From c3468a58f2dee982e64afcd12a84f8b16eeb461c Mon Sep 17 00:00:00 2001 From: jacobcook1995 Date: Wed, 1 Oct 2025 11:29:53 +0100 Subject: [PATCH 1/4] Added basic description of how the split of nutrient input between pools works --- .../theory/soil/litter_theory.md | 25 +++++++++++++++++++ 1 file changed, 25 insertions(+) diff --git a/docs/source/virtual_ecosystem/theory/soil/litter_theory.md b/docs/source/virtual_ecosystem/theory/soil/litter_theory.md index e84bce217..c15337c59 100644 --- a/docs/source/virtual_ecosystem/theory/soil/litter_theory.md +++ b/docs/source/virtual_ecosystem/theory/soil/litter_theory.md @@ -120,6 +120,31 @@ 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 have be determined, we have to +determine how the various nutrients contained in the input biomass are split between +pools. Lignin 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 we do not define litter pools 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. To address this, we +follow {cite:t}`kirschbaum_modelling_2002` in making the assumption that there's a fixed +ratio between the carbon:nutrient ratios of the paired metabolic and structural litter +pools, e.g. that the carbon:nitrogen ratio of the above ground structural pool will be +$X$ times higher than the above ground structural pool. In order to maintain these fixed +ratios, inputs to the pools must also follow them. The ratios are model parameters and +are set by {attr}`structural_to_metabolic_n_ratio +` +and {attr}`structural_to_metabolic_p_ratio +`. +It is important to note, that though 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 From 2bb2b3611f073b94bce43b7018d3652976d36f00 Mon Sep 17 00:00:00 2001 From: jacobcook1995 Date: Fri, 3 Oct 2025 09:48:37 +0100 Subject: [PATCH 2/4] Added equations to nutrient split documentation to (hopefully) make the description easier to follow --- .../theory/soil/litter_theory.md | 51 ++++++++++++------- 1 file changed, 33 insertions(+), 18 deletions(-) diff --git a/docs/source/virtual_ecosystem/theory/soil/litter_theory.md b/docs/source/virtual_ecosystem/theory/soil/litter_theory.md index c15337c59..3c7d0a20e 100644 --- a/docs/source/virtual_ecosystem/theory/soil/litter_theory.md +++ b/docs/source/virtual_ecosystem/theory/soil/litter_theory.md @@ -122,28 +122,43 @@ 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 have be determined, we have to +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. Lignin 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 we do not define litter pools 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. To address this, we -follow {cite:t}`kirschbaum_modelling_2002` in making the assumption that there's a fixed -ratio between the carbon:nutrient ratios of the paired metabolic and structural litter -pools, e.g. that the carbon:nitrogen ratio of the above ground structural pool will be -$X$ times higher than the above ground structural pool. In order to maintain these fixed -ratios, inputs to the pools must also follow them. The ratios are model parameters and -are set by {attr}`structural_to_metabolic_n_ratio +pools. For lignin 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 make the assumption +that the nutrient concentrations of the inputs to a metabolic/structural pool pair +always follow a fixed ratio, i.e. + +$$\rho = \frac{r_s}{r_m},$$ + +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 for the input +to both pools can be calculated using + +$$r_m = r_i * \left(f_{m,i} + \frac{(1 - f_{m,i})}{\rho}\right)$$ + +and + +$$r_s = \rho*r_m$$ + +where $r_i$ is the carbon:nutrient ratio of the total input (to both pools). 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 though 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. +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 From 4e306e5bc2e8e7abb6345f8d358a0ef215f1a7b0 Mon Sep 17 00:00:00 2001 From: Hao Ran Lai Date: Sat, 4 Oct 2025 14:30:02 +1300 Subject: [PATCH 3/4] minor suggestion, plus a more verbose explanation of r_m --- .../theory/soil/litter_theory.md | 22 +++++++++++-------- 1 file changed, 13 insertions(+), 9 deletions(-) diff --git a/docs/source/virtual_ecosystem/theory/soil/litter_theory.md b/docs/source/virtual_ecosystem/theory/soil/litter_theory.md index 3c7d0a20e..7dec9d87f 100644 --- a/docs/source/virtual_ecosystem/theory/soil/litter_theory.md +++ b/docs/source/virtual_ecosystem/theory/soil/litter_theory.md @@ -124,7 +124,7 @@ in the product of lignin proportion and carbon:phosphorus ratio. 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 is straightforward, as by definition only woody and structural litter +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. @@ -132,25 +132,29 @@ The situation is more complex for nitrogen and phosphorus, as litter pools are n 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 make the assumption -that the nutrient concentrations of the inputs to a metabolic/structural pool pair -always follow a fixed ratio, i.e. +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 for the input -to both pools can be calculated using +pool, and $\rho$ is their ratio. Based on this, the nutrient concentrations that +flow into each pool is therefore -$$r_m = r_i * \left(f_{m,i} + \frac{(1 - f_{m,i})}{\rho}\right)$$ +$$r_m = r_i * \left[f_{m,i} + \frac{(1 - f_{m,i})}{\rho}\right]$$ and $$r_s = \rho*r_m$$ -where $r_i$ is the carbon:nutrient ratio of the total input (to both pools). At present, -we allow $\rho$ to vary between nutrients but not between strata (above- vs +where $r_i$ is the carbon:nutrient ratio of the total input (to both pools). +The component in square brackets can be interpreted as total input $r_i$ flows into the +metabolic litter pool first through the metabolic fractional split $f_{m,i}$, and then +plus the remaining nutrient not flown into the structural fraction +$\frac{(1 - f_{m,i})}{\rho}$. +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 From 198ea25ecfb49047c62607f2f2ba279818de6136 Mon Sep 17 00:00:00 2001 From: jacobcook1995 Date: Mon, 6 Oct 2025 09:49:25 +0100 Subject: [PATCH 4/4] Added explanation of the form of the litter nutrient split equation --- .../theory/soil/litter_theory.md | 17 +++++++++-------- 1 file changed, 9 insertions(+), 8 deletions(-) diff --git a/docs/source/virtual_ecosystem/theory/soil/litter_theory.md b/docs/source/virtual_ecosystem/theory/soil/litter_theory.md index 7dec9d87f..e2e3808d6 100644 --- a/docs/source/virtual_ecosystem/theory/soil/litter_theory.md +++ b/docs/source/virtual_ecosystem/theory/soil/litter_theory.md @@ -143,19 +143,20 @@ $r_s$ is the carbon:nutrient ratio of the input to the corresponding structural pool, and $\rho$ is their ratio. Based on this, the nutrient concentrations that flow into each pool is therefore -$$r_m = r_i * \left[f_{m,i} + \frac{(1 - f_{m,i})}{\rho}\right]$$ +$$r_m = r_i * f_{m,i} + r_i *\frac{(1 - f_{m,i})}{\rho}$$ and $$r_s = \rho*r_m$$ -where $r_i$ is the carbon:nutrient ratio of the total input (to both pools). -The component in square brackets can be interpreted as total input $r_i$ flows into the -metabolic litter pool first through the metabolic fractional split $f_{m,i}$, and then -plus the remaining nutrient not flown into the structural fraction -$\frac{(1 - f_{m,i})}{\rho}$. -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 +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 `.