Continuous Forest Inventory Using a Linear Filter

Abstract

Abstract Timber management may be conceptualized as a stochastic optimal control problem because of uncertainty about forest dynamics and the sequential nature of the decisionmaking process. Given this point of view, it follows that decisions will be based on the conditional distributions of unknown model parameters where the distributions are derived recursively. By making various approximations, the management actions become a function of the conditional mean of timber inventories. This conditional mean and the conditional covariance of the inventories are generated by a Kalman filter. The conditional mean can alternatively be interpreted as an estimate of the unknown timber inventories. This estimate thus has the virtue of being optimal with respect to the overall timber management problem. The partial replacement estimator of Ware and Cunia is shown to be a special case of the Kalman estimator. The variance of the Ware and Cunia estimator is always greater than or equal to the variance of the corresponding Kalman estimator. Numerical results show that the variance of the Kalman estimator is almost always less than the variance of the Ware and Cunia estimator. In some cases when using the Kalman filter simple random sampling is shown to yield estimates with lower variance than partial replacement sampling. Forest Sci. 25:675-689.