Abstract
Growth and yield models are needed for practical use within the framework of a forestry planning system. This is easier said than done, considering that it is necessary to project forest development for a broad spectrum of site and treatment conditions, and for different levels of detail. Variations in the level of detail of the available information requires models of varying levels of resolution.
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Example: 50% of 1hc trees presently residing in diameter class i of width 4cm are assumed to move to class i+1 in a given time step, if Δdi=2cm.
The method is sometimes complemented using a stochastic component to overcome the problem (Sloboda, 1984; Gaffrey, 1996).
The variables crown radius, crown surface area and crown radius at reference height may be calculated as follows
Relative to the joint density fx,y(x,y), the densities of X and Y, fx(x) and fy(y), are called the marginal densities. From a practical perspective, the marginal distributions describe the individual behavior of the measurements X and Y, but they often lack, even when taken together, information regarding the joint behavior of the measurements. Although the marginal densities can be recovered from the joint density, in general, the joint density can not be constructed from a knowledge of the marginal densities. In the discrete case, the marginal density fx(x) is found by holding x fixed and summing over y, whereas in the continuous case, it is found by holding x fixed and integrating over y. An analogous comment applies to finding fy(y) (see Dougherty, 1990, p. 208-9 & 215).
The extraction of information about one random variable, when given information about the behavior of another, leads to the problem of conditioning. If X and Y are discrete and posess the joint density F(x, y), then conditional probabilities regarding Y take the form of conditional probabilities concerning the relevant events. The probability that Y = y, given that X = x, is Intuitively, the observation X = x is recorded, and one is left with probabilistic knowledge concerning the random variable Y. Since Y is discrete, only the conditional probabilities of its possible outcomes need to be specified. In the case of jointly distributed continuous random variables, as long as, f(x, y)/fx(x) is still defined. This expression is taken as the general definition of the conditional density. The random variable associated with the conditional density is known as the conditional random variable of Y given x, and is denoted by Y x (see Dougherty, 1990, p. 249).
Vectors of form quotients are known as taper series or Ausbauchungsreihen (Grundner u. Schwappach, 1942; Schober, 1952; Gadow et al., 1995).
See for example, Demaerschalk (1973); Clutter (1980); Reed u. Green (1984); Brink u. Gadow (1986); Kozak (1988); LeMay et al. (1993); Nagashima u. Kawata (1994).
Named after C. Brink, who had a major share in developing the model (Brink and Gadow, 1986).
See Chapters 3 and 6 with more detail about this test.
An equivalent equation was used by Nagumo et al. (1988) to compute ÎĽr from the other variables, but this is only feasible when ÎĽt is already known.
For details of the derivation, refer to Murray and Gadow (1991).
However, Kahle (1995) found a great degree of consistency displayed by the same forester who was asked to simulate a thinning in the same stand several times in monthly intervals.
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© 1999 Springer Science+Business Media Dordrecht
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Von Gadow, K., Hui, G. (1999). Size-class Models. In: Modelling Forest Development. Forestry Sciences, vol 57. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4816-0_4
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DOI: https://doi.org/10.1007/978-94-011-4816-0_4
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