Tree growth inference and prediction from diameter censuses and ring widths

Estimation of tree growth is based on sparse observations of tree diameter, ring widths, or increments read from a dendrometer. From annual measurements on a few trees (e.g., increment cores) or sporadic measurements from many trees (e.g., diameter censuses on mapped plots), relationships with resources, tree size, and climate are extrapolated to whole stands. There has been no way to formally integrate different types of data and problems of estimation that result from (1) multiple sources of observation error, which frequently result in impossible estimates of negative growth, (2) the fact that data are typically sparse (a few trees or a few years), whereas inference is needed broadly (many trees over many years), (3) the fact that some unknown fraction of the variance is shared across the population, and (4) the fact that growth rates of trees within competing stands are not independent. We develop a hierarchical Bayes state space model for tree growth that addresses all of these challenges, allowing for formal inference that is consistent with the available data and the assumption that growth is nonnegative. Prediction follows directly, incorporating the full uncertainty from inference with scenarios for filling the gaps for past growth rates and for future conditions affecting growth. An example involving multiple species and multiple stands with tree-ring data and up to 14 years of tree census data illustrates how different levels of information at the tree and stand level contribute to inference and prediction.