allocation_and_phenology - PIK-LPJmL/LPJmL GitHub Wiki

LPJmL represents vegetation structure explicitly. The average individual is the fundamental characteristics of the model. The average individual is scaled up to the population of the grid cell. Every plant species belong to a plant or crop functional type Plant functional types or Crop functional types. These functional types, determined by a set of key attributes, are characterized by a set of state variables, and by the population density. Woody PFTs are designated by its crown area and the size of four tissue Carbon_pools (leaf, root, sapwood and heartwood). Herbaceous PFTs are represented by 2 tissue pools (leaf and root), which are treated as a ‘big leaf’. CFTs correspond to particular crops/grasses, or to groups of crops with broadly similar functions. CFTs tissue pools are represented by storage organs, leaves, stems and reserves, roots.

PFT-Allocation

Carbon increment is determined by NPP minus reproduction costs and is allocated yearly for the PFT (while daily for the CFT) by satisfying allometric relationships to the different C-compartments. Woody biomass increment per year is allocated to the three living carbon pools (leaf, root,stem sapwood) in such a way that the basic allometric relationships equations 2 - 3 below are always satisfied. The pipe model (Shinozaki et al. 1964a, b; Waring et al 1982) prescribes that each unit of leaf area must be supported by a corresponding area of transport tissue, the sapwood cross-sectional area (SA).

Leaf pool:
LA is the average individual leaf area.
$LA = k_{la:sa} \cdot SA$
eq(1)

Root pool:
A functional balance exists between the investment in fine root biomass and the investment in leaf biomass. Plants in water-limited conditions allocate relatively more carbon to fine root biomass. lrmax is a PFT-specific constant and $\omega$ is a PFT-specific index of water availability representing the mean fraction of water holding capacity in the upper soil layer, on days with non-zero leaf cover (Haxeltine & Prentice, 1996a).

$C_{leaf} = lr_{max} \cdot \omega \cdot C_{roots}$
eq(2)

Stem pool:
The relation between vegetation height (H) and stem diameter (D) is used as described in Huang et al. (1992).

$H = k_{allom2} \cdot D^{k_{allom3}}$
eq(3)

The crown area (CA) to stem diameter relation is based on inverting Reinecke’s rule (Zeide, 1993), which relates tree density to stem diameter under self-thinning conditions. The inversion used in LPJmL gives the expected relation between individual crown area and stem diameter. Canopy closure is assumed, but no crown overlap.

$CA = k_{allom1} \cdot D^{kep}$
eq(4)

By combining the allometric relations 3 - 4 with relationships between leaf area, crown area and leaf mass, it follows that the relative contribution of sapwood respiration increases with height, which restricts the possible height of trees.

Derived parameters:
Other vegetation parameters can be derived from the state variables. Assuming cylindrical stems and constant wood density (WD), tree height is related to the sapwood cross sectional area, which is assumed to be proportional to leaf area (Equation 3). Leaf area is related to leaf biomass by specific leaf area (SLA). From this follows:

$H=\frac {C_{sapwood} \cdot k_{la:sa}} {WD \cdot C_{leaf} \cdot SLA}$

The leaf area index (LAI) is given by:

$LAI_{ind} = \frac{C_{leaf} \cdot SLA} {CA}$

SLA is related to leaf longevity ( $\alpha_{leaf}$ ) in years, which determines whether deciduous or evergreen phenology suits a given climate (Reich et al., 1997).

$SLA = 2 \cdot 10^{-4}\cdot \frac{e^{6.15}}{(12 \cdot \alpha\_{ leaf})^{0.46}}$

The overall foliar projective cover (FPC, which is the proportion of ground area covered by leaves) of a PFT in a grid cell is obtained by the product of individual FPC, mean individual crown area, and mean number of individuals per unit area (P). FPC directly measures the ability of the canopy to intercept radiation. We therefore simply equate the fraction of incoming radiation intercepted by green vegetation (fAPAR) to $FPC\_{ind}$ (Haxeltine & Prentice, 1996).

$FPC = CA \cdot P \cdot FPC_{ind}$

PFT-Phenology

Phenology

CFT-Allocation

Daily NPP accumulates to total biomass and is allocated daily to crop organs in a hierarchical order: roots, leaves, storage organ, mobile reserves and stem (pool). The fraction of biomass that is allocated to each compartment depends on the phenological development stage (fPHU). The fraction of total biomass that is allocated to the roots (froot) ranges between 40 % at planting and 10 % at maturity, modified by water stress:

$f_{root} = \frac{0.4-(0.3 \cdot fPHU) \cdot wdf} {wdf+\exp(6.13-0.0883 \cdot wdf)}$

where the water deficit (wdf) is defined as the ratio between accumulated daily transpiration and accumulated daily water demand since planting, representing a measure of the average water stress. After allocation to the roots, biomass is allocated to the leaves. Leaf area development follows a CFT-specific shape that is controlled by phenological development (fPHU), the onset of senescence (ssn), and the shape of green LAI decline after the onset of senescence. The ideal CFT-specific development of the canopy (Eq. 81) is thus described as a function of the maximum LAI (LAI_max) and the phenological development (fPHU) with two turning points in the phenological development (fPHU_c and fPHU_k) and the corresponding fraction of the maximum green LAI reached at these stages ( $fLAI_{max_c}$ and $fLAI_{max_k}$ ):

$\mathrm{flai}_{\max}=\frac{\mathrm{fphu}}{\mathrm{fphu}+c \cdot (c/k)^\frac{\mathrm{fphu}_c-\mathrm{fphu}}{\mathrm{fphu}_k-\mathrm{fphu}_c}}$

with $c = \frac{\mathrm{fphu}_c}{\mathrm{flai}_{\max_c}-\mathrm{fphu}_c}$

$k = \frac{\mathrm{fphu}_k}{\mathrm{flai}_{\max_k}-\mathrm{fphu}_k}$

The onset of senescence is defined as a point in the phenological development fphu_sen. After the onset of senescence, i.e. $fphu \leq fphu_\mathrm{sen}$ , no more biomass is allocated to the leaves and the maximum green LAI is computed as:

$\mathrm{flai}_{\max}=\left(\frac{1-\mathrm{fphu}}{1-\mathrm{fphu}_\mathrm{sen}}\right)^\mathrm{ssn} \cdot (1-\mathrm{flai}_{\max_h})+\mathrm{flai}_{\max_h}$

with $flai_{\max_h}$ as the green LAI fraction at which harvest occurs. This optimal development of LAI is modified by acute water stress. For this, the daily increment lai_inc, which is optimal for day t is computed as:

$\mathrm{lai}_{\mathrm{inc}_t} = (\mathrm{flai}_{\max_t} - \mathrm{flai}_{{\max}_{t-1}}) \cdot \mathrm{lai}_{\max}$

with $flai_{{\max}_{t}}$ as the maximum green LAI of day t and $flai_{{\max}_{t-1}}$ as the maximum green LAI of the previous day. The daily increment lai_inc is additionally scaled with the daily water stress ( $\omega$ ), which is calculated as the ratio of actual transpiration and demand (see transpiration) on that day. The calculation of lai_inc applies to daily LAI increments which are independent of each other. The LAI on day t is accumulated from daily LAI increments,

$\mathrm{LAI}_t=\sum_{t'=\mathrm{sdate}}^{t}\mathrm{lai}_{\mathrm{inc}_{t'}} \cdot \omega$

and implies that the LAI development cannot recover from water-limitation induced reductions in LAI. Until the onset of senescence, the daily LAI determines the biomass allocated to the leaves by dividing LAI by specific leaf area (SLA). SLA is computed using the $\beta_0$ value for grasses (2.25) and CFT-specific $\alpha_\mathrm{leaf}$ values. Its calculation was adjusted for SLA values given in Xu et al. (2010). Biomass in the storage organ is computed by phenological stage and the harvest index (HI), which describes the fraction of the above ground biomass that is allocated to the storage organ:

$\mathrm{HI}= \begin{cases} \mathrm{fhi}_\mathrm{opt} \cdot \mathrm{hi}_\mathrm{opt}, & \quad \text{if } \mathrm{hi}_\mathrm{opt} \geq 1 \\ \mathrm{fhi}_\mathrm{opt} \cdot (\mathrm{hi}_\mathrm{opt}-1)+1, & \quad \text{otherwise} \end{cases}$

with $\mathrm{fhi}_\mathrm{opt}=100 \cdot \mathrm{fphu}/(100 \cdot \mathrm{fphu}+\exp(11.1-10.0 \cdot \mathrm{fphu}))$

As the harvest index HI is defined relative to above-ground biomass, roots and tubers have HI values larger than 1.0 which needs to be accounted for in the allocation of biomass to the storage organ (see above). If biomass is limiting (low NPP), biomass is allocated in hierarchical order, starting with roots (which can always be satisfied, as it is 40% of total biomass maximum), followed by leaves (C_leaf) (where eventually the LAI is temporarily reduced, impacting APAR and thus NPP) and the storage organ (C_so). If biomass is not limiting, the allocation to the storage organ, this is computed from the harvest index (HI) and total above ground biomass:

$C_\mathrm{so}=\mathrm{HI} \cdot (C_\mathrm{leaf} + C_\mathrm{so} + C_\mathrm{pool})$

Excess biomass after allocating to roots, leaves and storage organ is allocated to a pool (C_pool) that represents mobile reserves and the stem. At harvest, storage organs are collected from the field and crop residues can be left on the field or removed. If removed, a fraction of 10% of the above-ground biomass (leaves and pool) is assumed to remain on the field as stubbles. Stubbles and root biomass enter the litter pools after harvest.

CFT-Phenology

In crop science, development is distinct from growth, although they generally proceed simultaneously. Development has been defined as a sequence of phenological events controlled by external factors, each event making important changes in the morphology and/or function of some organs. Growth refers to increase in crop dry weight, the net result of acquisition and loss of resources (i.e. Landsberg, 1977 in: Slafer and Rawson, 1994; Hay and Porter, 2006).

In LPJmL phenology is simulated by only one phase from crop emergence to maturity. CFT-phenology is driven by a thermal model (accumulation of growing degrees days,(GDD), also called heat units, hu), for some crops in combination with vernalization (wheat, rapeseed) and sensitivity to photoperiodism (see below).

Each day the following main variables are computed:

husum
fphu
senescence
harvest
flaimax

husum

husum (°Cd) is the sum of heat units accumulated until the current day:

$husum=\sum hu\cdot vrf\cdot prf$

where hu is the daily heat unit, vrf is the vernalization reduction factor, prf is the photoperiod reduction factor.

Thermal time: hu

Within a certain range of temperature the relation between temperature and the rate of development can be considered linear. Within this linear phase the plant cannot distinguish between 5 hours at 20°C and 10 hours at 10°C, and this provides the basis for the use of thermal time, in degrees days (°Cd), in charting development (Hay and Porter, 2006).

Figure 1. Exemplification of the linear function between temperature and the rate of development, with a base temperature of 0°C.

Thermal time is strictly the integral over time of the environmental temperature above a base temperature, but in practice, a daily mean approach is normally used (Hay and Porter, 2006). The daily hu (°Cd) is computed as:

$hu=\max(0,(temp-basetemp))\cdot time$

In the model script, time is not explicit, since it is assumed to be equal to 1 day.
In the example husum due to temperature effect only is equal to the grey area in Fig 2 (basetemp=0 °C).

Figure 2. sum of heat units due to temperature only. The grey area represents husum from day 1 to 10. The base temperature is 0°C.

Vernalization: vrf

the vernalization reduction factor is dimensionless, range [0,1]. Some parameters are needed for calculating it: pvd is the total number of vernalization days required by the crop; trg is temperature under which vernalization is possible (°C), two values are defined trg.low and trg.high; VD_SLOPE is used for computing a reduction of vernalization effect, for temperatures outside trg.low and trg.high.

where vdsum is the sum of vernalization days the current day, computed as follows:

$vdsum=vdsumyesterday+\max(0,vd\_{inc})$

where vd_inc is:

$vd\_{inc}=1-(|temp-trg|/VD\_SLOPE)$

Photoperiod: prf

The photoperiod reduction factor is dimensionless. The following parameters are used: psens is the sensitivity to the photoperiod effect [0-1] (1 means no sensitivity); pb is the basal photoperiod (h) (pb<ps for longer days plants; ps is the saturating photoperiod (h) (ps<pb for shorter days plants).

$prf=(1-psens)\cdot \min(1,\max(0,(daylength-pb)/(ps-pb)))+psens$

Fraction of growing season: fphu

fphu is the fraction of growing season

$fphu=\min(1.0,husum/phu)$

where phu is the total amount of heat unit that the crop must reach to complete its cycle, getting to maturity phase.

Senecence: fphusen

Parameter fphusen [0-1] is the fraction of growing period at which senescence starts (LAI starts decreasing).

$\text{if}~ fphu\leq fphusen, senecence=FALSE$

$\text{if}~ fphu<fphusen, senecence=TRUE$

Harvest

Harvest occurs if phu is reached or if the duration of the growing season is longer than a prefixed maximum duration, even if the crop cycle is not completed yet.

$\text{if}~ husum<phu, harvesting=FALSE$

$\text{if}~ husum\geq phu, harvesting=TRUE$

$\text{if}~ growingdays=hlimit, harvesting=TRUE$

LAI

LAI development is prescribed by a sigmoid curve, for which the 2 turning points fphuc and flaimaxc and fphuk and flaimaxk and the maximum laimax LAI are specified (see parameter). Daily LAI increments from this prescribed curve are scaled with the daily ratio of supply vs. demand, wscal, see phenology_crop.c.

$LAI_{inc}=(lai000 - lai00)\cdot wscal$

The parameter wscal is computed in water_stressed.c, lai00 is the theoretical value the LAI curve should have reached on the day before and lai000 is the theoretical value the LAI curve should have reached on the current day. If there was water stress on the previous days (i.e. ) both variable values are reduced.

Figure 3. Flowchart of phenology_crop.c. Parameters are in the circles, state variables are in the squared nodes, driving variables (input data) are in the cylindrical nodes.

Technical Note

For CFT allocation, see allocation_daily_crop.c

For the functions of CFT-phenology, see phenology_crop.c
For the definition of the crop variables and parameters, see crop.h (Pftcrop; Pftcroppar)
for the settings of parameters values, see pft.par

allocation_and_phenology - PIK-LPJmL/LPJmL GitHub Wiki

PFT-Allocation

PFT-Phenology

CFT-Allocation