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Background calculation

The background may be estimated using one of several smoothing functions. Each function requires specifying the window size to determine how tightly the curve follows the orginal data.

LOWESS: Robust locally-weighted regression. This method estimates the long-term trend using a locally-fitted regression. Outlier values are down-weighted using several 'robustifying' iterations. In this version, five iterations are used. This method was translated into BASIC directly from W.S. Cleveland's (1979) FORTRAN program LOWESS, with a few exceptions. (FORTRAN code available from netlib). In particular, Charster's version of LOWESS uses all observations (samples or resampled values) within one-half of the window width. In contrast, the original LOWEESS uses a constant fraction of the data to define the window to fit the LOWESS curve. Defining the window based on the time axis, not the fraction of data, allows the curve to vary with equal sensitivity over time regardless of varying sample density (which result from different sedimentation rates).

Tricube filter: A center-weighted moving average using the tricube function following Huntley et al. (1989):

where S(l) is the smoothed value at position l with a window width of ±0.5w, m is the position along the record within 0.5w of l, V(l,m) is the tricube weighting function, and C(m) is the charcoal series value (CHAR or concentration). The summation of weights occurs over all samples (m), up to the length of the record (T), though only samples within the window width are used. The tricube function for the weighting of the distance between l and m is:

Moving median, or a moving percentile: A percentile of the observations within a window is computed. Options are moving median, 25th percentile, 10th percentile, or the minimum. This percentile is then smoothed using the tricube weights as described above, thus smoothing out any step-like changes. See Gavin et al. 2003.

None (zero values): Select this option if you do not wish to remove a background from the data.

updated 21 June 2006