BGBiogeosciencesBGBiogeosciences1726-4189Copernicus GmbHGöttingen, Germany10.5194/bg-12-835-2015Recent changes in the global and regional carbon cycle: analysis of first-order diagnosticsRaynerP. J.prayner@unimelb.edu.auhttps://orcid.org/0000-0001-7707-6298StavertA.ScholzeM.https://orcid.org/0000-0002-3474-5938AhlströmA.AllisonC. E.https://orcid.org/0000-0002-7796-6917LawR. M.https://orcid.org/0000-0002-7346-0927School of Earth Sciences, University of Melbourne, Melbourne, AustraliaCSIRO Oceans and Atmosphere Flagship, Melbourne, AustraliaDepartment of Physical Geography and Ecosystem Science, Lund University, SwedenP. J. Rayner (prayner@unimelb.edu.au)11February201512383584429May201425June201417November20148January2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://www.biogeosciences.net/12/835/2015/bg-12-835-2015.htmlThe full text article is available as a PDF file from https://www.biogeosciences.net/12/835/2015/bg-12-835-2015.pdf
We analyse global and regional changes in CO2 fluxes using
two simple models, an airborne fraction of anthropogenic emissions
and a linear relationship with CO2 concentrations. We show
that both models are able to fit the non-anthropogenic (hereafter
natural) flux over the length of the atmospheric concentration
record. Analysis of the linear model (including its
uncertainties) suggests no significant decrease in the response of the
natural carbon cycle. Recent data points rather to an increase. We apply the same linear diagnostic to
fluxes from atmospheric inversions. Flux responses show clear
regional and seasonal patterns driven by terrestrial uptake in the
northern summer. Ocean fluxes show little or no linear
response. Terrestrial models show clear responses, agreeing
globally with the inversion responses, however the spatial structure
is quite different, with dominant responses in the tropics rather
than the northern extratropics.
Introduction
The interplay of various timescales in anthropogenically forced
climate change is both problematic and fascinating. It is problematic
since temperature responses integrate radiative forcing and radiative
forcing by greenhouse gases integrates sources. Thus changes in source
processes can, if sustained, drive surprisingly large changes in the
trajectory of temperature.
For the most important greenhouse gas, CO2, this double
integration gives a respectable utility to an inherently fascinating
question: are there changes in the underlying processes of the carbon
cycle? The utility comes from the natural carbon cycle's role in
mitigating the anthropogenic perturbation by absorbing about half the
anthropogenic input of carbon to the atmosphere
. Optimal policy response relies on projections of
this uptake so changes in the natural carbon cycle have direct policy
implications.
We have had conceptual models for these changes for many years. For the
ocean these are predominantly changes in chemical buffering
and changes in physical circulation
. For terrestrial uptake there are many
countervailing factors at work such as extension of the high latitude
growing season and the varied responses of
terrestrial ecosystems to changes in temperature and rainfall.
combined many of these responses into a reasonably
complete model of the earth system and projected a strong reduction in
carbon uptake with the land becoming a net source around 2050.
showed that this was one of many possible
responses. Such studies naturally prompted observational tests of the
important processes such as the reaction of the Amazon forest to
drying . Several studies have suggested sink
saturation or reduction in various regions such as
for the North Atlantic, for the Southern Ocean and
for European forests.
Meanwhile the 5-decade record of atmospheric CO2 raises the
possibility of detecting changes in the results of these processes
directly. This was first taken up by who suggested
that sinks were saturating, at least relative to emissions. This was
made more explicit by who attempted to isolate the
anthropogenic and natural contributions to long-term changes in
CO2 growth-rate. The statistical significance of the trends
noted by and was challenged by
. also pointed out difficulties in
interpreting changes in the relationship between emissions and
growth-rate in terms of the response of the system. They used a linear
perturbation model and developed diagnostics of the airborne fraction
from it. We will use the same model but, rather than diagnosing the
behaviour of a yet simpler model (airborne fraction) we will use
it to diagnose the behaviour of inferred
or modelled fluxes from more complex systems.
Along with this controversy over long-term changes in the sink
efficiency, different questions have emerged on more recent changes.
used a combination of the atmospheric growth-rate,
anthropogenic inputs and an ocean model to posit an abrupt change in
the terrestrial uptake around 1988. and
pointed out that, since the early 2000s, the growth-rate
of atmospheric CO2 had failed to keep pace with the
acceleration in reported fossil fuel use. Their conclusion was to
question the timing of this acceleration.
Some confusion has
arisen between the two discussions of changes in airborne fraction.
In general they address different time-scales.
To provide context for subsequent discussions, Fig.
plots the history of anthropogenic carbon fluxes and the growth-rate
in atmospheric CO2. It also shows the predicted growth-rate
from two simple models to be discussed later. Data is taken from
. We see a clear increase in anthropogenic fluxes and
a much noisier increase in the atmospheric growth-rate. We also see an
increasing divergence between these curves, connoting an increasing
uptake. This uptake is a response to a range of perturbations,
atmospheric CO2 itself, nutrient input, land management and
land-use change and doubtless many others. Here we analyse this uptake
as a simple linear response to CO2 concentration. We use
CO2 concentration as a surrogate for forcings with a similar
time course, that is we do not attempt to separate CO2 forcing
of the response from other drivers. Rather we ask whether there has
been significant departure from this linear response evident in
recent years. Further we analyse regional contributions to this
linear response. This provides a simple diagnostic of model
responses which can be compared with inverse estimates of regional
fluxes. Our focus is on the change of uptake rather than its mean
value. Such analysis of trends requires reasonably long records and is
hence less certain at regional than global scales.
Anthropogenic inputs (red) and atmospheric growth rate
(black) from . Anthropogenic inputs include both
fossil and land-use. The dotted line shows the predicted
atmospheric growth-rate from the airborne fraction model while the
dashed line shows the growth-rate from the β-model.
The outline of the paper is as follows: Sect.
describes the simple diagnostics we use and the data.
Section analyses the global record in terms
of this diagnostic. Section applies the same
diagnostic to regional fluxes from inverse estimates while Sect.
applies it to terrestrial models. Section points
out some of the caveats and implications in the preceding analysis and
Sect. summarizes the main points.
Methods and toolsDefining the carbon budget
Our aim is to analyse the response of parts of the carbon budget to
changes in forcing. We must therefore define which terms of the carbon
budget we consider. We start with the decomposition used by the
Global Carbon Project (GCP) ∂M∂t=Ffossil+FLUC-Fland-Focean,
where M is the mass of carbon in the atmosphere, FLUC is
the flux due to land-use change (LUC) and all other fluxes have their usual
meanings. Throughout the paper we will talk of uptakes by land and
ocean so we have not followed the usual convention of writing fluxes
with a single direction (towards the atmosphere or surface).
We will also frequently combine the two anthropogenic fluxes as
Fanthro=Ffossil+FLUC.
Some terms in Eq. () are ambiguous, especially the
partition between FLUC and Fland. This point
is discussed by . When discussing global budgets we
will follow the GCP definitions. The atmospheric inversion studies we
draw on do not separate these two fluxes. Globally we will correct
Fland by FLUC from the GCP. When we consider
regional budgets we will ascribe changes in the combined flux to
Fland and discuss the implications of this approximation.
Two models
We follow in using two models for the change in
atmospheric CO2 concentration in response to anthropogenic
inputs. The provenance of these two models and the relationship
between them is thoroughly described by so we will only
summarize them here.
Airborne fraction model
This expresses the change in the atmospheric mass of carbon as
∂M∂t=αFanthro,
where α is known as the airborne fraction.
Airborne
fraction can also be quoted relative to Ffossil.
Combining this with Eq. () we see
Fland+Focean=(1-α)Fanthro.
It is important to remember that Eq. () represents
a relationship following from mass conservation rather than a causal
relationship between anthropogenic inputs and contemporaneous uptakes.
It is hard to conceive a mechanism that would link the three fluxes in
Eq. ().
The β-model
An alternative to the airborne fraction model is to parameterize
CO2 uptakes as a linear function of CO2 concentration
or, equivalently, CO2 mass
. Thus we write
Fland+Focean=β(M-M0),
where M is the mass of CO2 in the atmosphere and M0 is the
background or equilibrium mass of CO2 in the atmosphere. Given the
near-equilibrium of the preindustrial carbon cycle evident from the
data of and we often use the
preindustrial value of M for M0. With our focus in this paper on
changes rather than mean values we are not interested in M0 so we
simplify Eq. () to
Fland+Focean=βM+F0.β has
units of yr-1 and plays the role of an inverse residence time
for excess carbon against the processes of land and ocean uptake.
Substituting Eq. () into Eq. () yields
∂M∂t=Fanthro-βM-F0.
With independent data available on Fanthro and M it
is possible to estimate β and F0 using standard statistical
techniques such as linear regression. Below we apply this technique to
flux estimates at several scales and from several sources. Although we
consider some aspects of uncertainty in the calculation we have not
applied our diagnostics to the ensembles of results available in
intercomparisons of forward or inverse models.
Global responses
In this section we compare the behaviour of the two models introduced
in Sect. . We use the data from the Global Carbon
Project to estimate α from
Eq. () and β from Eq. (). Data in
comes from many sources. M (and consequently
∂M∂t) come from concentration measurements
of CO2 at South Pole and Mauna Loa before 1980 and a range of
marine boundary layer sites thereafter. Ffossil is derived
from inventories from the Carbon Dioxide Information Analysis Center.
FLUC and Focean come from a combination of
inventories and models. Fland is derived as a residual.
We use
the standard maximum likelihood least squares formulation so that
x=KJTR-1y,
where x is the vector of unknowns we seek, y the data,
J the Jacobian matrix mapping x to y and
R the uncertainty covariance for y. K is
given by
K=[JTR-1J]-1.
After some simplification the uncertainty covariance for x is
given by
C(x)=K-1.
For the α-model J=Fanthro and y=∂M∂t while for the β-model
J=1M and y=Fanthro-∂M∂t. For the β-model we include
a constant term in the inversion (see Eq. ). This is mathematically the uptake
when M=0. Physically it represents uptakes which do not vary with
M, e.g. those caused by reforestation. It also contributes to the
mean uptake over a period. We stress that we are not here concerned
with the mean uptake over the whole or part of the study period.
For R there are two contributions, data uncertainties and
modelling errors. The uncertainties in y are quoted in
as 5 % for Ffossil,
0.5 PgCyr-1 for FLUC and 0.7 or
0.2 PgCyr-1 for ∂M∂t before
or after 1970. We add these quadratically. Growth-rate uncertainty
dominates before 1970 while FLUC is the largest
contributor later. The root mean square value of the uncertainty is
0.69PgCyr-1. The errors due to the simplicity of
the models can only be calculated once we have performed the fit.
did not give clear guidance on temporal correlation
for their uncertainties. The most likely form for these is positive
temporal correlation arising from systematic errors in reporting or
biogeochemical models. Our analysis is concerned with trends, that is
of year-to-year differences. Positive temporal correlations will
increase the significance of these trends. Thus we make the
conservative assumption of temporal independence. The one case where
this is not true we will treat explicitly.
Figure also shows the observed and predicted atmospheric
growth-rate from the two models. The regression solutions give
α=0.45 and β=0.016yr-1. The two models
produce mean-square residuals of 0.95PgCyr-1. Thus
we use this value as the uncertainty R for the dependent variable in the
regression for the β-model. It yields a 1σ uncertainty of
0.002yr-1. Calculating the uncertainty of α is
more difficult since the most uncertain term is the Jacobian. We can
approximate it by noting that the relationship between
Fanthro and ∂M∂t can be
integrated to give Mfinal-Minitial=α∑Fanthro. The total change of CO2 mass in the
atmosphere is constrained by the initial and final concentration
uncertainties and these concentrations are very well known. Thus
the percentage error in α is the percentage error in ∑Fanthro. The
uncertainty in ∑Fanthro can be calculated for the
limiting cases of complete independence and perfect temporal
correlation. For the independent case we sum uncertainties
quadratically to give 4.3 PgC of a total of
372 PgC, or about 1 % uncertainty. For the case of
perfect correlation the 5 % uncertainty in annual values
translates to a 5 % uncertainty in the total.
Thus the uncertainty in
α lies between 1 % and 5 %.
Figure shows the residuals from the α and
β models from Fig. .
The two models produce similar residuals. Both residuals are driven by
short-term changes in the atmospheric growth-rate and arise from the
failure of these simple integrated models to reproduce such changes.
One striking similarity is the increase in the amplitude of the
residuals with time. The amplitudes grow by 60 % from the first to
the second half of the period. The interannual variability has been
used by and to assess the sensitivity of
the carbon cycle to forcing.
Residuals in the growth rate (observed - predicted) for
the α model (yellow) and β model (black).
By construction, β provides an optimal fit to the time course of
∂M∂t but this does not mean it is optimal
throughout. We can ask whether different periods suggest different
magnitudes for β. Here we focus on the 11-year
period 2002–2012. We repeat the calculation, obtaining β=0.057±0.018yr-1. This is much larger but much more uncertain
than the overall value of β=0.016±0.002yr-1. The
large β value is a direct result of the negative trend in the
residuals evident from 2002. The difference can be considered
statistically significant with a 5 % probability of a larger value
occurring by chance over this period. We can also ask whether it is
robust, that is how sensitive is the result to our choice of period.
We repeat the analysis for every 11-year period in the record
(i.e starting with 1959, 1960 etc). This
yields 6 values greater than 0.057yr-1.
We can also ask whether the mean residual of the fit of the β-model
is significantly different from 0. The mean residual for 2002–2012
is -0.07±0.27PgCyr-1. The large error bar
is a result of the large interannual variability. In summary, the mean
CO2 uptake over the last decade is not significantly different
from that predicted by a linear response to concentration. The
change in trend over that time is approaching significance but is not
robust. Let us now analyse some spatially resolved estimates of fluxes
to try to attribute the behaviour over the full period and more
recently.
Land and ocean contributions
One useful property of Eq. () is that, if we can
decompose fluxes as F=F1+F2+… we can decompose the
corresponding β values as β=β1+β2+…. We
will show decompositions into land or ocean, by latitude band and by
season. In each case we replace y in Eq. with
the corresponding flux.
First we calculate β for land and ocean separately using the
values and uncertainties from . The uncertainties are
0.5 PgCyr-1 for the ocean and
0.8 PgCyr-1 for the land. We obtain
β=0.010±0.001yr-1 for ocean and
β=0.006±0.002yr-1 for land. The root mean square
residuals are 0.18 PgCyr-1 for ocean and
0.96 PgCyr-1 for land. The calculated residuals for
land have a larger magnitude than assumed which suggests we should increase
the land β uncertainty to 0.003 yr-1.
Figure shows the GCP estimates and the linear fits.
When analysing these we must remember that the GCP land estimate is
calculated as a residual from Eq. (). The
relatively small residuals from the ocean fit and the additive form of
the β decomposition imply that the residuals in the land uptake
resemble those in the total uptake.
Ocean uptake (blue) and land uptake (green) in
PgCyr-1. Dashed lines are estimates from
while the solid lines are predictions from the
β model.
Again considering the period 2002–2012 we obtain 0.047 yr-1
for land and 0.01 yr-1 for ocean. As with the total uptake,
there are 6 periods of 11 years with larger β for the
land while the ocean value is at the mean and median for the set of
11-year periods. Thus even when accounting for the different
interannual variability of each environment the relative changes in
the land flux are much larger than for the ocean. Changes in land
uptake explain all the increase in total uptake over 2002–2012 but
this change cannot be regarded as robust.
Diagnostics for inversions
We can further decompose land and ocean fluxes into their regional
contribution and calculate the related β to attribute regional
contributions to trends.
Regional flux estimates can come either from atmospheric inversions or
models. In this section we use an
update of the Cubic Conformal Atmospheric Model (CCAM) inversion used in which extended
the study of . The update extends the study period from
1992–2012. required that stations must report
measurements during 70% of months in their study period in order to
be included.
We apply the same criterion but the different study period means the
network will be different from that of . The 13CO2
records are also extended to 2012. Calculations for the data
uncertainties are as in . We use only the CCAM model
from the earlier study.
Before we can trust the inversion to identify regional changes we
verify its ability to match the atmospheric growth-rate. This is best
done by comparing the net, non-fossil flux. For the GCP this is the
sum of the LUC, land and ocean fluxes while for the inversion it is
the annual mean, non-fossil flux. We are interested in
variability so we adjust the GCP and inverse mean fluxes to be equal
for plotting purposes. The inclusion of the constant term in
Eq. means this will have no effect on the calculated β.
Figure shows the results for the GCP and
inversion. As we would hope we see good agreement for both short and
long term variability. We stress that this is a necessary but not
sufficient condition for successful regionalization of trends.
Next we can ask whether the GCP and inversion agree on the land–ocean
division of recent sink changes. Table presents
the results for the inversion and GCP budget for the periods
1992–2012 and 2002–2012. For comparison we calculate the net land
flux for the GCP as the difference between LUC and land
uptake. Similarly we calculate the uncertainty here from the residual
budget between the growth rate, fossil fuel flux and ocean uptake.
Most β values agree to within their uncertainties. We see
general agreement on the predominance of land over ocean responses and
the much stronger response over 2002–2012. Thus, as far as we can
tell from independent evidence, the inversion is partitioning
reasonably the linear responses of land and ocean. We stress that this
was not preordained since the ocean models which control the trend in
land–ocean partition for the GCP estimates do not inform the
inversion.
We can
proceed to discuss the regional form of these responses.
Land and ocean β values from the GCP budget and
inversion for the periods 1992–2012 and 2002–2012.
Figure shows the estimated flux and fit from the
β model for land and ocean and northern extratropics, tropics
and southern extratropics separately. The groupings are taken from
rather than a latitudinal separation. This allows us
to calculate the uncertainty of the regional fluxes correctly.
The
uncertainties used in the β-model fit are the generated annual
uncertainties from the posterior covariance of the inversion. Results
of the fit are shown in Table for 1992–2012 and
2002–2012. Both Fig. and Table
show strong spatial patterns in the linear response of uptake.
Net uptake from (black) and from the
inversion (blue). Means over the period have been adjusted to be
equal.
As one might expect from the small global β for the ocean, most
ocean regions show weak response and, given their uncertainties, none
could be reliably distinguished from 0. One exception is the
southern extratropical ocean for 2002–2012. The large uncertainties
counsel caution but the apparent increase in the response does not
support findings of long-term reductions in uptake
e.g.. This is in line with the results of
.
For land, there is a strong positive response of uptake in the
northern extratropics and near cancellation between the tropics and
southern extratropics. The tropics shows a large negative β over
the whole period. The tropical β depends strongly on the
changes in FLUC. This is particularly evident for
2002–2012 where the increase in β is coincident with a sharp
downward trend in FLUC. Any error in trends of
FLUC will be aliased into the calculated β.
The dipole in response between the tropics and southern extratropics
raises the possibility of highly uncertain responses with strong error
correlations. This was certainly the case for the mean flux noted by
who reported large uncertainty correlations between
these regions in atmospheric inversions.
The response with the largest signal-noise occurs in the northern
extratropical land. The response is large over the whole period and
much larger for 2002–2012 where it dominates the global signal. The
increase in relative uncertainty as we move to smaller regions
precludes a more detailed spatial examination of the signal. The
results suggest that, notwithstanding the cautionary finding of
, the strong trend in greenness
e.g. has made a strong imprint on the pattern
of CO2 uptake.
We can further decompose the β for the northern extratropical
land into the positive and negative components of the flux. The
growing season net flux (GSNF) is defined as the sum of all the
negative (uptake) components over a year. We further define the
quiescent season net flux (QSNF) as the sum of all the positive
(source) fluxes. The annual uptake can be decomposed as
annual flux=GSNF-QSNF and thus β can
be decomposed as
βannual=βGSNF-βQSNF.
The term βGSNF+βQSNF reflects a change
in the integrated amplitude of the seasonal flux and hence to a likely
change in the seasonal amplitude of concentration. These changes in
amplitude have been noted by and in
surface and airborne measurements in the Northern Hemisphere. Roughly
paraphrased, the argument of is that near cancellation
between βGSNF and βQSNF means that
changes in amplitude need not (and probably do not) correspond to
changes in net flux.
Land and ocean β values from the inversion for
northern extratropics, tropics and southern extratropics for the periods 1992–2012 and 2002–2012.
Temporally decomposed β values for northern and southern
extratropical land are also listed in Table . As
might be expected, the uncertainties on seasonal fluxes are
considerably larger than their annual means so again some caution is
suggested in interpreting these values. We see a large response in the GSNF but not in the QSNF. We can hence say that the
response in net flux is due to the productive part of the year but it
is still a step to say the response is related to production since
atmospheric inversions sense only the net flux which is always the
difference between production and respiration. One further clue to the likely driver
is given by a similar analysis for the maximum uptake in each year.
The uncertainties are even larger here but we do see similar increases
for the maximum as for the GSNF. This suggests that it is the
productivity which mediates the linear response in the net flux
and its change over time and that this change in productivity is the
likeliest cause of the increasing annual uptake in the northern
extratropics.
Estimated uptake from inversion (black) and β-model fit
(red) for the north (top row), tropics (middle) and south (bottom)
with land on the left and ocean on the right.
An example of model responses
If the linear diagnostic is a reasonable way to summarize the
behaviour of the large-scale carbon cycle we can also apply it to
models. This has the further advantage that we can create process
diagnostics the same way. As examples, we analyse the linear
response of the LPJ-GUESS model and the LPJ model
. LPJ combines mechanistic treatment of terrestrial
ecosystem structure (vegetation composition, biomass) and function
(energy absorption, carbon cycling). Vegetation dynamics are updated
annually based on the productivity, disturbance, mortality, and
establishment of nine plant functional types (PFTs). Modelled
potential vegetation cover (including C3-/C4-plant distribution)
depends on competition and climate history. LPJ-GUESS' process
formulation of plant physiology and ecosystem biogeochemistry is
similar to LPJ. However, in contrast to the area-based representation
of vegetation structure and dynamics for mean individual plant types
of LPJ, LPJ-GUESS employs a more detailed scheme that distinguishes
woody plant type individuals (cohorts) and represents patch-scale
heterogeneity. LPJ-GUESS explicitly models resource competition (light
and water) and subsequent growth between woody plant type individuals
on a number of replicate patches. Similar to LPJ, herbaceous
under-storey (simulated using the grass PFT) is modelled, but
individuals are not distinguished. While the LPJ simulation used here
represents potential natural vegetation, LPJ-GUESS takes into account
present day land use by accounting for croplands and pastures as grass
PFT using the 2005 cropland and pasture map from the Hyde 3.1 database
. Both LPJ and LPJ-GUESS use fixed land cover so we
fit the β-model to the output directly rather than correcting
with FLUC.
First we compare the global fluxes for the two models with
Fland from the GCP. Figure shows the
three fluxes with means adjusted to agree with Fland. We
see that LPJ agreement is poor for the first half of the period but
improves considerably after 1980. The two models do comparably well in
this period.
Global and regional β values for the LPJ and
LPJ-GUESS models along with the GCP land estimates.
We have fluxes computed until 2011 for LPJ and 2010 for LPJ-GUESS so
we analyse the longest possible period for each model for the closest
comparison with the inversion. The β values for land in the
northern semi-hemisphere, tropics and southern semi-hemisphere are
listed in Table . We note that we cut the regions at
30∘ here rather than the more complex boundaries from
used in the inversion. We see reasonable agreement for the global β
for the whole period but only LPJ shows the dramatic increase in the
second half of the period.
The regional structure of the linear response in both models is
quite different from that suggested by the inversions. Model responses
are dominated by the tropics as is the intensification in response in
the last decade. This strong positive response is offset by smaller
negative responses in the extratropics. The inversion suggests
positive responses in the extratropics (especially the north) with
ambiguous response in the tropics.
Discussion
It is tempting to compare our β values with those of
. The important difference is that do not
include a constant term in their linear model (their Eq. 2) while we
do. This means their value of β (τS in their formulation)
will attempt to fit the mean value of uptake while ours will not.
Given the likely role of other processes in uptake we would expect
that our β value would underestimate mean uptake if used without
the mean term. This, indeed, is the case with a mean uptake for
1959–2010 of 2.3 yr-1 compared to the GCP value of
3.8 yr-1. predict an uptake of
3.5 yr-1. We stress that the formulation of
is valid for their purposes but that our focus made it
important to separate the mean and trends.
Terrestrial uptakes from (black), LPJ
(red) and LPJ-GUESS (blue). Means have been adjusted to give equal
uptake over the whole period.
We have analysed the CO2 uptake throughout as a linear
response to concentration. We have not, however, proposed a causal
link with CO2 concentration itself since there are many other
variables (e.g. time, temperature and LUC) which are highly
colinear with CO2 concentration. The record, especially of
regionally resolved fluxes, is not long enough compared to the various
exponential doubling times of emission and concentration to allow
a clear separation between linear and exponential changes. The
evidence from the inversion of a deepening of the growing season flux
minimum does suggest a role for productivity. Given the mechanistic
link between productivity and concentration this does suggest
increasing concentration changes have contributed to increased land uptake. The two ecosystem models we studied are too
dissimilar in their responses to the inversion to use them as
a diagnostic of the inferred flux behaviour.
The results for the most recent decade suggest a strong, but not yet
robust increase in the linear response. It suggests that if there
is a change in carbon-cycle behaviour, it is in a direction to
mitigate rather than exacerbate climate change.
We note the much weaker response of tropical uptake and the
sensitivity of our result to FLUC estimates.
Finally, the linear diagnostic suggests an interesting
interpretation for the recent result of . They noted
a large increase in the interannual variability of the terrestrial
carbon cycle over the second half of the GCP period. We noted the same
thing when considering the residuals from our linear fit. While
it is tempting to interpret this increase as an increase in the
climate sensitivity of the carbon cycle it seems equally possible that
it is a constant modulation of a more strongly forced process. As an
analogy we may consider a container with a tap at the bottom which is being randomly
opened and closed. The variation in flow will increase as the height
of water in the container increases even if the variation in the tap
is unchanged. A weakness in this argument is the difference between
the location of peak variability (usually located in the tropical
land) and the dominant response (located by the inversion
in the extratropics).
The calculations in this paper are mainly exemplary. We have made
little attempt yet to see how robust the findings are across different
terrestrial models and inverse systems. The first of these is
relatively easy, aided by several intercomparisons which collect model
output. The specification of uncertainty is difficult for models
however. For inversions the difficulty is to isolate the components of
the flux which are legitimate targets for these
diagnostics. FLUC is often included in inverse models as
part of the prior flux and it must be separated. Similarly, with an
in-house inversion system it is possible to calculate uncertainty on
the same scale as the flux estimates while this information is often
not available for data from intercomparisons such as that of
. That said, these diagnostics do seem a simple way of
summarizing longer-term behaviour of any flux estimate. It will be
interesting to see if the finding of that interannual
variability in flux is more robust across the model ensemble than the
mean flux also holds for these long-term changes.
Conclusions
We have characterized the global and regional response of the carbon
cycle as a linear response to CO2 concentration (or any
colinear variable). We have seen that this fit works as well as the
airborne fraction model with the advantage that it can be decomposed
by time and space. We see an increase in the linear global
response in recent years dominated by land. Inverse flux estimates
show a similar response and locate it in the northern extratropics and
the growing season. Terrestrial ecosystem models show a similar global response but, by
contrast, locate it in the tropics.
Acknowledgements
P. J. Rayner is in receipt of an Australian Professorial Fellowship
(DP1096309). This research was undertaken on the NCI National Facility in Canberra, Australia,
which is supported by the Australian Commonwealth Government.
Edited by: A. Michalak
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