years ago for non-forested areas, covering the main land uses in France in a 16 × 16 km grid (King, Stengel, Jamagne, Le Bas, & Arrouays, 2005). Similarly, in Sweden, soil monitoring is performed at two geographical levels (national and regional) and with different levels of application: forest land, integrated monitoring (areas with minor impact of forest management), intensive monitoring plots (223 forest plots) and arable land monitoring (Olsson, 2005). Poland has also different soil monitoring systems for forest and cropland soils. For the case of croplands, monitoring soils started in 1994 and since then soils have been sampled every 8 years with different soils' properties measured (Białousz, Marcinek, Stuczyński, & Turski, 2005). In Denmark, soils are sampled every 8-10 years to 1 m depth on a regular 7 km grid covering both agricultural and forest soils .
In contrast, EU Mediterranean countries such as Italy, Spain or Greece are examples of European regions where systematic national soil monitoring systems are underdeveloped or non-existent, despite the risks of SOC losses, and soil erosion events resulting from a combination of crop management and regional impacts of climate change (Trnka et al., 2011). For example, in the case of Italy, there is no monitoring system, but there is willingness to develop it. In Spain, over the last 20 years, two independent soil national inventories have been performed; one to assess soil erosion and the other to asses soil heavy metal pollution (Ibáñez, Sánchez Díaz, de Alba, López Arias, & Bioxadera, 2005). However, the inventories have not been linked and there is no firm schedule for future resampling yet in place.

| LONG -TERM E XPERIMENTS OF SO C CHANG E
Since changes in bulk soil carbon occur slowly (Smith, 2004a), long-term measurements are required to show the relatively small change against the large background carbon stock. To this end, long-term field experiments exist in various parts of the world, with some dating from the 19th century. Although many of these experiments were originally set up to examine the effects of management (often fertilization) on crop or grass yield, many have a history of measurements of soil carbon and nitrogen change. Over recent decades, results from these field experiments have been central to testing the accuracy of models of turnover of SOC. As noted by Smith et al. (2012), the long-term experiments in various parts of the world existed largely in isolation of each other, but in the 1990s, there were attempts to bring the various experiments together into shared networks (Barnett, Payne, & Steiner, 1995), with two such networks focussing on soil C; the Soil Organic Matter Network (SOMNET) and EuroSOMNET (the more detailed European component of the larger global network) were two attempts to couple SOC models with observations from long-term experiments (Smith et al., 1997), with the aims or both testing models and the sharing, comparing and use of data from across the experiments to estimate carbon sequestration potential (Smith, Powlson, Smith, Falloon, & Coleman, 2000). SOMNET later evolved into an online, real-time inventory project with a website known as Long-Term Soil-Ecosystems Experiments, which now has collected metadata on well over 200 long-term soil experiments Richter, Hofmockel, Callaham, Powlson, and Smith (2007), with the metadata currently hosted by the International Soil Carbon Network (iscn.fluxd ata. org/partn er-netwo rks/long-term-soil-exper iment s/). Smith et al. Long-term field studies have proved extremely valuable for understanding the long-term dynamics of SOC and wider issues of soil sustainability (Richter et al., 2007). In terms of MRV, the longterm experiments serve as (a) a long-term record of change; (b) a test bed for SOC models; (c) locations where new practices could be tested and measured; and (d) sites where shorter term (e.g. flux measurements) could be taken to better understand shorter term processes. Such experiments could therefore form vital components of national and international MRV platforms for SOC change.
Existing long-term monitoring sites are extremely valuable but do not exist in every global region, making a compelling case for starting new long-term experimental/ monitoring sites in underrepresented regions.

| MODEL S OF SO C CHANG E
The soil organic matter (SOM) dynamics can be described by different mathematical formulations (Parton, Grosso, Plante, Adair, & Luz, 2015), as presented in Table 1, and different model approaches (Campbell & Paustian, 2015;Manzoni & Porporato, 2009). Most common SOM models are compartment models, which use between two and five carbon pools . While the stability and complexity of the organic compounds is not represented explicitly in models, it is represented by varying turnover and residence times of OC in different carbon pools (Stockmann et al., 2013). The residence times are controlled by the decay rate of the carbon in the different pools, which is usually described by the first-order kinetics (e.g. Parton et al., 2015;Paustian, 1994). A wide range of different models show this structure, either as independent SOM model or as part of an ecosystem model, dynamic vegetation model or a general circulation model (Campbell & Paustian, 2015;Ostle et al., 2009;Parton et al., 2015). Manzoni and Porporato (2009) identified about 250 different models, but there are still new developments, as there are still unresolved challenges.
Despite the development of different approaches that allow the measurement of different carbon pools in the models (e.g. Janik et al., 2007;Skjemstad, Spouncer, Cowie, & Swift, 2004;Zimmermann, Leifeld, Schmidt, Smith, & Fuhrer, 2007), SOC pools are often still initialized in a spin-up run (Nemo et al., 2017). This is a practical approach if information about the fractionation is not available, but it relies on ideal assumptions of equilibrium (Smith, Smith, Monaghan, & MacDonald, 2002) which impacts the results (Bruun & Jensen, 2002). Furthermore, the residence times of most pools exceed the duration of available measurements, which makes the calibration and validation of the models difficult (Campbell & Paustian, 2015;. Additionally, not all relevant processes (e.g. priming) are represented in the models (Guenet, Moyano, Peylin, Ciais, & Janssens, 2016;Wutzler & Reichstein, 2013). Recently, there has been a discussion about the ability of existing models to reflect changes in temperature (Conant et al., 2011;Moyano, Vasilyeva, & Menichetti, 2018), which is most relevant to simulate climate change impacts (Conant et al., 2011). Many operational SOC models only simulate turnover and decomposition of the SOC pools and the added OC (Toudert et al., 2018). These models thus rely heavy on proper estimation of carbon inputs in residues and organic amendments (manure, compost, etc.) as well as on information on the biological quality of these inputs. Most modelling approaches used for inventory purposes rely on input data from harvest residues or decaying plant parts and external organic amendments. The plant C inputs are mostly derived from measured agricultural yields using simple allometric equations, where the C inputs is related linearly or non linearly to crop yield (Keel, Leifeld, & Mayer, 2017). Comparison of different published approaches of estimating C input, but using the same decomposition model, has demonstrated large uncertainties in simulated changes in SOC (Keel et al., 2017). The selection of allometric functions for estimating C input is therefore a critical step in the choice of model approach. Recent research has also questioned the appropriateness of using simple allometric functions such as fixed shoot:root ratios for estimating C input (e.g. Hu et al., 2018). Rather than assuming a fixed shoot:root ratio, using a fixed amount of belowground C input depending on site and crop may provide the TA B L E 1 List of different functions to simulate the decomposition in models following the discussion of Parton et al. (2015). The publications listed refer to the example models. The abbreviations describe the carbon (C) at the start (C 0 ) and at a certain time (t) step (C t ), the decomposition rate (k), the Michaelis-Menten constant (K m ) and the maximum reaction velocity for the process (V m ), the carbon demand by the microbes (X 0 ), the Monod constant (K t ) and the maximum growth rate (µ max ). The graphs show C t in a time series for one set of arbitrary parameters Approach Equation

Microbial growth
This has implications for modelling application where changes in crop productivity are a main driver of C inputs.

| Operational soil MRV systems in use in GRA countries
We  For accurate soil monitoring in China, it will be necessary to set up routine monitoring systems at various scales (national, provincial and local scales), taking into consideration monitoring indicators and quality assurance (Teng et al., 2014).
samples for each stratum (Brus & de Gruijter, 1997;De Gruijter, Brus, Bierkens, & Knottters, 2006;Louis et al., 2014). Such an approach will allow a (geo)statistical analysis of SOC stock changes for the soil/ land use/climate units under consideration as an alternative or test for process-based models. Continuous soil monitoring for SOC at time intervals of 10 year is often proposed as a compromise between minimum detectability of changes (Garten & Wullschleger, 1999) and temporal shifts in trends (Bellamy et al., 2005;Schrumpf, Schulze, Kaiser, & Schumacher, 2011;Steinmann et al., 2016). This may be longer than the duration of many land-use management projects that involve the measurement of SOC stock changes (Milne et al., 2012).
New Zealand has developed a model-based approach (McNeill, Golubiewski, & Barringer, 2014;Tate et al., 2005)  While changes in national or large regional scale carbon stock measurements can be addressed using geostatistical sampling approaches, aligned targeted approaches (such as sampling of chronosequences and paired land uses) can directly determine land-use change factors, while controlling for other spatially dependent variables, that is, they can determine the carbon gain/loss that will occur with a change in land use or management. When coupled with monitored changes in land area undergoing these changes, estimates of national scale carbon stock changes can be calculated. The change in carbon stocks determined from paired site sampling can also be used to validate interpretations derived from national scale measurements.

| Methods used by GRA countries for estimating SOC changes for the 'cropland remaining cropland' category in national inventories
All countries that are party to the United Nations Framework  Soil C stocks are influenced by multiple factors that affect primary production and decomposition, including changes in land use and management and feedbacks between management activities, climate and soils. However, only a few countries have taken into F I G U R E 2 Tier methods used by Global Research Alliance of Agricultural Greenhouse Gases countries for estimating the changes in mineral soil carbon stock for the 'Cropland remaining Cropland' category. NA indicates that the country has not developed a GHG inventory. NE indicates that the country has not included soil organic carbon changes in croplands in the inventory. Countries reporting carbon stock change associated with agricultural land use and management activities are indicated by (*) TA B L E 3 Methodology used to estimate changes in soil C stocks for cropland remaining cropland, including agricultural land use and management activities on mineral soils Average SOC calculated annually per soil type and region based on process-based model (C-TOOL) using data on temperature and estimated C input from crop residues and manure using national databases

| PROP OS ED G LOBAL SOIL MRV PL ATFO R M
The sections above describe the methods available to measure and monitor carbon; models that can be used to simulate and project changes in SOC, different types of experimental platform and the data needed to test models and allow them to be run from plot to global scale; and methods/platforms that could be used to verify any simulated change in SOC (summarized in Figure 3).
These form the components of a system suitable for MRV of SOC change ( Figure 3).
Central to the system are benchmark sites, which could be located at existing or new long-term experiments (Figure 3, item 2; Richter et al., 2007), or could consist of well-characterized chronosequences or paired sampling sites (e.g. He et al., 2009;Oliver et al., 2004). The benchmark sites would preferably be located on representative land cover/land-use types, soil types and with representative management. At these sites, proposed practices to increase SOC could be tested in fully randomized block designs, and SOC change measured over time (measurements every few years), while measuring shorter term processes (such as GHG emissions) more frequently (continuously with EC flux towers or frequently with automated chambers; Figure 3, item 2; Baldocchi, 2003 Simplified version of the ECOSSE model (Smith, Gottschalk et al., 2010), coupled with a litter decomposition model derived from the ForClim-D model (Liski, Perruchoud, & Karjalainen, 2002;Perruchoud, Joos, Fischlin, Hajdas, & Bonani, 1999) Matthews et al. (2014) United States DAYCENT biogeochemical model Utilizes the soil C modelling framework developed in the Century model (Parton et al., 1987(Parton et al., , 1988(Parton et al., , 1994Metherell, 1993), but has been refined to simulate dynamics at a daily time step Schimel (1998), Del Grosso et al. (2001), Del Grosso and Parton (2011) Abbreviation: GRA, Global Research Alliance of Agricultural Greenhouse Gases. novel combinations (Figure 3, item 3; e.g. Richards et al., 2017). To establish confidence that the chosen model or models are capable of accurately and reliably simulating SOC change, they need to be tested across the full range of parameter space (i.e. multiple soils types, climate zones, land-use types and soil management options; Ehrhardt et al., 2018;Smith et al., 1997). If necessary, the models can be further developed or parameterized using data from the same long-term experiments, or from shorter term experiments, before being evaluated again against a data set not used in development or parameterization .
When the model(s) are deemed to be reliable, they could be applied (a) to derive IPCC Tier 2 emission or SOC stock change factors, which are specific to the region and conditions represented within the region (e.g. Begum et al., 2018); or (b) spatially over the whole landscape (or the entire land area of a country) using spatial databases of soil characteristics, and land cover, management and climate data (Figure 3, item 4), to directly simulate SOC change and GHG emissions, thereby delivering a Tier 3 methodology to report emissions . Data on changes in soil management are necessary for estimating changes in SOC/GHG emissions, and this could also be provided by self-reported or farm survey-derived activity data (Figure 3, item 5).
If self-reported activity data are used as the primary mechanism for reporting, such activity data could be verified through spot checks/ farm visits or could be done using remote sensing (Figure 3, item 7), which can show, for example, the presence of bare fallow, cover crop or residue retention (Gallo et al., 2018;Rogge et al., 2018). In addition to providing a mechanism for verification of activity data, remotely sensed earth observation products could also provide spatial data to run the SOC/ GHG models. For example, earth observation can be used to estimate changes in carbon input to soils, through changes in NPP/GPP (Chen et al., 2019;Neumann & Smith, 2018), land degradation (Sims et al., 2019) and can also be used to determine land cover/ land cover change (e.g. Chen et al., 2019).
Well-calibrated models, supported by measurements, can also be used to establish relationships between a management change in a particular situation (combination or soil, climate, land use and management) and a change in SOC/ GHG emissions, including estimates of uncertainty (Fitton et al., 2017). This would allow activity data (Figure 3, item 5), self-reported by the farmer/land manager, to be used as the primary source of data for reporting, in place of the need to directly measure SOC of GHG emission change (Smith, 2004b). More broadly, uncertainties and potential biases in all components of the MRV framework, including all measurements and modelling schemes, need to be addressed. For transparency, there is a need for unified protocols for such uncertainty assessments.
In terms of verification, change in SOC stocks, spatial soil monitoring networks (Figure 3, item 6) could be used to ground-truth SOC changes estimated by the Tier 2 method or Tier 3 model projections over time. If resampled every few years, the soil monitoring network (on a grid as shown in Figure 3 item 7, e.g. Bellamy et al., 2005, or using a stratified sampling protocol; Montanarella et al., 2011) could provide independent estimates of large-scale SOC change.