Sedproxy: a forward model for sediment-archived climate proxies - Climate of the Past
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Clim. Past, 14, 1851–1868, 2018
https://doi.org/10.5194/cp-14-1851-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Sedproxy: a forward model for sediment-archived
climate proxies
Andrew M. Dolman and Thomas Laepple
Alfred-Wegener-Institut Helmholtz-Zentrum für Polar- und Meeresforschung, Research Unit Potsdam,
Telegrafenberg A45, 14473 Potsdam, Germany
Correspondence: Andrew M. Dolman (andrew.dolman@awi.de)
Received: 16 February 2018 – Discussion started: 2 March 2018
Revised: 6 September 2018 – Accepted: 9 November 2018 – Published: 30 November 2018
Abstract. Climate reconstructions based on proxy records 1 Introduction
recovered from marine sediments, such as alkenone records
or geochemical parameters measured on foraminifera, play Climate proxies are an imperfect record of the earth’s past
an important role in our understanding of the climate system. climate. Climate variations are encoded by geo- or bio-
They provide information about the state of the ocean rang- chemical processes into a medium which survives, archived,
ing back hundreds to millions of years and form the backbone until it is sampled and the physical or chemical signal de-
of paleo-oceanography. coded back into estimates of direct climate variables. For
However, there are many sources of uncertainty associ- example, the ratio of magnesium to calcium in the shells
ated with the signal recovered from sediment-archived prox- (tests) of foraminifera varies with the water temperature at
ies. These include seasonal or depth-habitat biases in the which they calcify and thus encodes a temperature signal
recorded signal; a frequency-dependent reduction in the am- (Nürnberg et al., 1996). Upon death, these shells (the car-
plitude of the recorded signal due to bioturbation of the sed- rier) become buried (archived) in the sediment. They can
iment; aliasing of high-frequency climate variation onto a later be recovered from sediment cores and their Mg/Ca ra-
nominally annual, decadal, or centennial resolution signal; tio measured. Using the modern-day relationship between
and additional sample processing and measurement error in- foraminiferal Mg/Ca and temperature, down-core variations
troduced when the proxy signal is recovered. in the Mg/Ca ratio in foraminiferal tests can then be decoded
Here we present a forward model for sediment-archived back into an estimate of temperature variations back in time
proxies that jointly models the above processes so that the (Anand et al., 2003; Elderfield and Ganssen, 2000; Barker
magnitude of their separate and combined effects can be in- et al., 2005).
vestigated. Applications include the interpretation and anal- The climate signal is distorted and obscured at many
ysis of uncertainty in existing proxy records, parameter sen- points during the encoding, archiving, and subsequent read-
sitivity analysis to optimize future studies, and the genera- ing of a climate proxy, and these diverse sources of noise
tion of pseudo-proxy records that can be used to test recon- and error need to be taken into account when estimating
struction methods. We provide examples, such as the sim- the true past climate from proxy records. One way to de-
ulation of individual foraminifera records, that demonstrate velop, test, and improve our ability to reconstruct climate
the usefulness of the forward model for paleoclimate stud- from proxies is to create mechanistic forward models. These
ies. The model is implemented as an open-source R package, models attempt to simulate the key processes on the entire
sedproxy, to which we welcome collaborative contributions. path from the climate signal to the reconstructed climate:
We hope that use of sedproxy will contribute to a better un- from the encoding of the signal; its archiving in, for exam-
derstanding of both the limitations and potential of marine ple, ice, sediments, wood, or coral; recovery of the archived
sediment proxies to inform researchers about earth’s past cli- material; cleaning and processing of samples; measurement
mate. of the physical or chemical proxy; and its conversion back
into a climate variable such as temperature. Models that at-
Published by Copernicus Publications on behalf of the European Geosciences Union.1852 A. M. Dolman and T. Laepple: Sedproxy
tempt to cover this entire process are known as proxy system used for any proxy sensor that records water conditions and
models (PSMs; Evans et al., 2013) and detailed PSMs have is then deposited and archived in the sediment. We consider
recently been proposed and implemented for oxygen isotope here, as examples, two climate sensors: the Mg/Ca ratio in
proxies archived in ice, trees, speleothems, and corals (Dee the tests of foraminifera, and the alkenone unsaturation in-
0
et al., 2015). dex (UK 37 ). Foraminifera are single-celled protozoa that ex-
Climate proxies recovered from sediment cores are widely ude a calcite shell (test) in which a certain proportion of the
used to reconstruct past climate evolution on timescales from calcium ions are substituted for magnesium. The ratio of Mg
centuries (Black et al., 2007) up to millions of years (Za- to Ca ions is dependent on the ambient temperature during
chos et al., 2001). Several processes affecting the climate the process of calcite formation, and thus the Mg/Ca ratio
signal during recording, recovery, and measurement have in foraminiferal tests acts as a proxy for temperature during
been described in the literature and analysed in specific stud- their creation (Nürnberg et al., 1996). Similarly, alkenones
ies. Examples include the influence of seasonal recording are a class of large organic molecules synthesized by some
(Schneider et al., 2010; Leduc et al., 2010; Lohmann et al., Haptophyte phytoplankton species. The proportion of unsat-
2013), the effect of bioturbation (Berger and Heath, 1968; urated carbon to carbon bonds in the synthesized molecules
Goreau, 1980), the sample size of foraminifera (Killingley is temperature dependent and thus the relative unsaturation
et al., 1981; Schiffelbein and Hills, 1984), measurement un- of alkenone molecules found in sediments can be used as
certainty (Greaves et al., 2008; Rosell-Melé et al., 2001), a proxy for temperature (Prahl and Wakeham, 1987). Sec-
and inter-test variability (Sadekov et al., 2008). Despite this ondary effects such as the effect of salinity on the Mg/Ca
body of knowledge, in practice these processes are often con- of foraminifera (Hönisch et al., 2013), or nutrient availability
0
sidered only in isolation, or not at all, when marine proxy on the UK 37 recorded by the alkenone producers (Conte et al.,
records are interpreted, or when model–data comparisons are 1998), might further effect the recorded proxy signal.
made.
The R package sedproxy provides a forward model for
sediment-archived climate proxies so that the above pro- 2.1.1 Seasonal and habitat bias in the sensor
cesses can be considered during study design, the inter-
pretation of marine proxy records, and when comparing One source of uncertainty common to most climate prox-
models with data. Sedproxy is based on and expands the ies is a bias towards recording the climate during periods of
model described and used by Laepple and Huybers (2013) the year when the proxy generating process is most active
to explain differences in variance between alkenone (U37 K0 ) (Mix, 1987). Both the foraminifera and the alkenone pro-
and Mg/Ca-based climate reconstructions. We first give an ducing haptophytes have growth rates, abundances and rates
overview of the stages of sedimentary proxy record creation of export to the sediment that vary predictably throughout
and then describe how these are implemented in sedproxy. the year (Jonkers and Kučera, 2015; Leduc et al., 2010; Uitz
We then demonstrate how to use the package with a di- et al., 2010), and hence bias these proxies towards recording
verse series of use cases. The source code for sedproxy is the climate during their respective periods of peak produc-
available from the public git repository https://github.com/ tion and export. Furthermore, the proxy creating organisms
EarthSystemDiagnostics/sedproxy. A snapshot of the ver- do not necessarily live at and record the surface of the ocean.
sion used here is archived on Zenodo (Dolman and Laepple, The producers of alkenones are restricted to the photic zone
2018). and thus are close to the surface; however, for foraminifera,
the preferred habitat depth and the depth at which their shells
2 Creation of sediment-archived proxy records calcify is strongly species dependent and can vary from being
close to the surface to the thermocline or deeper (Fairbanks
The creation of a proxy climate record can be thought of as and Wiebe, 1980; Kretschmer et al., 2018). Therefore, the
having three stages: sensor, archive, and observation (Evans recorded temperature will not necessarily reflect the sea sur-
et al., 2013). Here we describe, for sediment-archived proxy face temperature (SST) (Jonkers and Kučera, 2017). Whether
records, the key processes that occur in each of these stages or not these biases represents an error will depend on how the
and outline which of these are included in sedproxy. resulting proxy record is interpreted. However, even when
a proxy is interpreted as representing a particular season or
depth habitat, the season and depth that a given proxy rep-
2.1 Sensor stage
resents will rarely be known with certainty. Furthermore, it
In the context of a climate proxy, a sensor is a physical, bio- is likely that the seasonal and depth-habitat preferences of
logical, or chemical process that is sensitive to climate (e.g. proxy-producing organisms will respond to changes in the
temperature), and creates a measurable record of the climate climate, i.e. they will show homeostasis or habitat tracking
signal. For example, the widths of tree growth rings are sen- (Mix, 1987; Jonkers and Kučera, 2017), which will likely
sitive to temperature and water availability and are preserved damp the climate variations in proxy records (Fraile et al.,
in tree trunks (Douglass, 1919). Our forward model can be 2009).
Clim. Past, 14, 1851–1868, 2018 www.clim-past.net/14/1851/2018/A. M. Dolman and T. Laepple: Sedproxy 1853
0
2.2 Archive stage is increased. For organic proxies such as UK 37 , samples com-
prise many thousands of molecules and aliasing is likely a
After the creation of proxy carriers such as foraminiferal
minor issue, although clustering in sediment export and dis-
shells or alkenone molecules, a proportion of these are ex-
tribution is possible (Wörmer et al., 2014).
ported to and buried in the sediment. The upper few centime-
tres of marine sediments are typically mixed by burrowing
organisms down to a depth of around 2–15 cm (Boudreau,
1998, 9.8 ± 4.5 cm, 1 SD) (Teal et al., 2010; Trauth et al., 2.3.2 Other non-climate variability: inter-individual
1997, 8.37 ± 6.19 cm), although laminated sediments absent variation, cleaning and processing, and
of bioturbation do exist. Marine sediment accumulation rates instrumental error.
vary over many orders of magnitude (Sadler, 1999; Sommer-
field, 2006) but rates at core locations used for climate recon- The measurement of proxy values on material recovered
structions are typically of the order of 1–100 cm kyr−1 . Thus, from sediment cores will necessarily involve some amount
bioturbation can mix and smooth the climate signal over a of error. In particular, foraminiferal tests need to be cleaned
period of decades to millennia and have a strong effect on prior to Mg/Ca measurements and this is an imprecise pro-
the effective temporal resolution that can be recovered from cess. Too little cleaning risks leaving Mg-rich mineral phases
a sediment-archived proxy (Anderson, 2001; Goreau, 1980). (Barker et al., 2003), too much may bias the Mg/Ca down-
Other processes occurring during the archive stage may wards. Some cleaning, processing, and measurement errors
influence the proxy, e.g. differential dissolution of Mg/Ca will be independent between samples while others may be
in foraminiferal shells (Barker et al., 2007; Rosenthal and correlated, e.g. due to differences between labs (Greaves
Lohmann, 2002; Mekik et al., 2007) and preferential degra- et al., 2008). In addition to measurement error, there will
0
dation of UK37 (Hoefs et al., 1998; Conte et al., 2006). also be inter-individual variation between foraminifera in
their recording of the same climate signal (Haarmann et al.,
2.3 Observation stage 2011; Sadekov et al., 2008). For example, test Mg/Ca ra-
tios vary between individual foraminifera even when grown
During the observation phase, samples of sediment are taken under identical conditions (e.g., Dueñas-Bohórquez et al.,
at intervals along a core and material is recovered in which 2011). Similar inter-individual variation and “vital effects”
0
the proxy signal has been encoded. For UK 37 extraction and also occur for δ 18 O (Duplessy et al., 1970; Schiffelbein and
foraminifera picking, these samples are typically taken from Hills, 1984).
1 to 2 cm thick sediment layers. Therefore, even in the ab-
sence of bioturbation the proxy record will be smoothed by
a time period determined by the sedimentation rate and layer
thickness. 3 Implementation
2.3.1 Aliasing of inter- and intra-annual climate variation Here we give an overview of the model implementation, de-
scribing which features of proxy creation can be simulated
For proxy signals embedded in the tests of foraminifera,
with sedproxy. The essential input data, variables, and pa-
measurements are typically made on relatively small sam-
rameters are listed in Table 1 and described in the following
ples of about 5–30 individuals. Due to both bioturbation
paragraphs. Additional optional function arguments are de-
and the width of the sampled sediment layer, these individ-
scribed in the sedproxy package documentation.
uals will be a mixed sample that integrate the climate sig-
nal over an extended time period; however, individual plank-
tonic foraminifera live for a period of only 2–4 weeks (Bi-
jma et al., 1990; Spero, 1998) and hence each encodes cli- 3.1 Input climate matrix (clim.signal)
mate at an approximately monthly resolution. Therefore, if
a measurement is made on a sample containing 30 individ- Sedproxy takes as input an assumed “true” climate signal,
uals mixed together from a period of 100 years, the result- which may come from a climate model or instrumental read-
ing value is a noisy 100-year mean and hence inter- and ings, and returns a simulated proxy value for each of a set
intra-annual scale climate variation is aliased into the nomi- of requested time points. The input climate signal is re-
nally centennial-resolution proxy record (Laepple and Huy- quired as a matrix Cy,h where “y” rows are the years and
bers, 2013; Schiffelbein and Hills, 1984). This effect may be the “h” columns resolve the habitats being modelled. For ex-
particularly strong for high-latitude cores where the seasonal ample, to model seasonal biases in the recording process and
temperature cycle is large. However, the stronger the sea- noise aliased from monthly climate variation, there should be
sonal climate cycle, the more likely an organism is to grow 12 columns representing 12 months of the year. To include
preferentially during a specific season (Jonkers and Kučera, other habitat effects, e.g. foraminiferal depth habitats, this
2015), and thus aliasing will be reduced, while seasonal bias matrix can be extended to have, for example, 12×z columns,
www.clim-past.net/14/1851/2018/ Clim. Past, 14, 1851–1868, 20181854 A. M. Dolman and T. Laepple: Sedproxy
Table 1. Required input data and parameters to generate a pseudo-proxy record with sedproxy. The final argument controls the experimental
design rather than the proxy record creation process itself.
Function argument Description Possible sources Default
clim.signal Input climate signal from which a pseudo-proxy Climate model, instrumental record.
will be forward modelled.
timepoints Time points at which to generate pseudo-proxy Arbitrary, or to match an existing proxy record.
values.
0
calibration.type Type of proxy, e.g. UK 37 or MgCa, to which the identity
clim.signal is converted before the
archiving and measurement of the proxy is sim-
ulated. Defaults to “identity” which means no
conversion takes place.
habitat.weights Habitat weights provide information on Sediment trap data, dynamic equal for all
seasonal and habitat (e.g. depth) differences in population/biogeochemical model (e.g. Fraile
the amount of proxy material produced. et al., 2008; Uitz et al., 2010), or temperature
This allows seasonal and habitat biases in the dependent growth function (e.g. from FAME,
recorded climate to be modelled. Roche et al., 2017).
bio.depth Bioturbation depth in cm, the depth down to Estimated from radiocarbon or from global 10
which the sediment is mixed by distribution (Teal et al., 2010).
burrowing organisms.
sed.acc.rate Sediment accumulation rate in cm kyr−1 . Sediment core age model. 50
layer.width Width of the sediment layer in cm from which Core sampling protocol. 1
samples were taken, e.g. foraminifera
were picked or alkenones were extracted.
n.samples No. of, for example, foraminifera sampled per Core sampling protocol. 30
time point. A single number or a vector with
one value
for each time point. Can be set to Inf for
0
non-discrete proxies, e.g. UK37 .
sigma.meas Standard deviation of measurement error. Reproducibility of measurements on real
world material.
sigma.ind Standard deviation of individual variation.
n.replicates Number of replicate pseudo-proxy time series
to simulate from the climate signal.
where z is the number of discrete depths to be included. tity”, then no transformation takes place. This gives the op-
tion for the input climate matrix to be pre-transformed into
Cy1 ,h1 Cy1 ,h2 · · · Cy1 ,h12z any proxy type by the user.
Cy2 ,h1 Cy2 ,h2 · · · Cy2 ,h12z
..
Uncertainty in the relationship between temperature and
.. .. ..
. . . . proxy units can be modelled by requesting multiple repli-
Cyn ,h1 Cyn ,h2 ··· Cyn ,h12z cate pseudo-proxies. For each replicate, a random set of cal-
ibration parameters are drawn from a bivariate normal dis-
3.2 Sensor-model and calibration tribution that represents the uncertainty in the fitted calibra-
tion model. The bivariate distributions are parameterized by
The input climate signal can be converted to proxy units us- mean values for the regression coefficients and correspond-
ing a transfer function based on an established temperature ing variance-covariance matrices. We have estimated these
calibration. If the argument calibration.type is set variance-covariance matrices for the supplied calibrations by
to either “Uk37” or “MgCa”, the input climate matrix will refitting regression models to the calibration data used in the
0
be converted using the global UK 37 to temperature calibration original publications. Due to small differences in the data sets
from Müller et al. (1998), or the multi-species Mg/Ca to tem- and methods, our parameter estimates deviated slightly from
perature calibrations from Anand et al. (2003), respectively. the published values, but for consistency the mean parameter
The argument calibration can be used to specify one of values are set to the published values.
the taxon-specific calibrations from Anand et al. (2003). If
calibration.type is left at its default value of “iden-
Clim. Past, 14, 1851–1868, 2018 www.clim-past.net/14/1851/2018/A. M. Dolman and T. Laepple: Sedproxy 1855
As sedproxy does not explicitly model the differential dis-
0 0
solution of foram tests, nor the preferential degradation of
0
UK37 , the implicit assumption is made that, where used, these
effect are either minimal or otherwise corrected for during
sample processing (e.g. by exclusion of extensively dissolved
foram tests). Where a bias due to differential dissolution can 25 500
be estimated, this could be corrected for using a custom
dissolution-correcting temperature calibration (e.g., Mekik
Depth [years]
et al., 2007; Rosenthal and Lohmann, 2002). 40 800
Depth [cm]
0
Both the Mg/Ca and UK 37 calibration functions will accept
Bioturbation depth
optional arguments that replace their default parameter val- 50 Focal depth 1000
ues and variance-covariance matrices. For alternative calibra-
tion models that have a different functional form, the function
ProxyConversion would need to be modified.
75 1500
3.3 Weights matrix
While sedproxy conceptually modifies the climate signal ac-
cording to a sequence of sensor, archive, and observation
processes, in practice the value of the simulated proxy at a 100 2000
given time point is calculated in a single step as the mean 0.000 0.025 0.050 0.075 0.100
of a weighted sample from the original climate signal, plus Fraction of material
some independent error term. For each requested time point,
a matrix of weights, Wy,h , is constructed which determines Figure 1. The origin of material archived at a focal core depth of
the probability of sampling any particular value from the cli- 50 cm. In this example the bioturbation depth is 10 cm, and the sed-
mate matrix. iment accumulation rate is 50 cm kyr−1 .
The elements of the weights matrix Wy,h are the product
of annual weights, w y , which depend on bioturbation, and
either a vector or matrix of habitat weights, w h or wy,h , cor- taxa. More complex models, such as FORAMCLIM (Lom-
responding to “static” or “dynamic” habitat weights, respec- bard et al., 2011) or PLAFOM (Fraile et al., 2008), could also
tively. Static weights correspond to habitat preferences (e.g. be used outside of R to precalculate the weights matrix.
depth or season) that do not vary over time with climate. Dy- There is considerable potential for lateral transport of
0
namic weights correspond to season and habitat preferences proxy carriers, particularly the organic proxies such as UK 37
that change in response to climate – such as might be ex- (Mollenhauer et al., 2003; Benthien and Müller, 2000) and
pected from organisms adapting to changing water tempera- potentially also foraminifera (van Sebille et al., 2015); so that
tures by altering their depth in the water column or the timing proxy material in a given sediment core may have come from
of their production. a different location or be a mixed sample representing an area
of ocean of considerable size. Lateral transport of proxy ma-
terial in the water column or at the sediment surface could
3.3.1 Habitat weights (habitat.weights) be modelled by using an input climate matrix with columns
Static habitat weights, wh , are given by a user-defined vec- for multiple spatial locations, and habitat weights represent-
tor defining the seasonality and potentially the depth habi- ing the probability that material was transported from a given
tat of the proxy recording process. It has the same length location.
as the number of columns in the input climate signal. Dy-
namic habitat weights can be specified either by passing a 3.3.2 Annual weights (bioturbation)
named function that will calculate these weights from the in-
put climate matrix or by passing a precalculated matrix of For simplicity, sedproxy assumes complete mixing within the
weights of the same size as the input climate matrix. Non- bioturbated layer, a constant sedimentation rate in the region
static habitat weights could be generated using either the sim- of each sampled time point, and a constant concentration of
ple Gaussian response approach of Mix (1987) or something the proxy carrying material. Under these assumptions, the
more advanced such as the proposed FAME module (Roche origin (pre-bioturbation) of material recovered from a given
et al., 2018). Sedproxy includes an R implementation of the focal depth is described by the impulse response function
growth_rate_l09 function from the FAME v1.0 Python Eq. (1) (Berger and Heath, 1968). This function is equiv-
module (Roche et al., 2018) that can be used to predict habi- alent to an exponential probability density function, with
tat weights from water temperatures for several foraminifera mean equal to the focal depth and standard deviation equal
www.clim-past.net/14/1851/2018/ Clim. Past, 14, 1851–1868, 20181856 A. M. Dolman and T. Laepple: Sedproxy
to the bioturbation depth divided by the sedimentation rate. 3.3.3 Summing or sampling
The value of a proxy measured on material recovered from a
For proxies such as foraminiferal Mg/Ca, where typically
given depth can thus be viewed as a weighted mean of mate-
a small number of foraminiferal tests (N) are cleaned and
rial originally deposited over a range of depths, with weights
measured for each depth or time point in a sediment core,
given by Eq. (1) (Fig. 1). By assuming a locally constant sed-
the proxy at time t, Prt , is the mean of a random sample of
iment accumulation rate, α, around each focal point, and a
N elements of the input climate matrix C, with the probabil-
fixed bioturbation depth, δ, the bioturbation function can be
ity that a particular element is sampled given by the weights
expressed in units of time rather than space or depth.
matrix W, plus some independent error term ε (Eq. 3).
In this model, the probability that a particle found at a
given focal depth was mixed down from a distance greater
1 i=N
X
than the bioturbation depth, δ, is zero. Theoretically, particles Prt = {C(i) , W(i) } + ε (3)
can be brought up from any distance below the focal depth, N i=1
but for computational reasons the annual weights vector is
0
restricted to a distance of three bioturbation depths below the For proxies such as UK 37 , it is assumed that there are effec-
focal horizon; this region contains 99 % of the mass of the tively infinite samples taken for each time point at which the
impulse response function. proxy is evaluated. In this case the proxy at time y Prt is the
( λy −λyt −1 sum of the element-wise product of the climate and weights
α·e f
δ if yt − yf + αδ ≥ 0, matrices (Eq. 4).
wyt = (1)
0 if yt − yf + αδ < 0, X
Prt = (C · W) + ε (4)
where α is sediment accumulation rate in cm yr−1 , δ is the
bioturbation depth in cm, λ is the αδ , and yf os the focal year. 3.4 Independent error (sigma.meas, sigma.ind)
To account for the fact that foraminiferal tests are col-
0 The error term ε is added as an independent Gaussian ran-
lected, or UK37 extracted, from a layer of sediment of a cer- dom variable with mean µ = 0 and standard deviation σ . The
tain thickness (layer.width). The bioturbation function
value of σ is controlled by the parameters sigma.meas
is convolved with a uniform probability density function with
(σmeas ), and sigma.ind (σind ); σmeas describes both the
a width equal to the layer thickness (Eq. 2). The effect of
analytical error of the measurement process and any other
layer.width is small unless the bioturbation depth is
sources of error that are introduced during the preparation of
small relative to the layer width.
the sample (e.g. cleaning for Mg/Ca); σind quantifies inter-
individual variation for proxies that are measured on sam-
0 if z < −L,
−λL−λz λL+λz ples of discrete individuals such as foraminifera, and its con-
e · e −1
wyt = if − L ≤ z ≤ L, (2) tribution to ε is scaled by the square root of the number of
2L
e2λL −1 ·e−λL−λz
if z > L, individuals in the sample, N (Eq. 5).
2L
s
where z = yt − yf + αδ and L = layer.width/2. σ2
σ = σmeas 2 + ind (5)
While the assumption of complete mixing with a sharp N
cutoff is unlikely to be true, the general effects of bioturba-
tion should also apply under conditions of incomplete mixing Appropriate values for these error parameters will depend
and the code could be modified to use a more complex bio- on the proxy type, and for σind in particular they may also
turbation model (e.g., Guinasso and Schink, 1975; Steiner be site and species dependent, although the empirical esti-
et al., 2016). However, when sedimentation rates are low rel- mates of the sum of both error terms in Laepple and Huybers
ative to mixing rates, more complex mixing models converge (2013) suggested similar values between study sites. We pro-
to the simple box-type model that is employed here (Mati- pose that σmeas should be set to typical lab values for the
soff, 1982). Sedproxy further assumes a constant bioturbation reproducibility of measurements on real-world material. For
0
depth over time, as the bioturbation depth is generally not UK ◦
37 we use a value of 0.23 C, which was the mean repli-
K 0
known for each setting and cannot easily be reconstructed cate error of all U37 studies used in Laepple and Huybers
down-core. Bioturbation depth may be related to productiv- (2013). For foraminiferal Mg/Ca we use 0.26 ◦ C for σmeas ,
ity and sedimentation rate, but its predictability for a given which corresponds to about 0.07–0.11 mmol mol−1 at 20 and
core seems to be low (Trauth et al., 1997). The recent de- 25 ◦ C, respectively, and lies within the typical reported range
velopment of radiocarbon measurements on small samples (Skinner and Elderfield, 2005; Groeneveld et al., 2014).
(Wacker et al., 2010) might allow the extent of bioturbation The value of σind is less constrained as it depends on how
to be constrained using replicate measurements from individ- much of this variation has been explicitly modelled, e.g. via a
ual depth layers (e.g. Lougheed et al., 2018) and such infor- seasonally and depth-resolved input climate signal and habi-
mation could be included in sedproxy in the future. tat weights. We use 2 ◦ C for σind , as most examples here do
Clim. Past, 14, 1851–1868, 2018 www.clim-past.net/14/1851/2018/A. M. Dolman and T. Laepple: Sedproxy 1857
not explicitly include depth habitat. This value is similar to (a)
the inter-test variability of approximately 1.6 ◦ C estimated 0.12
for fresh Globigerinoides ruber samples by Sadekov et al.
G. ruber ab. index
(2008). Assuming a typical number of 30 foraminifera in-
0.09
dividuals per sample, these two sources add up to approx-
imately 0.45 ◦ C, the mean replicate error across all Mg/Ca
0 0.06
studies used in Laepple and Huybers (2013). For UK 37 we set
σind to zero as we typically assume an infinite sample size.
Values of σmeas and σind are entered in units of ◦ C by de- 0.03
fault, but can be entered in proxy units if scale.noise is
set to FALSE. 0.00
3.5 Replication
(b)
Multiple replicate proxy records can be simulated with a
Mean temperature [°C]
single set of parameters. Due to the stochastic sampling of
habitats and depths, the random noise terms, and the ran- 28
domly sampled calibration parameters, replicates will not be
identical. An additional random bias can be added to each 27
replicate-simulated proxy record. This bias is drawn from
a Gaussian distribution with mean equal to 0 and a user-
26
definable standard deviation (meas.bias defaults to 0).
This bias will be constant for all points in a given replicate
and can be used to include additional uncertainty in the proxy 25
Feb May Aug Nov
calibration, or inter-lab variation in analytical results.
Month
4 Using sedproxy Figure 2. Abundance index of G. ruber from PLAFOM (Fraile et
al., 2008) (a), and the mean monthly sea surface temperature in the
To illustrate the use of sedproxy, we here provide a number TraCE21ka simulation at MD97-2141 (b). In this model, G. ruber
of examples together with the R code to execute them. occurs over the whole year with a small maximum during the cooler
months of January–March, therefore biasing the recorded tempera-
ture towards colder temperatures.
4.1 Example 1: a foraminiferal Mg/Ca pseudo-proxy
record for sediment core MD97-2141
The function ClimToProxyClim is used to forward
In this first example, we demonstrate how to simulate an
model a proxy record from an assumed climate. We request
already measured proxy record as closely as possible. We
values of the proxy at the time points of the observed
use the foraminiferal Mg/Ca-based temperature reconstruc-
proxy. Descriptions of the main function arguments can be
tion for sediment core MD97-2141 (Table 2) in the Sulu Sea
found in Table 1, other optional arguments are described
(Rosenthal et al., 2003).
in the package documentation. From the R console type
As an input climate signal we take the monthly SST out-
?ClimToProxyClim to see the help page.
put from the TraCE-21ka “Simulation of Transient Climate
Evolution over the last 21 000 years” (Liu et al., 2009), using
library(sedproxy)
the grid cell closest to core MD97-2141.
We use an Mg/Ca calibration with user-supplied mean
# Reverse matrix so that top row is most
values for the slope and intercept set to those used by
recent
Rosenthal et al. (2003) which reduce a bias due to partial
# year, also convert from Kelvin to Â◦ C
dissolution. The seasonality of Globigerinoides ruber, the
n.rows1858 A. M. Dolman and T. Laepple: Sedproxy
Table 2. Details for sediment core MD97-2141.
Core Location Lat. Long. Proxy Foram.sp Reference
MD97-2141 Sulu Sea 8.78◦ N 121.28◦ E Mg/Ca G. ruber Rosenthal et al. (2003)
(1) Input climate (4) +Aliasing YM
(2) +Bioturbation (5) +Independent error
(3) +Habitat bias (*) Observed proxy
30
4.5
28
Climate units
Proxy units
4.0
26
3.5
24 3.0
0 5 10 15 20 0 5 10 15 20
Age [ka]
Figure 3. A forward modelled foraminiferal Mg/Ca pseudo-proxy record together with the observed Mg/Ca proxy record at core MD97-
2141 in the Sulu Sea. The input climate is shown at annual resolution with the full monthly input time series in grey.
PLAFOM (modern static) FAME (dynamic) set.seed(20170824)
0
# Call the forward model
Mg_Ca.calA. M. Dolman and T. Laepple: Sedproxy 1859 plotting data. PlotPFMs returns a ggplot object that can be of the observed Mg/Ca proxy by Rosenthal et al. (2003), customised using the standard ggplot functions (Wickham, from which they estimate the Last Glacial Maximum– 2009). For brevity, we show here only code to generate the Holocene temperature increase, but find no other significant default figure, complete code for the publication figure is pro- features. However, the features visible in a forward modelled vided as Supplement. proxy are of course dependent on both the input climate sig- plot.dat
1860 A. M. Dolman and T. Laepple: Sedproxy
PLAFOM (modern static) FAME (dynamic)
28
Temperature [°C]
(1) Input climate
27 (2) +Bioturbation
(3) +Habitat bias
(4) +Aliasing YM
26
(5) +Independent error
25
0 5 10 15 20 0 5 10 15 20
Age [ka]
Figure 5. A comparison of forward modelled Mg/Ca-based pseudo-proxies using static and dynamic seasonal weighting.
Mg Ca : G. ruber x 1 Mg Ca : G. ruber x 30 Uk'37
30
Temperature [°C]
Replicate
1
2
25 3
20
5 10 15 20 5 10 15 20 5 10 15 20
Age [ka]
0
Figure 6. Forward modelled proxy-based temperature reconstructions for Mg/Ca with 1 and 30 tests of G. ruber, and for UK
37 . Three replicate
runs of the forward model are shown.
sonal aliasing, we simulate two artificial Mg/Ca records with Uk37A. M. Dolman and T. Laepple: Sedproxy 1861
(7) Reconstructed climate
30
Temperature [°C]
29
Proxy
28 Mg/Ca
Uk'37
27
26
5 10 15 20
Age [ka]
0
Figure 7. Replicate hypothetical Mg/Ca- and UK
37 -based records.
The two proxy types sample different parts of the seasonal cycle.
Ten replicate records are shown for each proxy.
4.3 Example 3: correlation between two proxy types
Sedproxy can be used to explore the expected correlation be- Figure 8. Correlation between replicate pairs of forward modelled
tween pairs of proxy records. Here we correlate Mg/Ca- and proxy records.
0
UK37 -based proxies generated for the same hypothetical sed-
iment core. Records from different locations could be com-
sigma.meas = 0.26, sigma.ind = 2,
pared by supplying a different input climate matrix for each
n.samples = 30, n.replicates = 1000)
site.
To emphasize the potential effect of contrasting proxy sea- proxies1862 A. M. Dolman and T. Laepple: Sedproxy
0
Mg/Ca and UK 37 records over the Holocene (Leduc et al.,
Climate signal
0
2010). Correlations between UK 37 pairs are slightly higher Bioturbated climate signal
than those between Mg/Ca pairs, due to the lower measure- Mean of 45 foraminifera
0
ment noise and lack of aliasing we assume for UK 37 . When the Individual foraminifera
proxy records include a large climate transition, such as the
deglaciation between 21 and 10 ka, correlations between all
pairs become high. Biot.depth: 3 Biot.depth: 5 Biot.depth: 10
0
1
4.4 Example 4: individual foraminiferal analysis
Rep 1
2
In individual foraminiferal analysis (IFA), the population
statistics (e.g. standard deviation or range) of proxy val- 3
ues measured on individual foraminifera recovered from the
Simulated proxy
0
same depth are used to infer changes in climate variabil-
1
ity – such as changes in the El Niño Southern Oscillation
Rep 2
(ENSO) system (e.g., Koutavas and Joanides, 2012; Killing- 2
ley et al., 1981), or changes in the amplitude of the seasonal 3
cycle (e.g., Ganssen et al., 2011; Wit et al., 2010). Sedproxy
can be used to simulate IFA by setting n.samples = 1 and 0
n.replicates to the number of individuals measured per 1
Rep 3
time point. This approach bears some similarity with INFAU-
2
NAL (Thirumalai et al., 2013); however, while INFAUNAL
was designed to test the sensitivity of IFA to the seasonal cy- 3
cle and inter-annual variability, and therefore includes a spe- 90 130 170 90 130 170 90 130 170
cific analysis on the simulated IFA distributions, sedproxy is Age [ka]
more general and also includes the effects of bioturbation and
habitat weighting. Figure 9. Simulated δ 18 O measured from single foraminiferal tests
Motivated by the study from Scussolini et al. (2013), (circles) and bulk samples (lines). Subplots show six replications
which examined changes in the IFA distribution of δ 18 O dur- with the same parameterization.
ing the penultimate deglaciation, we simulate a case study
that demonstrates the effect of bioturbation on the IFA distri-
bution.
To mimic the reconstructed climate signal of Scussolini solini et al. (2013) (Fig. 9). As in Scussolini et al. (2013),
et al. (2013) we generate an input climate signal in units of for each simulated IFA sample we calculate the variance be-
δ 18 O. We assume a logistic S-shaped climate transition from tween individual foraminiferal δ 18 O and subtract the vari-
1.4 ‰ at 131 ka, to 2.6 ‰ at 135 ka. To this signal we add ance due to measurement error.
stochastic climate variability following power law scaling At the observed sediment accumulation rate of
with slope equals 1 (Laepple and Huybers, 2014) and vari- 1.3 cm kyr−1 and with assumed bioturbation depths of
ance equals 0.0025. In this region, the foraminifera Globoro- 3, 5 or 10 cm, the expected standard deviation in ages of
talia truncatulinoides (sinistral coiling variety) calcifies at a material found at a given depth is approximately 2300,
mean depth of approximately 520 m, with a standard devia- 3800, and 7700 years, respectively. Thus, bioturbation mixes
tion of 50 m (Scussolini and Peeters, 2013). We model indi- material across the deglaciation so that samples with a mean
vidual variation arising from this using an input climate ma- age of between 110 and 140 ka contain a mixture of glacial
trix with 13 columns representing depths from 370 to 670 m, and inter-glacial material, and hence show a higher standard
with δ 18 O anomalies corresponding to the observed δ 18 O deviation in δ 18 O, with a peak at around 135 ka (Fig. 10).
gradient of approximately 0.003 ‰ m−1 and habitat weights The peak in variance remains clear for bioturbation depths
from a Gaussian distribution with mean equals 520 and SD as low as 3 cm, but its absolute value and width are a little
equals 50. The sedimentation rate is set to 1.3 cm kyr−1 . We lower than that seen in Fig. 2 of Scussolini et al. (2013).
run the forward model with bioturbation depths of 3, 5, and At the same time, at bioturbation depths of 3 and 5 cm,
10 cm and simulate 20 foraminiferal tests for the IFA anal- the apparent speed of the climate transition is consistent
ysis, 45 foraminiferal tests for the bulk measurements. We with the sharpness of transition (approximately 8 ka) seen
set measurement noise (sigma.meas) to 0.1 ‰ δ 18 O for in the bulk record for G. truncatulinoides, but for 10 cm of
the IFA and the bulk measurements and add no additional in- bioturbation the transition is too spread out. The forward
dividual variation (sigma.ind = 0). These choices repro- modelling exercise therefore indicates that bioturbation is
duce similar IFA and bulk variance as those shown in Scus- a possible alternative mechanism for the variance peak,
Clim. Past, 14, 1851–1868, 2018 www.clim-past.net/14/1851/2018/A. M. Dolman and T. Laepple: Sedproxy 1863
Biot.depth: 3 Biot.depth: 5 Biot.depth: 10
0.6
IFA variance 0.4
0.2
0.0
110 130 150 170 110 130 150 170 110 130 150 170
Age [ka]
Figure 10. Variance in simulated δ 18 O measured on sets of 20 individual foraminiferal tests. Lines show six replications with the same
parameterization.
but also indicates that the conclusions are sensitive to the record of sampling a small number of foraminiferal tests
parameterization. (Schiffelbein and Hills, 1984; Thirumalai et al., 2013). By
Forward modelling cannot disprove enhanced Agulhas integrating these key features of proxy formation into a sin-
leakage as the source of increased IFA variance across the gle model, sedproxy allows for the interactions and combined
MIS 5–6 transition (Marine Isotope Stage), and there is other effect of these processes on the proxy record to be studied
evidence for increased leakage such as the tight coupling be- for the first time. The relative importance of bioturbation,
tween the Agulhas rings proxy and the δ 18 O of G. truncat- seasonal biases, aliasing, and other noise sources will vary
ulinoides Scussolini et al. (2015). However, given that bio- according to the physical characteristics of the sediment core
turbation depths as low as 3 cm still produce a quite visible (e.g. sediment accumulation rate), the length of the record,
variance peak, we argue that bioturbation is at least a plausi- the amplitude of the seasonal cycle, and the amplitude of the
ble mechanism behind some of the change in variance over signal that is being reconstructed (e.g. a glacial–interglacial
the MIS 5–6 transition. transition vs. ENSO). Most importantly, the type of infor-
mation that is sought from the proxy record will determine
whether these errors are important.
5 Discussion and conclusions
sedproxy has many potential applications in paleoclimate
research, not limited to those in the examples given above. It
We present the first forward model for the simulation of
can serve as a forward model to create more realistic surro-
sediment-based proxy records from climate data. We include
gate records that can be used to test climate field reconstruc-
the main well-constrained processes affecting sedimentary
tion methods (e.g., Smerdon et al., 2011) and it can further
signals while keeping it general enough to be usable for a
act as a forward model for inversion-based climate recon-
large set of problems in paleo-oceanography. The sedproxy
struction methods, i.e. using Bayesian hierarchical models
model is implemented as a user-friendly R package in an
(Tingley and Huybers, 2009) or data assimilation schemes
open-source framework (R Core Team, 2017).
(e.g., Klein and Goosse, 2017). Importantly, it allows quan-
Our forward model relies on and extends the work of
tification of the full uncertainty in proxy records related to the
many previously published studies and models concerning
processes included in the model. By providing an ensemble
single processes in the formation of sedimentary records.
of surrogate (pseudo-) proxy realizations, rather than single
For example, several prior studies have suggested or inves-
error values, the full temporal structure of the uncertainty can
tigated the effect of seasonality and/or depth habitat on the
be characterized. Proxy uncertainty can be determined as a
recorded proxy signal (e.g., Leduc et al., 2010; Liu et al.,
function of timescale, thus separating uncertainties affecting
2014; Lohmann et al., 2013; Schneider et al., 2010). Oth-
long-term means or time slices, such as the seasonal record-
ers have examined how bioturbation reduces the amplitude
ing effects, from temporarily independent noise, such as that
of recorded signals and, in combination with noise, puts a
caused by aliasing of the seasonal cycle. This enables more
limit on the temporal resolution of climate events that can be
quantitative comparisons to be made between climate models
resolved in proxy records (Anderson, 2001; Goreau, 1980).
and proxy data than a classical direct comparison would.
Further studies have investigated the effect on the resulting
www.clim-past.net/14/1851/2018/ Clim. Past, 14, 1851–1868, 20181864 A. M. Dolman and T. Laepple: Sedproxy
The ability to analyse intermediate stages of the simulated Author contributions. TL led the design of the proxy forward
proxy (see Example 1) allows for the effects of different er- model, AMD wrote the code, created the example analyses and
ror sources to be evaluated. Used in this way, sedproxy can figures, and wrote the manuscript. Both authors significantly con-
help optimize and test sampling strategies for sediment cores tributed to the discussion of the model and to the revision of the
by evaluating the effect of, for example, the sample thick- manuscript.
ness, number of foraminifera, or analytical uncertainty in the
final record. This information can be used to improve the de-
Competing interests. The authors declare that they have no con-
sign of studies and to test, prior to a study, whether signals
flict of interest.
of interest such as centennial-scale climate variations could
theoretically be resolved by the proxy record.
While sedproxy largely relies on well-understood pro- Special issue statement. This article is part of the special issue
cesses that have been previously described in the literature, “Paleoclimate data synthesis and analysis of associated uncertainty
there is a strong need to refine this and other proxy system (BG/CP/ESSD inter-journal SI)”. It is not associated with a confer-
models and to confront them with observational data. For ence.
this purpose, more systematic multi-proxy studies compar-
ing independent proxies from the same archives (e.g., Ho
and Laepple, 2016; Laepple and Huybers, 2013; Weldeab Acknowledgements. This work was supported by the German
et al., 2007; Cisneros et al., 2016) would be useful. Studies Federal Ministry of Education and Research (BMBF) as a Re-
analysing replicability inside and between sediment cores in search for Sustainability initiative (FONA) through the PalMod
analogue to studies for ice- and coral-based proxies (DeLong project (FKZ: 01LP1509C). Thomas Laepple was supported
et al., 2013; Smith et al., 2006; Münch et al., 2016) would from the European Research Council (ERC) under the European
allow for a better constraint of the sample error parameter. Union’s Horizon 2020 research and innovation programme (grant
agreement no. 716092) and the Initiative and Networking Fund
Likewise, further investigation of potentially important pro-
of the Helmholtz Association grant VG-NH900. We thank Guil-
cesses occurring during the preservation of archived proxy laume Leduc for suggesting example uses of the forward model and
signals (e.g., Münch et al., 2017; Zonneveld et al., 2007; Jeroen Groeneveld, Michal Kučera, and Lukas Jonkers for helpful
Kim et al., 2009) would allow these to be included in proxy comments on the manuscript and advice during development of the
system models. Finally, modern core-top studies of individ- ideas. We also thank Brett Metcalfe and one anonymous referee for
ual foraminifera distributions (e.g., Haarmann et al., 2011) their suggestions which significantly improved this work.
would allow further testing of the assumption that there is a
direct link between proxy variability and climate variability. The article processing charges for this open-access
We hope that this tool will be useful to the paleocli- publication were covered by a Research
mate research community and we hope that it can pro- Centre of the Helmholtz Association.
vide a starting point for a more complete future proxy
Edited by: André Paul
system model for sediment proxies. We invite external
Reviewed by: Brett Metcalfe and one anonymous referee
contributions via the GitHub repository https://github.com/
EarthSystemDiagnostics/sedproxy (last access: 23 Novem-
ber 2018).
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