A general model of intra-annual tree growth using dendrometer bands.

Tree growth is an important indicator of forest health, productivity, and demography. Knowing precisely how trees' grow within a year, instead of across years, can lead to a finer understanding of the mechanisms that drive these larger patterns. The growing use of dendrometer bands in research forests has only rarely been used to measure growth at resolutions finer than yearly, but intra-annual growth patterns can be observed from dendrometer bands using precision digital calipers and weekly measurements. Here we present a workflow to help forest ecologists fit growth models to intra-annual measurements using standard optimization functions provided by the R platform. We explain our protocol, test uncertainty in parameter estimates with respect to sample sizes, extend the optimization protocol to estimate robust lower and upper annual diameter bounds, and discuss potential challenges to optimal fits. We offer R code to implement this workflow. We found that starting values and initial optimization routines are critical to fitting the best functional forms. After using a bounded, broad search method, a more focused search algorithm obtained consistent results. To estimate starting and ending annual diameters, we combined the growth function with early and late estimates of beginning and ending growth. Once we fit the functions, we present extension algorithms that estimate periodic reductions in growth, total growth, and present a method of controlling for the shifting allocation to girth during the growth season. We demonstrate that with these extensions, an analysis of growth response to weather (e.g., the water available to a tree) can be derived in a way that is comparable across trees, years, and sites. Thus, this approach, when applied across broader data sets, offers a pathway to build inference about the effects of seasonal weather on growth, size- and light-dependent patterns of growth, species-specific patterns, and phenology.