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SIPNET Model States and Parameters {#sec-parameters}

Lists SIPNET state variables and tunable parameters, mapping symbols to the model equations, configuration names, units, and I/O fields. See Model Inputs and Model Outputs for file formats. Units are those used in sipnet.param; internal conversions are noted. Unless noted, pools are mass per ground area. The actual parameter set that is used depends on the configured model structure. For equation references, see the model structure documentation.

Notation

Variables (Pools, Fluxes, and Parameters)

Category Symbol Description
State variables
$C$ Carbon pool
$N$ Nitrogen pool
$W$ Water pool or content
$CN$ Carbon-to-Nitrogen ratio
Fluxes and rates
$F$ Generic flux of carbon, nitrogen, or water
$A$ Photosynthetic assimilation (net photosynthesis)
$R$ Respiration flux
$R_H$ Heterotrophic respiration (soil/litter decomposition)
$R_A$ Autotrophic respiration (vegetation respiration)
$ET$ Evapotranspiration
$F^W_{\text{trans}}$ Transpiration
$GPP$ Gross Primary Production
$NPP$ Net Primary Production
$NEE$ Net Ecosystem Exchange
Environmental drivers
$T$ Temperature
$VPD$ Vapor Pressure Deficit
$PAR$ Photosynthetically Active Radiation
$LAI$ Leaf Area Index
Parameters
$K$ Rate constant (e.g., for decomposition or respiration)
$Q_{10}$ Temperature sensitivity coefficient
$\alpha$ Fraction of NPP allocated to a plant pool
$f$ Fraction of a pool or flux other than NPP
$k$ Scaling factor
$D$ Dependency or damping function
$SLW$ Specific Leaf Weight (leaf carbon per unit leaf area)

Note on superscripts: Most variables use superscripts and subscripts (e.g., $F^C_{\text{growth}}$ for growth respiration flux). However, some terms that are widely used in the scientific literature use the common notation $NPP$, $GPP$, $R_H$, $R_A$, and $ET$.

Subscripts (Temporal, Spatial, or Contextual Identifiers)

Category Subscript Description
Temporal identifiers
$X_0$ Initial value
$X_t$ Value at time $t$
$X_d$ Daily value or average
$X_{\text{avg}}$ Average value (e.g., over a timestep or spatial area)
$X_{\text{max}}$ Maximum value (e.g., temperature or rate)
$X_{\text{min}}$ Minimum value (e.g., temperature or rate)
$X_{\text{opt}}$ Optimal value (e.g., temperature or rate)
Structural components
$X_{\text{leaf}}$ Leaf pools or fluxes
$X_{\text{wood}}$ Wood pools or fluxes
$X_{\text{root}}$ Root pool (general)
$X_{\text{fine root}}$ Fine root pool
$X_{\text{coarse root}}$ Coarse root pool
$X_{\text{soil}}$ Soil pools or processes
$X_{\text{litter}}$ Litter pools or processes
$X_{\text{veg}}$ Vegetation processes (general)
Processes context
$X_{\text{resp}}$ Respiration processes
$X_{\text{growth}}$ Growth respiration
$X_{\text{dec}}$ Decomposition processes
$X_{\text{vol}}$ Volatilization processes
$X_{\text{drain}}$ Drainage processes
Chemical / environmental identifiers
$X_{\text{org}}$ Organic forms
$X_{\text{mineral}}$ Mineral forms
$X_{\text{anaer}}$ Anaerobic soil conditions
$X_{\text{HC}}$ Water holding capacity

Subscripts may be used in combination, e.g., $X_{\text{soil,mineral},0}$.

Run-time Parameters

Run-time parameters can change from one run to the next, or when the model is stopped and restarted. These include initial state values and parameters related to plant physiology, soil physics, and biogeochemical cycling.

Initial State Values

Symbol Parameter Name Definition Units Notes
$C_{\text{wood},0}$ plantWoodInit Initial wood carbon $\text{g C} \cdot \text{m}^{-2} \text{ ground area}$ Above-ground + roots
$C_{\text{wood,storage}}$ Wood carbon storage pool (delta), initialized internally to 0 $\text{g C} \cdot \text{m}^{-2} \text{ ground area}$ Not a runtime param; $C_{\text{wood,total}} = C_{\text{wood}} + C_{\text{wood,storage}}$
$LAI_0$ laiInit Initial leaf area $\text{m}^2 \text{ leaves} \cdot \text{m}^{-2} \text{ ground area}$ Multiply by SLW to get initial plant leaf C: $C_{\text{leaf},0} = LAI_0 \cdot SLW$
$C_{\text{litter},0}$ litterInit Initial litter carbon $\text{g C} \cdot \text{m}^{-2} \text{ ground area}$
$C_{\text{soil},0}$ soilInit Initial soil carbon $\text{g C} \cdot \text{m}^{-2} \text{ ground area}$
$f_{\text{WHC},0}$ soilWFracInit Initial soil water fraction unitless May exceed 1.0 when modeling flooded conditions; $W_{\text{soil},0} = f_{\text{WHC},0} \cdot W_{\text{WHC}}$
$N_{\text{org, litter},0}$ litterOrgNInit Initial litter organic nitrogen content $\text{g N} \cdot \text{m}^{-2}$
$N_{\text{org, soil},0}$ soilOrgNInit Initial soil organic nitrogen content $\text{g N} \cdot \text{m}^{-2}$
$N_{\text{min, soil},0}$ mineralNInit Initial mineral nitrogen content $\text{g N} \cdot \text{m}^{-2}$ Single mineral N pool used by soil and litter N fluxes
$N_{\text{plant,storage},0}$ plantStorageNInit Initial plant nitrogen storage pool $\text{g N} \cdot \text{m}^{-2}$ Use 0 unless initial storage pool is known or estimated
$f_{\text{fine root},0}$ fineRootFrac Fraction of plantWoodInit allocated to initial fine root carbon pool unitless
$f_{\text{coarse root},0}$ coarseRootFrac Fraction of plantWoodInit allocated to initial coarse root carbon pool unitless
$W_{\text{snow},0}$ snowInit Initial snow water equivalent cm water equivalent

Stoichiometry Parameters

Symbol Name Description Units Notes
$CN_{\text{wood}}$ woodCN Carbon to Nitrogen ratio of wood $CN_{\text{coarse root}} = CN_{\text{wood}}$
$CN_{\text{leaf}}$ leafCN Carbon to Nitrogen ratio of leaves
$CN_{\text{fine root}}$ fineRootCN Carbon to Nitrogen ratio of fine roots
$k_{CN}$ kCN Decomposition CN scaling parameter

Photosynthesis Parameters

Symbol Parameter Name Definition Units Notes
$A_{\text{max}}$ aMax Maximum net CO$_2$ assimilation rate $\text{nmol CO}_2 \cdot \text{g}^{-1} \text{ leaf} \cdot \text{s}^{-1}$ Assuming maximum PAR, full interception, no stress
$f_{A_{\text{max},d}}$ aMaxFrac Average daily $A_{\text{max}}$ as fraction of instantaneous unitless Accounts for diurnal variation in photosynthesis
$R_{\text{leaf,opt}}$ baseFolRespFrac Basal foliar maintenance respiration as fraction of $A_{\text{max}}$ unitless
$T_{\text{psn,min}}$ psnTMin Minimum temperature for net photosynthesis $^\circ\text{C}$
$T_{\text{psn,opt}}$ psnTOpt Optimum temperature for net photosynthesis $^\circ\text{C}$
$T_{\text{psn,max}}$ psnTMax Maximum temperature for net photosynthesis $^\circ\text{C}$ Calculated internally as $2 \cdot T_{\text{psn,opt}} - T_{\text{psn,min}}$
$K_{\text{VPD}}$ dVpdSlope Slope of VPD–photosynthesis relationship $\text{kPa}^{-1}$ $D_{\text{VPD}} = 1 - K_{\text{VPD}} \cdot VPD^{K_{\text{VPD,exp}}}$
$K_{\text{VPD,exp}}$ dVpdExp Exponent for VPD effect on photosynthesis unitless $D_{\text{VPD}} = 1 - K_{\text{VPD}} \cdot VPD^{K_{\text{VPD,exp}}}$
$\text{PAR}_{1/2}$ halfSatPar Half-saturation point of PAR–photosynthesis relationship $\text{Einsteins} \cdot \text{m}^{-2} \text{ ground area} \cdot \text{day}^{-1}$ Must match PAR units used by runtime light calculations
$k_{\text{atten}}$ attenuation Canopy PAR extinction coefficient unitless

Phenology-Related Parameters

Symbol Parameter Name Definition Units Notes
$D_{\text{on}}$ leafOnDay Day of year when leaves appear unitless day of year (1–365); 0 to turn off
$GDD_{\text{on}}$ gddLeafOn GDD threshold for leaf appearance (GDD-based phenology) $°\text{C} \cdot \text{day}$
$T_{\text{on}}$ soilTempLeafOn Soil temperature threshold for leaf appearance (temp-based phenology) $°\text{C}$
$D_{\text{off}}$ leafOffDay Day of year for leaf drop unitless day of year (1–365); 0 to turn off
$\Delta C_{\text{leaf}}$ leafGrowth Additional leaf growth at start of growing season $\text{g C} \cdot \text{m}^{-2}$
$f_{\text{realloc}}$ leafOnReallocFrac Fraction of wood and coarse root carbon available for leaf-on reallocation unitless
$f_{\text{fall}}$ fracLeafFall Additional fraction of leaves that fall at end of growing season unitless
$f_{\text{N,resorp}}$ leafNResorptionFrac Fraction of leaf nitrogen resorbed to plant N storage at leaf off unitless Only used when nitrogen cycling is enabled
$\alpha_{\text{leaf}}$ leafAllocation Fraction of $NPP$ allocated to leaf growth unitless
$K_{\text{leaf}}$ leafTurnoverRate Average turnover rate of leaves $\text{year}^{-1}$ converted to per-day rate internally

Allocation Parameters

Symbol Parameter Name Definition Units Notes
$\alpha_{\text{fine root}}$ fineRootAllocation Fraction of $NPP$ allocated to fine roots unitless
$\alpha_{\text{coarse root}}$ coarseRootAllocation Fraction of $NPP$ allocated to coarse roots unitless Calculated internally from remainder: $\alpha_{\text{coarse root}} = 1 - \alpha_{\text{leaf}} - \alpha_{\text{wood}} - \alpha_{\text{fine root}}$
$\alpha_{\text{wood}}$ woodAllocation Fraction of $NPP$ allocated to wood unitless

Autotrophic Respiration Parameters

Symbol Parameter Name Definition Units Notes
$R_{\text{a,wood},0}$ baseVegResp Wood maintenance respiration rate at $0^\circ C$ $\text{g C respired} \cdot \text{g}^{-1} \text{ plant C} \cdot \text{year}^{-1}$ converted to per-day rate internally; only counts plant wood C; leaves handled elsewhere (both above and below-ground: assumed for now to have same resp. rate)
$Q_{10v}$ vegRespQ10 Vegetation respiration Q10 unitless Scalar determining effect of temp on veg. resp.
$f_{\text{growth}}$ growthRespFrac growth respiration as a fraction of recent mean NPP. unitless
$D_{\text{frozen}}$ frozenSoilFolREff amount that foliar resp. is shutdown if soil is frozen unitless 0 = full shutdown, 1 = no shutdown
$T_{\text{frozen}}$ frozenSoilThreshold soil temperature below which frozenSoilFolREff and frozenSoilEff kick in °C
$R_{\text{fine root}}$ baseFineRootResp base respiration rate of fine roots $\text{year}^{-1}$ converted to per-day rate internally
$R_{\text{coarse root}}$ baseCoarseRootResp base respiration rate of coarse roots $\text{year}^{-1}$ converted to per-day rate internally
$Q_{10,\text{fine root}}$ fineRootQ10 Q10 for fine root respiration unitless
$Q_{10,\text{coarse root}}$ coarseRootQ10 Q10 for coarse root respiration unitless

Soil Respiration Parameters

Symbol Parameter Name Definition Units Notes
$K_\text{litter}$ litterBreakdownRate rate at which litter is converted to soil / respired at 0°C and max soil moisture $\text{g C broken down} \cdot \text{g}^{-1} \text{ litter C} \cdot \text{year}^{-1}$ converted to per-day rate internally
$f_{\text{litter}}$ fracLitterRespired of the litter broken down, fraction respired (the rest is transferred to soil pool) unitless
$K_{\text{soil}}$ baseSoilResp Soil respiration rate at $0 ^{\circ}\text{C}$ and moisture saturated soil $\text{g C respired} \cdot \text{g}^{-1} \text{ soil C} \cdot \text{year}^{-1}$ converted to per-day rate internally
$Q_{10s}$ soilRespQ10 Soil respiration Q10 unitless scalar determining effect of temp on soil respiration
$D_{\text{moisture}}$ soilRespMoistEffect scalar determining effect of moisture on soil resp. unitless
$f_{\text{till}}$ tillageEff Effect of tillage on decomposition that exponentially decays over time fraction Documented in model structure; event-level term in events.in
$C_{\text{soil,saturation}}$ soilCSaturation Maximum amount of carbon that can be stabilized in the soil, used when carbon-saturation is enabled. $\text{g C} \cdot \text{m}^{-2} \text{ ground area}$

Nitrogen Cycle Parameters

Run-time parameters support mineral nitrogen losses through volatilization and leaching.

Symbol Parameter Name Definition Units Notes
$K_\text{vol}$ nVolatilizationFrac Nitrogen volatilization rate constant that determines the maximum rate of N volatilization as a proportion of available $N_\text{min}$ $\text{day}^{-1}$ \eqref{eq:n_vol}
$f^N_{\text{leach}}$ nLeachingFrac Fraction of $N_\text{min}$ available to be leached, applied after scaling by $\phi = \min(F^W_\text{drainage}/W_\text{WHC}, 1)$ $\text{day}^{-1}$ \eqref{eq:n_leach}
$f^N_{\text{resorb}}$ leafNResorptionFrac Fraction of senescing leaf nitrogen transferred to the plant nitrogen storage pool unitless

Moisture-Related Parameters

Symbol Parameter Name Definition Units Notes
$f_{\text{trans,avail}}$ waterRemoveFrac fraction of plant available soil water which can be removed per day by transpiration without water stress occurring $\text{day}^{-1}$
$D_{\text{frozen,water}}$ frozenSoilEff fraction of water that is available if soil is frozen (0 = none available, 1 = all still available) unitless if frozenSoilEff = 0, then shut down psn. even if WATER_PSN = 0, if soil is frozen (if frozenSoilEff > 0, it has no effect if WATER_PSN = 0)
$WUE$ wueConst water use efficiency constant unitless
$WHC_{\text{soil}}$ soilWHC soil (transpiration layer) water holding capacity cm
$f_{\text{WHC}}$ Soil water content as fraction of WHC unitless
$f^*_{\text{WHC}}$ Clipped soil water content as fraction of WHC unitless internally clipped to [0,1]
$WHC_{\text{leaf}}$ leafPoolDepth leaf/canopy evaporative pool capacity per unit leaf area (used to limit interception evaporation when enabled) cm Only used when LEAF_WATER = 1 (--leaf-water). defines LAI-scaled cap on interception evaporation: $immedEvap \le LAI \cdot WHC_{\text{leaf}}$. Excess throughfall goes to the soil.
$f_{\text{intercept}}$ immedEvapFrac fraction of rain that is immediately intercepted & evaporated unitless
$f_{\text{fastflow}}$ fastFlowFrac fraction of water entering soil that goes directly to drainage unitless
$f_{\text{drain}}$ waterDrainFrac fraction of excess soil water that drains per day $\text{day}^{-1}$
$f_a$ fAnoxia Soil wetness fraction at which oxygen diffusion begins to limit aerobic respiration unitless Used in moisture partitioning between aerobic and anaerobic pathways (\eqref{eq:water_rh_2} in model structure)
$\eta$ anaerobicDecompRate Relative anaerobic decomposition rate unitless Active when anaerobic pathway is enabled; expected range $(0,1]$
$p$ anaerobicTransExp Methane anoxia sensitivity exponent in $D_{\text{water,CH}_4}=A^p$ unitless Expected range $\ge 1$
$K_{\text{CH}_4\text{,soil}}$ soilMethaneRate First-order methane production rate constant for the soil C pool $\text{day}^{-1}$ Expected range $\ge 0$
$K_{\text{CH}_4\text{,litter}}$ litterMethaneRate First-order methane production rate constant for the litter C pool $\text{day}^{-1}$ Expected range $\ge 0$
$M_{\text{snow}}$ snowMelt rate at which snow melts cm water equivalent per degree Celsius per day
$r_{d}$ rdConst scalar determining amount of aerodynamic resistance unitless
$r_{s,1}$ rSoilConst1 unitless soil resistance = $\exp(r_{s,1} - r_{s,2} \cdot f^*_\text{WHC})$
$r_{s,2}$ rSoilConst2 unitless soil resistance = $\exp(r_{s,1} - r_{s,2} \cdot f^*_\text{WHC})$

Tree Physiological Parameters

Symbol Parameter Name Definition Units Notes
$SLW$ leafCSpWt Specific leaf weight (leaf carbon per unit leaf area) $\text{g C} \cdot \text{m}^{-2} \text{ leaf area}$
$C_{\text{frac}}$ cFracLeaf Carbon fraction of leaf dry mass $\text{g leaf C} \cdot \text{g}^{-1} \text{ leaf}$
$K_\text{wood}$ woodTurnoverRate average turnover rate of woody plant C $\text{year}^{-1}$ converted to per-day rate internally; leaf loss handled separately
$K_\text{fine root}$ fineRootTurnoverRate turnover of fine roots $\text{year}^{-1}$ converted to per-day rate internally
$K_\text{coarse root}$ coarseRootTurnoverRate turnover of coarse roots $\text{year}^{-1}$ converted to per-day rate internally

Hard-coded Values

Parameter Value Description
C_WEIGHT 12.0 molecular weight of carbon
MEAN_NPP_DAYS 5 over how many days do we keep the running mean
MEAN_NPP_MAX_ENTRIES MEAN_NPP_DAYS*50 assume that the most pts we can have is two per hour
LAMBDA 2501000 latent heat of vaporization (J/kg)
LAMBDA_S 2835000 latent heat of sublimation (J/kg)
RHO 1.3 air density (kg/m^3)
CP 1005. specific heat of air (J/(kg K))
GAMMA 66 psychometric constant (Pa/K)
E_STAR_SNOW 0.6 approximate saturation vapor pressure at 0°C (kPa)