SimFromEmpiricalSpec: Simulate a random timeseries consistent with an arbitrary...

In EarthSystemDiagnostics/paleospec: Spectral tools for the ECUS group

Simulate a random timeseries consistent with an arbitrary numerical power spectrum

Description

Adapted from SimPowerlaw

Usage

SimFromEmpiricalSpec(spec, N)

Arguments

spec	Numerical power spectrum consisting of a list with components $freq and $spec
N	length of timeseries to be generated

Value

vector containing the timeseries

Author(s)

Thomas Laepple and Andrew Dolman

See Also

Other functions to generate timeseries with powerlaw like spectra: SimPLS(), SimPowerlaw(), SimProxySeries()

Examples

# Create a piecewise spectrum

## helper function to generate continuous piecewise spectrum

PiecewiseLinear <- function(x, val.at.min.x, breaks, slopes){

breaks <- c(-Inf, breaks, Inf)
slp.vec <- slopes[findInterval(x, breaks)]
d.x <- diff(x)
d.y <- c(d.x * tail(slp.vec, -1))

y <- cumsum(c(val.at.min.x, d.y))

data.frame(x, y)

}
slps <- c(-1, -0.5, -1)
brks <- c(1e-03, 1e-02)
emp.spec <- PiecewiseLinear(log(seq(1/1e05, 1/2, 1/1e05)), 0, log(brks), slps)
emp.spec <- exp(emp.spec)
names(emp.spec) <- c("freq", "spec")

plot(emp.spec, type = "l", log = "xy")

# Sample consistent with spectrum
ts1 <- ts(SimFromEmpiricalSpec(emp.spec, 50000))

# re-estimate power spectrum
spec1 <- SpecMTM(ts1)
LPlot(spec1)
lines(emp.spec, col = "Red")
abline(v = brks, col = "Green")

EarthSystemDiagnostics/paleospec documentation built on Feb. 17, 2024, 4:36 p.m.