Perspectives from a REIT Growth and Yield Modeling Architecture and Treatment Response Models – The Rayonier Approach J.P. MCTAGUE Western Mensurationists 2016 Annual Meeting, June 20,2016 Skamania Lodge, Stevenson, WA

Rayonier methodology in US South Stand-level → good biological behavior Tree-level → merchandizing and valuation

Model architecture for D. Fir/W. hemlock in PNW Components - Juvenile - Stand-level - Tree-level

How does Rayonier augment the value of cooperatives? 1.Rayonier develops regional G&Y models by pooling data from numerous (coop and non-coop) sources. 2.Rayonier places little reliance on coop models which are created with smaller or restricted data sets. The coop models sometimes lack the level of resolution that we require.

The Rayonier PNW model pooled UW-SMC, Forest Service, and proprietary permanent plot data

Southern pine basal area model has two key features related to compatibility where B = stand basal area, A = stand age, N = trees per acre, H = dominant height 1.Path invariant: Projection of yield from A 1 →A 2 →A 3 is identical to A 1 →A 3 2.Simultaneous fit for prediction and projection Prediction

Prediction is useful in young stands that have not been cruised. Following an inventory, we project forward from X X Prediction Projection

Projection equation (represented by dashed line) Basal area at time 2 is a function of basal area at time 1 and changes in other stand attributes. The compatible equation above was estimated simultaneously with the prediction equation and the b 1 – b 5 coefficients are identical

Following a timber inventory, what should be done with the observed diameter distribution?  Pienaar (1989) has made the plea that this information should not be discarded when estimating future stand tables.  Parameter recovery (Weibull) methods should not be used since (Weibull) techniques can only predict smooth unimodal distributions.

At age 11, the stand attributes for both the top panels are N = 523 and B = 101, while at age 15 the attributes change to N = 498 and B = 137 for both bottom panels. The Weibull parameter recovery method in the upper-right panel displays a smoothed unimodal distribution that ignores the observed timber cruise tree diameter data.

The differences between the diameter distribution in the bottom two panels are important for merchandizing, since the lower- left distribution contains 20.9 tons/ac of potential grade (dbh ≥ 9 inches) while the lower-right distribution possesses only 13.3 tons/ac. Aside: approximately 25% of age 11 stands in US South resemble distribution on left

Rayonier uses a growth model for thinned stands based on a theory that originated from the Correlated Curve Trend (CCT) thinning studies of South Africa for slash pine  A serious underestimate of yield of thinned stands will occur if the prediction equation computes no difference in stand-level basal area growth between thinned and unthinned stands of the age, site index, and basal area per acre.  The yield of a thinned stand will asymptotically approach that of an unthinned (counterpart) stand of the same age, site index, and number of trees per acre.

The relative difference in basal area between the thinned (B t ) and unthinned stand (B u ) with the same number of trees per acre is called the index of suppression (IS)

Over time it is assumed that the thinned stand yield (Curve 1) will approach that of an unthinned stand (Curve 2) of the same age, site index, and number of trees per acre.

What governs the time needed for a thinned stand to approach its unthinned counterpart?  Thesis from Burrow, A.M. 2001, SFASU  Initial index of suppression  Years since treatment  Site index

Response to intensive silviculture: hierarchical system

Response to intensive silviculture

Base component: fit using hierarchical mixed models. We have no interest in the base model. It is discarded. It’s function is to make the R B signal stronger Amateis et al. (2000) have taken a different approach to modelling the effect of fertilization on the development of dominant height and basal area. They constructed response models for fertilized stands using R H, and R B as dependent variables. R B is defined as the difference in basal area between a fertilized and unfertilized (control) stand. During their fitting procedure, the increase of basal area in fertilized stands, due to R H, was unobservable

Response to intensive silviculture and the burden of path invariance Prediction Base modeltreatment response Let’s project from age 9 to age 16

Steps 1.Remove treatment effect at age 9 2.Project untreated stand 3.Add back cumulative effect of treatment at age 16 to untreated projection This tedious procedure complicates very quickly. Imagine a stand fertilized at age 12, thinned at age 14, with a post-thin cruise at 15. Suppose we wish to project the stand yield from age 15 to age 18. Yikes!