We describe the development of the “Paleoclimate PLASIM-GENIE (Planet Simulator–Grid-Enabled Integrated Earth system model) emulator” PALEO-PGEM and its application to derive a downscaled
high-resolution spatio-temporal description of the climate of the last 5×106 years. The 5×106-year time frame is interesting for a range of
paleo-environmental questions, not least because it encompasses the
evolution of humans. However, the choice of time frame was primarily
pragmatic; tectonic changes can be neglected to first order, so that it is
reasonable to consider climate forcing restricted to the Earth's orbital
configuration, ice-sheet state, and the concentration of atmosphere CO2.
The approach uses the Gaussian process emulation of the singular value
decomposition of ensembles of the intermediate-complexity atmosphere–ocean
GCM (general circulation model) PLASIM-GENIE. Spatial fields of bioclimatic variables of surface air
temperature (warmest and coolest seasons) and precipitation (wettest and
driest seasons) are emulated at 1000-year intervals, driven by time series
of scalar boundary-condition forcing (CO2, orbit, and ice volume) and
assuming the climate is in quasi-equilibrium. Paleoclimate anomalies at
climate model resolution are interpolated onto the observed modern
climatology to produce a high-resolution spatio-temporal paleoclimate
reconstruction of the Pliocene–Pleistocene.
Introduction
A high-resolution climate reconstruction of the Pliocene–Pleistocene will
provide an unprecedented opportunity to advance the understanding of many
long-standing hypotheses about the origin and maintenance of biodiversity.
Climate is among the strongest drivers of biodiversity and has played an
important role throughout the history of life on Earth (Svenning et al., 2015). Indeed, changes in climate over time have influenced core biological
patterns and processes such as diversification, adaptation, species
distribution, and ecosystem functioning (Svenning et al., 2015;
Nogués-Bravo et al., 2018). However, studies on the relationship between
climate and biodiversity are still limited by the lack of high-resolution, deep-time spatio-temporal paleoclimatic estimates, as the few studies
available are at very sparse time slices (Lima-Ribeiro et al., 2015). Thus, a
high-resolution spatio-temporal paleoclimate data series of the past 5×106 years will be useful to address many pressing questions on
biodiversity dynamics. For instance, did the onset of glacial cycles promote
more extinctions than recent climate cycles? Do species hold “evolutionary
memory” of the warmer temperature of the Miocene? How did biodiversity
respond to the increase in strength and frequency of glacial cycles during
the Pliocene? Such knowledge is essential to understand biodiversity
patterns and to forecast how organisms will respond to the current
anthropogenic climatic change (Nogués-Bravo et al., 2018).
Spatio-temporal paleoclimatic estimates are essential to drive process-based
models that are capable of exploring causal mechanisms (Nogués-Bravo et al., 2018). For instance, a recent ecological coupling study using climate
emulation addressed the role of natural climate variability in shaping the
evolution of species diversity in South America during the late Quaternary
(Rangel et al., 2018). That study used a paleoclimate emulator (Holden et al., 2015) of the climate model PLASIM (Planet Simulator)-ENTS (Holden et al., 2014). The key
limitations of the climate emulator were the lack of ocean dynamics in
PLASIM-ENTS and the simplified emulation approach, which only considered
orbital forcing; large-scale approximations were made to account for the
effects of time-varying ice sheets and CO2. Here we address these
weaknesses by using ensembles of a fully coupled atmosphere–ocean GCM with
varied orbit, ice-sheet, and CO2 boundary conditions. However,
simulation alone would not be possible for an application of this ambition.
We use the computationally fast low-resolution AOGCM (atmosphere–ocean general circulation model) PLASIM-GENIE (Holden et al., 2016), a coupling of the
spectral atmosphere model Planet Simulator (PLASIM; Fraedrich, 2012) to the
Grid-Enabled Integrated Earth system model (GENIE; Lenton et al., 2006), but even with this relatively simple model a 5×106-year
transient simulation would demand ∼300 CPU years of
computing, which could not readily be parallelized. We overcome this
intractability by using statistical emulation.
Emulators are computationally fast statistical representations of
process-driven simulators, most useful when the application of the simulator
would be computationally intractable (Sacks et al., 1989; Santner et al., 2003;
O'Hagan, 2006). Climate applications of emulation have included the
exploration of multi-dimensional parameter input space in order to, for
instance, generate probabilistic outputs (Sansó et al., 2008; Rougier et al., 2009; Harris et al., 2013) or calibrate simulator inputs (Sham Bhat et al., 2012; Olson et al., 2012; Holden et al., 2013). Climate emulators have also been
developed as fast surrogates of the simulator for use in coupling
applications (Castruccio et al., 2014; Holden et al., 2014). In addition to
Rangel et al. (2018), coupling applications have included climate change
impacts on energy demands (Labriet et al., 2015; Warren et al., 2019) and
adaptation to sea-level rise (Joshi et al., 2016).
Our methodology uses principal component analysis to project spatial fields
of model output onto a lower-dimensional space of the dominant simulated
patterns of change and then derives regression relationships between the
simulator inputs and the coefficients of the dominant patterns. The method
is analogous to the widely used pattern-scaling technique (Tebaldi and
Arblaster, 2014), which assumes that an invariant pattern of simulated change
can be scaled by global warming. Our approach extends this by including
several (here 10) principal components for each climate variable, thereby
allowing us to capture non-linear patterns of change. The regression approach
we use involves Gaussian process (GP) emulation (Rasmussen, 2004).
GP emulators are non-parametric regression models that have become widely
used tools in a variety of scientific domains. We train the emulators using ensembles of paleoclimate simulations, driven by variable
orbital, CO2, and ice-sheet forcing inputs, in order to predict spatial
fields of bioclimatic variables as functions of these inputs. This builds on
previous studies that have emulated two-dimensional climate fields from
CO2 forcing (Holden and Edwards, 2010; Holden et al., 2014), orbital
forcing (Bounceur et al., 2015; Holden et al., 2015), combined CO2 and
ice-sheet forcing (Tran et al., 2016), and combined orbital and CO2
forcing (Lord et al., 2017). Lord et al. (2017) additionally considered two
ice-sheet states (modern and a reduced Pliocene configuration), but, to our
knowledge, these three Pliocene–Pleistocene forcings have not previously
been varied together except in the emulation of scalar indices (Araya-Melo
et al., 2015). Ice-sheet forcing complicates the emulation problem because ice
sheets are three-dimensional input fields. Although climate emulators with
dimensionally reduced input and output fields have been developed (Holden et al., 2015; Tran et al., 2018), we simplify the problem by assuming there is an
approximate equivalence between the ice-sheet state and global sea level.
This reduces the emulation to the more usual problem of relating scalar
inputs to high-dimensional outputs.
The motivation for our approach is to generate spatio-temporal climate fields
for use in dynamic coupling applications that need temporal variability and
therefore cannot use snapshot AOGCM simulations. To this end, we need
forcing time series that extend back 5×106 years and have sufficient
temporal resolution to capture orbitally forced climate variability. For
PALEO-PGEM v1.0 we use the sea-level reconstructions of Stap et al. (2017)
for the whole period and their CO2 reconstruction prior to 800 000 BP
(when ice core records are not available).
The model PLASIM-GENIE
PALEO-PGEM was built from quasi-equilibrium simulations of the intermediate-complexity AOGCM PLASIM-GENIE. The
component modules, coupling, and pre-industrial climatology are described in
detail in Holden et al. (2016). PLASIM-GENIE is not flux corrected. The
moisture flux correction required in the Holden et al. (2016) tuning was
removed during a subsequent calibration (Holden et al., 2018). PLASIM-GENIE
has been applied to studies on Eocene climate (Keery et al., 2018) and
climate–carbon-cycle uncertainties under strong mitigation (Holden et al., 2018).
We applied PLASIM-GENIE at a spectral T21 atmospheric resolution (5.625∘) with 10 vertical layers, and a matching ocean grid with 16
logarithmically spaced depth levels. We enabled the ocean BIOGEM (Ridgwell
et al., 2007) and terrestrial ENTS (Williamson et al., 2006) carbon-cycle
modules, as described in Holden et al. (2018). We do not consider ocean
biogeochemistry outputs here.
The 2000-year spun-up simulations required for emulation were performed with
atmosphere–ocean gearing enabled (Holden et al., 2018). In geared mode,
PLASIM-GENIE alternates between conventional coupling (for 1 year) and a
fixed-atmosphere mode (for 9 years), reducing spin-up time by an order of
magnitude, to roughly 4 d CPU.
Experimental overview
We first provide a summary of the entire approach in five steps, as
illustrated schematically in Fig. 1. Each step is described in more detail
in Sect. 4.
Ensemble calibration: we previously developed a 69-member ensemble of
plausible parameter sets using “history matching” (see, e.g., Williamson et al., 2013). Applying any of these parameter sets to PLASIM-GENIE gives a
reasonable climate–carbon-cycle simulation of the present day, as evaluated
by 10 large-scale metrics; all 69 parameter sets produce simulated outputs
that lie within the 10 history match acceptance ranges listed in Table 1.
This step has been published elsewhere (Holden et al., 2018).
Model selection: we do not address parametric uncertainty in PALEO-PGEM and so required a single favoured PLASIM-GENIE parameter set. One of the 69
history-matched parameter sets was identified by picking the parameter set
whose simulator output had the largest likelihood (defined in Sect. 4.1)
and this “optimized” parameter set was used in all subsequent simulations.
We require PALEO-PGEM to describe glacial states and so, as part of the
calibration, we performed an additional ensemble with the 69 parameter sets
forced by Last Glacial Maximum (LGM) boundary conditions. The calibration
considered simulated LGM cooling in addition to the 10 present-day metrics
(Table 1).
Paleoemulator construction: PALEO-PGEM was constructed via a two-stage
process, in both stages applying Gaussian process emulation to a singular
value decomposition of the outputs of a PLASIM-GENIE simulation ensemble
(cf. Wilkinson, 2010; Bounceur et al., 2015; Holden et al., 2015; Lord et al., 2017). The first stage emulated the simulated climate response to variable
orbital and CO2 forcing, while the second stage emulated the
incremental climate anomaly due to the presence of glacial ice sheets. The
motivation for this two-stage approach was to impose physical meaning on the
decomposition by isolating the ice-sheet-forced components from the orbitally
and CO2-forced components. Note that we do not assume a linear
superposition of the forcing components, and interactions between ice
sheets, CO2, and orbit are represented in the second stage (see Sect. 4.2). All simulations used the optimized parameter set and only varied the
climate forcing.
Paleoclimate emulation: forcing time series of orbital parameters,
atmospheric CO2 concentration and sea level (as a proxy for ice-sheet
volume) were applied to the two-stage emulator at 1000-year intervals to
generate emulated climates at the native climate model resolution.
Downscaling. The emulated climates were converted to anomalies with
respect to the emulated pre-industrial state and interpolated onto a
high-resolution grid. These interpolated anomalies were applied to the
observed climatology to derive a high-resolution paleoclimate reconstruction
at 1000-year intervals from 5 Ma.
Schematic of experimental design.
Simulation output metrics for history matching and maximum
likelihood calibration.
HistoryML (maximum likelihood)matchingcalibrationOptimizedacceptance(mean, 1σ)simulationiOutput metricObservationsrange±μiσigiθ∗1Global average surface air temperature (∘C)∼14 Jones et al. (1999)11 to 1714±1.514.12Global vegetation carbon (GtC)450 to 650 Bondeau et al. (2007)300 to 800550±1256963Global soil carbon (GtC)850 to 2400 Bondeau et al. (2007)750 to 25001625±437.511704Maximum Atlantic Overturning (Sv, sverdrup)∼19 Kanzow et al. (2010)10 to 3020±517.85Maximum Pacific Overturning (Sv)<150±7.52.46Global ocean averaged dissolved O2 (µmol kg-1)∼170 Conkright et al. (2002)130 to 210170±201397Global deep-ocean CaCO3 flux (Gt CaCO3-C yr-1)∼0.4 Feely et at. (2004)0.2 to 0.80.4±0.150.568Atmospheric CO2 in 1870 (ppm)288 Rubino et al. (2013)N/A288±12.52809Atmospheric CO2 in 2005 (ppm)378 Keeling et al. (2005)353 to 403378±12.5380101864–1875 to 1994– 2005 warming (∘C)∼0.78 IPCC (2013) SPM (Summary for policy makers)0.6 to 1.00.78±0.10.7811Last Glacial Maximum temperature change (∘C)4.0±0.8 Annan and Hargreaves (2013)N/A-4.0±1.2-5.9The simulation ensemblesThe optimized parameter set θ∗
Given computational constraints we chose to neglect parametric uncertainty
in PALEO-PGEM and selected a single “optimized parameter set” for all
simulations. Earlier work (Holden et al., 2018) had developed a calibrated
ensemble of 69 plausible PLASIM-GENIE parameter sets through a history
matching approach. In summary, these authors built and applied emulators of
seven scalar metrics (items 1–7 in Table 1) to search for plausible input
space. They considered hundreds of millions of potentially valid model
parameterizations, each selected randomly by drawing from priors for 32
varied input parameters (Table 2). Each of these 32-element parameter
vectors were applied to the seven emulators in turn, and 200 of them were
selected to maximize a criterion that combined the distance of candidate
points to the other points already in the design (to ensure the design
points fully span the input space) and the probability (according to the
emulator) of reasonably simulating the observational targets: global average
surface air temperature, global vegetation carbon, global soil carbon,
Atlantic overturning circulation strength, Pacific Ocean overturning
circulation strength, global average dissolved ocean oxygen concentration, and global average calcium carbonate flux to the ocean floor. The 200
parameter sets were applied to simulation ensembles of the pre-industrial
state and transient historical CO2 emissions forcing (1805 to 2005).
Finally, 69 of these parameter sets were selected as acceptable on the basis
of the seven pre-industrial metrics and three additional metrics that relate
only to the transient simulations (items 8–10 in Table 1): emissions-forced
CO2 concentration in 1870 and 2005 and transient warming (from 1865 to 2005).
Prior distributions for PLASIM-GENIE varied parameters (uniform
between ranges in log or linear space as stated).Prior distributions are discussed
and derived from Holden et al. (2010, 2013a, b, 2014, 2016). The final column tabulates the optimized parameter set.
ModuleParameterDescriptionUnitsMinMaxPriorOptimized θ∗PLASIMTDISSDHorizontal diffusivity of divergenced0.0110LOG0.01245TDISSZHorizontal diffusivity of vorticityd0.0110LOG0.04627TDISSTHorizontal diffusivity of temperatured0.0110LOG1.03202TDISSQHorizontal diffusivity of moistured0.0110LOG0.06188VDIFFVertical diffusivitym101000LOG12.9576TWSR1Short-wave clouds (visible)0.010.5LOG0.32403TWSR2Short-wave clouds (infrared)0.010.5LOG0.03297ACLLWRLong-wave cloudsm-2 g-10.015LOG0.50152TH2OCLong-wave water vapour0.010.1LOG0.02357RCRITMINMinimum relative critical humidity0.71.0LIN0.94867GAMMAEvaporation of precipitation0.0010.05LOG0.00799ALBSMEquator–pole ocean albedo difference0.20.6LIN0.44992ALBIS1Ice-sheet albedo0.80.9LIN0.8APM2Atlantic–Pacific moisture flux adjustmentSv0.00.32LIN0.0GOLDSTEINOHDIsopycnal diffusivitym2 s-15005000LOG2005.24OVDReference diapycnal diffusivitym2 s-12×10-52×10-4LOG1.35386e-4ODCInverse ocean dragd13LIN2.55463SCFWind stress scaling24LIN2.44654OP1Power law for diapycnal diffusivity profile0.51.5LIN1.07740BIOGEMPMXMaximum PO4 uptakemol kg-1 yr-15×10-75×10-5LOG2.27102×10-5PHSPO4 half-saturation concentrationmol kg-15×10-85×10-6LOG1.21364×10-6PRPInitial proportion POC export as recalcitrant fraction0.010.1LIN0.031471PRDE-folding remineralization depth of non-recalcitrant POCm1001000LIN802.258PRCInitial proportion CaCO3 export as recalcitrant fraction0.11.0LIN0.22708CRDE-folding remineralization depth of non-recalcitrant CaCO3m3003000LIN1315.25RRSRain ratio scalar0.010.1LIN0.076452TCPThermodynamic calcification rate power0.22.0LIN0.510763ASGAir–sea gas exchange parameter0.30.5LIN0.46006ENTSVFCFractional vegetation dependence on carbon densitym2 kgC-10.11.0LIN0.84249VBPBase rate of photosynthesiskgC m-2 s-19.5×10-82.2×20-7LIN1.2040×10-7LLRLeaf litter rates-12.4×10-98.2×10-9LIN2.4197×10-9SRTSoil respiration activation temperature or dependenceK197241LIN218.356VPC3CO2 fertilization Michaelis–Menton half-saturationppm29725LOG215.368
(1) ALBIS ice-sheet
albedo was fixed at 0.8 in the final ensemble. (2) APM was fixed at zero in
the final ensemble (no flux correction). (3) VPC was not constrained by the
emulator filtering as this parameter has no effect in the pre-industrial spin-up state. The final calibration step, selecting 69 simulations that satisfy present-day plausibility after the historical transient was primarily an exercise to calibrate the VPC parameter.
In addition to these 10 plausibility tests of Holden et al. (2018), we also
required the optimized model to exhibit a reasonable response to glacial ice
sheets. We therefore performed an additional 69-member PLASIM-GENIE
ensemble, applying Last Glacial Maximum forcing of 180 ppm CO2
concentration, “ICE-5G” LGM ice sheets (Peltier, 2004), and the LGM orbital
configuration of Berger (1978), with an eccentricity of 0.0019, obliquity of 22.949∘, and longitude of the perihelion at vernal equinox of 114.4∘.
For each of j=1,..., 69 parameter combinations, we calculate a
score Pj which indicates how successful simulation j was, in terms of
matching the observations for each of the 11 metrics. These are
tabulated in the “Calibration” column of Table 1, where μi denotes
the observational estimate for metric i and σi an estimate of
uncertainty, cognizant of both observational and model error.
Pj=∏i=1,11e-giθj-μi2/2σi2,
where giθj is the output of the simulator
corresponding to the ith metric when it is run at parameter setting
θj. The optimized parameter set θ∗ was selected to be the
ensemble member with the highest score, equivalent to minimizing a weighted
sum of squared errors. This optimized parameter set was used in all
simulations that follow. The optimized output metrics are provided in Table 1 and the input parameter values in Table 2. The most notable bias is the
cold LGM when compared to observational target, though the optimized model
lies within the 3.1 to 5.9 ∘C ranges simulated by the CMIP5/PMIP3 (Coupled Model Intercomparison Project 5/Palaeoclimate Modelling Intercomparison Project 3)
and PMIP2 ensembles (Masson Delmotte et al., 2013).
The climate sensitivity of the optimized parameter set is 3.2 ∘C.
The Maximum Atlantic Overturning is 17.8 Sv, at a depth of 1.1 km with the
10 Sv contour, an indicator of the location of NADW (North Atlantic Deep Water) formation, at a latitude
of 56∘ N. Under LGM forcing, Atlantic overturning weakens to a
peak of 11.1 Sv at a depth of 1.0 km and the 10 Sv contour shifts southward to
45∘ N. Under doubled CO2 forcing, Atlantic overturning
weakens substantially to a peak of 7.6 Sv at a depth of 0.4 km.
Ensemble design
Our approach to emulating climate output fields relies on dimension
reduction using the singular value decomposition. This is a statistical
technique which rotates the data onto a new orthogonal coordinate system, so
that the first coordinate is in the direction of maximum variance in the
data, the second coordinate is then in the direction of maximum variance
conditional on being orthogonal to the first coordinate, etc. The new
coordinates are often called principal components (or empirical orthogonal
functions), and whilst they are orthogonal, they are not expected to cleanly
isolate distinct physical processes. In order to impose a physical
separation of the components, and therefore to enforce a clean response to a
distinct forcing, we chose to build the emulator as a two-stage process. We
first decomposed and emulated the smoothly varying climate response to
changing orbit and CO2 concentration with fixed present-day ice sheets
(the “E1” emulator). The land–sea mask is held fixed at the present day in
all simulations. We then separately emulated the incremental climate
response to a change in ice-sheet state under the same orbital and CO2
forcing (the “E2” emulator) so that the final emulation is the sum of these
two components.
To build the E1 and E2 emulators, two separate 50-member boundary-condition
ensembles were performed (BC1 and BC2) with the optimized parameter set. The
statistical design of both ensembles was the same 5×50 maximin Latin
hypercube (MLH,) varying the three orbital parameters, the CO2
concentration, and the ice-sheet state. The only difference between the two
ensembles was that the fifth hypercube variable, reserved for ice sheets,
was ignored for the BC1 ensemble and the present-day ice-sheet configuration
imposed for all BC1 simulations. The BC1 ensemble is designed to simulate
the model response to orbit and CO2 forcing only, while the BC2
ensemble simulates the different response driven by the presence of glacial
ice sheets under the same set of choices of orbital and CO2 forcing.
The sampling strategy for the orbital variables (eccentricity e, the
longitude of the perihelion at the vernal equinox ω, and obliquity
ε) followed Araya-Melo et al. (2015), uniformly sampling esinω and ecosω in the range -0.05 to 0.05 and ε
in the range 22 to 25∘. This transformation was chosen
because the insolation at any point in space and time of year is generally
well approximated as a linear combination of these terms. Carbon dioxide was
varied uniformly in log space, in the range log(160 ppm) to log(1000 ppm).
For ice sheets, relevant only to the BC2 ensemble, four states were allowed
in the training ensemble, being the Peltier Ice-5G ice sheets (Peltier, 2004)
at 10, 13, 15, and 20 ka. These times were chosen as they correspond to
well-spaced ice-volume intervals as evidenced by benthic δ18O
(Lisiecki and Raymo, 2005). These times correspond to sea-level falls of 29,
45, 64, and 107 m relative to modern values in the Stap et al. (2017) reconstruction
that we use to force the time-series emulation (Sect. 6).
In contrast to Araya-Melo et al. (2015), we did not restrict input space to
exclude combinations of high CO2 and high glaciation levels, preferring
instead to use all BC1 ensemble members (i.e. including those with high
CO2) in the BC2 ice-sheet anomaly ensemble. This maintained the maximin
and orthogonal properties of the MLH design and moreover avoided any risk
of extrapolation outside of training input space during the Pliocene.
Present-day (∼400 ppm) CO2 levels can be associated with
significant (∼50 m) sea-level falls according to the Stap et al. (2017) reconstructions (see Fig. 2). However, the trade-off for this
simplicity is that realistic input space during glacial periods was less
well sampled than it would be for a more targeted ensemble of the same size
(cf. Araya-Melo et al., 2015).
Emulator time-series forcing and reconstructed global surface air
temperature. Orbital forcing is Berger and Loutre (1991, 1999). Ice-sheet
forcing is the sea-level reconstruction of Stap et al. (2017). Carbon dioxide
forcing after 800 000 BP is ice core data (Luethi et al., 2008), using
the Stap et al. (2017) reconstruction in the earlier period.
Emulator construction
Emulators were built for four bioclimatic variables: the mean temperature of
the warmest and coolest quarters and the mean daily precipitation of the
wettest and driest quarters. Each variable was calculated on a grid-point
basis as the maximum and minimum of the DJF (December–January–February), MAM (March–April–May), JJA (June–July–August), and SON (September–October–November) seasons. These
emulated variables were chosen as being of bioclimatic relevance (cf. Rangel et al., 2018) and suitable for a wide range of ecological and impact
coupling applications, defining the extremes of climate experienced over
each grid cell during a (decadally averaged) annual cycle. Emulators of DJF
and JJA temperature and precipitation were also built for validation
purposes (Sect. 6.1).
We derived emulators from inputs of esinω, ecosω,
ε, log(CO2), and sea-level S, each normalized on the
range -1 to 1. Sea level provides a proxy for ice-sheet volume and hence
ice-sheet state (under the assumption of an invariant correspondence between
ice sheets and sea level). This neglects the asymmetry of ice sheets under
glaciation and deglaciation. The E1 emulator was built from the outputs of
the BC1 ensemble (after centring the data, by subtracting the ensemble mean
field M from each simulation before singular value decomposition). The E2
emulator was built from the anomaly outputs BC2–BC1. For E2, we appended the
training data with a synthetic 50-member ensemble with the hypercube inputs
repeated except that sea level was randomly assigned to be between -25 and
+100 m. In these synthetic data, no simulations were performed, but instead
all the climate anomalies were set to zero, equivalent to performing a
second ice-sheet-forced ensemble with a present-day ice sheet (and
therefore with no anomaly by construction). This was needed so that the
ice-sheet anomaly emulator can be used when glacial ice sheets are absent
(i.e. sea level greater that -25 m), i.e. when the ice-sheet-emulated anomaly
(E2) is trained to be zero and the emulation is determined only by the orbit
and CO2 emulator (E1). Note that this approach neglected the loss of
Antarctic and/or Greenland ice, compared to modern values, that is implicit when paleo sea level exceeded the present day.
All emulators were built following the “one-step emulator” algorithm
described by Holden et al. (2015), summarized briefly here. For each ensemble
member, we formed the 2048-element vector which describes the 64×32 output field to be emulated. The vectors for the N ensemble members were
combined into a (2048×N) matrix Y describing the entire ensemble
output of that variable. The matrices Y used to train the E1 emulators
comprised decadally averaged outputs of the BC1 ensemble, and these matrixes
were centred by subtracting the ensemble mean field. The matrices for the
E2 emulators were constructed from the decadally averaged anomalies BC2–BC1.
This separation of the forcing elements is a key difference with earlier
work; every BC1 member has an identical BC2 member with the same inputs
except for the incremental ice-sheet forcing, which cleanly isolates the
emulation of ice-sheet forcing from the orbital and CO2 forcing.
Singular value decomposition was performed to reduce the dimensionality of
the simulation fields:
Y=LDRT,
where L is the (2048×N) matrix of left singular vectors
(“components”), D is the N×N diagonal matrix of the square
roots of the eigenvalues, and R is the N×N matrix of right
singular vectors (“component scores”). This decomposition produced a
series of orthogonal components, ordered by the percentage of variance
explained. We truncated the decompositions, considering only the first 10
components. Each of the 10 retained sets of scores thus comprised a vector
of N coefficients, representing the projection of each simulation onto the
respective component. As each simulated field is a function of the input
parameters, so are the coefficients that comprise the scores, so that each
component score can be emulated as a scalar function of the input parameters
to the simulator.
We used Gaussian process (GP) emulation (Rasmussen, 2004) in preference to
stepwise linear regression. The principal motivation for using this more
sophisticated approach was that GPs are highly flexible non-parametric
regression models which have greater modelling power than linear models.
Linear models live in a finite dimensional space defined by polynomial
functions of the covariates. Gaussian processes live in a much richer space
of functions. An additional motivation was that GP emulation provides both a
central estimate and an estimate of uncertainty and therefore provides us
with a means to generate uncertain climate emulations in the absence of
parametric uncertainty. It is important to note that emulator uncertainty is
entirely distinct from (and therefore incremental to) parametric
uncertainty.
Emulator cross-validation and model selection
Gaussian process models are generalized models but nevertheless require
some user choices, the most important being the choice of covariance
function. We used an anisotropic covariance function (different length
scales for each input dimension) and estimated the unknown length scale
parameters using the type II maximum likelihood estimators (Rasmussen and
Williams, 2006). In order to evaluate the optimal covariance function, we
considered the cross-validation metric P; see Sect. 4.3.1 of Holden et al. (2014):
P=∑c=1,10Rc2Vc,
where Rc2 is the coefficient of determination of the emulator of
principal component c, evaluated under leave-one-out cross-validation of all
simulations, and Vc is the percentage of the total variance explained by that component, summed
across the leading 10 components. The metric is designed to quantify the
percentage of the spatial variance explained by the emulator, capturing the
explained variance due to principal component truncation (only 10
components are considered) and to the emulation itself (i.e. the explained
variance of the simulated component scores).
Table 3 summarizes the cross-validation of the eight emulators (i.e. four
bioclimatic variables, two forcing categories). The second column tabulates
the percentage of variance explained by the leading 10 principal
components, ∑c=1,10Vc, and represents the maximum
variance that could be explained by the emulators if they were perfect. The
remaining columns tabulate the metric P when building the emulator with a
series of different covariance functions, the alternatives being available
in the DiceKriging R package (Roustant et al., 2012). The reduction in variance explained
(relative to column 2) reflects additional errors due to emulation.
Optimization of the Gaussian process covariance function. The
variance explained by the first 10 components of the decomposition is
quantified by “PC variance explained”, which would be the expected
variance explained if the emulators were perfect. The percentage of variance
explained by the emulators is quantified by the metric P (Eq. 3, including
10 components) for each of the eight emulators, considering various tested
covariance functions. A power exponential is favoured for the final emulator,
having similar average performance to exponential covariance function but
outperforming it for the more difficult precipitation variables.
The temperature decompositions explain 94 %–99 % of the ensemble variance,
compared to 87 %–90 % for the precipitation decompositions. Under emulation,
the variance explained is 81 %–98 % for the temperature fields and 73 %–83 %
for precipitation fields. The emulator performance is weaker for
precipitation because the low-order components needed to explain much of
the ensemble variability are more difficult to emulate.
The power exponential was found to give comparable or better performance
compared to the other covariance functions in all eight emulators and was
therefore chosen as the default covariance function and used in all
analysis that follows.
Table 4 summarizes the variance explained under cross-validation of the
seasonal and annual average emulators used in the following Sect. 7. DJF
(JJA) temperature emulator performance is similar to min (max) temperature
emulator performance, suggesting that Northern Hemisphere temperature is
more difficult to emulate than Southern Hemisphere temperature, as would be
expected for the ice-sheet emulator in particular. The performance of the
various seasonal precipitation emulators is similar (82.7 % to 84.8 %
for the orbit and CO2 emulator, 72.4 % to 75.4 % for the ice-sheet
emulator), but annual precipitation is easier to emulate than seasonal
precipitation (88.6 % for the orbit and CO2 emulator, 81.9 % for
the ice-sheet emulator).
Seasonal and annual mean emulator performance (as used in Sect. 7), measured by the metric P (Eq. 3, including 10 components). A power
exponential covariance is used in all cases. Note that max and min values
repeat data from Table 3.
The emulators generate a paleoclimate as
Ee,ω,ε,CO2,S=M+E1e,ω,ε,CO2+E2e,ω,ε,CO2,S,
where M is the simulation mean field that was subtracted to centre the
ensemble before decomposition (Sect. 5). To generate a paleoclimate time
series, we therefore require time series of the boundary condition inputs e,ω,εCO2, and S.
For the orbital parameter inputs, we applied the 5×106-year calculation
of Berger and Loutre (1991, 1999). We used CO2 from Antarctic ice cores
for the last 800 000 years (Luethi et al., 2008). Prior to 800 000 BP, and for
the entire sea-level record, we used the CO2 and sea-level
reconstructions of Stap et al. (2017). These authors used a zonally averaged
energy balance model coupled to a six-level ocean model, a thermodynamic
sea-ice model and to one-dimensional mass-balance modules for each of the
five major Cenozoic ice sheets (East and West Antarctica, Greenland,
Laurentide, and Eurasian). The Stap model is forced with benthic δ18O records and uses an inversion routine to de-convolve the
temperature and ice-volume components of the isotope signal and generate a
self-consistent time series of CO2 and sea level (ice volume).
Figure 2 plots the forcing time series and an illustrative application of
the emulator, for which we emulated the time-varying annual mean surface air
temperature field and plotted its area-weighted global average through time.
In order to validate the emulators, we performed a series of experiments
with Mid-Holocene (MH), Last Glacial Maximum (LGM), Last Interglacial (LIG)
and mid-Pliocene warm period (MPWP) CO2, ice sheets, and orbital
forcing. These time slices have been well-studied in Paleo-Modelling
Inter-comparison Projects and are well suited to exploring variability driven
by all three forcings. The MH and LIG responses are dominantly forced by
orbit, while the MPWP is dominantly forced by CO2 and the LGM by both
CO2 and ice-sheet state.
Mid-Holocene emulated ensemble
To assist comparison with readily available PMIP2 data (Braconnot et al., 2007), we here emulate seasonal (DJF and JJA) fields rather than seasonal (MAX and MIN) fields, plotted in Fig. 3. Uncertainty is associated with
the emulation of the component scores. Gaussian process emulation quantifies
this uncertainty by providing a mean prediction and an estimate of the
uncertainty associated with that prediction. We generated a 200-member
emulation ensemble with MH forcing. The 200 ensemble members differ because
we do not assume the mean prediction for the emulated component scores but
instead draw randomly from the posterior distributions. In Fig. 3 this
ensemble is summarized with mean and standard deviation fields. (We note
that for applications in which climate uncertainty is not addressed, it is
appropriate to use the mean predictions of principal component scores to
generate the best estimate.)
PALEO-PGEM emulated ensemble comparison with PMIP2
ocean–atmosphere–vegetation ensemble (Braconnot et al., 2007) for the Mid-Holocene.
Figure 3 (top panels) compares emulated MH surface temperature (anomalies relative
to pre-industrial) with the PMIP2 OAV (coupled atmosphere–ocean–vegetation)
ensemble. In northern winter DJF, high-latitude warming is apparent in the
emulated ensemble mean, although it is of uncertain sign (variability > mean). Cooling is apparent over all other land regions. In northern summer
JJA, robust warming is apparent at mid- to high latitudes, while changes in
variable signs are apparent in the tropics, with cooling apparent over the
Sahel, India, and SE Asia. Each of these features is also found in the PMIP
ensemble. The most significant difference is Antarctic cooling of
∼3∘C in PALEO-PGEM, which contrasts with a warming
signal in the ensemble mean of PMIP2 (although we note the DJF Antarctic cooling
of 0.5 ∘C was simulated in HadCM3M2). A significant cold Antarctic
bias is also apparent during the Last Interglacial (Sect. 7.4). High
southern latitudes are poorly modelled by PLASIM-GENIE. The pre-industrial
state exhibits a warm Antarctic bias, with greatly understated sea ice, a
slow Antarctic Circumpolar Current, and weak, northerly shifted zonal winds
(Holden et al., 2016), which are likely associated with the well-known
difficulties of resolving Southern Ocean wind stress at low meridional
resolution (Tibaldi et al., 1990; Schmittner et al., 2010).
Figure 3 (lower panels) compares emulated MH precipitation with the PMIP2 OAV
ensemble. In DJF, significant drying is emulated over central and
northwestern South America, southern Africa, eastern Asia, and northern
Australia, while wetter conditions are emulated over northeastern South
America. In JJA the largest changes are seen as a strengthening of the Asian
monsoon precipitation, and significantly wetter conditions are also seen
over the Sahel and western South America. These changes all reflect a
general agreement with PMIP2.
Last Glacial Maximum emulated ensemble
We follow the emulated ensemble procedure for the Last Glacial Maximum. Figure 4 (upper panels) compares the emulated Last Glacial Maximum temperatures with
the PMIP2 OA (ocean–atmosphere) ensemble. We neglect the OAV LGM ensemble
because it has only two simulations. LGM cooling is dominated by cooling of
up to ∼40∘C over the Northern Hemisphere glacial
ice sheets. The most significant differences are apparent in the emulated
uncertainty, which is understated by a factor of roughly 2 relative to
PMIP. This is expected because the emulator is built from a single
parameterization of PLASIM-GENIE and therefore does not capture uncertain
climate sensitivity. We note that by applying the principles of invariant
temperature pattern scaling (Tebaldi and Arblaster, 2014), the temperature
uncertainties due to neglected climate sensitivity could be approximated by
inflating the variance of the principal component scores.
PALEO-PGEM emulated ensemble comparison with the PMIP2
ocean–atmosphere ensemble (Braconnot et al., 2007) for the Last Glacial
Maximum. Note the different scales for SD temperature. Reduced variance in
PALEO-PGEM is due to the understated uncertainty of climate sensitivity,
which arises from the neglect of parametric uncertainty.
Figure 4 (lower panels) compares emulated Last Glacial Maximum precipitation
with the PMIP2 OA ensemble. In DJF, the drying apparent in central Africa,
northern America, and the Amazon are captured by the emulator, while JJA
drying at northern latitudes and in the Asian and African monsoon regions and increased precipitation in South America are common to the emulator and
the PMIP2 ensemble.
Glacial–interglacial variability
The emulated global temperature change over the last 800 000 years is
plotted in Fig. 5, reflecting the familiar glacial cycles and compared to
the observationally based global temperature reconstructions of Koehler et al. (2010). Ten separate emulators were built (following the steps described
in Sect. 5 applied to annual average temperature), and the mean prediction
time series for all 10 emulators are plotted.
The Last Glacial Maximum cooling across these 10 emulators is 4.1±0.2∘C, which compares to uncertainty estimates of ±0.3∘C when emulated values are drawn randomly from a single
emulator. The emulated estimates are lower than the simulated LGM cooling of
5.9 ∘C (Table 1) and may reflect bias in the ice-sheet emulator
under the extreme of LGM forcing; the ice-sheet emulator was only able to
explain 81 % of the variance of cold season temperatures (Table 3).
However, the seasonal patterns of emulated change are reasonable (Fig. 4)
and the annual average cooling is well-centred on the 3.1 to 5.9 ∘C range simulated by the CMIP5/PMIP3 and PMIP2 ensembles (Masson-Delmotte et al., 2013).
Maximum warming of 0.3±0.1∘C is emulated in the Last
Interglacial (Marine Isotope Stage 5), peaking at 125 ka. This is
consistent with CMIP estimates of 0.0±0.5∘C, but lower
than data-based estimates of ∼1 to 2 ∘C (Masson-Delmotte et al., 2013). Maximum warming in Marine Isotope Stage 11 is 0.1±0.2∘C, peaking at 401 ka.
Last Interglacial transients
Zonally averaged emulated temperature changes are compared with the Last
Interglacial transient model inter-comparison of Bakker et al. (2013) in
Fig. 6 and Table 5. The latitudinal temporal trends are well captured by
the emulator, considering the inter-model spread of Bakker et al. (2013).
Notably, temperatures in June–July–August generally peak earlier (∼125 ka) than temperatures in December–January–February (∼120 ka).
A maximum warming of ∼2 to 3 ∘C is emulated in
northern summer mid- to high latitudes, peaking at 126 ka and consistent with
inter-model estimates in the range 0.3 to 5.3 ∘C, peaking between
125 and 128 ka. Eight of the emulated peak warming estimates are consistent
within the 1σ multi-model uncertainty ranges, and the remaining two
are consistent within 2σ multi-model uncertainty (Table 5). The
clearest difference is seen in Antarctic winter, where cooling of up to
3 ∘C is emulated, significantly greater than in any of the models.
The mid-Pliocene warm period
The emulated climate of the mid-Pliocene warm period is plotted in Fig. 7.
The only emulator forcing is CO2 increased to 405 ppm, as assumed in the
model inter-comparison of Haywood et al. (2013). Ice sheets are fixed at
the present day, in contrast to Haywood et al. (2013), where the boundary
conditions included a reduced West Antarctic Ice Sheet.
Emulated global temperature over the last 800 000 years. An
emulator was built 10 times, and the mean prediction time series of each
emulator are plotted as grey lines, with the mean of these plotted as the
single black line. The blue dotted line is the observationally based
reconstruction of Koehler et al. (2010).
Emulated Last Interglacial temperature anomalies with respect to
pre-industrial temperatures. An emulator was built 10 times, and the mean prediction time
series of each emulator are plotted. Data are provided for December–January–February and
June–July–August averaged over five latitude bands; cf. Figs. 2 and 3 of Bakker
et al. (2013).
Last Interglacial peak warming (∘C) and year of peak
warming (BP) compared to the model inter-comparison ±1σ
ranges of Bakker et al. (2013). Emulated data are provided for December–January–February
and June–July–August, compared to January and July data in the model
inter-comparison, and comparisons are provided for five latitude bands.
60–90∘ N30–60∘ N30∘ S–30∘ N60–30∘ S90–60∘ SDJF peak warming ∘C1.4 (-5.8 to 1.2)0.5 (-0.8 to 2.1)0.5 (0.6 to 1.2)0.2 (-0.7 to 1.0)-0.0 (-1.3 to 2.3)DJF year of peak warming BP124 (118 to 124)119 (117 to 121)119 (116 to 119)119 (119 to 121)118 (116 to 118)JJA peak warming ∘C2.4 (0.3 to 3.7)3.2 (0.7 to 5.3)0.7 (0.3 to 2.5)0.1 (-0.7 to 1.0)-0.4 (-1.3 to 2.3)JJA year of peak warming BP126 (125 to 128)126 (126 to 129)126 (127 to 130)119 (124 to 130)119 (126 to 129)
Emulated mid-Pliocene temperature and precipitation anomalies with
respect to pre-industrial values. The ice-sheet and orbital inputs are set to
pre-industrial values, and the emulated change is driven by an assumed CO2
concentration of 405 ppm.
Ensemble-averaged emulated warming is 1.6±0.2∘C and
global precipitation change 0.10±0.01 mm d-1. These compare to
multi-model estimates of 1.8 to 3.6 ∘C and precipitation changes
of 0.09 to 0.18 mm d-1 in Experiment 2 (the coupled atmosphere–ocean
configuration) of Haywood et al. (2013). Emulated high-latitude warming of
∼4∘C is low-biased, but within the wide
multi-model uncertainty range of ∼3 to 14 ∘C.
Similarly, the emulated peak precipitation change of ∼0.3 mm d-1 near the Equator is low-biased, but within the multi-model range of
∼0 to 1.3 mm d-1.
Downscaling
A spatial resolution higher than the native resolution of the underlying
climate model may be required for paleo-applications given the scale
dependency of many patterns and processes (e.g. Rahbek, 2005), such as
scale-dependent climate heterogeneity (Rangel et al., 2018). We address this
need by interpolating the low-resolution climate model anomalies onto
fine-resolution climatological data. This approach is widely used in climate
impact assessment (e.g. Osborn et al., 2016) and has also been applied in
paleo-applications in anthropology (Melchionna et al., 2018) and ecology
(Rangel et al., 2018).
Downscaling can be performed in any given grid. Here we illustrate
downscaling on a global hexagonal grid build on a geodesic dome because it
minimizes geographic distortions in shape, area, and distance that are common
to map projections. The hexagonal grid is composed of 17 151 quasi equal-area
cells of 6918±859 km2 whose area variation is not spatially
structured.
The four present-day (pre-industrial) emulated bioclimatic variables E were
linearly interpolated onto the geodesic grid. All emulations used the mean
prediction, and the E1 and E2 emulators were both truncated at 10 principal
components. Contemporary observations of the bioclimatic variables C were
derived from WorldClim (Hijmans et al., 2005), which provides temperature and
precipitation estimates at 1 km2 resolution, interpolated from
temporally averaged measurements (1950 to 2000) from ∼15 000 to 50 000 weather stations globally (depending upon the variable). The
raw emulated climate data E and the difference with observed climatology
E0-C are illustrated in Fig. 8.
Downscaling the emulated climate. Panels (a) and (c) are the
pre-industrial emulations of the seasonal bioclimatic variables at native
(T21) model resolution, interpolated into the high-resolution grid. Panels (b)
and (d) illustrate the differences with respect to high-resolution
climatology (Hijmans et al., 2005).
The emulated climatology is reasonable, accepting the low resolution of the
underlying climate model. Cold biases are generally confined to
northern winter high latitudes. Warm biases are more modest except for the
Tibetan Plateau and Andes where the lapse rate cooling in these narrow
mountain chains is poorly resolved by the climate model (but corrected for
by the downscaling approach described below). Excess precipitation bias is
mostly apparent in the (wet-season) monsoon regions. Deserts are generally
well resolved in the emulator, a notable exception being the hyper-arid
Atacama, which is an orography-driven feature that cannot be captured at low
resolution. Conversely, orography-driven precipitation is understated in the
Tibetan Plateau. Precipitation is also understated in the Sahel.
We apply anomaly adjustments to derive downscaled emulated climate fields
through time Ct. This approach preserves the high-resolution spatial
heterogeneity of climatology. In the case of temperature this is
straightforward. Emulated anomalies Et-E are interpolated onto the
hexagonal grid and applied additively; i.e. Ct=C0+Et-E0.
For precipitation, the situation is more complex. In arid regions that are
not well captured by the emulator, a multiplicative anomaly approach is
preferable Ct=C0×Et/E0, preserving hyper-arid
(topographically forced) desert and preventing unphysical negative
precipitation when Et-E0<0. Conversely, in wet regions that are
understated by the emulator, a multiplicative anomaly approach can create
unphysically high precipitation, but an additive approach ensures a
physically reasonable solution. A pragmatic solution to this is to apply an
additive precipitation anomaly when E0<C0 and a multiplicative
precipitation anomaly when E0>C0. This approach is well-behaved, noting
that the additive and multiplicative anomalies are equivalent when E0=C0.
Consider, when E0<C0,
Ct=C0+Et-E0>Et,
and the additive anomaly partially compensates for the low bias in emulated
climatological precipitation. Conversely, when E0>C0,
Ct=C0×Et/E0<Et,
and the multiplicative anomaly partially compensates for the high bias in
emulated climatological precipitation.
The present-day climatology and downscaled emulated LGM climate are
illustrated in Fig. 9. An animation of the entire 5 000 000-year
reconstruction is provided as a Supplement.
Limitations of the approach
PALEO-PGEM is to our knowledge the first attempt to provide a detailed
spatio-temporal description of the climate of the entire Pliocene–Pleistocene
period. It is essential to understand the main limitations of our modelling
framework, discussed below, some of which may induce large errors or
uncertainties in specific applications or even rule out certain
applications completely. For all practical purposes and for the foreseeable
future, substantial uncertainties exist in any paleoclimate reconstruction
as a result of incomplete knowledge, computing limitations, and irreducible
climatic noise. Ideally, these uncertainties should be quantified in
relation to any reconstruction and their implications propagated through the
analysis. Our approach provides an estimate of inherent uncertainty derived
from the emulation step of the reconstruction and thus underestimates the
full uncertainty, but nevertheless in some aspects remains comparable to the
uncertainty in state-of-the-art reconstructions of particular periods as
measured by the variance across ensembles of PMIP simulations.
Compared to state-of-the-art models, PLASIM-GENIE is a relatively low-resolution, intermediate-complexity climate model. This implies that
processes operating at spatial and temporal scales below the native
resolution of the climate model cannot be properly represented, although
certain aspects of spatial variation are reintroduced in a highly idealized
way by the downscaling process. The temporal effects of dynamical processes
operating at sub-millennial timescales are further filtered out by the
approximation inherent in the emulator construction that the climate is in
quasi-equilibrium with the forcing, which is then only resolved at 1000-year
time intervals.
Downscaled emulated climate. Panels (a) and (c) are the downscaled
emulated bioclimatic variables at the Last Glacial Maximum. Panels (b) and (d) are the present-day climatology (Hijmans et al., 2005). Note that
downscaled climates are derived by applying emulated anomalies to this
present-day climatology. An animation of the complete 5 Ma reconstruction is
provided as Supplement.
In applications where (downscaled) time-slice simulations are adequate and
are available from higher-complexity models and/or multi-model ensembles
(Sect. 7), these would normally be preferable to PALEO-PGEM as errors and
biases will generally be smaller, particularly in high latitudes, regions of
steep topography, close to coastlines, or in known regions of locally extreme
climate. We note that HadCM3 climate simulations (Singarayer et al., 2017),
downscaled to 1∘ resolution are available back to 120 ka (Saupe
et al., 2019), which would provide preferable (or supplementary) climate data
for applications restricted to this time domain.
The emulator uncertainty captures much of the uncertainty seen in
multi-model inter-comparisons (Figs. 3 and 4), but PALEO-PGEM cannot fully
represent model uncertainty because it is derived from a single
configuration of a single model. Most clearly in this respect, the 90 %
uncertainty range of climate sensitivity (3.8±0.6∘C) is
understated relative to multi-model estimates of 3.2±1.3∘C (Flato et al., 2013). Some significant biases in spatial patterns are also
apparent, most clearly temperature biases in high southern latitudes.
Emulator forcing is limited to orbit, CO2, and ice sheets. Ice meltwater
forcing is not considered, so that millennial variability, especially
important in North Atlantic, is neglected. The land–sea mask and orography
are held fixed, so that ocean circulation changes driven by changing
gateways (e.g. the closing Panama isthmus, with implications for the
thermohaline circulation) are neglected and feedbacks driven by changing
orography are neglected, especially important in regions of rapid tectonic
uplift.
The representation of ice sheets applies Peltier ICE-5G deglaciation ice sheets
(Peltier, 2004), assuming a fixed relationship between global sea-level
reconstructions (derived from benthic oxygen isotopes) and the spatial form
and extent of ice sheets. This approximation neglects the substantial
asymmetry between build-up and decay phases of ice sheets and assumes that
ice sheets were located similarly in all previous Pliocene–Pleistocene
glaciations, which may not have been the case. Particular caution is
therefore essential when applying the climate reconstruction at locations
near the margins of ice sheets.
We apply a downscaling approach because spatial climate gradients can be
critically important for ecosystem dynamics, especially in mountainous
regions which are poorly resolved at native climate model resolution (Rangel
et al., 2018). The downscaling approximation assumes that the lapse rate
within a downscaled grid cell does not change with time, but it does capture
the first-order effect of topographic complexity by assuming a constant
present-day lapse rate. Similarly, the downscaling cannot capture feedbacks
between atmospheric circulation and high-resolution topography, which could
alter the patterns of rain shadowing. However, for many applications, it is
preferable to neglect this second-order feedback rather than to neglect the first-order effect of a rain shadow that could not be resolved at native climate
model resolution (e.g. the Atacama), which downscaling imposes through the
baseline climatology. Other simplifications include the implicit assumptions
of fixed mountain glaciers and ecotone distributions. In short, the
high-resolution reconstructions should not be interpreted as a faithful
reconstruction of high-resolution climate but should serve to introduce a more
realistic degree of spatial variability.
Conclusions and summary
We have used dimensionally reduced emulators of the intermediate-complexity
AOGCM PLASIM-GENIE, downscaled onto high-resolution observed climatology, to
generate a high-resolution transient climate reconstruction of the last 5×106 years. The reconstruction substantially improves on a previous
emulated reconstruction (Rangel et al., 2018) in the following ways.
The underlying climate model is a fully coupled AOGCM. Rangel et al. (2018) used PLASIM-ENTS (Holden et al., 2014), which has a slab ocean and
therefore neglected ocean circulation feedbacks.
The new simulation ensembles considered climate forcing by orbit,
CO2, and ice sheets. Rangel et al. (2018) considered only orbit forcing,
with large-scale adjustments to crudely approximate the effects of CO2
and ice sheets.
We use Gaussian process emulation. Rangel et al. (2018) used linear
regression emulation, which cannot capture complex (non-linear)
relationships between inputs and outputs.
These improvements allow us to provide a global emulation; the previous
emulation was inappropriate for the Northern Hemisphere due to the crude
approximation of the response to ice-sheet forcing. Additionally, we were
able to extend the emulation back to 5×106 years; the previous emulation
was limited by the length of an existing 800 000-year transient GENIE
simulations (Holden et al., 2010) for CO2 and ice-sheet forcing.
Finally, GP emulation provides uncertainty estimates that we show
in Figs. 3 and 4 and can be used to provide a reasonable proxy for model
error, neglected in our single-parameterization boundary condition
ensembles.
The limitations of the reconstruction (see Sect. 9 for details) arise from
the underlying climate model (low-resolution, intermediate-complexity), the
approximated boundary conditions (in particular the use of only five
ice-sheet states), uncertainties in the forcing time series (especially for
sea level and CO2), the assumption of quasi-equilibrium (so that, e.g., millennial variability is neglected) and the limitations of downscaling. We
note that the emulations and associated uncertainty compare favourably to
existing ensembles of simulations with higher-complexity models (Figs. 3
and 4). We note further that reconstructing climates with different forcing
time series is straightforward. Future improvements are anticipated by
including a representation of changing topography. For instance, the Andes
have uplifted by 25 % to 40 % of their 3700 m present-day elevation over the
last 5×106 years (Gregory-Wodzicki, 2000) and Himalayan uplift has been
associated with intensification of the Asian monsoon about 3.6 to 2.6 Myr
ago (Zhisheng et al., 2001). Ensembles that address changing orography, land
sea masks, and ocean gateways will improve the simulated climate and allow
the extension of the emulation further back in time, to periods in which it
would be unreasonable to ignore tectonically driven change.
Code availability
The Supplement contains all of the files needed to build the emulators. PALEO-PGEMv1.0_5M_1Ka.mp4 is an animation of the four bioclimatic variables over 5Ma. PALEO-PGEMv1.0.R is the R code to build and run the emulators. A series of files are inputs to the R code. These are ensemble.dat (the ensemble input design for the BC1/BC2 ensembles), 5000_1000_forcing.dat (time series forcing for 5 Ma at 1 kyr intervals), MH_forcing.dat (Mid-Holocene ensemble forcing), LGM_forcing.dat (Last Glacial Maximum forcing), and area.dat (grid cell areas for area weighting). Two subdirectories contain the simulation data: data (outputs of the BC1 PLASIM-GENIE ensemble) and icedata (outputs of the BC2 PLASIM-GENIE ensemble). Supporting data are included in two spreadsheets: ensemble (supporting calculations for the ensemble design) and 5000ka_forcing (supporting calculations for the time series forcing).
PALEO-PGEMv1.0.R was saved with settings to emulate DJF temperature and
produce a 5 Ma time series using the GP mean prediction (no emulator
uncertainty), 10 principal components, and a power exponential covariance
function. Each of these settings can be changed as documented in the code.
The code outputs the area-weighted average to screen and three data sets to
file: emul.dat (the full spatio-temporal output), mean.dat, and SD.dat (the
mean and standard deviation of the emulated fields, most relevant when code
is set to generate an ensemble, e.g. with MH or LGM forcing).
The supplement related to this article is available online at: https://doi.org/10.5194/gmd-12-5137-2019-supplement.
Author contributions
PBH, NRE, and TFR developed the concept. PBH performed the PLASIM-GENIE
simulations, using boundary conditions developed by GTT. PBH and RDW
developed the GP emulators. TFR and EBP developed the downscaling, with
advice from PBH and NRE. PBH wrote the paper with contributions from
all authors.
Competing interests
The authors declare that they have no conflict of interest.
Financial support
Philip B. Holden and Neil R. Edwards were funded by NERC (grant no. NE/P015093/1). Elisa B. Pereira is supported by a doctorate fellowship from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001.
Review statement
This paper was edited by Didier Roche and reviewed by Michel Crucifix and one anonymous referee.
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