Detecting instabilities in tree-ring proxy calibration

Abstract

Abstract. Evidence has been found for reduced sensitivity of tree growth to temperature in a number of forests at high northern latitudes and alpine locations. Furthermore, at some of these sites, emergent subpopulations of trees show negative growth trends with rising temperature. These findings are typically referred to as the "Divergence Problem" (DP). Given the high relevance of paleoclimatic reconstructions for policy-related studies, it is important for dendrochronologists to address this issue of potential model uncertainties associated with the DP. Here we address this issue by proposing a calibration technique, termed "stochastic response function" (SRF), which allows the presence or absence of any instabilities in growth response of trees (or any other climate proxy) to their calibration target to be visualized and detected. Since this framework estimates confidence limits and subsequently provides statistical significance tests, the approach is also very well suited for proxy screening prior to the generation of a climate-reconstruction network.Two examples of tree growth/climate relationships are provided, one from the North American Arctic treeline and the other from the upper treeline in the European Alps. Instabilities were found to be present where stabilities were reported in the literature, and vice versa, stabilities were found where instabilities were reported. We advise to apply SRFs in future proxy-screening schemes, next to the use of correlations and RE/CE statistics. It will improve the strength of reconstruction hindcasts.

Higher CO2 Concentrations and Lower Acidic Deposition Have Not Changed Drought Response in Tree Growth But Do Influence iWUE in Hardwood Trees in the Midwestern United States

“…Therefore, to evaluate the robustness of a potential change in the response of climate variability, we also used a state‐space model with time varying parameter regression (Durbin and Koopman, 2001) and the Kalman filter (Kalman , ) to examine the time dependence of the relationship between tree growth and JJA P‐PET using the R package “dlm” (Petris, 2010). The time varying method with the Kalman filter has been successfully used to examine the temporal variability of climate‐growth relationships of tree rings (Bishop et al, ; Cook & Johnson, ; Visser et al, ). The Kalman filter relaxes the least squares assumption that assumes that growth rate is consistently determined by the most limiting factor, allowing the detection of changes in the responses of radial growth to a particular climate variable.…”

Nonannual tree rings in a climate‐sensitive Prioria copaifera chronology in the Atrato River, Colombia

“…Both trend (μ t ) and response weights (α) were estimated using the discrete Kalman filter (Harvey & Shephard, 1993;Visser & Molenaar, 1988); this filter is ideal in the sense that it yields the minimum mean square error estimates (normally distributed noise processes) for μ t and α t along with maximum-likelihood estimates for unknown noise variances (Visser et al, 2010). The explained variance used here was computed as:…”

Inferences on weather extremes and weather-related disasters: a review of statistical methods

“…Trends from the class of structural time series models (STMs), as shown here in Figs. 1 and 4, give a generalization of the OLS linear trend: they also give full statistical uncertainty information (Visser, 2004;Visser et al, 2010).…”