diff --git a/docs/source/virtual_ecosystem/theory/soil/litter_theory.md b/docs/source/virtual_ecosystem/theory/soil/litter_theory.md index e84bce217..e2e3808d6 100644 --- a/docs/source/virtual_ecosystem/theory/soil/litter_theory.md +++ b/docs/source/virtual_ecosystem/theory/soil/litter_theory.md @@ -120,6 +120,51 @@ the responsiveness of the split to changes in the product of lignin proportion a 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 litter pools are not +defined in terms of their nitrogen and phosphorus contents. Furthermore, the division +between metabolic and structural litter is a modelling convenience rather than a +measurable split, so pool elemental proportions cannot be determined based on empirical +data. Instead, following {cite:t}`kirschbaum_modelling_2002`, we assume +that the nutrient concentrations of the inputs to a structural/metabolic pool pair +always follow a fixed ratio, + +$$\rho = \frac{r_s}{r_m},$$ + +where $r_m$ is the carbon:nutrient ratio of the input to the metabolic litter pool, +$r_s$ is the carbon:nutrient ratio of the input to the corresponding structural litter +pool, and $\rho$ is their ratio. Based on this, the nutrient concentrations that +flow into each pool is therefore + +$$r_m = r_i * f_{m,i} + r_i *\frac{(1 - f_{m,i})}{\rho}$$ + +and + +$$r_s = \rho*r_m$$ + +where $r_i$ is the carbon:nutrient ratio of the total input (to both pools). The first +term of the first equation captures how much nutrient will flow to the metabolic pool +for a given input concentration ($r_m$), the second term then captures how much nutrient +would have to flow to the structural pool to maintain the ratio ($\rho$). This equation +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 +{attr}`structural_to_metabolic_n_ratio +` +and {attr}`structural_to_metabolic_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