The components of change for an annual forest inventory design
The sample design of the USDA Forest Service's Forest Inventory and Analysis Program (FIA) with respect to a three-dimensional population (forest area X time) of tree attributes is formally defined and evaluated. The definitions for both the traditional components of growth, as presented by Meyer (1953, Forest Mensuration), and a discrete analog to the time invariant redefinition of the components of change given by Eriksson (1995, Forest Sci. 41(4):796-822), are compared and contrasted. Special problems in the application of the traditional definitions due to the continuous and overlapping temporal intervals featured in the sample design are explored. This exploration supports a contention that the traditional definitions are at a theoretical disadvantage because they are not based purely on the population(s) of interest, while the redefinitions dubbed the components of change by Eriksson (1995) were based solely on population attributes. The temporally discrete analog to the Eriksson definitions are used in this article to define the three-dimensional populations in terms of a set of mutually exclusive component matrices that can be summed to represent the entire population, independently of the sample design.