2. Wood Supply Models

Wood supply models (WSM) are software packages that simulate forest activities to assist in the development of forest plans, wood supply analysis and sustainable forest management. WSM aim to provide foresters, landowners and stakeholders with information about how a forested land base will progress through time. They help by providing a glimpse into the future of how a forested land base could change through time given a particular set of proposed management objectives and activities.

Although there are many different WSM software implementations available for forest planners, there are some commonalities across these implementations with respect to the required input data, the development process and approach to identifying a solution.

2.1. Area of Interest

All WSP require the identification of an Area of Interest (AOI). On a simple level an AOI is spatial explicit delineation of a forested area that you wish to project forward through time on which activities are applied. AOI’s can be defined by legal or administrative boundaries, terrain or landscape features, forest type or any characteristic that separates the area you are interested vs. the area you are not interested in. In some instances defining an AOI is simple process and potentially has been predefined by higher level management, the landowners or other stakeholders. In other instances AOI’s are not predefined and require defining at the start of the project.

2.1.1. Defining AOI

Defining an AOI is typically the starting point for a WSPP. Generally, an AOI is defined in a spatially explicit way based on landscape features or landownership. If you are starting a WSP project and are tasked with delineating an AOI, the first place to start is by having a discussion with the project stakeholders. The second step is finding the required corresponding spatial data layers. Depending on the context, this step may be more or less difficult based on availability of geospatial databases.

Generally, an AOI will be defined by a vector polygon dataset (e.g., stored in ESRI Shapefile or Geodatabase layer format, or perhaps as a geoJSON file). This polygon data layer outlines the boundary of the area you want to model. Anything outside the AOI boundary will not be included in your model. All other spatial data being used as part of the project will be clipped to the extent of your AOI. Often multiple data layers will be used to define an AOI. For example, one aspect of an AOI might be defined by the presence of private landownership and another aspect might be defined by the extent of the forest.

2.1.2. Landscape Classification

In addition to defining an AOI, WSP typically require some initial landscape classification. This initial landscape classification is an essential part of WSM since features not defined are inevitably unmanageable. When starting an initial landscape classification, most WSP will start by ensuring that all legally required management objectives are included. For example in most jursidictions in Canada, different riparian classes have different management requirements, including different no harvest buffers. Collecting spatial data of different riparian features is required, and creating of legal sized buffers so it is possible to change the potential future harvesting activities that can take place on the land base.

Beyond identifying legally mandated management requirements, this initial landscape classification will often include delineation of the Timber Harvest Land Base (THLB) and the Non-Timber Harvest Land Base (NTHLB). The THLB includes all forested lands that the WSP will be able to harvest volume from for the duration of the planning horizon. The NTHLB includes all areas classified as not forested, and any forested stands that are excluded from harvesting for the duration of the planning horizon for other reasons (e.g., inaccessible, low productivity, steep slopes, high host, protected status, etc.). THLB and NTHLB net-down are often displayed in summary tables in timber supply review technical documentation (outlining the different features and areas that are in each section of the AOI). Completing this step is typically a time consuming process, and requires a strong understanding of regionally appropriate forest legislation and input from multiple stakeholders.

The more care that is taken in this step, the easier it will be to ensure that you create a WSM that is adaptable enough to capture the diversity of different scenarios you might want to build and model into the future. Ideally, a WSP for one area will have one set of input data and landscape classification schema. Sometimes this is not possible, and it might be required to build two (or more) concurrent models with distinct classification schema to see how this impacts future wood supply. An example of this might be delineating the THLB and NTHLB differently which would potentially require two distinct landscape classifications.

Ultimately, all of these different features will be combined into one layer or file, that will be joined with initial forest inventory.

2.2. Initial Forest Inventory

Given that the primary purpose of a WSM is to project the state of a forested area through time under various patterns of management activities (and possibly natural disturbances or other external factors), it is essential to start this projection from an initial forest inventory. Initial inventories can have many different structures, but generally contain information about stand delineation, merchantable wood volume, tree species and age, site productivity, biogeoclimactic variables, management or disturbance history, administrative or other zoning, slope, watershed membership, etc.

All initial forest inventories need to have some initial grouping into stands or blocks. This can be presented spatially or aspatially. Spatial delineations of stands are polygons defined simply by being different from their neighbours. These spatial block or boundary delineations often use tree species, volume, age, and terrain features (such as rivers, or streams) to determine where one areas starts and ends. These initial stand delineations often (but not always) are linked with stand origin. An area that had the same disturbance (either anthropomorphic or natural) and the same regeneration (planted or natural), at the same time, in one spatially continuous extent, will often reflect one group or delineation. Aspaital delineation is much the same as spatial except different groups do not have neighbours or defined polygon boundaries.

2.3. Stratifying the Forest

The forest inventory data is typically aggregated into a manageable number of development types (i.e., strata or analysis units), which simplifies the modelling, by reducing the state space that needs to be modelled. The exact mechanism for stratifying the forest will vary from one WSM implementation to another, but typically there will be a way to define a number of stratification variables that will be used to aggregate stands into stand types. These stratification variables are often derived from the forest inventory data (e.g., biogeoclimactic zone, leading species, watershed, THLB, first or second growth status, etc.). A stratum will be defined by unique combinations of these stratification variables. The curse of dimensionality definitely applies here—the more stratification variables there are the more possible combinations that exist, resulting in geometric growth of the state space (i.e., potential number of development types) as a function of the number of stratification variables.

Stand age (or age class) is generally not used as a stratification in WSM software implementations, because it is linked to time and is reserved for use as the dependent (input) variable in the yield curves that WSM use to predict how stands evolve (grow) between stand-replacing disturbances.

2.4. Basic Components of WSM State Logic

The WSM state logic is a set of rules that define how the stand attributes can change over time. The set of all possible states that a given stand can be in is the state space. A WSM simulates trajectories through state space, primarily driven by the passage of time and application of disturbances.

Below, we define some basic concepts that are used in the WSM state logic.

2.4.1. Development Types

Each development type is linked to growth and yield functions describing the change in key stand attributes.

Each development type may also be associated with one or more actions, which can yield output products (e.g., species-wise assortments of raw timber products, cost incurred from exection of managment activities, treated area, etc.). Development types can also be used to define transitions, which are transitions between development types as a result of actions being applied at specific ages.

2.4.2. Yield Curves

Growth and yield functions are one of the major inputs to WSM. These will be used to predict and project stand attributes over time, as a function of stand age (e.g., species-wise standing timber volume, number of merchantable stems per unit area, wildlife habitat suitability index value, etc.). These growth and yield functions could be the output from a stand growth model, yield model, or other stand-level models that predict changes in stand attributes as a function of stand age. They could also be derived from expert knowledge, or from output from various simulation or statistical regression models.

2.4.3. Actions

Actions are used to apply management actions at specific ages in WSM. Actions are typically used simulate various silviculture treatments (e.g., site preparation, planting, pre-commercial thinning, fertilization, commercial thinning, final felling, etc.). However, actions may also be used to model transitions in management policy, such as transitions between management regimes (e.g., transition to an intensive management regime could trigger eligibility for various intensive management actions).

Action eligibility is typically defined as a function of management regime (which is implicitly encoded into the stratification variables that define development types), whereas action operability is defined as a function of stand age (which may vary by development type, e.g., some stand types grow faster than others so would be eligible for harvesting at a younger age).

2.4.4. Transitions

Applying an action to a development type induces a state transition (i.e., applying an action may modify one or more stratification variables, effectively transitioning the treated area to a different development type).

2.5. Scenarios

The set of all possible combinations of actions, across development types and time steps, is the solution space for a given WSM. One of the primary functions of a WSM is the allow the analyst to explore this solution space, and to generate scenarios. A scenario is a specific combination of actions that simulates a specific management regime. A scenario is typically generated by emulating existing mangement policies, or by exploring a new management regime.

There are two basic approached that can be used (independently, or in combination) to generate the dynamic activity schedules for each scenario.

2.5.1. Heuristics

The simplest approach, which we call the heuristic activity scheduling method, involves defining period-wise targets for a single key output (e.g., total harvest volume) along with a set of rules that determines the order in which actions are applied to eligible development types. At each time step, the model iteratively applies actions according to the rules until the output target value is met, or it runs out of eligible area. At this point, the model simulates one time-step worth of growth, and the process repeats until the end of the planning horizon.

2.5.2. Optimization

A slightly more complex approach, which we call the optimization activity scheduling method, involves defining an optimization problem (i.e., an objective function and constraints), and solving this problem to optimality (using one of several available third-party mathematical solver software packages).

Although the optimization approach is more powerful than the heuristic approach for modelling harvesting and other anthopic activities, an optimization approach is not appropriate for modelling strongly-stochastic disturbance processes (e.g., wildfire, insect invasions, blowdown). Thus, a hybrid heuristic-optimization approach may be best when modelling a combination of anthopic and natural disturbance processes.