Hierarchical regression models for dendroclimatic standardization and climate reconstruction

Abstract

Tree-ring based paleoclimate reconstructions entail several sequential estimation or processing steps. Consequently, it can be difficult to isolate climatic from non-climatic variability in the raw ring width measurements, estimate the uncertainty associated with a reconstruction, and directly infer how specific techniques used to sequentially fit growth curves or to reconstruct climate influence the final estimates. This paper explores the use of hierarchical regression models to address these problems. The proposed models simultaneously model the entire reconstruction process in a way that is consistent with the existing step-by-step estimation framework, but allow for uncertainty estimation and propagation across steps, which can help determine how best to improve a candidate model. The utility of hierarchical models is tested for an example, the reconstruction of summertime temperatures in northern Sweden in a cross-validated framework relative to 1) a sequential process of growth curve fitting followed by chronology development, 3) an iterative, "signal-free" approach, and 2) a signal-free regional curve standardization (RCS-SF). Further, an exploration of different structures within the unifying hierarchical framework is provided to illustrate how one could easily test a variety of choices of model design. We focus on a subset of choices relevant to recent dendroclimatic studies using hierarchical methods and related to 1) data transformation, 2) the benefits of biological detrending and climate reconstruction in a single step 3) partial pooling of the age model across trees, 4) the homogeneity of variance across tree-ring residuals, 5) the structural form of the age model, and 6) the inclusion of autoregressive processes for the tree-ring residuals. The work described here represents part of a series of ongoing explorations of potential advances over current dendroclimatic reconstruction approaches 3 and commonly implemented ways in which they have and are specifically implemented.The results show that hierarchical modeling appears to offer improved climate reconstructions over the standardization techniques explored in this exercise, substantially so for the non-RCS sequential and iterative methods.

Six Centuries of Upper Indus Basin Streamflow Variability and Its Climatic Drivers

“…We find that BR typically, but not always, produces slightly wider uncertainty intervals. Commonly used statistical approaches for tree ring reconstructions of past streamflow and climate include PCR (e.g., Allen et al, ; Anchukaitis et al, ; Cook et al, , , ; Palmer et al, ; Stahle et al, ), a Bayesian framework (Devineni et al, ; Luterbacher et al, ; Steinschneider et al, ; Tingley & Huybers, ), along with other statistical methods (e.g., Bracken et al, ; Gangopadhyay et al, ; Woodhouse et al, ). Our results suggest that for a one predictand variable case at the Partab Bridge gauge, both PCR and BR methods produce comparable reconstructions in terms of their estimates, uncertainties, and reconstruction skill statistics.…”

Application of dendroclimatology in evaluation of climatic changes

“…Due to the growth-limiting effects of low precipitation and high temperatures, dendroclimatic (as one of the branches of dendrochronology) studies would be successful in part (Conkey 1979). Dendroclimatology is concerned with constructing records of past climates and climatic events by the analysis of tree growth characteristics and especially annual rings (Steinschneider et al 2017). Reviews show that tree-ring data have been successfully applied to reconstruct hydrologic variables such as river dis-charge (Woodhouse, Meko 2002;Liu et al 2010).…”

Hierarchical modeling of space-time dendroclimatic fields: Comparing a frequentist and a Bayesian approach

“…"segment length curse" (Cook et al 1995), the joint modeling approach is able to propagate the parameter estimation uncertainty from the standardization through the reconstruction. Using the same set of data (i.e., the Torneträsk ring-width data) used by Schofield et al (2016), first Steinschneider et al (2017) and then Schofield and Barker (2017) investigated the predictive performance of several modeling choices, including data transformation, inclusion of temporal autocorrelation, and homogenous or heterogeneous variance. However, none of these recent modeling efforts took explicitly into account spatial (auto)correlation.…”