Theory of litter decay#
The litter model we use is based on the well established approach of (Kirschbaum and Paul, 2002). In our model, litter is divided into a number of separate pools based on input material type, chemistry and spatial location (i.e. above- vs below-ground). These pools each have a characteristic decay rate, which gets modified by environmental conditions and, for some of the pools, by their lignin concentrations. Notably, these decay rates are not affected by the nitrogen and phosphorus concentrations of the pools. Instead, nitrogen and phosphorus concentrations affect the partitioning of input organic matter between litter pools, i.e. if the nutrient concentrations of a particular input are low, then a higher proportion of the input goes into slow decaying litter pools. This indirectly captures the impact of nitrogen and phosphorus chemistry on litter decay.
The rest of this page provides details on the specific litter pools, the partitioning of organic matter input between them, the tracking of litter chemistry and the impacts animals have on litter accumulation and decay.
Litter pools#
In our model, pools are principally defined by input type, e.g. woody, structural and metabolic. They are then further subdivided into above- and below-ground pools. Some of these pools cannot be fully characterised due to insufficient data, so we neglect them following (Fatichi et al., 2019). This means that we use a single above-ground woody litter pool, rather than coarse and fine woody, and we do not include any below-ground woody pool. This leaves us with the following pools:
Above-ground metabolic litter#
Above-ground metabolic litter can originate as any non-woody above-ground plant matter (e.g. bark, leaves, fruit, etc). By definition the pool contains plant matter that is easily broken down, and so this pool by definition contains no lignin.
Above-ground structural litter#
High lignin concentration biomass from leaves etc is instead included in the above-ground structural litter pool. This pool shares a set of sources with the metabolic pool, but is defined as containing the more recalcitrant material.
Above-ground woody litter#
Above-ground dead wood is treated separately due to its substantially different turnover dynamics, i.e. all wood losses from tree falls, branch fall etc, are assumed to be added to an above-ground woody pool. We assume that the vast majority of dead wood ends up decaying on top of the soil, and so there is no corresponding below-ground pool. We considered including a separate pool for standing dead trees, as wood decaying in this form would experience a very different environment and hence would be expected to decay at a different rate. However, this felt like too much effort for what is likely to be a small effect.
Below-ground metabolic litter#
For the below-ground pools, roots (both fine and coarse) are the major source of biomass. The below-ground metabolic litter pool then includes the easily broken down root debris, which is likely to come predominantly from fine-root turnover.
Below-ground structural litter#
As with the above-ground case only the structural pool contains lignin, this pool represents hard to break down components of root turnover.
Litter chemistry#
Three aspects of litter chemistry are tracked. Lignin is tracked because its concentration is one of the biggest factors effecting litter decay rates. Nitrogen and phosphorus are also major factors in determining litter quality and the total rate of litter breakdown. However, our primary reason for tracking litter nitrogen and phosphorus concentrations is to track the rate of entry of phosphorus and nitrogen into the soil, where both can be major limiting factors for microbial activity. For this reason, we consider only lignin concentration to have a direct impact on decay rates (for the pools that contain lignin) and not nitrogen and phosphorus concentrations. In order to capture the impact of lignin on decay, decay rates are reduced by multiplying them with a factor that takes the following form
where \(L\) is the proportion of the litter pool which is lignin and \(r\) is a (negative) empirical constant setting the strength of the inhibition. This choice of function form follows Kirschbaum and Paul (2002).
The litter model takes in input biomass from the plant model as four separate biomass streams: wood, leaves, roots, and reproductive biomass (e.g. fruits and flowers). All wood input goes to the woody litter pool, but the other three streams need to be partitioned between the relevant metabolic and structural litter pools. This partition depends on the lignin concentration of the input biomass, as well as its nitrogen and phosphorus concentrations. The fraction of a given input biomass stream (\(i\)) that goes into the relevant metabolic litter pool is given by
where \(f_M\) is the maximum fraction that can go to the metabolic pool, \(l_i\) is the lignin proportion for input stream \(i\), \(N_i\) is the carbon:nitrogen ratio of input stream \(i\), \(P_i\) is the carbon:phosphorus ratio of input stream \(i\), \(s_N\) parametrises the responsiveness of the split to changes in the product of lignin proportion and carbon:nitrogen ratio, and \(s_P\) parametrises the responsiveness of the split to changes in the product of lignin proportion and carbon:phosphorus ratio.
Split of nutrient inputs between pools#
Now that the split of input sources between pools has been determined, we have to determine how the various nutrients contained in the input biomass are split between pools. For lignin it is straightforward, as by definition only woody and structural litter pools contain lignin. So, all lignin from input biomass is added to the relevant structural (or woody) pool and none of it is added to the metabolic pools.
The situation is more complex for nitrogen and phosphorus, as both litter pools contain them. Furthermore, the division between metabolic and structural litter is a modelling convenience rather than an empirically measurable split. We use a simple relation (see above) to determine the fraction of the carbon mass flows to metabolic (\(f_m\)) and structural litter (\(f_s\)), while in theory this relation could be extended to also predict nitrogen and phosphorus flow, doing so would introduce a large number of parameters that cannot be estimated based on empirical data. So, in order to keep the number of unmeasurable parameters down, we assume (following Kirschbaum and Paul (2002)) that the nutrient concentrations of the inputs to a metabolic/structural pool pair always follow a fixed ratio,
where \(r_m\) is the concentration of the nutrient (relative to the carbon mass) in the input to the metabolic litter pool, \(r_s\) is the concentration in the input to the corresponding structural litter pool, and \(\rho\) is their ratio. Based on this, the nutrient mass that flow into each pool is therefore
and
where \(n_T\) is the total nutrient input (to both pools), and \(C_m\) and \(C_s\) are the
carbon flows to the metabolic and structural pools, respectively. The equations above
will only be satisfied when the sum of the nutrient input flows to the pools matches the
total input. At present, we allow \(\rho\) to vary between nutrients but not between
strata (above- vs below-ground). These values are set in
metabolic_to_structural_n_ratio
and metabolic_to_structural_p_ratio.
It is important to note, that the choice of these ratios will only affect the nitrogen
and phosphorus mineralisation rates and not the broader litter decay dynamics. This is
because the nitrogen and phosphorus concentrations do not directly affect pool decay
rates.
Litter decay dynamics#
The decay of all litter pools are assumed to follow linear kinetics, with the rate of change in the carbon mass, \(P\), of litter pool \(j\) being given by
where \(I_j\) is the rate of input to pool \(j\) (in carbon terms), \(T\) is the temperature, \(\psi\) is the soil water potential and \(K_j(T,\psi,L)\) is the decay rate of the pool. The decay rate of the pool will always depend on temperature, but only for the below-ground pools will it be affected by soil water potential. Further, lignin content only affects the decay rates of pools which contain lignin (i.e. structural and woody pools). As an example, the decay rate of the below-ground structural litter pool is calculated as
where \(k_{bs}\) is the decay rate constant for the below-ground structural litter pool, \(f_l(L)\) is a factor (defined above) capturing the impact of lignin on decay rate, \(f_t(T)\) is a factor capturing the effect of soil temperature on decay rates, and \(A(\psi)\) is a factor capturing the effect of soil moisture on decay rates.
The dynamics defined above are analytically solvable provided that the input does not vary over the timescale of interest. Because of this, the litter model does not numerically integrate the dynamics and instead just uses the exact solution for the litter pool size at the end of the model update interval (\(\tau\)). This solution can be expressed as
where \(P_{j,0}\) is the size of litter pool \(j\) at the start of the update interval. We don’t use comparable exact solutions for the nitrogen, phosphorus and lignin dynamics. Instead, we estimate the loss of each chemical based on the loss of carbon. This estimation assumes that old litter (i.e. litter that is there at the start of the time step) decays first and that litter added during the update only decays if the total decay of litter exceeds the initial litter pool size. Total loss of the chemicals is then found either using the initial pool chemistry (if total decay is less than the initial pool size), or a weighted average of the initial pool chemistry and the chemistry of the input biomass.
Future directions 🔭
Obtaining exact solutions for the nitrogen, phosphorus and lignin dynamics would improve the accuracy of the model. For the nitrogen and phosphorus case, this shouldn’t be particularly difficult, but as nitrogen and phosphorus concentrations don’t affect litter pool decay rates the improvement in model accuracy would be marginal. Obtaining an exact solution for the lignin dynamics would be both trickier to accomplish as changes in lignin concentration will change litter pool decay rates. However, this feedback makes tracking lignin concentration accurately far more important for overall model accuracy.
Animal impacts on litter#
Animals interact with the litter model in two ways. Firstly, all litter pools are available to be scavenged from by animals. So, the presence of functional groups with the right traits to exploit a certain litter pool (e.g. termites for woody litter) will increase the breakdown rate of the pool. Secondly, herbivores often remove more biomass from plants than they actually consume (e.g. elephants with pull off entire branches from saplings and then eat only the easy to chew bits). This excess plant biomass gets added to the litter.
The litter model does not track the decay of animal excrement or carcasses. This is because the animal model already models their decay, tracking these within the litter model would essentially force them to decay twice. Instead the flow of decayed matter from carcasses and excrement flows straight from the animal model to the soil model.