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Validation of Volume and Taper Equations For Loblolly Shortleaf and Slash Pine

Inside-bark diameter measurements at 6.64 intervals of 137 loblolly, 52 shortleaf, and 64 slash pines were used to calculate the actual volume and taper of each species for comparison with volumes and tapers predicted from published equations. The loblolly pine wera cut in Texas (TX) and Louisiana (LA) while the shortleaf was sampled only in TX. The slash pine were sampled in Mississippi (MS). The models had been developed using trees that had the same diameter and height distributions as the validation data; however, the validation trees were generally older. For loblolly and slash pine, the volume equations over-predicted the average volume by 1.5 and 3.7 d/tree, respactlvaly, or about 5 to 10 percent of tree volume. The taper equation for loblolly was adequate, but the slash pine taper equation did not fit the data well. There is no appropriate volume or taper model for shortleaf pine. However, the loblolly equations predicted both volume and taper of the shortleaf pine data as well as or better than they did for the loblolly data. The loblolly and slash pine equations can be used with confidence-about half of the errors appear to be random, indicating that the best equations will have an error of about 1.5 f?/tree regardless of tree size. Most prediction ermrs occurred In larger trees, indicating that some improvement could be made in taper-volume models by adding age as a variable. Specks seems to be less important, and future modeling efforts should evaluate combined species equations. INTRODUCTION Valid volume and taper models are required for estimating tree volumes and stem shapes from simple measurements such as total tree height and diameter at breast height (d.b.h.). The models are used to estimate stand volume and site productivity, as well as to develop growth and yield models. There are numerous volume and taper models available for loblolly pine (e.g., Amateis and Burkhart 1987, Baldwin and Feduccia 1991, Lenhart and others 1987) and slash pine (e.g., Lohrey 1985, Thomas and Parresoll991). The usual procedure to develop a model is to collect data over a suitably wide range of tree sizes, and then fit appropriate regression equations to the data set. Although validation with independent data is desirable, sufficient resources are rarely available to repeat the data collection process. In the process of establishing long-term soil productivity (LTSP) plots on the national forests, we collected stem analysis data to determine the height growth patterns of existing stands over time. The upper-stem diameters collected as part of stem analysis are also suitable for validation of current volume and taper equations. One of the strengths of these data is that an intensive soil survey was conducted on each site, and the plots within each site were located within a stand on uniform soils. Our objective was to use these data to validate some existing volume and taper models. METHODS Sample trees were selected on four LTSP sites on the Kisatchie National Forest in Louisiana (LA), three on the Davey Crockett National Forest in Texas (TX), and three on the DeSoto National Forest in Mississippi (MS). Each site consisted of nine l-acre plots within stands that were to be harvested. A tenth plot was established on two sites in LA and one site in MS. After establishing the plots, we measured the d.b.h. of all pines with a diameter tape. Three sample trees on each plot were selected from the low, mid, and highest one-third of the diameter distribution. The sample trees were felled and inside bark diameter was recorded every 8.8 ft, beginning at the base. We calculated the volume of each tree using Smalian’s formula and recorded total height and species. Tree age was determined by counting the number of rings at the base. For the validation procedure, tree volume and taper for each tree were estimated using equations for loblolly and slash pine that were developed in LA. The volume equation tested for thinned loblolly pine (Baldwin and Feduccia 1987) was: In(V)=-8.885331 +2.040995ln(D)+1.150022ln(H) (1) where V = estimated total volume inside bark (ti), D = d.b.h. (in.), and H = total height (ft). For planted slash pine, we tested the volume equation of Lohrey (1985): In(V)=-8.93385+2.07195ln(D)+1.13845ln(H) (2) We tested prediction accuracy of both volume models using the Fit Index (Schlaegel1982), expressed as: ’ Paper presented at the Tenth Biennial Southern Silvicultural Research Conference, Shreveport, LA, February 16-16,1999. *Supervisory Soil Scientist and Supervisory Research Forester, USDA Forest Service, Southern Research Station, Pineville. LA 71360, respectively.