Developing a well-behaved dynamic site equation using a modified Hossfeld IV function y3 = (axm)/(c + xm-1), a simplified mixed-model and scant subalpine fir data

TLDR: In this paper, the authors developed a dynamic height growth model by using a simplified form of mixed effects modeling and subalpine fir (Abies lasiocarpa [Hook.] Nutt.) stem analysis data.

Abstract: I developed a dynamic height growth model by using a simplified form of mixed effects modeling and subalpine fir (Abies lasiocarpa [Hook.] Nutt.) stem analysis data. The new dynamic equation uses directly heights at any age to predict consistent heights (e.g., y 2 = f(t 2 ,t 1 ,y 1 ) ⇔ y 1 = f(t 1 ,t 2 ,y 2 )) and f(t 3 ,t 1 ,y 1 ) = f(t 3 ,t 2 ,f(t 2 ,t 1 ,y 1 ))), and therefore constitutes compatible site indexand height models in one common equation. The parametersforthe model were estimated by analysis of fixed and random effects with corrections for first- and second-order serial autocorrelation. The correction for second-order autocorrelation was necessary to assure the model's proper representation of the data and to remove a seeming cross-sectional autocorrelation across different sites/series. Estimating the errors in site indices as random effects eliminated the effects of stochastic predictive variables. The proposed model has outperformed all other base-age specific and base-age invariant models in both the fit to the data and in its behavior during extrapolations. It also outperforms the model (developed on amabilis fir data) that is currently, operationally used for subalpine fir. The new model's advantages are parsimony, mathematical tractability, base-age invariance, and greater consistency in curvatures of the generated height-age trajectories. FOR. Sci. 49(4):539-554.