0309-B1

TimSuM - A Timber Supply Model to Project Forest Growing Stocks

Tian-Ting Shih^[1]

Abstract

Among all the goods and services that forests provide, timber always serves as one of the most basic resources for the economy. Fast growth of human population and dramatic shrinkage of available timberland make the sustainability of timber supply a hot topic widely debated in society.

A Timber Supply Model, TimSuM, has been designed as an educational and communicational decision-support tool to enable the general public and policy-makers to discuss current forest conditions and to project future timber supplies at regional and state level, while considering any likely changes on all forest resources and their hosting environment. TimSuM employs the scheme of annual compound rate to construct its model engine and its fundamental components are: land base, forest growth, stand mortality and timber harvest. Knowledge about regional forestry and expectations about the local economy may serve dynamically in formulating various scenarios to drive TimSuM for all possible projections. TimSuM also allows users to conduct sensitivity analysis on each component for what-if simulations.

In this paper, example runs on the privately owned softwood timberland in California’s North Interior region, located in the southwestern United States, demonstrate some of TimSuM’s capabilities and potentials.

I. Introduction

Timber is always one of the most basic commodities to help the development of human civilization. Although forestry is shifting its focus more to the enjoyment of scenery and recreation, to the protection for wildlife and watershed, and to the sustainability on biodiversity and ecosystem, timber is still playing a crucial role in the economy to feed people’s needs for house construction, paper making, energy generation, etc. Comparing to its substitute materials, timber inherits its distinctive characteristics of being able to be regenerated successfully on the same piece of land and produced harmoniously in its environment through sound management.

The fast growth of human population has impounded heavier demands on timber while more and more commercial timberland in either private or public domain has been converted to other uses or set aside for wildlife, riparian, or other environmental protections. The dramatic drop of timber harvest on public land in the United States has put additional pressures on its private timberland and all other timberland in the world. To understand whether timber supply is sufficient and sustainable in the future provides a foundation for the communications between public agencies and private owners and between forest industries and environmental groups. Thus, a simple, logical, robust, and educational tool used to project future timber supplies at regional or state level under various scenarios is in extreme demand. TimSuM, a Timber Supply Model, is developed for this purpose.

II. Model Engine and Fuel

Timber supply has been discussed for thousands of years. Mencius (371-289 BC), a famous Chinese scholar, once said that timber could be sustainable for human uses as long as there were right harvesting schedules. Studies on timber supply have made major developments over a century and have advanced quickly for the past thirty years (Alig et al. 1984). However, timber supply models developed recently usually possess very complicated system structures requiring sophisticated operation procedures and are not easy to be used as a communication or a decision support tool to allow general users to specify forest objectives and expectations and to allow the system to adapt newly advanced forestry knowledge into model projections.

Instead of imbedding forest growth equations and employing mathematical programming in the model, TimSuM simply adopts a scheme of annual compound rate for its engine to project growing stocks in a region. Also, instead of using huge amounts of tree lists from forest inventories, TimSuM utilizes the most easily obtained public or summarized information on forest inventory for its initial input, such as those published in the Forest Inventory and Analysis (FIA) reports by U.S. Department of Agriculture, Forest Service. These data serve as the fuel for the engine and include timber volume of the periodic growth, mortality, and harvest in that region of concern.

Figure 1: TimSuM’s Structure and Major Components

With these inputs, TimSuM calculates the compound annual growth rate of that certain period of time and then projects forest growing stocks into future based on specified patterns in growth, mortality, harvest, and land base while considering the differences existed in forest types, site qualities, and ownership. Figure 1 outlines the system structure and its major components of TimSuM. Since TimSuM includes forestry knowledge and expectations inside its scenario as the fuel to drive the model and not inside the engine, TimSuM holds the features of easily adopting any knowledge retrieved from each component through modeling and easily communicating among different users to allow them to discuss and formulate various scenarios and to play with “what-if” questions on future timber supply. The entire process shown in the following example runs may provide a demonstration on some of TimSuM’s capabilities and potentials.

Figure 2: California’s North Interior Region (Waddell and Bassett 1997)

III. Model Simulation

Located in the southwest of the North America, California has 40 percent of its land covered by forests. North Interior, as shown in Figure 2 (Waddell and Bassett 1997), is a major timber region in the state. These five counties encompass 13,922,000 acres of land and 70 percent of them are forests. Although 60 percent of the forestland is in national forests, forest industry and other private owners still manage 2,276,000 acres of timberland in this region. Among these acres, 83 percent are conifers. TimSuM will take the private softwood timberland of this region for example runs in this paper.

A. Initial Input

As an input to TimSuM, Table 1 summarizes the periodic gross growth, mortality, and removal or harvest from the FIA report (Waddell and Bassett 1997). TimSuM converts the periodic variables into annuals and assumes that annual mortality and annual harvest occur evenly at the end of each year. Thus, TimSuM calculates the compound annual gross growth rate for the private softwood timberland in California’s North Interior from 1985 to 1994 and finds that it was 4.09% on average to raise the growing stocks from 4,161 to 4,928 million cubic feet while 14.5 and 92.2 million cubic feet of mortality and harvest, respectively, were removed from the growing stock bases at the end of each year.

Table 1: Periodic Changes of Growing Stocks from 1985 to 1994 on North Interior Private Timberland

B. Land Base

To project timber supply in the future, in addition to growth, mortality, and harvest, land base is another major influencing factor. Through increased public concerns on protecting wildlife, biodiversity, riparian, watershed, recreation, and scenery, many acres of timberland have been set aside from timber production. Timberland conversions to rangeland, subdivisions, and other non-timber uses also shrink the available timberland supplying timber. Since TimSuM employs growth rate approach in its model engine, the acreage loss or gain on timberland is going to affect the growing stock base before the next compound rate being applied to it. All the knowledge on land base patterns, such as from the Markov chain or other probability models, can be formulated into scenarios.

For a simple example here, from public records, Figure 3 depicts the acreage of timberland conversion in northern California from 1969 to 1998 (Shih 2002). Timberland converted to other uses was averaged at 807 acres per year from 1985 to 1994 and reached at 2,550 acres per year from 1995 to 1998. Thus, we may generalize this knowledge conservatively in a scenario to see what if 1,000 acres of timberland are reduced annually in the North Interior for the next 40 years. The projection results using this scenario is shown later in this paper.

Figure 3: Acreage of Timberland Conversion in Northern California from 1969 to 1998

C. Growth

Although we may certainly assume that growing stocks will grow at the same rate as in the last decade for the next four decades and execute the projection with TimSuM, growth rate is actually a function of stocking, site quality, and forest type. Yield tables may serve as a good reference then to control or calibrate forest growth patterns on growing stock projections.

On the private softwood timberland in the North Interior, three forest types are generalized and summarized by site quality and ownership as shown in Table 2. Mixed conifer covers 70 percent of the acreage.

Table 2: Acreage of Private Softwood Timberland by Forest Type, Site Quality, and Ownership in the North Interior

We may also generalize and combine yield tables from Dunning and Reineke (1933) for mixed conifers, Meyer (1938) for Ponderosa pines and other pines, and Schumacher (1926) for white firs and other firs for the North Interior and apply them to Table 2. Table 3 shows the result representing the potential growing stocks as one of its land capacities while assuming that the entire forest is managed into a fully regulated forest based on their biological rotations for each forest type and site quality based on these yield tables.

Table 3: Potential Growing Stocks of Private Softwood Timberland in the North Interior

Comparing Table 3 with Table 1, it revels that, in 1994, the private softwood growing stocks on North Interior timberland reached almost 85 percent of its fully regulated potential and the growth also reached about 90 percent of its long-term sustained yield (LTSY). TimSuM, thus, provides us an opportunity to understand more about the current conditions and potentials of the forest in concern.

With a similar approach on yield tables for growth rates, Figure 4 provides another indicator to examine the current forest growth comparing to its potentials. In 1994, with the averaged growing stocks at 2,591 cubic feet per acre, the net growth on the private softwood timberland in the region was about 1.2% less than its potential found on yield tables. Figure 4 delivers that growth rate is negatively correlated to the growing stocks per acre, or stocking. The growth rate pattern may also be used to adjust the growing stock projection in TimSuM.

Figure 4: Correlation of Growth Rate and Stocking for the North Interior Private Softwood Timberland

Knowledge on the influences from any possible factor, such as global warming, intensive management, genetic stocks, etc. affecting forest growth, can be used as an input for scenarios. For a simple example, we may assume optimistically that the forest is going to grow 0.07% additional to its current annual growth rate for the next 40 years and follow the growth pattern as shown in Figure 4. Currently, based on 12,000 sampling plots, a research team is working on redefining the yield curves in California (Krumland 2002). These yield curves may represent forest growth more realistically for the present time than those yield tables generated about 70 years ago. TimSuM is capable of incorporating any results from new yield and growth studies into its projections.

D. Harvest

Harvest is always a hot and sensitive issue in California. Figure 5 shows that timber harvest volume in California’s North Interior dropped almost one billion board feet from 1978 to 2000 on public ownership and stayed level on private (Shih 2001). In order to formulate future scenarios on harvest, LTSY may again serve as a good reference.

Figure 5: Timber Harvest Volume on North Interior by Ownership from 1978 to 2000

California’s harvests are mainly on softwood timber for lumber uses. Harvest volume from 1985 to 1994 accounted only about 50 percent of its LTSY, as shown in Table 3, on the private softwood timberland in the North Interior. However, California’s lumber consumption is expected to increase 42 percent from 1994 to 2050 (Shih 2001) due to the strong population growth in the state. While harvesting on public land has been dramatically reduced, more pressures on timber supply may be imposed heavily on private timberland. Based on this understanding, we may formulate a scenario on harvest for our example run by assuming that harvest will increase linearly from 50 percent to 65 percent of LTSY at 2004 and reach linearly to 80 percent of LTSY at 2014 and to 90 percent of LTSY at 2024. The same level will then be maintained up to the end of this forty-year simulation. Knowledge on forest policies regarding harvesting and expectations on wood demands for timber products can always serve as the guides to formulate scenarios in TimSuM.

E. Mortality

Mortality plays a small but important role in growing stock projections, especially in California, where fire is always a threat and the damages from forest pests and diseases are increasing. Any advanced knowledge on mortality in California’s forests can be used to formulate scenarios. However, for a simple example here, we may assume that forest mortality in this region is proportional to its growing stocks and even assume that an additional 0.12% will be added to the current mortality ratios for the next forty years based on an expectation of having larger impacts from fires and all other natural and human damages in the future.

F. Projection

If we put together all these simple examples assumed above in each component to formulate a scenario called the Alternative Scenario, TimSuM can then project the growing stocks based on it. We may also formulate another scenario here called the Base Scenario by assuming that, for the next 40 years, no additional changes are going to be expected on the land base while keeping the growth rate, harvest volume, and mortality ratio same to those in the decade from 1985 to 1994. TimSuM can then also project growing stocks based on it. Figure 6 demonstrates the results from these two TimSuM example runs for the next 40 years from 1995.

Figure 6: Projections of Softwood Growing Stocks on North Interior Private Timberland based on Two Scenarios

The differences shown in these two projections are distinct and represent the integrated effects on the changes of future growing stocks due to expectations assumed for the land base, growth rate, harvest level, and mortality ratio in each scenario. In Figure 6, the lowest horizontal line indicates the growing stock level in 1994 at 4,928 million cubic feet as briefed in Table 1. The “regulated” line points out the fully regulated growing stock level at 5,902 million cubic feet as shown in Table 3. The “r-capacity” line shows another growing stock level at 13,302 million cubic feet by assuming all stands are reaching their highest biological rotation age appeared in the yield tables. The maximum land capacity for forest growing stocks can be even higher though it may not be possible to be happened on the ground. These three lines and the estimated LTSY provide good references on examining the current and projected growing stocks, growth, harvest, and other forest conditions.

G. Sensitivity Analysis

Since TimSuM is a simulation model running on formulated scenarios employing knowledge in forestry and expectations on economy, it possesses the sensitive analysis capability to illuminate the effects on projections from any change specified in each component of a scenario. For example, besides the comparisons on the overall growing stocks projected on the Alternative and Base Scenarios, we may also test whether that additional 0.12% increase added to the annual mortality ratio for the next forty years may finally create distinctive differences in projections.

Comparing to the Base Scenario projection, Table 4 reveals that only two percent of growing stock volume in 20 years or four percent in 40 years will be in difference by adding the Alternative mortality assumption alone. Also, in four decades, the sole change in growth rate and the sole change in harvest level as formulated in the Alternative Scenario may generate a same effect on growing stock volume for the private softwood timberland in the North Interior.

Table 4: Growing Stock Changes based on Various Scenarios in Model Projections

H. Aggregation

When forests are diverse in their conditions, policies, management, and economy, they can be delineated or combined for TimSuM’s projections. For example, as shown in Table 5, the Sierra Nevada region including mostly the Sacramento and San Joaquin areas has distinctively higher mortality ratio than the Coast region including the North Coast and Central Coast areas. The differences in the forest growth rates between the softwood and hardwood timberland or between the private and public ownership are also significant.

Table 5: Growth, Mortality, and Harvest by Region, Ownership, and Forest Type in California

TimSuM is flexible enough to project growing stocks for each sector by its own initial components and its own formulated scenarios. These results can then be aggregated together to discuss future timber outputs at the state or even higher level.

IV. Conclusion and Discussion

TimSuM is not designed to model land base, growth pattern, mortality ratio, or harvest level in its framework. However, with a pure projection engine, TimSuM can fully absorb any results from these modeling works to project timber supply. Without imbedding these modeling in its structure, TimSuM inherits a full advantage of serving as a knowledge sink and a communication tool for its users having various objectives in formulating possible scenarios to get future projections. This feature also allows TimSuM easily to incorporate financial and investment considerations in its analyses and to expand the model to the projection of biomass and fuel loading to discuss energy generation and fire protection.

As a simple, logic, robust, and educational tool, TimSuM not only can project growing stocks in the future under various scenarios but can also provide the opportunity for its users to examine the current and projected forest conditions comparing to the land capacity. With its flexibility on further refinements, TimSuM shows the potentials in discussing future timber supplies and in supporting dynamic decision-makings for the fast changing forestry and economy.

Literature Cited

Alig, Ralph J., Bernard J. Lewis and Paul A. Morris, 1984. Aggregate timber supply analysis. General Technical Report RM-106, U.S. Department of Agriculture, Forest Service, Rocky Mountain Forest and Range Experiment Station, 49 p.

Dunning, Ducan and L.H. Reineke, 1933. Preliminary yield tables for the second-growth stands in the California pine region. Technical Bulletin No. 354, U.S. Department of Agriculture, Forest Service, California Forest and Range Experiment Station, 23 p.

Krumland, Bruce, 2002. (Personal communication on 2/8/2002 at California Department of Forestry and Fire Protection, Fire and Resource Assessment Program).

Meyer, Walter H, 1938. (revised 1961). Yield of even-aged stands of Ponderosa pine. Technical Bulletin No. 630, U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station, 59 p.

Schumacher, Francis X., 1926. Yield, stand, and volume tables for white fir in the California pine region. Bulletin 407, University of California, College of Agriculture, Agricultural Experiment Station, 26 p.

Shih, Tian-Ting, 2002. Timberland conversion in California from 1969 to 1998. Technical Working Paper 1-01-02, California Department of Forestry and Fire Protection, Fire and Resource Assessment Program, 13 p.

Shih, Tian-Ting, 2001. California’s timber assessment - demand, supply, constraint, and opportunity. (draft). California Department of Forestry and Fire Protection, Fire and Resource Assessment Program, 21 p.

Waddell, Karen L., Patricia M. Bassett, 1997. Timber resource statistics for the north interior resource area of California. Resource Bulletin PNW-RB-222, U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station, 49 p.