Developing Optimal Commercial Thinning Prescriptions: a New Graphical Approach

Developing Optimal Commercial Thinning Prescriptions: A New Graphical Approach

KaDonna C. Randolph, USDA Forest Service Forest Inventory and Analysis, Knoxville, TN 37919; and Robert S. Seymour and Robert G. Wagner, Department of Forest Ecosystem Science, University of Maine, Orono, ME 04469.

ABSTRACT: We describe an alternative approach to the traditional stand-density management diagrams and stocking guides for determining optimum commercial thinning prescriptions. Predictions from a stand-growth simulator are incorporated into multiple nomograms that graphically display postthinning responses of various financial and biological response variables (mean annual increment, piece size, final harvest cost, total wood cost, and net present value). A customized ArcView GIS computer interface (ThinME) displays multiple nomograms and serves as a tool for forest managers to balance a variety of competing objectives when developing commercial thinning prescriptions. ThinME provides a means to evaluate simultaneously three key questions about commercial thinning: (1) When should thinning occur? (2) How much should be removed? and (3) When should the final harvest occur, to satisfy a given set of management objectives? North. J. Appl. For. 22(3):170–174.

Key Words: Nomogram, silvicultural system, financial analysis, FVS, simulation.

Careful regulation of stand density through thinning North America in the late 1970s (Drew and Flewelling arguably distinguishes truly intensive management above 1979, Newton 1997a). SDMDs graphically depict the rela- all other silvicultural treatments (Smith et al. 1997), and in tionship between stand density and average tree size (either every important forest region, rigorously derived thinning quadratic mean dbh or stemwood volume, and frequently schedules are crucial in meeting production objectives. Typ- supplementary isolines depicting tree height; Newton ically thinnings are prescribed using stocking guides or 1997b, Wilson et al. 1999). SDMDs are used to determine stand-density-management diagrams. Since the 1970s in the the specific stand density required to meet various produc- northeastern United States, stocking guides developed in the tion objectives, including minimizing time to operability manner of Gingrich (1967) have dominated practice (Sey- and attaining specified mean diameters and log dimensions mour 1995, 1999). These stocking guides are based on at the end of a rotation. Volume-based SDMDs are useful tree-area ratios that define an expected maximum density for predicting yields of various thinning regimes and even to for a given forest type and use easily measured stand at- evaluate their consequences on wildlife habitat (Newton tributes such as basal area, quadratic mean diameter, and 1997a). trees per unit area to assess stocking of a single stand at a Although stocking guides and SDMDs are very useful particular point in time (Nyland 1996). Typically, the stock- for prescribing thinnings, users must tacitly assume that the ing guide charts are divided into zones of overstocking, full typical recommendations of researchers to maximize yields stocking, and understocking with the familiar A-, B-, and (e.g., thinning to the B-Line or 40% relative density) will C-Lines, respectively. automatically meet their objectives. More commonly, forest A common alternative to Gingrich-style stocking guides managers are interested in balancing maximum yields with is the stand-density management diagram (SDMD). Formu- financial and piece-size targets. Stocking guides and SD- lated initially by Reineke (1933), SDMDs were later devel- MDs are not designed to identify a specific residual density oped by Japanese scientists in the 1960s and introduced to that simultaneously optimizes multiple objectives. For example, SDMDs do not include any financial information, and therefore net present value or internal rate of return NOTE: Robert Seymour can be reached at (207) 581-2860; Fax: (207) 581-4257; [email protected]. This work was sup- must be calculated separately, a time-consuming and error- ported by the Cooperative Forestry Research Unit, University prone process. of Maine and is Publication 2759 of the Maine Agriculture and Forest Experiment Station. Copyright © 2005 by the Society of Our objective was to develop an analytical framework American Foresters. that would facilitate the application of existing stocking

170 NJAF 22(3) 2005 Figure 1. Steps in plotting simulation model output for producing a single nomogram. (A) Stand development is projected after three different thinning prescriptions (to residual densities of 400, 325, or 260 trees/ac) and the calculated effects on mean annual increment are plotted against residual stand density and stand age. (B) Isolines are drawn through the mean annual increment “heights” shown in (A) to yield a response surface. diagrams and stand-growth simulators in formulating den- ibility by identifying the range of feasible strategies. This sity-management regimes that can achieve user-specified article outlines the conceptual approach of such an analyt- goals. Rather than deriving a single “optimum” strategy, we ical tool and provides an example of how this strategy was sought to develop a method or tool that could illustrate the incorporated into the customized ArcView GIS application trade-offs among multiple biological and financial response called ThinME (short for Thin Maine) for developing com- variables by using an interactive format that promotes flex- mercial thinning prescriptions in Maine spruce-fir stands.

Figure 2. Steps in applying nomograms to derive a commercial thinning prescription. (A) Unacceptable outcomes for two management-objective variables (mean annual increment and piece size) are shaded indi- vidually. (B) The individual nomograms of (A) are overlaid, yielding an unshaded area in which the two management objectives are met simultaneously. (C) The range of residual density and final harvest ages that meet the management objectives are read from the axes. Note: TPA reference lines slant slightly downward to reflect tree mortality simulated by the FVS model.

NJAF 22(3) 2005 171 Figure 3. Shadings for a set of management objectives result in different areas of acceptability when commercial thinning is implemented at three stand ages: (A) age 27; (B) age 32; and (C) age 37. Unshaded regions define the conditions in which final harvest piece size is less than 20 trees/cord and mean annual increment is at least 0.85 cords/ac/year; for clarity in illustration, other variables .70 ؍ are not considered. Density of the simulated spruce-fir stand before simulated commercial thinning was 750 trees/ac; site index

Conceptual Approach analyzing commercial thinning prescriptions owing to its intuitive graphical nature: by overlaying alternative scenar- If unlimited time and resources were available, one could ios, nomograms can depict numerous management response use a stand growth simulator, along with appropriate finan- variables simultaneously. cial postprocessors, to derive a “custom” thinning prescription for every stand to be treated. Of course, such an Individual Nomograms approach is impractical. Efficiently developing silvicultural prescriptions requires a method to synthesize results from The nomogram consists of two main axes and a response numerous simulations in an easy-to-use, understandable surface of a variable of interest relative to the main axes. For manner. The many decision variables that forest managers commercial thinning applications, the horizontal axis is age must incorporate make it difficult to visualize the multidi- at the simulated final harvest and the vertical axis is residual mensional space in which the management objective(s) stand density (trees per acre) after thinning. The variable of must be optimized. To overcome this difficulty, Peterman interest reflects a stand-management objective and could be (1975, 1977) developed a graphical technique (nomogram) average piece size, mean annual increment, net present to compress the outputs of simulation models into an un- value, or any other density-dependent variable that changes derstandable, two-dimensional format, while retaining all as a stand develops over time. possible information. Generating nomograms requires several sequential steps. The nomogram technique used by Peterman graphically First, initial stand conditions are entered into the growth and depicts one response variable, a measure of system perfor- yield model. After examining three different growth and mance that a manager seeks to influence such as stand yield, yield models, we selected the USDA Forest Service’s Forest as a function of two other input variables that are under the Vegetation Simulator NE-TWIGS variant (Bush 1995, Teck manager’s control such as stand density and rotation age. et al. 1996) for this application. Next, thinning prescriptions This format effectively captures a three-dimensional rela- are repeatedly applied to the stand of interest with the goal tionship in the form of a contour plot or response surface. of spanning the range of feasible densities and thinning Using the nomogram, a user can quickly and easily deter- methods. Stand development is projected, and the effect of mine if certain levels of a response variable are attainable, the thinning prescription on the management variable(s) is distinguish trade-offs required to achieve certain goals, and recorded (in a spreadsheet) at successive ages and plotted examine alternative outcomes. We selected this method for (Figure 1A). Finally, to complete the nomogram, isolines

172 NJAF 22(3) 2005 Figure 4. ThinME display illustrating three nomograms queried for areas meeting a set of specified management objectives. The unshaded region defines the intersection of three objectives: net present value > $75/ac; piece size < 18 trees/cord; and mean annual increment > 0.80 cords/ac/year. Initial stand conditions and commercial thinning ages are the same as in Figure 3.

(lines of equal value) are generated via mathematical inter- Multiple Nomograms polation to define “contours” of the management response Just as a stand can be thinned to various residual densi- variables (Figure 1B). ties, a stand also can be thinned at different ages. Deter- Once a nomogram is generated, users can “shade out” mining when to commercially thin is accomplished by eval- unacceptable outcomes in the nomograms to arrive at a uating nomograms generated from thinning prescriptions target residual stand density and final harvest age (Figure applied at different stand ages. In essence, the process 2A). When the nomograms for two response variables illustrated in Figures 1 and 2 is repeated for the same (mean annual increment and final-harvest piece size) are hypothetical stand thinned once commercially at different overlaid, the remaining unshaded zone represents the range ages. Figure 3 illustrates this approach for commercially of residual densities and final harvest ages that simulta- thinning the same stand at 27, 32, or 37 years of age. neously meet both objectives (Figure 2B). This process can Using the same combination of five response variables be repeated for as many response variables or nomograms (mean annual increment, piece size, final harvest cost, total as needed. Figure 2C illustrates that for any given residual wood cost, and net present value) for each thinning age, the density, there is a range of rotation ages at which the final nomograms in Figure 3 are shaded to show the combina- harvest must occur: after the stand “grows’ into the high- tions of residual density and final harvest age that simulta- lighted region and before the stand ”grows“ beyond it. For neously meet two objectives simultaneously: piece size at this reason, residual stand density and final harvest age final harvest less than 20 trees per cord; and mean annual should be read in tandem from the vertical and horizontal increment at least 0.85 cords/ac/year. Figure 3A is com- axes, respectively. In this example, the greatest flexibility in pletely shaded, indicating that thinning at age 27 cannot final harvest age (about 54–68 years) appears to result from meet these multiple objectives, regardless of the residual thinning to 500 TPA. density or final harvest age. The objectives can be met,

NJAF 22(3) 2005 173 however, if the stand is thinned at age 32 (Figure 3B) or 37 ing guides. By incorporating financial and biological vari- (Figure 3C). To determine which of these two ages is better, ables into an easy-to-use graphical system, forest managers the size of the unshaded region is considered. Taller areas are able to more quickly and thoroughly explore a variety of imply more flexibility in residual density, whereas wider commercial thinning prescriptions. The nomogram ap- areas imply more flexibility in final harvest age. In this proach also allows forest managers to weigh the different example, we consider the third timing, age 37 (Figure 3C), outcomes and determine acceptable trade-offs among an to be the best option because it provides the most flexibility array of specific management objectives. in setting the commercial thinning and final harvest pre- ThinME is our first attempt to integrate postthinning scriptions and, thus, the greatest robustness against unex- growth responses and the formulation of silvicultural pre- pected pest outbreaks or abiotic stresses (Peterman 1977). scriptions using the nomogram methodology. We envision future versions of the model that will allow users to enter Application their own stand data and directly interface with existing When Peterman first suggested these methods, produc- stand simulators such as the USDA Forest Service Forest tion of nomograms required tedious manual interpolation, Vegetation Simulator. As data become available from on- plotting on transparent media, and shading of unacceptable going commercial thinning studies in the region (Wagner et outcomes, so it is no surprise that few applications ensued. al. 2001), ThinME will be improved through the use of Modern GIS automate these tasks and allow users to create growth and yield models specifically calibrated to project a customized visual user-interface using ArcView GIS (En- postthinning growth responses. vironmental Systems Research Institute1997). By means of the customized interface (ThinME), the effects of different Literature Cited BUSH, R.R. 1995. Northeastern TWIGS variant of the Forest Vegetation commercial thinning prescriptions on biological and finan- Simulator. USDA Forest Service. Available online at www.fs.fed.us/ cial variables are illustrated for a variety of stand conditions fmsc/fvs/fvs_variant_overviews.htm; accessed by author Nov. 24, and thinning options applicable to Maine spruce-fir forests. 2002. 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Nov. 15–16, 1999, Augusta, ME, Wagner, R.G., et al., (eds.).University of Maine Office of Professional Development, Orono, limits for each management objective; on clicking an ME. “okay” button, ArcView queries the nomogram and high- SMITH, D.M., B.C. LARSON, M.J. KELTY, AND P.M.S. ASHTON. 1997. The lights the acceptable regions (Figure 4). Successively practice of silviculture: Applied forest ecology, 9th Ed. John Wiley and smaller adjustments in the response variables quickly allow Sons, New York. 537 p. TECK, R., M. MOEUR, AND B. EAV. 1996. Forecasting ecosystems with the the user to converge on the optimal thinning age, residual forest vegetation simulator. J. For. 94(12):7–10. density, and final harvest age. WAGNER, R.G., R.S. SEYMOUR, AND D.J. MCCONVILLE. 2001. Commercial thinning research network. P 23–35 in Cooperative Forestry Research Unit, 2001 annual report. NSFA College Miscellaneous Report 428. Conclusion 73 p. 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