### 2.26.2.4. Allocation[¶](#allocation "Permalink to this headline")

Allocation changes based on the crop phenology phases phenology (section [2.26.2.3](#phenology)). Simulated C assimilation begins every year upon leaf emergence in phase 2 and ends with harvest at the end of phase 3; therefore, so does the allocation of such C to the crop’s leaf, live stem, fine root, and reproductive pools.

Typically, C:N ratios in plant tissue vary throughout the growing season and tend to be lower during early growth stages and higher in later growth stages. In order to account for this seasonal change, two sets of C:N ratios are established in CLM for the leaf, stem, and fine root of crops: one during the leaf emergence phase (phenology phase 2), and a second during grain fill phase (phenology phase 3). This modified C:N ratio approach accounts for the nitrogen retranslocation that occurs during the grain fill phase (phase 3) of crop growth. Leaf, stem, and root C:N ratios for phase 2 are calculated using the new CLM5 carbon and nitrogen allocation scheme (Chapter [2.19](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/CN_Allocation/CLM50_Tech_Note_CN_Allocation.html#rst-cn-allocation)), which provides a target C:N value ([Table 2.26.3](#table-crop-allocation-parameters)) and allows C:N to vary through time. During grain fill (phase 3) of the crop growth cycle, a portion of the nitrogen in the plant tissues is moved to a storage pool to fulfill nitrogen demands of organ (reproductive pool) development, such that the resulting C:N ratio of the plant tissue is reflective of measurements at harvest. All C:N ratios were determined by calibration process, through comparisons of model output versus observations of plant carbon throughout the growing season.

The BGC part of the model keeps track of a term representing excess maintenance respiration, which supplies the carbon required for maintenance respiration during periods of low photosynthesis (Chapter [2.17](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Plant_Respiration/CLM50_Tech_Note_Plant_Respiration.html#rst-plant-respiration)). Carbon supply for excess maintenance respiration cannot continue to happen after harvest for annual crops, so at harvest the excess respiration pool is turned into a flux that extracts CO2 directly from the atmosphere. This way any excess maintenance respiration remaining at harvest is eliminated as if such respiration had not taken place.

#### 2.26.2.4.1. Leaf emergence[¶](#leaf-emergence-to-grain-fill "Permalink to this headline")

During phase 2, the allocation coefficients (fraction of available C) to each C pool are defined as:

(2.26.4)[¶](#equation-25-4 "Permalink to this equation")\\\[\\begin{split}\\begin{array}{l} {a\_{repr} =0} \\\\ {a\_{froot} =a\_{froot}^{i} -(a\_{froot}^{i} -a\_{froot}^{f} )\\frac{GDD\_{T\_{{\\rm 2m}} } }{GDD\_{{\\rm mat}} } {\\rm \\; \\; \\; where\\; \\; \\; }\\frac{GDD\_{T\_{{\\rm 2m}} } }{GDD\_{{\\rm mat}} } \\le 1} \\\\ {a\_{leaf} =(1-a\_{froot} )\\cdot \\frac{a\_{leaf}^{i} (e^{-b} -e^{-b\\frac{GDD\_{T\_{{\\rm 2m}} } }{h} } )}{e^{-b} -1} {\\rm \\; \\; \\; where\\; \\; \\; }b=0.1} \\\\ {a\_{livestem} =1-a\_{repr} -a\_{froot} -a\_{leaf} } \\end{array}\\end{split}\\\]

where \\(a\_{leaf}^{i}\\), \\(a\_{froot}^{i}\\), and \\(a\_{froot}^{f}\\) are initial and final values of these coefficients ([Table 2.26.3](#table-crop-allocation-parameters)), and _h_ is a heat unit threshold defined in section [2.26.2.3.3](#grain-fill). At a crop-specific maximum leaf area index, \\({L}\_{max}\\) ([Table 2.26.3](#table-crop-allocation-parameters)), carbon allocation is directed exclusively to the fine roots.

#### 2.26.2.4.2. Grain fill[¶](#grain-fill-to-harvest "Permalink to this headline")

The calculation of \\(a\_{froot}\\) remains the same from phase 2 to phase 3. During grain fill (phase 3), other allocation coefficients change to:

(2.26.5)[¶](#equation-25-5 "Permalink to this equation")\\\[\\begin{split}\\begin{array}{ll} a\_{leaf} =a\_{leaf}^{i,3} & {\\rm when} \\quad a\_{leaf}^{i,3} \\le a\_{leaf}^{f} \\quad {\\rm else} \\\\ a\_{leaf} =a\_{leaf} \\left(1-\\frac{GDD\_{T\_{{\\rm 2m}} } -h}{GDD\_{{\\rm mat}} d\_{L} -h} \\right)^{d\_{alloc}^{leaf} } \\ge a\_{leaf}^{f} & {\\rm where} \\quad \\frac{GDD\_{T\_{{\\rm 2m}} } -h}{GDD\_{{\\rm mat}} d\_{L} -h} \\le 1 \\\\ \\\\ a\_{livestem} =a\_{livestem}^{i,3} & {\\rm when} \\quad a\_{livestem}^{i,3} \\le a\_{livestem}^{f} \\quad {\\rm else} \\\\ a\_{livestem} =a\_{livestem} \\left(1-\\frac{GDD\_{T\_{{\\rm 2m}} } -h}{GDD\_{{\\rm mat}} d\_{L} -h} \\right)^{d\_{alloc}^{stem} } \\ge a\_{livestem}^{f} & {\\rm where} \\quad \\frac{GDD\_{T\_{{\\rm 2m}} } -h}{GDD\_{{\\rm mat}} d\_{L} -h} \\le 1 \\\\ \\\\ a\_{repr} =1-a\_{froot} -a\_{livestem} -a\_{leaf} \\end{array}\\end{split}\\\]

where \\(a\_{leaf}^{i,3}\\) and \\(a\_{livestem}^{i,3}\\) (initial values) equal the last \\(a\_{leaf}\\) and \\(a\_{livestem}\\) calculated in phase 2, \\(d\_{L}\\), \\(d\_{alloc}^{leaf}\\) and \\(d\_{alloc}^{stem}\\) are leaf area index and leaf and stem allocation decline factors, and \\(a\_{leaf}^{f}\\) and \\(a\_{livestem}^{f}\\) are final values of these allocation coefficients ([Table 2.26.3](#table-crop-allocation-parameters)).

#### 2.26.2.4.3. Nitrogen retranslocation for crops[¶](#nitrogen-retranslocation-for-crops "Permalink to this headline")

Nitrogen retranslocation in crops occurs when nitrogen that was used for tissue growth of leaves, stems, and fine roots during the early growth season is remobilized and used for grain development ([Pollmer et al. 1979](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#pollmeretal1979), [Crawford et al. 1982](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#crawfordetal1982), [Simpson et al. 1983](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#simpsonetal1983), [Ta and Weiland 1992](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#taweiland1992), [Barbottin et al. 2005](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#barbottinetal2005), [Gallais et al. 2006](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#gallaisetal2006), [Gallais et al. 2007](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#gallaisetal2007)). Nitrogen allocation for crops follows that of natural vegetation, is supplied in CLM by the soil mineral nitrogen pool, and depends on C:N ratios for leaves, stems, roots, and organs. Nitrogen demand during organ development is fulfilled through retranslocation from leaves, stems, and roots. Nitrogen retranslocation is initiated at the beginning of the grain fill stage for all crops except soybean, for which retranslocation is after LAI decline. Nitrogen stored in the leaf and stem is moved into a storage retranslocation pool for all crops, and for wheat and rice, nitrogen in roots is also released into the retranslocation storage pool. The quantity of nitrogen mobilized depends on the C:N ratio of the plant tissue and is calculated as

(2.26.6)[¶](#equation-25-6 "Permalink to this equation")\\\[leaf\\\_ to\\\_ retransn=N\_{leaf} -\\frac{C\_{leaf} }{CN\_{leaf}^{f} }\\\]

(2.26.7)[¶](#equation-25-7 "Permalink to this equation")\\\[stemn\\\_ to\\\_ retransn=N\_{stem} -\\frac{C\_{stem} }{CN\_{stem}^{f} }\\\]

(2.26.8)[¶](#equation-25-8 "Permalink to this equation")\\\[frootn\\\_ to\\\_ retransn=N\_{froot} -\\frac{C\_{froot} }{CN\_{froot}^{f} }\\\]

where \\({C}\_{leaf}\\), \\({C}\_{stem}\\), and \\({C}\_{froot}\\) is the carbon in the plant leaf, stem, and fine root, respectively, \\({N}\_{leaf}\\), \\({N}\_{stem}\\), and \\({N}\_{froot}\\) is the nitrogen in the plant leaf, stem, and fine root, respectively, and \\(CN^f\_{leaf}\\), \\(CN^f\_{stem}\\), and \\(CN^f\_{froot}\\) is the post-grain fill C:N ratio of the leaf, stem, and fine root respectively ([Table 2.26.3](#table-crop-allocation-parameters)). Since C:N measurements are often taken from mature crops, pre-grain development C:N ratios for leaves, stems, and roots in the model are optimized to allow maximum nitrogen accumulation for later use during organ development, and post-grain fill C:N ratios are assigned the same as crop residue. After nitrogen is moved into the retranslocated pool, the nitrogen in this pool is used to meet plant nitrogen demand by assigning the available nitrogen from the retranslocated pool equal to the plant nitrogen demand for each organ (\\({CN\_{\[organ\]}^{f} }\\) in [Table 2.26.3](#table-crop-allocation-parameters)). Once the retranslocation pool is depleted, soil mineral nitrogen pool is used to fulfill plant nitrogen demands.

#### 2.26.2.4.4. Harvest[¶](#harvest-to-food-and-seed "Permalink to this headline")

Whereas live crop C and N in grain was formerly transferred to the litter pool upon harvest, CLM5 splits this between “food” and “seed” pools. In the former—more generally a “crop product” pool—C and N decay to the atmosphere over one year, similar to how the wood product pools work. The latter is used in the subsequent year to account for the C and N required for crop seeding.

Live leaf and stem biomass at harvest is transferred to biofuel, removed residue, and/or litter pools.

For the biofuel crops Miscanthus and switchgrass, 70% of live leaf and stem biomass at harvest is transferred to the crop product pool as described for “food” harvest above. This value can be changed for these crops—or set to something other than the default zero for any other crop—with the parameter \\(biofuel\\\_harvfrac\\) (0-1).

50% of any remaining live leaf and stem biomass at harvest (after biofuel removal, if any) is removed to the crop product pool to represent off-field uses such as use for animal feed and bedding. This value can be changed with the parameter \\(crop\\\_residue\\\_removal\\\_frac\\) (0–1). The default 50% is derived from [Smerald et al. 2023](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#smeraldetal2023), who found a global average of 50% of residues left on the field. This includes residues burned in the field, meaning that our implementation implictly assumes the CLM crop burning representation will handle those residues appropriately.

The following equations illustrate how this works. Subscript \\(p\\) refers to either the leaf or live stem biomass pool.

(2.26.9)[¶](#equation-25-9 "Permalink to this equation")\\\[ CF\_{p,biofuel} = \\left({CS\_{p} \\mathord{\\left/ {\\vphantom {CS\_{p} \\Delta t}} \\right.} \\Delta t} \\right) \* biofuel\\\_harvfrac\\\]

(2.26.10)[¶](#equation-harv-c-to-removed-residue "Permalink to this equation")\\\[ CF\_{p,removed\\\_residue} = \\left({CS\_{p} \\mathord{\\left/ {\\vphantom {CS\_{p} \\Delta t}} \\right.} \\Delta t} \\right) \* (1 - biofuel\\\_harvfrac) \* crop\\\_residue\\\_removal\\\_frac\\\]

(2.26.11)[¶](#equation-25-11 "Permalink to this equation")\\\[ CF\_{p,litter} = \\left({CS\_{p} \\mathord{\\left/ {\\vphantom {CS\_{p} \\Delta t}} \\right.} \\Delta t} \\right) \* \\left( 1-biofuel\\\_harvfrac \\right) \* \\left( 1-crop\\\_residue\\\_removal\\\_frac \\right) +CF\_{p,alloc}\\\]

with corresponding nitrogen fluxes:

(2.26.12)[¶](#equation-25-12 "Permalink to this equation")\\\[ NF\_{p,biofuel} = \\left({NS\_{p} \\mathord{\\left/ {\\vphantom {NS\_{p} \\Delta t}} \\right.} \\Delta t} \\right) \* biofuel\\\_harvfrac\\\]

(2.26.13)[¶](#equation-harv-n-to-removed-residue "Permalink to this equation")\\\[ NF\_{p,removed\\\_residue} = \\left({NS\_{p} \\mathord{\\left/ {\\vphantom {NS\_{p} \\Delta t}} \\right.} \\Delta t} \\right) \* \\left( 1 - biofuel\\\_harvfrac \\right) \* crop\\\_residue\\\_removal\\\_frac\\\]

(2.26.14)[¶](#equation-25-14 "Permalink to this equation")\\\[ NF\_{p,litter} = \\left({NS\_{p} \\mathord{\\left/ {\\vphantom {NS\_{p} \\Delta t}} \\right.} \\Delta t} \\right) \* \\left( 1-biofuel\\\_harvfrac \\right) \* \\left( 1-crop\\\_residue\\\_removal\\\_frac \\right)\\\]

where CF is the carbon flux, CS is stored carbon, NF is the nitrogen flux, NS is stored nitrogen, and \\(biofuel\\\_harvfrac\\) is the harvested fraction of leaf/livestem for biofuel feedstocks.

Annual food crop yields (g dry matter m\-2) can be calculated by saving the GRAINC\_TO\_FOOD\_ANN variable once per year, then postprocessing with Equation [(2.26.15)](#equation-25-15). This calculation assumes that grain C is 45% of the total dry weight. Additionally, harvest is not typically 100% efficient, so analysis needs to assume that harvest efficiency is less—we use 85%.

(2.26.15)[¶](#equation-25-15 "Permalink to this equation")\\\[ \\text{Grain yield} = \\frac{GRAINC\\\_TO\\\_FOOD\\\_ANN)\*0.85}{0.45}\\\]

Table 2.26.3 Crop allocation parameters for the active crop plant functional types (PFTs) in CLM5BGCCROP. Numbers in the first row correspond to the list of PFTs in [Table 2.26.1](#table-crop-plant-functional-types).[¶](#id22 "Permalink to this table")           
|  | temperate corn
 | spring wheat

 | temperate soybean

 | cotton

 | rice

 | sugarcane

 | tropical corn

 | tropical soybean

 | miscanthus

 | switchgrass

 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| IVT

 | 17, 18

 | 19, 20

 | 23, 24

 | 41, 42

 | 61, 62

 | 67, 68

 | 75, 76

 | 77, 78

 | 71, 72

 | 73, 74

 |
| \\(a\_{leaf}^{i}\\)

 | 0.6

 | 0.9

 | 0.85

 | 0.85

 | 0.75

 | 0.6

 | 0.6

 | 0.85

 | 0.9

 | 0.7

 |
| \\({L}\_{max}\\) (m 2 m \-2)

 | 5

 | 7

 | 6

 | 6

 | 7

 | 5

 | 5

 | 6

 | 10

 | 6.5

 |
| \\(a\_{froot}^{i}\\)

 | 0.1

 | 0.05

 | 0.2

 | 0.2

 | 0.1

 | 0.1

 | 0.1

 | 0.2

 | 0.11

 | 0.14

 |
| \\(a\_{froot}^{f}\\)

 | 0.05

 | 0

 | 0.2

 | 0.2

 | 0

 | 0.05

 | 0.05

 | 0.2

 | 0.09

 | 0.09

 |
| \\(a\_{leaf}^{f}\\)

 | 0

 | 0

 | 0

 | 0

 | 0

 | 0

 | 0

 | 0

 | 0

 | 0

 |
| \\(a\_{livestem}^{f}\\)

 | 0

 | 0.05

 | 0.3

 | 0.3

 | 0.05

 | 0

 | 0

 | 0.3

 | 0

 | 0

 |
| \\(d\_{L}\\)

 | 1.05

 | 1.05

 | 1.05

 | 1.05

 | 1.05

 | 1.05

 | 1.05

 | 1.05

 | 1.05

 | 1.05

 |
| \\(d\_{alloc}^{stem}\\)

 | 2

 | 1

 | 5

 | 5

 | 1

 | 2

 | 2

 | 5

 | 2

 | 2

 |
| \\(d\_{alloc}^{leaf}\\)

 | 5

 | 3

 | 2

 | 2

 | 3

 | 5

 | 5

 | 2

 | 5

 | 5

 |
| \\({CN}\_{leaf}\\)

 | 25

 | 20

 | 20

 | 20

 | 20

 | 25

 | 25

 | 20

 | 25

 | 25

 |
| \\({CN}\_{stem}\\)

 | 50

 | 50

 | 50

 | 50

 | 50

 | 50

 | 50

 | 50

 | 50

 | 50

 |
| \\({CN}\_{froot}\\)

 | 42

 | 42

 | 42

 | 42

 | 42

 | 42

 | 42

 | 42

 | 42

 | 42

 |
| \\(CN^f\_{leaf}\\)

 | 65

 | 65

 | 65

 | 65

 | 65

 | 65

 | 65

 | 65

 | 65

 | 65

 |
| \\(CN^f\_{stem}\\)

 | 120

 | 100

 | 130

 | 130

 | 100

 | 120

 | 120

 | 130

 | 120

 | 120

 |
| \\(CN^f\_{froot}\\)

 | 0

 | 40

 | 0

 | 0

 | 40

 | 0

 | 0

 | 0

 | 0

 | 0

 |
| \\({CN}\_{grain}\\)

 | 50

 | 50

 | 50

 | 50

 | 50

 | 50

 | 50

 | 50

 | 50

 | 50

 |

Notes: Crop growth phases and corresponding variables are described throughout the text. \\({CN}\_{leaf}\\), \\({CN}\_{stem}\\), and \\({CN}\_{froot}\\) are the target C:N ratios used during the leaf emergence phase (phase 2).

