03.SOC_Modelling.rmd

# | SOC Modelling 
Modelling is an approach used to infer SOC stocks and distributions in conditions where they have not been measured, such as: under future climatic conditions, at locations or regions where no measurement exists, for management scenarios that have not yet been implemented (FAO, 2019). In the last decades, a number of numerical models have been developed, including mathematical representations that quantitatively describe soil characteristics and processes. The breadth of these approaches can be illustrated by the recent compilation of 90 mathematical models describing SOC changes and biogeochemical related soil processes developed in the last 80 years (Falloon and Smith, 2009; Manzoni and Porporato, 2009; Campbell and Paustian, 2015). However, according to their structure, number of input variables required and temporal and spatial resolution, not all available C models are suitable for all studies (Manzoni and Porporato, 2009). 

## Process-oriented models
Among the different types of SOC models, process-oriented multicompartment models have been dominant in efforts to simulate changes in SOC in agricultural lands, grasslands and other production systems (Stockmann et al., 2013).
Process-oriented models are built considering the processes involved in the transfer of SOC across the soil profile and its transformations (Smith et al., 1998). They are generally used to predict SOC dynamics based on different conceptual C pools or compartments that alter in size via decomposition rates and stabilization mechanisms (each compartment or pool being a fraction of SOC with similar chemical and physical characteristics; Stockmann et al., 2013). Models belonging to this class can potentially have a variable degree of complexity, from one compartment to multiple compartments (Jenkinson et al., 1990). Early models simulated SOC as one homogeneous compartment (Jenny, 1949). Beek and Frisel (1973) and Jenkinson and Rayner (1977) proposed two-compartment models, and as computational tools became more accessible, multi-compartment models were developed (McGill, 1996). 

According to Falloon and Smith (2009), decay rates $k$ are usually expressed in this type of models by first-order kinetics with respect to the concentration $C$ of the pool:  
\begin{equation}
\tag{3.1}
\frac{dC}{dt} =- kC 	
\end{equation}

The flows of carbon within most models represent a sequence of carbon going from plant and animal debris to the microbial biomass and then, to soil organic pools of increasing stability. The output flow from an organic pool is usually split. It is directed to a microbial biomass pool, another organic pool and, under aerobic conditions, to CO~2~ . This split simulates the simultaneous anabolic and catabolic activities and growth of a microbial population feeding on one substrate. Two parameters are generally required to quantify the split flow, often defined as a microbial (utilization) efficiency and a stabilization (humification) factor, which control the flow of decayed carbon to the biomass and humus pools, respectively.

## Examples of process-oriented models
CENTURY ( Parton, 1996), RothC (Jenkinson et al 1990; Coleman and Jenkinson, 1996), SOCRATES (Grace et al., 2006), DNDC (Li, 1996), CANDY (Franko et al., 1997), DAISY (Hansen et al., 1991), NCSOIL (Hadas et al., 1998) and EPIC (Williams et al., 1983; 1984) are known examples of this kind of process-oriented multicompartment models. They have been developed and tested using long-run data sets, and in general they show a good ability to predict SOC dynamics over decades across a range of land uses, soil types and climatic regions (Smith et al., 1997). As mentioned before, process-oriented models can be combined with GIS software, giving a modelling platform well suited for global, national, and regional scale studies  (e.g. Smith et al. 2005; Milne et al., 2007; Kamoni et al., 2007; Falloon et al., 2007; Gottschalk et al., 2013; Lugato et al., 2014).
The review by Campbell and Paustian (2015) emphasizes the fact that among these known process-oriented models, no one clearly outperforms the others. The increase in multi-model comparison publications in the last decades shows the lack of consensus in SOC modelling approaches. It is also noteworthy that among these multi-model comparisons, there was no single model identified with conclusively higher performance capacity. For a detailed comparison between some of the most used SOC models refer to Campbell and Paustian (2015).

However, in order to obtain consistent results in SOC sequestration estimates at a global scale, and to allow comparisons between countries and regions, the use of a standard 'process-oriented' SOC model, following standardized procedures is required in this first step.
The Rothamsted soil organic carbon model (RothC; Coleman and Jenkinson, 1996, Chapter 4) is proposed as the standard comparison model in this Technical Manual, for the following reasons:

*   It requires less and more easily obtainable data inputs when compared to other process-oriented models 
*   It has been applied using data from long-term experiments across several ecosystems, climate conditions, soils and land use classes;
*   It has been successfully applied at national, regional and global scales; e.g. Smith et al. (2005), Smith et al. (2007), Gottschalk et al. (2012), Wiesmeier et al. (2014),  Farina et al. (2017),  Mondini et al. (2018), Morais et al.(2019);
*   It (or its modified/derived version) has been used to estimate carbon dioxide emissions and removals in different national GHG inventories as a Tier 3 approach; according to the latest review by Smith et al. (2020): Australia (as part of the FullCam model, Japan (modified RothC), Switzerland, and UK (CARBINE, RothC).  

The following Chapter describes the RothC model and its general requirements. Users are nevertheless encouraged to use modified versions of the RothC model (e.g. Farina et al., 2013) if it has been demonstrated that these versions improve estimations under local conditions. Users are also encouraged to provide supplementary SOC sequestration maps developed using alternative preferred SOC models and procedures. The use of a multi-model ensemble approach (e.g. Riggers et al, 2019; Lehtonen et al., 2020) with selected models is intended for future versions of the GSOCseq map.