ClimToProxyClim simulates the creation of a proxy climate record from a climate signal that is assumed to be true.

The following aspects of proxy creation are currently modelled.

1. Seasonal bias in the encoding of a proxy due to the interaction between climate seasonality and any seasonality in the life cycle of the organism encoding the climate signal (e.g. Foraminifera for Mg/Ca ratios, or phytoplankton for Alkenone unsaturation indices).

2. Bioturbation of the sediment archived proxy. For each requested timepoint, the simulated proxy consists of a weighted mean of the climate signal over a time window that is determined by the sediment accumulation rate sed.acc.rate and the bioturbation depth bio.depth which defaults to 10 cm. The weights are given by the depth solution to an impulse response function (Berger and Heath, 1968).

3. Aliasing of seasonal and inter-annual climate variation onto to bioturbated (smoothed) signal. For proxies measured on a small number of discrete particles both seasonal and inter-annual climate variation is aliased into the proxy record. For example, Foraminifera have a life-cycle of approximately 1 month, so they record something like the mean temperature from a single month. If Mg/Ca is measured on e.g. n.samples = 30 individuals, the measured proxy signal is a mean of 30 distinct monthly mean temperatures and will thus be a stochastic sample of the true mean climate.

4. Measurement noise/error is added as a pure Gaussian white noise process with mean = 0, standard deviation = sqrt(sigma.meas^2 + sigma.ind^2/n.samples).

5. Additionally, a random bias can be added to each realisation of a proxy record. Bias is simulated as a Gaussian random variable with mean = 0, standard deviation = meas.bias. The same randomly generated bias value is applied to all timepoints in a simulated proxy record, when multiple replicate proxies are generated (n.replicates > 1) each replicate has a different bias applied.

ClimToProxyClim returns one or more replicates of the final simulated proxy as well as several intermediate stages (see section Value below).

## Usage

ClimToProxyClim(
clim.signal,
timepoints,
calibration.type = c("identity", "Uk37", "MgCa"),
calibration = switch(calibration.type, identity = NA, Uk37 = "Mueller global", MgCa =
"Ten planktonic species_350-500"),
slp.int.means = NULL,
slp.int.vcov = NULL,
= "multiplicative"),
plot.sig.res = 100,
habitat.weights = rep(1/ncol(clim.signal), ncol(clim.signal)),
habitat.wt.args = NULL,
bio.depth = 10,
sed.acc.rate = 50,
layer.width = 1,
sigma.meas = 0,
sigma.ind = 0,
meas.bias = 0,
scale.noise = switch(calibration.type, identity = FALSE, Uk37 = TRUE, MgCa = TRUE),
n.samples = Inf,
n.replicates = 1,
top.of.core = NULL,
n.bd = 3
)

## Arguments

clim.signal

The "assumed true" climate signal, e.g. climate model output or instrumental record. A ts object consisting of a years x 12 (months) x n habitats (e.g. depths) matrix of temperatures. The time series should be at annual resolution and in reverse, i.e. "most recent timepoint first" order.

timepoints

The timepoints for which the proxy record is to be modelled

calibration.type

Type of proxy, e.g. Uk'37 or MgCa, to which the clim.signal is converted before the archiving and measurement of the proxy is simulated. Defaults to "identity" which means no conversion takes place.

calibration

The name of a specific calibration for which calibration parameters are provided by sedproxy. Currently applies only to calibration.type MgCa.

slp.int.means

Optional user supplied vector of values for the slope and intercept of the calibration function. Overides the defaults.

slp.int.vcov

Optional user supplied variance covariance matrix calibration parameters. Overides the defaults.

noise.type

Determines whether additive or multiplicative measurement noise is added. The appropriate type depends on the units of the proxy. Defaults to multiplicative for MgCa, additive for Uk'37 and identity (none) calibration types. Can be overidden with a string, "additive" or "multiplicative" in the case that pre-converted climate signal and measurement noise values are used in combination with an "identity" calibration type.

plot.sig.res

The resolution, in years, of the smoothed (block averaged) version of the input climate signal returned for plotting. This does not affect what the proxy model uses as input. If set to NA, no smoothed climate output is generated, this can speed up some simulations.

habitat.weights

Production weights for the proxy / proxy-carrier either as a vector of values with length = ncol(clim.signal), i.e. 1 weight for each month x habitat combination, a matrix of the same dimensions as the input climate signal matrix, or a function that produces an index of productivity as a function of temperature. Defaults to a vector of length = ncol(clim.signal) of equal weights.

habitat.wt.args

A named list of parameter values to be passed to a function named in habitat.weights.

bio.depth

Depth of the bioturbated layer in cm, defaults to 10 cm.

sed.acc.rate

Sediment accumulation rate in cm per 1000 years. Defaults to 50 cm per ka. Either a single value, or vector of same length as "timepoints"

layer.width

the width of the sediment layer from which samples were taken, e.g. foraminifera were picked or alkenones were extracted, in cm. Defaults to 1 cm. If bio.depth and layer.width are both set to zero, each timepoint samples from a single year of the clim.signal, equivalent to sampling an annually laminated sediment core.

sigma.meas

The standard deviation of the measurement error added to each simulated proxy value.

sigma.ind

The standard deviation of error between individuals (e.g. Forams) not otherwise modelled. This could included "vital effects" or aliasing of depth habitat variation not modelled via a depth resolved input climate signal and habitat weights. sigma.ind is scaled by n.samples before being combined with sigma.meas.

meas.bias

The amount of bias to add to each simulated proxy time-series. Each replicate proxy time-series has a constant bias added, drawn from a normal distribution with mean = 0, sd = meas.bias. Bias defaults to zero.

scale.noise

Scale noise to proxy units. Defaults to TRUE if calibration.type is not "identity"

n.samples

Number of e.g. Foraminifera sampled per timepoint, this can be either a single number, or a vector of length = timepoints. Can be set to Inf for non-discrete proxies, e.g. for Uk’37.

n.replicates

Number of replicate proxy time-series to simulate from the climate signal

top.of.core

The theoretical minimum age at the top of the core, ie. the year the core was sampled, defaults to the start of clim.in

n.bd

Number of multiples of the bioturbation width at which to truncate the bioturbation filter

## Value

ClimToProxyClim returns an object of class "sedproxy.pfm", a list with three elements:

1. a dataframe simulated.proxy

2. a dataframe smoothed.signal

3. a dataframe everything

The dataframe simulated.proxy contains a single realisation of the final forward modelled proxy, as well as the intermediate stages and the original climate signal at the requested timepoints.

The dataframe smoothed.signal contains a block averaged version the input climate signal, defaults to 100 year means but this is set by the parameter plot.sig.res. This is useful for plotting against the resulting simulated proxy.

The dataframe everything contains all of the above but with multiple replicates of the pseudo-proxy records if requested. The data are in "long form", with the column "stage" inidcating the proxy stage or input climate resolution and column "value" giving the values.

Named elements of the returned proxy record:

timepoints

Requested timepoints

clim.signal.ann

Input climate signal at requested timepoints at annual resolution

clim.signal.smoothed

Input climate signal at regular time intervals and resolution = plot.sig.res

clim.timepoints.ssr

Input climate signal at requested timepoints, smoothed to resolution = plot.sig.res

proxy.bt

Climate signal after bioturbation

proxy.bt.sb

Climate signal after bioturbation and habitat bias

proxy.bt.sb.inf.b

Climate signal after bioturbation, habitat bias, and calibration bias

proxy.bt.sb.inf.b.n

Climate signal after bioturbation, habitat bias, and measurement error

proxy.bt.sb.sampY

Climate signal after bioturbation, habitat bias, and aliasing of inter-annual variation

proxy.bt.sb.sampYM

Climate signal after bioturbation, habitat bias, and aliasing of inter-annual and intra-annual variation such as monthly temperatures or depth habitats

proxy.bt.sb.sampYM.b

Climate signal after bioturbation, habitat bias, and aliasing of inter-annual and intra-annual variation such as monthly temperatures or depth habitats, and calibration bias

proxy.bt.sb.sampYM.b.n

Climate signal after bioturbation, habitat bias, aliasing, and measurement error

simulated.proxy

Final simulated pseudo-proxy, this will be same as proxy.bt.sb.inf.b.n when n.samples = Inf, and proxy.bt.sb.sampYM.b.n when n.samples is finite

observed.proxy

True observed proxy (when supplied)

## Examples

library(ggplot2)
set.seed(26052017)
clim.in <- ts(N41.t21k.climate[nrow(N41.t21k.climate):1,] - 273.15, start = -39)

PFM <- ClimToProxyClim(clim.signal = clim.in,
timepoints = round(N41.proxy$Published.age), calibration.type = "identity", habitat.weights = N41.G.ruber.seasonality, sed.acc.rate = N41.proxy$Sed.acc.rate.cm.ka,
layer.width = 1,
sigma.meas = 0.46,
sigma.ind = 0, n.samples = Inf,
plot.sig.res = 10, meas.bias = 1,
n.replicates = 10)

PlotPFMs(PFM$everything, max.replicates = 1, stage.order = "seq") + facet_wrap(~stage) #> Joining with by = join_by(stage, scale) #> Scale for alpha is already present. #> Adding another scale for alpha, which will replace the existing scale. PlotPFMs(PFM$everything, max.replicates = 1, stage.order = "var")
#> Joining with by = join_by(stage, scale)
#> Scale for alpha is already present.
#> Adding another scale for alpha, which will replace the existing scale.

PlotPFMs(PFM\$everything, stage.order = "var", plot.stages = "all")
#> Joining with by = join_by(stage, scale)
#> Scale for alpha is already present.
#> Adding another scale for alpha, which will replace the existing scale.