Introduction and context
Coupled climate models are the most
reliable tools that we have today for large-scale climate projections, such
as in the Coupled Model Intercomparison Project Phase 5 (CMIP5;
). Regional-scale information is obtained by using these
global simulations as a basis for downscaling exercises. Dynamical
downscaling, as opposed to empirical statistical downscaling
e.g., is carried out either with (very)
high-resolution regional climate models (RCMs) e.g. or
high-resolution atmospheric global circulation models . In
both cases, information about the projected changes in sea surface
conditions, such as sea surface temperatures (SST), sea-ice concentration
(SIC) and sea-ice thickness (SIT), is required as a lower boundary condition
for the higher-resolution models. However, SST and SIC conditions modelled by
coupled atmosphere–ocean global circulation models (AOGCMs or CGCMs) show
important biases for the present climate
. For
example, it has been highlighted that most of the CMIP5 models had
difficulties in reliably modelling the seasonal cycle and the trend of
sea-ice extent in the Antarctic over the historical period
. Therefore, the validity and reliability of such coupled
simulations is questionable for future climate projections (e.g. the end of the
21st century), and so is their use as boundary conditions when performing
dynamical downscaling of future climate projections.
Prescribing correct SST is crucial for atmospheric modelling because SST
determines heat and moisture exchanges with the atmosphere
. The absence of the Pacific cold tongue
bias and the reduction of the double ITCZ problem in AMIP experiments with
respect to the CMIP5 model experiments shows the importance of forcing atmospheric
models by SST close to the observations. For instance, improvements in the
modelling of tropical cyclone activity in the Gulf of Mexico
and of summer precipitation in Mongolia
were obtained by bias correcting SST and other AOGCM outputs before using
them as forcing for RCMs. At high latitudes, SIC and, in some cases, SIT
are two additional crucial boundary conditions for atmospheric models.
demonstrated that for the Antarctic climate as simulated
by an atmospheric general circulation model, prescribed SST and sea-ice
changes have greater influence than prescribed greenhouse gas concentration
changes. Large-scale average winter sea-ice extent and summer SST have been
identified among the key boundary forcings for regional modelling of the
Antarctic surface mass balance , which is the only
potentially significant negative contributor to the global eustatic sea level
change over the course of the 21st century . We note that while there is a considerable body of scientific
literature on the effect of varying SST and SIC on simulated climate, very
few studies focused on the role of varying SIT in atmosphere-only simulations
, although air–sea fluxes in the
presence of sea ice are strongly influenced by the thickness of the sea ice
and the overlying snow cover. and have
shown that the atmospheric response to changes in Arctic SIT can induce
atmospheric signals that are of similar magnitude as those due to changes in
sea-ice cover. In most atmosphere-only general circulation models (AGCMs),
SIT will therefore also need to be prescribed along with SST and SIC. When
SST and SIC from a coupled climate model are directly used, SIT from that
same run should of course be used; however, in the case that SST and SIC from the
coupled model run are bias corrected, as we strongly suggest here, we argue
that SIT should be prescribed in a physically consistent manner in the
atmosphere-only simulation.
In this study, we describe, evaluate and discuss different existing and new
methods for the construction of bias-corrected future SST, SIC and SIT. These
methods generally take into account observed oceanic boundary conditions as
well as the climate change signal coming from CMIP5 AOGCM scenarios to build
more reliable SST and SIC conditions for future climate, which should reduce
the uncertainties when used to force future climate projections. The
different methods have been evaluated using a perfect model approach and by
carrying out real-case applications to observations. Applied changes in mean
and variances have been investigated as well as the coherence of SIC and SST
after applying bias-correction methods. The analysis of the results focuses
on methods for sea ice, as the bias correction of SIC is a more complicated
issue to deal with. For SIT, we propose a diagnostic using SIC following
, and an example of its application is shown in Fig. .
Because there were no reliable observational data sets available until
recently e.g., we directly evaluate
diagnosed SIT against new observations. In the following, we present the
bias-correction methods, the data and the evaluation methods in
Sect. . The results of the evaluation are shown in
Sect. . Because SST and SIC are bias corrected separately,
Sect. presents a few considerations about SST and SIC
consistency after performing bias corrections. The results are then discussed
together with general considerations on the bias correction of oceanic surface
conditions in Sect. . Finally, we sum up our findings and draw
conclusions in Sect. .
Data and methods
Data
The application and validation of the methods for bias correction have been
achieved using observational SST and SIC data from the Program for Climate
Model Diagnosis and Intercomparison (PCMDI) that are generally used as
boundary conditions for Atmospheric Model Intercomparison Project (AMIP)
experiments , called “PCMDI obs.” or “observations” in
this paper. The AOGCM's historical and projected sea surface conditions come
from CMIP5 simulations . Only the first ensemble members of
the historical and the Representative Concentration Pathway (RCP;
) 4.5 and 8.5 simulations have been considered. Most
methods have been tested using CNRM-CM5, IPSL-CM5A-LR and HadGEM-ES coupled
GCM. Data from NorESM1-M, MIROC-ESM, EC-EARTH and CCSM4 have also been
used as analogue candidates in the analogue method for sea ice. Prior to any
application of the bias-correction methods, AOGCM data have been bilinearly
regridded onto a common regular 1∘×1∘ grid. For the
evaluation of the diagnosed SIT, we used the data for the
Arctic. For the Antarctic, in spite of recent observations with autonomous
underwater vehicles by , which tend to suggest the occurrence
of thicker Antarctic sea ice than previously acknowledged, we will use the
data because of their large spatial coverage.
Sea surface temperature methods
The bias correction of simulated SST is a relatively easy and a
straightforward issue to deal with. Different methods have been developed and
presented in the literature. Here we re-evaluate two different frequently
used methods. The first is an absolute anomaly method (e.g.
), which consists of simply adding the SST difference
for a given month from an AOGCM scenario to the climatological mean in the
observations. The second is a quantile–quantile method presented in
in which for each quantile and each month, the climate
change signal coming from the AOGCM scenario is added to the corresponding
quantile in the observations. Presenting these well-known methods in detail
is of limited interest for the main part of this paper. However, interested
readers can find a more complete description of the methods in
Appendix .
Sea-ice concentration methods
SIC is more difficult to bias correct because it is a relative quantity that
must be strictly bounded between 0 % and 100 %. This difficulty led
some authors to neglect SIC bias correction altogether in studies with
prescribed corrected future SSTs that did not specifically focus on polar
regions e.g.. In this section, we present
three methods: a look-up table, an iterative relative anomaly and an analogue
method.
Look-up table method
This method has been developed at the Royal Netherlands Meteorological
Institute (KNMI). It is used in and within the framework
of the High Resolution Model Intercomparison Project (HighResMIP)
. A regression of SIC as a function of SST is also used in
the HAPPI project .
In this method, the assumption is made that SIC is a function of SST.
Therefore, SSTs are ranked per 0.1 K bin and the corresponding average SIC
for each temperature bin between -2 and +5 ∘C is calculated.
Relations between SST and SIC have been found to be dependent on seasons and
hemispheres. Therefore, using monthly mean values of SST and SIC from
historical observations, look-up tables are built separately for the Arctic
and the Antarctic for each calendar month (Fig. ). Then, with the
help of future SSTs, these look-up tables (LUTs) are used to retrieve future
SIC.
Look-up tables (a, c) linking SST and SIC for the
Arctic (a, b) and the Antarctic (c, d) built using
1971–2000 PCMDI observations and the associated uncertainty (root mean
square error) in the computed SIC average (b, d).
Iterative relative anomaly method
Here we follow a method described by . It is based on
relative regional sea-ice area (SIA) changes and is essentially an iterative
scheme of mathematical morphology for image erosion and dilation
. The Arctic and the Antarctic are divided into sectors
of equal longitude. In each sector, the average SIA is calculated by
spatially integrating SIC. With respect to the method described in
, we introduce the use of a quantile–quantile method to
determine the targeted SIA in the bias-corrected projection. This targeted
SIA is then calculated for each sector and each quantile with the help of
the following equation:
SIAFut,est=SIAobs⋅SIAFut,AOGCMSIAHist,AOGCM.
In Eq. (), SIAFut,est is the estimated projected SIA
for the current month and sector, SIAObs the SIA from the
observations, and SIAFut,AOGCM and SIAHist,AOGCM
are the respectively computed SIAs for the corresponding quantile to the
observations using SIC from a future scenario and a historical AOGCM
simulation. Starting from an observed present SIC map and using the computed
relative SIA change for a given sector, the decrease (increase) in SIC is
then realised using an iterative process: SIC in each grid box is replaced by
the minimum (maximum) SIC of all adjacent pixels (Fig. ); the new
spatially integrated SIA is calculated and the operation is repeated until
the obtained change converges towards the computed targeted SIA retrieved
from AOGCM-simulated sea-ice data and observations. Afterwards, the
decrease–increase process is repeated on the hemisphere scale in order to
ensure that the change in SIC reproduces the total hemispheric SIA change.
Iteratively constructing a “corrected” future SIC field using the
iterative relative anomaly method (see Sect. ).
Analogue method
In this method, we divide the Arctic and the Antarctic into ns
geographical sectors that correspond to different seas of the Arctic
and the southern oceans; we defined ns=12 sectors for the Arctic
and ns=7 sectors for the Antarctic (a map of these sectors can
be seen in the Appendix,
Fig. ). For each sector and each month, the quantiles of the
sea-ice extent (SIE: total area with SIC above 15 %) and the SIA are
computed from SIC observations over the AMIP period. Corresponding quantile
changes in SIE and SIA are computed using SICs from a CMIP5 AOGCM historical
simulation and a projected scenario run. Computed quantile changes are then
applied to the corresponding quantiles in the observations in order to obtain
targeted future SIA and SIE for each month, quantile and sector. Then, a
library of future SIC fields is built by collecting SIC observations from the
AMIP period as well as SIC from CMIP5 projections. We build this library by
selecting a non-exhaustive list of CMIP5 AOGCMs that represent the historical
SIE annual cycle in both the Arctic and Antarctic reasonably well after
consulting the literature ; a list of
the AOGCMs used can be found in the Appendix (Table ). The
presence of SIC maps from AOGCM projections in this library is justified by
the need to take into account physically plausible future SIC distributions
outside of the current observed range. Future SIC is then finally
reconstructed by searching the analogue for each quantile (q), sector (s) and
month (m) in the library, which is to say the SIC field that minimises the
cost function C expressed by
C(q,m,s)=SIAs-SIAT(q,m,s)SIAmax(q,m,s)2+SIEs-SIET(q,m,s)SIEmax(q,m,s)2,
where SIAs and SIEs are the SIA and SIE of the
processed sectors of the analogue candidate from the library,
SIAT(q,m,s) and SIET(q,m,s) are the
targeted projected SIE and SIA computed using the quantile–quantile method,
and SIAmax(q,m,s) and SIEmax(q,m,s) are
the maximum SIA and SIE of the processed sector. The double criterion on both
SIE and SIA was introduced in order to distinguish cases in which
the total SIE in a sector is similar but the average SIC is very different
(and vice versa). In order to avoid issues introduced by different land masks
between AOGCM and PCMDI data, we filled land grid points with sea ice using
a nearest neighbour method and masked all the grid points with the same land
mask built with land fraction from PCMDI data in order to compute SIEs and
SIAs for each region with the same reference. Analogues are attributed without
taking into account the month of the analogue candidate in the library. This
allows, for instance, for the attribution of a summer sea-ice map from present
observations for a future winter month reconstructed sea-ice field. For each
quantile (q), month (m) and sector (s), this procedure yields a hemispheric SIC
field SICopt(i,q,m,s) that minimises the cost
function for the given sector, month and quantile. For a given month and
quantile, there are thus ns hemispheric SIC fields
SICopt(i,q,m,s). At each grid point i, the
corresponding ns SIC values are then blended using a weight
function w(i,s) depending on the distance
d(i,s) of that grid point to the centre of each of the
sectors in order to obtain the final reconstructed SIC,
SIC(i,q,m), for a given quantile (q) and month (m):
SIC(i,q,m)=∑s=1nsw(i,s)×SICopt(i,q,m,s),
with
w(i,s)=1+d(i,s)dr4-1.
Here, dr is a reference distance of 500 km, yielding a smooth
transition at the boundaries between two adjacent sectors. At the centre of a
sector, this yields a weight that is very close to 1 for the relevant field
that was identified as optimal for that sector and that is close to 0 for the
fields identified as optimal for the other sectors; at the boundary between
two sectors, the weights are typically 0.5 for the two relevant sectors and
close to 0 for the others.
Sea-ice thickness method
Diagnosing sea-ice thickness from sea-ice concentration
As described by , the parameterisation of sea-ice
thickness (SIT denoted hS in the following) as a function of the
local instantaneous SIC f and annual minimum SIC fmin is
designed to yield hS of the order of 3 m for multi-year
sea ice (deemed to be dominant when the local annual minimum fraction
fmin≫0), hS below 60 cm (with a stronger
annual cycle) in regions where sea ice completely disappears in summer (that
is, fmin=0) and intermediate values for intermediate cases:
hS=c1+c2fmin2⋅1+c3f-fmin,
with c1=0.2 m, c2=2.8 m and c3=2 m. This corresponds to the
observed characteristics of Arctic and Antarctic sea ice, with multi-year
sea ice being generally much thicker than first-year ice. The parameter c3
introduces a seasonal ice thickness variation in areas where there is a
concomitant seasonal cycle of SIC. A more parsimonious formulation using only
two parameters could have been designed to comply with these constraints.
However, for the sake of consistency with previous work, we used the equation
proposed by , who designed the parameterisation to
allow for a fairly strong seasonal cycle of SIT also in regions with
intermediate values of fmin.
Spring (MAM) estimated mean SIT (m) using parameterisation from
and IPSL-CM5A-LR SIC data from the historical run
(1971–2000, a) and the RCP8.5 scenario
(2071–2100, b).
Evaluation
Evaluation of the above methods is mainly achieved with a perfect model
approach. A perfect model approach usually consists of using model data as a
substitute for observations and trying to predict projected model data from
that model; this prediction can then be evaluated against the available model
projections e.g.. In the real world, as observations
of future climate are obviously not yet available, an equivalent approach is
impossible if one cannot wait long enough for the future to become reality.
Another type of perfect model approach involves “big brother” experiments for
evaluating downscaling techniques. In such studies, high-resolution model
output is degraded in resolution and downscaling methods are then applied to
these low-resolution data. The resulting synthetic high-resolution fields are
then compared to the original high-resolution output
e.g.. Here, we consider SST and SIC from the
historical simulation of one coupled AOGCM as being the observations. Then,
we apply the different bias-correction methods using the climate change
signal coming from a scenario of the same model. Obtained projected SST and
SIC using this perfect model test are finally compared with original SST and
SIC from the AOGCM climate change experiment.
Additionally, we performed an assessment of real-case applications using
observations and climate change signals coming from AOGCM projections.
Changes in mean and variance in the coupled model projection with respect to
the historical simulation are compared to the introduced change in mean and
variance in the estimated future SST and SIC using bias-correction methods
with respect to the observed climatological data. We consider here that an
ideal bias-correction method should reproduce the same change in mean and
variance between the observations and the bias-corrected projected SST and
SIC as between the coupled GCM historical simulation used and its climate
change scenario. For SIT, since the method is a diagnostic using SIC in order
to ensure consistency between these two variables, the evaluation of the
method is achieved by comparing estimated SIT with observations that were not
available until recently .
As SST and SIC are bias corrected separately, Sect. presents a
few considerations about SST and SIC consistency after performing bias
corrections. The effects of the corrections applied a posteriori in
order to ensure physical consistency between the two variables are
evaluated within the framework of the perfect model test.
Mean and standard deviation change between present and future SST
data sets for the North Atlantic (45 to 58∘ N, 105 to
85∘ W).
Mean change
SD change
(∘C)
(∘C)
CNRM-CM5 RCP8.5 – CNRM-CM5 hist.
+3.04
+0.59
Anomaly meth. app. – PCMDI obs.
+3.06
+0.66
Quantile–quantile meth. app. – PCMDI obs.
+3.04
+0.68
Results
Sea surface temperatures
Perfect model test
Absolute anomaly or quantile–quantile methods have been used for SST in
previous bias-correction applications cited previously in this paper. As a
consequence, the utility of a perfect model test here is limited for SSTs,
and it was only applied in order to be consistent with the evaluation of the
method for SIC. For both methods, the relation between the bias-corrected
projected SST and the SST directly obtained from the AOGCM projection is
trivial when we replace observed SST with the one from the AOGCM historical
simulation, for instance in Eq. (). As a result, the resulting
errors were null or close to zero, and the results are therefore not
presented or discussed.
Real-case application
Here, we present the application of the anomaly and the quantile–quantile
methods in a real-case application. For this application, we use SST from
the PCMDI observation data set over 1971–2000, from IPSL-CM5A-LR and CNRM-CM5
historical simulation over the same period, and the RCP8.5 scenario
over 2071–2100. Histograms of the frequency distribution of SST for different
regions of the world (Weddell Sea, central Pacific and North Atlantic) have
been plotted in order to compare frequency distributions in the observations,
in the GCM historical and future simulations, and in the estimated
bias-corrected future SST using the quantile–quantile and anomaly
methods (Fig. ). In this figure, we can appreciate the change in
mean and variance between the GCM historical simulation and the GCM future
scenario and between the PCMDI observations and the bias-corrected SST
scenario. Figure c also shows the large cold bias of IPSL-CM5A-LR
with respect to the observations in the North Atlantic, as coupled models
usually struggle to correctly represent the Atlantic Meridional Overturning
Circulation (AMOC). The change in mean and variance due to the climate change
signal is more explicitly presented for the North Atlantic for the
application with CNRM-CM5 in Table . Results from the anomaly
method and from the quantile–quantile method are very similar, and both
methods succeed in applying the same change in mean and variance coming from
the AOGCM scenario to the observations when producing bias-corrected SST.
Frequency distribution of SST for PCMDI observations (black),
IPSL-CM5A-LR historical (red) over 1971–2000 and RCP8.5 (green), and
quantile–quantile method (pink) and anomaly method (blue) applications over
2071–2100 for the Weddell Sea (a), central Pacific (b) and
North Atlantic (c).
Sea-ice concentration
Perfect model test
In this section, we present the results of the application of the perfect
model test for the three methods for the bias correction of SIC. The term
“perfect model test” is not absolutely pertinent for the evaluation of the
look-up table method, as we first computed LUTs using SST and SIC from an
AOGCM historical simulation. Then, we used the SST of the climate change
projection from the same AOGCM and retrieved SIC with the help of the
previously computed LUT. An example of computed LUT using data from the
historical simulation of CNRM-CM5 can be seen in the Appendix
(Fig. ). It is noteworthy that this new LUT is significantly
different from the one using PCMDI observations (Fig. ). Even
though the use of this LUT for the perfect model test instead of LUTs
computed using observed SST and SIC over the AMIP period can be discussed,
the use of LUT computed using observations would necessarily produce a poorer
result for the reconstruction of SIC of the AOGCM scenario in a perfect model
test. Using AOGCM data, inconsistent or missing results were found for most
SST bins at or below the freezing point of seawater (-1.8 ∘C). In
order to fill the LUT, we therefore fixed SIC =99 % for SST =-2.0 ∘C and linearly interpolated SIC between -1.7 and
-2.0 °C.
The perfect model test is more rigorously applied for the evaluation of the
relative anomaly and the analogue method, as we simply replaced time series of
the observed SIC with the one from the AOGCM historical simulation before
applying the method without any specific modification or calibration. For the
analogue method, the tested AOGCM projection was excluded from the
possible analogue candidates before applying the method and the perfect model
test.
Errors (%) after applying the perfect model test are shown for the three
methods for the RCP4.5 and RCP8.5 scenarios of the IPSL-CM5A-LR and CNRM-CM5
AOGCM (Fig. ). These errors are generally lower for the LUT method:
the mean root mean square error (RMSE) in the estimation for each scenario
for the Arctic and the Antarctic is 4.8 %. The mean error (ME) using this
method tends to be positive in the Arctic and negative in the
Antarctic seas. Errors using the
relative anomaly method exhibit some larger values (mean RMSE =8 %).
The errors using the analogue method have intermediate values with respect to
the first two methods (mean RMSE =5.9 %). Some of the errors of the
analogue method for regions with very complex coastal geography, such as the
Canadian Archipelago, are due to the differences in land mask between the
tested and the chosen AOGCM as an analogue candidate, despite the care taken
for this issue. The pattern of the errors using the iterative relative
anomaly seems robust among the different AOGCM scenarios. It is also
noteworthy that the pattern of the errors is similar among different methods,
especially if we consider the results in the Arctic for the scenarios of the
CNRM-CM5 model. The spatial distribution of the errors for HadGEM2-ES SIC in
RCP4.5 and RCP8.5 scenarios within the frame of the perfect model test is
also presented in the Appendix for the analogue and LUT methods
(Fig. ). The magnitude of the errors is very similar,
which increases the confidence in the independence of the results from the
selected model.
With the results of the perfect model test, we also performed a comparison
between the frequency distribution of the mean SIC in the AOGCM future
scenario (here CNRM-CM5, RCP8.5) and in the corresponding estimation using
the bias-correction methods (Fig. ). In these plots, we represented
the histogram of the frequency of SIC for four regions: Ross Sea
(72–77∘ S, 174∘ E–163∘ W), Weddell Sea
(63–73∘ S, 45–25∘ W), Arctic Basin (80–90∘ N,
180∘ W–180∘ E), and the Canadian Archipelago
(66–80∘ N, 130–80∘ W). These regions have been chosen
because they are the principal regions where a significant amount of sea ice
remains by the end of the 21st century under the RCP8.5 scenario. With the
LUT method (blue lines in Fig. ), the distribution of SIC is quite
well reproduced in the Arctic (Fig. c and d), whereas in the
Antarctic seas the distribution (Fig. a and b) exhibits well-marked
peaks that we do not find in the GCM data set (black lines). The presence of
such peaks is easy to explain by taking into account the structure of the LUT
as (i) for a given month, the SIC does not always increase monotonically with
decreasing SST, and (ii) the discrete nature of LUT is not in favour of a
continuous SIC frequency distribution. Moreover, using this method, we find a
large underestimation of SIC above 90 %, mainly in the Southern
Hemisphere, with almost no occurrence of these high SIC values in the
estimations using the LUT method for the Ross and Weddell seas. The frequency
distribution of the sea ice using the relative anomaly method (green lines in
Fig. ) is closer to the distribution in the AOGCM, even if there is
a slight overestimation of the frequency for concentrations between 70 %
and 90 % and an underestimation for very high SICs (above 90 %).
Finally, the distribution obtained using the analogue method (red lines in
Fig. ) is very close to the distribution of the original AOGCM
scenario. The results are robust because differences in sea-ice frequency
distribution between bias-corrected projections and AOGCM scenarios are very
similar for other scenarios and coupled models (figures not shown).
Mean error in the estimation of SIC with respect to the original
AOGCM future scenario for the LUT, iterative relative anomaly and analogue
methods with CNRM-CM5 and IPSL-CM5A-LR RCP4.5 and RCP8.5 scenarios for the
Arctic (a) and the Antarctic (b).
Frequency distribution of SIC in CNRM-CM5 RCP8.5 scenario (black)
and in estimation using different methods in a perfect model test: look-up
table (blue), analogue (red) and iterative relative anomaly (green). Regions
are (a) Ross Sea (72–77∘ S,
174∘ E–163∘ W); (b) Weddell Sea
(63–73∘ S, 43–25∘ W);
(c) Arctic Basin (80–90∘ N,
180∘ W–180∘ E); (d) Canadian Archipelago
(66–88∘ N, 130–80∘ W).
Real-case application
We applied the three bias-correction methods using PCMDI SIC data from the
1971–2000 period, as well as the IPSL-CM5A-LR and CNRM-CM5 historical data
over the same period and data from the RCP4.5 and RCP8.5 scenarios from
2071–2100, in order to obtain future bias-corrected SIC. The reliability of
the methods is evaluated by comparing the change in mean and variance between
the observations and the bias-corrected projected SICs with the corresponding
changes in the original AOGCM scenario with respect to the historical
simulation. We consider here that an ideal method should apply the same
statistical changes to observed sea ice as the one present in the climate
change projection used to derive climate change signal.
In Fig. , the bias-corrected mean SIC change is plotted against the
corresponding change in mean SIC in the AOGCM scenario used to determine the
climate change signal. All points in the plot are obtained by the same four
AOGCM scenarios as well as the same four “test regions” as in the previous
section (Ross and Weddell seas, Arctic Basin, Canadian Archipelago).
Similarly, in Fig. , applied changes in standard deviation for the
bias-corrected projected SIC are plotted against the corresponding standard
deviation change in the AOGCM climate change experiment.
For the LUT method (Fig. a), future SSTs have been bias corrected
using the quantile–quantile method before using computed LUT for the
retrieval of future SIC. Using this method, there seems to be no systematic
error in the applied change in mean SIC. The mean error in the estimation of
the change in mean SIC for every region and scenario is -2.2 % and
the RMSE is 42 %. The spread of the points seems to increase for stronger
decreases in sea ice. Main outliers with a high overestimation of the
decrease in SIC are points representing the evolution of sea ice in the
Weddell Sea, mainly for CNRM-CM5 scenarios. If we consider change in SIC
variability (Fig. 9a), systematic error (-14.9 %) and RMSE (69.3 %)
are strong. The decrease in SIC variability in the Antarctic seas in the
projection is strongly overestimated. Indeed, due to the structure of the
LUTs themselves, the variability of SIC in the bias-corrected projections is
much lower than in the observations or in the original scenarios.
The application of the relative anomaly method shows a more general
overestimation (ME =-11.6 %; RMSE =52.2 %) of the decrease in
mean SIC (Fig. b). This overestimation is more pronounced for the
Weddell Sea area and for the scenarios of the CNRM-CM5 model. Only the
decrease in mean SIC in the Arctic Basin is correctly reproduced with respect
to the AOGCM scenarios. Concerning the change in SIC variability
(Fig. b), the scores are comparable to the application of the LUT
method (ME =-11.6 %; RMSE =64.7 %). The increase in
variability in the Arctic Basin and in the Canadian Archipelago is correctly
reproduced, whereas for the Antarctic seas and particularly the Weddell
sector, the decrease in SIC variability is once again dramatically
overestimated.
Change in mean bias-corrected SIC projections using
(a) look-up table, (b) iterative relative anomaly and
(c) analogue methods against corresponding mean change in the A
OGCM projection for the four test
regions: Canadian Archipelago (blue), Arctic Basin (orange), Weddell Sea
(red) and Ross Sea (green) for projections from CNRM-CM5 and IPSL-CM5A-LR.
Change in bias-corrected SIC projection standard deviation using
(a) look-up table, (b) iterative relative anomaly and
(c) analogue methods against corresponding mean change in the
AOGCM projection for the four test
regions: Canadian Archipelago (blue), Arctic Basin (orange), Weddell Sea
(red) and Ross Sea (green) for projections from CNRM-CM5 and IPSL-CM5A-LR.
Mean error in the estimation of SST with respect to the
corresponding original AOGCM scenario after applying the analogue method for
sea ice, the quantile–quantile method for SST, and the correction for SST and
SIC consistency for the Arctic (a) and the southern
oceans (b).
Finally, the application of the analogue method gives intermediate scores
(ME =-8 %; RMSE =48.7 %) with respect to the two previous
methods for the estimation of the change in mean SIC (Fig. c).
These scores are greatly deteriorated by distinct outliers corresponding to
the Weddell Sea sector for each AOGCM scenario, with an overestimation of the
decrease in sea ice. As for the relative anomaly method, the change in SIC
variability (Fig. c) is correctly reproduced (ME =-9.3 %;
RMSE =60.3 %), especially in the Arctic, while there is an
overestimation of the decrease in variability around Antarctica, particularly
for the Weddell Sea.
Consistency between sea surface temperature and sea-ice concentration
As bias corrections of SST and sea ice are performed separately, the physical
consistency between the two variables needs to be ensured a posteriori. To do
so, three different issues are examined.
There is a considerable amount of sea ice (>15 %) in the corrected
scenario in which the SST is above the freshwater freezing point (273.15 K). In
this case, we set SST equal to the seawater freezing point (271.35 K) for
any SIC equal to or greater than 50%. If the future calculated SIC is between
15 % and 50 %, the future SST is obtained by linearly interpolating
between the seawater freezing point and the freshwater freezing point.
The future corrected SST is below the freshwater freezing point but
there is no significant (<15 %) SIC in the bias-corrected scenario. In
this case, we put the SST of the concerned grid point equal to the freshwater freezing point.
SST has been used to remove very localised suspicious sea ice
(no ice) in the Arctic in summer. Any sea ice for SST above 276.15 K has
been removed, this temperature being the highest temperature at which
a significant amount of sea ice (15 %) is found in the Arctic for the
computed LUT using PCMDI data.
The impact of these modifications has been evaluated using the framework of
the perfect model test. After applying the analogue method for SIC and the
quantile–quantile method for SST in a perfect model approach, we applied the
correction for SST and SIC consistency and compared obtained SSTs to the
original AOCGM future scenario used to carry out the experiment. The error
can be seen in Fig. for the application of the method with
IPSL-CM5A-LR and CNRM-CM5 scenarios. Error is negligible in most regions.
Very locally, it can reach up to 1 ∘C. These regions generally
correspond to regions where the analogue method has shown some errors for the
reconstruction of sea ice, especially for CNRM-CM5 scenarios. The occurrences
of the three cases mentioned above have been assessed for both the perfect
method test and the real-case application. The first and third cases are very
rare and about 1 % or less of global oceanic surfaces experience at
least one case during a 30-year experiment. The second case is more frequent;
more than 20 % of global oceanic surfaces experience at least one
occurrence during a 30-year experiment, while the mean occurrence at each
time step is about 1 % to 2 % of global oceanic surfaces. This
case is responsible for the small (0.25 to 0.5 K) but widespread warm bias
in SST that can be seen in the Antarctic seas for the reconstruction of IPSL
model scenarios in Fig. . Nevertheless, this slight decrease in the
quality of the reconstruction of SST is worth considering in order to ensure
physical consistency between SST and SIC.
Sea-ice thickness
The original formulation by was parameterised for both
hemispheres. We will therefore first present results for the original unique
parameter set c1,2,3 applied to both hemispheres. In a second step,
we will present results for separate Arctic and Antarctic parameter sets,
yielding a better fit to the observations. The reasoning is that, at the
expense of generality of the diagnostic parameterisation, one could argue
that the strong difference between the Arctic and Antarctic geographic
configuration – a closed small ocean favouring ice ridging and thus thicker
sea ice in the Arctic versus a large open ocean favouring thinner sea ice around
Antarctica – justifies choosing different parameter sets for the two
hemispheres. As changes in the position of the continents will be irrelevant
over the timescales of interest here, climate change experiments will not be
adversely affected by this loss of generality.
Option 1: global parameter set
A comparison between the observed and our diagnosed
evolution of the Arctic mean SIT is given in Fig. a. The
geographical patterns of the observed (in fact, observation-regressed) and
parameterised Arctic ice thickness for March and September over the
observation period 2000–2013 (Fig. a) do bear some resemblance,
but they also show some clear deficiencies in the diagnostic
parameterisation. The diagnostic parameterisation reproduces high SIT north
of Greenland and the Canadian Archipelago linked to persistent strong ice
cover, but underestimates maximum ice thickness (due in part to compression
caused by the ocean surface current configuration). Thinner sea-ice over the
seasonally ice-free parts of the basin is reproduced, but it is actually too
thin, particularly in winter (for example in the Chukchi Sea). Obvious
artifacts appear in September north of about 82∘ N where the SIC in
the ERA-Interim data set clearly bears signs of limitations due to the
absence of satellite data.
Both for spring (October–November) and fall (May–June), our diagnosed SIT
(Fig. ) compares generally well with the ICESat data except for an
overestimate in the Weddell Sea in both seasons. The geographical pattern of
alternating regions with thin and thick sea ice is remarkably well
reproduced.
Observed (black, after ) and diagnosed (red)
12-month moving average mean sea-ice SIT of the Arctic basin (see
Fig. ) using (a) the global parameter set and
(b) the Arctic-specific parameter set. Slight differences to
Figure of appear because here we mask
ice-free (SIC <15 %) areas that have a finite, non-zero ice
thickness in the regression proposed by , who extend their
regression to the entire Arctic Basin in all seasons.
Observed (regressed, ) and parameterised Arctic
SIT (in m) for March and September and the difference between these (right)
with (a) the global parameter set and (b) the Arctic
parameter set.
Observed and parameterised Antarctic sea-ice
thickness (in m) for spring and fall and the difference between these (right)
with (a) the global parameter set and (b) the
Antarctic-specific parameter set.
Option 2: separate Arctic and Antarctic parameter sets
A slightly better fit for the two poles can be obtained with separate
parameter sets. For the Arctic, it seems desirable to increase winter SIT in
the Chukchi Sea area (by increasing c3 slightly) and to decrease the
average SIT over the central Arctic (by decreasing c2).
Figures b and b show results for the Arctic with c1=0.2 m, c2=2.4 m and c3=3 m. The spatial fit is slightly
better, but the recent Arctic mean decadal trend towards decreased average
SIT is somewhat less well reproduced. For the Antarctic, the main feature to
improve is the maximum ice thickness in the Weddell Sea, which can be
decreased by lowering c2 to 2.0 m. The Antarctic parameter set then
becomes c1=0.2 m, c2=2 m and c3=2 m. The result
(Fig. b) is indeed a decreased thickness of the perennial Weddell
Sea ice with little impact elsewhere.
In any case, these hemisphere-specific sea-ice parameter sets are not very
different from each other and are fairly similar to the original formulation.
Discussion
Sea surface temperatures
The bias correction of projected SST coming from AOGCM scenarios is fairly
easy to deal with, and different appropriate solutions have already been
proposed in the literature e.g.. In these papers, it has been demonstrated
that the use of bias-corrected SSTs has considerable influences on the
modelled climate and its response in projected scenarios for regions and
processes as different as precipitation and temperature in the tropics, the
West African monsoon and the climate of Antarctica.
In this paper, we reviewed two existing bias-correction methods and propose a
validation that allows for an objective evaluation of the efficiency of these methods
with the use of a perfect model test and a real-case application. Since both
methods show no biases in the perfect model test and succeed in reproducing
the change in mean and variability coming from the AOGCM future scenarios, we
can be confident in the use of these methods for the bias correction of future
AOGCM scenarios.
Sea-ice concentration
SIC is a quantity that has to remain strictly bounded between 0 % and
100 %, exhibits some sharp gradients, and has to remain physically
consistent with SST. Therefore the empirical bias correction of future SIC
from coupled model scenarios is a much more complex issue to deal with than
the bias correction of SSTs. The absence of satisfying solution proposals for
this issue in the literature has led to the incorrect bias correction of future
SIC in a recent study . Yet, the proposal of
convenient solutions for the bias correction of sea ice for projected
scenarios is crucial for the community interested in the downscaling of
climate scenario experiments for polar regions.
The perfect model test revealed that the LUT method shows some reduced
errors over most regions (Fig. ). However, we have seen that the
frequency distribution of future SIC obtained using this method is very
different than the original distribution in the AOGCM and unavoidably
exhibits some peaks due to the structure of LUT (Fig. ). Moreover,
the absence of SIC above 90 % in the Antarctic is also a considerable
limitation to the method considering the large differences in terms of heat
and moisture exchanges in winter between an ocean fully covered by sea ice
and an ocean that exhibits some ice-free channels . In
addition, the use of SST as a proxy for SIC is physically questionable, as we
should expect a large SIC gradient around the freezing point. The fact that
both SST and SIC are averaged over a long period (1 month) and over a
considerable area (1∘×1∘) is probably the main reason
why we nevertheless find a relation between the two variables. The real-case
application of the method also shows some difficulties for the reconstruction
of large decreases in mean SIC (Fig. a) as well as a poor
reconstruction of the change in variability in future SIC (Fig. a).
The relative anomaly method shows the largest spatial
mean errors in the perfect model test (Fig. ). The structure of
some errors seems to be constant across the reconstruction of different
climate scenarios used in the perfect model test. The empirical reduction of
SIC by an iterative “erosion” from the edges of sea-ice-covered regions
most likely has the tendency to overestimate the decrease in sea ice for some
coastal regions, while it probably fails to reproduce some processes involved
in the disappearance of sea ice in the future, such as the inflow
of warmer waters through the Barents Sea or the Bering Strait in the Arctic.
The real-case application of the relative anomaly method has shown some
systematic negative errors in the reconstruction of the decrease in mean SIC
(Fig. b) and a substantial overestimation of the decrease in
variability in the Antarctic seas (Fig. b).
The evaluation of the analogue method with the perfect model test shows that
the mean error can be locally slightly higher than for the LUT method
(Fig. ). However, the frequency distribution of the bias-corrected
SIC perfectly reproduces the frequency distribution of the sea ice in the
original AOGCM scenario (Fig. ). The real-case application of the
method succeeds in reproducing the change in mean and variability of SIC for
most of the tested regions and scenarios (Fig. c). However, the
decrease in mean (Fig. c) and variability (Fig. c) of the
sea ice in the Antarctic, particularly the Weddell Sea, is also largely
overestimated using this method. With respect to the relative anomaly method,
the fact that we use observed or AOGCM-simulated sea-ice maps to reconstruct
estimated future sea ice, and that we use a criterion for both SIA and SIE,
allows us to better reproduce some critical features of future sea-ice cover
and to obtain a more realistic frequency distribution. It should be noted
that in the perfect model test as well as in the real-case application, the
original AOGCM is not present among the possible analogue candidates. If this
is done, the results are even better using this method.
The fact that the analogue method and the relative anomaly method share the
same errors in the real-case application with a strong overestimation of the
decrease in mean and variability of the sea ice in the Weddell Sea,
particularly for the scenarios of the CNRM-CM5 model, is not a coincidence.
For both methods, the targeted future SIE (or SIA) for a given sector is a
product of the division of the integrated SIE (SIA) in the AOGCM scenario by
the corresponding quantity in the historical simulation. As a consequence,
the targeted projected SIE (SIA) for a given sector and a given month is null
when the integrated SIE (SIA) is null in the future AOGCM scenario.
Therefore, the bias in the scenario is not corrected in that case. The fact
that both methods overestimate the decrease in sea ice mainly for CNRM-CM5
scenarios is linked to the fact that the historical simulation of this
AOGCM shows some considerable negative biases for the sea ice in the Weddell
Sea with respect to the observations. Consequently, SIC in the Weddell Sea in
the CNRM-CM5 RCP8.5 scenario is low and the number of months with a complete
disappearance of sea ice is large. For these months, SIC in these sectors is
not bias corrected with the latter two methods. This means that although the
methods described here are in principle applicable to any AOGCM output, it
seems wise to exclude AOGCMs with a large negative bias in sea ice from
their historical simulation as initial material for the bias correction.
Sea-ice thickness
Given the simplicity of the proposed diagnostic SIT parameterisation, the
results are, at least in some aspects such as the predicted average Arctic
sea-ice thinning, surprisingly good. The central Arctic SIT results are
clearly adversely affected by the input SICs north of 82∘ N. Arctic
winter SIT in the marginal seas appears underestimated. In the Antarctic, the
spatial pattern of SIT is very well represented.
We think that in the absence of pan-Arctic and pan-Antarctic satellite-based
data before approximately 2000, this parameterisation can serve as a
surrogate and that it can, because it seems to have predictive power, also
serve for climate change experiments with AGCMs or RCMs. Because of its
simplicity, implementing this parameterisation should not be too complicated
in any case provided the model does explicitly take into account SIT in its
computations of heat flow through sea ice. In that case, SIT can either be
calculated online (with the need to keep track of annual minimum SIC during
the execution of the code) or be input as a daily boundary condition along
with the SIC.
Of course, another possibility would be to prescribe SIT anomalies from
coupled models. In this case, it would probably be wise to compute the
prescribe SIT using its relative thickness changes. For example, in a climate
change experiment, this would read hpresc(t)=hobs,2003-2008hsim(t)/hsim,2003-2008.
Problems could of course occur in areas where the coupled model simulates no
sea-ice cover at present. A physically consistent diagnostic parameterisation
of SIT as a function of constructed SIC, as proposed here, would not suffer
from such problems.
In any case, it is very probable that Arctic SIT will further decrease as
multi-year sea ice will be replaced by a predominantly seasonal sea-ice
cover. This should probably be taken into account in future modelling
exercises similar to CORDEX or HighResMIP given the non-negligible impact of
sea-ice thinning on winter heat fluxes in particular.
General considerations on bias correction of oceanic forcings
As already mentioned, one may doubt whether it is possible to bias correct a
GCM that has overly large biases in present-day climate. Indeed, most of the
bias-correction methods rely on the hypothesis than the climate change signal
coming from an AOGCM scenario is not dependent on the bias in the historical
simulations. This hypothesis can largely be questioned in a non-linear system
(formed by SIC and SST). For example, in a model with a large negative bias
in sea ice for present-day climate, most of the additional energy due to an
enhanced greenhouse effect will be used to heat the ocean, while it would be
primarily used to melt sea ice in a model with a correct initial sea-ice
state. For such a model, the reliability of the climate change signal in SST
is thus necessarily questionable. The selection of climate models based on
their credibility for climate change scenarios is a complex issue
e.,g. dependent on the purposes,
processes and region of study. Whether the climate change signal should
be corrected remains on open question , even though there
are good reasons to believe that model biases are time invariant
.
The skills of coupled GCMs in reproducing the observed climate and its
variability for a region of interest are often evaluated in order to use the
GCM output as forcing for downscaling experiments. However, the skills of
atmospheric GCMs are generally better when forced by observed oceanic
boundary conditions .
Similarly, even though bias-correction methods have some limitations, for
future climate experiments, there are good reasons to believe that
simulations produced using bias-corrected oceanic forcings bear reduced
uncertainties with respect to simulations realised with “raw” oceanic
forcings from coupled model scenarios such as those from the CMIP5
experiments.
Bias-corrected oceanic forcings can be used to force a regional climate model
(RCM), but in this case an additional modelling step has to be carried out,
as bias-corrected oceanic forcings should be used to force an atmosphere-only
GCM that will provide atmospheric lateral boundary conditions for the RCM in
order to ensure consistency between oceanic and atmospheric forcings,
such as in . In this framework, the use of a
variable-resolution GCM which allows us to directly use bias-corrected oceanic
forcings and downscale climate scenarios is an alternative worth considering,
as it also allows for two-way interactions between the downscaled regions and the
general atmospheric circulation.
Conclusions
In this paper, we reviewed existing methods for the bias
correction of SST and SIC and proposed new ones, such as the analogue method
for sea ice. We also proposed validation methods that allow for an objective
evaluation of bias-correction methods with the use of a perfect model test and
real-case applications.
The bias correction of SST is an issue that has already been widely addressed
in recent papers and its importance for the modelling and downscaling of
future climate scenarios has been demonstrated for multiple regions of the
world. In our analysis, we were able to demonstrate the reliability and the
suitability of absolute anomaly and quantile–quantile methods for the bias
correction of future SST scenarios.
The bias correction of SIC is a more difficult issue to address. With the
analogue method, we propose a method that shows promising results in most cases
and that allows for a reconstruction of future SIC with a realistic frequency
distribution. However, the fact that the relative anomaly
between an AOGCM scenario and its historical simulation is also used in this
method in order to determine future targeted sea-ice extent and area prevents
the bias correction of cases in which sea ice disappears entirely in a given
sector or even a hemisphere. Despite the absence of a perfect and definite
solution to this issue, we propose a new and improved method as well as a
convenient, objective way to evaluate bias-correction methods for climate
scenarios. The bias correction of sea ice is currently somewhat overlooked by
the community. The application of a multivariate bias-correction method
is also a perspective that could help with the bias
correction of SST and SIC projected scenarios at the same time. Nevertheless,
corrected SIC using the analogue method represents a substantial improvement
with respect to other previously existing bias-correction methods for sea-ice
scenarios and will therefore be made available to anyone willing to use them
as forcing for bias-corrected downscaling experiments.