Environmental impacts on soil processes#
Litter decay and soil nutrient transformations are both affected by environment. At the most basic level these are impacts on the microbial components of the soil and litter models, which then impact the models more broadly. There are three different ways that these impacts are represented in the models. The rates of processes that are implicitly driven by microbes can change, the growth rates of the different microbial groups can be directly affected, or the enzymatic rates can be affected. Each of these cases will be dealt with in detail below.
At present, the only environmental impact we represent that isn’t mediated by microbes is the the rate at which nutrients leach from the soil. As such, this process does not fit into any of the cases mentioned already, and so it will be discussed in a separate section.
Changes to rates of implicitly microbially driven processes#
The soil model explicitly represents the soil microbes involved in decomposition. However, extending this representation to all the processes would be incredibly hard to parameterise, so some processes are instead represented by empirically obtained expressions that implicitly represent the actions of the microbial community. As these processes are driven by microbes they are affected by environmental conditions, in particular soil temperature and moisture.
Litter decay temperature response#
The decay rates of all classes of litter are affected by temperature. For the above-ground pools, this temperature is simply the air temperature just above the soil surface. For the below ground pools, the temperature is an average of the temperatures for the biologically active soil layers. The “intrinsic” litter decay rates are altered to capture the effect of temperature by multiplying them with a factor that takes the following form
where \(T\) is the litter temperature, \(T_\mathrm{ref}\) is reference temperature used to establish “intrinsic” litter decay rates, \(T_\mathrm{off}\) is an offset temperature, and \(\gamma\) is a parameter capturing how responsive litter decay rates are to temperature changes.
Litter decay moisture response#
Breakdown rates for below-ground litter pools are significantly impacted by soil moisture. In very dry soils, breakdown rates are extremely slow because microbial movement is restricted from reaching the substrate to break it down. As soils get wetter, microbial motility increases resulting in faster breakdown rates. However, further increasing soil moisture makes oxygen less permeable in the soil, so after a certain peak breakdown rates begin to decrease with increasing soil moisture as oxygen becomes limiting. The “intrinsic” process rates are altered to capture the effect of soil moisture by multiplying them with a factor that takes the following form
where \(\psi\) is the soil water potential, \(\psi_{o}\) is the “optimal” water potential at which substrate breakdown is maximised, \(\psi_{h}\) is the water potential at which substrate breakdown stops entirely, and \(\alpha\) is an empirically determined parameter which sets the curvature of the response to changing soil water potential.
Nitrification temperature factor#
The rate of nitrification in the soil changes with temperature. We capture this effect using an empirical function taken from (Xu-Ri and Prentice, 2008), where the impact of temperature on nitrifaction rate captured as
where \(T_m\) is the maximum temperature that nitrification occurs at, \(T_o\) is the optimal temperature for nitrification, and \(s_n\) is the sensitivity of nitrification to changes in temperature.
Nitrification moisture factor#
The rate of nitrification in the soil also varies with soil moisture. In this case, we use a function taken from (Fatichi et al., 2019) to capture this effect. The factor capturing the impact of soil moisture on nitrification rate is calculated as
where \(S_e\) is the effective saturation.
Denitrification temperature factor#
Denitrification rate is also impacted by temperature. To capture this we modify an empirical expression provided in (Xu-Ri and Prentice, 2008). This allows the impact that temperature has on denitrification rate to be calculated as
where \(f_\infty\) is the impact of the factor at infinite temperature, \(s_d\) is the (inverse) sensitivity of denitrification to changes in temperature and \(T_h\) is the temperature below which denitrification halts.
Denitrification moisture factor#
Soil moisture also effects the rate of denitrification. We capture this effect using a function taken from (Fatichi et al., 2019), which is expressed as
where \(S_e\) is the effective saturation.
Environmental effects on enzymes#
Many processes in the soil model are mediated by extra-cellular enzymes produced by the microbial groups. The kinetics of these enzymes are modified by a wider range of environmental factors: soil clay content, soil pH, soil temperature and soil moisture. These environmental factors can change the maximum rates of the processes or alternatively change the half saturation of the process. We will now discuss each of these factors in detail.
Impact of clay on enzyme saturation#
Clay in the soil protects substrates from enzymatic activity, which increases enzyme saturation constants. The factor capturing this increase is calculated as
where \(c\) is the clay proportion of the soil, \(P_b\) is the basic protection that the soil provides against enzymatic activity and \(P_c\) is the rate at which that protection increases with increasing clay content.
Impact of pH on enzyme rate#
pH values that lie outside the optimal range tend to inhibit microbial activities. We capture this as
where \(pH\) is the soil pH, \(pH_\mathrm{min}\) is the minimum pH at which enzymatic activity can occur, \(pH_l\) is the lowest pH for which enzymatic activity is maximised, \(pH_u\) is the highest pH for which enzymatic activity is maximised, and \(pH_\mathrm{max}\) is the maximum pH at which enzymatic activity can occur.
Impact of temperature on enzyme rate and saturation#
Future directions 🔭
The Arrhenius equation is a simple model for the impact of temperature on biological rates. We use this equation as a simple initial approach to incorporating temperature in the model, and anticipate deprecating it in favour of more refined models in future.
The thermal response of enzymatic rates and saturations is modelled using the Arrhenius equation. The form of this equation is as follows
where \(E_a\) is the activation energy of the process of interest, \(R\) is the molar gas constant, \(T\) is the environmental temperature, and \(T_{\mathrm{ref}}\) the reference temperature.
Impact of soil moisture on enzyme saturation#
The response of enzymatic rates to changing soil water potential is modelled using the same approach as for the below ground litter pools.
Direct environmental impacts on microbes#
Environmental factors also directly impact the growth of the different microbial groups in the model. The rate at which microbes can take up resources is affected by a wide range of environmental conditions. The efficiency microbes can grow is also affected by temperature, as is rate at which they lose biomass due to cell death and protein degradation.
Microbial uptake#
The uptake of resources by microbes is effected by a wide range of environmental factors, affecting both uptake rate and saturation. We use the same approach to
calculate the environmental impacts on uptake rate and saturation as was used for enzymatic rate and saturation.
Microbial growth efficiency#
The efficiency of microbial growth is often expressed in carbon terms as a carbon use efficiency (CUE). This is defined as the proportion of carbon used for the synthesis of new biomass to the total amount of carbon taken up. This is an emergent property that arises from a large number of underlying processes (e.g. basal respiration, DNA synthesis efficiency, etc.), most of which would be expected to vary with temperature. Carbon use efficiency usually does not increase exponentially with temperature, therefore the Arrhenius model is rarely an appropriate model. Instead we use a simple logistic model to describe the temperature dependence of carbon use efficiency
where \(\epsilon_{\mathrm{ref}}\) is the carbon use efficiency at the reference temperature, \(\alpha\) is the change in carbon efficiency with temperature, \(T\) is the environmental temperature and \(T_{\mathrm{ref}}\) is the reference temperature. The logit link function is used to ensure that carbon use efficiency \(\epsilon\) is bound between 0 and 1 as it is a proportion.
Biomass loss#
The impact of temperature on the rate of biomass loss is assumed to follow the Arrhenius equation
Soil nutrient removal by water#
Soil nutrient removal by water occurs when the movement of water though the soil carries away dissolved nutrients with it. As such, this process only applies to the soluble forms of nutrients, i.e. the simplest and most readily uptaken forms. To calculate the leaching rate for a given solute, we first have to calculate the amount of it that we would expect to find in a dissolved form using
where \(N_i\) is the density of solute \(i\) in the soil and \(C_i\) is the solubility coefficient for solute \(i\). The solubility coefficient represents the proportion of the solute that you would expect to find in a dissolved form and ranges between zero and one. We then need to know the rate at which the water column gets completely replaced, this can be calculated as
where \(J\) is the rate a which water exits the microbially active part of the soil, and \(W\) is the amount of water contained in the water column (in the microbially active region of the soil). We can then combine the above to calculate the leaching rate for substrate \(i\) as