A Closer Look at Regional Curve Standardization of Tree-Ring Records: Justification of the Need, a Warning of Some Pitfalls, and Suggested Improvements in Its Application

Abstract

Some background describing the rationale and early development of regional curve standardization (RCS) is provided. It is shown how, in the application of RCS, low-frequency variance is preserved in the mean values of individual series of tree indices, while medium-frequency variance is also preserved in the slopes. Various problems in the use of the RCS approach are highlighted. The first problem arises because RCS detrending removes the average slope (derived from the data for all trees) from each individual tree measurement series. This operation results in a pervasive ‘trend-in-signal’ bias, which occurs when the underlying growth-forcing signal has variance on timescales that approach or exceed the length of the chronology. Even in a long chronology (i.e., including subfossil data), this effect will bias the start and end of the RCS chronology. Two particular problems associated with the use of RCS on contemporaneously growing trees, which might represent a typical (i.e., modern) sample, are also discussed. The first is the biasing of the RCS curve by the residual climate signal in age-aligned samples and the undesirable subsequent removal of this signal variance in RCS application. The second is the ‘differing-contemporaneous-growth-rate’ bias that effectively imparts a spurious trend over the span of a modern chronology. The first of these two can be mitigated by the application of ‘signal-free’ RCS. The second problem is more insidious and can only be overcome by the use of multiple sub-RCS curves, with a concomitant potential loss of some longer-timescale climate variance. Examples of potential biasing problems in the application of RCS are illustrated by reference to several published studies. Further implications and suggested directions for necessary further development of the RCS concept are discussed.

Appendix: Signal-Free Standardization

In this review, we make several references to the ‘signal-free’ method in tree-ring standardization (see Sections 5.4.1, 5.5, 5.6.1, and 5.7). A more detailed discussion of the topic (in the context of ‘data-adaptive’ standardization involving ‘curve fitting’ to individual measured series) can be found in Melvin and Briffa (2008). However, for the convenience of the reader, a brief description of the rationale and application of the signal-free approach is provided here.

1.1 Background and Rationale

The signal-free concept stems from the observation that individual tree-ring measurement series represent a mixture of potential growth influences, among which are included first, that of climate variability through time and second, that of changing allocation processes and tree geometry that both affect the size of annual stem increments. Standardization has always aimed to remove or reduce the allocation bias; e.g., the signal of reducing ring width with age, so that the remaining variability in ring width indices over time provides a clearer representation of the influence of climate variability. Developing standardization curves from measurement series that contain the climate signal, where the standardization curve may track the climate signal, at least to some extent, will lead to the removal of some climate-related variance and so bias the resulting chronology. This bias is well known with respect to the removal of variance representing timescales longer than the typical life span of the sample trees (Cook et al. 1995). However, it can also arise where a common, externally forced growth signal influences the more localized fit of a standardization curve, resulting in the partial, or even complete, loss of a relatively short-term climate signal (in the case of more flexible standardization curves) and the distortion of medium-term climate trends in adjacent periods (where less flexible, but still ‘fitted,’ standardization functions are employed).

The rationale behind ‘signal-free’ standardization is that it should be possible to produce an improved (i.e., locally unbiased) chronology if the individual measurement series could be detrended without allowing the fitting of standardization curves to be affected by the presence of climatically forced variability. One suggestion for achieving this condition is to remove the common variability (chronology signal) from all measurement series to yield less-biased detrending curves.

1.2 Implementing Signal-Free Standardization

Melvin and Briffa (2008) describe one such approach, applied in the context of ‘curve-fitting’ standardization using options offered in the ARSTAN program (Cook 1985). They demonstrate how a combination of the ‘segment length curse’ and localized distortion of standardization curves can produce a biased ring-width chronology, apparent as a failure by the standardized chronology to express recent climatic trends. Details of their implementation of this signal-free approach, in the context of curve-fitting standardization, are given in Melvin and Briffa (2008).

When this approach is applied in the case of regional curve standardization (RCS), a first chronology is produced by division of the tree-ring measurements by the appropriate RCS curve values. Each original measurement value is then divided by the appropriate chronology value for that year to produce a first set of ‘signal-free’ measurements. The standardization is then repeated on these signal-free data, and a new chronology is produced from the new signal-free indices. The process is repeated until the point where the signal-free data make up a chronology that has virtually zero variance. In practice, the magnitude of residual bias (i.e., as represented by the variance of the signal-free chronology) after each iteration is 20% of its initial value. A zero-variance signal-free chronology is considered here to be one where all values are within the range 1.0 ± 0.002. This condition is achieved generally within four or five signal-free iterations. At this point, the final RCS curve is unaffected by any external growth-forcing signal and should, therefore, yield a less-biased chronology.