ANALYSIS OF SOIL ORGANIC MATTER TRANSFORMATION DYNAMICS MODELS

In this paper we consider the models describing the dynamics of soil organic matter transformation. The results of practical implementation of the ROMUL, CENTURY and ROTHAMSTED models are presented. These models propose theoretical approaches to the modelling of organic remains transformation based on describing physicochemical processes during humus formation with differential relations. Following the analysis, their strengths and weaknesses have been distinguished.


Introduction
Soil is one of the most fundamental parts of the earth's ecosystem. It carries out unique functions in the turnover of biological elements. Specifically, in the soil the organic matter of dead organisms and their lifelong excretions is mineralized. Part of organic substance settles in the soil as humus, which ensures the sustainability of ecosystem and facilitates its renewal after natural and artificial disruptions. Therefore, the study of organic matter formation in the soil is a priority issue of dynamical soil systems modelling. Model of dynamical soil organic matter formation can be logically included into other ecosystem model as a basic component. It should be noted that the majority of existing ecosystem models do not consider soil processes that govern the productivity of photosynthetic organisms by reactive coupling of nutritive compounds incoming from the soil and physical environment optimization [4].
Soil is a highly complex object for modelling. It is quite difficult to describe adequately all dynamical processes taking place in the soil and determine relations between the coefficients of organic matter transformation. Two principal processes occurring in the soil can be distinguished: soil organic matter mineralization and it humification. Transformation of organic remains is occurring by the means of microorganisms, reductionoxidation processes, destruction, mineralization, hydrolysis and humification of organic matter.
Most of the models describing the transformation of organic remains differ by the ways of considering different organic profiles, representation of certain types of destructor organisms, and different transformation processes.
Modelling of organic matter formation in the soil is usually conducted in one of the two approaches. The first approach represents soil as a mixture of different organic compounds, where the transformation of organic remains depends on temperature, moisture and acidity degree. The well-known models realized in computer programs are ROMUL [2] and CENTURY [9]. Another approach does not separate organic remains into components, and is based on the integral description of the transformation. In this case, an essential role is played by the microorganismsdestructors of the organic matter. Their activity depends on the dynamics of nutritive compounds, especially on the nitrogen content in the soil (e.g. ROTHAMSTED model) [6].
The developed models are adequately imitating the soil system functioning. Although there exists a great number of soil dynamics models, they still require further theoretical justification, improvement of model structure, preparation and arranging of input data.
The model allows to calculate dynamics of soil organic matter formation and the quantity of mineral nitrogen. It is assumed in the model, that the litter can be separated into various cohorts characterized by a particular position in the soil, ash, and nitrogen content.
Principal organic matter destruction and mineralization processes are related to the vital activities of microorganisms, that are forming distinct types of humus (mor, moder and mull) on each level.
The general assumption on the model involves the sequence of correlated changes in destructor organisms during the decay of organic matter. Quantity and species composition of destructor organisms depend on biochemical properties of leaf litter, hydrological and heat conditions. The rate of nutrients release due to mineralization corresponds to the rate of organic matter mineralization. The model assumes destructor organisms spend 20% of nitrogen on the complex of humic compounds, and 80% on the humus formation.
The process of complex organic matter mineralization in the soil layers can be described by the following system of differential equations:  (2) describes the nitrogen formation in the litter layer. Equation (3) governs organic matter transformation in the layers that are not decomposed by belowground cohorts. Equation (4) governs nitrogen formation in the layers that are not decomposed by belowground cohorts. Equation (5) governs humic compounds content in the belowground soil layer. Equation (6) determines the quantity of humic compounds coming from aboveground cohorts and corresponds to nitrogen content in the soil. Equation (7) calculates the quantity of humic compounds coming from belowground cohorts. Equation (8) evaluates the quantity of completely humified matter (humus) that will be formed in the soil. Equation (9) determines nitrogen quantity that will be formed in the soil.
Values of iS k and iL k coefficients vary depending on nitrogen and ash content in the litter, temperature, and moisture. The model considers differences between organic remains decomposition by belowground and aboveground cohorts.
Linear dependencies of model coefficients on the ash and nitrogen content can be expressed by the equations [5]: where 1 x is ash content in the soil, 2 x is nitrogen content in the soil.
In the ROMUL model, temperature and moisture dependence is considered in the form of correction to parameters i k . It accounts for the temperature and moisture of organic matter decomposition.
The correctional coefficients are determined using the relations [5]: 11 where m H is humus content in mineral soil horizon. Experimental data indicated [4], that mineral soil has influence over organic remains decomposition rate. On the other hand, soil texture does not impact belowground organic matter decomposition rate.
where N M is nitrogen mineralization rate, ov M is organic matter mineralization rate, 1 xinitial nitrogen content in undecomposed soil layer, 2 xcurrent nitrogen content in decomposed organic soil layer.
The quantity of mineralized humus and nitrogen available for plants is a substantial parameter in the ROMUL model. On each time step, the quantity of mineralized humus is calculated as () Nitrogen available for plants is determined as To evaluate soil moisture we use the following data: precipitation amount, air and soil temperature. As soil moisture data are difficult to find, we used balance equations to determine water content in the active soil layer: , Evapotranspiration is determined as Using the given model we evaluated the quantity of organic matter that will be formed in the soil in 10 years for different soil types (Fig. 2). To do so we used soil moisture (soil moisture at the end of month, average within 0-1 m layer) and temperature data (monthly average soil temperature at 0.2 m depth), represented in Table 1.
The quantity of formed organic matter was calculated for the following soil types: mor sandy podzol, mor loamy gley-podzolic and loamy sand sod-podzolic. Initial organic matter quantity in mor sandy podzol -5. Based on input data, we calculated model correction coefficients that account for the influence of moisture and temperature on soil organic layer formation ( Table 2).  The results indicate that quantity of formed organic matter is substantially influenced by the soil type, ash content, nitrogen content, soil moisture and temperature.
Two aspects of the model can be distinguished: 1) there is a clear influence of mineral soil layer over humic compounds decomposition, but no impact of the soil texture on decomposition rate is present; 2) Mineralization rate depends on soil granulometric composition.
The model can also be used for estimating carbon flow from the soil into the atmosphere due to mineralization of humic compounds.
Soil temperature is modelled based on Gaussian distribution, considering autocorrelation and correlation with air temperature. To determine evapotranspiration, authors used the Blaney and Criddle model [1], which allows to evaluate potential evapotranspiration based on the air temperature only. Soil organic matter is represented by three layers: surface litter, soil litter and organic matter of mineral soil horizons.
The ROMUL model enables to calculate a quite complex balance of organic matter, nitrogen and, potentially, other elements in forest soils by introducing separate organic matter layer cohorts, which clearly is its advantage. However, a weakness has been found while doing calculations according to the model methods. Mineralization rate, computed by the model, exceeds its rate in the natural conditions.

CENTURY model
CENTURY is a model of soil biogeochemistry based on interrelations between climate, soil properties, crop productivity and decomposition of organic remains. The model considers carbon, nitrogen, phosphorus, and sulphur [9].
The organic remains are classified into: 1) fresh organic remains (surface litter) consisting of two parts: structural and metabolic; 2) "active" organic remains that comprise microbial biomass with 5-year complete mineralization time; 3) "slow" organic remains that are mineralized in less than 59 years; 4) "passive" organic remains that are mineralized in less than 1000 years.
In this model, lignin (plant material) fraction does not constitute microbial biomass and decomposes directly in the "slow" organic remains layer. It is accounted that 60% of carbon is spent on microbial breathing. State variables are calculated by the following equations: where , MR j x is a fraction of recomposed carbon received from metabolic organic matter layer and is included into humic compounds complex; , Sj xslow organic remains layer; S vdecomposition rate of slow organic remains layer; , Pj x passive organic remains layer; P vdecomposition rate of passive organic remains layer; j vdecomposition rate of all organic remains. Monthly organic matter decomposition rate is determined by the following relation: where * () j km is a decomposition rate coefficient of organic matter with respect to the corresponding soil layer j that is taking into account soil temperature, moisture and texture variations; () j Cm is initial carbon content in the soil.
Also, the Crank-Nicolson method can be applied to determine organic matter decomposition rate using average values () Сm  is current carbon content in the soil.
The quantity of humified organic carbon is determined using the following differential equation: (1 ) , where i S is initial carbon content, j rheterotrophic breathing rate coefficient, ji ffraction transition from j th to i th layer; i k moisture variation rate coefficient, j ktemperature variation rate coefficient.
Discretization yields the following differential equation: describes cryoturbation process.
All carbon decomposition streams are related to microbial activity. Mineralization rates depend on temperature and moisture. The model assumes that decaying plant litter forms active and passive layers. Regarding soil productivity, CENTURY uses the following statistical criterions: sample determination coefficient, normalized mean square error, index of agreement. The advantage of the model lies in the possibility to predict system behaviour and reaction to such manipulations as irrigation or changes in land use. The disadvantage is that the model does not include a function to account for the influence of acidity on plant growth. Thus, during testing it failed to simulate organic matter development in acidic grasslands.

ROTHAMSTED model
ROTHAMSTED is a model of calculating organic carbon content in arable topsoil. The model can also be used for longterm prediction of carbon content change due to climate change, calculating carbon loss rate or carbon sequestration in the agricultural soils. The model assumes organic remains consist of: 1) decomposable plant material; 2) resistant plant material; 3) microbial mass; 4) humified organic matter. For every soil layer, a constant of organic matter decomposition rate is set.
The organic remains transformation process is described by the equation:    Quantity of carbon decomposed in each of the compartments is described by the exponential decomposition function: where 0 Yinitial quantity of carbon, arate modifying factor for temperature, brate modifying factor for moisture, сsoil cover rate modifying factor, kdecomposition rate constant for that compartment, 1 12 t  for a monthly period (since k is based on a yearly decomposition rate).
The driving force of carbon loss from the soil is a microbial decomposition process that influences temperature and content of ground waters. The model adjusts for soil texture by altering the partitioning between CO 2 , microbial biomass and humified organic matter. This ratio is calculated from the clay content of the soil using the following equation: g is the percent of clay in the soil. Basing on the given model, we calculated the quantities of total organic carbon (TOC), particulate organic carbon (POC), humified organic matter (HUM) and inert organic matter (IOM) formed in the soil (Fig. 6).
Yearly organic matter contribution was calculated as a sum of carbon content in organic fertilizers and belowground crop biomass. The disadvantage of the model is that the model can only be used for arid climate territories and requires a considerable number of experimental data.
We also compared the quantity of carbon that will be formed in the soil in 10 years calculated using the models discussed above (Fig. 7).
We used the following initial model parameters for crust mor sandy surface-podzolic soil: initial nitrogen content in the organic soil layer -0.01689, ash concentration in upper soil litter layer -0.523, soil moisture and temperature data ( Table 1). Based on the obtained results, we conclude that the process of carbon formation in the crust mor sandy surface-podzolic soil is modelled the most accurately by the Century model, as compared to the laboratory research.

Conclusion
Using the meteorological database, we analysed and compared the results of the three dynamic soil organic matter formation models. The study suggests each model has its advantages and drawbacks. The common disadvantage of the models represented is a simplified representation of mineralization and humification processes. To improve these models, more attention should be payed to physico-chemical processes of humus formation, and the impact of soil granulometric composition on organic matter and nitrogen formation examined further.