Understanding Forest Dynamics: Growth, Management, and Modeling

Posted on May 8, 2024 in Mathematics

1. Forest Types and Functions

Productive Forests

  • Wood
  • Biomass
  • Seed
  • Resin

Protective Forests

  • Carbon sequestration
  • Water regulation
  • Oxygen production
  • Soil protection

Special Function Forests

  • Recreation
  • Landscape
  • Tourism
  • Game

2. Forest Rotation Management Processes

Clear Cut Method

Positives: Simple logistics, ideal for intolerant species regeneration (e.g., Douglas fir).

Negatives: High environmental impact, potential soil erosion, replantation required.

Shelterwood Cut Method

Positives: Remaining trees protect natural regeneration.

Negatives: Complex regeneration activities, infrequent seed years.

3. Components of Forest Dynamics

Growth

Biomass or size increase of a plant or stand over time.

Yield

Accumulated biomass since establishment.

* Growth and disturbances drive forest dynamics.

4. Forest Stand Maturity

Physical Maturity

Onset of degradation processes.

Physiological Maturity

Capability to regenerate.

Economical Maturity

Profit maximization.

5. Assessing Forest Dynamics Data

  • Present measurements
  • Historical monitoring
  • Growth projection using growth theory

6. Number of Trees per Hectare in Equal-Aged Forests

Dynamics:

  • Light-demanding species have fewer trees per hectare than shade-tolerant species at the same age.
  • Poor stands have more trees per hectare than good stands.
  • Naturally regenerated stands typically have more trees per hectare than artificially regenerated ones.

7. Average Tree Diameter in Equal-Aged Forests

Dynamics:

  • Average tree diameter develops regularly, influenced by stand characteristics (Bonita).
  • Diameter frequency curve in even-aged forests follows a Gaussian distribution, often with left-sided asymmetry.

Calculation Methods

  1. Diameter of average stem (v = V/N -> d)
  2. Diameter of average basal area (g = K/N -> d)
  3. Weighted average of tree diameter classes (d = n1.d1 + n2.d2 + … + ni.di / N)

8. Process Model Components

Physiological characteristics.

9. Diameter Class Frequency Curve in Equal-Aged Forests

Dynamics: To be described based on the curve.

10. L-Systems in Forest Dynamics

(Not covered in the exam)

11. Reineke’s Stand Density Rule

Expresses the decreasing relationship between the number of trees per unit area and the median diameter of a fully stocked, naturally developed stand. The exponent (Reineke’s constant) is independent of tree species and habitat.

Higher trees = Less density (in natural forests)

12. Forest Model Types

Empirical Models

Based on empirical observations, focusing on physical characteristics (diameter, height, volume).

Structural Models

Based on forest structure.

Functional-Structural Models

Consider the 3D architecture of plants driven by physiological processes and environmental factors, allowing visualization and connection to other research fields.

13. Average Tree Height Dynamics in Equal-Aged Forests

Calculated using the formula V = G * H * F (Volume, Basal Area, Height, Form), assuming constant form (F).

14. Total Volume Production (TVP)

The sum of all volume produced in a stand, indicating thinning impact and serving as an optimization variable.

15. Growth Function vs. Increment Function

Growth Function

Describes the correlation between time and a growth variable, typically S-shaped.

Increment Function

Change of the growth variable over time (first derivative of the growth function).

16. Models in Forest Dynamics

Representations of reality on a small scale, relating variables and serving as predictive tools.

17. Forest Model Classes

Ecophysiological Models

Focus on physiological processes (transpiration, photosynthesis, carbon fixation).

Examples: Biomass, Tregrow, Fagus, Tragic, Pixgrow

Tree Models

Focus on individual trees.

Stand Models

The oldest models, such as yield tables.

18. Physiological vs. Empirical Models

Physiological (Mechanistic) Models

  • Focus on physiological processes.
  • Input variables are difficult to measure.
  • May be extrapolated to other regions under certain circumstances.

Empirical Models

  • Easy to construct.
  • Based on empirical data.
  • Valid only within the database region.

19. Yield Tables

Present growth and yield variables for even-aged silvicultural systems, with limited application to complex structures. Deviations from assumptions result in different stand characteristics compared to predictions.

20. Stand Description (Site Index, Bonita)

Site Index

Describes the potential for tree growth at a particular location, measured as the height of dominant and co-dominant trees at a base age (e.g., 25, 50, 100 years).

Bonita

A classification system for forest stands based on productivity and site quality.

21. Maximal Potential Growth in Sibyla

Based on site description (precipitation, temperature, altitude) and considering growth conditions and disturbances.

22. Leaf Area Index (LAI)

A dimensionless quantity representing leaf area per unit ground surface area, used in various forest dynamics models.

23. Competition Models

Competition Index by Hegyi

Considers the diameters of central and surrounding trees and the distances between them.

Crown Light Competition Index by Pretzsch

Evaluates angles between crowns, basal area ratios, and transmission coefficients.

24. Single Tree Model Outputs

Provide information on individual tree variables (diameter, height, crown parameters, volume) at different levels of detail.

25. Total Volume Production (TVP) in Management

Indicates thinning impact and serves as an optimization variable.

26. Single Tree Model Advantages and Disadvantages

Advantages

  • More precise
  • Can model complex scenarios

Disadvantages

  • Difficult to develop
  • Require computers

27. Biodiversity in Management

Variety of organisms in an ecosystem, with a goal of maximizing biodiversity while balancing other management objectives.

28. Structural Diversity

Variety in the size and vertical richness of a forest, with selected forests (A) exhibiting greater diversity than even-aged forests (B).

29. Structural Diversity Index

Pretzsch Index

Measures structural diversity based on the number of species and their distribution in different vertical layers.

30. Biosociological Status

Classification of trees as dominant or shaded, influencing management decisions based on goals.

31. Thinning Types

Clear Cut Method

Simple logistics, ideal for intolerant species regeneration.

Shelterwood Cut Method

Remaining trees protect natural regeneration.

Selective Cut Method

Results in a more ecological and diverse forest, ideal for shade-tolerant species.

32. Thinning from Below in Mixed Stands

Reduces competition in early stages, leading to taller trees with smaller diameters, similar to tropical forests.

33. Model Classes Based on Scaling

Ecophysiological Models

Focus on physiological processes.

Tree Models

Focus on individual trees.

Stand Models

Example: yield tables.

Succession Models

Describe natural forest development at a larger scale than stand models.

Biome Models

Operate at a larger scale than succession models, often using biogeography tools.

34. Forest Production Simulation Software

Sybila and TreesCount.

35. Disturbance Types

Anthropogenic Disturbances

  • Harvest
  • Deforestation
  • Extensive livestock farming

Natural Disturbances

  • Wind
  • Fire
  • Drought

36. Shannon Index

Describes the diversity of a stand based on the number of species and their relative proportions (assessed by number or basal area).

37. Horizontal (Spatial) Structures

(Not covered in the exam)

38. Process Model Input Data

  • Radiation
  • Water flow in the tree
  • Stomatal conductivity
  • Photosynthesis activity

39. Soil Humidity and Soil Water Potential

Soil Humidity

Amount of water in soil.

Soil Water Potential

Amount of water extractable by roots.

40. Optimization in Forestry

Commonly used for developing harvest schedules that meet landowner or land manager objectives, often involving linear or non-linear optimization techniques.