Z308 Forest dinamics

Model name

Z308 Forest dinamics

Original author(s)

Hartmut Bossel

References and/or links for original model

Bossel, H. 1986: Dynamics of forest dieback – systems analysis and simulation. Ecological Modelling 34 (S. 259-288).

Bossel, H. 1987/1989: Simulation dynamischer Systeme – Grundwissen, Methoden, Programme. Vieweg Braunschweig/ Wiesbaden (S. 245-268).

Format of original model

Vensim

Converted by

Francesco Benveuti

Date submitted

20/04/2012

Purpose

The leaf mass of a forest canopy continues to increase until the canopy has becomes so dense that net production ceases in lower leaf layers where radiation is insufficient due to multiple shading, and new leaves cannot develop (cf. model Z307 “Photosynthesis”). A large portion of the energy assimilated in the canopy is used for respiration to maintain the life processes of the trees. Surpluses are used to produce wood increment and corresponding growth of the trees. The energy demand for respiration increases as (individual) tree biomass increases, and wood increment vanishes when energy gains just compensate energy losses. Obviously the net balance of energy flows (expressed in units of C, CO₂ or organic dry matter odm) therefore determines the development of a forest stand. Pollutants can impair the energy balance of forests considerably and lead to increment losses and forest dieback by different mechanisms: (1) reduction of photosynthesis, (2) damage of energy assimilating leaves, or (3) by increased photosynthate demand for the replacement of leaf and/or feeder root losses.

This simple model describing the dynamic interaction of leaf biomass and wood biomass with their respective energy gains and losses, allowing for an examination of their interrelated effects.

Description

The model is documented in the simulation diagram of Figure Z308a and in the following model equations. It has two state quantities: leaf biomass and wood biomass. All quantities are expressed per hectare of forest area; i.e. the model does not describe development of individual trees.

Logistic growth up to leaf volume capacity is assumed for leaf biomass, with (initial) growth corresponding to max leaf flushing rate. The limitation of leaf biomass (per hectare!) arises from the fact that further increase would reduce radiation on, and photosynthesis of lower leaf layers to a point where the small gains cannot compensate for respiration losses (cf. model Z307 “Photosynthesis”). The production of photosynthates (assimilates) (canopy production) is proportional to leaf biomass and specific canopy production; it can be subject to production loss by pollutants (in percent) which starts in initial year of environmental stress. The leaf proportional energy utilization accounts for the respiration share of leaves and feeder roots. Further consumption of assimilates (stem respiration with stem proportional respiration rate) is proportional to (sap) wood biomass and to leaf flush (leaf goal). Losses of leaf biomass arise from leaf loss; losses of wood biomass occur from deadwood loss with deadwood loss rate. Any surpluses remaining after accounting for these different losses contribute to wood increment.

Model size indicators

Simile diagram

Simile equations

Rate of change = + wood increment - deadwood loss

actual leaf flushing = if assimilate_surplus>0 then leaf_goal else (if canopy_production-stem_respiration>0 then canopy_production-stem_respiration else 0)

deadwood loss = deadwood__loss_rate*wood_biomass

leaf loss = leaf_loss__rate*leaf_biomass

wood increment = canopy_production-actual_leaf__flushing-stem_respiration

assimilate surplus = canopy_production-leaf_goal-stem_respiration

canopy production = leaf_proportional_energy_utilization*leaf_biomass*specific_canopy_production*(1-production__decrease)

leaf goal = max_leaf_flushing_rate*leaf_biomass*(1-leaf_biomass/leaf_volume_capacity)

production decrease = if time(1)> initial_year_of_environmental_stress then production_loss_from_pollutants else 0 (int)

stem respiration = stem_proportional__respiration_rate*wood_biomass

deadwood loss rate = 0.01

initial year of environmental stress = 40

leaf loss rate = 0.2

leaf proportional energy utilization = 0.5

leaf volume capacity = 10

max leaf flushing rate = 0.5

production loss from pollutants = 0

specific canopy production = 6

stem proportional respiration rate = 0.03

Files

The model and associated files are listed at the bottom of this page. The model may be provided in more than one format (e.g. as Vensim .mld and Simile .sml files).

Notes on the conversion process

Extra information on original model