ABCDE: A Bidirectional Coupling of Differential Equations—Data-Trends Derivation of Dynamic Site Equations from Growth Rates and Site Gradients
Ključne riječi:
GADA, UTADA, ABCDE method, VASI, BAI, path invariance, dynamic equations, self-referencing models, site models, site index, growth rate, site gradient, polymorphism, variable asymptotesSažetak
I introduce here “A Bidirectional Coupling of Differential Equations” (ABCDE), yet another method for deriving flexible base-age-invariant, variable-age site index equations with polymorphism and variable asymptotes. My earlier approaches, including GADA and UTADA, concentrate on theory for formulating and structuring equations using theories of algebraic constructs. The ABCDE approach focuses instead on modeling the data trends of growth rates and site gradients that the final model should comprise. Its theories concern the component trends in two directions of the data structure, rather than presumed forms of asymptotes or growth rates. Simple height trends over age at fixed sites and over site quality at fixed ages supply two partial definitions: the longitudinal growth rate P = Hₜ and the cross-sectional site gradient Q = Hₛ. Coupling them through the common integration of dH = P dt + Q ds defines one surface H(t,s) exactly when Pₛ = Qₜ on a simply connected domain. Compatibility also transfers information between directions: the growth rate and the index-age normalization (base-age conditioning) determine the site gradient, and the site gradient with one reference age profile determines the growth rate. Unique site inversion then gives a self-referencing dynamic equation with exact base-age invariance and path invariance as in the other methods. As with the foundational GADA and UTADA papers, this note presents general principles; empirical applications and method comparisons on specific data sets will follow separately in the future.
Reference
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