Growth Curve Modeling: Theory and Applications

5

DYNAMIC SITE EQUATIONS OBTAINED FROM GROWTH MODELS

5.1 INTRODUCTION

This chapter focuses primarily on the derivation of a variety of dynamic site equations, which constitute a critical component of forest growth and yield models, from the growth model-based equations introduced in Chapter 3.¹ In particular, we shall examine selected categories of site-quality models based on stand-height data for evaluating site productivity.

Three broad categories of site-quality models will be recognized:

1. Base-age-specific (BAS) models
2. Algebraic difference approach (ADA) models
3. Generalized algebraic difference approach (GADA) models

5.2 BASE-AGE-SPECIFIC (BAS) MODELS

Traditional height-based methods for assessing site quality employ site-index curves (i.e., site-index-based height vs. age curves), where each such curve defines an expected height–age relationship referenced by a specified base age. In fact, when estimating the parameters of a size–age equation, it has typically been assumed that site index S equals the observed height value at the base age t_b or S = H(t_b) and thus serves as a data-based measure of site quality. This assumption clearly results in so-called BAS parameter estimates.

Base-age-specific site models are essentially static models—they select a fixed base age and then identify the site curves by site-index class at this age. To see this, let us begin with a model of the form

where H is average dominant height, t is stand age, θ is a vector of parameters, and ε is ...