We present a new global reconstruction of seasonal climates at the
Last Glacial Maximum (LGM, 21 000 years BP) made using 3-D variational data
assimilation with pollen-based site reconstructions of six climate variables
and the ensemble average of the PMIP3—CMIP5 simulations as a prior (initial estimate of LGM climate). We
assume that the correlation matrix of the uncertainties in the prior is both
spatially and temporally Gaussian, in order to produce a climate
reconstruction that is smoothed both from month to month and from grid cell
to grid cell. The pollen-based reconstructions include mean annual
temperature (MAT), mean temperature of the coldest month (MTCO), mean
temperature of the warmest month (MTWA), growing season warmth as measured
by growing degree days above a baseline of 5 ∘C (GDD5), mean
annual precipitation (MAP), and a moisture index (MI), which is the ratio of
MAP to mean annual potential evapotranspiration. Different variables are
reconstructed at different sites, but our approach both preserves seasonal
relationships and allows a more complete set of seasonal climate variables
to be derived at each location. We further account for the ecophysiological
effects of low atmospheric carbon dioxide concentration on vegetation in
making reconstructions of MAP and MI. This adjustment results in the
reconstruction of wetter climates than might otherwise be inferred from the
vegetation composition. Finally, by comparing the uncertainty contribution
to the final reconstruction, we provide confidence intervals on these
reconstructions and delimit geographical regions for which the palaeodata
provide no information to constrain the climate reconstructions. The new
reconstructions will provide a benchmark created using clear and defined
mathematical procedures that can be used for evaluation of the PMIP4–CMIP6
entry-card LGM simulations and are available at 10.17864/1947.244 (Cleator et al., 2020b).
Introduction
Models that perform equally well for present-day climate nevertheless
produce very different responses to anthropogenic forcing scenarios through
the 21st century. Although internal variability contributes to these
differences, the largest source of uncertainty in model projections in the
first 3 to 4 decades of the 21st century stems from differences
in the response of individual models to the same forcing (Kirtman et al.,
2013). Thus, the evaluation of models based on modern observations is not a
good guide to their future performance, largely because the observations
used to assess model performance for present-day climate encompass too
limited a range of climate variability to provide a robust test of a model's
ability to simulate climate changes. Although past climate states do not
provide analogues for the future, past climate changes provide a unique
opportunity for out-of-sample evaluation of climate model performance
(Harrison et al., 2015).
At the Last Glacial Maximum (LGM, conventionally defined for modelling
purposes as 21 000 years ago), insolation was quite similar to the present,
but global ice volume was at a maximum, eustatic sea level was close to a
minimum, long-lived greenhouse gas concentrations were lower, and
atmospheric aerosol loadings were higher than today; land surface
characteristics (including vegetation distribution) were also substantially
different from today. These changes gave rise to a climate radically
different from that of today; indeed the magnitude of the change in
radiative forcing between LGM and pre-industrial climate is comparable to
high-emissions projections of climate change between now and the end of the
21st century (Braconnot et al., 2012). The LGM has been a focus for
model evaluation in the Paleoclimate Modelling Intercomparison Project
(PMIP) since its inception (Joussaume and Taylor, 1995; Braconnot et al.,
2007, 2012). The LGM is one of the two “entry card”
palaeoclimate simulations included in the current phase of the Coupled Model
Intercomparison Project (CMIP6) (Kageyama et al., 2018). The evaluation of
previous generations of palaeoclimate simulations has shown that the
large-scale thermodynamic responses seen in 21st century and LGM
climates, including enhanced land–sea temperature contrast, latitudinal
amplification, and scaling of precipitation with temperature, are likely to
be realistic (Izumi et al., 2013, 2014; Li et al., 2013; Lunt et al., 2013; Hill et
al., 2014; and Harrison et al., 2014, 2015). However, evaluation
against palaeodata shows that even when the sign of large-scale climate
changes is correctly predicted, the patterns of change at a regional scale
are often inaccurate and the magnitudes of change often underestimated
(Brewer et al., 2007; Mauri et al., 2014; Perez Sanz et al., 2014; and Bartlein
et al., 2017). The current focus on understanding what causes mismatches
between reconstructed and simulated climates is a primary motivation for
developing benchmark data sets that represent regional climate changes
comprehensively enough to allow a critical evaluation of model deficiencies.
Many sources of information can be used to reconstruct past climates.
Pollen-based reconstructions are the most widespread, and pollen-based data
were the basis for the current standard LGM benchmark data set from Bartlein
et al. (2011). In common with other data sources, the pollen-based
reconstructions were generated for individual sites. Geological preservation
issues mean that the number of sites available inevitably decreases through
time (Bradley, 2014). Since pollen is only preserved for a long time in
anoxic sediments, the geographic distribution of potential sites is biased
towards climates that are relatively wet today. Furthermore, the actual
sampling of potential sites is highly non-uniform, so there are large
geographic gaps in data coverage (Harrison et al., 2016). The lack of
continuous climate fields is not ideal for model evaluation, and so attempts
have been made to generalize the site-based data through gridding,
interpolation, or some form of multiple regression (see e.g. Bartlein et
al., 2011; Annan and Hargreaves, 2013). However, there has so far been no
attempt to produce a physically consistent, multivariable reconstruction
which provides the associated uncertainties explicitly.
A further characteristic of the LGM that creates problems for quantitative
reconstructions based on pollen data is the much lower atmospheric carbon
dioxide concentration, [CO2], compared to the pre-industrial Holocene.
[CO2] has a direct effect on plant physiological processes. Low
[CO2] as experienced by plants at the LGM is expected to have led to
reduced water-use efficiency – the ratio of carbon assimilation to the
water lost through transpiration (Bramley et al., 2013). Most
reconstructions of moisture variables from pollen data, including most of
the reconstructions used by Bartlein et al. (2011), do not take [CO2]
effects into account. Yet several modelling studies have shown that the
impact of low [CO2] around the LGM on plant growth and distribution was
large (e.g. Jolly and Haxeltine, 1997; Cowling and Sykes, 1999; Harrison and
Prentice, 2003; Bragg et al., 2013; Martin Calvo et al., 2014; and Martin Calvo
and Prentice, 2015). A few reconstructions of LGM climate based on the
inversion of process-based biogeography models have also shown large effects
of low [CO2] on reconstructed LGM palaeoclimates (e.g. Guiot et al.,
2000; Wu et al., 2007). The reconstructions of moisture variables in the
Bartlein et al. (2011) data set are thus probably not reliable and likely
to be biased low.
Prentice et al. (2017) demonstrated an approach to correct reconstructions
of moisture variables for the effect of [CO2], but this correction has
not been applied globally. A key side effect of applying this [CO2]
correction is the reconciliation of semi-quantitative hydrological evidence for wet
conditions at the LGM with the apparent dryness suggested by the vegetation
assemblages (Prentice et al., 2017). Similar considerations apply to the
interpretation of future climate changes in terms of vegetational effects.
Projections of future aridity (based on declining indices of moisture
availability) linked to warming are unrealistic, in a global perspective,
because of the counteracting effect of increased water-use efficiency due to
rising [CO2] – which is generally taken into account by process-based
ecosystem models, but not by statistical models, using projected changes in
vapour pressure deficit or some measure of plant-available water (Keenan et
al., 2011; Roderick et al., 2015; and Greve et al., 2017).
In this paper, we use variational data assimilation based on both
pollen-based climate reconstructions and climate model outputs to arrive at
a best-estimate analytical reconstruction of LGM climate, explicitly taking
account of the impact of [CO2]. Variational techniques provide a way of
combining observations and model outputs to produce climate reconstructions
that are not exclusively constrained to one source of information or the
other (Nichols, 2010). We use the uncertainty contributions to the
analytical reconstruction to provide confidence intervals for these
reconstructions and also to delimit geographical regions for which the
palaeodata provide no constraint on the reconstructions. The resulting data
set is expected to provide a well-founded multivariable LGM climate data set
for palaeoclimate model benchmarking in CMIP6.
MethodsPollen-based climate reconstructions
Bartlein et al. (2011) provided a global synthesis of pollen-based
quantitative climate reconstructions for the LGM. The Bartlein et al. (2011)
data set includes reconstructions of climate anomalies (differences between
LGM and recent climates) for six variables (and their uncertainties),
specifically mean annual temperature (MAT), mean temperature of the coldest
month (MTCO), mean temperature of the warmest month (MTWA), growing degree
days above a baseline of above 5 ∘C (GDD5), mean annual
precipitation (MAP), and an index of plant-available moisture (the ratio of
actual to equilibrium evapotranspiration, α). There are a small
number of LGM sites (94) in the Bartlein et al. (2011) data set where model
inversion was used to make the reconstructions of α, and MAP; no
[CO2] correction is applied to these reconstructions. There are no data
from Australia in the Bartlein et al. (2011) data set, and we therefore use
quantitative reconstructions of MAT and another moisture index (MI), the
ratio of MAP to potential evapotranspiration, from Prentice et al. (2017).
Prentice et al. (2017) provide values of MI both before and after correction
for [CO2]; we use the uncorrected values in order to apply the
correction for [CO2] within our assimilation framework. For consistency
between the two data sets, we re-expressed reconstructions of α in
terms of MI via the Fu–Zhang formulation of the Budyko relationship between
actual evapotranspiration, potential evapotranspiration, and precipitation
(Zhang et al., 2004; Gallego-Sala et al., 2016).
The distribution of the site-based reconstructions of climatic
variables at the Last Glacial Maximum. The individual plots show sites
providing reconstructions of (a) moisture index (MI), (b) mean annual
precipitation (MAP), (c) mean annual temperature (MAT), (d) mean temperature
of the coldest month (MTCO), (e) mean temperature of the warmest month
(MTWA), and (f) growing degree days above a baseline of 5 ∘C (GDD5). The original
reconstructions are from Bartlein et al. (2011) and Prentice et al. (2017).
The spatial coverage of the final data set is uneven (Fig. 1). There are
many more data points in Europe and North America than elsewhere. South
America has the fewest (14 sites). The number of variables available at each
site varies; although most sites (279) have reconstructions of at least
three variables, some sites have reconstructions of only one variable (60).
Nevertheless, in regions where there is adequate coverage, the reconstructed
anomaly patterns are coherent, plausible, and consistent among variables.
For this application, we derived absolute LGM climate reconstructions by
adding the reconstructed climate anomalies at each site to the modern
climate values from the Climate Research Unit (CRU) historical climatology
data set (CRU CL v2.0 data set, New et al., 2002), which provides
climatological averages of monthly temperature, precipitation, and cloud
cover fraction for the period 1961–1990 CE. Most of the climate variables
(MTCO, MTWA, MAT, and MAP) can be calculated directly from the CRU CL v2.0
data set. GDD5 was calculated from pseudo-daily data derived from a linear
interpolation of the monthly temperatures. MI was calculated from the CRU
climate variables using the radiation calculations in the SPLASH model
(Davis et al., 2017). For numerical efficiency, we non-dimensionalized all
of the absolute climate reconstructions (and their standard errors) before
applying the variational techniques (for details, see Cleator et al.,
2020a).
Details of the models from the third phase of the Palaeoclimate Modelling Intercomparison Project (PMIP3) that were used for the Last Glacial Maximum (LGM) simulations used to create the prior. Coupled ocean–atmosphere models are indicated as OA; the OAC models have a fully interactive carbon cycle. The resolution in the atmospheric, oceanic, and sea ice components of the models is given in terms of numbers of grid cells in latitude and longitude.
Model nameTypeResolution Year lengthReferenceAtmosphereOceanSea iceCCSM4OA192, 288320, 384320, 384365Gent et al. (2011)CNRM-CM5OA128, 256292, 362292, 362365–366Voldoire et al. (2012)MPI-ESM-POA96, 192220, 256220, 256365–366Jungclaus et al. (2006)MRI-CGCM3OA160, 320360, 368360, 368365Yukimoto et al. (2011)FGOALS-g2OA64, 12864, 12864, 128365Li et al. (2013)COSMOS-ASOOAC96, 48120, 101120, 101360Budich et al. (2010)IPSL-CM5A-LROAC96, 96149, 182149, 182365Dufresne et al. (2013)MIROC-ESMOAC64, 128192, 256192, 256365Watanabe et al. (2011)Climate model simulations
Eight LGM climate simulations (Table 1) from the third phase of the
Palaeoclimate Modelling Intercomparison Project (PMIP3; Braconnot et al.,
2012) were used to create a prior. The PMIP LGM simulations were forced by
known changes in incoming solar radiation, changes in land–sea geography and
the extent and location of ice sheets, and a reduction in [CO2] to 185
ppm (see Braconnot et al., 2012, for details of the modelling protocol). We
used the last 100 years of each LGM simulation. We interpolated monthly
precipitation, monthly temperature, and monthly fraction of sunshine hours
from each LGM simulation and its pre-industrial (PI) control to a common 2∘×2∘ grid. Simulated climate anomalies (LGM minus PI) for each grid
cell were then added to modern climate values calculated from the CRU CL v2.0
data set (New et al., 2002), as described for the pollen-based
reconstructions, to derive absolute climate values. We calculated the
multi-model mean and variance (Fig. 2) across the models for each of the
climate variables to produce the gridded map used as the prior.
Uncertainties associated with the climate prior. The climate is
derived from a multi-model mean of the ensemble of models from the
Palaeoclimate Modelling Intercomparison Project (PMIP) and is shown in
Fig. S1 in the Supplement. The uncertainties shown here are the standard deviation of the
multi-model ensemble values. The individual plots show the variance for the
simulated (a) moisture index (MI), (b) mean annual precipitation (MAP), (c) mean annual temperature (MAT), (d) mean temperature of the coldest month
(MTCO), (e) mean temperature of the warmest month (MTWA), and (f) growing degree
days above a baseline of 5 ∘C (GDD5).
Water-use efficiency calculations
We applied the general approach developed by Prentice et al. (2017) to
correct pollen-based statistical reconstructions to account for [CO2]
effects. The approach as implemented here is based on equations (Appendix A)
that link moisture index (MI) to transpiration and the ratio of
internal leaf to ambient [CO2]. The correction is based on the principle
that the rate of water loss per unit carbon gain is inversely related to
effective moisture availability as sensed by plants. The method involves
solving a nonlinear equation that relates rate of water loss per unit
carbon gain to MI, temperature, and CO2 concentration. The equation is
derived from a theory that predicts the response of the ratio of internal leaf
to ambient [CO2] to vapour pressure deficit and temperature (Prentice
et al., 2014; Wang et al., 2014).
Application of variational techniques
Variational data assimilation techniques provide a way of combining
observations and model outputs to produce climate reconstructions that are
not exclusively constrained to one source of information or the other
(Nichols, 2010). We use the 3-D variational method, described in Cleator et al. (2020a), to find the maximum a posteriori estimate (or analytical
reconstruction) of the palaeoclimate given the site-based reconstructions
and the model-based prior. The method constructs a cost function, which
describes how well a particular climate matches both the site-based
reconstructions and the prior, by assuming the reconstructions and prior
have a Gaussian distribution. To avoid sharp changes in time and/or space in
the analytical reconstructions, the method assumes that the prior temporal
and spatial covariance correlations are derived from a modified Bessel
function, in order to create a climate anomaly field that is smooth both
from month to month and from grid cell to grid cell. The degree of
correlation is controlled through two length scales: a spatial length scale
that determines how correlated the covariance in the prior is between
different geographical areas and a temporal length scale that determines
how correlated it is through the seasonal cycle. The site-based
reconstructions are assumed to have negligible correlations at these scales of space
and time. The maximum a posteriori estimate is found by using the
limited memory Broyden–Fletcher–Goldfarb–Shanno method (Liu and Nocedal,
1989) to determine the climate that minimizes the cost function. A 1st-order
estimate of the analysis uncertainty covariance is also computed.
An observation operator based on calculations of the direct impact of [CO2]
on water-use efficiency (Sect. 2.3) is used in making the analytical
reconstructions. The prior is constructed as the average of eight LGM
climate simulations (Sect. 2.2). We use an ensemble of different model
responses to the same forcing to provide a series of physically consistent
possible states, which can be viewed as perturbed responses and provide the
variance around the climatology provided by the ensemble average. The prior
uncertainty correlations are based on a temporal length scale (Lt) of 1
month and a spatial length scale (Ls) of 400 km. Cleator et al. (2020a) have
shown that a temporal length scale of 1 month provides an adequately smooth
solution for the seasonal cycle, both using single sites and over multiple
grid cells, as shown by the sensitivity of the resolution matrix (Menke,
2012; Delahaies et al., 2017) to changes in the temporal length scale.
Consideration of the spatial spread of variance in the analytical
reconstruction shows that a spatial length scale of 400 km also provides a
reasonable reflection of the large-scale coherence of regional climate
change.
Uncertainties in the analytical reconstructions. These
uncertainties represent a combination of the uncertainty in the site-based
reconstructions and the grid-based variance in the prior and the global
variance from the prior.
We generated composite variances on the analytical reconstructions (Fig. 3) by combining the covariances from the site-based reconstructions and
the prior. There are regions where all of the models systematically differ
from the site-based reconstructions (Harrison et al., 2015), but, nevertheless,
the inter-model variability is low, which would lead to a very small
contribution to the composite uncertainties from the prior. We therefore
calculated the uncertainty of the prior from an equal combination of the
global uncertainty, the average variance between each grid cell, and local
uncertainty (the variance between the different models). The reliability of
the analytical reconstructions was assessed by comparing these composite
covariances with the uncertainties in the prior. We masked out cells where
the inclusion of site-based reconstructions does not produce an improvement
of > 5 % from the prior. Since this assessment is based on a
change in the variance, rather than absolute values, this masking removes
regions where there are no pollen-based reconstructions or the pollen-based
reconstructions have very large uncertainties.
Analytically reconstructed climate, where areas for which the
site-based data provide no constraint on the prior have been masked out. The
individual plots show reconstructed (a) moisture index (MI), (b) mean annual
precipitation (MAP), (c) mean annual temperature (MAT), (d) mean temperature
of the coldest month (MTCO), (e) mean temperature of the warmest month
(MTWA), and (f) growing degree days above a baseline of 5 ∘C (GDD5). The
anomalies are expressed relative to the long-term average (1960–1990) values
from the Climate Research Unit (CRU) historical climatology data set (CRU CL
v2.0 data set, New et al., 2002).
Results
The analytical reconstructions (Fig. 4) show an average year-round cooling
of -7.9∘C in the northern extratropics. The cooling is larger
in winter (-10.2∘C) than in summer (-4.7∘C). A
limited number of grid cells in central Eurasia show higher MAT. Temperature changes are more muted in the tropics,
with an average change in MAT of -4.7∘C. The cooling is
somewhat lower in summer than winter (-3.7∘C compared to -4.1∘C). Reconstructed temperature changes were slightly smaller in
the southern extratropics, with average changes in MAT of -3.0∘C, largely driven by cooling in winter.
Changes in moisture-related variables (MAP, MI) across the Northern
Hemisphere are geographically more heterogeneous than temperature changes.
Reconstructed MAP is greater than present in western North America (204 mm) but less than present in eastern North America (−276 mm). Most of Europe is
reconstructed as drier than present (-386 mm), the same for eastern Eurasia
(-118 mm) and the Far East (-88 mm). The patterns in MI are not identical to
those in MAP, because of the influence of temperature on MI, but regional
changes are generally similar to those shown by MAP. Most of the tropics are
shown as drier than present while the Southern Hemisphere extratropics are
wetter than present, in terms of both MAP and MI.
Impact of [CO2] on reconstructions of moisture-related
variables. The individual plots show (a) the change in moisture index (MI)
and (b) the change in mean annual precipitation (MAP) compared to the
original pollen-based reconstructions for the LGM before (circles) and after
(crosses) the physiological impacts of [CO2] on water-use efficiency
are taken into account. The third plot (c) shows the relative difference between
MI and MAP as a result of [CO2], shown as the percentage difference
between the no-[CO2] and [CO2] calculations.
The reconstructed temperature patterns are not fundamentally different from
those shown by Bartlein et al. (2011), but the analytical data set provides
information for a much larger area (755 % increase), thanks to the imposition of consistency among different climate variables, and of smooth variations both in space and through the seasonal cycle, by the method. There are
systematic differences, however, between the analytical reconstructions and
the pollen-based reconstructions in terms of moisture-related variables
(MAP, MI) because the analytical reconstructions take account of the direct
influence of [CO2] on plant growth. The physiological impact of [CO2] leads
to analytical reconstructions indicating wetter-than-present conditions in
many regions (Fig. 5a, b); for example in southern Africa,
several of the original pollen-based reconstructions show no change in MAP
or MI compared to present, but the analytical reconstruction shows wetter
conditions than present. In some regions, incorporating the impact of
[CO2] reverses the sign of the reconstructed changes. Part of northern
Eurasia is reconstructed as being wetter than present, despite pollen-based
reconstructions indicating conditions drier than present (in terms of both
MAP and MI), as shown by Fig. S3. The relative changes in MAP and MI are
similar across all sites (Fig. 5c), implying that the analytically
reconstructed changes are driven by changes in precipitation rather than
temperature.
Discussion
Variational data assimilation techniques provide a way of combining
observations and model outputs, taking account of the uncertainties in both, to
produce a best-estimate analytical reconstruction of LGM climate. These
reconstructions extend the information available from site-based
reconstructions both spatially and through the seasonal cycle. Our new
analytical data set characterizes the seasonal cycle across a much larger
region of the globe than the data set that is currently being used for
benchmarking of palaeoclimate model simulations. We therefore suggest that
this data set (Cleator et al., 2020b) should be used for evaluating the
CMIP6–PMIP4 LGM simulations.
Some areas are still poorly covered by quantitative pollen-based
reconstructions of LGM climate, most notably South America. More
pollen-based climate reconstructions would provide one solution to this
problem – and there are many pollen records that could be used for this
purpose (Flantua et al., 2015; Herbert and Harrison, 2016; and Harrison et al.,
2016). There are also quantitative reconstructions of climate available from
individual sites (e.g. Lebamba et al., 2012; Wang et al., 2014; Loomis et
al., 2017; and Camuera et al., 2019) that should be incorporated into future
data syntheses. It would also be possible to incorporate other sources of
quantitative information, such as chironomid-based reconstructions (e.g.
Chang et al., 2015), within the variational data assimilation framework.
One of the benefits of the analytical framework applied here is that it
allows the influence of changes in [CO2] on the moisture
reconstructions to be taken into account. Low [CO2] must have reduced
plant water-use efficiency, because at low [CO2] plants need to keep
stomata open for longer in order to capture sufficient CO2. Statistical
reconstruction methods that use modern relationships between pollen
assemblages and climate under modern conditions (i.e. modern analogues,
transfer functions, and response surfaces; see Bartlein et al., 2011) cannot account for such effects. Climate reconstruction methods
based on the inversion of process-based ecosystem models can do so (see e.g.
Guiot et al., 2000; Wu et al., 2007, 2009; and Izumi and Bartlein,
2016) but are critically dependent on the reliability of the vegetation
model used. Most of the palaeoclimate reconstructions have been made by
inverting some version of the BIOME model (Kaplan et al., 2003), which makes
use of bioclimatic thresholds to separate different plant functional types
(PFTs). As a result, reconstructions made by inversion show “jumps” linked
to shifts between vegetation types dominated by different PFTs, whereas, as
has been shown recently (Wang et al., 2017), differences in water-use
efficiency of different PFTs can be almost entirely accounted for by a
single equation, as proposed here. Sensitivity analyses show that the
numerical value of the corrected moisture variables (MI, MAP) is dependent
on the reconstructed values of these variables but is insensitive to
uncertainties in the temperature and moisture inputs (Prentice et al.,
2017). The strength of the correction is primarily sensitive to [CO2], but
the LGM [CO2] value is well constrained from ice-core records. The response
of plants to changes in [CO2] is nonlinear (Harrison and Bartlein,
2012), and the effect of the change between recent and pre-industrial or
mid-Holocene conditions is less than that between pre-industrial and glacial
conditions. Nevertheless, it would be worth taking the [CO2] effect on
water-use efficiency into account in making reconstructions of interglacial
time periods as well.
The influence of individual pollen-based reconstructions on the analytical
reconstruction of seasonal variability, or the geographic area influenced by
an individual site, is crucially dependent on the choice of length scales.
We have adopted conservative length scales of 1 month and 400 km, based on
sensitivity experiments made for southern Europe (Cleator et al., 2020a).
These length scales produce numerically stable results for the LGM, and the
paucity of data for many regions at the LGM means that using fixed,
conservative length scales is likely to be the only practical approach.
However, in so far as the spatial length scale is related to atmospheric
circulation patterns, there is no reason to suppose that the optimal spatial
length scale will be the same from region to region. The density and
clustering of pollen-based reconstructions could also have a substantial
effect on the optimal spatial length scale. A fixed 1-month temporal length
scale is appropriate for climates that have a reasonably smooth and
well-defined seasonal cycle, in either temperature or precipitation.
However, in climates where the seasonal cycle is less well defined, for
example in the wet tropics, or in situations where there is considerable
variability on sub-monthly timescales, other choices might be more
appropriate. For time periods such as the mid-Holocene, which have an order
of magnitude more site-based data, it could be useful to explore the
possibilities of variable length scales.
We have used a 5 % reduction in the analytical uncertainty compared to
prior uncertainty to identify regions where the incorporation of site-based
data has a negligible effect on the prior as a way of masking out regions
for which the observations have effectively no impact on the analytical
reconstructions. The choice of a 5 % cut-off is arbitrary, but little
would be gained by imposing a more stringent cut-off at the LGM given that
many regions are represented by few observations. A more stringent cut-off
could be applied for other time intervals with more data. We avoid the use
of a criterion based on the analytical reconstruction showing any
improvement on the prior because this could be affected by numerical noise
in the computation. Alternative criteria for the choice of cut-off could be
based on whether the analytical reconstruction had a reduced uncertainty
compared to the pollen-based reconstructions or could be derived by a
consideration of the condition number used to select appropriate length
scales.
There have been a few previous attempts to use data assimilation techniques
to generate spatially continuous palaeoclimate reconstructions. Annan and
Hargreaves (2013) used a similar multi-model ensemble as the prior and the
pollen-based reconstructions from Bartlein et al. (2011) to reconstruct MAT
at the LGM. However, they made no attempt to reconstruct other seasonal
variables, either independently or through exploiting features of the
simulations (as we have done here) to generate seasonal reconstructions.
Particle filter approaches (e.g. Goosse et al., 2006; Dubinkina et al.,
2011) produce dynamic estimates of palaeoclimate, but particle filters
cannot produce estimates of climate outside the realm of the model
simulations. Our 3-D variational data assimilation approach has the great
merit of being able to produce seasonally coherent reconstructions
generalized over space, while at the same time being capable of producing
reconstructions that are outside those captured by the climate model,
because they are not constrained by a specific source (Nichols, 2010). This
property is of particular importance if the resulting data set is to be used
for climate model evaluation, as we propose.
We define e as the water lost by transpiration (E) per unit carbon gained by
photosynthesis (A). This term, the inverse of the water-use efficiency, is
given by
e=E/A=1.6D/((1-χ)ca),
where D is the leaf-to-air vapour pressure deficit (Pa), ca is the
ambient CO2 partial pressure (Pa), and χ is the ratio of
internal leaf CO2 partial pressure (ci) to ca. An
optimality-based model (Prentice et al., 2014), which accurately reproduces global
patterns of χ and its environmental dependencies inferred from leaf
δ13C measurements (Wang et al., 2017), predicts that
χ=(Γ*/ca)+(1-Γ*/ca)ξ/(ξ+√D),
and
ξ=√(β(K+Γ*)/1.6η*),
where Γ* is the photorespiratory compensation point of C3
photosynthesis (Pa), β is a constant (estimated as 240 by Wang et al.,
2017), K is the effective Michaelis–Menten coefficient of Rubisco (Pa), and
η* is the ratio of the viscosity of water (Pa s) at ambient
temperature to its value at 25 ∘C. Here K depends on the
Michaelis–Menten coefficients of Rubisco for carboxylation (KC) and
oxygenation (KO), and on the partial pressure of oxygen O (Farquhar et al.,
1980); it is calculated by the following:
K=KC(1+O/KO).
Standard values and temperature dependencies of KC, KO,
Γ*, and η* are assigned as in Wang et al. (2017).
The moisture index MI is expressed as
MI=P/Eq,Eq=∑n(Rn/λ)s/(s+γ),
where P is annual precipitation, Rn is net radiation for month n,
λ is the latent heat of vaporization of water, s is the derivative
of the saturated vapour pressure of water with respect to temperature
(obtained from a standard empirical formula also used by Wang et al., 2017), and
γ is the psychrometer constant. We assume that values of MI reconstructed
from fossil pollen assemblages, using contemporary pollen and climate data
either in a statistical calibration method or in a modern-analogue search,
need to be corrected in such a way as to preserve the contemporary
relationship between MI and e, while taking into account the change in e that
is caused by varying ca and temperature away from contemporary values.
The sequence of calculations is as follows. (1) Estimate e and its derivative
with respect to temperature (∂e/∂T) for the contemporary
ca and climate, using Eqs. (A1)–(A3) above. (2) Use e and
∂e/∂T to calculate ∂D/∂T given the palaeo-ca (measured in ice-core data) and temperature (reconstructed from
pollen data), via a series of analytical equations that relate ∂e/∂T to ∂D/∂T and hence to s. (3) Use the new
∂D/∂T and relative humidity (from the PMIP3 average) to derive a new value of s. (4) Recalculate MI using
a palaeo-estimate of Rn (modelled as in Davis et al., 2017) and the new
value of s.
Data availability
The gridded data for the LGM reconstructions are
available from 10.17864/1947.244 (Cleator et al., 2020b); the code used to generate these
reconstructions is available from 10.5281/zenodo.3719332 (Cleator et al., 2020c).
The supplement related to this article is available online at: https://doi.org/10.5194/cp-16-699-2020-supplement.
Author contributions
All authors contributed to the design of the study; ICP developed the theory
underlying the CO2 correction; SC implemented the analyses. SC and SPH
wrote the first version of the paper, and all authors contributed to
the final version.
Competing interests
The authors declare that they have no conflict of interest.
Special issue statement
This article is part of the special issue “Paleoclimate Modelling Intercomparison Project phase 4 (PMIP4) (CP/GMD inter-journal SI)”. It is not associated with a conference.
Acknowledgements
Sean F. Cleator was supported by a UK Natural Environment Research Council (NERC)
scholarship as part of the SCENARIO Doctoral Training Partnership. Sandy P. Harrison
acknowledges support from the ERC-funded project GC 2.0 (Global Change 2.0:
Unlocking the past for a clearer future; grant number 694481). I. Colin Prentice
acknowledges support from the ERC under the European Union Horizon 2020
research and innovation programme (grant agreement no: 787203 REALM). This
research is a contribution to the AXA Chair Programme in Biosphere and
Climate Impacts and the Imperial College initiative on Grand Challenges in
Ecosystems and the Environment (ICP). Nancy K. Nichols is supported in part by the NERC
National Centre for Earth Observation (NCEO). We thank PMIP colleagues who
contributed to the production of the palaeoclimate reconstructions. We also
acknowledge the World Climate Research Programme Working Group on Coupled
Modelling, which is responsible for CMIP, and the climate modelling groups
in the Paleoclimate Modelling Intercomparison Project (PMIP) for producing
and making available their model output. For CMIP, the U.S. Department of
Energy, Program for Climate Model Diagnosis and Intercomparison, provides
coordinating support and led development of software infrastructure in
partnership with the Global Organization for Earth System Science Portals.
The analyses and figures are based on data archived at CMIP on 12 September 2018.
Financial support
This research has been supported by the Natural Environment Research Council (grant no. 1859127), the European Research Council (grant no. GC2.0 (694481)), and the European Research Council (grant no. REALM (787203))
Review statement
This paper was edited by Masa Kageyama and reviewed by Michel Crucifix and two anonymous referees.
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