The biogeochemical processes that govern soil organic matter (SOM) formation and persistence impact more than half of the terrestrial carbon (C) cycle and thus play a key role in climate–C feedbacks (Jones and Falloon, 2009; Arora et al., 2013). In order to predict changes to the C cycle, it is imperative that mathematical models describe these processes accurately. However, most ecosystem-scale biogeochemical models represent SOM dynamics with first-order transfers between conceptual pools defined by turnover time, limiting their capacity to incorporate recent advances in scientific understanding of SOM dynamics (Campbell and Paustian, 2015). Due to the use of conceptual pools, empirical data from SOM fractionation cannot be used directly to constrain parameter values that govern fluxes between pools because diverse SOM compounds can have similar turnover times but are differentially influenced by environmental variables (Schmidt et al., 2011; Lehmann and Kleber, 2015). As a result, empirical data are commonly abstracted and transformed before being used to parameterize or evaluate the processes of SOM formation and persistence that the model is intended to simulate (Elliott et al., 1996; Zimmermann et al., 2007). This has resulted in many conventional SOM models (e.g. RothC, Jenkinson and Rayner, 1977, DNDC, Li et al., 1992, EPIC, Williams et al., 1984, and CENTURY, Parton et al., 1987) being structurally similar (i.e. partitioning total SOM into discrete pools based on turnover times determined from radiocarbon experiments; see Stout and O'Brien, 1973, and Jenkinson, 1977) but each taking different approaches to simplify the complex mechanisms that govern SOM dynamics. Consequently, simulations of SOM can vary greatly between models, often predicting contrasting responses to the same driving inputs and environmental change (e.g. Smith et al., 1997).

Structuring SOM models around functionally defined and measurable pools that result from known biogeochemical processes is one way to help minimize these discrepancies. Two recent insights into SOM dynamics present a path towards addressing this issue. There is now strong evidence that (1) low molecular weight, chemically labile molecules, primarily of microbial origin (Liang et al., 2017), persist longer than chemically recalcitrant C structures when protected by organo-mineral complexation (Mikutta et al., 2006; Kögel-Knabner et al., 2008; Kleber et al., 2011); and (2) each soil type has a finite limit to which it can accrue C in mineral-associated fractions (i.e. the C-saturation hypothesis) (Six et al., 2002; Stewart et al., 2007; Gulde et al., 2008; Ahrens et al., 2015). Structuring an SOM model around these known and quantifiable biogeochemical pools and processes has the potential to drastically reduce uncertainty by enhancing opportunities for parameterization and validation of models with empirical data. Furthermore, mechanistic models can have value in process explanation as well their value in predictive capabilities; such models can pinpoint the processes that have the greatest influence on a system even when they are not traditionally determined empirically.

Conventional SOM models readily acknowledge the importance of microbes in plant litter decomposition and SOM dynamics, but model improvement was initially constrained by the concept that stable SOM included “humified” compounds (Paul and van Veen, 1978). This quantified stable SOM using an operational proxy (high pH alkaline extraction) rather than relating stabilization to the mechanisms that are now widely recognized, such as organo-mineral interactions and aggregate formation (Lehmann and Kleber, 2015). As our contemporary understanding of stable SOM moves away from humification theory, so too must the way we represent SOM stabilization pathways in biogeochemical models. Similarly, many SOM models partition plant residues into labile and recalcitrant pools with turnover times that reflect the assumption of selective preservation (i.e. chemically recalcitrant litter-C is only used by microorganisms when labile compounds are scarce). While many existing models do include a flux from labile residues into stable SOM, this is typically a much smaller absolute amount than the flux from recalcitrant residues. Evidence indicates that biochemically recalcitrant structural litter C compounds may not be as important in the formation of long-term persistent SOM as originally thought (Marschner et al., 2008; Dungait et al., 2012; Kallenbach et al., 2016). Instead, they form light particulate organic matter (POM) (Haddix et al., 2015), a relatively vulnerable fraction of SOM with a turnover time of years to decades (von Lützow et al., 2006, 2007). Consequently, there have been several calls to represent this new understanding and re-examine how microbial activity is simulated in SOM models (Schmidt et al., 2011; Moorhead et al., 2014; Campbell and Paustian, 2015; Wieder et al., 2015).

Current conceptual frameworks more clearly link the role of microbes to SOM dynamics (e.g. Cotrufo et al., 2013; Liang et al., 2017) and generally isolate two discrete litter decomposition pathways for SOM formation (Cotrufo et al., 2015): a “physical” path through perturbation and cryomixing that moves fragmented litter particles into the mineral soil forming coarse POM and a “dissolved” path, through which soluble and suspended C compounds are transported vertically through water flow and, when mineral surfaces are available, form mineral associated organic matter (MAOM). Microbial products and very small litter particles can be transported by both pathways, forming a heavy POM fraction with “biofilms” and aggregated litter fragments around larger mineral particles (i.e. sand; Heckman et al., 2013; Ludwig et al., 2015; Buks and Kaupenjohann, 2016). Attempts to formulate these empirical observations of litter decomposition into mathematical frameworks recently culminated with the development of the LIDEL model (Campbell et al., 2016), which in turn built upon the relationships of litter decomposition described by Moorhead et al. (2013) and Sinsabaugh et al. (2013). While the LIDEL model was evaluated against a detailed lab experiment of litter decomposition (Soong et al., 2015), it does not simulate SOM pools and dynamics. In nature, litter decomposition processes and SOM formation processes are necessarily coupled but are often studied and modelled separately. However, models that link litter decomposition to SOM formation are required to represent SOM dynamics in ecosystem models.

Beside the processes of leaching and fragmentation that control the two pathways mentioned above, litter decomposition processes that form SOM are governed by the balance between microbial anabolism and catabolism (Swift et al., 1979; Liang et al., 2017). A recent paradigm has emerged that emphasizes the role of microbial life strategies (e.g. K vs. r, referring to copiotrophic and oligotrophic microbial functional groups) and carbon use efficiency (CUE) in the formation of SOM from plant inputs (Dorodnikov et al., 2009; Cotrufo et al., 2013; Lehmann and Kleber, 2015; Kallenbach et al., 2016). As a result, scientists have explored several approaches to represent microbes in SOM models. Research has indicated that explicitly representing microbes in an SOM model can provide very different predictions of SOM dynamics and include important feedbacks such as acclimation, priming and pulse responses to wet–dry cycles (Bradford et al., 2010; Kuzyakov et al., 2010; Lawrence et al., 2009; Schmidt et al., 2011). This research has shown that, compared to conventional models, microbially explicit SOM models have drastically different simulated responses to environmental change (Allison et al., 2010; Wieder et al., 2015; Manzoni et al., 2016). However, these responses are generally validated against data on microsite spatial scales and are not necessarily generalizable over larger spatial scales (Luo et al., 2016).

Microbes have been explicitly represented in SOM models in many ways and for many years, from relatively simple approaches using a single microbial biomass pool or fungal:bacterial ratios (e.g. McGill et al., 1981; Wieder et al., 2013; Waring et al., 2013) to more complex associations with microbial guilds or community dynamics based on dominant traits derived through genetic profiling (Miki et al., 2010; Allison et al., 2012; Wallenstein and Hall, 2012). The MIcrobial-MIneral Carbon Stabilization (MIMICS) model (Wieder et al., 2014) consolidated existing research at the time and uses the size of a microbial biomass pool together with Michaelis–Menten kinetics to feedback on C decay rates of SOM pools. While the MIMICS model and others (for an example see Manzoni et al., 2016) provide a potentially viable framework for explicitly representing microbes in an SOM model, it remains unclear whether this is practical given the lack of input data required to drive and validate these relationships (Treseder et al., 2012; Sierra et al., 2015). Furthermore, parsimony and analytical tractability are both key concerns for ecosystem models designed to operate over large spatial and temporal scales. While microbially explicit models may be essential for addressing research questions on small spatial scales, they may introduce unnecessary, additional uncertainty to global simulations (Stockmann et al., 2013).

While microbial efficiency largely controls SOM formation rates, and microbial products are major components of the MAOM and the coarse, heavy POM fractions of SOM (Christensen, 1992; Heckman et al., 2013) the long-term persistence of SOM is determined by mineral associations that are subject to saturation. Saturation limits for SOM were proposed more than a decade ago (Six et al., 2002) and have been supported by several empirical studies (e.g. Gulde et al., 2008; Stewart et al., 2008; Feng et al., 2012; Beare et al., 2014). Briefly, the concept of C saturation suggests that each soil has an upper limit to the capacity to store C in mineral-associated (i.e. silt + clay <53 µm) fractions due to biochemical and physical stabilization mechanisms (e.g. cation bridging, surface complexation and aggregation) that are limited by a finite area of reactive mineral surfaces. While saturation kinetics are easy to define conceptually (Stewart et al., 2007), C saturation as a concept has been adopted by only a few SOM models (Struc-C, Malamoud et al, 2009; COMISSION, Ahrens et al., 2015; Millennial, Abramoff et al., 2017). This is partly because its use in an SOM model requires a robust estimate of the specific site's saturation capacity. SOM saturation has been modelled using (i) empirical regressions between silt + clay content and C concentration of that fraction (Six et al., 2002, as applied in COMISSION), and (ii) empirical relationships between clay content and the derived Q max parameter of Langmuir isotherm functions (Mayes et al., 2012, as applied in Millennial). As noted by Ahrens et al. (2015), the use of C-saturation kinetics in an ecosystem model would require a map of mineral-associated C saturation capacity, and since soil C stocks in silt + clay fractions can make up the majority of total soil C stocks, a lot of weight would be put on that single driving variable for each site. However, it is worth noting that, when applying C-saturation concepts, only the mineral-associated organic matter (MAOM) fraction saturates. Other SOM fractions (e.g. particulate organic matter, POM) theoretically have no saturation limit (Stewart et al., 2008; Castellano et al., 2015).

Attempts to consolidate the concepts of microbial control on litter decomposition and mineral control on SOM stabilization resulted in the MEMS framework (Cotrufo et al., 2013). To date, we are aware of only one attempt to represent MEMS within a mathematical model, the Millennial model (Abramoff et al., 2017). However, this model does not simulate litter decomposition explicitly and as a result does not include the impact of litter input chemistry, which is a fundamental component of the MEMS framework and needed to improve ecosystem modelling, as discussed previously.

In this study we describe and demonstrate the application of a new mathematical model (MEMS v1.0) that applies three major concepts of SOM dynamics: (1) litter input chemistry-dependent microbial CUE informing SOM formation (Cotrufo et al., 2013), (2) separate dissolved and physical pathways to SOM formation (Cotrufo et al., 2015), and (3) soil C saturation related to litter input chemistry (Castellano et al., 2015). The scope of this inaugural model description is limited to representing these three concepts and is not intended to include every mechanism relevant to SOM cycling. Our objective is to demonstrate the benefits of structuring an SOM model around key biogeochemical processes rather than turnover times. Using measured SOM physical fractions from 154 forest and grassland sites across Europe, key parameters were optimized to improve model performance when simulating POM-C (consisting of both light and heavy POM) and MAOM-C under equilibrium conditions. The resulting model was then used to test whether the behaviour of simulated SOM dynamics concur with the expected theoretical relationships. Finally, the model performance in predicting soil C stocks at equilibrium was evaluated by simulating 8192 forest and grassland sites across Europe, representing a diverse set of driving variables (i.e. climate, soil type and vegetation type).