astrochron (version 1.4)

timeOpt: TimeOpt: Evaluation of eccentricity-related amplitude modulation and bundling in paleoclimate data

Description

TimeOpt: Evaluation of eccentricity-related amplitude modulation and bundling in paleoclimate data, as in Meyers (2015). The method can also be used to evaluate records that express obliquity, as in Meyers (2019).

Usage

timeOpt(dat,sedmin=0.5,sedmax=5,numsed=100,linLog=1,limit=T,fit=1,r2max=1,
        fitModPwr=T,flow=NULL,fhigh=NULL,roll=NULL,targetE=NULL,targetP=NULL,
        detrend=T,output=0,title=NULL,genplot=T,check=T,verbose=T)

Value

if output = 1, a data frame containing the following will be returned: Sedimentation rate (cm/ka), r^2_envelope, r^2_spectral, r^2_opt

if output = 2, a data frame containing the following will be returned: Time (ka), tuned time series, filtered precession, precession envelope, TimeOpt-reconstructed eccentricity model, full TimeOpt-regression model

Arguments

dat

Stratigraphic series for astrochronologic assessment. First column should be depth or height (in meters), second column should be data value.

sedmin

Minimum sedimentation rate for investigation (cm/ka).

sedmax

Maximum sedimentation rate for investigation (cm/ka).

numsed

Number of sedimentation rates to investigate in optimization grid.

linLog

Use linear or logarithmic scaling for sedimentation rate grid spacing? (0=linear, 1=log; default value is 1)

limit

Limit evaluated sedimentation rates to region in which full target signal can be recovered? (T or F)

fit

Test for (1) precession amplitude modulation or (2) short eccentricity amplitude modulation?

r2max

Which maximum in r2 do you want to use for the time model calibration? (1) r^2_opt, (2) r^2_spectral, (3) r^2_envelope

fitModPwr

Include the modulation periods in the spectral fit? (T or F)

flow

Low frequency cut-off for Taner bandpass (half power point; in cycles/ka)

fhigh

High frequency cut-off for Taner bandpass (half power point; in cycles/ka)

roll

Taner filter roll-off rate, in dB/octave.

targetE

A vector of eccentricity periods to evaluate (in ka). These must be in order of decreasing period, with a first value of 405 ka.

targetP

A vector of precession periods to evaluate (in ka). These must be in order of decreasing period.

detrend

Remove linear trend from data series? (T or F)

output

Which results would you like to return to the console? (0) no output; (1) return sedimentation rate grid, r^2_envelope, r^2_power, r^2_opt; (2) return optimal time series, filtered precession, precession envelope, TimeOpt-reconstructed eccentricity model, full TimeOpt-regression model

title

A character string (in quotes) specifying the title for the graphics window (optional)

genplot

Generate summary plots? (T or F)

check

Conduct compliance checks before processing? (T or F) In general this should be activated; the option is included for Monte Carlo simulation.

verbose

Verbose output? (T or F)

Details

TimeOpt is an astronomical testing algorithm for untuned (spatial) stratigraphic data. The algorithm identifies the sedimentation rate(s) that simultaneously optimizes: (1) eccentricity amplitude modulations within the precession band, and (2) the concentration of spectral power at specified target astronomical periods (Meyers, 2015). The method can also be adapted to evaluate records that express obliquity, as in Meyers (2019).

For each temporal calibration investigated (i.e., sedimentation rate), the observed precession band amplitude envelope is extracted using bandpass filtering and the Hilbert transform. The fit of the extracted precession envelope to the eccentricity periods is evaluated using a linear regression onto sine and cosine terms that reflect the five dominant eccentricity periods (~405.7, 130.7, 123.8, 98.9 and 94.9 kyr); amplitude and phase of the eccentricity terms are not assigned, but are determined during the linear model optimization. This approach is advantageous, as (1) the transfer functions associated with the climate and depositional systems can alter the amplitude and phase of the theoretical eccentricity terms (e.g, Laurin et al., 2005), and (2) the amplitude and phase of the eccentricity terms are unconstrained for deep-time investigations (>50 Ma). The quality of the "fit" is estimated by calculation of the correlation of the fitted eccentricity model time series to the observed precession band envelope (r^2_envelope), indicating the fraction of variance shared between the model and envelope.

The concentration of power at the target astronomical periods is evaluated using a linear regression of the temporally-calibrated series onto sine and cosine terms that reflect the dominant eccentricity and precession periods. As above, the amplitude and phase of each term is determined during the linear model optimization, and the quality of the "fit" is estimated by calculation of the correlation of the fitted astronomical model series to the temporally-calibrated series (r^2_spectral).

The final measure of fit (r^2_opt) is determined as:

r^2_opt = r^2_envelope * r^2_spectral

which is simply the product of the fraction of variance shared between "model and envelope" and "model and time-calibrated data". This optimization approach identifies the sedimentation rate at which the precession envelope strongly expresses expected eccentricity modulation, while simultaneously, spectral power is concentrated at the target astronomical periods. r^2_opt can take on values ranging from 0 to 1 (a perfect fit to the astronomical model), and provides a measure of overall quality of the astronomically calibrated time series. A similar approach is applicable to evaluate short eccentricity amplitude modulations. The statistical significance of the r^2_opt is determined via Monte Carlo simulation (see timeOptSim).

See the examples below and Meyers (2019) for a demonstration of how TimeOpt can be adapted to evaluate records that express obliquity.

References

J. Laurin, S.R. Meyers, B.B. Sageman, and D.A. Waltham, 2005, Phase-lagged amplitude modulation of hemipelagic cycles: A potential tool for recognition and analysis of sea level change: Geology, 33, doi.org/10.1130/G21350.1.

S.R. Meyers, 2015, The evaluation of eccentricity-related amplitude modulation and bundling in paleoclimate data: An inverse approach for astrochronologic testing and time scale optimization: Paleoceanography, 30, doi.org/10.1002/2015PA002850.

S.R. Meyers, 2019, Cyclostratigraphy and the problem of astrochronologic testing: Earth-Science Reviews, 190, doi.org/10.1016/j.earscirev.2018.11.015.

See Also

asm, eAsmTrack, testPrecession, timeOptPlot, and timeOptSim

Examples

 if (FALSE) {
# generate a test signal with precession and eccentricity
ex=etp(tmin=1,tmax=1000,dt=5,pWt=1,oWt=0,eWt=1,esinw=TRUE,genplot=FALSE,verbose=FALSE)
# convert to meters with sedimentation rate of 2 cm/kyr
ex[1]<-ex[1]*0.02
timeOpt(ex,sedmin=0.5,sedmax=5,numsed=100,fit=1,output=0)
# evaluate short eccentricity modulations
timeOpt(ex,sedmin=0.5,sedmax=5,numsed=100,fit=2,output=0)

# generate a test signal with precession
ex=etp(tmin=1,tmax=1000,dt=5,pWt=1,oWt=0,eWt=0,esinw=TRUE,genplot=FALSE,verbose=FALSE)
# convert to meters with sedimentation rate of 2 cm/kyr
ex[1]<-ex[1]*0.02
timeOpt(ex,sedmin=0.5,sedmax=5,numsed=100,fit=1,output=0)

# generate a test signal with precession, obliquity and eccentricity
ex=etp(tmin=1,tmax=1000,dt=5,pWt=1,oWt=1,eWt=1,esinw=TRUE,genplot=FALSE,verbose=FALSE)
# convert to meters with sedimentation rate of 2 cm/kyr
ex[1]<-ex[1]*0.02
# define target periods for obliquity and precession
targetOP=c(41.15226,23.62069,22.31868,19.06768,18.91979)
timeOpt(ex,sedmin=0.5,sedmax=5,numsed=100,fit=1,targetP=targetOP,output=0)

# generate a test signal with obliquity
ex=etp(tmin=1,tmax=1500,dt=5,pWt=0,oWt=1,eWt=0,genplot=FALSE,verbose=FALSE)
# convert to meters with sedimentation rate of 2 cm/kyr
ex[1]<-ex[1]*0.02
# define target periods for obliquity and obliquity amplitude modulation
targetO=c(41.15226)
targetO_AM=c(1250,175.4386,109.8901,95.2381)
timeOpt(ex,sedmin=0.5,sedmax=5,numsed=100,fit=1,fitModPwr=F,targetP=targetO,
  targetE=targetO_AM,flow=1/70,fhigh=1/26,roll=10^15,output=0)
 }