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Detrending & standardization

Standardization removes the low-frequency biological growth trend from each raw ring-width series, converting it to a dimensionless ring-width index (RWI) centered near 1.0 so series of different sizes and ages can be averaged into a chronology. dplPy offers the dplR curve-fitting methods plus regional curve, signal-free, age-dependent-spline, and power-transform approaches.

detrend: curve fitting

detrend fits a growth curve to each series and divides (or subtracts) it out:

import dplpy as dpl

rwl = dpl.readers("ca533.rwl", header=True)
rwi = dpl.detrend(rwl, fit="Spline")

The fit argument selects the curve (dplR's names are the canonical spelling, and are case-insensitive):

fit Curve
"Spline" (default) Cubic smoothing spline
"AgeDepSpline" Age-dependent (increasing-stiffness) spline
"ModNegExp" Negative exponential a·exp(b·t)+k, fit by nonlinear least squares (dplR), with a negexp → linear → mean fallback chain
"NegExp" The same negative-exponential curve, fit by ARSTAN's deterministic method (Ed Cook's curve)
"ModHugershoff" Hugershoff a·t^b·exp(c·t)+d, fit by nonlinear least squares (dplR)
"Hugershoff" The Hugershoff curve, fit by ARSTAN's log-linearised closed form (Ed Cook's hughdi)
"GeneralExp" General exponential a·t·exp(b·t) — Hugershoff with the power fixed at 1 (ARSTAN option 8)
"LinearAny" (alias "Linear") Best-fit straight line, any slope (ARSTAN option 4)
"LinearNegative" Best-fit line constrained to a non-positive slope, falling back to the mean if the slope is positive (ARSTAN option 5)
"Mean" Horizontal line at the series mean

Two of these come as deterministic/nonlinear pairs — NegExp/ModNegExp and Hugershoff/ModHugershoff — pairing ARSTAN's deterministic fit with dplR's nonlinear-least-squares fit of the same curve. The two behave differently in each case:

  • Negative exponential. Both members minimise the same data-space error for the same model, so when the nonlinear fit converges NegExp and ModNegExp give the same curve. NegExp's advantage is robustness: being deterministic it never fails to converge, so it still returns a curve on series where the nls diverges and ModNegExp falls back to a line or the mean — handy for batch processing.
  • Hugershoff. Here the two genuinely differ: dplR's ModHugershoff minimises data-space error, while ARSTAN's Hugershoff linearises the model and minimises log-space error, so the fitted curves are not the same even when both succeed.

Other important arguments:

  • method — "ratio" (default; divide by the curve) or "difference" (subtract). Ratios are the traditional RWI; differences suit variance-stabilized workflows.
  • period / f — spline stiffness (wavelength) and frequency response. period defaults to a 67 %-of-length spline; a negative value is read as a percent spline (ARSTAN convention), and a value in (0, 1] as a fraction of length. f is the amplitude cutoff at that wavelength (default 0.5 = 50 %).
  • pos_slope — whether to allow a positively-sloped fitted curve.
  • return_info / verbose — return or print the per-series curve choices.

You can also pass a list of curves to try in order (as in dplR), and detrend a single series (pandas.Series) as well as a whole collection.

rcs: regional curve standardization

Regional curve standardization aligns series by cambial age and divides by a single regional growth curve, preserving low-frequency (e.g. multi-centennial) signal that curve-by-curve detrending removes:

rwi = dpl.rcs(rwl, po=pith_offsets, biweight=True)

po is a pith-offset table (see po_to_wc/wc_to_po). preset="crust" builds the regional curve the CRUST way (Melvin & Briffa 2014).

sfrcs: signal-free RCS

Ordinary RCS builds one regional curve and detrends every series by it, but when the sample's age structure varies over calendar time that curve absorbs part of the common signal and biases the low frequencies ("trend distortion"). sfrcs breaks the feedback by iterating: each pass rebuilds the regional curve from measurements that have had the current chronology divided out, while still forming the tree indices from the original measurements.

rwi = dpl.sfrcs(rwl, po=pith_offsets)
info = dpl.sfrcs(rwl, po=pith_offsets, return_info=True)  # + chronology, curve, convergence

It is a port of CRUST's single-curve signal-free RCS (Melvin & Briffa 2014) — a method with no dplR counterpart, so it is faithful to CRUST rather than validated against dplR. On CRUST's own sample data it reproduces a headless build of CRUST to about 1×10⁻³.

  • biweight_curve (default False) / biweight_crn (default False) — form the regional curve and the chronology with the arithmetic mean, matching CRUST's defaults; set either to True for a Tukey biweight robust mean.
  • ss (default 10) — the age-dependent spline stiffness offset for the curve (an 11-year minimum), as in CRUST.
  • max_iterations (default 40) / tol (default 1e-3) — the signal-free iteration budget and convergence threshold (max |Δchronology| < tol), as in CRUST. Running at max_iterations=1 performs no signal removal and reduces to one-pass CRUST RCS.

Signal-free RCS needs a wide spread of tree start dates to work well: Melvin & Briffa (2014) show distortion of the recovered signal appears once the range of starting years falls below about 200 years, and is considerable below about 100. Use it on collections whose trees germinate across a broad time range, not on a narrow single-cohort sample.

Multi-curve RCS (several regional curves with tree-to-curve allocation) is not yet implemented.

ssf: signal-free standardization

Signal-free standardization iterates detrending and chronology-building to reduce the trend-distortion (end-effect) bias of ordinary detrending:

rwi = dpl.ssf(rwl)

It repeats until the high-frequency chronology stops changing (median absolute difference below mad_threshold). preset="crust" selects the CRUST variant.

ads and powt

  • ads fits an age-dependent spline to a single series — a spline whose stiffness increases with cambial age. It is also available inside detrend via fit="AgeDepSpline".
  • powt applies a power transformation (Cook & Peters) as an alternative to ratio detrending for variance stabilization. plot=True draws an ARSTAN-style "data transform statistics" diagnostic — per-series skew and spread-vs-level correlation, before and after the transform — and return_stats=True returns those numbers as a table, so you can check the transform actually made the series symmetric and decoupled variance from level.

Choosing a method

Spline and ModNegExp are the everyday choices for site chronologies. Reach for rcs when you need to retain long-timescale climate signal, sfrcs when you want RCS and the signal-free correction for trend distortion under an uneven age structure, ssf when end-effect bias matters in curve-by-curve detrending, and powt/difference detrending when heteroscedastic variance is the concern. See the Detrending & standardization reference for every parameter.