Individual Tree Taper, Volume and Weight for Loblolly Pine Bruce E. Borders Western Mensurationists Fortuna, CA June 18-20, 2006

Current Models Compatible total/merchantable tree volume/weight/taper functions Fitted separately by physiographic region (LCP, UCP, Piedmont) Large number of sample trees used in fit – however the range of data is limited in stem size (approximately 1500 trees largest DBH = 14” class) Problems using ratios low on the stem Implied Taper functions not very realistic (taper function derived from ratio volume equation)

Need More Data and Better Models! Large stumpage value drop for pulpwood in many areas of the South (about 2000) have resulted in more interest in solid wood production Hence, more users are finding the need to merchandise stems into products that require estimates for stem sections found in the lower stem – current models do not work well

Other Data Sources CAPPS Destructively Sampled Trees Age 6, 10, 12 years – data will be added to PMRC individual tree database Wood Quality Consortium Destructively Sampled Trees – 272 trees distributed across southern U.S. U.S. Forest Service – FIA unit has a relatively large database with volume, weight and taper information available

Data Used to Fit Functions

Data Used to Test Functions NOTE – all data will be combined for final model fits

Existing Model Form Where: V/W = cubic volume or weight to a top dob of Dm inches H = total height (ft); D = dbh (inches) Pienaar, L.V., T.R. Burgan and J.W. Rheney Stem volume, taper and weight equations for site-prepared loblolly pine plantations. PMRC Technical Report

Existing Model Forms Simple models – a lot of appeal for ease of use Models fitted separately by LCP, UCP, Piedmont Predict cubic volume inside/outside bark Predict green weight inside/outside bark Predict dry weight with and without bark

Existing Model Forms These models were developed for use in estimating volume or weight to a given top diameter However, the model form has limited flexibility in reflecting stem form realistically and it was fitted by Pienaar et al. (1987) with data bases structured to have Dm values of 6” and smaller Today – users require capability to merchandise stems into various products that may be found anywhere within the stem

Existing Model Form NOTE – the functions did not perform any better when fitted to the new database

New Functions – Taper/Volume Objective – provide two sets of functions 1. Simple and easy to implement (e.g. a ratio volume/weight equation and associated taper function) – realize that weaknesses will exist – fitted and evaluated model forms suggested by Bailey (1994), Zhang et al. (2002) and Fang et al. (2000) – only present results for Fang (2000) model 2. Sophisticated and very flexible system that should provide very accurate estimates of stem volume and weight for any stem segment – realize that implementation will require thorough understanding of the functions to be programmed (based on work of Clark, A. III, R.A. Souter and B. Schlaegel. 1991)

New Functions - Weight 1. Weights will be predicted using a per cubic foot density measure (lbs of wood and bark per cubic foot of wood) 2. Thus, to determine the green weight of wood and bark in any specific stem section we will calculate the cubic foot volume of wood and multiply by lbs of wood and bark per cubic foot of wood 3. These densities have been studied extensively by Alex Clark and others. Estimates currently available for different regions by age classes.

Simple Models Function flexibility and complexity increase from Bailey (1994), Zhang et al. (2002) to Fang et al. (2000). Of course, stem shape is complex and therefore it is not surprising the Fang et al. performed best of these three alternatives Fang, Z., B.E. Borders, and R.L. Bailey Compatible volume-taper models for loblolly and slash pine based on a system with segmented-stem form factors. For. Sci. 46(1)

Simple Approach – Alternative 3 In this work the stem profile was modeled with 3 segments each with its own form factor The join points of the segments were estimated as parameters The model was derived to insure that the taper function integrated to a total volume that was consistent with a total stem volume prediction equation that was fitted simultaneously

Revised Fang et al. Model I have revised the model as follows: First join point is at 4.5 feet Taper function is constrained to go through DBH No constraint to insure taper function integrates to a given total volume equation (as in the original paper) Form factors and upper join point vary with tree dbh and height

Revised Fang et al. Model

Revised Fang Model

Not So Simple Approach (Because Tree Shapes Are Not So Simple!!) Clark, Souter and Schlaegel 1991 Souter and Clark 2001 Clark, A. III, R.A. Souter and B. Schlaegel Stem profile equations for southern tree species. Research Paper SE-282. Asheville, NC. USDA Forest Service, Southeastern For Exp Sta. 113 pp. Souter, R.A. and A. Clark III Taper and volume prediction in southern tree species. USDA For. Serv. Southern Research Station. FIA Work Unit Administrative Report.

Souter & Clark Model Three segment stem profile equation used to define stem shape from ground line to total height – each segment is fitted independently of one another and are constrained to be continuous at the join points of 4.5’ and 17.3’ The first segment is divided into two sub- segments to allow for more flexibility The topmost segment is divided into three sub-segments to allow for more flexibility

Souter & Clark Model Function uses dbh, diameter at 17.3’ (Girard form class (GFC) height), and total tree height Recall GFC = 17.3’/dbh Note – functions are provided to predict dbhib from dbh and to predict dob and dib at 17.3 as a function of dbh and total height

Souter & Clark Taper Function

Souter & Clark Taper Function Volume Equation

Souter & Clark Taper Function Height Prediction for Given Top Diameter

Souter & Clark Taper Function Auxiliary Variable Prediction

To implement – predict dbhib from dbh (eq. 1); predict dib17.3 from dbh (eq. 4); predict dob17.3 from dib17.3 (eq. 3) – do not use eq. 2 or 5. Any parameters shown in equations above that do not appear in the parameter estimate lists below should be set to 0

Weight Density Clark, A. III, R.F. Daniels and B.E. Borders Effect of rotation age and physiographic region on weight per cubic foot of planted loblolly pine. Southern Silvicultural Confernce. Memphis, TN. March 2005.

Weight Density All individual tree weight data from the PMRC, WQC and U.S. Forest Service was used for this work Loblolly plantations were separated into two regions – Atlantic and Gulf Coastal Plains combined and Piedmont, Upper Coastal Plain and Hilly Coastal Plain (Inland) combined

Weight Density

Three age classes 10 to 18 years 19 to 27 years > 27 years

Weight Density Green weight of wood and bark per cubic foot of wood – can use in conjunction with inside bark cubic volume functions shown above to obtain estimated weight of wood and bark

Weight Density Coastal Plains – lbs wood and bark/cubic foot of wood (66.91 to 69.33) Inland – lbs wood and bark/cubic foot of wood (65.89 to 67.32)

Weight Density Lbs wood and bark/cubic foot of wood RegionAge ClassMeanLCLUCL Coastal10 – Coastal19 – Coastal> Inland10 – Inland Inland>

Weight Density Reasons why this density decreases as trees age: As dbh increases (as trees age) the proportion of stem weight in bark decreases (thus denominator (cubic feet of wood) tends to be larger for older trees) Wood moisture content decreases with increasing tree age (averaged 124% for 14 yr old trees, 114% for 24 yr old trees, 104% for 34 yr old trees)

Weight Density Further work is underway to look at defining density of green weight of wood/cubic foot of wood and dry weight of wood per cubic foot of wood Also – developing functions to predict these density measures for different tree ages along the stem and how best to use these functions in conjunction with the taper/volume functions

Summary Bottomline – several improved functions available for taper/cubic volume/weight determination for loblolly pine plantations – user’s choice (if Clark et al. model is not used the best choice is the revised Fang model) Same work will be done for slash pine

THE END Remember – it is important to get out of the truck every now and then!

Revised Fang OB Fit

Revised Fang IB Fit

Clark & Souter Taper Function Taper Parameters NOTE – any parameters that do not appear in the estimate lists below should be set to 0.

Clark & Souter Taper Function Taper Parameters - ib

Souter & Clark Taper Function Predict dbhib from dbh

Souter & Clark Taper Function Predict dib173 from dbh

Souter & Clark Taper Function Predict dob173 from dib173