Forest growth and dynamics (theory)

Miquel De Cáceres, Rodrigo Balaguer

Ecosystem Modelling Facility, CREAF

Outline

  1. Simulation models and processes
  2. Carbon pools and carbon balance
  3. Growth and senescence
  4. Mortality and recruitment
  5. Fire effects
  6. Biomass balance

M.C. Escher - Three worlds, 1955

1. Simulation models and processes

About growth() and fordyn() models

  1. Simulation functions in medfate have been designed and implemented in a nested manner.
  2. The two water balance models (basic and advanced) are available for simulations with growth() and fordyn().
  3. The growth() model implements several daily processes:
    1. Carbon balance processes resulting from the interplay of sources (photosynthesis) and sinks (maintenance respiration, growth respiration, root exudation, etc.).
    2. Growth and senescence processes that modulate changes in leaf area, sapwood area and fine root area of woody plant cohorts.
    3. Structural changes (diameter and height for trees; cover and height for shrubs) derived from growth and senescence processes.
    4. Background and drought-related mortality, which reduces tree cohort density or shrub cover.
    5. Fire severity effects, including foliage burning and mortality.
  4. For applications spanning more than a few years, users will use the growth() model indirectly, via calls to fordyn(), which includes other processes implemented at annual steps:
    1. The impact of forest management
    2. Natural regeneration: recruitment or resprouting.

  1. Simulation models and processes

2. Carbon compartments, pools and carbon balance

Carbon compartments and pools

Carbon pool types

Structural carbon - Cell membranes, cell walls & cytosolic machinery.

Metabolic carbon - Labile carbon (sugar) concentration used to sustain cell functioning.

Storage carbon - Labile carbon (starch) concentration used as long-term carbon source.

Pools

Compartment Structural Metabolic Storage
Leaves Leaf dry biomass \(B_{leaf}\) Leaf sugar \(SS_{leaf}\) Leaf starch \(ST_{leaf}\)
Sapwood Sapwood dry biomass \(B_{sapwood}\) Sapwood sugar \(SS_{sapwood}\) Sapwood starch \(ST_{sapwood}\)
Fine roots Fine root dry biomass \(B_{fineroot}\)

Important

Sapwood carbon includes branches, stem and coarse roots

  1. Carbon compartments, pools and carbon balance

Labile carbon balance equations

A. Changes in leaf metabolic carbon result from considering gross photosynthesis ( \(A_{g}\) ), leaf maintenance respiration ( \(M_{leaf}\) ), phloem transport ( \(F_{phloem}\) ) and sugar-starch dynamics ( \(SC_{leaf}\) ) and translocation to sapwood storage ( \(TS_{leaf}\) ):

\[\Delta{SS_{leaf}} \cdot V_{storage,leaf} = A_g - M_{leaf} - F_{phloem} - SC_{leaf} - TS_{leaf}\]

B. Changes in leaf storage carbon result from sugar-starch dynamics and translocation to sapwood storage ( \(TT_{leaf}\) ):

\[\Delta{ST_{leaf}} \cdot V_{storage,leaf} = SC_{leaf} - TT_{leaf}\]

C. Changes in stem metabolic carbon result from considering phloem transport, maintenance respiration of sapwood ( \(M_{sapwood}\) ) and fineroot ( \(M_{fineroot}\) ) tissues, sugar-starch dynamics and translocation to sapwood storage ( \(TS_{sapwood}\) ):

\[\Delta{SS_{sapwood}} \cdot V_{storage,sapwood} = F_{phloem} - M_{sapwood} - M_{fineroot} - SC_{sapwood} - TS_{sapwood}\]

D. Changes in stem storage carbon result from considering sugar-starch dynamics, translocation from other pools, growth respiration and root exudation:

\[\Delta{ST_{sapwood}} \cdot V_{storage,sapwood} = SC_{sapwood} + TS_{leaf} + TT_{leaf} + TS_{sapwood} - G_{sapwood} - G_{leaf} - G_{fineroot} - RE_{sapwood}\]

  1. Carbon compartments, pools and carbon balance

Labile carbon balance equations

E. Changes in labile carbon pools can be reduced to the balance between gross photosynthesis ( \(A_g\) ), maintenance respiration ( \(M\) ), growth respiration ( \(G\) ) and root exudation ( \(RE\) ):

\[\Delta{S_{labile}} = A_g - (M + G + RE)\]

  1. Carbon compartments, pools and carbon balance

Design of labile carbon processes

  • Phloem transport is only explicitly modelled when using the advanced water submodel.

  • Sugar/starch dynamics are meant to keep sugar levels at a prescribed equilibrium value.

  • The usual separation between maintenance and growth respiration is followed, with maintenance costs depending on temperature and phenology.

  • Translocation of labile carbon towards sapwood storage occurs whenever there is senescence in a given tissue (leaves, branches).

  • Root exudation is not a process competing for metabolic carbon, but a consequence of plant storage capacity being surpassed 1.

  1. Carbon compartments, pools and carbon balance

3. Growth and senescence

Drivers of growth and senescence

  1. Growth and senescence

Tissue growth

Daily leaf area increment \(\Delta LA\), sapwood area increment \(\Delta SA\) and fine root biomass increment \(\Delta B_{fineroot}\) are defined as the minimum of three constraints:

\[\Delta LA = \min( \Delta LA_{alloc}, \Delta LA_{source}, \Delta LA_{sink})\] \[\Delta SA = \min(\Delta SA_{source}, \Delta SA_{sink})\] \[\Delta B_{fineroot} = \min( \Delta B_{fineroot,alloc}, \Delta B_{fineroot,source}, \Delta B_{fineroot,sink})\]

  • \(\Delta LA_{alloc}\) and \(\Delta B_{fineroot,alloc}\) are the increments allowed according to the targets set by allocation rules.
  • \(\Delta LA_{source}\), \(\Delta SA_{source}\) and \(\Delta B_{fineroot,source}\) are the maximum increments allowed by current starch availability.
  • \(\Delta LA_{sink}\), \(\Delta SA_{sink}\) and \(\Delta B_{fineroot,sink}\) are the increments expected due to growth rates, which are affected by temperature and turgor limitations 1.

Important

  • Sapwood area growth is not limited by allocation rules, effectively determining overall plant growth.
  • Carbon is preferentially allocated to leaves and fine roots whenever storage levels are low because \(\Delta SA_{source}\) is more restrictive than \(\Delta LA_{source}\) or \(\Delta B_{fineroot,source}\).
  1. Growth and senescence

Tissue growth

Key growth parameters

Parameter R Definition Explanation
\(a_{fbt}\), \(b_{fbt}\), \(c_{fbt}\) Afbt, Bfbt, Cfbt Allometric coefficients for tree leaf biomass, including competition Determine allocation target for tree leaf area and influence sapwood area growth rates
\(RGR_{cambium, max}\) RGRcambiummax Maximum daily tree sapwood growth rate relative to cambium perimeter length Determines overall maximum growth rates for tree species
\(RGR_{sapwood, max}\) RGRsapwoodmax Maximum daily shrub sapwood growth rate relative to cambium perimeter length Determines overall maximum growth rates for shrub species
\(1/H_v\) Al2As Leaf area to sapwood area ratio Determines allocation target for sapwood and, hence, sapwood senescence rates.
\(RGR\) Ar2Al Root area to leaf area ratio Determines allocation target for fine roots and influences root maintenance costs
\(RSSG\) RSSG Minimum relative starch for sapwood growth to occur Determines preference for maintenance over growth under low carbon availability (e.g. shade-tolerant species)
  1. Growth and senescence

Tissue senescence

  • Leaf senescence rates are determined by:
    • Aging (leaf lifespan)
    • Phenology (winter deciduous)
    • Dessication (via stem cavitation)
  • Sapwood senescence rates are determined by:
    • Aging (depending on temperature)
    • Sapwood area target (only if \(SA > SA_{target}\))
  • Fine root senesence rates are determined by:
    • Aging (depending on temperature)

Note

  • Leaf and fine root senescence create a need to constantly replace tissues.
  • Sapwood senescence aims to keep sapwood area close to its functional target (either constant leaf area to sapwood area ratio or a constant whole-plant conductance).
  1. Growth and senescence

Updating structural variables

Trees

New sapwood area, \(\Delta SA\), is translated to an increment in DBH, \(\Delta DBH\), following:

\[\Delta DBH = 2 \cdot \sqrt{(DBH/2)^2+({\Delta SA}/\pi)} - DBH\]

Increments in height are linearly related to increments in diameter through a coefficient depending on light conditions 1, and are limited by a maximum height.

Crown ratios are updated following static allometric relationships.

Shrubs

Leaf area changes are translated to changes in shrub volume, cover and shrub height via allometric equations.

As for trees, shrub height is limited to a maximum value.

  1. Growth and senescence

4. Mortality and recruitment

Plant mortality

  1. Small trees ( \(1 < DBH < 7.5\) ) die at a rate determined by a self-thinning rule depending on its size.
  1. Species-specific parameters determine a daily constant baseline mortality rate for adults.
  1. Daily mortality rates increase due to carbon starvation whenever sapwood metabolic carbon, \(SS_{sapwood}\), becomes lower than a threshold, set by default to 40% of the homeostatic (equilibrium) concentrations. The daily starvation rate at the threshold corresponds to an annual mortality of 50%.

  1. Daily mortality rates increase due to dessication whenever the average of stem relative water content and stem relative hydraulic conductance becomes lower than a pre-specified threshold, set to 40% by default.
  1. Mortality and recruitment

Recruitment

Unlike mortality, recruitment is simulated at the end of a simulated year (only in fordyn()).

Recruitment from seed

  • Seed banks are full whenever trees of the species are present with a size above a maturity threshold (or a seed rain is forced). Otherwise, they are reduced following an exponential decay function.
  • The following conditions need to be met for a species to recruit:
    1. Mean temperature of the coldest month is above a bioclimatic threshold.
    2. The fraction of light reaching the ground is above a bioclimatic threshold.
    3. The moisture index (annual precipitation over annual evapotranspiration) is larger than a bioclimatic threshold.
  • A probability of recruitment is used to stochastically determine whether recruitment actually occurs.

Resprouting

  • Resprouting occurs if plants have been cut, burned or dessicated.
  • Resprouting survivorship depends on the disturbance (different effects on buds).
  • Resprouting vigour for trees depends on \(DBH\).
  1. Mortality and recruitment

5. Fire effects

Design of fire effects

  1. Fire effects

6. Biomass balance

Biomass balance

Balance in structural carbon pools

The change in structural biomass of each compartment results from the interplay between growth and senescence:

\[\Delta{B_{leaves}} = B_{leaves, growth} - B_{leaves, senescence}\] \[\Delta{B_{sapwood}} = B_{sapwood, growth} - B_{sapwood, senescence}\] \[\Delta{B_{fineroot}} = B_{fineroot, growth} - B_{fineroot, senescence}\]

The following equation defines the structural biomass balance at the plant level:

\[\Delta{B_{structure}} = \Delta{B_{leaves}} + \Delta{B_{sapwood}} + \Delta{B_{fineroot}}\]

Balance at the cohort level

At the cohort level we need to take into account that some individuals will die, so that the biomass balance needs to incorporate mortality losses:

\[\Delta{B_{cohort}} = \Delta{B_{plant}} \cdot N_{cohort} - B_{mortality}\]

where \(N_{cohort}\) is the initial cohort density (before mortality occurred) and \(B_{mortality}\) is the biomass loss due to mortality of individuals, which in order to close the balance has to be defined as:

\[B_{mortality} = (B_{plant} + \Delta{B_{plant}}) \cdot N_{dead}\]

where \(N_{dead}\) is the density of dead individuals and \(B_{plant}\) is the initial plant biomass.

  1. Biomass balance

M.C. Escher - Three worlds, 1955