Peak detection in sediment–charcoal records: impacts of alternative data analysis methods on fire-history interpretations

Over the past several decades, high-resolution sediment–charcoal records have been increasingly used to reconstruct local fire history. Data analysis methods usually involve a decomposition that detrends a charcoal series and then applies a threshold value to isolate individual peaks, which are interpreted as fire episodes. Despite the proliferation of these studies, methods have evolved largely in the absence of a thorough statistical framework. We describe eight alternative decompositionmodels (four detrendingmethods usedwith two threshold-determinationmethods) and evaluate their sensitivity to a set of known parameters integrated into simulated charcoal records. Results indicate that the combination of a globally defined threshold with specific detrending methods can produce strongly biased results, depending on whether or not variance in a charcoal record is stationary through time. These biases are largely eliminated by using a locally defined threshold, which adapts to changes in variability throughout a charcoal record. Applying the alternative decomposition methods on three previously published charcoal records largely supports our conclusions from simulated records. We also present a minimum-count test for empirical records, which reduces the likelihood of false positives when charcoal counts are low. We conclude by discussing how to evaluate when peak detection methods are warranted with a given sediment–charcoal record. Additional keywords: bias, paleoecology, sensitivity. Introduction High-resolution charcoal records are an increasingly common source of fire-history information, particularly in ecosystems where tree-ring records are short relative to average fire-return intervals (Gavin et al. 2007). Over the past several decades, numerous studies have used peaks in charcoal accumulation in sediment records to estimate the timing of ‘fire episodes’, one or more fires within the sampling resolution of the sediment record (Whitlock and Larsen 2001). Identifying fire episodes from charcoal records is most promising when fires: (1) are large; (2) burn with high severity; and (3) recur with average intervals at least five times the sampling resolution of the sediment record (Clark 1988b; Whitlock and Larsen 2001; Higuera et al. 2005, 2007). Sediment–charcoal records are thus particularly valuable for studying stand-replacing fire regimes in boreal and subalpine forests, where all three of these conditions are typically met. Interpreting fire episodes from sediment–charcoal records would be straightforward if they were characterised by low levels of charcoal punctuated by unambiguous peaks. In reality, however, charcoal records are complex and non-stationary, i.e. their mean and variance change over time (Clark et al. 1996; Clark and Patterson 1997; Long et al. 1998). Empirical and theoretical studies (e.g. Marlon et al. 2006; Higuera et al. 2007) suggest that non-stationarity in charcoal records can arise from at least two sets of processes: (1) changes in the fire regime, including the rate of burning, the intensity of fires, the type of vegetation burned, and thus charcoal production per unit time; or (2) changes in the efficiency of charcoal delivery to the lake centre (taphonomy) due to changing rates of slope wash or within-lake redeposition. The latter process, known as sediment focussing, can greatly affect the sediment accumulation rate as a lake fills in over time (Davis et al. 1984; Giesecke and Fontana 2008) and may produce long-term trends in charcoal records unrelated to changes in the fire regime. Recognising the importance of these processes, paleoecologists have applied a range of statistical methods to charcoal data in order to isolate the signal related to ‘local’ fire occurrence (e.g. within 0.5–1.0 km; Gavin et al. 2003; Lynch et al. 2004a; Higuera et al. 2007) and reconstruct fire history. Despite the proliferation of statistical methods for peak identification, seemingly no study has CSIRO PUBLISHING International Journal of Wildland Fire 2010, 19, 996–1014 www.publish.csiro.au/journals/ijwf IAWF 2010 10.1071/WF09134 1049-8001/10/080996 discussed the assumptions underlying alternative methods and their impacts on fire-history interpretations. Here, we address several key issues related to peak identification in high-resolution, macroscopic charcoal records by using simulated and empirical charcoal records. We start by discussing some important statistical properties of macroscopic charcoal records and then describe themotivation for statistical treatments. We briefly review how different methods have been applied, and then introduce a typology of methods, including their respective assumptions and justifications. Second, we illustrate and quantify the biases that these techniques can introduce to fire-history interpretations by applying them to simulated charcoal records. Third, we apply the same methods to three previously published charcoal records to demonstrate potential biases in empirical records, and we introduce a technique to minimise some of these biases. Finally, we conclude with recommendations of specific methodologies and a discussion of how analysts can evaluate the suitability of records for peak identification rather than other qualitative or quantitative analyses. Temporal variability in charcoal time series Charcoal time series can be generally characterised as ‘noisy’, and they contain many forms of non-stationarity, including changing short-term variability superimposed on a slowly varying mean (Long et al. 1998; Higuera et al. 2007). Changes in variability (i.e. heteroscedasticity) have implications for the particular goal of data analysis. When the goal is to quantify changes in total charcoal input, as an index of biomass burning for example, heteroscedasticity violates the assumptions of parametric statistics useful in this context, e.g. analysis of variance and regression. In particular, in analysis of variance (or in the t-test of the difference of means in the case of two periods), heteroscedasticity increases the probability of Type I error, falsely inferring significant differences between periods (Underwood 1997). Similarly, in regression analysis, fitting a trend line to charcoal data with changing variability over time can increase the variability of the slope coefficient. Changes in variability (besides being interesting in their own right) can thus lead to false conclusions about the significance of longterm trends or differences between different parts of a record. In practice, heteroscedasticity is usually dealt with by applying a ‘variance-stabilising transformation’ (Emerson 1983) that acts to homogenise variance across a record. As will be illustrated below, when the goal of charcoal analysis is peak identification, transformation can lead to the exaggeration of some peaks and suppression of others. Consequently, the specific approach taken (whether to transform or not) should depend on the overall focus of an analysis. In this paper, we focus on the goal of detecting local fires through peak detection. Analytical methods for inferring local fire occurrence Following the pioneering work of Clark (1988b, 1990) in which fire events surrounding small lakes were identified from charcoal in thin-sections of laminated sediments, similar approaches were developed for quantifying macroscopic charcoal abundance and subsequently adopted by a large number of research groups (Table 1; see also Whitlock and Larsen 2001). Most techniques quantify charcoal as either the total number of pieces or surface area (mm) of charcoal in a particular size class, within volumetric subsamples taken contiguously through sediment cores (typically at 0.5to 1.0-cm resolution, corresponding to ,10–25-year resolution for most lakes). The resulting concentration of charcoal (pieces cm , ormm 2 cm ) in each level is multiplied by the estimated sediment accumulation rate (cmyear ) to obtain the charcoal accumulation rate (CHAR, pieces cm 2 year 1 or mm 2 cm 2 year ). Sediment accumulation rates, and the age of each sample, are estimated by an age–depth model based on radiometric dates, tephra layers, and any additional sources of age information. The use of accumulation rates can potentially correct for changing sediment accumulation rates that would dilute or concentrate charcoal in a given volume of sediment, and as mentioned above, may also be affected by sediment focussing processes. Usually, the CHAR series is interpolated to a constant temporal resolution to account for unequal sampling intervals resulting from variable sediment accumulation rates. This step is necessary to develop threshold statistics that are not biased to a particular portion of a record, and to standardise withinand between-site comparisons. Hereafter, we refer to the interpolated CHAR series as C. The analytical choices and sources of error in the development of a charcoal record are briefly summarised in Table 2 and discussed in detail by Whitlock and Larsen (2001). At this point, most C series can be characterised as irregular time series with discrete peaks superimposed on a slowly varying mean. Although the size of any individual peak reflects the size, location, and charcoal production of individual fires, the average size of peaks may change through time, contributing to a slowly changing variance. This nonstationaritymay arise, as discussed above, owing to variations in charcoal production per unit time or variable taphonomic and sedimentation processes. Without knowledge of whether nonstationarity is due to changes in taphonomy and sedimentation or to real changes in fire history, it is reasonable to stabilise the variance of peak heights so as to not ‘pass over’ periods of low charcoal. This motivates the manipulation of C to produce a stationary series in which all local fires would theoretically result in a similar range of peak sizes. Doing so would allow for the application of a single global threshold value to the final series to separate fire-related from non-fire-related peaks. In practice, determining the size of peaks that represents local fires involves a three-step ‘decomposition’ of theC series (Clark et al. 1996; Long et al. 1998; Fig. 1). First, the slowly varying mean, or ‘background’ component, Cback, is modelled through a curve-fitting algorithm, e.g. a locally weighted regression that is robust to outliers (e.g. Cleveland 1979). The window size for this smoothing varies between studies but is typically between 100 and 1000 years. Background estimation may be preceded by transformingC (e.g. logarithmically). Second, thebackground trend is removed from the series by subtraction (C Cback) or We refer to macroscopic charcoal records as those quantifying charcoal not passing through a sieve of 125 mm or larger. When sampling intervals are not standardised within a record or between two records, then biases may be introduced when applying criteria uniformly. Interpolation helps minimise, but not remove, this bias, as noted in the last section of this paper. Fire history from sediment charcoal records Int. J. Wildland Fire 997