Offline forcing methods for ice-sheet models often make use of an index
approach in which temperature anomalies relative to the present are calculated by
combining a simulated glacial–interglacial climatic anomaly field,
interpolated through an index derived from the Greenland ice-core temperature
reconstruction, with present-day climatologies. An important drawback of this
approach is that it clearly misrepresents climate variability at millennial
timescales. The reason for this is that the spatial glacial–interglacial
anomaly field used is associated with orbital climatic variations, while it
is scaled following the characteristic time evolution of the index, which
includes orbital and millennial-scale climate variability. The spatial
patterns of orbital and millennial variability are clearly not the same, as
indicated by a wealth of models and data. As a result, this method can be
expected to lead to a misrepresentation of climate variability and thus of
the past evolution of Northern Hemisphere (NH) ice sheets. Here we illustrate
the problems derived from this approach and propose a new offline climate
forcing method that attempts to better represent the characteristic pattern
of millennial-scale climate variability by including an additional spatial
anomaly field associated with this timescale. To this end, three different
synthetic transient forcing climatologies are developed for the past
120
The climate history of the late Quaternary is marked by alternating episodes
of growth and decay of Northern Hemisphere (NH) ice sheets on orbital timescales as evidenced by different proxy data
In addition to proxy data, glacial isostatic adjustment (GIA) models have
been used to reconstruct the past temporal evolution of ice sheets
Forward ice-sheet modeling can help overcome the intrinsic limitations of
the GIA technique by directly simulating the paleo-evolution of ice sheets.
Ideally, Earth system models (ESMs) including fully coupled ice-sheet
components are the appropriate tools to simulate the past as well as the
present and future evolution of ice sheets. However, because of their high
computational cost, the long-term simulation of ice sheets generally relies
on simpler tools such as intermediate-complexity climate models coupled to
ice-sheet models
An alternative and even simpler method is to use ice-sheet models forced
offline by a time-varying climatology. These exercises are carried out on
a regular basis, as they are needed to calibrate ice-sheet models, to assess
model sensitivity to different parameters and to compare the sensitivities
of different models. To obtain adequate initial conditions for the ice sheet,
a relatively long spin-up is required, involving one or more glacial cycles
depending on the ice sheets involved. Because of the lack of continuous,
spatially well-distributed proxy data, a synthetic time-varying climatology
is often built based on a combination of climate-model and proxy data and
used to force the ice-sheet model. Often an index approach is followed in
which temperature anomalies relative to the present are calculated by combining
a simulated glacial–interglacial climatic anomaly field, interpolated
through an index derived from the Greenland ice-core temperature
reconstruction, with present-day climatologies. A similar procedure is
applied to precipitation but considering ratios rather than anomalies
Key ice-sheet model and climate forcing parameters. Conversion factor units are meters of water equivalent per positive degree day (mwe/PDD).
Here we illustrate the problems derived from this approach and propose a new
offline climate forcing method that attempts to better represent the
characteristic pattern of millennial-scale climate variability. Ice-core
records
The paper is organized as follows: in Sect.
The model used in this study is the GRISLI ice-sheet model, developed by
Temporal components of the three forcing methods.
GRISLI is a hybrid three-dimensional thermomechanical ice-sheet model
combining the shallow ice approximation
Spatial components of the different methods. The reference climate
is based on the ERA-INTERIM (1981–2010) reanalysis
Synthetic time-varying climatologies are built using three different methods.
All three use a perturbative approach as explained above (Sect.
The first method (hereafter M1) follows the usual index approach used in many
previous studies
The second method (M2) is similar to M1 but the temperature and precipitation
variability are split into two spectral components, corresponding to orbital
and millennial timescales, respectively. The time-varying climatology is now
given by
M2 significantly underestimates the amplitudes of millennial-scale
fluctuations at the NGRIP ice-core location, as compared to the KV
reconstruction (see Fig.
Here,
Finally, in order to keep the same structure as in the previous methods, the
amplification factors are both included within the so-called optimized
indices (
The amplification factors reflect the skill of the climate model to reproduce
the characteristic spectral amplitudes of the KV reconstruction at the NGRIP
site. Since the model tends to underestimate the KV reconstruction,
To evaluate the capability of the different methods to provide a realistic
forcing for the ice-sheet model, the resulting synthetic climatologies should
be compared against reconstructions. However, continuous, high-resolution NH
temperature reconstructions spanning the entire last glacial cycle are
scarce. We now compare the performance of each method in regions where
proxies are available (see locations in Fig.
We first compare the synthetic temperature curves generated in the location
of the NGRIP ice core using each method to the KV reconstruction
(Fig.
We further evaluate the three methods through comparison with available
temperature and precipitation reconstructions derived from speleothems in
central Europe (the Alps) and North America. Time series of SAT in central
Europe show an overall qualitative agreement among all three methods
(Fig. 3b), which reproduce the phasing and timing of millennial-scale climate
variability registered in terrestrial records from the northern European Alps
NH ice-sheet configurations at different stages of the last
glacial–interglacial period as simulated under M3:
Temporal evolution of SAT anomalies (
The lack of continuous reconstructions in NH continental areas hampers the
evaluation of the temperature signal derived from the three methods.
Nonetheless, the synthetic temperature time series obtained at two sites, in
North America and Fennoscandia, are assessed
(Fig.
Finally, in M1 the amplitude of millennial-scale fluctuations is very similar
at both sites as a consequence of the nearly symmetric temperature pattern
around Greenland, with two centers of negative values of similar amplitude
coinciding with the selected sites (Fig.
Temporal evolution of ice volume (
The temporal evolutions of the simulated NH ice sheets that result from
imposing the different forcings to the GRISLI model all show the
characteristic modulation by orbital climate variability over the last
glacial cycle (Fig.
Important differences are found among the three methods. For all ice sheets,
M1 and M3 show the smallest and largest volumes throughout the LGP,
respectively; M2 shows intermediate values between the two. As a consequence,
of all three methods only M3 agrees with the available LGM minus present SLE
reconstructions within their ranges of uncertainties, both for the LIS and
the FIS. As mentioned before, by construction, the climates of M1 and M2 are
identical at orbital timescales and only differ at millennial timescales. The
lower ice volume in M1 relative to M2 is due to the larger amplitude of its
millennial-scale fluctuations, resulting from the large amplitude of its
orbital spatial component. Indeed, the orbital anomalies used by standard
index methods to represent millennial changes are larger than the
millennial-scale anomalies. Thus, the forcing and the response are
overestimated. Although these sometimes lead to smaller temperatures with
respect to the orbital background curve, in general they result in large
positive anomalies that, through enhanced ablation, induce a disruption of
the growth of large ice sheets in the NH. In contrast, at millennial
timescales M2 shows a muted response of ice-volume variations in all ice
sheets as a result of the small amplitude of its millennial-scale component.
Finally, the higher volumes in M3 compared to M2 are a result of tuning to
the lower NGRIP temperature, which results in colder temperatures throughout
most of the LGP in the NH (Fig.
Throughout the LGP, differences in global SLE between the most extreme
ice-volume cases, M1 and M3, are generally larger for the LIS, than for the
FIS. Regarding the evolution of the LIS, M2 resembles M1 more than M3, but
for the evolution of the FIS, M2 resembles M3 more than M1. Around
48
In terms of the extent of NH ice sheets at the LGM, M3 appears to be the best of the three methods, showing the most satisfactory agreement with reconstructions: ICE-5G (Peltier, 2004) for the LIS and DATED-1 (Hughes et al., 2016) for the FIS (Fig. 4c; see also the Supplement). Major deficiencies are found in the southeastern margin of the Scandinavian Ice Sheet (SIS), the southwestern border of the LIS and the northern part of the Cordilleran Ice Sheet (CIS), where the ice extent is underestimated as compared to reconstructions, and northwestern Siberia, where it is overestimated. In M1 and M2, these discrepancies with reconstructions are more evident. Furthermore, in the corridor that separates the CIS and the LIS a significant ice retreat is observed that is absent in M3 (see Supplement).
Finally, the deglaciation shows a different behavior in the three methods.
M1 shows a much more abrupt transition into the Holocene, with ice already
vanishing by the beginning of this period. This is a consequence of the
abrupt temperature evolution in NGRIP that, by construction, in M1 is
extrapolated to the rest of the globe, leading to peak temperatures already
reached at the beginning of the Holocene and subsequently decreasing. In
contrast, M2 and M3 show a smoother temperature evolution at the NH ice-sheet
sites (Fig.
We now focus specifically on M3, which provides the best time-varying
climatology. The time slices of ice thickness and velocities simulated under
M3 provide a consistent picture of the spatial structure of NH ice sheets
throughout the LGP (Fig.
In this study, a new method to force ice-sheet models offline is presented
and compared with the more traditional approach. Three different time-varying
climatologies are developed for the past 120
The time series derived from these methods are compared at several locations
with the available proxy data: the Greenland ice-core record and
reconstructions of temperature and precipitation based on
Note that offline index methods assume that the temperature variability
reconstructed over Greenland is representative of the entire NH, but this
does not mean either that the amplitude or the sign is the same in the whole
NH. This is actually the case in the usual methods but not in our new method,
which is one of the reasons why it represents an improvement. The reason is
that the millennial-scale anomaly pattern introduces its own (spatial)
scaling. The details of this spatial pattern will depend on the particular
climate model used to produce the climate anomaly fields and might well
improve with higher complexity and resolution. Most models agree in showing
that NH temperature changes coevally with Greenland in response to northward
heat transport changes caused by Atlantic meridional
overturning circulation (AMOC) variations, the prevailing paradigm to
explain abrupt glacial climate changes
The different climatologies have a large impact on the development of NH ice
sheets. In these areas, such as North America and Fennoscandia, traditional
methods yield millennial-scale fluctuations of very large amplitude,
comparable to those recorded in Greenland. Improving the representation of
millennial-scale variability by including a stadial–interstadial anomaly
field leads to a strong reduction in the amplitude of millennial-scale
temperature fluctuations by more than 10
The lack of continuous reconstructions in NH continental areas precludes the
evaluation of the temperature time series derived for these regions. However,
the fact that in the traditional method the amplitude of temperature
variations at sites such as the LIS and the FIS is very similar to those of
the Greenland ice-core record strongly suggests that these temperature
fluctuations are overestimated. If the mechanisms behind millennial-scale
variability are transitions between states of reduced AMOC, with
southward-shifted deep water formation
Our results show that the traditional method leads to the lowest ice-volume
values throughout the whole LGP. Indeed, millennial-scale climate variability
enhances NH ice-volume variability on millennial timescales. This leads to an
underestimation of ice volume throughout most of the LGP. Including
millennial-scale patterns (in M2) yields an important increase in ice volume
in all NH ice sheets but especially in the FIS. Additionally improving the
orbital and millennial-scale fields through the scaling is found to increase
it further. Note although sea-level records provide essential information to
interpret past ice-volume variations, continuous highly resolved sea-level
reconstructions are scarce and frequently rely on an insufficient temporal
control. In addition, they generally provide inferences on global sea-level
changes. This complicates the evaluation of our simulated NH ice-volume
time series against the paleorecord. However, the contribution to sea level of
individual ice sheets can be assessed at specific time slices such as the
LGM, for which reconstructions are actually available. Estimates of the SLE
change at the LGM relative to the present
The climate model used to build the present-day, LGM, and interstadial fields
used in this study is an intermediate-complexity model with low spatial
(latitude
In a similar manner, although our ice-sheet model accounts for the surface elevation change feedback on temperature and precipitation, other important climate–ice-sheet feedbacks such as surface albedo changes are not represented. Note, however, that our goal is precisely to improve offline forcing methods, for which most of these feedbacks are inherently absent. It would nevertheless be interesting to investigate this issue further by coupling our ice-sheet model to a regional energy–moisture-balance model where feedbacks such as the ice–albedo feedback, the effect of continentality and the orographic effect on precipitation are better represented.
Finally, the novelty of this work lies in the consideration of an additional climatic pattern associated with millennial-scale climate variability to reconstruct the climate variability of the last glacial–interglacial cycle for the whole NH. Our results reveal that an incorrect representation of the characteristic pattern of millennial-scale climate variability within the climate forcing not only affects NH ice-volume variations at millennial timescales but has consequences for glacial–interglacial ice-volume changes too. Thereby, our new forcing method contributes to clarify the still uncertain role of abrupt glacial climate change in past ice-volume variations, thus shedding light on the evolution of the NH ice sheets. As mentioned above, one aspect that remains to be assessed is the role of the ocean; this should be the focus of future work.
The code used to generate the synthetic climatologies
of this study is based on the equations described within the paper. The
specific scripts are available from the corresponding author upon request.
The variables associated with the three synthetic time-varying climatologies
originating in this study are available via this link:
The supplement related to this article is available online at:
RB carried out the simulations, analyzed the results and wrote the paper. All other authors contributed to the design of the simulations, the analysis of the results and the writing of the paper.
The authors declare that they have no conflict of interest.
This work was funded by the Spanish Ministerio de Economía y Competitividad through project MOCCA (Modelling Abrupt Climate Change, grant CGL2014-59384-R). Rubén Banderas was funded by a PhD thesis grant of the Universidad Complutense de Madrid. Alexander Robinson is funded by the Marie Curie Horizon2020 project CONCLIMA (Grant 703251). Part of the computations of this work were performed in EOLO, the HPC of Climate Change of the International Campus of Excellence of Moncloa, funded by MECD and MICINN. This is a contribution to CEI Moncloa. We would like to thank the two anonymous reviewers for their suggestions and comments, which have contributed to improve the paper. Edited by: Philippe Huybrechts Reviewed by: Petra Langebroek and one anonymous referee