by Lee C. Wensel and Timothy A. Robards
Abstract

	Previous height growth models were developed using stem analysis 
(Wensel and Koehler, 1985).   DBH growth models were developed using,
first, stem analysis data and, then, increment core data collected
at the time of the initial measurement of the Coop permanent plots 
(Wensel, Meerschaert, and Biging, 1987).  These estimates of growth
were applied to stand conditions that were back dated to the beginning 
of the growth respective periods.
	Remeasurement of these permanent plots yielded growth estimates
by difference.  The previous growth models consistently underestimated
the growth rates observed on these remeasurement data.  Thus, new 
parameter estimates were constructed to agree with the remeasurement 
data.  However, it is not clear whether the differences in the growth 
projections between the previous and present models represent a 
difference in the actual growth rates or a difference in the 
measurement and analytical techniques used.


                             INTRODUCTION

	CACTOS, the CAlifornia Conifer Timber Output Simulator, is 
in widespread use by federal, state, private, and industrial foresters.  
The simulator makes it very easy to produce estimates of timber yields 
for 5-year growth periods -- with or without management intervention.  
The operation of the CACTOS System is described by Wensel and Biging 
(1987) and the operation of the individual programs by a series of 
user's guides.  The CACTOS users' guide (Wensel, Daugherty, and 
Meerschaert, 1986) is the principal reference for the operation of 
the program and the various components of the program have been 
described in papers by Biging (1984, 1985, and 1988), Biging and 
Wensel (1984, 1985, 1987), Biging and Meerschaert (1987), 
Meerschaert and Wensel (1988), Van Deusen and Biging (1984), and 
Wensel and Koehler (1985).  These papers describe the modelling 
processes used to obtain estimates of tree volume and taper, site 
index, crown geometry, tree growth rates and other mensurational 
relationships important to the growth modelling process. 

	This paper presents the results of a study of the remeasurement 
of permanent plots maintained by the Northern California Forest Yield 
Cooperative.   The six conifer species studied are listed in Table 1 
along with the two-letter species codes used in the following tables.  
The objective of this study was to (1) use the current set of 
remeasurement data to test the validity of the growth equation 
coefficients and (2) to revise the coefficients if warranted. Under 
the assumption that the difference between two measurements of the same 
trees at two points in time is the best estimate of tree growth, 
differences between actual and predicted growth rates is referred to 
here as bias.   

	In a previous study, Wensel and Koehler (1985) presented both 
height and DBH growth coefficients based upon stem analysis.  For DBH, 
these coefficients were revised based upon a more extensive series of 
measurement on the initial measurement of over 720 permanent plots 
(Wensel, Meerschaert, and Biging 1987). Thus, the previous height 
growth coefficients were based entirely upon stem analysis but the DBH 
growth rates benefitted from both stem analysis data and increment 
cores taken on the initial measurement of the permanent plots.

	 The percentage bias in the growth rates given by Wensel, 
Meerschaert, and Biging (1987) when tested against the remeasurement 
data set is given in Figure 1.  The apparent bias in these predicted 
growth rates vary with diameter growth rates underestimated by 38 to 
76 percent and height growth underestimated from 11 to 54 percent.  
These underestimates certainly justify the development of revised 
estimates of the growth estimation coefficients.  Thus this paper 
is devoted to the development of revised estimates of the growth 
coefficients.


Table 1.  Definition of species codes used.
	____________________________________________________ 
	Code       Definition
	____________________________________________________
	 PP	Ponderosa pine
		Pinus ponderosa  (Laws.)

	 SP	Sugar pine
		Pinus lambertiana  (Dougl.)

	 IC	Incense cedar
		Libocedrus decurrens  (Torr.)

	 DF	Douglas-fir
		Pseudotsuga menziesii  (Mirb.) Franco 

	 WF	White fir
		Abies concolor  (Gord. and Glend.) Lindl.

	 RF	Red fir
		Abies magnifica  (A. Murr.)

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Figure 1. Average underestimate (bias) in growth rates for DBH2 and 
          height using growth coefficients by    Wensel, Meerschaert, 
          and Biging (1987) and data from remeasured plots.