In a study of height growth patterns of quaking aspen (Populus tremuloides Michx.) in Minnesota Wisconsin and Michigan, we represented the height-age pattern using a second order ordinary differential equation with environmentally governed parameters. Solving a second order differential equation that has been converted to a system of two first order equations requires knowledge of, or information on, initial conditions for both state variables, height and height growth. We used the natural boundary condition, h(t = 0) = 0. Initial conditions for the second state variable height growth were estimated when fitting the equations to observations. This paper reports our research to predict the initial height growth from stem analysis data, and to assess the sensitivity of predicted height to differences in initial condition estimates. We found initial height growth to be the single most important 'parameter' to be estimated in our model.
- Height growth
- Lake States
- Populus tremuloides
- Second order differential equations