ESDEarth System DynamicsESDEarth Syst. Dynam.2190-4987Copernicus PublicationsGöttingen, Germany10.5194/esd-9-413-2018Earth system model simulations show different feedback strengths of the terrestrial carbon cycle under glacial and interglacial conditionsDifferent feedback strengths of the terrestrial carbon cycleAdloffMarkusmarkus.adloff@bristol.ac.ukhttps://orcid.org/0000-0001-7515-6702ReickChristian H.ClaussenMartinhttps://orcid.org/0000-0001-6225-5488Max Planck Institute for Meteorology, Bundesstraße 53, 20146 Hamburg, GermanyMeteorological Institute, Centrum für Erdsystemforschung und Nachhaltigkeit (CEN), Universität Hamburg, Grindelberg 5, 20144 Hamburg, Germanynow at: School of Geographical Sciences, University of Bristol, University Road, BS8 1SS, UKMarkus Adloff (markus.adloff@bristol.ac.uk)25April20189241342526June201716March20189March20183July2017This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://esd.copernicus.org/articles/9/413/2018/esd-9-413-2018.htmlThe full text article is available as a PDF file from https://esd.copernicus.org/articles/9/413/2018/esd-9-413-2018.pdf
In simulations with the MPI Earth System Model, we study the feedback between
the terrestrial carbon cycle and atmospheric CO2 concentrations under
ice age and interglacial conditions. We find different sensitivities of
terrestrial carbon storage to rising CO2 concentrations in the two
settings. This result is obtained by comparing the transient response of the
terrestrial carbon cycle to a fast and strong atmospheric CO2
concentration increase (roughly 900 ppm) in Coupled Climate Carbon Cycle Model Intercomparison Project (C4MIP)-type simulations
starting from climates representing the Last Glacial Maximum (LGM) and
pre-industrial times (PI). In this set-up we disentangle terrestrial
contributions to the feedback from the carbon-concentration effect, acting
biogeochemically via enhanced photosynthetic productivity when CO2
concentrations increase, and the carbon–climate effect, which affects the
carbon cycle via greenhouse warming. We find that the carbon-concentration
effect is larger under LGM than PI conditions because photosynthetic
productivity is more sensitive when starting from the lower, glacial
CO2 concentration and CO2 fertilization saturates later. This
leads to a larger productivity increase in the LGM experiment. Concerning the
carbon–climate effect, it is the PI experiment in which land carbon responds
more sensitively to the warming under rising CO2 because at the
already initially higher temperatures, tropical plant productivity
deteriorates more strongly and extratropical carbon is respired more
effectively. Consequently, land carbon losses increase faster in the PI than
in the LGM case. Separating the carbon–climate and carbon-concentration
effects, we find that they are almost additive for our model set-up; i.e. their synergy is small in the global sum of carbon changes. Together,
the two effects result in an overall strength of the terrestrial carbon cycle
feedback that is almost twice as large in the LGM experiment as in the PI
experiment. For PI, ocean and land contributions to the total feedback are of
similar size, while in the LGM case the terrestrial feedback is dominant.
Introduction
At the Last Glacial Maximum (21 000 years before present, referred to as LGM hereafter), global mean surface temperature was 4 to 5 ∘C
lower than today . Vegetation was not only less widespread
but primary productivity was also smaller . This
was the consequence of the lower CO2 concentrations during that time (about 200 ppm less than today), acting physically via the
resulting lower temperatures (greenhouse effect) and biogeochemically via
the reduced photosynthetic activity due to less available CO2 in the
atmosphere (reduced CO2 fertilization) .
From measuring isotopic carbon composition in ocean sediment cores
and the isotopic oxygen composition of air
trapped in ice cores , it has been estimated that
terrestrial carbon storage was several hundred gigatons less than today. This
is consistent with less primary productivity, the effect of which on carbon storage
must have been larger than the reduction in soil respiration by the lower
temperatures . This describes how CO2
shaped the terrestrial carbon cycle at the LGM. But the terrestrial carbon
cycle also has an effect on the atmospheric CO2 concentration. Hence, one
may wonder whether the strength of this feedback was different from today in
glacial times. This is what we investigate in the present paper by performing
Earth system simulations for conditions of the Last Glacial Maximum and
pre-industrial (PI) times. Indeed one could ask this question also for the
oceanic carbon cycle component, but this paper focuses on the terrestrial
component, which will be shown to dominate the difference in feedback
strength between the two Earth system states.
To quantify the feedback between carbon cycle and climate,
introduced two sensitivities characterizing the
change in stored carbon (terrestrial and/or oceanic) due to different
drivers: biogeochemical effects of changed atmospheric CO2
concentration, called the carbon-concentration effect measured by
the β sensitivity (PgCppm-1), and climate change,
called the carbon–climate effect measured by the γ
sensitivity (PgCK-1). For the recent climate, these sensitivities
have been quantified in numerous Earth system simulations, especially within
the international Coupled Climate Carbon Cycle Model Intercomparison Project
(C4MIP) see, e.g.,. Attempts to
quantify carbon cycle sensitivities for perturbations of climates from even
earlier times are rare. The few observational studies relate reconstructions
of atmospheric CO2 concentrations to reconstructions of temperature
seefor a review, but the resulting “observed”
sensitivity estimates of atmospheric CO2 concentration to temperature
typically involve the combined carbon-concentration and carbon–climate effect
and thus neither measure β nor γ as defined by
. An exception is the study by ,
who considered temperature and CO2 reconstructions for the last
millennium before the industrial revolution: their estimate should be a good
proxy for γ since during this period the changes in atmospheric
CO2 concentration were only a few parts per million so that the
carbon-concentration effect should be negligible. The resulting γ
sensitivity turns out to vary in time showing values compatible with the low
end of the range of values found in the C4MIP studies for the recent climate.
obtained similar values for γ from Earth system
simulations of the last millennium. The compatibility of those γ
values for the last millennium with those from the C4MIP for the recent climate may not be that surprising since the climates differ only moderately.
On the other hand, the C4MIP values result from simulations that perturb
the PI climate dramatically (≈ quadrupling of atmospheric CO2
concentration), while those for the last millennium are obtained from
historical climate and CO2 variations observed byand
simulated by , that are
rather moderate so that it is unclear what such a comparison of γ
values actually means. To ensure comparability, in the present study we adopt
the C4MIP methodology to determine carbon cycle sensitivities for past
and recent times.
While there have been attempts to determine climate sensitivity for various
climates of the deep past see, e.g., , similar studies
for carbon sensitivities are apparently missing. Nevertheless, for the
climate during the LGM studied here, the underlying carbon-concentration and
carbon–climate effects have been isolated in simulations to understand their
separate importance for shaping the geographical distribution of vegetation
as compared to today e.g. . While in these
studies it was sufficient to simulate time slices for past and recent times,
transient simulations are needed to determine carbon cycle sensitivities that
could be compared to C4MIP values. In the present study we employ a fully
coupled general circulation model including dynamic vegetation for transient
simulations starting either from a climate state representing the LGM or from
PI conditions and forced by a strong increase in atmospheric CO2.
Letting the CO2 act either physically or biogeochemically, we isolate
the individual contributions from the carbon-concentration and carbon–climate
effects to changes in the terrestrial carbon budgets. Using this C4MIP-type experiment design, we quantify their contribution not only by computing
β and γ for land carbon but also by performing a factor
analysis following to investigate in particular the
additivity of the two effects, which it is a precondition to obtain from those
two sensitivities the feedback strength.
The paper is organized as follows. First we lay out the design of our
simulation experiments. Next, in Sect. , we describe the
mathematical framework used for our factor and feedback analysis. The
analysis of the simulation results starts in Sect.
with a description of the two initial climate states representing the LGM and
PI conditions (1850 AD). This is preparation for the analysis of the transient
simulation in Sect. , which contains the main
results of our investigation. By applying the factor and feedback analysis we
demonstrate that the intensity of the considered feedback is very different
for the Last Glacial Maximum and the recent climate and identify the underlying
mechanisms explaining the observed differences in system behaviour. The paper
concludes with a critical discussion of our results.
Experiment set-up
To quantify the feedback between carbon cycle and atmospheric CO2
concentrations, we combine the C4MIP experiment design Box
6.4 in the variant of concentration-driven simulations with
a factor separation following . Technically, we proceed
by investigating the reaction in the climate and carbon cycle to a prescribed
strong rise in atmospheric CO2. More precisely, we perform a set of four
simulations called ctrl, clim, conc
and full. While for the quantification of the feedbacks by the
C4MIP approach, only three of these simulations are needed, by using the
full set of all four simulations we are able to demonstrate that – in
contrast to other models –
the linearity assumption implicit to the C4MIP feedback analysis is
indeed justified for our model. Starting from a control simulation
(ctrl) performed at constant CO2 concentration, three
transient simulations forced by rising CO2 concentrations are
performed. In the first of those transient simulations (conc) only
the carbon-concentration effect is active, which means that the rising
CO2 concentration is “seen” only by the photosynthesis code of the
model, while the radiation code constantly “sees” the CO2 value of
the control simulation. Conversely, in the second transient simulation
(clim) only the carbon–climate effect is active; i.e. only the
radiation code sees the rising CO2 concentrations but not the
photosynthesis model. In the third simulation (full) both effects
are simultaneously active. These simulations are run once for LGM and once
for PI conditions. In the following, we will use the term “experiment”
to refer to one of the two cases LGM or PI. “Simulation” will refer to one
of the four model runs ctrl, clim, conc or
full.
CO2 change scenarios as prescribed for the LGM and PI experiments: starting from 185 ppm (Last Glacial
Maximum, green line) and starting from 285 ppm (pre-industrial, red line).
Differences between the LGM and PI climates obtained in the respective ctrl simulations: (a) difference in
global mean near-surface temperatures and (b) difference in plant water availability. Here the values in the LGM state are
substracted from the values in the PI state. Land areas that are covered by ice in the LGM but not in the PI equilibrium state show
soil humidity differences >0.4.
The CO2 concentrations for the ctrl simulations of the two experiments are 185 ppm (LGM) and 285 ppm
(PI), which are also the initial conditions for the respective transient simulations. Experiments were performed with Earth-System Model of the Max Planck
Institute (MPI-ESM; see below). In fact, we performed only the LGM experiment for this study since we could use published MPI-ESM Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations (called
piControl, esmFdbk1, esmFixClim1 and 1pctCo2) for our purpose that were performed for PI conditions
with the same model version. The LGM simulations were initialized from restart files of the MPI-ESM CMIP5 Last Glacial Maximum spin-up
experiment (1800 simulation years long), extended by another 200 years with dynamic vegetation now switched on. The PI
simulations used for our study were initialized from a spin-up experiment covering more than 3000 years. For the transient
simulations clim, conc and full, the same atmospheric CO2 concentration increase is imposed over
a period of 150 years in both experiments (see Fig. ), acting differently in the three simulations as
explained above. The forcing for our LGM experiment is obtained by reducing the standard PI CO2 forcing by 100 ppm to
account for lower glacial CO2 concentrations while preserving the rate of change. Because CO2 concentrations thereby
increase by the same amount, the different reaction of the Earth system to the CO2 rise in the two experiments should mostly be
attributable to the different initial conditions, i.e. the glacial–interglacial atmospheric CO2 offset and the particular
characteristics of the initial climates. The distribution of ice sheets is prescribed for the appropriate LGM and PI conditions and is
kept constant in all simulations.
The experiments are conducted with the MPI-ESM using the version described in .
The MPI-ESM consists of the atmosphere component ECHAM6 and the ocean
component MPIOM, both including submodels for simulating the land and ocean
carbon cycles. Because atmospheric CO2 concentrations are prescribed
in our experiments, the oceanic and terrestrial carbon cycles are decoupled
so that changes in the ocean carbon cycle are irrelevant for terrestrial
carbon reservoirs that are the main interest here; nevertheless oceanic carbon
fluxes play a role in calculating the overall carbon cycle feedback in our
study and the physical ocean remains an important component of the climate
dynamics affecting also the land carbon cycle. The land component JSBACH comprises the DYNVEG model for simulation of natural changes in the
geographical distribution of vegetation controlled by competition and wind
and fire disturbances and the BETHY model
for simulation of the fast biochemical and biophysical
processes of the biosphere, in particular photosynthetic production that is
simulated following the Farquhar model for C3 plants and the
Collatz model for C4 plants. Vegetation is represented by
eight plant functional types that differ in phenology and physiology and
interact dynamically seefor an evaluation of the present
implementation of dynamic biogeography. There is no
anthropogenic land cover change considered in the experiments here.
Terrestrial carbon dynamics are calculated with the CBALANCE carbon submodel of JSBACH , representing vegetation, litter and soils by seven
carbon pools, where the temperature dependence of heterotrophic respiration is
modelled by a Q10 formula and turnover rates are in addition dependent on soil
humidity. The oceanic biogeochemistry model HAMOCC
calculates sea–air gas exchange, water column processes and sediment
dynamics. CO2 exchange between sea and air is calculated with
a temperature-dependent rate based on the thermodynamic disequilibrium at the
interface. Carbon is then cycled as organically fixed carbon, dissolved
inorganic carbon and calcium carbonate in the water column and sediments.
Temperature-, nutrient- and light-dependent biological cycling of carbon within
the water column is represented by an extended NPZD model
; inorganic carbon cycling is based on , using updated
chemical constants by .
Analysis framework
Here we introduce the mathematical framework for analysing our simulations in
the next sections. First we describe how we apply the factor separation
method by to separate the relative contributions of the
carbon-concentration and carbon–climate effects to the overall changes in
terrestrial carbon reservoirs. In the remainder of the section we describe
the mathematical framework to disentangle the oceanic and atmospheric
contributions to the overall carbon cycle feedback, as well as the
contributions of those two effects to the feedback. This feedback framework
was originally introduced by and further discussed
by . We apply it here in the variant with prescribed
atmospheric CO2Box 6.4.
We apply the factor separation method of as follows. Let
CL denote the total land carbon. The pure effects of the
carbon-concentration and carbon–climate effects are individually quantified
by the differences
ΔCL,conc(t):=CL,conc(t)-C‾L,ctrlΔCL,clim(t):=CL,clim(t)-C‾L,ctrl,
where the indices of the right-hand side CL values refer to the simulations from which the values were obtained, while the indices
of the ΔCL values at the left-hand side refer to the effect considered. The time dependence t appears only for the values
from transient simulations but not for values from the control simulations which enter our calculations as mean values (indicated as
a bar over the symbol). In addition, we quantify the “synergy” between the carbon-concentration and the carbon–climate effects, which
is that part of the land carbon storage difference between the full and ctrl simulation that cannot be explained by
a linear addition of the individual effects:
ΔCL,syn(t):=(CL,full(t)-C‾L,ctrl)-(ΔCL,conc(t)+ΔCL,clim(t)).
Note that in this way all separate factors sum up to the land carbon change in the full simulation:
ΔCL,full(t)=ΔCL,conc(t)+ΔCL,clim(t)+ΔCL,syn(t).
For the feedback analysis we consider the following differences in near-surface temperature and atmospheric CO2 concentration
that develop in the transient simulations:
ΔTclim(t):=Tclim(t)-T‾ctrlΔcc(t):=cc(t)-ccctrl.
The concentration of atmospheric CO2 is denoted here by “cc” and measured in ppm CO2. Since cc(t) is the same for
all transient simulations of a particular experiment, the index specifying the simulation has been omitted. With these definitions one
can now introduce the two land carbon sensitivities
βL(t):=ΔCL,conc(t)Δcc(t)γL(t):=ΔCL,clim(t)ΔTclim(t).βL (PgCppm-1) measures how strongly land carbon is affected in the conc simulation by changes in
atmospheric CO2; since in the conc simulation only the carbon-concentration effect is active, βL measures the
strength of this effect alone. Analogously, γL (PgCK-1) measures how strongly land carbon is affected by
temperature changes in the clim simulation; because in this simulation only the carbon–climate effect is active, it represents
the strength of this effect alone. Similar sensitivities can be defined for ocean carbon but they will not be needed in this study.
In addition to βL and γL we will need the sensitivity of temperature to increasing CO2 concentrations in
our simulations below, known as temperature sensitivity (Kppm-1) :
α(t):=ΔTclim(t)Δcc(t).
Note that in this framework α, βL and γL are time dependent – a point that will be further discussed below.
To introduce a measure for the feedback strength, the global carbon balance needs to be considered. Since the CO2 concentration is prescribed in our simulations, atmospheric carbon is not affected by ocean–atmosphere or land–atmosphere carbon fluxes; i.e. the
global carbon budget is not closed. But one can diagnose how much external CO2 emissions into the atmosphere would be needed to
close the global carbon budget. Considering our full simulation, the prescribed change in atmospheric carbon must match the imagined
external carbon emissions Iext(t) minus the carbon uptake by ocean and land ΔCOL,full(t):
ΔCA(t)=Iext(t)-ΔCOL,full(t).
Assuming that ocean and land carbon uptake are proportional to the increase in atmospheric CO2, one can define the
proportionality factor f(t) by
ΔCOL,full(t)=:-f(t)ΔCA(t),
where the reason for introducing a minus sign here will become clear below. With
this, one obtains from Eq. ()
ΔCA(t)=A(t)Iext(t),withA(t)=11-f(t).A(t) is called the airborne fraction compare, e.g.,.
If atmospheric carbon content would not be prescribed, A(t) would describe
how much of the carbon Iext(t) added to the atmosphere would
remain in it. Following , from the viewpoint of feedback
analysis A(t) is the “gain” of the feedback: for A(t) larger/smaller than 1
the feedback is positive/negative; i.e. the forcing Iext(t)
induces, via Eq. (), additional carbon fluxes
into/out of the atmosphere. In Eq. () the gain of the
feedback is completely determined by the value of f(t), which – also
following – is called the “feedback factor”. Note that the
sign in Eq. () is chosen such that
a positive/negative feedback corresponds to a positive/negative sign of
f(t).
In the present study we focus on the terrestrial contribution to the carbon
cycle feedback. This contribution is obtained as follows. Splitting ΔCOL,full(t) in Eq. () into the
separate contributions ΔCL,full(t) from land and ΔCO,full(t) from ocean, one can define individual land and ocean
feedback factors
ΔCO,full(t)=:-fO(t)ΔCA(t)ΔCL,full(t)=:-fL(t)ΔCA(t)
so that
f(t)=fO(t)+fL(t).
Hence, the individual feedback factors from ocean and land contribute additively to the global feedback factor.
To disentangle the contributions of the carbon-concentration and the
carbon–climate effect to fL(t), we assume that the synergy
term in Eq. () is small compared to the others. Then one
can express the carbon change in the full simulation induced by the
combined action of the two effects by summing the carbon changes induced by
the individual effects diagnosed in the simulations conc and
clim. Using the definitions for α, βL and
γL from above, and noting that atmospheric carbon content
and atmospheric CO2 concentration are related via the conversion
factor m=2.12Pgppm-1p. 471, one thus finds
fL(t)=-α(t)γL(t)+βL(t)m.
Here the first term quantifies the contribution from the carbon–climate effect, while the second does so for the carbon-concentration effect.
Please note that the feedback considered here is different from that
originally considered by or in the C4MIP
study : besides the fact that we focus on the
feedbacks induced by terrestrial processes only, the more important
difference to our study is that considered only
the feedback induced by the carbon–climate effect (see
, , Eq. 8b,
, , Eq. 1, or
, , Eq. 17), while in our
study, following Eq. 16, we quantify the feedback
induced by the carbon–climate and carbon-concentration feedback
together (see our Eq. ). Please note also that there is
confusion in the literature concerning the names gain and feedback
factor; in our study we follow the naming convention of ,
who highlighted this confusion.
Vegetation cover and carbon storage in the LGM and PI ctrl simulations. Vegetation cover is given as fraction of grid
cell covered with vegetation, and carbon storage is given in kgCm-2.
Comparison of the simulated LGM and PI equilibrium states
Here we compare key climate and carbon variables from the LGM and PI
ctrl simulations that are the initial states for the transient
simulations analysed in the next sections. Globally, mean near-surface
temperatures are 4.5 K colder in the LGM state than in the PI state, but locally temperatures differ by 20 K and more (see
Fig. ). Compared to PI, more water is available for
vegetation growth in the LGM state, especially in the tropics and subtropics.
This plant water availability is measured here in terms of the relative
amount of water above the wilting point in the root zone of the soil, a value of
1 indicating optimal moisture levels and 0 indicating that photosynthesis is
inhibited by water scarcity. Inland glaciers extend throughout most of North
America and northern Europe in the LGM state, and the sea level is
considerably lower, leading to a different geography, especially in the
Bering Strait and the Malay Archipelago. On a global scale, less area is
covered by vegetation and dense vegetation is restricted to the tropical zone
(compare Fig. ). In the PI state, vegetation reaches far
more into the extratropics and the midlatitudes are more densely covered by
vegetation. Terrestrial carbon reservoirs are larger in the PI experiment
almost everywhere (see Fig. ). Globally, terrestrial carbon
reservoirs contain 1986 PgC in the LGM and 3041 PgC in
the PI state. Our difference in carbon storage (1055 PgC) matches
the difference of 1030±625PgC in non-permafrost land carbon
obtained by from combining model simulations
with carbon and oxygen isotope data from sediment and ice cores; note that
changes in permafrost carbon are not part of our simulations.
Climatic changes in the full simulation (continuous lines), clim simulation (dashed lines) and the
conc simulation (dotted lines) due to rising CO2 concentrations in the LGM experiment (red) and PI experiment
(black). Panel (a) shows the globally averaged change in near-surface temperature and (b) that in plant water availability.
Change in terrestrial carbon storage (PgC) in the full simulations (black curves) and split into factors
(coloured curves) as computed from Eqs. () and () for (a) the LGM
experiment and (b) the PI experiment.
Reaction of the Earth system to rising CO2 concentration under different boundary conditions
The climate system reacts differently to rising CO2 concentrations
under LGM and PI boundary conditions. Figure shows
changes in global mean near-surface temperature and plant water availability
in the transient simulations. Due to rising CO2 concentrations,
global mean near-surface temperature increases in the clim and
full simulations while plant water availability decreases. Both of
these changes are larger in the LGM experiment. The similarity of temperature
changes in the clim and full simulations shows that the
carbon-concentration and synergistic effects do not considerably affect
global mean near-surface temperature. Nevertheless, also the
carbon-concentration effect creates a small global warming towards the end of
both experiments, as can be seen from the curves of the conc
simulations. explained this by less evapotranspiration
under increased CO2 concentrations. The radiative effect of increased
stomatal closure has been shown by previous studies, e.g.
. The influence of the carbon-concentration effect on
other physical variables, however, is more important for the terrestrial
carbon dynamics. For example, plant water availability, the second most
important environmental constraint on most terrestrial carbon fluxes in the
model, rises in the global average due to increased water use efficiency in
connection with the carbon-concentration effect and decreases due to higher
evapotranspiration losses under the higher temperatures as a consequence of
the carbon–climate effect. Climate change dominates plant water availability
changes in the full simulation, but a clear influence of the
carbon-concentration effect and their synergies on plant water availability
is also apparent.
Sensitivities βL and γL to the
carbon-concentration and carbon–climate effect, respectively, and temperature
sensitivity α in the LGM (blue) and the PI experiment (red). Values are computed as a 20-year average around the
indicated data point.
Figure shows the change in terrestrial carbon storage in the transient simulations. Overall, the
carbon-concentration effect increases terrestrial carbon storage in response to the rising CO2 concentration in both
experiments (see the curves ΔCL,conc). This effect is stronger in the LGM than in the PI experiment. Carbon reservoir
changes due to the carbon–climate effect are negative and of similar size in the two experiments (see curves ΔCL,clim). In both experiments, synergies of the two effects are small in the global integral (see curves ΔCL,syn). This shows that linear additivity of the carbon–climate and carbon-concentration effects can be assumed on the
global scale for our experiments, even for the large climate perturbations considered here. This is important in the following because
by this additivity one can separate the individual contributions of the two effects to the feedback strength by means of
Eq. () (see the discussion there).
Dependence of gross assimilation per square metre leaf area on
ambient CO2 concentration at 20 ∘C leaf
temperature according to the implemented photosynthesis model for C3 plant physiology. Abbreviations stand for
individual vegetation types: TET for tropical evergreen trees, TDT for tropical deciduous trees, EET for extratropical evergreen trees,
EDT for extratropical deciduous trees, RGS for raingreen shrubs,
DCS for deciduous shrubs and C3G for C3 grasses.
From Fig. it becomes clear that the same absolute increase in atmospheric CO2 concentration triggers
different reactions of terrestrial carbon storage in corresponding simulations of the LGM and PI experiments. This is also reflected in
the terrestrial carbon cycle sensitivities as shown in Fig. where the sensitivity values for the LGM and PI
experiments are presented as a function of simulation time. In the following, before discussing the strength of the carbon cycle
feedback, first the sensitivities and their temporal development will be studied separately.
The carbon-concentration effect
Initially βL increases in both experiments but the increase is steeper under glacial conditions. This stronger
carbon-concentration effect in the LGM experiment is mostly due to the lower CO2 concentrations: in both experiments,
photosynthesis is initially carboxylation rate limited. In other words, in both experiments the fraction of available radiative energy
that the plants are able to use to build up organic matter is initially limited by low atmospheric CO2 concentrations. This
initial CO2 limitation is lifted by increasing CO2 concentrations, which leads to increasing primary productivity that
allows for the extension of vegetation and increasing terrestrial carbon storage. This mechanism becomes obvious from
Fig. , which shows the dependence of the primary production rate on CO2 concentration calculated directly from
the equations for C3 photosynthesis, which dominates global natural productivity, implemented in JSBACH. At low ambient CO2
concentrations, productivity increases steeply with rising CO2, but its sensitivity gets smaller at higher CO2
concentrations due to the convex nature of the underlying functionality. In our experiments the carbon-concentration effect on
productivity differs most substantially in the tropics, where temperatures are similar but the lower LGM ambient CO2
concentration makes productivity more sensitive to CO2 increases in the glacial setting. Additionally, vegetation has more room
to expand and can generally grow denser in the glacial tropics than under the drier pre-industrial conditions where tropical forests
are more regularly perturbed by wild fires.
Figure a shows that, after 30 to 40 years, the
increase of βL slows down and its values eventually start
to decrease. attribute this behaviour to the different
response time of primary production and biomass decomposition. While
productivity increases almost instantaneously with rising CO2
concentration, biomass decomposition initially remains unchanged and
increases only when after a temporal delay of the order of the lifetime of
plants the additional carbon from higher plant productivity reaches the
litter and soil carbon reservoirs. Additionally the carbon-concentration
effect becomes less effective at high productivity levels because the carbon
density of living vegetation is reaching upper limits. In fact, the amount of
carbon allocatable to biomass carbon reservoirs is limited in JSBACH to
account for a down-regulation of productivity in mature vegetation. But the sensitvity of productivity to ambient CO2 also changes:
Fig. shows a transition point from high to low
dependence on CO2 changes. Below the transition point photosynthesis
is carboxylation rate limited, while beyond the transition point it is
limited by a lack of radiation (see any textbook on photosynthesis).
Accordingly, as long as CO2 availability stays to be the main
limitation for productivity, the carbon-concentration effect of rising
CO2 concentration leads to large increases in productivity. In our
experiments, the prescribed CO2 concentration rise is, however, large
enough to reach a point where insolation becomes more limiting to
productivity than CO2 availability. From that transition point on,
the effectivity of the carbon-concentration effect saturates. In the PI
experiment ambient CO2 concentration reaches that point of saturation
earlier than in the LGM experiment, leading to a shorter period in the PI
experiment where primary productivity is limited by CO2 availability
and thus highly sensitive to rising CO2 concentrations.
The carbon–climate effect
The sensitivity γL grows increasingly negative in both experiments (see Fig. b) and
increasingly larger in absolute value in the PI experiment than in the LGM experiment. Although γL values are
clearly different in the two experiments, the overall terrestrial carbon reservoir changes in the clim simulations, from which
the γL values are computed (see Eq. ), are almost similar (compare
Fig. ). The reason for this is that the temperature sensitivity α also varies between the two
experiments. Throughout the simulation α is larger in the LGM experiment. The higher temperature sensitivity and the lower
carbon cycle sensitivity γL partially compensate for differences between the PI and LGM cases as is seen from
Fig. d where the product αγL is plotted; it is this combination of sensitivities that
determines the strength of the carbon–climate effect (compare Eq. ). Thereby, the carbon–climate effect differs
much less between the LGM and PI case than the carbon-concentration effect discussed above.
Sensitivity of net primary productivity (NPP) and soil respiration, Rh, to the carbon–climate effect.
These sensitivities (ΔNPP/ΔT and ΔRh/ΔT) are computed from the clim simulation by
first integrating NPP and Rh over the particular region (tropics, extratropics) and over the full simulation period and then dividing
by the temperature change in this region. ΔRh/ΔNPP is the quotient of the two sensitivities. “Tropics”
refers here to the latitudinal belt between 30∘ S and 30∘ N and “extratropics” to the remaining part of the
globe. Here, ΔNPP and ΔRh are considered positive for plant carbon uptake and soil carbon loss,
respectively.
To understand the processes behind the different γL sensitivity in the two experiments, it is useful to analyse first how
climate change induces carbon losses differently in the tropics and extratropics. Table lists the
change in soil respiration ΔRh and net primary productivity ΔNPP per degree temperature change as well as their ratio
separately for tropics and extratropics in the two clim simulations. In both simulations this ratio is smaller than 1 in the
tropics (carbon fluxes into land reservoirs change more than fluxes into the atmosphere) but larger than 1 in the extratropics (carbon
fluxes into the atmosphere change more than fluxes into land carbon reservoirs), indicating a very different reaction of the carbon
cycle under climate change in these two regions. In the tropics, net primary productivity and soil respiration decrease (see Table 1),
indicating that living conditions deteriorate. This has two reasons: firstly, it gets drier so that plant productivity and also soil
decomposition decrease. Secondly, the already hot tropical climate is getting even hotter so that physiological limitations are reached
more frequently, deteriorating plant productivity by damaging the photosynthetic apparatus (implemented as “heat inhibition” in
JSBACH). The reduction in NPP is much larger than the reduction in soil respiration; hence, in the tropics land carbon losses are mostly
driven by reduced plant productivity. In the extratropics the situation is different: values of NPP and soil respiration (see Table 1)
both rise under the warming climate because physiological processes speed up. But since ultimately soil respiration is fed from NPP,
the considerably larger increase in soil respiration cannot be a result of the enhanced carbon input. The explanation, instead, is
the enhanced decomposition of soil carbon that had accumulated in those vast cold boreal areas already in the control simulation from which
the transient simulations are initialized. Hence, in the extratropics land carbon losses are mostly driven by the enhanced soil respiration
of “old” carbon.
Having identified the major drivers for carbon losses in the tropics and extratropics, one can now understand why the sensitivity
γL is larger in the PI than in the LGM experiment. In the tropics reduced plant productivity is the major driver, and
productivity is more sensitive in the PI than the LGM experiment (see Table ) because growth conditions
deteriorate from already initially drier and hotter levels. In the extratropics the enhancement of soil respiration was found to be the
major driver, and soil respiration reacts more sensitively in the PI than in the LGM experiment (see
Table ) because vegetation extends much farther north under the warmer conditions and in the absence of ice
sheets, going along with vastly more extratropical old soil carbon. Hence, both in the tropics and in the extratropics the land
carbon cycle is more sensitive to climate change in the PI experiment.
While our model set-up allows us to study the reaction of active carbon
reservoirs to perturbations, it does not include inert carbon reservoirs
which could be activated under a strong forcing (i.e. permafrost soils). This
might be particularly important for the comparison of γL
between the LGM and the PI state since estimate
that there was a considerably larger amount of inert carbon stored on land at
the LGM than in the Holocene. Therefore, it has to be stressed that the
sensitivities found in this study do only consider active carbon reservoirs.
Feedback strength fL computed from Eq. () for the terrestrial carbon cycle in the LGM and the
PI experiment.
Feedback strength of the terrestrial carbon cycle
The carbon–climate and the carbon-concentration effect cause a feedback of the terrestrial carbon cycle to rising atmospheric
CO2 concentrations. The constantly negative values of the strength fL of this feedback (see Fig. )
demonstrate that it dampens the effect of the forcing so that less carbon is left in the atmosphere than emitted. Accordingly, the
feedback is negative in both experiments. From the beginning of the simulations, the feedback strength grows increasingly negative in
both experiments, a trend that reverses later on with an earlier minimum in the PI experiment. This reflects the different development
of βL that dominates the feedback strength for both PI and LGM (compare
values of βL and αγL in
Fig. ). The dominance of βL is particularly visible towards the end of the simulations, where the timing
of the reversal of the trends in fL match those in βL
(compare Fig. ). The constantly higher absolute
values of fL in the LGM setting show that the feedback is much stronger
under LGM conditions, especially towards the end of the
simulations. Because βL is dominating fL, the stronger terrestrial LGM feedback is also explained by the mechanisms
identified in Sect. to cause the higher LGM sensitivity to the carbon-concentration effect.
Discussion and conclusion
In the present study we investigated in simulations how the terrestrial carbon cycle feedback differs between pre-industrial (PI) times
and during the Last Glacial Maximum (LGM). This was done by separating the contributions from the carbon-concentration and
carbon–climate effects that induce this feedback in C4MIP-type simulations. These simulations starting either at PI or LGM
conditions are rather artificial, since the CO2 forcing scenario used to probe the feedbacks neither resembles the atmospheric
CO2 changes during the Holocene nor is it realistic for recent times (compare Fig. ). But they are not meant
to be historically realistic. Instead, such artificial scenarios have been introduced to facilitate the comparison of the carbon cycle
feedback across different models . In our study we adopted this approach for a comparison of this feedback between
different climate states.
An important question for the applicability of the C4MIP-type
feedback analysis is the additivity of the two effects for global land carbon
storage because only then can the feedback strength be properly split into
separate contributions from the two effects seeand our discussion in
Sect. . Our factor separation analysis
revealed that their synergy is rather small for both the
PI and LGM case, meaning that we can indeed consider the two effects
independently to understand the simulated feedback behaviour. Concerning this
additivity models seem to behave differently: reported
significant deviations from additivity for the HadCM3LC model.
Terrestrial carbon sensitivities βL and γL, associated feedback factor fL,
as well as the global feedback factor f that includes the oceanic feedback (see Eq. ) from our
simulations for PI and LGM, as well as their published CMIP5 model range for PI. Our values (columns PI and LGM) are taken as their
value after 140 years of simulation. The CMIP5 model range is taken from , considering only models without
nitrogen cycle. The CMIP5 ranges for fL and f have been computed using the published CMIP5 sensitivities in
Eq. () and its ocean analogue together with Eq. (). Because the intermodel
range for α is not given in , αs were calculated from the gain g^E provided
in Fig. 9 in .
LGM exp.PI exp.CMIP5βL (PgCppm-1)2.191.420.74 to 1.46γL (PgCK-1)-53.0-68.6-30.1 to -88.6fL-0.87-0.48-0.07 to -0.48f-1.27-0.81-0.42 to -0.85
Generally, the values of the carbon sensitivities βL and
γL are time dependent (compare
Fig. ), but for easier comparison they are usually
reported taking their values at the end of the simulation period see, e.g., . The respective values from our simulations are given
in Table , together with their CMIP5 intermodel
range. Since we used the same data from
MPI-ESM for the analysis of PI conditions that entered the CMIP5 study by , one should expect
that published values for βL and γL
should be similar. This is indeed true for βL, for which we
find 1.42 PgCppm-1 while Table 2 find
1.46 PgCppm-1. But for γL we calculate
-68.6 PgCK-1 while they report
-83.2 PgCK-1. We attribute this apparent inconsistency to
differences in the way we and compute sensitivities: while
we use as a reference mean values from the control simulation (see
Eqs. and ), we
guess that use as a reference the value from the first year
of the respective transient simulation. Thereby, the resulting sensitivity
values are not only sensitive to random climate variations at the end of the
simulations (which are typically smaller than changes from the strong
forcing) but also sensitive to such variations at their beginning. For the
considered sensitivities, this effect should be the largest for temperature that
varies at much shorter timescales than carbon stocks. Accordingly,
βL values should be less sensitive to the way they are
computed and this may explain why our βL values are
similar but γL values differ.
For our further considerations it is interesting to see how our LGM carbon sensitivities relate to published PI values. In view of the
technical complications just mentioned, such a comparison makes sense only for βL. We see from
Table that our LGM βL is considerably larger than the PI value of any CMIP5 model. This may be
taken as an indication that our result for differences in βL between PI and LGM is even robust against uncertainties in
representing climate and carbon cycle in models. Since, as we discussed in Sect. , the terrestrial feedback
strength, as measured by the feedback factor fL, is dominated by the contribution from βL (compare also
Eq. ), it is clear that for LGM and PI the feedback is dominated by the carbon-concentration effect. Hence, also
the much larger LGM feedback factor fL – almost twice the PI value – should be a robust result from our study.
So far, we have concentrated our study on the terrestrial part of the Earth system, but it is interesting to consider for a moment also
the oceanic contributions to the feedback to discuss the relevance of our results for the carbon cycle feedback in the Earth system as
a whole. Our simulations have been performed also with the ocean carbon cycle being active. Accordingly, one can calculate from our
simulations also the ocean feedback factor fO (see Eq. ). A basic property of the global feedback
strength is that ocean and land contributions to the overall feedback factor f are additive (compare
Eq. ). Obtaining in this way the global feedback strength, one sees from the values in
Table that in our simulations the terrestrial component dominates the global feedback in the LGM case,
while both contributions are of approximately equal size for pre-industrial climate.
As discussed in Sect. and , the difference in carbon sensitivities between the LGM and the PI
experiments comes mostly from the different initial conditions of these experiments. But there is also a strong dependence on the
strength of the CO2 forcing. For example, the difference in βL depends largely on whether the CO2 reaches values
high enough to produce a switch from carboxylation-limited assimilation to radiation-limited assimilation. Additionally, bioclimatic
limits of vegetation, model-specific maximum productivity rates, the choice of the global value for the wilting point and the assumed
maximum vegetation density introduce limitations to the system that shape the behaviour of terrestrial carbon storage in the
model. Such limitations should also exist in reality but are hard to quantify.
Besides the dependence on the forcing scenario, the calculated sensitivity parameters are also time dependent. This is due to the fact
that the Earth system's response to the imposed forcing is not entirely instantaneous. Many physical and biogeochemical processes react
on longer timescales (e.g. plant and ecosystem growth and inertia in heat and carbon reservoirs), which also interact and thereby
complicate the system's response. This simultaneous dependence of the α, β and γ values on system state and forcing
is well known . Accordingly, these sensitivity metrics do not characterize an Earth system state as such but only a combination of initial state and forcing scenario. Hence, to isolate their state dependence one must consider simulations
with similar forcing. This is the reason why in our study we subjected the LGM and PI state to the same increase in CO2.
To conclude, the present study has demonstrated that C4MIP-type simulations can be used to understand why the Earth system may react
differently to rising CO2 concentrations under LGM and PI conditions. In the two experiments performed here for LGM and PI
conditions, the terrestrial biosphere and associated land carbon dynamics show a clear, climate-state-dependent transient reaction to
increasing CO2 concentrations. More precisely, under conditions of the Last Glacial Maximum, the terrestrial carbon flux
balance is more sensitive to the carbon-concentration effect than under pre-industrial conditions. This is due to the lower CO2
concentration in the LGM initial state that allows for a larger productivity increase under CO2 concentration rise. The
carbon–climate effect, in contrast, is larger under PI conditions, which is caused by higher initial temperatures and larger amounts of
extratropical terrestrial carbon in the PI initial state. As a consequence of this behaviour, the terrestrial feedback is stronger for
LGM than PI conditions.
The model code is publicly available after registration at
http://www.mpimet.mpg.de/en/science/models/mpi-esm (MPI, 2018).
Simulation data are available on request from the authors.
The study was led by MA who also performed the simulations and data analysis. All authors contributed
to the design of the study and the manuscript.
The authors declare that they have no conflict of
interest.
Acknowledgements
We would like to thank Irina Fast and the DKRZ team for their technical
support and Gitta Lasslop for her careful comments on the final version of
our draft. Additionally, we would like to thank our editor Christoph Heinze
and the three anonymous reviewers as well as Peter Rayner for their
constructive comments and suggestions. Their critical assessments helped us
to significantly improve our manuscript, especially regarding the theoretical
framework of the feedback analysis.The article
processing charges for this open-access publication were
covered by the Max Planck Society.
Edited by: Christoph Heinze
Reviewed by: Peter Rayner and three anonymous referees
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