Current developments in soil organic matter modeling and the expansion of model applications: a review

Soil organic matter (SOM) is an important natural resource. It is fundamental to soil and ecosystem functions across a wide range of scales, from site-specific soil fertility and water holding capacity to global biogeochemical cycling. It is also a highly complex material that is sensitive to direct and indirect human impacts. In SOM research, simulation models play an important role by providing a mathematical framework to integrate, examine, and test the understanding of SOM dynamics. Simulation models of SOM are also increasingly used in more ‘applied’ settings to evaluate human impacts on ecosystem function, and to manage SOM for greenhouse gas mitigation, improved soil health, and sustainable use as a natural resource. Within this context, there is a need to maintain a robust connection between scientific developments in SOM modeling approaches and SOM model applications. This need forms the basis of this review. In this review we first provide an overview of SOM modeling, focusing on SOM theory, data-model integration, and model development as evidenced by a quantitative review of SOM literature. Second, we present the landscape of SOM model applications, focusing on examples in climate change policy. We conclude by discussing five areas of recent developments in SOM modeling including: (1) microbial roles in SOM stabilization; (2) modeling SOM saturation kinetics; (3) temperature controls on decomposition; (4) SOM dynamics in deep soil layers; and (5) SOM representation in earth system models. Our aim is to comprehensively connect SOM model development to its applications, revealing knowledge gaps in need of focused interdisciplinary attention and exposing pitfalls that, if avoided, can lead to best use of SOM models to support policy initiatives and sustainable land management solutions.


Introduction
Soil organic matter (SOM) is generated from the dynamic biotic and abiotic processing of plant and animal detritus, representing the balance of inputs versus losses via such pathways as mineralization and leaching. In most soils, SOM is only a small percentage of soil mass, for example ranging from lows of <1% to highs of 8% to 9% in mineral soils under agricultural use (Davidson andAckerman 1993, Haynes andNaidu 1998). However, SOM impacts many soil and ecosystem processes, including soil fertility, soil physical structure (Tisdall andOades 1982, Six et al 2004), water infiltration, water holding capacity (Doran andParkin 1994, Hudson 1994), and atmospheric greenhouse gas (GHG) emissions (Heimann and Reichstein 2008). SOM is fundamental to many soil and ecosystem functions across a wide range of scales. It is also sensitive to the direct and indirect human impacts, e.g. through agricultural management practices (Matson et al 1997, West andMarland 2002), land use changes (Post and Kwon 2000), and shifts in nitrogen deposition and precipitation patterns (Schlesinger and Andrews 2000, Esser et al 2011). SOM's quantity, quality, and dynamics can be used an indicator of human impacts on a wide array of ecosystem functions (Tiessen et al 1994), as well as a mechanism to improve soil health and its sustainable use as a natural resource Coleman 1988, Lal 2004).
SOM is challenging to bring into a single comprehensive analytical framework (Manzoni andPorporato 2009, Stockmann et al 2013). Direct measurements do not easily account for SOM's extreme physical, chemical, spatial, and temporal complexity (Dungait et al 2012), particularly using operationally defined (e.g., by mesh size, chemical extraction, density) measures of soil fractions with variable linkages to mechanisms affecting SOM dynamics (Wander 2004, von Lützow et al 2007. For decades, simulation models of SOM have therefore played a crucial role in research by providing an explicit mathematical framework to integrate hypotheses for soil processes, supporting hypothesis testing by predicting SOM dynamics across space and time. Their importance in SOM research is evidenced in citation records: on Web of Science, three of the five highest cited publications under the search phrase 'SOM' are model analyses 3 . However, SOM modeling approaches are diverse and continually evolving. Ideally, a SOM model would be based on mechanistic understanding of SOM dynamics, use SOM pools that can be informed by measured data, and be valid across multiple scales. At this point in time, however, no single SOM model yet fits this ideal. Indeed, inherent tradeoffs between model attributes (e.g., generality, predictive capacity, complexity) relative to their intended purpose suggest that no such ideal model can exist (Levins 1966, Sharpe 1990, Smith et al 1997. SOM dynamics have become an increasingly important consideration in many areas of sustainability research and policy (Manlay et al 2007). These areas range from small-scale projects to preserve or improve soil health, to large-scale climate change mitigation strategies (Paustian et al 1998, Lal 2004, Karlen et al 2011, Powlson et al 2011. Direct SOM measurements alone do not easily support these types of efforts. Simulation models of SOM, however, provide the capacity for numeric evaluation of changes, including comparison of predicted impacts on SOM. This has led to an expanding use of SOM models in 'applied' settings, specifically to predict SOM dynamics in order to apply policy or to make decisions for how land is used (e.g. Taghizadeh-Toosi et al 2014). Considering the potential economic and policy implications of these model applications (carbon credits, for example, or payments for changing land management practices), there is an immediate need to better connect advances in SOM understanding with SOM model development and these rapidly expanding applications where SOM models are being used in decision making.
Here we review the state of recent SOM model developments and their connection to SOM model applications. We first provide an overview of SOM modeling, focusing on SOM theory, data-model integration, and model development as evidenced by a quantitative review of SOM literature. Second, we present the landscape of SOM model applications, focusing on examples in climate change policy. We then conclude with a discussion of five areas of recent developments in SOM modeling, in order to examine their connection with SOM model applications in greater depth. These developments include (1) the role of microbes in SOM stabilization, (2) modeling SOM saturation kinetics, (3) temperature controls on decomposition, (4) SOM dynamics in deep soil layers, and finally (5) the representation of SOM in earth system models (ESMs). The aim of this review is to comprehensively connect SOM model development to its applications, revealing knowledge gaps in need of focused interdisciplinary attention and exposing pitfalls that, if avoided, can lead to best use of SOM models to support policy initiatives and sustainable land management solutions.
2. Overview of SOM modeling 2.1. Model theory and data-model integration A model of a system must balance the conceptual understanding the model is intended to represent, the mathematical approach that best represents that understanding, and the data available to inform and evaluate how the model functions, within the constraints of available computational capacity. For SOM dynamics, the scale of model hypotheses and model uses require careful consideration, as different scales exert different types of limitations (figure 1). SOM models developed at one scale but used at another can lead to erroneous results (Manzoni and Porporato 2009), an area of concern in model applications driven by policy and land management decision making, where data to support model analyses may not be available at the scale of the decision being evaluated.
Across any scale, the 'toolbox' of mathematical approaches has seen relatively little recent expansion in SOM modeling. Rather, advancements are largely derived from new conceptual understanding of SOM dynamics (Parton et al 2015), although they are sometimes derived from the expansion of available data or improvements in computational systems. Many SOM models are formulated with multiple pools using firstorder decay kinetics for mass loss. First-order decay is a modeling approach where the flux of material from a pool is linearly related to the quantity of material in that pool (example presented in figure 2). It is a mathematically (and therefore computationally) simple expression of decomposition using conceptual, kinetically-defined SOM pools that are not directly measurable per se, but have been proven through decades of testing as useful general approach (Paustian 1994), particularly over the long-term (e.g. Jenkinson andRayner 1977, Parton 1987). Other emerging models define SOM pools based on specific stabilization mechanisms or as analytically measureable fractions 3 'Soil organic matter' searched in the topic category 30 July, 2015.
to better simulate short-term change (Tipping et al 2012, Segoli et al 2013, Davidson et al 2014.
A fundamental concern for any type of SOM modeling is the quality and quantity of available measured data to support modeling efforts. Other reviews have discussed the linkages between specific measurement methods and SOM model pools and dynamics (Wander 2004, von Lützow et al 2007, Dungait et al 2012, Simpson and Simpson 2012. Here, we focus more generally on how data are integrated into different SOM model components. There are several ways SOM models and SOM data interact. These can be grouped into four general categories: data to (1) formulate, (2) calibrate, (3) drive, and (4) evaluate a SOM model (figure 2). Data used to formulate SOM models are tied to the hypotheses that a model represents. An example: using incubation data from temperature-response experiments to mathematically define a SOM decomposition temperature response curve (e.g. Parton et al 1987, adapted in figure 2(A)). Data to calibrate a SOM model are used to parameterize components of an SOM model, optimizing model performance by 'tuning' parameter values to match observations when parameters are not measured directly ( figure 2(B)). Data to drive a SOM model, on the other hand, are typically based on external factors known or hypothesized to force SOM behavior. These data, depending on their scale and variation (e.g. soil texture or daily temperature and precipitation), can link spatial and temporal heterogeneity to simulated SOM dynamics (figure 2(C)). Finally, data to evaluate SOM models are used to validate model performance, evaluate uncertainty, and support hypothesis testing through the comparison of SOM simulations with measured results (figure 2(D)).
There are different potential pitfalls for model-data integration in each category. From the formulation side, data link to the hypotheses mathematically represented by a model. New data may prompt model changes, for example if new data alter the shape of an empirical relationship, or if new measurement methods yield new hypotheses for SOM processes. Data for model calibration act as a reference for the underlying modeled system, determining the extent to which the then calibrated SOM model can be used to test hypotheses and project across scales. Data for drivers, on the other hand, affect how spatial and temporal heterogeneity-e.g. in climate, soil texture-are represented. In either case, these components of SOM model analyses are sensitive to data limitations. Ideally calibration and driving data match the scale of the model simulation (i.e. as presented in figure 1), with fine resolution Figure 1. Breaking the continuum of SOM dynamics into three scales commonly used to formulate SOM models, describing the use of each scale, the limitations of models constructed at these scales, and models that exemplify these scales. Examples of microsite, ecosystem, and global models were selected from models classified in Manzoni and Porporato (2009) as M (microbiology/aggregate/ rhizosphere), S or E (soil model without or with dynamic vegetation), and G (coupled model for global applications).
for microsite-scaled model simulation up to broad coverage for a global-scaled model analyses. However, data limitations may necessitate the use of data of coarser resolution, for example, or mixing data of varying quality from varying sources. Model results are based on the assumption that calibration and driving datasets are reasonable reflections of true conditions, and are biased if this assumption is violated. Model evaluation entails similar limitations determined by the scale at which an SOM model is being used (Falloon et al 2002). However, data availability for model evaluation will affect assessment of model accuracy, as well as its ability to support hypothesis testing.
The suite of datasets for model formulation, calibration, driving, and evaluation yield different sources of uncertainty in SOM model predictions (Keenan et al 2011, Palosuo et al 2012. Suites of datasets are also often difficult to identify or compare between SOM models, particularly in large-scale ecosystem or global analyses. This is an area with the potential for rapid improvement, given advances in networks for modeldata integration. For example, model research could connect to data management systems (  . An example of a single pool SOM dynamic model, and the connection to hypothetical data used to formulate (A), calibrate (B), drive (C), and evaluate (D) model functions. The equation is expressed in continuous time and is simple enough to solve analytically for a constant k. However, models that incorporate variable climate (or other driving variables) and models with greater structural complexity do not have analytical solutions. Such models must be resolved to specific time steps and solved numerically using computer functions that depend on the mathematical characteristics of the model. This can lead to substantial increases in computational time and complexity. 4 Manzoni and Porporato (2009) compared modeling approaches for carbon and/or nitrogen cycling processes in soils across a broad range of temporal and spatial scales (10 0 →10 4 m, 10 0 →10 3 days). The authors selected model publications with high citation history and/or novel approaches to modeling soil carbon and nitrogen dynamics. The model publications are presented in Manzoni and Porporato (2009), including subsequent publications on the same model if it included a sufficient level of change to warrant separate consideration. The reviews by Falloon and Smith (2000) and Stockmann et al (2013) present soil carbon models selected by the more general criteria of 'common use' or 'current modeling approaches', and included some model publications unique from those presented by Manzoni and Porporato (2009).

Quantitative literature review methods
We treated the list of model publications of Manzoni and Porporato (2009)-202 publications, of the 221 total-as a record of model development from 1933 to 2009, due to their selection criteria emphasizing impact and novelty of modeling approaches. We recorded the number of times each of these 202 model publications had been cited in the Web of Science (WoS) Core Collection (as of 27 to 28 July, 2015). Some alternative search methods were used where WoS cited references were incomplete (see appendix and supplemental data). Using total citation values, we then evaluated: (1) the number of new model publications across decades, (2) total citations per publication, and (3) average yearly citations per publication.
In order to evaluate SOM model uses in scientific literature we chose to focus on 'named' models, pulling all unique model names from the three reviews where SOM or soil carbon dynamics were explicitly included in the model's foundational formulation 5 . This yielded a final list of 87 named models that we then searched for 〈model name〉 AND 'soil' AND 'model' on WoS, again in the Core Collection. The goal for this search was to yield citations that included that model name explicitly in the title, abstract, or key words, which we could then treat as an example of the model being used as a central component of that analysis. This resulted in paring the initial list of 87 models down to a final list of 74 model names that were effectively searchable. See appendix for discussion of the 13 model names that were too common to be searched effectively, and had to be excluded from subsequent analyses.
Finally, the top ten most cited of the 74 named models were searched with 〈top ten highest cited model names, separated by OR〉 AND 'soil' AND 'models' AND '〈comparison NEAR/2 models〉', and then manually refined, to identify publications for multi-model comparison analyses involving widely used SOM models. The publications yielded by this search were further manually refined to a subset using the single highest cited named model. This subset was then evaluated for the number of models compared in each publication, the purpose of each analysis, temporal and spatial scales, and main results.
Full results for all analyses are reported in the supplemental data.  3(A)). However, while the number of SOM modeling approaches exhibits growth, there is evidence for strong influence from a small subset of key SOM model publications. For example, of the 202 model publications from Manzoni and Porporato (2009), the top ten most highly cited account for a disproportionate number of total citations, with only ∼5% of publications representing 35.5% of total citations. CENTURY model publications outrank every other model, in three publications (Parton et al 1987(Parton et al , 1988(Parton et al , 1993 accounting for almost 11% of total citations. There is also some direct cross-over of model theories: approximately 10% (21) of the 202 models from Manzoni and Porporato (2009) were noted by the authors as being explicitly based on theory from prior publications. Of these 21 publications, almost half (10) cited theory from either CENTURY or RothC model publications. The remaining 11 cite theory from a variety of other sources (Verberne, DocMod, DNDC, NICA, TRACE, PHOENIX). The impact of key publications on SOM model development is further supported by the citations averaged across years since initial publication. Of the publications ranked top ten for yearly average citations, seven (including all three CENTURY model publications) were published before 1995, and all but one of these show consistent or increasing annual citations in recent years (appendix, figure A1).
Analysis of the 74 searchable 'named' models drawn from Manzoni andPorporato (2009), Falloon andSmith (2000), and Stockmann et al (2013) suggest that a relatively small subset of SOM models also dominate SOM model uses in the scientific literature ( figure 3(B)). The model names that were ranked in the top five for citations account for 61% of total citations in this analysis. However, no single model clearly outdistances the others ( figure 3(B)).
Multi-model comparison publications support a lack of consensus in SOM modeling approaches, particularly at the 'ecosystem' scale described in figure 1. A search for model comparisons including the top ten most cited named models (the first ten names in figure 3(B)) identified 34 multi-model comparison analyses published from 1995 to 2014. These multi-model comparisons showed an increase in frequency through time, with almost half (47%) of the 34 identified in this analysis published in just the last four years. The subset of these publications that include the highest cited named model (the CENTURY model, used in 8 of the 34 multi-model comparison publications) showed a dominant focus on multi-year time periods, and site-and regionalspatial scales. In all eight of the multi-model 5 Foundational model formulations were evaluated in the first publication for each named model. We excluded named models that included only dynamic soil nitrogen in their foundational model formulation, but not soil carbon or SOM, as being less focused on broader SOM dynamics. The foundational publication of the APSIM model, for example, was reviewed by Manzoni and Porporato (2009) for simulating dynamic soil nitrogen. There are later versions of the APSIM model that do simulate dynamic soil organic carbon modeling and have been used in model analyses (e.g. Zhao et al 2013). However, APSIM publications are predominantly using the model for its initial purpose (crop modeling and nitrogen cycling).
comparisons that included CENTURY, there was no single model identified with conclusively higher performance. Rather, some models were shown to perform better than others for specific components or locations within the comparative analyses. One study suggested multi-model means perform better against measured data than any model individually (Palosuo et al 2012).
The results of this quantitative literature review show a dominance of a limited set of theories in SOM modeling approaches, alongside a great deal of uncertainty across scales. The latter is an important factor that continues to drive SOM model development, and that should be considered in SOM model applications.
3. The landscape of SOM model applications in policy 3.1. Connecting SOM models to policy instruments There is ongoing expansion in the application of SOM models outside of academic research and linked more directly to policy. Historically, SOM models were one component of scientific evidence (Oades 1984, Elliott and Coleman 1988, Paul and Robertson 1989 informing the types of land uses and soil management practices selected for policy support in agriculture. However, soil health, function, and productivity can connect to policies in fields as diverse as commodity production, urban growth, ecosystem services, and social justice. In these areas, SOM models can generate quantitative evaluations of SOM and ecosystem dynamics which can then be applied in decision making (e.g. van Ittersum et al 2008). The recent expansion of SOM model applications is therefore based in large part on their potential for direct roles in policy instruments (i.e., the tools a government or other organization uses to create change).
SOM models are appearing in policy instruments where the management of SOM is a component of policy goals, such as sequestering more carbon in soils as a climate change mitigation strategy (Stockmann et al 2013). SOM models are often one component of what Jasanoff (2003) calls 'predictive methods' (p 238), a general term for integrating scientific knowledge within a framework specific to policy needs. Predictive methods help simplify complexities at the interface of policy and science, particularly in the areas of natural resources and the environment 6 . However, as discussed in section 2, scientific development of SOM modeling is ongoing (figure 3(A)). New developments can easily be obscured or ignored in multi-faceted predictive methods for policy. This can lead, at best, to a lack of clarity in how a SOM model contributes to the results of a given predictive method, or, at worst, erroneous and misleading information.
A better connection is needed between ongoing advances in SOM research and SOM model applications in policy and decision making. Climate change policy is driving many recent developments in SOM model applications, and will be the focus of this component of our review. We base our selection of examples on expert knowledge in these types of SOM model applications.
3.2. SOM models in climate change policy A common goal in climate change policy is to directly reduce or mitigate atmospheric GHG emissions. These efforts require applying scientific understanding of biogeochemical and ecological processes, a challenge both from the perspective of natural and physical scientists aiming to create 'usable' scientific knowledge (Dilling 2007, Logar andConant 2007), as well as from the perspective of scientists and policy makers aiming to integrate scientific knowledge into better policy (Jasanoff and Wynne 1998, Jasanoff 2003, Sterner and Coria 2003, Brouwer and van Ittersum 2010. Landbased GHG emissions and soil carbon changes are important targets in policy instruments for GHG abatement, but are difficult to assess directly. This has led to widespread application of SOM model simulations in 'predictive methods' for the GHG assessment of these areas (Bryan et al 2010, Gawel andLudwig 2011, Stockmann et al 2013). Predictive methods are just one component of the complex economic, social, and political systems that shape policy. We therefore developed a basic policy instrument typology to categorize the use of GHG assessments in climate change policy (table 1), as a framework to explore specific examples of SOM model applications.
The policy instrument typology presented in table 1 drew from an approach discussed in Carrots, Sticks, and Sermons (Bemelmans-Videc et al 1998), using the following categories: regulation, economic policy, and information programs 7 . Developed from Etzioni's classification of three kinds of power (Etzioni 1961), the typology is linked to the degree to which the government directly influences the governed-i.e., using regulation to require actions of the recipients (mandated obligation), using economic policy to encourage recipients to take action via material resources (self-selective, incentivized obligation), or using information to persuade recipients to take action (no obligation) (Bemelmans-Videc et al 1998).
In table 1 we present the theoretical connection between the degree to which a policy instrument type obligates change, the contribution of that type of policy instrument to GHG reduction/mitigation targets, and the resulting requirements of predictive methods for GHG assessment.
We used this typology to examine the role of three types GHG assessments in which we identified examples of SOM model applications. These include: (1) GHG inventories, (2) carbon offsets, and (3) greenhouse house gas life cycle assessments. The conceptual . The IPCC uses a three-tiered approach for GHG assessments, with basic data inputs and simple empirical models forming the basis of Tier 1 inventories while additional data and more sophisticated analyses are needed for Tier 2 and 3 inventories (Intergovernment Panel on Climate Change 2006b). Tier 2 and 3 approaches are suggested by the IPCC for evaluating Key Categories, identified as 'categories that have a significant influence on a country's total inventory of GHGs in terms of the absolute level of emissions and removals, the trend in emissions and removals, or uncertainty in emissions and removals' (Intergovernmental Panel on Climate Change 2006a, p 1.6). Agricultural systems and land use change are often key categories, in particular with the former a major source of nitrous oxide (N 2 O) emissions, a powerful GHG (Forster et al 2007). Therefore, these are often areas targeted for higher tiered analytical approaches that require the use of SOM models for land-based GHG evaluation (US Environmental Protection Agency 2013).
IPCC methods for national GHG inventories provide an example of a rigorous standardized approach to GHG assessment, establishing best practices that encourage transparency, completeness, consistency, comparability, and accuracy (Eggleston et al 2006). IPCC methods also require uncertainty evaluations, with the expectation that areas of high uncertainty will be targeted for future improvements (Eggleston et al 2006). This creates the potential for a mutually beneficial connection between GHG inventory assessments and SOM model research. Areas of uncertainty in GHG inventory assessments can identify SOM model shortfalls (Del Grosso et al 2006, Lugato et al 2010. Scientific development of SOM models can then be iterating across the standardized GHG assessment framework to generate improved GHG inventory assessments. We suggest that the use of SOM models within GHG inventories for entities at any scale should emulate IPCC methods.

Carbon offsets
Carbon offsets are a component of carbon markets that have emerged in wake of the Kyoto protocol and other climate policy initiatives where the primary target is economic incentives. Carbon offsets convert activities that reduce GHG emissions into priced commodities, aiming to harness market forces for climate change mitigation. Carbon offsets can be a component of either voluntary carbon markets (Kollmuss et al 2008) or compliance markets created to support mandated GHG reductions (e.g. the clean development mechanism for Kyoto Protocol GHG reduction targets). In either case, carbon offsets must be measurable and verifiable by independent third parties as well as meet criteria for additionality, permanence and leakage (Seeberg-Elverfeldt 2010b); i.e., they must be a demonstrable and long-lasting reduction in GHG emissions beyond what would have occurred under 'business as usual', and without causing increases in emissions elsewhere.
SOM dynamics can play an important role in carbon offset projects, particularly through agricultural management and land use change targeted to increase soil carbon sequestration. However, the complexity of SOM dynamics and the spatial variability of soil carbon stocks creates a challenge in meeting measurement and verifiability criteria. This challenge extends on both sides of carbon market transactions. Buyers are concerned with the quality and potential reversibility of these carbon offsets, while offset generators incur high costs to meet certification requirements. Soil carbon sequestration is currently excluded from the clean development mechanism for these reasons (Larson et al 2011).
Carbon offsets demand high certainty and credibility from GHG assessments (table 1). They do not easily accommodate complexity, variability, and scientific uncertainty in SOM dynamics. However, interest in bringing SOM management under the umbrella of carbon market valuation continues to be driven by its potential high value. Soils can also be managed for multiple sustainability criteria, supporting economic valuation for other ecosystem services (Powlson et al 2011). There is an emergence of land management-based GHG assessment standards in voluntary carbon markets (Seeberg-Elverfeldt 2010a). These standards are often based on a hybrid combination of direct measurement and SOM model simulations. Under these approaches, direct measurements are used to support and/or verify results of SOM models applied to integrate interacting site-specific factors of a given project. The Verified Carbon Standard (VCS) and the American Carbon Registry (ACR) methodologies, for example, both include the use of models like CENTURY, DNDC, or APEX to evaluate baseline 'business as usual' emissions versus emissions under other management practices (Earth Partners 2012, Dell et al 2013). The VCS methodology recognizes the potential for model improvements, requiring new simulations if a new model version is used (Earth Partners 2012). The ACR requires extensive project-specific peer-reviewed model parameterization and validation, as well as proof of meeting criteria for model uncertainty standards (Dell et al 2013). In either case, carbon offset standards require the use of SOM models that have proven their applicability to the specific project being evaluated, requiring close engagement with experts in model use as well as the collection of sufficient data to accurately parameterize, drive, and evaluate the model. From the standpoint of SOM research, this suggests an opportunity for an ideal testbed of standardized data collection for model evaluation and development.
Carbon offset project reporting is already a component of carbon offset standards. We suggest projectspecific measured data, meta-data, and SOM model simulation driver data should be made equally as accessible, allowing for more openly sourced use of these data for model testing. These data resources could contribute towards model development at the 'ecosystem' scale, which we recognized in section 2.2.2. as a particularly challenging scale for SOM modeling. Carbon markets would benefit by supporting SOM model development with improved model accuracy and quantified uncertainty, potentially expanding land-based GHG reductions that can generate carbon offsets.

GHG life cycle assessments
Life cycle assessment (LCA) is a framework used to quantify the impacts of a product 'from cradle to grave', i.e. from when a product is created to when it is disposed of or destroyed (Lee 2004). LCAs can be constructed to target any environmental aspect of a product, including GHG emissions, water impacts, or the use of nonrenewable material resources (e.g. Powers 2007, Cherubini 2010. They are a useful tool for informing policy and decision-making, by providing comparable numeric evaluation of production chains. Conceptually, GHG-specific LCAs are similar in purpose to GHG inventories by accounting for all GHG emission sources and sinks. However, their focus is on products and production processes rather than entities. GHG LCAs are often needed when a policy aims to change the carbon intensity of products, providing numeric evaluations for information program or economic incentive policy instruments. This is an area that has seen development in policy supporting alternative fuels as a climate change mitigation strategy. For example, in the United States the expanded renewable fuels standard (RFSII)-a component of the Energy Independence and Security Act of 2007 -mandates the blending of increasing levels of renewable fuels, with an emphasis on cellulosic ethanol and 'advanced' fuels. In order to qualify, producers must use GHG life cycle assessments to demonstrate their fuels meet the RFSII requirement to reduce life-cycle GHG emissions by at least 20% compared to petroleum-based fuels (Congressional Research Service 2007).
Land-based GHG emissions become an important consideration when the product in question (or its production chain) impacts land use. This emerges for biofuels created from agricultural crops. Crop-based biofuels are tightly connected to land use concerns, particularly with their potential to conflict with food production ( GHG LCAs are targeted towards shaping the decision making behind products and production chains. They can therefore be applied at a wide range of scales, and often are a component of multifaceted assessments that include net energy yields or other material impacts (e.g. water). The value of SOM models in these types of applications is to inform better land use decision making (Sheehan et al 2003). However, given the wide diversity of production systems (e.g. varying by scales, types of land use change, crop types), there may be limited data for model calibration and evaluation. For example, SOM model simulations may be coarser for a new type of land management, crop, or region, identifying where additional research or data collection would be valuable. Finer-scaled simulations, or model simulations with a higher level of certainty, may be needed to improve LCAs (Kwon et al 2013), for example to assess the incorporation of biofuels into a complex mosaic of multiple land uses to optimize environmental outcomes (Field et al 2016). Parallels can be drawn between LCA frameworks and the IPCC best practices for GHG inventories, with the emphasis on transparency, acknowledgment of areas of uncertainty, and the creation of an analytical structure where improvements (in model performance or data availability) can be iterated through a LCA to improve accuracy. This is an area where collaborative data sharing and development of data-model networks would yield great benefits.

Conclusions for SOM models in policy
This section demonstrates that the connection between SOM research, SOM model development, and the applications of SOM models in policy depends on: (1) the policy-specific demands on SOM model applications, (2) tolerance for predictive uncertainty in model simulations, and (3) the ability of SOM models to meet these demands based on current understanding of SOM dynamics. SOM model applications in policy are best served by establishing infrastructure that links SOM model applications to the data used to formulate, calibrate, drive, and evaluate model simulations. This is important for transparency. It also creates a more direct connection between model improvements and support for better policy and decision making.

New directions in SOM model development
In this final section we review five areas of recent scientific developments in SOM modeling: microbial roles in SOM stabilization, SOM saturation kinetics, temperature controls on SOM dynamics, deep SOM dynamics, and modeling SOM in ESMs. We selected these five areas as both important to current SOM research and representative of a range of SOM development considerations (e.g. model complexity, scale, uncertainty, data availability). We reviewed each of these areas based on literature selected as representing main scientific developments and/or topics of controversy. Our aim was to connect developments in SOM modeling to specific challenges and considerations in SOM model applications.

Microbial role in SOM stabilization: why does SOM remain in soils, and for how long?
The persistence of OM in soils indicates operation of protective mechanisms that slow or prevent OM decomposition (Hedges et al 2000, Kleber 2010, Schmidt et al 2011. For example, some OM inputs are accessed quickly by soil microbes, mineralized within minutes, hours, or days. Organic matter that becomes protected from microbial activity, e.g. tightly bound to soil minerals within micro-aggregates or more temporarily stabilized within macro-aggregates (Tisdall and Oades 1982, Oades 1984, Golchin et al 1994, Six et al 2004, Pronk et al 2012, Six and Paustian 2014, can remain in soils for years, decades, centuries or millennia (Oades 1988, Jastrow 1996. The net result of complex, interacting stabilization mechanisms is a mixture of organic residues, at different stages of decomposition and varying ages, that potentially react differently to change (Schimel et al 1994, Trumbore 2000. This is a predominant SOM research area (Campbell et al 1967, Jenkinson and Rayner 1977, Parton et al 1987, Oades 1988) that has been subject to numerous reviews (table 2), as it is key to the role of soils in larger-scale processes (e.g. global carbon cycling), as well as their potential to either exacerbate or mitigate climate change (Schimel 1995, Jobbagy and Jackson 2000, Friedlingstein et al 2001. Until recently, mechanisms for SOM stabilization were generally grouped into three categories: (1) physical protection from microbial processes (e.g. through aggregate formation), (2) mineral associations that limit exposure to lytic enzymes, and (3) increasing OM recalcitrance by selective preservation of less biodegradable litter inputs and the formation of complex, stable humic molecules (Sollins et al 1996, Six et al 2002, von Lützow 2008. Physical separation and mineral associations (categories (1) and (2)) continue to be recognized as important SOM stabilization mechanisms (table 2). However, the hypothesis that a large portion of SOM persists through gradual transformation of primary biomolecules into complex secondary 'humic' molecules resistant to decomposition (category (3)) has been challenged. Evidence supports the characterization of SOM as a complex mixture of smaller biopolymers distributed across the soil matrix, rather than as large complex humic molecules  Smith (1979) emerged alongside models using implicit microbial controls, such as the first 'Rothamsted model' of Jenkinson and Rayner (1977). At the time, research came down largely in favor of models employing simple decay kinetics without explicitly including microbial biomass, as those approaches were more successful modeling long-term SOM dynamics (Paustian 1994). However, currently implicit approaches to modeling microbes are criticized for not reflecting new hypotheses for SOM stabilization (Schmidt et al 2011). It is unlikely that a single 'ideal' model will emerge from more explicit connections between microbial mechanisms and SOM persistence. The degree to which microbial mechanisms are integrated into SOM models will likely depend on the scale at which a given model is being used (Stockmann et al 2013). In SOM model applications, care should be taken to use a model most applicable to the scale of the system being evaluated.

SOM saturation: how much OM can soils hold?
Single and multi-pool 1st order decomposition kinetics are a relatively simple SOM modeling approach that performs reasonably well across a diversity of soils and land use changes (Paustian 1994). Mathematically, however, 1st order kinetics implies a constant maximum specific decay rate (i.e., 'k' in figure 2) and thus a linear proportional relationship between OM inputs and the quantity of SOM storage when a soils system is at equilibrium (Stewart et al 2007). This is a reasonable mathematical approach for some theorized mechanisms of SOM stabilization (e.g. Kleber et al 2007). However, field and laboratory research suggest there is an upper limit, or 'saturation Table 2. A selection of SOM reviews.

Publication
Title of review paper and description Oades (1988) 'The retention of organic matter in soils'-clarifies terminology for soil carbon cycling and the linkage between the terms 'humus' and 'biomass'. Emphasis on physical stabilization and soil matrix interaction mechanisms that impact rates at which SOM is mineralized. Sollins et al (1996) 'Stabilization and destabilization of soil organic matter: mechanisms and controls'-a conceptual framework for SOM dynamics aiming to bring together the state of the art in terms of mechanisms underlying SOM stability. Falloon and Smith (2000) 'Modeling refractory soil organic matter'-review of soil organic matter models-including static, dynamic, single compartment, multi-compartment, and non-compartment approaches to modeling SOM with the longest turnover times. Kuzyakov et al (2000) 'Review of mechanisms and quantification of priming effects'-consideration of SOM priming, and its potential to increase or slow SOM turnover rates. Additional: Fontaine et al (2007)-'Stability of organic carbon in deep soil layers controlled by fresh carbon supply ' Six et al (2002) 'Stabilization mechanisms of soil organic matter: Implications for C-saturation of soils'-evaluates mechanisms for SOM protection that have potential for saturation, proposing a fractionation method to evaluate soils for saturation kinetics. von Lützow et al (2006) 'Stabilization of organic matter in temperate soils: mechanisms and their relevance under different soil conditions-a review'-methodical discussion of all SOM stabilization mechanisms occurring in temperature soils, identifying uncertainties and inconsistencies. Questions inherent chemical recalcitrance as a stabilization mechanism. Trumbore (2009) 'Radiocarbon and soil carbon dynamics'-a review of radiocarbon dating as an integrated measure of SOM cycling processes and turnover time over long-term timescales, centered on a state-factor approach to test hypotheses for SOM dynamics and showing differences in cycling dynamics across ecosystem components and timescales. Additional: Paul et al (1997)-'radiocarbon dating for determination of soil organic matter pool sizes and dynamics'. Kleber (2010) 'What is recalcitrant soil organic matter'-complete examination of the term 'recalcitrant' in terms of general, mechanistic, and operational definitions. Examines logic for recalcitrance as a concept, arguing that it is largely semantic rather than providing meaningful connection to SOM dynamics.
level', in the amount of SOM that can be held in soil, determined by its physical characteristics 9 (i.e., texture and mineralogy; Paustian et al 1997, Six et al 2002, Stewart et al 2007, Gulde et al 2008. Models based on 1st-order kinetics will therefore overestimate OM gains (e.g. due to increasing C inputs to soil) in soils that are approaching their saturation point ( figure 4). This is an important consideration for SOM model applications in climate policy, given the potential to overestimate effects of land management intended to increase SOM storage. Six et al (2002) defined three categories of SOM stabilization mechanisms; (1) mineral-associations (termed 'chemical protection'), (2) physical protection through aggregate compartmentalization, and (3) protection through inherent recalcitrance of SOM (termed 'biochemical protection'), with the remaining OM in the 'unprotected' pool. They linked these pools to measurable SOM fractions in order to evaluate the potential for saturation within each fraction and to link these mechanisms to a maximum capacity for total SOM protection (Six et al 2002). The 'biochemically protected' conceptual pool-i.e. complex, recalcitrant humic substances-have been largely dropped from studies evaluating saturation kinetics (following rationale from section 4.1). However, the potential for saturation kinetics to affect bulk SOM storage as well as dynamics between mineral-associated, aggregate protected, and unprotected SOM fractions have continued to be developed (Dungait et al 2012).
In experimental research, bulk soils have been evaluated to determine how close experimental soils are to their saturation capacity (Zhang et al 2010, Heitkamp et al 2012, with long-term studies suggesting a distinction between the absolute maximum capacity of soils to stabilize C versus a soil's 'effective stabilization capacity' given external factors such as disturbance by tillage (Balesdent et al 2000, Stewart et al 2007). Several studies used the Six et al (2002) framework to successfully evaluate soils for saturation behavior (Stewart et al 2008b(Stewart et al , 2009. Other studies supported a hierarchy in SOM saturation, showing increasing OM inputs leading to SOM accumulation in labile, faster cycling fractions once mineral fractions were saturated (Gulde et al 2008, Castellano et al 2012). Concentration of SOM in the more labile pools due to saturation of more stable SOM pools are a concern for managing soils to increase SOM storage, as SOM in labile fractions are at greater risk for loss (Stewart et al 2012). One study suggested management practices to increase SOM storage should target soils with greater initial SOM deficits (Stewart et al 2008a), while another supported the need to intervene before soils reach a degradation threshold when stabilization mechanisms begin to decline (Kimetu et al 2009). 9 If organo-mineral complexation is a predominant mechanism for SOM stabilization in soils (section 4.1), then it follows that the existence of a finite mineral surface-area would imply a finite amount of organic matter capable of being stabilized.
Saturation capacity for SOM is conceptually well defined, simple (on its own) to express mathematically, and increasingly supported by experimental evidence. It is notable, then, that saturation kinetics have not been widely invoked in SOM models, with only a few examples since the Six et al (2002)  A key challenge in modeling SOM saturation is determining the maximum capacity for a given soil to store SOM. If a SOM model is based on measurable soil fractions, SOM maximum storage could be calculated based on soil chemistry or an empiric relationship observed at a specific site. However, for SOM models based on conceptually-defined SOM pools, maximum SOM storage is more difficult to link to measurable data.
Until SOM saturation kinetics can be appropriately implemented in SOM models, the potential for bias in SOM models based on kinetically-defined SOM pools should be recognized in SOM model applications aimed towards increasing SOM storage. High OM soils in systems with high OM inputs are vulnerable to overestimation of SOM storage and accumulation, when simulated using conventional first-order decay SOM models.
4.3. Temperature controls on SOM: Will temperature change make SOM increase or decrease? Temperature is a key driver of SOM dynamics. This has been long established (Jenny 1941), and is not in dispute. However, in the last two decades debate has surrounded how SOM dynamics respond to temperature change (figure 5), motivated in part by the importance of understanding whether soils will become a stronger sink or source of CO 2 as temperatures increase under global climate change (Kirschbaum 1995, Trumbore et al 1996. Uncertainty in this area of SOM research is driven by the fact that temperature effects are difficult to isolate, and behaviors observed in controlled laboratory incubations are often less consistent and/or less discernible under more realist in situ experiments 10 (Kirschbaum 2000). At a micro-scale, for example, microbial decomposition processes are strongly affected by temperature in their immediate environment This is an ideal area for SOM models to integrate and test hypotheses (Kirschbaum 1995, Jones et al 2003. Modeling approaches take the general form of defining a temperature response curve and associating it with a rate parameter that regulates SOM dynamics (e.g. figure 5). Differences in temperature sensitivity are reflected by either changing the shape of a temperature response curve (e.g R 1 versus R 2 , figure 5), or having specific temperature response curves associated with specific SOM pools. There is no one universal mathematical expression of temperature response curves, although some have been shown superior to others 11 (Tuomi et al 2008).
Regardless of modeling approach, the mathematical expressions for temperature responses are linked to the underlying hypotheses for SOM structure (e.g. based on kinetically defined pools versus measured soil fractions). This creates the potential for wide variety in predictions of SOM responses to temperature change, leading to extensive debate. For example, one hypothesis proposed that 'labile' and 'recalcitrant' Figure 5. Hypothetical decomposition response curves with increasing temperature. The ΔR 2 is larger in magnitude than ΔR 1 over the same temperature interval, showing the greater temperature sensitivity of R 2 versus R 1 . SOM fractions have different temperature sensitivities, with the latter being more sensitive than the former. This hypothesis was originally connected to a model now called the carbon quality-temperature theory (Fierer et al 2005), based on the concept that SOM decomposition dynamics were determined by substrate quality, via the number of enzymatic steps-and therefore the total free energy change-required to mineralize organic matter carbon 12 . An argument against this theory suggested old SOM is less temperature sensitive than newer litter, leading to less carbon loss and even some carbon gain with increasing temperatures (Liski et al 1999). However, this argument was criticized for the assumption of fixed residence times in the pools used to model SOM and temperature effects on respiration (Ågren 2000). Subsequent studies have proved to be inconclusive for the temperature sensitivity of different SOM pools , and a high level of uncertainty remains on this theory. However, it has been argued as largely irrelevant for mineralassociated SOM and SOM that is cycling more slowly (Kleber 2010, Conant et al 2011, as older SOM is not necessarily more thermodynamically stable or chemically different than 'newer' SOM (Kleber et al 2011).
This debate demonstrates the importance of the linkage between hypotheses for temperature responses on SOM dynamics and underlying SOM model formulations. For example, some widely used SOM models like CENTURY and DNDC may not directly reflect hypotheses for temperature-sensitive mechanisms 12 The carbon quality-temperature theory predicts greater temperature sensitivity in low quality substrates compared to high quality substrates, as well as greater temperature sensitivity at low temperatures versus high temperatures (Bosatta and Ågren 1999). Based on the assumption that 'old' SOM is more chemically complex and a poorer microbial substrate than 'new' SOM, this made a logical linkage to the hypothesis that 'older' (i.e. more stable, 'recalcitrant') SOM will be more sensitive to temperature than 'newer' (i.e. less stable, 'labile') SOM. due to their basis on kinetically-defined SOM pools (Dungait et al 2012). Kinetically-based SOM models are commonly implemented in ESMs, often using Q 10 functions to simulate temperature sensitivity (Todd-Brown et al 2013). This approach has been strongly criticized (Davidson et al 2006, Tang and Riley 2015), and shown to perform poorly simulating tropical and arctic ecosystems where climate change is of particular concern (e.g. Koven et al 2011). Researchers are beginning to explore more mechanistic approaches, based on understanding of factors such as substrate diffusion, enzyme activity, membrane transport, and microbial community dynamics (Grant et al 2003, Davidson et al 2006. Other recent models include mechanistic linkages to a wider array of SOM pools, for example differentiating between processes that make SOM available for decomposition (e.g. physical protection and aggregate turnover) versus processes that decompose SOM once it is available (e.g. microbial enzyme dynamics, depolymerization, figure 6) (Conant et al 2011). However, it is not yet clear if these modeling approaches lead to improved predictions at larger scales.
The impact of temperature change on SOM dynamics is likely to remain an area of SOM research with high uncertainty. For SOM model applications, this means care should be taken that the formulation of temperature responses in a given SOM model is empirically reflective of the system being assessed, even as the mechanistic understanding behind those responses are imprecisely understood. In systems where SOM model simulations perform poorly, temperature responses may be an area to consider models using different approaches. Greater standardization and clarity in how experimental data are reported and interpreted would support better integration with modeling efforts (Subke and Bahn 2010). Further experimental exploration of temperature-sensitive decomposition mechanisms-particularly including large-scale studies that cross a range of ecosystem types 4.4. Deep soil dynamics: can subsurface soils be managed to store OM? Soils can range in depth from a few centimeters to many meters. Our use of the term 'deep soil' refers to everything below the surface soil layer, which is typically considered to extend from 0 to 20 or 30 cm. Surface soils generally contain a large fraction of total SOM, in addition to SOM that is often younger, more rapidly cycling, more uniform (particularly in tilled agricultural soils), and more responsive to management perturbations than SOM in deeper soil layers (Scharpenseel et al 1989, Batjes 1996, Jobbagy and Jackson 2000. Historically, SOM in subsurface soil layers were thought to consist mainly of relatively inert humic material and mineral-bound OM. Consequently many SOM models only simulate dynamics in surface soil layers. However, while mineral-bound OM remains supported as a stabilization mechanism in subsurface soils (Rumpel and Kögel-Knabner 2010), more recent analyses show SOM in deeper layers to consist predominantly of highly processed microbial products ( Subsurface SOM dynamics involve similar mechanisms to surface soils, but with the potential for time lags and differences in soil environments that may separate subsurface and surface SOM responses to change (Fierer et al 2003a, Salomé et al 2010, Sanaullah et al 2011. A review by Rumpel and Kögel-Knabner (2010) provides a framework for recent experimental work focusing on subsurface SOM dynamics. They summarized key organic matter inputs to deeper soil layers as (1) the movement of dissolved organic matter (DOM) with water, (2) root growth, exudates, and turnover, and (3) physical OM transport through bioturbation or physical soil processes. Mechanisms that destabilize SOM in subsurface soils include aggregate disturbance and increases in microbial access to nutrients and labile carbon. Mechanisms that stabilize SOM in these layers are linked to mineral associations and the physical separation between dispersed microbes and SOM at depth. The relative importance of these factors is likely variable across ecosystems (Jobbagy and Jackson 2000, Schmidt et al 2011).
Experimental evidence for the interaction of stabilization and destabilization mechanisms in subsurface soils remains scarce, particularly from in situ field experiments (Rumpel and Kögel-Knabner 2010). Dissolved organic matter (DOM) is perhaps the best understood subsurface SOM input, known to cycle rapidly and play an important role linking surface OM with deep soil mineral fractions, SOM stabilization, and the potential for SOM long-term storage (Fröberg et al 2009, Rumpel and Kögel-Knabner 2010). The quantity and quality of DOM from different parts of the soil profile can also serve as a metric for sorption, desorption, decomposition and leaching processes, as they interact with soil minerals, pH, litter, and hydrology (Kalbitz et al 2000). For any OM input, physical separation from microbes-as opposed to inherent OM chemical resistance to decomposition -has received widespread experimental support as an important stabilization mechanism ( Models of subsurface SOM dynamics are accordingly diverse and can be highly complex, particularly simulating multiple soil layers and dynamic movement of material between them (table 3). The Community Land Model (CLM), for example, was modified to simulate subsurface SOM dynamics using a vertical cascade approach, where SOM passes through layers in the soil profile with loss at each transition (Koven et al 2013). However, some models aim for simplicity; the DAYCENT model was modified to simulate deeper soil C dynamics by slowing SOM pool turnover and increasing allocation to passive soil C, without separating soil layers (Wieder et al 2014b), while the C-TOOL model took a practical approach by simplifying assumptions and solely focusing on whole-soil SOM dynamics in agricultural systems (Taghizadeh-Toosi et al 2014). Subsurface SOM models vary in explicitly or implicitly simulating DOM movement (table 3). Root inputs tend to show more consistency in mathematical approaches, often simulated using exponential functions (table 3), although one study argued for modifying models to accept root distribution data directly (Iversen 2010). Bioturbation has been shown to be largely inconsequential compared to other input and transport mechanisms (Braakhekke et al 2013). Overall there is strong need for additional data to confirm or refute testable hypotheses suggested by different modeling approaches.
Recent research on subsurface SOM dynamics still only reveals pinpoints of understanding in a complex belowground system. Logistical challenges and lack of data are profoundly limiting. In this context, perhaps even more so than in other areas of SOM research, integration between experimental research and SOM model development is needed to advance understanding. For example, carbon isotope labeling and tracers are emerging as particularly important tools for subsurface SOM research, by allowing for OM dynamics to be observed with minimal disturbance. There is also likely value in using other, non-carbon tracers with known dynamics and interactions with SOM. For example, the use of 210 Pb ex was able to inform SOMPROF model parameters, although use in addition with 14 C or other carbon labeling was suggested as a more powerful approach (Braakhekke et al 2013). Given logistical challenges in studying subsurface soils, collaborative efforts between modelers and experimental researchers are needed identify, understand, evaluate, and predict SOM dynamics in soils below the 20-30 cm boundary that delineates much of our current understanding.
From the perspective of SOM model applications, this is an area of development that has the potential to add entirely new areas of consideration in predicting the SOM impacts of land management. It also could add the capacity to manage soils more effectively for long-term carbon storage, which is of high value in efforts to mitigate climate change. Policy efforts that involve SOM model applications could likely yield high value from supporting SOM data collection and model development efforts to better represent dynamics in subsurface soils.
4.5. SOM in global models: will soils contribute to or mitigate climate change? As the largest terrestrial ecosystem carbon pool (Jobbagy and Jackson 2000), soils play an important role in determining global land-based carbon cycling and land-atmosphere carbon interactions. Models of SOM are accordingly needed in ESMs to dynamically link atmospheric carbon, climate change effects, and land-based carbon storage (Falloon and Smith 2000, Wieder et al 2014a. However, the inclusion of SOM models in ESMs present new challenges in SOM model development and validation, due to uncertainty, variability, and uneven coverage in data needed to drive and evaluate SOM model performance at such large scales. Dynamic modeling of terrestrial carbon cycling in ESMs appeared in the 1990s, when the mechanistic representation of photosynthesis and stomatal conductance (e.g. implementing the model from Farquhar et al 1980) created a dynamic linkage between the atmospheric carbon cycle and terrestrial net primary productivity (NPP), allowing carbon movement to be simulated through other terrestrial ecosystem processes (Pitman 2003). For the sake of simplicity, initially ESMs simulated climate change effects on soils separately from climate forecasting models (Jenkinson et al 1991, Schimel et al 1994. Subsequent coupled atmospheric and terrestrial carbon cycling models predicted the potential for soils to accelerate climate change (Friedlingstein et al 2001), with the effects of increased CO 2 concentrations on photosynthesis being surpassed by temperature effects on soil respiration (Cox et al 2000). Following this, ESM simulations and multi-model comparisons included some form of SOM modeling, varying in the number of soil pools but generally using 1st order kinetics (Sitch et al 2003, Krinner et  Multi-model comparisons of ESMs are needed to evaluate SOM modeling approaches, using validation datasets that range from regional to global scales. A number of ESM model comparisons, parameter validation, and benchmarking projects are ongoing (table 4) (Luo et al 2012), with organizations like the world climate research programme providing resources to support project development. Researchers have repeatedly recognized that development and application of ESMs is fundamentally an interdisciplinary effort (Bonan et al 2002, Pitman 2003. Given the importance of climate change prediction across temporal and spatial scales, alongside the increasing sophistication in developing and evaluating climate change scenarios for mitigation and adaptive measures (Moss et al 2010), we would like to emphasize the importance of this area of research and the need for collaboration between ESM researchers, SOM model developers, and SOM field and laboratory researchers alike to advance predictive abilities. Expanding the network of scientists involved in projects like the coupled model intercomparison project (CMIP5) could lead to more rapid advances in understanding climate-soil interactions in the context of the global carbon cycle, in addition to supporting better predictions of future climate change.
In SOM model applications, this is an area of SOM model development likely most relevant for policies at regional and national scales. In particular, ESMs may help identify areas where SOM model performance is poor or biased in the context of observed OM patterns at large scales. This may help identify regions where SOM model applications need to be adjusted based on

Conclusions
Our aim for this review was to connect the current state of SOM model developments to the expanding application of SOM models in policy. We see SOM modeling as entering an exciting time. New measurement methods reveal new insights for the relationship between SOM's chemical nature, spatial distribution, and dynamics in the soil environment. Advances in computational capacity and development of collaborative networks for data sharing, management, and data-model integration increasingly relieve the bottlenecks in advancing the conceptual understanding of SOM. These efforts provide better environments to apply SOM models and test hypotheses for SOM dynamics across scales. Within this context there is also room for more openly sourced involvement in model-data integration. Data management is an increasingly sophisticated branch of research. Particularly for US federally funded efforts, projects must make data management and the open provision of data a component of proposals and final products from research efforts. Libraries are developing capacity to house citable datasets, with standardized approaches to metadata and organizational structure.
We believe data-model integration has only touched the surface of what is feasible, given more openly source collaborative networks of data sharing and model-data integration.
We also see the potential for SOM model applications in policy to provide an opportunity for establishing repeatable SOM modeling computational infrastructure, as well as a platform to standardize inputs, model references, and output streams. Policy applications of SOM models could support this by including sufficient metadata to repeat analyses, for example identifying the SOM model type and version, as well as the data used to drive the model and evaluate its uncertainty. Ideally SOM model applications would also be integrated within computation infrastructure with some level of open access, allowing model applications to be improved, or tested against new model versions and additional data. From the model development perspective, collaboration with model application efforts would add value by providing a standardized testbed to evaluate model improvements. This would allow SOM model developments to be more easily incorporated into model applications, better supporting policy and decision making.  Porporato (2009). In those cases, titles were searched on Web of Science individually. Where they still could not be found, the citation number listed with that publication title on Google Scholar was recorded. The Google Scholar value is likely inflated relative to the WoS Core Collection value, but was used as a proxy only when no better record could be found on WoS.

A2. Adjusted searches for SOM model use: 87 named models
While the search string of 〈model name〉 AND 'soil' AND 'model' on WoS in the Core Collection worked well for unique model names, there were challenges posed by models with non-unique names. A selection of citations were evaluated in each set of search results to confirm the search yielded the specific model name of interest. When results failed to yield the model of interest, the search was either refined or manually searched to identify model publications. In some instances this yielded the targeted results. However, in others refining was ineffective, the number of results very high (100's to 1000's), and the overall citation record for the original model publication too small to warrant manual search. For example, short model names (e.g. ELM, GEM, TCS) often were used as acronyms across many fields. If the long names of the models were similarly composed of ubiquitous terms (e.g. 'ecosystem level model', 'grassland ecosystem model', 'terrestrial carbon sequestration'), it was not easily possible to isolate citations using the full name as a search term. Thirteen named models were excluded for this reason. Total citations yielded by these searches for the remaining 74 named models were used as a comparative measure for model uses in the scientific literature. The exclusion of models due to non-unique names suggests the potential importance of unique model names as an identifier to trace model development and uses in scientific literature.  Table A1. Complete list of all publications and named models (where model names were given) considered in the analyses for section 2.2.

Publication
Model Name Publication Model Name