Pseudo-CFI for Industrial Forest Inventories

-Corporate inventory systems have historically had a greater spatial and temporal intensi ty than is common in the public sector . For many corporat ions, these inventory systems might be descr ibed as dynamic in that current es t imates rely on a small amount of recent data and a large amount of information resulting from the imputat ion of older data that have been subjected to various growth and mortal i ty models. Usually the “best available” models are used for this purpose, with little attention paid to any populat ion dynamics that may have occurred since development of the models. This paper gives the theory and an example application of a family of sample designs that possess cont inuous forest inventory (CFI) at t r ibutes . This family of Pseudo-CFI sample designs was devised to faci l i ta te the incorporat ion of a continuous monitoring and cal ibrat ion mechanism for the imputed data. I t is important to industr ia l forest enterprises to know what is and what will be on the ground (by a wide array of measures) at any given point in time. For this reason, corporate inventory systems have his tor ical ly had a greater spat ial and temporal intensi ty than is common in the public sector. For many corporations, these systems might be described as dynamic in that current est imates rely on a small amount of recent data and a large amount of imputed data values based on older data that have been subjected to a growth model. Usually the “best available” growth and yield models are used for this purpose, with l i t t le at tent ion paid to the appropriateness of the models for specific applications. Unfortunately, industrial forest populations are themselves quite dynamic and ever more frequently prove to be quite different from any of those upon which existing models were built. Furthermore, we can expect this trend to continue indefinitely. Therefore, i t would be prudent to incorporate a continuous monitoring and cal ibrat ion mechanism into the inventory system in order to provide the abi l i ty to adapt to changing condit ions and populat ions. This paper presents a family of sample designs, which l ie between periodic inventories and continuous forest inventories with respect to the variance and cost scales. An example application is also included. Because the designs are obtained by relaxing the requirements of continuous forest inventory, these designs might be dubbed Pseudo-CFI. Much work has been devoted to s tudying the continuum along which different methods of scientif ic inquiry could be posit ioned with respect to the level of control over responses (Basu 1980; Cochran 1965; Cochran and Rubin 1974; Rubin 1973a, 1973b, 1974, 1976a, 1976b, 1978, Mathematical Stat is t ician, USDA Forest Service, Forest Inventory and Analysis , Southern Research Stat ion, PO Box 2680, Asheville, NC 28802, USA. 1979, 1980, 1986; Wickramarante and Holford 1987; Wold 1956). The subject was briefly introduced into the forestry l i terature in a discussion of forest response studies by Green and Roesch (1993). A major premise of this paper is that there is a point at which observational forest inventory data can begin to overrule the results of controlled growth and yield experiments. Here, we show how one might exploit that premise in the design of a dynamic inventory system. Arguments for strict experimental control in growth and yield est imation and for the use of the less control led cont inuous forest inventory (CFI) approach both rely on a very basic truth about random variables. That truth is that the variance of the difference between two random variables (A and B) is: Var(A B) = h-(A)+ Var(B) 2 Cov(A, B) If we let A equal time 2 volume and B equal time 1 volume, we see that A-B equals volume growth. Both controlled experiments and CFI plots attempt to maximize the third term on the r ight-hand side (rhs) of the equat ion, 2Cov ( A, B) , by measuring time 1 and time 2 volumes on the same population elements. This results in a decrease, of course, on the left-hand side (0~s) of the equat ion. Control led experiments go one step further by also reducing the first two terms on the rhs. This is accomplished by control l ing the populat ion elements enter ing the experiment to a particular subset of the population of interest. That is, the point of an experiment is to deduce the effect of an action, and in order to do that one tr ies to el iminate potent ial noise factors . A potential weakness of the experimental design approach is the assumption that an effect measured on a very control led subset of the populat ion is going to be the same as the effect on the entire population. Unfortunately,