Three methods of deriving advanced dynamic site equations demonstrated on inland Douglas-fir site curves

With two examples of five-parameter, fixed-base-age site index and height growth equations, I demonstrate three methods for deriving dynamic equations that are base-age invariant and use only three parameters. These are initial condition difference equations that compute appropriate heights at all base ages and provide compatible height and site index values from one common equation. Despite having fewer parameters, they can model a broader selection of curves than the original equations. The new equations are applicable for all situations in which the original equations could be applied. Methods demonstrated in this paper can enhance the development of all recursive and otherwise implicitly defined equations used for modeling of height, diameter, basal area, volume, number of trees per hectare, and investment yields.