Generalized Algebraic Difference Approach: Theory Based Derivation of Dynamic Site Equations with Polymorphism and Variable Asymptotes

By Chris J. Cieszewski, R. Bailey. Forestry sciences, 2000

218 citations recorded by the source corpus.

Biologically realistic site models require the ability to concurrently express variable asymptotes and polymorphism in curve shapes. Moreover, it is only logical and rational to require that these models be invariant to changes in the index or base age. This manuscript explains the Generalized Algebraic Difference Approach that can be used effectively to derive truly base-age invariant difference equations capable of describing concurrent polymorphism and variable asymptotes. This new generic methodology for derivation of even the most complex dynamic equations is mathematically sound. The equations derived with it can be extremely flexible and may generate intricate patterns of concurrent polymorphism and variable asymptotes. This methodology is relevant to all situations in which the dependent variable is a function of an unobservable variable, and the models can be implicitly defined by their initial conditions. It is equally useful for derivation of new equations and for improvement of existing base-age specific equations. For. Sci. 46(1):116-126.

Subfields: Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ba0c4a46820493e6eff59e7f317993298d4f0243

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Numerical Analysis

Citations in the corpus

Site index model for Pinus sylvestris in north-east Spain (2004, methodology): “412 The generic equation derived from the Schumacher 413 function using the GADA approach (F11) was poly414 morphic and had different asymptotes, two desirable 415 characteristics when constructing site index curves 416 (Cieszewski and Bailey, 2000).”
Site quality curves for birch stands in north-western Spain (2006, methodology): “Cieszewski and Bailey (2000) introduced a generalization of the ADA, the Generalized Algebraic Difference Approach (GADA), which can be used to derive the same models derived by the ADA.”
Modelling dominant height growth and site index curves for rebollo oak (Quercus pyrenaica Willd.) (2006, methodology): “GADA is more parsimonious than most traditional approaches (fixedbase-age equations), it can derive more complex equations than ADA and it assures a high degree of robustness in applications [17].”
Geographic variation and parameter assessment in generalized algebraic difference site index modelling (2007, methodology): “Cieszewski and Bailey (2000) generalized the ADA formulation by means of making ‘a priori’ assumptions about the relationship of some growth function parameters with a theoretical growth intensity factor (GIF), which is considered to be a variable or a function of variables representing site (climat”
Site-specific height growth models for six common tree species in Denmark (2009, methodology): “Keywords: Abies alba, base-age invariant, Fagus sylvatica, GADA, Picea abies, Picea sitchensis, Pseudotsuga menziesii, Quercus petraea, Quercus robur, site index.”
Forest Growth and Yield Modeling (2011, methodology): “The generalized algebraic difference approach (GADA) is a method for deriving and fitting dynamic growth equations (Cieszewski and Bailey, 2000), which extends the original approach of Bailey and Clutter (1974).”
Development of a basal area growth system for maritime pine in northwestern Spain using the generalized algebraic difference approach (2006, methodology): “Since X cannot be reliably measured or even functionally defined, the final step of GADA involves the substitution of X by equivalent initial conditions t0 and Y0 (Y = f(t, t0, Y0)) so that the model can be implicitly defined and practically useful (Cieszewski and Bailey 2000; Cieszewski 2002).”
Developing a Well-Behaved Dynamic Site Equation Using a Modified Hossfeld IV Function Y3 = (axm)/(c + x m–1), a Simplified Mixed-Model and Scant Subalpine Fir Data (2003, methodology): “The later are more desirable for derivation of site models (Cieszewski and Bailey 2000, Cieszewski and Bella 1989) because they allow for more flexible solutions to various combinations of varying parameters.”