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Document on plant respiration
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‎components/elm/docs/tech-guide/CNP_pools.md‎

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# 1. Carbon, nitrogen, and phosphorus allocation
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E3SM is fully prognostic for all carbon, nitrogen, and phosphorus state variables in the vegetation, litter, and soil organic matter pools.
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At each model time step and for each PFT occupying a soil column, the carbon available for allocation to new growth ($F^C_{avail}$) is calculated. The carbon available is then allocated to new plant growth.
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## 1.1 Carbon available for new growth
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Implemented in subroutine: `Allocation1_PlantNPDemand`
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Total plant nitrogen and phosphorus demand for new growth is estimated as:
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Total plant nitrogen and phosphorus demand for each time step is calculated from carbon allometry and nitrogen and phosphorus concentrations for each tissue type (specified by PFT).
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$$
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\begin{equation}

‎components/elm/docs/tech-guide/index.md‎

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- [TOP Parameterization](top_solar_parameterization.md):
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Parameterization of sub-grid topographical effects on solar radiation.
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- [Longwave Radiation](longwave_radiation.md): Longwave radiation model
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- [Carbon, Nitrogen, and Phosphorus allocation](CPN_pools.md)
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- [Respiration](plant_respiration.md)
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- [Carbon, Nitrogen, and Phosphorus allocation](CNP_pools.md)

‎components/elm/docs/tech-guide/plant_respiration.md‎

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# 1. Plant respiration
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## 1.1 Autotrophic Respiration
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The model treats maintenance and growth respiration processes separately (Lavigne and Ryan, 1997[@lavigne1997growth]; Sprugel, et al., 1995[@sprugel1995respiration]).
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### 1.1.1 Maintenance Respiration
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Maintenance respiration (MR) is a function of temperature and tissue N concentration (Ryan, 1991[@ryan1991effects]) for live biomass (excludes dead stem and coarse root pools) (Thornton and Rosenbloom, 2005[@thornton2005ecosystem]).
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Rates for aboveground pools are based on the prognostic 2-meter air temperature, and rates for belowground pools (fine and coarse roots) depend on fractional rooting distribution with depth and the associated prognostic soil temperatures.
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Implemented in subroutine: `MaintenanceResp`
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$$
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\begin{equation}
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F^C_{mr,leaf} = (lmr_{sun} \times lai_{sun} + lmr_{sha} \times lai_{sha}) \times C_{umolCO2\_to\_gC}
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\end{equation}
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$$
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$$
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\begin{eqnarray}
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\label{eqn_mr}
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F^C_{mr,livestem} &=& S^N_{livestem} \times br_{mr} \times q_{10}^{\left(\frac{T_{2m} - T_{frz} - 20}{10}\right)} \\
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F^C_{mr,livecroot} &=& S^N_{livecroot} \times br_{mr} \times q_{10}^{\left(\frac{T_{2m} - T_{frz} - 20}{10}\right)} \\
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F^C_{mr,grain} &=& S^N_{grain} \times br_{mr} \times q_{10}^{\left(\frac{T_{2m} - T_{frz} - 20}{10}\right)} \\
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F^C_{mr,fineroot} &=& \sum_{j=1} ^{nlevsoi} S^N_{fineroot} \times root_{fr,j} \times br_{mr} \times q_{10}^{\left(\frac{T_{s,j} - T_{frz} - 20}{10}\right)}
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\end{eqnarray}
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$$
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$$
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\begin{equation}
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mr = F^C_{mr,leaf} + F^C_{mr,livestem} + F^C_{mr,livecroot} + F^C_{mr,grain} + F^C_{mr,fineroot}
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\end{equation}
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$$
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### 1.1.2 Growth Respiration
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Growth respiration is calculated as the parameter $gr_{perc}$, times the total carbon in new growth on a given timestep, based on construction costs for a range of woody and non-woody tissues (Larcher, 1995[@larcher2003physiological]).
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Implemented in subroutine: `GrowthResp`
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$$
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\begin{eqnarray}
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\label{eqn_gr}
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F^C_{gr,leaf} &=& F^C_{alloc,leaf} \times gr_{perc} \\
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F^C_{gr,leaf\_stor} &=& F^C_{alloc,leaf\_stor} \times gr_{perc} \times gr_{pnow} \\
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F^C_{gr,froot} &=& F^C_{alloc,froot} \times gr_{perc} \\
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F^C_{gr,froot\_stor} &=& F^C_{alloc,froot\_stor} \times gr_{perc} \times gr_{pnow} \\
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F^C_{gr,livestem} &=& F^C_{alloc,livestem} \times gr_{perc} \\
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F^C_{gr,livestem\_stor} &=& F^C_{alloc,livestem\_stor} \times gr_{perc} \times gr_{pnow} \\
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F^C_{gr,deadstem} &=& F^C_{alloc,deadstem} \times gr_{perc} \\
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F^C_{gr,deadstem\_stor} &=& F^C_{alloc,deadstem\_stor} \times gr_{perc} \times gr_{pnow} \\
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F^C_{gr,livecroot} &=& F^C_{alloc,livecroot} \times gr_{perc} \\
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F^C_{gr,livecroot\_stor} &=& F^C_{alloc,livecroot\_stor} \times gr_{perc} \times gr_{pnow} \\
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F^C_{gr,deadcroot} &=& F^C_{alloc,deadcroot} \times gr_{perc} \\
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F^C_{gr,deadcroot\_stor} &=& F^C_{alloc,deadcroot\_stor} \times gr_{perc} \times gr_{pnow} \\
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F^C_{gr,grain} &=& F^C_{alloc,grain} \times gr_{perc} \\
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F^C_{gr,grain\_stor} &=& F^C_{alloc,grain\_stor} \times gr_{perc} \times gr_{pnow} \\
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\end{eqnarray}
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$$
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Parameter $gr_{pnow}$ is currently set to 1.0. This parameter could be changed to a smaller value to transfer some portion (1 - $gr_{pnow}$) of the growth respiration forward in time to occur at the time of growth display from storage.
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## 1.2 Variable definitions
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| Symbol | Description | Units| ELM Variable |
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| ----------- | ----------- | ----------- | ----------- |
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| $lmr_{sun}$ | sunlit leaf maintenance respiration rate | $umolCO_{2}~m^{-2}~sec^{-1}$ | `photosyns_vars%lmrsun_patch` |
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| $lmr_{sha}$ | shaded leaf maintenance respiration rate | $umolCO_{2}~m^{-2}~sec^{-1}$ | `photosyns_vars%lmrsha_patch` |
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| $lai_{sun}$ | sunlit projected leaf area index | - | `canopystate_vars%laisun_patch` |
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| $lai_{sha}$ | shaded projected leaf area index | - | `canopystate_vars%laisha_patch` |
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| $br_{mr}$ | base rate for maintenance respiration | $gC~gN^{-1}~sec^{-1}$ | `br_mr` |
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| $q_{10}$ | temperature sensitivity for maintenance respiration | - | `q10` |
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| $T_{2m}$ | 2 m height surface air temperature | K | `veg_es%t_ref2m` |
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| $T_{s,j}$ | soil temperature at soil level j| K | `col_es%t_soisno` |
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| $T_{frz}$ | freezing point of water (273.15 K) | K | `SHR_CONST_TKFRZ` |
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| $root_{fr,j}$ | fraction of roots in each soil layer | - | `soilstate_vars%rootfr_patch` |
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| $S^N_{livestem}$ | live stem N | $gN~m^{-2}$ | `veg_ns%livestemn` |
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| $S^N_{livecroot}$ | live coarse root N | $gN~m^{-2}$ | `veg_ns%livecrootn` |
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| $S^N_{fineroot}$ | fine root N | $gN~m^{-2}$ | `veg_ns%finerootn` |
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| $S^N_{grain}$ | grain N | $gN~m^{-2}$ | `veg_ns%grainn` |
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| $F^C_{mr,leaf}$ | leaf maintenance respiration | $gC~m^{-2}~sec^{-1}$ | `veg_cf%leaf_mr` |
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| $F^C_{mr,livestem}$ | live stem maintenance respiration | $gC~m^{-2}~sec^{-1}$ | `veg_cf%livestem_mr` |
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| $F^C_{mr,livecroot}$ | live coarse root maintenance respiration | $gC~m^{-2}~sec^{-1}$ | `veg_cf%livecroot_mr` |
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| $F^C_{mr,fineroot}$ | fine root maintenance respiration | $gC~m^{-2}~sec^{-1}$ | `veg_cf%fineroot_mr` |
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| $F^C_{mr,grain}$ | crop grain or organs maintenance respiration | $gC~m^{-2}~sec^{-1}$ | `veg_cf%grain_mr` |
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| $gr_{perc}$ | growth respiration parameter | - | `grperc` |
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| $gr_{pnow}$ | growth respiration parameter | - | `grpnow` |
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| $F^C_{alloc,leaf}$ | allocation to leaf C | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_leafc` |
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| $F^C_{alloc,leaf\_stor}$ | allocation to leaf C storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_leafc_storage` |
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| $F^C_{alloc,froot}$ | allocation to fine root C | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_frootc` |
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| $F^C_{alloc,froot\_stor}$ | allocation to fine root C storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_frootc_storage` |
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| $F^C_{alloc,livestem}$ | allocation to live stem C | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_livestemc` |
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| $F^C_{alloc,livestem\_stor}$ | allocation to live stem C storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_livestemc_storage` |
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| $F^C_{alloc,deadstem}$ | allocation to dead stem C | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_deadstemc` |
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| $F^C_{alloc,deadstem\_stor}$ | allocation to dead stem C storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_deadstemc_storage` |
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| $F^C_{alloc,livecroot}$ | allocation to live coarse root C | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_livecrootc` |
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| $F^C_{alloc,livecroot\_stor}$ | allocation to live coarse root C storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_livecrootc_storage` |
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| $F^C_{alloc,deadcroot}$ | allocation to dead coarse root C | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_deadcrootc` |
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| $F^C_{alloc,deadcroot\_stor}$ | allocation to dead coarse root C storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_deadcrootc_storage` |
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| $F^C_{alloc,grain}$ | allocation to grain C for prognostic crop | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_grainc` |
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| $F^C_{alloc,grain\_stor}$ | allocation to grain C storage for prognostic crop | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_to_grainc_storage` |
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| $F^C_{gr,leaf}$ | leaf growth respiration | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_leaf_gr` |
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| $F^C_{gr,leaf\_stor}$ | leaf growth respiration to storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_leaf_storage_gr` |
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| $F^C_{gr,froot}$ | fine root growth respiration | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_froot_gr` |
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| $F^C_{gr,froot\_stor}$ | fine root growth respiration to storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_froot_storage_gr` |
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| $F^C_{gr,livestem}$ | livestem growth respiration | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_livestem_gr` |
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| $F^C_{gr,livestem\_stor}$ | livestem growth respiration to storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_livestem_storage_gr` |
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| $F^C_{gr,deadstem}$ | deadstem growth respiration | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_deadstem_gr` |
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| $F^C_{gr,deadstem\_stor}$ | deadstem growth respiration to storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_deadstem_storage_gr` |
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| $F^C_{gr,livecroot}$ | livecroot growth respiration | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_livecroot_gr` |
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| $F^C_{gr,livecroot\_stor}$ | livecroot growth respiration to storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_livecroot_storage_gr` |
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| $F^C_{gr,deadcroot}$ | deadcroot growth respiration | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_deadcroot_gr` |
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| $F^C_{gr,deadcroot\_stor}$ | deadcroot growth respiration to storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_deadcroot_storage_gr` |
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| $F^C_{gr,grain}$ | grain growth respiration | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_grain_gr` |
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| $F^C_{gr,grain\_stor}$ | grain growth respiration to storage | $gC~m^{-2}~sec^{-1}$ | `veg_cf%cpool_grain_storage_gr` |

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