Using Maximum Autocorrelation Factors (MAFS) to Identify Common Trends in Proxy Data: A Tree-Ring Case Study

Proxy records of climate and environmental variability are most reliable when they are based on more than one sample per site. Therefore, prior to any type of process-modeling of the proxies themselves, it is often necessary to combine multiple samples into a single chronology. In doing so, it may be useful to develop numerical techniques that clearly identify trends that are in common among the individual samples. To this end, data are commonly analyzed using methods closely related to principal components analysis, although such methods are not specifically optimized for time trend detection. Less common alternative analyses use variants of MAF, maximal autocorrelation factor analysis. We describe MAF optimality properties that are specific to time trend extraction for proxy data, and illustrate MAFs trend extraction possibilities in low signal- to-noise situations by applying them to ring-width measurements taken on a total of 92 western juniper (Juniperus occidentalis Hook.) samples collected at two sites within the Walker River basin, on the eastern slopes of the Sierra Nevada near the California-Nevada boundary. Although the tree-ring dataset spans 2300 years, from 300 BC to AD 2001, the analysis had to be conducted on periods of overlap between individual samples. The resulting temporal trends are presented, and their interpretation in terms of biological and climatic processes is discussed.