Download On the persistent spread in snow-albedo feedback

Clim Dyn (2014) 42:69–81
DOI 10.1007/s00382-013-1774-0
On the persistent spread in snow-albedo feedback
Xin Qu • Alex Hall
Received: 1 August 2012 / Accepted: 16 April 2013 / Published online: 1 May 2013
Ó Springer-Verlag Berlin Heidelberg 2013
Abstract Snow-albedo feedback (SAF) is examined in
25 climate change simulations participating in the Coupled
Model Intercomparison Project version 5 (CMIP5). SAF
behavior is compared to the feedback’s behavior in the
previous (CMIP3) generation of global models. SAF
strength exhibits a fivefold spread across CMIP5 models,
ranging from 0.03 to 0.16 W m-2 K-1 (ensemblemean = 0.08 W m-2 K-1). This accounts for much of the
spread in 21st century warming of Northern Hemisphere
land masses, and is very similar to the spread found in
CMIP3 models. As with the CMIP3 models, there is a high
degree of correspondence between the magnitudes of seasonal cycle and climate change versions of the feedback.
Here we also show that their geographical footprint is
similar. The ensemble-mean SAF strength is close to an
observed estimate of the real climate’s seasonal cycle
feedback strength. SAF strength is strongly correlated with
the climatological surface albedo when the ground is
covered by snow. The inter-model variation in this quantity
is surprisingly large, ranging from 0.39 to 0.75. Models
with large surface albedo when these regions are snowcovered will also have a large surface albedo contrast
between snow-covered and snow-free regions, and therefore a correspondingly large SAF. Widely-varying treatments of vegetation masking of snow-covered surfaces are
probably responsible for the spread in surface albedo where
snow occurs, and the persistent spread in SAF in global
climate models.
X. Qu (&) A. Hall
Department of Atmospheric and Oceanic Sciences,
University of California, Los Angeles,
CA 90095-1565, USA
e-mail: [email protected]
Keywords
cycle
Snow-albedo feedback Spread Seasonal
1 Introduction
Snow-albedo feedback (SAF) enhances climatic anomalies
in Northern Hemisphere (NH) land masses because of two
changes in the snowpack as surface air temperature (Ts)
increases (Budyko 1969; Sellers 1969; Schneider and
Dickinson 1974; Robock 1983; Robock 1985; Cess et al.
1991; Randall et al. 1994; Hall 2004; Bony et al. 2006;
Winton 2006; Qu and Hall 2007; Flanner et al. 2011;
Fletcher et al. 2012). First, snow cover shrinks, and where
it does it generally reveals a land surface that is much less
reflective of solar radiation. Second, the remaining snow
generally has a lower albedo due to snow metamorphosis.
For example, wet melting snow, more common in a warmer climate, has a lower surface albedo than dry frozen
snow (Robock 1980).
The strength of SAF, including both effects, can be
quantified by the amount of additional net shortwave
radiation at the top of atmosphere (TOA) averaged over
NH extratropical land masses (R) as surface albedo (as)
decreases in association with a 1oC increase in Ts as follows (see also Hall and Qu 2006; Qu and Hall 2007):
net
DQ
1
ðtÞ ¼
AðRÞ
DT s
Z
oQnet
ðt; rÞDas ðt; rÞdAðrÞ=DT s ðtÞ
oas
R
Z
1
oap
Das ðt; rÞ
¼
dAðrÞ
Qðt; rÞ
ðt; rÞ AðRÞ
oas
DT s ðtÞ
ð1Þ
R
Here Q and Qnet are the incoming and net shortwave
radiation at the TOA, ap is the planetary albedo, A is the
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70
X. Qu, A. Hall
area of R; DT s is the increase in the regionally-averaged
R
surface air temperature (¼ DTs ðt; rÞdAðrÞ=AðRÞ), and
R
t represents the 12 months of year. Equation (1) indicates
that the strength of SAF is primarily determined by two
terms, a coefficient representing the variations in planetary
albedo with surface albedo (qap/qas) and another
representing the change in surface albedo associated with
a 1oC increase in Ts (Das =DT s ). (While Q appears in
Eq. (1), the variations in it from model to model are
negligible. Therefore it is not discussed in this work.) The
magnitude of the second term is determined by the
combined strength of the snow cover and snow
metamorphosis feedbacks described above. We note that
in some cases, changes in surface albedo (Das ) may not be
solely attributed to snow changes. For example, changes in
vegetation type and cover in areas where snow is found
may also contribute to Das :
Several methods have recently been used to estimate
qap/qas. Qu and Hall (2006) developed a physically-based
regression model for planetary albedo, in which planetary
albedo is expressed as a function of surface albedo, cloud
cover and cloud optical thickness, and clear-sky planetary
albedo. Based on this model, they estimated the typical
value of qap/qas in climate models and satellite-based
observational data sets to be about 0.5. Making some
simple assumptions about the shortwave radiation transfer
in the atmosphere, Donohoe and Battisti (2011) derived an
analytical model where planetary albedo is expressed as a
function of surface albedo and other quantities that can be
derived from TOA and surface shortwave fluxes. Based on
this model, they estimate qap/qas to be 0.34, 30 % smaller
than the estimate of Qu and Hall (2006). In spite of this
discrepancy, both studies show that climate models participating in the Coupled Model Intercomparison Project
version 3 (CMIP3) exhibit little intermodel variation in
qap/qas.
While there was consistency from model to model in
qap/qas in the CMIP3 ensemble, the second term in Eq. (1),
Das =DT s averaged over NH extratropical land masses
(referred hereafter to as D
as =DT s ) exhibited a threefold
spread (Qu and Hall 2006). Much of the spread in Das =DT s
originated in the snow cover rather than the snow metamorphosis component of this term (Qu and Hall 2007). The
spread in the strength of the snow cover component was in
turn mostly attributable to a correspondingly large spread
in mean effective snow albedo, defined as the albedo of
100 %-snow-covered surfaces. Models with large effective
snow albedos have a large surface albedo contrast between
snow-covered and snow-free regions, and exhibit a correspondingly large surface albedo decrease when snow cover
decreases.
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To constrain Das =DT s in the CMIP3 models (and hence
their SAF, since this is the term in which the feedback
spread is concentrated), Hall and Qu (2006) examined
seasonal variations of NH continental surface albedo
associated with the springtime warming. Their premise is
that SAF would behave similarly in the contexts of seasonal cycle and climate change. Therefore, the magnitudes
of Das =DT s in the two contexts may be comparable.
Indeed, they found almost a one-to-one correspondence
between Das =DT s in the two contexts. Since Das =DT s in
the seasonal cycle is a measurable quantity, these findings
map out a strategy to constrain SAF with observations and
ultimately reduce spread of SAF in climate simulations.
Hall and Qu (2006) examined the April value of
Das =DT s rather than the annual-mean value. This choice
was made based on two considerations: (1) The bulk of
SAF takes place in spring, and (2) the monthly values of
Das =DT s are strongly correlated across the spring months.
This work was extended by Fletcher et al. (2012) to include
March and May. Note that their region of interest is land
masses north of 45N rather than whole NH extratropical
land masses. They found that the springtime-mean values
of Das =DT s in the two contexts are still strongly correlated.
However, they also found that in most of the CMIP3
models, the feedback in the context of climate change is
weaker than the feedback in the context of seasonal cycle.
It is unknown whether this inconsistency with Hall and Qu
(2006) is due to methodological differences in the two
studies or statistical uncertainty in the SAF relationship
between the two contexts. Furthermore, the continued
development of climate models raises the question of
whether this relationship holds for the new generation of
global climate models participating in the Coupled Model
Intercomparison Project version 5 (CMIP5). For example,
many CMIP5 models include dynamic vegetation schemes.
Changes in vegetation type and cover are simulated in
models with these schemes. Conceivably, these changes
could differ in the contexts of the seasonal cycle and climate change, complicating the SAF relationship in the two
contexts.
In light of this background, the overarching goal of this
study is to provide an update on SAF and its behavior in the
CMIP5 climate simulations (see Table 1). The study has
four sub-aims: (1) To briefly clear up the lingering disagreement regarding the correct value for qap/qas in the
SAF context, (2) To see whether the spread in SAF has
narrowed in the CMIP5 ensemble, and determine the
consequences of this spread for NH climate change, (3) To
see whether the seasonal cycle/climate change relationship
also holds in the CMIP5 ensemble, and (4) To shed light on
what still might be causing the spread in SAF.
Persistent spread in snow-albedo feedback
71
Table 1 1st column: Reference letters of 25 CMIP5 models
Letter
Model name (Group)
SAF (NH)
SAF
(global)
Reference
A
ACCESS1.0 (CSIRO-BOM)
0.41
0.08
Collier and Uhe (2012)
B
BCC-CSM1.1 (BCC)
0.31
0.06
Wu et al. (2010)
C*
CCSM4 (NCAR)
0.42
0.08
Gent et al. (2011)
D
CNRM-CM5 (CNRM-CERFACS)
0.44
0.08
Voldoire et al. (2012)
E
CSIRO-Mk3.6.0 (CSIRO-QCCCE)
0.18
0.03
Rotstayn et al. (2010)
F
CanESM2 (CCCMA)
0.40
0.07
Chylek et al. (2011)
G
H
FGOALS-g2 (LASG-CESS)
FGOALS-s2 (LASG-IAP)
0.48
0.38
0.10
0.06
Yu et al. (2011)
Bao et al. (2013)
I
GFDL-CM3 (NOAA GFDL)
0.54
0.11
Donner et al. (2011)
J
GFDL-ESM2G (NOAA GFDL)
0.24
0.05
Dunne et al. (2012)
K
GFDL-ESM2M (NOAA GFDL)
0.24
0.04
Dunne et al. (2012)
L
GISS-E2-R (NASA GISS)
0.48
0.09
http://www.giss.nasa.gov
M*
HadGEM2-CC (MOHC)
0.45
0.09
Martin et al. (2011)
N*
HadGEM2-ES (MOHC)
0.43
0.08
Martin et al. (2011)
O
INM-CM4 (INM)
0.56
0.10
Volodin et al. (2010)
P*
IPSL-CM5A-LR (IPSL)
0.28
0.05
Dufresne et al. (2013)
Q*
IPSL-CM5A-MR (IPSL)
0.26
0.05
Dufresne et al. (2013)
Dufresne et al. (2013)
R*
IPSL-CM5B-LR (IPSL)
0.22
0.04
S*
MIROC-ESM (MIROC)
0.77
0.16
Watanabe et al. (2011)
T*
MIROC-ESM-CHEM (MIROC)
0.78
0.16
Watanabe et al. (2011)
U
MIROC5 (MIROC)
0.52
0.12
Watanabe et al. (2010)
V*
W*
MPI-ESM-LR (MPI-M)
MPI-ESM-MR (MPI-M)
0.44
0.44
0.08
0.08
Brovkin et al. (2013)
Brovkin et al. (2013)
X
MRI-CGCM3 (MRI)
0.29
0.05
Yukimoto et al. (2011)
Y*
NorESM1-M (NCC)
0.44
0.10
Bentsen et al. (2012)
Ensemble
0.42 ± 0.15
0.08 ± 0.03
Models with dynamic vegetation schemes are identified by the asterisk. Note that while CCSM4 includes a dynamic vegetation scheme, the
scheme was turned off in CCSM4’s CMIP5 simulations (Keith Oleson, personal communication). 2nd column: Acronyms of the models and
associated modeling groups (http://cmip-pcmdi.llnl.gov/cmip5/citation.html). 3rd column: SAF strength averaged over Northern Hemisphere
extratropical land masses. 4th column: Contribution of NH extratropical land masses to the global albedo feedback. It is obtained by re-scaling
regional-mean SAF strength by the product of two factors: One is the ratio of the area of NH extratropical land masses to the area of the globe and
the other is the ratio of increases in surface air temperature averaged over the NH extratropical land masses to increases in global-mean surface air
temperature. The ensemble-mean and intermodel standard deviation of the regional-mean SAF strength and its contribution to the global albedo
feedback are also shown. The unit of the numbers in 3rd and 4th columns is W m-2 K-1. 5th column: References are provided for each model.
Note that while several models listed in the table are capable of simulating biogeochemical cycles, simulations used in this work are those with
prescribed greenhouse gas concentrations (i.e., the ‘‘history’’ and ‘‘RCP8.5’’ simulations)
2 Quantifying SAF and its effects in CMIP5
We begin by briefly revisiting the dependence of planetary
albedo on surface albedo (qap/qas) in the SAF context. As
discussed above, there is some discrepancy in recent estimates of qap/qas. To clarify this, we employ surface albedo
radiative kernels recently developed by Shell et al. (2008)
and Soden et al. (2008). In these kernels, the TOA net
shortwave anomalies associated with a 1 % change in
surface albedo (while holding atmospheric conditions
unchanged) are estimated using radiative transfer codes in
the National Center for Atmospheric Research (NCAR)
and the Geophysical Fluid Dynamics Laboratory (GFDL)
atmospheric general circulation models. (These kernels
have been applied in the previous studies (Shell et al. 2008,
Soden et al. 2008, Flanner et al. 2011) to quantify modeled
and observed albedo feedback). To obtain qap/qas, we
divide these anomalies by the TOA incoming shortwave
radiation (Q). Since these kernels realistically simulate
radiative transfer in the atmosphere, the kernel method is
more likely to capture the functional dependence of planetary albedo on surface albedo than the analytical models
of Qu and Hall (2006) and Donohoe and Battisti (2011).
Therefore, qap/qas values based on these kernels are
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72
probably more accurate than either the estimates in Qu and
Hall (2006) or Donohoe and Battisti (2011).
Based on the two radiative kernels, we estimate the
monthly values of qap/qas at all locations for every month.
Figure 1a shows the monthly estimates of qap/qas averaged
over NH extratropical land masses for the 12 months. Both
the GFDL and NCAR estimates vary only slightly, hovering around 0.35 throughout the year. (Due to variations in
atmospheric conditions, both the GFDL and NCAR estimates of qap/qas vary somewhat from region to region.)
These estimates are broadly consistent with those of
Donohoe and Battisti (2011), indicating that the estimate of
Qu and Hall (2006) is indeed systematically and positively
biased by about 30 %. The identification of a bias in a
previous estimate of qap/qas would have the effect of
reducing the estimated global impact of SAF somewhat
(see Eq. (1)). However, since the bias is systematic, there is
no reason to revise the more fundamental conclusion,
drawn by both Qu and Hall (2006) and Donohoe and
Battisti (2011), that very little intermodel spread in SAF is
contained in this term.
Turning our attention to the other term in Eq. (1), the
ensemble-mean D
as =DT s in NH extratropical land masses
for each month is shown in Fig. 1b. This quantity ranges
from 0.6 to 0.9 % K-1 for most of the year, except for four
months, June through September. In these months,
D
as =DT s is somewhat smaller, ranging from 0.1 to 0.3 %
K-1. The intermodel standard deviations of D
as =DT s are
shown as whiskers in Fig. 1b. The intermodel spread in
D
as =DT s is large throughout the year. Comparison with
Das =DT s values in the CMIP3 ensemble (Hall and Qu
2006) reveals that the intermodel spread in this quantity has
not narrowed in the CMIP5 ensemble.
Based on oap =oas ; Das =DT s and Q, we quantify the
feedback strength using Eq. (1). To examine whether different radiative kernels introduce significant differences in
the feedback estimates, we quantify the feedback strength
using both the NCAR and GFDL estimates of qap /qas. It
turns out that both kernels give very similar seasonal
variations in the feedback strength (Fig. 1c): The bulk of
the ensemble-mean feedback takes place in spring, with
non-negligible contributions from February and June. This
is consistent with the previous studies (Robock 1983; Hall
2004; Qu and Hall 2007) demonstrating that SAF is
strongest when both Q and snow cover are large. We note
that due to the slightly larger GFDL estimate of qap /qas
(see Fig. 1a), the GFDL feedback estimate is also slightly
larger in most months.
The intermodel standard deviations of the feedback
strength are shown as whiskers in Fig. 1c. In both estimates, the largest intermodel spread occurs in springtime.
Interestingly, the spread is also relatively large in June. In
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X. Qu, A. Hall
a
b
c
Fig. 1 a Seasonal cycle of qap/qas averaged over NH extratropical
land masses. It is estimated based on the NCAR and GFDL radiative
kernels. For each monthly estimate, we first compute qap/qas at each
grid point, and then average it over land masses north of 30N. Land is
defined as grid boxes where land cover, specified in NCAR and
GFDL models, is greater than 65 %. This threshold was originally
used by the International Satellite Cloud Climatology Project
(Rossow and Schiffer 1991) and later adopted in Hall and Qu
(2006). To be consistent with Hall and Qu (2006), we use this
threshold throughout the paper. b Seasonal cycle of the ensemblemean (gray bars) and cross-model standard deviation (whiskers) of
Das =DT s averaged over NH extratropical land masses in 25 CMIP5
models. In each model, Das and DT s are calculated based on
climatological monthly values of as and Ts in the periods 1980–1999
and 2080–2099. Data for the period 1980-1999 is taken from
historical simulations and RCP8.5 simulations for the period
2080–2099. c Seasonal cycle of the ensemble-mean (gray bars) and
cross-model standard deviation (whiskers) of feedback strength
averaged over NH extratropical land masses (measured by Eq. (1))
in 25 CMIP5 models. In each model, we first regrid the radiativekernel-based estimates of qap/qas to the model-specific grid, and then
average the product of Q, qap/qas and Das =DT s over NH extratropical
land masses. Note that in all panels, supporting data are area-weighted
before computing the regional averages
all months, the intermodel spread in the feedback strength
in either the GFDL- or NCAR-based feedback estimate is
about an order of magnitude larger than the ensemble-mean
difference between the GFDL and NCAR feedback estimates. Therefore, we ignore the differences in the GFDL
and NCAR feedback estimates and use the mean of the two
estimates in the subsequent calculations. We acknowledge
that by doing so, the actual intermodel spread of the
feedback strength may be slightly underestimated.
Based on the feedback strength in each month, we
estimate the annual-mean feedback strength for each model
as follows
Persistent spread in snow-albedo feedback
net
DQ
DT s
¼
mean
73
X DQ
X
net
ðtÞDT s ðtÞ=
DT s ðtÞ
DT s
t
ð2Þ
t
where t represents the 12 months of year. The values of this
quantity for each model are shown in Table 1. It ranges
from 0.18 to 0.78 W m-2 K-1, a fourfold spread. It is also
informative to provide a global-mean estimate of the
feedback strength for each model to be consistent with the
conventional definition of global climate feedbacks. We
obtain this by re-scaling the regional-mean SAF strength
with the product of two factors: One is the ratio of the area
of NH extratropical land masses to the area of the globe
(ensemble-mean value is 0.12). Though it is calculated
based on the model-specific land cover, intermodel variations in this quantity are small. The other is the ratio of
increases in annual-mean surface air temperature averaged
over the NH extratropical land masses to increases in
annual- and global-mean surface air temperature. The
ensemble-mean and intermodel standard deviation of this
quantity are respectively: 1.60 and 0.13. The resultant
global-mean feedback strength for each model is also given
in Table 1. It ranges from 0.03 to 0.16 W m-2K-1, with
the ensemble-mean of 0.08 W m-2K-1. For comparison,
the ensemble- and global-mean of the net feedback strength
in the CMIP5 ensemble is -1.08 W m-2K-1 (Andrews
et al. 2012).
While these numbers suggest that SAF may not be the
strongest feedback on a global scale, the feedback is highly
relevant to climate change in heavily-populated NH
extratropical land masses. Calculations by Mark Zelinka
(personal communication) demonstrate that in springtime,
SAF is the largest positive feedback in NH extratropical
land masses and that the intermodel spread of SAF is as
large as the intermodel spread of cloud feedbacks in the
same region. (See also Zelinka and Hartmann (2012) for a
comparison of surface-albedo and cloud feedbacks in NH
extratropical land masses.) The importance of SAF to climate change in NH extratropical land masses can also be
assessed by correlating the annual-mean feedback strength
(the numbers in the third column of Table 1) with zonalmean surface air temperature change over land across
models. Figure 2 shows the correlation between the two
quantities for every month across the NH mid-latitudes. We
find that the feedback strength is well-correlated with
warming in February through June. The typical correlation
in springtime is 0.6– 0.7. Regions with the largest correlations tend to be found at higher latitudes as spring progresses into summer. Assuming that SAF is uncorrelated
with other feedbacks, this suggests that 40–50 % of the
intermodel variance in the local warming can be attributed
to differences in the strength of SAF from about February
through June. The link between SAF strength and warming
seems to persist throughout the summer, though it is
Fig. 2 Cross-model correlation between the annual-mean SAF
strength and zonal-mean surface warming over land areas, for each
month. Surface warming is quantified as the difference between the Ts
climatologies in the periods 1980–1999 and 2080–2099
weaker. (See Hall et al. 2008 for a discussion of the link
between SAF and summertime warming in mid-latitudes in
the CMIP3 ensemble.)
3 Seasonal cycle and climate change relationship
In this section, we explore whether the CMIP5 simulations
exhibit the same tight relation between the SAF strength in
the contexts of seasonal cycle and climate change as their
CMIP3 counterparts.
As discussed in the introduction, Das =DT s is used as a
proxy for the feedback strength in Hall and Qu (2006) and
Fletcher et al. (2012). In this study, however, we adopt a
more direct approach and focus on the feedback strength
itself. (For comparison, we also examine Das =DT s using
the same methodology as in Hall and Qu (2006). These
analyses are presented in the Appendix.) We examine not
only the three spring months (March through May), but
also February and June. These last two months are included
to make the results as robust as possible, as their contributions to the feedback are not negligible (Fig. 1c).
We first quantify the mean SAF strength in the five
months (February through June) for both climate change
and the seasonal cycle. For climate change, we average the
SAF strength over the five months using Eq. (2). We find
that the annual-mean SAF strength is almost perfectly
correlated with SAF strength averaged over the five months
(Fig. 3). This confirms that, apart from a scaling factor,
intermodel variations in the annual-mean SAF strength are
well represented by the February-June average (see also
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74
Fig. 3 Scatterplot of feedback strength averaged over 5 months from
February through June (FMAMJ) and annual-mean feedback strength,
as shown in the third column of Table 1 in 25 CMIP5 models. See
also Table 1 for the names of the models. The thick dashed line
represents the best-fit regression line
Fig. 1c). For the seasonal cycle, we first calculate SAF
strength for each of the five months based on Eq. (1).
Consistent with Hall and Qu (2006) and Fletcher et al.
(2012), we quantify SAF strength in each month based on
differences in climatological values of surface albedo and
temperature between this month and the subsequent month.
For example, to estimate SAF strength in February, we use
February and March. Once we obtain SAF strength for
each of the five months, we average the SAF strength over
the five months to get the mean SAF strength.
The mean feedback strength in the context of climate
change is scattered against the mean feedback strength in
the context of seasonal cycle in Fig. 4. We find a high
degree of correspondence between the two quantities
(r = 0.86) in the 25 CMIP5 models including even models
with dynamic vegetation schemes (color-coded in blue).
This is further supported by simple regression analysis,
which reveals that the slope of the best-fit line between the
two quantities (s = 0.96) is not significantly different from
one and the intercept of the line (i = - 0.003 W m-2 K-1)
is not significantly different from zero. To compare with
Fletcher et al. (2012), we also examine the seasonal cycle
and climate change relationship using only the three spring
months. The correlation, the slope of the best-fit line and
the intercept of the line for these months are respectively:
0.86, 1.21 and -0.21. We find no evidence that SAF
strength in the context of climate change is systematically
smaller than SAF strength in the context of seasonal cycle,
as suggested in Fletcher et al. (2012). In fact, the ensemblemean SAF strength in both contexts is close to 1 W
m-2K-1.
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X. Qu, A. Hall
Fig. 4 Scatterplot of the feedback strength averaged over 5 months
from February through June (FMAMJ) in the context of climate
change versus the same measure in the context of seasonal cycle in 25
CMIP5 models. The thick dashed line represents the best-fit
regression line. The observed feedback strength in the seasonal cycle
(the thin vertical line) and statistical uncertainty of the observed
estimate (the gray area) are estimated based on MODIS surface
albedo, ERA-Interim temperature, NCAR and GFDL surface albedo
radiative kernels (see the text for details). Models with dynamic
vegetation schemes (see Table 1) are color-coded in blue
The credibility of the physics behind the tight SAF
relation seen in Fig. 4 can be assessed in terms of the
similarity in the geographic distributions of SAF in the two
contexts. To do this, we first quantify the local contribution
to SAF for each model, month and context using Eq. (1)
without areal integration. We then average the local SAF
contribution over the five critical months for SAF (February through June) using Eq. (2) for each model and context.
Figure 5 shows the ensemble-mean of the local SAF contribution in the contexts of seasonal cycle and climate
change. The CMIP5 models generally exhibit broadly
similar geographic distributions in SAF whether the context is the seasonal cycle or climate change. In both cases,
the largest contributions to SAF originate in the Tibetan
Plateau, along the Rocky Mountains, and across much of
the forest zone in Siberia and northern Canada. The contribution from central Asia is also significant. Climatological snow cover in these regions generally persists for a
longer portion of the year than elsewhere (see also Fig. 7a).
Therefore, the effect of snow reduction on the surface
radiation budget as the climate warms also persists longer.
Note that similarly large contributions from Siberia,
northern Canada and central Asia in the context of seasonal
cycle are also reported in Fletcher et al. (2012) for CMIP3
models. The similarity in the ensemble-mean geographic
distributions of SAF can be quantified by correlating the
Persistent spread in snow-albedo feedback
Fig. 5 The ensemble-mean of
the local SAF contribution in
the contexts of a climate change
and b seasonal cycle. See the
text for a description of how
they are calculated
75
a
b
two spatial patterns in Fig. 5 (r = 0.80). (In this paper, to
compute the correlation between two spatial patterns, we
concatenate all grid points comprising each spatial pattern
into a series, and then apply simple correlation analysis to
the series.) The same spatial correlation is also high when it
is calculated based on data from individual models. (The
ensemble-mean value of this correlation is 0.64, with the
intermodel standard deviation of 0.2.) Clearly, the simulated seasonal cycle and climate change versions of SAF
have a similar geographic footprint in all models. This
lends credence to the SAF relationship between the two
contexts, since it implies that the physics linking the two
versions of the feedback operates at the local as well as the
hemispheric scale.
Given this tight relationship between SAF in the two
contexts and the credibility of the physics behind it, we can
constrain SAF in the context of climate change using
observed SAF in the context of seasonal cycle. To obtain
an observed estimate of SAF strength, we use the recent
(2001–2012) surface albedo measurements from the
Moderate Resolution Imaging Spectroradiometer (MODIS,
Jin et al. 2003) and surface air temperature from European
Center for Medium Range Weather Forecasts Reanalysis
(ERA-Interim, Dee et al. 2011) for the same period. (The
mean of the GFDL and NCAR estimates of qap/qas is used
in this calculation.) MODIS provides both black- and
white-sky surface albedos. To fully sample the uncertainty
in the observed estimate, we use both measures in the
analysis.
Observed SAF strength in each year is estimated by
plugging the observed monthly surface albedo and temperature data into Eqs. (1) and (2). Based on the 12 yearly
estimates, we obtain the mean SAF strength for the
2001–2012 period and the 95 % confidence interval of the
mean estimate. The resultant SAF estimates with the black-
and white-sky surface albedos are respectively:
0.91 ± 0.02 and 0.83 ± 0.02 W m-2K-1. (A similar difference is also reported in Flanner et al. 2011). Since the
actual surface albedo lies somewhere between black- and
white-sky surface albedos, depending on the relative
magnitudes of direct and diffuse incidence at the surface,
the actual SAF must also lie between the white-sky-albedo
and black-sky-albedo-based estimates. For simplicity, we
assume that the proportions of direct and diffuse incidence
in total surface incidence are equal, and obtain an estimate
of observed SAF by averaging the two mean estimates.
This leads to a value of 0.87 W m-2K-1 (represented by
the thin vertical line in Fig. 4). While the 95 % confidence
intervals of both the white-sky-albedo and black-skyalbedo-based estimates are 0.02 W m-2K-1, to account for
the error in our assumption for the relative magnitudes of
direct and diffuse incidence, we use a larger confidence
interval for our best estimate. We adopt the lower bound of
the white-sky-albedo-based estimate (0.81 W m-2K-1) for
the lower bound of the actual SAF and the upper bound of
the black-sky-albedo-based estimate (0.93 W m-2K-1) for
the upper bound of the actual SAF (see the gray area in
Fig. 4). Note that this is the maximum possible confidence
interval one could obtain, since the lower bound implies all
solar radiation is diffuse, while the upper bound implies it
is all direct.
Clearly, even with these generous confidence intervals
for the observed estimate, the simulated seasonal cycle
feedback strength in many models is biased. Some models
(e.g., S and T) overestimate the feedback by about 50 %,
while others (e.g., B, P, Q and R) underestimate it by the
same amount. Overall, there are more negatively-biased
models than positively-biased models. The ensemblemean seasonal cycle feedback strength turns out to be
0.81 W m-2K-1, precisely the lower bound of the
123
76
Fig. 6 The intermodel standard
deviation of local SAF
contribution in the contexts of
a climate change and b seasonal
cycle. See the text for a
description of how they are
calculated
X. Qu, A. Hall
a
b
Fig. 7 a The total number of
times the local climatological
monthly snow cover in the
1980–1999 period is greater
than 90 % in the 14 CMIP5
models with available snow
cover data. b The zonal-mean
values of as(90 %) in the 14
models (gray points). The
ensemble-mean (thick black
line) and cross-model standard
deviation (whiskers) of the
zonal-mean as(90 %) values are
also shown. Note that the
number of models used to
calculate the ensemble-mean
and standard deviation varies
with latitude from 9 to 14
a
b
observed estimate. In the eight models with SAF strength
in the seasonal cycle context within the observed range,
SAF strength in climate change ranges from 0.5 to 1 W
m-2K-1 (Fig. 4). In comparison, the full spread of the
feedback in climate change is from 0.3 to 1.4 W m-2K-1.
Therefore, roughly half of the intermodel spread in climate
change would be eliminated if simulated seasonal cycle
SAF strength were brought in line with observations.
4 Sources of SAF spread in the CMIP5 ensemble
In this section, we look into the causes of SAF spread
across the CMIP5 models. We first examine the geographic
123
distribution of the local contribution to SAF spread,
quantified by its intermodel standard deviation. (Procedures to get the local feedback contribution are described in
Sect. 3.) The feedback spread is distributed similarly in the
seasonal cycle and climate change contexts (Fig. 6). In
both cases, the largest spread occurs in Siberia, the Tibetan
Plateau, the Southern Rocky Mountains and northern
Canada. (These regions are also where local contribution to
the ensemble-mean feedback is the largest (Fig. 5)).
Interestingly, an appreciable spread is also found in the
coastal regions of Greenland. This is the result of strong
local SAF in 4 CMIP5 models, and negligible local SAF in
the others. (The influence of the four models to the
ensemble-mean local feedback is also visible in Fig. 5.)
Persistent spread in snow-albedo feedback
We suspect that the Greenland ice sheet is treated differently in these four models. In any case, the contribution of
Greenland to the overall feedback spread shown in Fig. 4 is
small because this region accounts for only a small percentage of NH extratropical land masses.
As demonstrated in Qu and Hall (2007) and Fletcher
et al. (2012), the single most important factor determining
the feedback strength in the CMIP3 models is mean
effective snow albedo, defined as the albedo of 100 %snow-covered surfaces. To explore whether this relationship still holds in the CMIP5 ensemble, we examine the 14
CMIP5 models that provide snow cover data. In about 1/3
of these models, snow cover in the NH land masses never
reaches 100 %, making it impossible to estimate effective
snow albedo in the same manner as Qu and Hall (2007). To
circumvent this difficulty, we relax the requirement that the
surfaces be 100 % snow-covered, and quantify the albedo
of surfaces with at least 90 % snow cover, referred hereafter to as as(90 %). To locate as(90 %), we compute the
total number of times the local climatological monthly
snow cover is greater than 90 % in the 14 models for the
late 20th century. (Thus a point that has greater than 90 %
snow cover throughout year in all models would have a
count of 14 models 9 12 months = 168). Not surprisingly,
heavily snow-covered surfaces generally occur at the high
latitudes including Greenland, northern Canada, Alaska
and northern Euraisa (Fig. 7a). Extensive snow cover is
also seen in the Tibetan Plateau and some isolated regions
in the Rocky Mountains.
To compare as(90 %) across models, we average
as(90 %) over all the cases within each latitude for every
model. (Greenland is excluded in this averaging because of
its minuscule contribution to the feedback (Fig. 5).) The
resulting zonal mean values of as(90 %) for all 14 models
are shown in Fig. 7b (gray points). Based on these zonalmean values, we compute the ensemble-mean and intermodel standard deviation of as(90 %) for each latitude.
The ensemble-mean as(90 %) (the thick line in Fig. 7b)
ranges from 0.50 to 0.78. The minimum values are found in
the 45–65N latitude range, a region generally occupied by
boreal forests. It is very likely that the small values of
as(90 %) in this region can be attributed to the masking
effect of vegetation canopy on the underlying snow-covered surface. The largest intermodel spread of as(90 %)
(represented by the whiskers in Fig. 7b) is found in the
boreal forest zone and the 30–40N latitude range. We find
that values of as(90 %) in these two regions are highly
correlated across models (r = 0.86), signifying high spatial
coherence in as(90 %) within each model. Note that the
two regions are also the regions where the largest spread in
the local feedback contribution is found (Fig. 6). This
provides a hint that differences in as(90 %) may be behind
the spread in local feedback contribution.
77
To examine the relationship between as(90 %) and
feedback strength across models, we first average as(90 %)
north of 30N for each model. The average as(90 %) in the
14 models exhibits a large range, from 0.39 to 0.75
(Fig. 8a). We then scatter the feedback strength in the
context of seasonal cycle versus the average as(90 %) in
Fig. 8b. There is a high correlation between the two
quantities (r = 0.80). We also scatter the feedback strength
in the context of climate change versus the average
as(90 %) in Fig. 8c. As would be expected given the
relationship seen in Fig. 4, there is a similarly high correlation between the two quantities (r = 0.76). Thus the
physics underpinning the relationship between the seasonal
cycle and climate change manifestations of SAF are rather
straightforward. In both cases, the models are providing
different estimates of the reflectivity of snow-covered
surfaces in the boreal forest zone, the Tibetan Plateau and
the Southern Rocky Mountains, leading to proportionately
different estimates of the surface albedo reduction in these
regions as the climate warms.
Qu and Hall (2007) suggest that the reflectivity of snowcovered surfaces is closely linked to the treatment of the
masking effect of vegetation canopy on the underlying
surfaces in the CMIP3 models. For example, they find that
unrealistically low albedos of snow-covered surfaces generally occur in models with explicit treatment of the
masking effect. In these types of models, the overall surface albedo is a weighted mean of canopy albedo and
ground albedo, with weights given by the fraction of vegetation coverage. Preliminary investigation indicates this
assessment may also be valid in the CMIP5 ensemble. For
example, model B (i.e, the model with the lowest value of
as(90 %)) uses an explicit scheme to account for the
masking effect (see the reference listed in Table 1). We
speculate that in this model and perhaps in others with
explicit schemes, either (1) vegetation coverage determining the weighting of canopy albedo and ground albedo is
too large, placing unrealistic emphasis on the vegetation
canopy in the determination of overall effective surface
albedo when the ground is at least partly snow-covered or
(2) prescribed albedos of snow-covered ground and canopy
when snow is present are too low.
5 Summary and implications
The two factors controlling SAF in transient climate
change are quantified based on RCP8.5 runs of 25 CMIP5
models. The first is the variation in planetary albedo with
surface albedo, representing the atmosphere’s attenuation
effect on surface albedo anomalies. It is quantified using
surface albedo radiative kernels recently developed with
the atmospheric general circulation models of the
123
78
Fig. 8 a Regionally-averaged
values of as(90 %) in the 14
CMIP5 models with available
snow cover data. b Scatterplot
of the feedback strength in the
context of seasonal cycle versus
the average as(90 %).
c Scatterplot of the feedback
strength in the context of
climate change versus the
average as(90 %). Dash line in
each scatterplot represents the
best-fit regression line
X. Qu, A. Hall
a
b
Geophysical Fluid Dynamics Laboratory and the National
Center for Atmospheric Research. The two kernels yield
similar values for this factor throughout the year, hovering
around 0.35. This new, more accurate, calculation clarifies
the discrepancy in the previous estimates for the factor in
Qu and Hall (2006) and Donohoe and Battisti (2011). It
turns out that Qu and Hall (2006) overestimate it by about
30 %, while Donohoe and Battisti (2011) give a more
accurate estimate. In spite of the systematic bias in one of
the previous estimates, there is very little intermodel spread
in this quantity.
The second factor is the sensitivity of surface albedo to
changes in surface air temperature, measured by the ratio of the
change in surface albedo over the 21st-century to the change in
surface air temperature for the same period. This term exhibits
a fivefold spread across models. This leads to a comparable
spread in simulated SAF strength, ranging from 0.03 to
0.16 W m-2K-1 (ensemble-mean = 0.08 W m-2K-1). The
spread in SAF is very similar to that found in CMIP3
models, and it accounts for much of the spread in the 21st
century warming of Northern Hemisphere land masses in
the CMIP5 ensemble, especially in spring and early
summer.
As with the CMIP3 models, SAF in the CMIP5 models
may be quantified in the context of the current climate’s
seasonal cycle. In the CMIP5 models, there is a high degree
123
c
of correspondence between the seasonal cycle and climate
change versions of the feedback strength. Thus the CMIP5
ensemble is tracing out an identical relationship between
SAF strength in two contexts as the CMIP3 ensemble. An
observed estimate of SAF strength in the seasonal cycle is
obtained. While the ensemble-mean SAF strength is found
to be close to the observed estimate, there are more negatively-biased models than positively-biased models. This
is qualitatively consistent with a recent SAF estimate based
on observed snow cover trends for the period 1979–2008
(Flanner et al. 2011).
For both seasonal cycle and climate change cases, the
feedback has a very similar geographic footprint. Most of
the feedback and its spread originate in the boreal forest
zone, the Tibetan Plateau and the Southern Rocky Mountains. Moreover, the SAF strength in both contexts is
strongly correlated with the climatological surface albedo
when ground is nearly or completely covered by snow in
these regions. This quantity ranges from 0.39 to 0.75 in the
14 models with available snow cover data. Models with a
large surface albedo when these regions are snow-covered
will also have a large surface albedo contrast between
snow-covered and snow-free regions, and therefore a correspondingly large SAF. (A similar conclusion is also
reached in Qu and Hall (2007) and Levis et al. (2007) for
CMIP3 models.) Thus the physics underpinning the
Persistent spread in snow-albedo feedback
relationship between the seasonal cycle and climate change
manifestations of SAF seem straightforward and credible.
If the biases in the seasonal cycle SAF were reduced in the
next ensemble of global simulations, a reduction in the
spread in the climate change version of SAF would result.
This reduction would be an improvement in overall model
quality because it would occur for reasons consistent with
climate physics that are easy to understand, and rather
difficult to ignore.
How then to achieve this? Clearly a first step would be
to constrain the bulk surface reflectivity when the surface is
snow-covered, with an emphasis on the heavily-vegetated
landscapes, for example, the boreal forest zone. A recent
effort was made by Flanner et al. (2011) to estimate the
albedos of various snow-covered surfaces based on the
MODIS surface albedo and NOAA/Rutgers snow cover
measurements. These estimates will be useful in constraining simulated albedos in climate models. Further
steps would involve delving into why individual models
give such different estimates of this quantity. The large
contribution of the most heavily-vegetated landscapes to
the spread in SAF hints that widely-varying treatments of
vegetation masking of snow-covered surfaces are partly
responsible. However, further investigation is required to
address this question satisfactorily.
79
April and May. In the case of climate change, D
as is
quantified by the difference in regionally-averaged, climatological April values of as between the current
(1980–1999) and future (2080–2099) climates. Likewise,
DT s is quantified by the difference in regionally-averaged,
climatological April value of Ts between the current and
future climates.
Figure 9 scatters the climate change values of D
as =DT s
versus the corresponding seasonal cycle values of D
as =DT s
in the 25 CMIP5 models. Consistent with Hall and Qu
(2006), there is a high degree of correspondence between
the two quantities (r = 0.86). This is further supported by
simple regression analysis, which reveals that the slope of
the best-fit line between the two quantities (s = 1.11) is not
significantly different from one and the intercept of the line
(i = 0.05 % K-1) is not significantly different from zero.
As in Hall and Qu (2006), we constrain the climate
change values of Das =DT s using observed Das =DT s value
in the context of seasonal cycle. To obtain an updated
observed estimate of Das =DT s ; we use the recent
(2001–2012) surface albedo measurements from MODIS
(Jin et al. 2003) and surface air temperature from ERAInterim (Dee et al. 2011) for the same period. By performing procedures similar to those described in Sect. 3,
we obtain an observed estimate of Das =DT s ð0:87 % K1 ;
Acknowledgments Both authors are supported by DOE’s Regional
and Global Climate Modeling Program under the project ‘‘Identifying
Robust Cloud Feedbacks in Observations and Model’’ (contract DEAC52-07NA27344). We acknowledge the World Climate Research
Programme’s Working Group on Coupled Modelling, which is
responsible for CMIP, and we thank the climate modeling groups
(listed in Table 1 of this paper) for producing and making available
their model output. For CMIP the U.S. Department of Energy’s
Program for Climate Model Diagnosis and Intercomparison provides
coordinating support and led development of software infrastructure
in partnership with the Global Organization for Earth System Science
Portals. MODIS data is distributed by the Land Processes Distributed
Active Archive Center, located at the US Geological Survey Earth
Resources Observation and Science Center (lpdaac.usgs.gov). ERAInterim data is downloaded from http://www.ecmwf.int/products/
data/archive/ and CERES data from http://ceres.larc.nasa.gov/. We
thank Dr. Mark Flanner and another anonymous reviewer for their
constructive comments on the original manuscript.
Appendix: Seasonal cycle and climate change
relationship in Das =DT s
Using the methodology in Hall and Qu (2006), we examine
the seasonal cycle and climate change relationship in
as is quantified
D
as =DT s : In the context of seasonal cycle, D
by the difference in regionally-averaged, climatological
values of as between April and May in NH extratropical
land masses. Likewise, DT s is quantified by the difference
in regionally-averaged, climatological values of Ts between
Fig. 9 Scatterplot of D
as =DT s in the context of climate change
as and
versus D
as =DT s in the context of seasonal cycle. To obtain D
DT s ; we average Das and DTs over NH extratropical land masses. In
both contexts, Das is weighted by the climatological April incoming
solar radiation at the surface prior to averaging. The thick dashed line
is the best-fit regression line. The observed estimate of D
as =DT s (the
thin vertical line) and statistical uncertainty of the observed estimate
(the gray area) are estimated based on MODIS surface albedo and
ERA-Interim surface air temperature (see the text for details).
Observed climatological April incoming solar radiation at the surface
is calculated based on the Clouds and Earth’s Radiant Energy System
(CERES) data (Wielicki et al. 1996)
123
80
represented by the thin vertical line in Fig. 9), and the
lower and upper bounds of the estimate (respectively: 0.78 and -0.96 % K-1, represented by the gray area in
Fig. 9). As in the case of the overall feedback strength, the
simulated seasonal cycle values of D
as =DT s in models S
and T are overestimated by about 50 %, while the
respective values in models P, Q and R are underestimated
by the same amount. Therefore, the assessment of model
biases is qualitatively similar no matter which measure (the
overall feedback strength or D
as =DT s Þ is used in the
analysis.
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