Goal: simplified biogeochemical model that is capable of simulating GHG balance, including soil carbon,
Start as simple as possible, add complexity as needed. When new features are considered, they should be evaluated alongside other possible model improvements that have been considered, and the overall list of project needs.
Model state is updated in the following order:
- Calculate fluxes — compute the model's native fluxes
- Process events — convert events to per‑day fluxes and accumulate into fluxes.
- Update pools — pools are updated from the accumulated fluxes and pool‑specific updates.
This document provides an overview of the SIPNET model’s structure. It was written to
- Consolidate the descriptions from multiple papers (notably Braswell et al 2005 and Zobitz et al 2008).
- Provide enough detail to support the addition of agronomic events, CH4, and N2O fluxes.
- Focus on features currently in regular use.
There are multiple ways to configure the model structure, and not all model structures or components are listed. Implementation in source code is annotated with references to specific publications.
- The general approach used to define variables and subscripts is defined in Notation.
- Specific parameter, flux, and state definitions are documented in Model States and Parameters.
SIPNET can be run with or without a separate litter pool (LITTER_POOL=1 or 0). Equations in this document assume LITTER_POOL=1 unless otherwise noted.
When LITTER_POOL=0:
- Carbon fluxes that would go to the litter pool (
$F^C_\text{litter}$ ) are routed directly to the soil carbon pool - This affects carbon routing from harvest events, organic matter additions, plant senescence, and other processes
involving
$F^C_\text{litter}$ - All decomposition occurs in the soil pool
- All nitrogen cycle modeling is off (NITROGEN_CYCLE=1 requires LITTER_POOL=1)
\begin{equation} \text{GPP}{\text{max}} = A{\text{max}} \cdot A_d + R_{leaf,0} \label{eq:Braswell_A6} \end{equation}
This is equation (A6) from Braswell et al. (2005).
The daily maximum gross photosynthetic rate $(\text{GPP}{\text{max}})$ represents the maximum potential GPP under
optimal conditions. It is modeled as the leaf-level maximum net assimilation rate $(A{\text{max}})$ multiplied by a
scaling factor
In SIPNET, plant leaf carbon is converted to leaf area index by dividing by leaf carbon per unit leaf area:
\begin{equation} LAI = \frac{C_{\text{leaf}}}{SLWC} \label{eq:lai_calculation} \end{equation}
where
Photosynthesis is affected by LAI in two ways.
First, LAI scales leaf-level photosynthetic capacity to canopy-scale carbon flux by contributing to the conversion from leaf-area based assimilation units to ground-area based GPP.
Second, LAI determines canopy light attenuation through
Thus, increasing
\begin{equation} \text{GPP}{\text{pot}} = \text{GPP}{\text{max}} \cdot D_{\text{temp}} \cdot D_{\text{VPD}} \cdot D_{\text{light}} \label{eq:Braswell_A7} \end{equation}
This is equation (A7) from Braswell, et al. (2005).
The potential gross primary production $(\text{GPP}{\text{pot}})$ is calculated by reducing $\text{GPP}{\text{max}}$ by temperature, vapor pressure deficit, and light.
\begin{equation} \text{GPP} = \text{GPP}{\text{pot}} \cdot D{\text{water}} \label{eq:Braswell_A17} \end{equation}
This is equation (A17) from Braswell, et al. (2005).
The total adjusted gross primary production (GPP) is the product of potential GPP $(\text{GPP}{\text{pot}})$ and the water stress factor $D{\text{water,}A}$.
The water stress factor
Note that nitrogen limitation does not directly reduce GPP, but indirectly reduces future potential GPP by reducing allocation to leaf growth; see Sec. Nitrogen Limitation.
\begin{equation} \text{NPP} = \text{GPP} - R_A \label{eq:npp} \end{equation}
Net primary productivity
To make explicit what contributes to autotrophic respiration, we decompose
\begin{equation} R_A = R_\text{leaf} + R_\text{wood} + R_\text{fine_root} + R_\text{coarse_root} +\ R_\text{growth} \label{eq:ra_components} \end{equation}
Here,
Note that
\begin{equation} \frac{dC_{\text{plant,}i}}{dt} = \alpha_i \cdot \overline{\text{NPP}} - F^C_{\text{harvest,removed,}i} - F^C_{\text{litter,}i} \label{eq:Zobitz_3} \end{equation}
This is equation (3) from Zobitz, et al. (2008), augmented with the harvest and litter terms. Summing over all plant pools shows that NPP is partitioned into biomass growth, removed harvest, and litter production.
Note that it is possible for
Plant death is checked automatically after pool updates. The model requires positive woody carbon, positive total woody carbon (including the NPP accounting / storage term \eqref{eq:wood_c_storage}), and positive total root carbon. When any of these become non-positive, SIPNET treats the plant as dead, transfers the remaining biomass to litter or soil as appropriate, zeros the living plant pools, and resets the running mean NPP tracker.
As stated above, SIPNET uses a five-day averaged NPP when allocating gained carbon to plant growth. To implement this, the current timestep's net primary production (adjusted GPP - autotrophic respiration) is added to the wood carbon pool where it acts as a storage pool, and all allocations from the averaged NPP are deducted from that pool.
Starting in SIPNET v2.1, to support mass balance tracking, this storage is explicitly tracked as a separate pool called
\begin{equation} \frac{dC_{\text{wood,storage}}}{dt} = (GPP - R_a) - \overline{\text{NPP}}_\text{alloc} \label{eq:wood_c_storage} \end{equation}
where
The total wood carbon is the sum of the structural wood carbon and the storage pool:
\begin{equation} C_{\text{wood,total}} = C_{\text{wood}} + C_{\text{wood,storage}} \end{equation}
Thus, changes to (non-storage) wood carbon over time are determined by:
\begin{equation} \frac{dC_\text{wood}}{dt} = \alpha_\text{wood} \cdot \overline{\text{NPP}} - F^C_\text{litter,wood} - F^C_{\text{creation,leafOn}}*k_\text{wood} \label{eq:Braswell_A1} \end{equation}
where
This is equation (A1) from Braswell, et al. (2005), modified to explicitly track the storage component.
\begin{equation} \frac{dC_\text{leaf}}{dt} = L - F^C_\text{litter,leaf} \label{eq:Braswell_A2} \end{equation}
This is equation (A2) from Braswell, et al. (2005)
The change in plant leaf carbon
\begin{equation} L = \alpha_\text{leaf} \cdot \overline{\text{NPP}} + F^C_{\text{creation,leafOn}} \label{eq:leaf_production} \end{equation}
\begin{equation} F^C_\text{litter,leaf} = K_\text{leaf} \cdot C_\text{leaf} + F^C_{\text{litter,leafOff}} \label{eq:leaf_litter} \end{equation}
The continuous components follow the same form as the other biomass pools \eqref{eq:Zobitz_3}: a fixed share
The pulse components carry the growing season transitions described in Sec. Leaf On/Leaf Off. At leaf on the plant has little or no canopy, so leaves are not built from current production. Instead, the leaf on term is a reallocation of carbon the plant already holds, moved into leaves from wood and coarse roots, and is therefore not part of the NPP partition in \eqref{eq:Zobitz_3}. At leaf off, the leaf off term adds to leaf litter and is routed onward in the same way as continuous leaf turnover.
If the growth term is negative and the leaf pool is not large enough to support the loss, the leaf pool is zeroed and the remaining loss is transferred to the wood pool. If the wood pool is not large enough to support the loss, the plant mortality check will conclude that the plant is dead.
Leaf on and leaf off events define the timing of leaf emergence and senescence, respectively. For these events,
transferred carbon and nitrogen are computed from model state and the parameters
When a leaf on event occurs, an amount of carbon
- Carbon: at most a fraction
$f_{\text{realloc}}$ of wood and coarse root carbon is available to be reallocated. Carbon held in the wood storage pool \eqref{eq:wood_c_storage} is not drawn on. - Nitrogen (when enabled): for a realized leaf-on carbon transfer
$C_{\text{leaf,on}}$ , plant nitrogen storage changes by$\Delta N = C_{\text{leaf,on}}(1/CN_{\text{leaf}} - 1/CN_{\text{wood}})$ . Positive$\Delta N$ is drawn from storage and can limit leaf on; negative$\Delta N$ is returned to storage.
The carbon constraint, and the nitrogen constraint when applicable, scale the transfer down. The scaled amount is applied to the pools and is not subsequently reduced by the general nitrogen limitation (Sec. Nitrogen Limitation).
When a leaf off event occurs, a fraction
Leaf on and leaf off events may be specified in the events input file (Sec. Leaf On/Leaf Off Events), or they may be calculated automatically by SIPNET based on:
- the growing season start and end dates as specified by the parameters
leafOnDayandleafOffDay, or - growing degree days when
GDD = 1, or - soil temperature when
SOIL_TEMP = 1.
Leaf on and leaf off events may only be specified in the events file OR calculated automatically by SIPNET. If both are specified, SIPNET will error.
Change in carbon for the fine root and coarse root pools is determined as follows::
\begin{equation} \frac{dC_\text{fine root}}{dt} = \alpha_\text{fine root} \cdot \overline{NPP} - F^C_\text{fine root,root loss} \label{eq:fine_root_carbon} \end{equation}
\begin{equation} \frac{dC_\text{coarse root}}{dt} = \alpha_\text{coarse root} \cdot \overline{NPP} - F^C_\text{coarse root,root loss} - F^C_{\text{creation,leafOn}}*k_\text{coarse root} \label{eq:coarse_root_carbon} \end{equation}
where
\begin{equation} F^C_\text{i,root loss} = k_\text{i,turnover} \cdot C_\text{i} \label{eq:root_loss} \end{equation}
for
If the growth terms are negative and either pool is not large enough to support the loss, SIPNET will attempt to draw from the other pool. If the combined pools are not large enough to support the total loss, the plant mortality check will conclude that the plant is dead.
\begin{equation} R_\text{leaf,opt} = k_\text{leaf} \cdot A_{\text{max}} \cdot C_\text{leaf} \label{eq:Braswell_A5} \end{equation}
Where
\begin{equation} R_\text{leaf} = R_\text{leaf,opt} \cdot D_{\text{temp,Q10}} \label{eq:Braswell_A18} \end{equation}
This is equation (A18) from Braswell, et al. (2005).
Actual foliar respiration
\begin{equation} R_\text{wood} = K_\text{wood} \cdot C_\text{wood} \cdot D_{\text{temp,Q10}_v} \label{eq:Braswell_A19} \end{equation}
This is equation (A19) from Braswell, et al. (2005).
Wood maintenance respiration
As with wood maintenance respiration, root respiration is calculated as
\begin{equation} R_\text{i} = K_\text{} \cdot C_\text{i} \cdot D_{\text{temp,Q10}_v} \label{eq:Zobitz_root_resp} \end{equation}
for
This is from Zobitz, et al. (2008), Sec. 5.4.2.
The change in the litter carbon pool over time is defined by the input of new litter and losses due to decomposition and methane production:
\begin{equation} \frac{dC_\text{litter}}{dt} = F^C_\text{litter} - F^C_{\text{decomp}} - F^C_{\text{CH}_4\text{,litter}} \end{equation}
Where
\begin{equation} F^C_\text{litter} = \sum_{i} K_{\text{plant,}i} \cdot C_{\text{plant,}i} + \left( \sum_{i} F^C_{\text{harvest,transfer,}i} + F^C_\text{fert,org} \right) \label{eq:litter_flux} \end{equation}
\begin{equation*} \small i \in {\text{leaf, wood}} \end{equation*}
Where
When soil carbon saturation is enabled, a fraction of soil carbon inputs may be redirected to the litter pool as fast-turnover carbon. This functionality is described in more detail below in Sec. Soil Carbon Saturation.
\begin{equation} \frac{dC_\text{litter}}{dt} = F^C_\text{litter} + F^C_{\text{soil}} \cdot \frac{C_{\text{soil}}}{C_{\text{soil,saturation}}} - F^C_{\text{decomp}} - F^C_{\text{CH}_4\text{,litter}} \label{eq:soil_carbon_to_litter} \end{equation}
Where
\begin{equation} F^C_{\text{decomp}} = K_\text{litter} \cdot C_\text{litter} \cdot D_{\text{temp}} \cdot D_{\text{water},R_H} \cdot D_{CN} \cdot D_{tillage} \label{eq:decomp_rate} \end{equation}
The total litter decomposition flux is partitioned between heterotrophic respiration and transfer of carbon to the soil pool, satisfying the mass-balance relationship:
\begin{equation} R_{\text{litter}} + F^C_{\text{soil,litter}} = F^C_{\text{decomp}} \label{eq:decomp_carbon} \end{equation}
Where
\begin{equation} R_{\text{litter}} = f_{\text{litter}} \cdot F^C_{\text{decomp}} \label{eq:r_litter} \end{equation}
The remainder of the decomposed litter carbon is transferred to the soil pool:
\begin{equation} F^C_{\text{soil,litter}} = (1 - f_{\text{litter}}) \cdot F^C_{\text{decomp}} \label{eq:soil_carbon} \end{equation}
The change in the soil organic carbon (SOC) pool over time is determined by: (i) inputs of carbon transferred from litter during decomposition, (ii) direct inputs from belowground plant turnover, and (iii) losses of carbon due to heterotrophic respiration and methane production:
\begin{equation} \frac{dC_\text{soil}}{dt} = F^C_{\text{soil}} - R_{\text{soil}} - F^C_{\text{CH}_4\text{,soil}} \label{eq:Braswell_A3} \end{equation}
where
This is equation (A3) from Braswell, et al. (2005), with the addition of the methane flux.
Total carbon input to the soil includes both (i) carbon transferred from the litter pool during decomposition \eqref{eq:soil_carbon} and (ii) inputs from root turnover:
\begin{equation} F^C_{\text{soil}} = F^C_{\text{soil,litter}} + F^C_{\text{soil,roots}} \label{eq:soil_carbon_flux} \end{equation}
When soil carbon saturation is enabled, only a saturation-dependent fraction of gross soil C inputs is added to the
soil pool. This fraction declines as
\begin{equation} \frac{dC_\text{soil}}{dt} = F^C_{\text{soil}} \cdot (1 - \frac{C_{\text{soil}}}{C_{\text{soil,saturation}}}) - R_{\text{soil}} - F^C_{\text{CH}_4\text{,soil}} \label{eq:soil_carbon_saturation} \end{equation}
where
Soil heterotrophic respiration is modeled as a first-order process proportional to soil organic carbon content and modified by environmental and management factors:
\begin{equation} R_{\text{soil}} = K_{dec} \cdot C_{\text{soil}} \cdot D_{\text{temp}} \cdot D_{\text{water},R_H} \cdot D_{CN} \cdot D_{\text{tillage}} \label{eq:r_soil} \end{equation}
SIPNET assumes no loss of SOC to leaching or erosion.
Total heterotrophic respiration,
\begin{equation} R_H = R_{\text{soil}} + R_{\text{litter}} \label{eq:rh} \end{equation}
Where the litter and soil components are defined above in \eqref{eq:r_litter} and \eqref{eq:r_soil}.
For the soil pool,
For the litter pool, litter decomposition
\begin{equation} F^C_{\text{CH}4\text{,}j} = K{\text{CH}4\text{,}j} \cdot C\text{j} \cdot D_{\text{water,CH}4} \cdot D\text{temp} \label{eq:ch4} \end{equation}
\begin{equation*} \small j \in {\text{soil, litter}} \end{equation*}
The calculation of methane flux $(F^C_{\text{CH}4})$ for soil and litter is analogous to that of $R_H$. It uses the same carbon pools as substrate and temperature dependence but has specific rate parameters $(K{\text{CH}_4\text{,}j})$, a moisture dependence function based on oxygen availability \eqref{eq:water_ch4}, and no direct dependence on tillage.
The carbon and nitrogen cycle are tightly coupled by the C:N ratios of plant and organic matter pools. The C:N ratio of plant biomass pools is fixed, while the C:N ratio of soil organic matter and litter pools is dynamic.
Plant biomass pools have a fixed CN ratio and are thus stoichiometrically coupled to carbon:
\begin{equation} N_i = \frac{C_i}{CN_{i}} \label{eq:cn_stoich} \end{equation}
\begin{equation*} \small i \in {\text{leaf, wood, fine root, coarse root}} \end{equation*}
Where
Soil organic matter and litter pools have dynamic CN that is determined below.
In SIPNET, the C:N ratio of soil and litter pools is calculated directly from the carbon and nitrogen pools.
\begin{equation} CN_j = \frac{C_j}{N_j}. \end{equation}
\begin{equation*} \small j \in {\text{soil, litter}} \end{equation*}
This is used to calculate C:N-dependency
To represent the influence of substrate quality on decomposition rate, we add a simple dependence function
\begin{equation} D_{CN} = \frac{k_{CN}}{k_{CN}+ CN} \label{eq:cn_dep} \end{equation}
Here,
Similar to the stoichiometric coupling of litter fluxes, the change in plant biomass N over time is stoichiometrically coupled to plant biomass C:
\begin{equation} \frac{dN_{\text{plant,}i}}{dt} = \frac{dC_{\text{plant,}i}}{dt} \cdot \frac{1}{CN_{\text{plant,}i}} \label{eq:plant_n} \end{equation}
\begin{equation*} \small i \in {\text{leaf, wood, fine root, coarse root}} \end{equation*}
When leaves senesce, nitrogen is resorbed from the leaves and returned to the plant. We represent this as a separate
nitrogen storage pool
\begin{equation} \frac{dN_\text{plant,storage}}{dt} = f_{\text{N,resorp}} \cdot \frac{F^C_\text{litter,leaf}}{CN_\text{leaf}} \label{eq:n_resorp} \end{equation}
As described above, leaf litter production is calculated as a combination of continuous turnover and a pulse at leaf off, all of which is subject to nitrogen resorption.
The nitrogen storage pool primarily represents nitrogen that is resorbed from leaves at leaf off, and is used to support leaf growth at leaf on. It also supports growth of other plant pools when it is available.
The change in litter nitrogen over time,
\begin{equation} \frac{dN_{\text{litter}}}{dt} = \sum_{i} F^N_{\text{litter,}i} + F^N_\text{fert,org} - F^N_\text{leaf, resorption} - F^N_\text{litter,min} - F^N_\text{soil} \label{eq:litter_dndt} \end{equation}
\begin{equation*} \small i \in {\text{leaf, wood}} \end{equation*}
Here,
When carbon saturation is enabled, a fraction of soil nitrogen inputs is redirected to the litter pool in an analogous
manner to the soil carbon inputs, based on the same saturation fraction
The change in soil nitrogen
\begin{equation} \frac{dN_\text{org,soil}}{dt} = \sum_{j} F^N_{\text{soil,}j} + F^N_\text{soil} - F^N_\text{soil,min} \label{eq:org_soil_dndt} \end{equation}
\begin{equation*} \small j \in {\text{fine root, coarse root}} \end{equation*}
When carbon saturation is enabled, a fraction of soil nitrogen inputs is redirected to the litter pool in an analogous
manner to the soil carbon inputs, based on the same saturation fraction
The soil mineral nitrogen pool
\begin{equation} \frac{dN_\text{min}}{{dt}} = F^N_\text{litter,min} + F^N_\text{soil,min} + F^N_\text{fert,min} - F^N_\text{vol} - F^N_\text{leach} - F^N_\text{uptake} \label{eq:mineral_n_dndt} \end{equation}
Mineralization and fertilization add to the mineral nitrogen pool. Losses include volatilization, leaching, and plant uptake, described below. Fixed N enters the plant pool directly (\eqref{eq:n_fix_demand}).
Total nitrogen mineralization is proportional to the total heterotrophic respiration from soil and litter pools, divided
by the C:N ratio of the pool. The effects of temperature, moisture, tillage, and C:N ratio on mineralization rate are
captured in the calculation of
\begin{equation} F^N_\text{min} = \sum_j \left( \frac{R_{H\text{j}}}{CN_{\text{j}}} \right) \label{eq:n_min} \end{equation}
\begin{equation*} \small j \in {\text{soil, litter}} \end{equation*}
\begin{equation} F^N_\text{vol} = K_\text{vol} \cdot N_\text{min} \cdot D_{\text{temp}} \cdot D_{\text{water},N_\text{vol}} \label{eq:n_vol} \end{equation}
Justification: SIPNET represents
\begin{equation} F^N_\text{leach} = N_\text{min} \cdot \phi \cdot f^N_\text{leach} \label{eq:n_leach} \end{equation}
where:
\begin{equation} \phi = \min\left(\frac{F^W_\text{drainage}}{W_\text{WHC}}, 1\right) \end{equation}
Plant N demand is the amount of N required to support plant growth. Growth from NPP allocation and the leaf on transfer are accounted for separately, as they are met from different supplies.
New tissue built from NPP requires nitrogen in proportion to the carbon allocated to each pool, at the fixed C:N ratio of that pool:
\begin{equation} F^N_{\text{demand,creation}} = \sum_{i} \frac{F^C_{\text{creation,}i}}{CN_{\text{i}}} \label{eq:creation_n_demand} \end{equation}
\begin{equation*} \small i \in {\text{wood, leaf, fine root, coarse root}} \end{equation*}
Each term in the sum is calculated according to \eqref{eq:plant_n}.
Leaf on moves existing tissue rather than building new tissue, so the carbon brings nitrogen with it and the demand is
only the difference in stoichiometry between the source and the destination. The carbon arrives holding the nitrogen it
held as wood or coarse root,
\begin{equation} F^N_{\text{demand,leafOn}} = \frac{F^C_{\text{creation,leafOn}}}{CN_{\text{leaf}}} - \frac{F^C_{\text{creation,leafOn}}}{CN_{\text{wood}}} \label{eq:leaf_on_n_demand} \end{equation}
Leaves are more nitrogen rich than the tissue the carbon comes from, so the transfer requires additional nitrogen. Coarse roots share the wood C:N ratio, so the split of the transfer between the two source pools does not change it.
The two demands are satisfied in sequence. Leaf on is met entirely from the plant nitrogen storage pool, which is
filled by nitrogen resorbed from leaves as they senesce, and it has first claim on that pool. If the pool cannot cover
the demand, the leaf on transfer itself is reduced (Sec. Leaf On/Leaf Off) rather than the
shortfall being carried forward, so leaf on never draws on fixation or soil uptake. Storage nitrogen left after that
claim,
\begin{equation} F^N_\text{storage} = \frac{N_\text{plant,storage}}{\Delta t} - F^N_{\text{demand,leafOn}} \label{eq:plant_n_storage_flux} \end{equation}
\begin{equation} F^N_{\text{demand}} = \max\left(0,; F^N_{\text{demand,}creation} - F^N_{\text{storage}}\right) \label{eq:plant_n_demand} \end{equation}
For N-fixing plants, symbiotic nitrogen fixation is represented as supplying a fraction of plant nitrogen demand, and is inhibited by high soil mineral N. Plant N demand is defined in \eqref{eq:plant_n_demand}.
The fraction of plant N demand met by biological N fixation is defined as:
\begin{equation} f_\text{fix} = f_{\text{fix,max}} \cdot D_{N_\text{min}} \label{eq:f_fix} \end{equation}
where:
-
$f_{\text{fix,max}}$ is the maximum fraction of plant N demand that can be met by fixation under low soil N ( dimensionless,$0 \le f_{\text{fix,max}} \le 1$ ), and -
$D_{N_\text{min}}$ represents inhibition of N fixation by soil mineral N ( dimensionless,$0 \le D_{N_\text{min}} \le 1$ ).
We use a simple down-regulation function with increasing soil mineral N:
\begin{equation} D_{N_\text{min}} = \frac{{K_N}}{{K_N} + N_\text{min}} \label{eq:n_fix_supp_demand} \end{equation}
where
Nitrogen fixation and soil N uptake are then partitioned from plant N demand
\begin{equation} F^N_\text{fix} = f_\text{fix} \cdot F^N_\text{demand} \label{eq:n_fix_demand} \end{equation}
\begin{equation} F^N_\text{uptake} = (1 - f_\text{fix}) \cdot F^N_\text{demand} \label{eq:n_uptake_demand} \end{equation}
Fixed N (
We do not consider free-living nonsymbiotic N fixation, which is approximately two orders of magnitude smaller (less than 2 kg N ha$^{-1}$ yr$^{-1}$, Cleveland et al. 1999) than crop N demand and typical N fertilization rates.
Nitrogen limitation occurs when plant nitrogen demand exceeds the supply of plant-available nitrogen. Plant nitrogen demand is diagnosed from the desired uptake flux \eqref{eq:n_uptake_demand} compared to the available supply of mineral nitrogen in the soil.
If plant nitrogen demand exceeds plant-available nitrogen, allocation of carbon to new growth is reduced to the level that available nitrogen can support. Carbon not allocated to growth remains in the wood storage pool (\eqref{eq:wood_c_storage}). Thus, nitrogen limitation does not directly affect carbon uptake; it reduces future photosynthesis by constraining increases in photosynthetically active leaf area \eqref{eq:lai_calculation}.
Nitrogen limitation is applied after the flux calculation stage of the model update sequence. N limitation is implemented as follows:
- Calculate the amount by which plant N demand exceeds available supply 1.
- Calculate the fraction by which biomass growth must be reduced so that N demand equals supply.
- Reduce biomass growth accordingly by scaling carbon allocation to plant biomass pools. Unallocated carbon remains in the wood storage pool \eqref{eq:wood_c_storage}.
- Calculate nitrogen uptake as the amount of N required to support the realized plant growth, based on fixed stoichiometry.
\begin{equation} \frac{dW_{\text{soil}}}{dt} = (1 - f_{\text{intercept}}),F^W_{\text{precip}} + F^W_{\text{irrig,soil}} - F^W_{\text{drainage}} - F^W_{\text{trans}} \label{eq:Braswell_A4} \end{equation}
This is equation (A4) from Braswell, et al. (2005).
The term
Drainage occurs when soil water content FLOODING is enabled
(CLI: --flooding).
If FLOODING is not enabled (the default behavior), all excess water drains away at each time step. This mode is
appropriate for well-drained soil.
\begin{equation} F^W_{\text{drainage}} = \frac{\max(W_{\text{soil}} - W_{\text{WHC}}, 0)}{\Delta t} \label{eq:drainage_no_flooding} \end{equation}
If FLOODING is enabled, the rate is controlled by the drainage parameter
\begin{equation} F^W_{\text{drainage}} = f_\text{drain} \cdot \max(W_{\text{soil}} - W_{\text{WHC}}, 0) \label{eq:drainage_flooding} \end{equation}
Flooding can be simulated by using a combination of low
This is adapted from the original SIPNET formulation (Braswell et al 2005), adding a new parameter that controls the drainage rate.
We define
\begin{equation} F^W_{\text{precip,soil}} = (1 - f_{\text{intercept}}),F^W_{\text{precip}} \end{equation}
\begin{equation} ET = E + T \end{equation}
Evapotranspiration (
There are two components of evaporation: (1) immediate evaporation from intercepted precipitation or canopy irrigation and (2) soil surface evaporation.
Interception (Immediate Evaporation)
\begin{equation} F^W_{\text{intercept,evap}} = f_{\text{intercept}},(F^W_{\text{precip}} + F^W_{\text{irrig,canopy}}) \end{equation}
If LEAF_WATER is enabled (CLI: --leaf-water), SIPNET limits immediate evaporation from canopy interception
using an LAI-scaled cap on the interception-evaporation flux. In calcPrecip(), potential interception evaporation is:
\begin{equation} E_{\text{int,pot}} = f_{\text{intercept}} \cdot F^W_{\text{precip}} \end{equation}
and is capped by an LAI-scaled maximum interception-evaporation flux:
\begin{equation} E_{\text{int,max}} = LAI \cdot WHC_{\text{leaf}} \end{equation}
so that:
\begin{equation} E_{\text{int}} = \min(E_{\text{int,pot}}, E_{\text{int,max}}) \end{equation}
Any rainfall not evaporated immediately becomes throughfall to the soil.
Soil Evaporation
Soil evaporation is computed as:
\begin{equation} F^W_{\text{soil,evap}} = \frac{\rho C_p}{\gamma}\frac{1}{\lambda} \frac{\text{VPD}\text{soil}}{r_d + r{\text{soil}}} \end{equation}
where:
\begin{equation*} r_d = \frac{\text{rdConst}}{u}, \qquad r_{\text{soil}} = \exp!\left(r_{\text{soil},1} - r_{\text{soil},2} f^_{\text{WHC}}\right) \end{equation}
For soil evaporation, SIPNET assumes a saturated-surface approximation by using the clipped fraction $f^*{\text{WHC}}$ before calculating $r\text{soil}$.
Negative (condensation) values are clipped to zero. If snow > 0 then
Total evaporation is calculated as the sum of intercepted water, soil evaporation, and sublimation:
\begin{equation} E = F^W_{\text{intercept,evap}} + F^W_{\text{soil,evap}} + F^W_{\text{sublim}} \end{equation}
\begin{equation} \text{WUE} = \frac{K_{\text{WUE}}}{\text{VPD}} \label{eq:Braswell_A13} \end{equation}
This is equation (A13) from Braswell, et al. (2005).
Water Use Efficiency (WUE) is defined as the ratio of a constant
\begin{equation} F^W_{\text{trans,pot}} = \frac{\text{GPP}_{\text{pot}}}{\text{WUE}} \label{eq:Braswell_A14} \end{equation}
This is equation (A14) from Braswell, et al. (2005).
Potential transpiration
\begin{equation} F^W_\text{trans} = \min(F^W_\text{trans, pot}, f \cdot W_\text{soil}) \label{eq:Braswell_A15} \end{equation}
This is equation (A15) from Braswell, et al. (2005).
Actual transpiration
Metabolic processes including photosynthesis, autotrophic and heterotrophic respiration, decomposition, nitrogen volatilization, and methanogenesis are modified directly by temperature, soil moisture, and / or vapor pressure deficit.
Below is a description of these functions.
Photosynthesis has a temperature optimum in the range of observed air temperatures as well as maximum and minimum
temperatures of photosynthesis
\begin{equation} D_\text{temp,A}=\max\left(\frac{(T_\text{max} - T_\text{air})(T_\text{air} - T_\text{min})}{\left(\frac{T_\text{max} - T_\text{min}}{2}\right)^2}, 0\right) \label{eq:Braswell_A9} \end{equation}
This is equation (A9) from Braswell, et al. (2005).
Where
Because the function is symmetric around
The temperature response of autotrophic
\begin{equation} D_{\text{temp,Q10}} = Q_{10}^{\frac{(T-T_\text{opt})}{10}} \label{eq:Braswell_A18b} \end{equation}
This is from equation (A18) from Braswell, et al. (2005)
The exponential function is a simplification of the Arrhenius function in which
We assume
This function provides two ways to reduce the number of parameters in the model. Braswell et al (2005) used two
Moisture dependence functions are typically based on soil water content as a fraction of water holding capacity, also
referred to as soil moisture or fractional soil wetness (
\begin{equation} f_{\text{WHC}} = \frac{W_{\text{soil}}}{W_{\text{WHC}}} \end{equation}
Where
-
$f_{\text{WHC}}$ : Soil water content fraction (unbounded) -
$W_{\text{soil}}$ : Soil water content -
$W_{\text{WHC}}$ : Soil water holding capacity
For moisture dependency functions (heterotrophic respiration, volatilization, and methanogenesis) and evapotranspiration, SIPNET uses the clipped ratio
\begin{equation} D_{\text{water,}A} = \frac{F^W_{\text{trans}}}{F^W_{\text{trans, pot}}} \label{eq:Braswell_A16} \end{equation}
This is equation (A16) from Braswell, et al. (2005).
The water stress factor
Aerobic water availability (dry limitation)
\begin{equation} D_\text{aer}(f^_{\text{WHC}}) = \frac{f^_{\text{WHC}}}{f_a}, \text{clipped to } [0, 1] \end{equation}
Anaerobic index (oxygen limitation proxy)
\begin{equation} A(f^_{\text{WHC}}) = \frac{f^_{\text{WHC}} − f_a}{1 - f_a}, \text{clipped to } [0, 1] \end{equation}
where
These two diagnostics partition moisture effects into water limitation at low moisture and oxygen limitation at high moisture.
The default heterotrophic respiration moisture dependence is a power-law of relative soil water content when soils are
above freezing. With the default exponent
\begin{equation} D_{\text{water},R_H} = \begin{cases} 1, & \text{if } T_{\text{soil}} \lt 0 \ (f^*{\text{WHC}})^b, & \text{if } T{\text{soil}} \ge 0 \end{cases} \label{eq:water_rh} \end{equation}
where
If the command-line option ANAEROBIC is on, the dependency is represented as a partition
between aerobic and anaerobic pathways:
\begin{equation} D_{\text{water},R_H} = (1 - A) D_\text{aer} + \eta A \label{eq:water_rh_2} \end{equation}
where
The volatilized nitrogen flux (treated as N2O-dominated in the absence of explicit speciation) is assumed to peak at intermediate redox conditions, where aerobic and anaerobic processes overlap:
\begin{equation} D_{\text{water},N_{vol}} = 0.05 + 3.8 A (1-A) \label{eq:water_nvol} \end{equation}
where 0.05 represents baseline aerobic volatilization and the factor 3.8 scales the quadratic term so that the maximum value is 1, and
\begin{equation} D_{\text{water},\text{CH}_4} = A^p \label{eq:water_ch4} \end{equation}
where
This represents a collapsed redox ladder (i.e.,
User-specified management events are read from events.in. Each record includes the date of the event, the type of
event, and any associated parameters. SIPNET can also generate internal event records such as leafon, leafoff,
and plantdeath, which are written to events.out when event handling is enabled.
Additions of Mineral N, Organic N, and Organic C are added directly to their respective pools via the
fluxes events.in configuration file.
Event parameters specified in the events.in file:
- Organic N added
$(F^N_{\text{fert,org}})$ - Organic C added
$(F^C_{\text{fert,org}})$ - Mineral N added
$(F^N_{\text{fert,min}})$
Mineral N includes fertilizer supplied as NO3, NH4, and Urea-N. Urea-N is assumed to hydrolyze to ammonium and bicarbonate rapidly and is treated as a mineral N pool. This is a common model assumption because of the fast conversion of Urea to ammonium, and is consistent with the DayCent formulation (Parton et al, 2001). Only relatively recently did DayCent explicitly model Urea-N to NH4 in order to represent the impact of urease inhibitors (Gurung et al 2021) that slow down the rate.
To represent the effect of tillage on decomposition rate, we define the tillage dependency function
\begin{equation} D_{\textrm{till}}(t) = 1 + f_{\textrm{till}}\cdot e^{-t/30} \label{eq:till} \end{equation}
events.in file, and
A value of
If multiple tillage events at times
\begin{equation} D_{\textrm{till}}(t) = 1 + \sum_{z} f_{\textrm{till,}z}, e^{-(t-t_{z})/30},\quad t\ge t_{z} \end{equation}
A planting event is defined by its emergence date and directly specifies the amount of carbon added to each of four plant carbon pools: leaf, wood, fine root, and coarse root. On the emergence date, the model initializes the plant pools with the amounts of carbon specified in the events file.
Following carbon addition, nitrogen for each pool is computed using the corresponding C:N stoichiometric ratios \eqref{eq:cn_stoich}.
A harvest event is specified by its date, the event type "harv", and the fractions of above and belowground carbon that is either removed from the system or transferred to litter or soil.
Because a harvest event only specifies the fraction of above and belowground carbon that is removed or transferred, assume that the above terms apply to leaf + wood, and below terms apply to fine root + coarse root.
The removed fraction is calculated as follows:
\begin{equation} F^C_{\text{harvest,removed}} = f_{\text{remove,above}} \cdot C_{\text{above}} + f_{\text{remove,below}} \cdot C_ {\text{root}} \label{eq:harvest_removed} \end{equation}
The fraction transferred to litter is calculated as follows:
\begin{equation} F^C_{\text{harvest,litter}} = f_{\text{transfer,above}} \cdot C_{\text{above}} \label{eq:harvest_litter} \end{equation}
This amount is then added to the litter flux in \eqref{eq:litter_flux}.
Finally, the fraction transferred to soil is calculated as follows:
\begin{equation} F^C_{\text{harvest,soil}} = f_{\text{transfer,below}} \cdot C_{\text{below}} \label{eq:harvest_soil} \end{equation}
Belowground harvest transfers are routed directly to the soil carbon pool and are therefore included in
the total soil carbon input flux
Event parameters:
- Irrigation rate
$(F^W_{\text{irrigation}})$ , cm/day - Irrigation type indicator
$(I_{\text{irrigation}}\in {0,1})$ :- Canopy irrigation (0): Water applied to the canopy.
- Soil irrigation (1): Water directly added to the soil.
The irrigation that reaches the soil water pool is:
\begin{equation} F^W_{\text{irrig,soil}} = \begin{cases} (1 - f_{\text{intercept}}) , F^W_{\text{irrig}}, & I_{\text{irrigation}} = 0 \ F^W_{\text{irrig}}, & I_{\text{irrigation}} = 1 \end{cases} \label{eq:irrig_soil} \end{equation}
Irrigation that is immediately evaporated:
\begin{equation} F^W_{\text{irrig,evap}} = \begin{cases} f_{\text{intercept}} , F^W_{\text{irrig}}, & I_{\text{irrigation}} = 0 \ 0, & I_{\text{irrigation}} = 1 \end{cases} \label{eq:irrig_evap} \end{equation}
Leaf on and leaf off events only specify the date, not the amount, of leaf biomass C and N added or subtracted.
Event parameters:
| Parameter | Value | Description |
|---|---|---|
| Year | integer | Year |
| Day | integer | Day of year |
| Type | leafon / leafoff |
The type of event |
There are no other parameters needed for these events, as the amount of transfer is determined by the parameters mentioned in Sec. Leaf On/Leaf Off.
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Parton, W. J., E. A. Holland, S. J. Del Grosso, M. D. Hartman, R. E. Martin, A. R. Mosier, D. S. Ojima, and D. S. Schimel. 2001. Generalized Model for NOx and N2O Emissions from Soils. Journal of Geophysical Research: Atmospheres 106 (D15): 17403–19. https://doi.org/10.1029/2001JD900101.
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Wang H, Yan Z, Ju X, Song X, Zhang J, Li S and Zhu-Barker X (2023) Quantifying nitrous oxide production rates from nitrification and denitrification under various moisture conditions in agricultural soils: Laboratory study and literature synthesis. Front. Microbiol. 13:1110151. https://doi.org/10.3389/fmicb.2022.1110151
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Footnotes
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Nitrogen limitation is evaluated accounting for biological nitrogen fixation and mineralization but before nitrogen fertilization. Any nitrogen fertilizer inputs alleviate N limitation in subsequent time steps. ↩