Radiative forcing and albedo feedback from the northern
hemisphere cryosphere between 1979 and 2008
M. G. Flanner1 *, K. M. Shell2 , M. Barlage3 , D. K. Perovich4 , & M. A. Tschudi5
1
Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor
MI, USA
2
College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis OR, USA
3
National Center for Atmospheric Research, Boulder CO, USA
4
Cold Regions Research and Engineering Laboratory, U.S. Army Engineer Research and Devel-
opment Center, Hanover NH, USA
5
Colorado Center for Astrodynamics Research, University of Colorado, Boulder CO, USA
* Corresponding author. Contact: [email protected]
1
Coverage of northern hemisphere snow1 and sea-ice2 has declined since 1979, coinciding with
1
hemispheric warming and indicating a positive albedo feedback on climate. Previous stud-
2
ies have quantified seasonal land snow albedo feedback in observations3–6 and century-scale
3
feedback in climate models7–10 , but total cryospheric radiative impact and albedo feedback
4
have yet to be determined from measurements. Here, we present estimates of the cryospheric
5
influence on Earth’s top-of-atmosphere solar energy budget, or cryosphere radiative forcing,
6
synthesized from a variety of remote sensing and field measurements. Mean northern hemi-
7
spheric forcing is −3.3 (−4.6 to −2.2) W m−2 , peaking in May at −9.0 ± 2.7 W m−2 , with
8
ranges indicating the spread in various scenarios of albedo contrast and cloud properties.
9
From 1979–2008, cryospheric cooling decreased by 0.45 (0.27 − 0.72) W m−2 , with nearly
10
equal contributions from land snow cover and sea-ice changes. Associated northern hemi-
11
sphere albedo feedback is thus +0.6 (0.3 − 1.1) W m−2 K−1 , two-fold stronger than mean
12
albedo feedback over the same period in 18 climate models. Although decreases in sea-ice
13
concentration have been largest in September, June ice loss has driven much larger change
14
in cryosphere forcing because of coincident peak insolation.
15
Climate feedback mechanisms are often characterized in terms of their influence on top-of-
16
atmosphere (TOA) net energy flux (F ) with changing surface temperature7–10 , highlighting utility
17
of understanding the direct impact of evolving Earth System components on F . Extending a pre-
18
vious analysis of seasonal snow radiative effect3 , we define cryosphere radiative forcing (CrRF) as
19
the instantaneous perturbation to Earth’s TOA energy balance induced by the presence of surface
20
cryospheric components. CrRF is thus directly analogous to cloud radiative forcing, a commonly
21
2
used diagnostic in climate model and remote sensing analyses. This study focuses entirely on the
22
shortwave (solar spectrum) component of northern hemisphere (NH) CrRF. Longwave CrRF may
23
be non-negligible in regions where snow or ice alters surface emissivity3 , and longwave feedbacks
24
associated with cryosphere evolution can also be large11 .
25
CrRF is influenced by several factors, including 1) the surface albedo change induced by
26
snow or ice, which depends on snow/ice albedo and characteristics of the snow-free surface (es-
27
pecially vegetation), and 2) local insolation and atmospheric state (primarily cloudiness), which
28
determine the propagation of surface albedo changes to TOA flux8, 12 . Here, we quantify plausible
29
CrRF ranges by combining observations of snow and sea-ice cover fraction (Sx , where x indicates
30
snow or sea-ice), surface albedo contrast between snow/ice-covered and snow/ice-free surfaces
31
(∆αx ), and TOA flux variation with surface albedo change (∂F/∂α). Our bottom-up approach
32
offers an independent assessment of land CrRF determined directly from TOA fluxes3 and the
33
potential of attributing observed TOA flux variability13 to cryospheric evolution.
34
Time- (t) dependent CrRF within a region R (here, the NH) of area A, composed of gridcells
r can be represented as:
35
36
∂α
∂F
1 Z
Sx (t, r)
(t, r)
(t, r) dA(r)
CrRF(t, R) =
A(R)
∂Sx
∂α
[W m−2 ]
(1)
R
Here, we assume that (monthly- and spatially-varying) ∂α/∂Sx and ∂F/∂α are constant
37
with Sx and α, respectively, and replace ∂α/∂Sx with mean albedo contrast (∆αx ) observations
38
that are specific to the applied snow/ice cover data. We use 1979–2008 monthly gridded binary
39
3
snow cover14 and sea-ice concentration15 derived, respectively, from visible and microwave re-
40
mote sensing. We derive monthly climatologies of ∆αsnow (Supplementary Figures S1 and S2)
41
from 2000–2008 Moderate Resolution Imaging Spectroradiometer (MODIS) observations and
42
coincident (binary) snow cover, filled with annual-mean MODIS or 1982–2004 Advanced Po-
43
lar Pathfinder (APP-x) monthly albedo data16 . We partition sea-ice into multi-year (MYI) and
44
first-year (FYI) concentrations17, 18 and apply to each ice type monthly-varying ∆αice functions
45
(Figure S3) derived from field measurements19 and remote sensing of FYI parcels20 .
46
To characterize uncertainty, we apply minimum, central, and maximum estimates of ∆α,
47
combined with six ∂F/∂α products, producing 18 scenarios of the time variation and trend of
48
CrRF from 1979 to 2008. Ranges of ∆αsnow and ∆αice are determined, respectively, from albedo
49
variance of different land classes21 (Table S1) and from extensive field measurements19 (Figure S3).
50
We apply spatially and monthly-varying (annually-repeating) ∂F/∂α “radiative kernel” datasets
51
created previously9, 10 from the NCAR Community Atmosphere Model (CAM3) and GFDL Atmo-
52
sphere Model 2 (AM2), and we derive two annually-varying ∂F/∂α kernels using radiative transfer
53
modeling with cloud fraction and optical depth data from 1) the International Satellite Cloud Cli-
54
matology Project (ISCCP-D2)22 , and 2) APP-x16 . We also include clear-sky ∂F/∂α products9, 10
55
to diagnose the magnitude of cloud damping. All products were remapped to 1◦ × 1◦ resolution for
56
analysis. Although these scenarios do not fully span the uncertainty in parameter space, they do
57
inform on the importance of two key terms in Eq. 1. The range of ∆α represents our estimate of
58
uncertainty in ∂α/∂S, whereas the different ∂F/∂α products illustrate the CrRF range produced
59
with different techniques (annually-varying or annually-repeating atmospheric states) and different
60
4
modeled and observed atmospheric conditions.
61
Table 1 lists mean 1979–2008 NH CrRF from all radiative kernel and albedo contrast sce-
62
narios. Mean (full range) of the 12 all-sky cases is −3.3 (−4.6 to −2.2) W m−2 , of which −2.0
63
(−2.9 to −1.2) W m−2 is from land-based snowpack. All-sky CrRF is about 15% greater with the
64
AM2 and APP-x kernels than with CAM3 and ISCCP kernels. Clear-sky CrRF is −5.9 (−4.3
65
to −7.7) W m−2 indicating that clouds mask slightly less than half of the cryosphere radiative
66
effect12, 23 .
67
Mean annual cycles of land and sea-ice CrRF are shown in Figure 1a. CrRFsnow peaks
68
broadly at about −4.5 W m−2 during March–May, when hemispheric insolation and snow cover
69
are both large. CrRFice peaks at −4.7 ± 1.3 W m−2 in May, despite greater June insolation, be-
70
cause of higher pre-melt ice albedo19 (Figure S3) and greater May ice extent. The NH reflects to
71
space an additional 9.0 ± 2.7 W m−2 during May because of the cryosphere. CrRFsnow increases
72
slightly during October–January with increasing snow cover, whereas diminishing polar insolation
73
maintains small CrRFice .
74
Spatial distributions of annual-mean and seasonal CrRF are shown in Figures 2a and S5,
75
respectively. Except during winter, CrRF is generally larger over the Arctic Ocean than over land,
76
a consequence of persistent ice cover and large ∆αice . Sparsely-vegetated land blanketed with
77
snow and exposed to intense spring insolation can have greater CrRF than sea-ice but, averaged
78
over 1◦ × 1◦ areas, ∆αsnow is always reduced by snow patchiness and/or vegetation. CrRF over
79
Greenland is somewhat arbitrary because of unknown ground albedo beneath the ice-sheet. We
80
5
assume uniform ice-free albedo of 0.26, typical of sparsely-vegetated land (Table S1).
81
Changes in NH CrRF from 1979 to 2008 (∆CrRF), expressed as linear trends multiplied by
82
the time interval, are listed in Table 2, and all-sky CrRF anomaly timeseries are shown in Figure S4.
83
The mean (full range) 30-year ∆CrRF of the 12 all-sky cases is +0.45 (0.27 to 0.72) W m−2 , to
84
which snow and sea-ice changes contributed almost equally. An analysis of 21st century albedo
85
feedbacks in models contributing to the Climate Model Intercomparison Project (CMIP3)8 also
86
found similar contributions from snow and sea-ice. All trends are significant at p = 0.01. Inter-
87
estingly, changes are largest with the ISCCP and APP-x kernels, which exhibit mean CrRF sim-
88
ilar to the model kernels. One explanation for greater ∆CrRF with annually-varying, coincident
89
cloud conditions is that cloud evolution amplified cryosphere-induced radiative anomalies. Qual-
90
itative evidence for such amplification comes from a study of surface-based cloud observations
91
in the Arctic Ocean24 . Our ability to assess cloud feedback is limited, however, by the monthly
92
resolution and temporal extent of the data and by large uncertainty in cloud retrievals over the
93
Arctic. Research with higher fidelity radar and lidar products shows that cloud cover may in-
94
crease over regions of fresh sea-ice loss during fall, but not summer25 . Because cloud changes
95
alter CrRF (even with constant snow/ice cover), a more straightforward interpretation of ∆CrRF
96
comes from the annually-constant model kernels, which show similar ∆CrRF in spite of different
97
base albedo, clouds, aerosols, and water vapor. Mean ∆CrRF obtained with annually-repeating
98
cloud conditions (conducted for each year of cloud data) from the ISCCP and APP-x datasets is,
99
respectively, 0.50 and 0.59 W m−2 . Thus, the observational kernels produce greater ∆CrRF even
100
without temporally-coincident cloud evolution. We suggest a central range of 0.38 − 0.59 W m−2
101
6
for ∆CrRF with annually-repeating cloud conditions.
102
Maximum (minimum) ∆αsnow and ∆αice scenarios increase (decrease) their respective all-
103
sky CrRF by 31% (34%) and 15% (15%), whereas variability across kernels is smaller. Previous
104
work found that ∆α is a greater source of variability than ∂F/∂α in determining snow feedback
105
strengths within CMIP3 models5, 8 . Variability in our estimates is greater for land than sea-ice,
106
which follows from large snow-covered albedo variability caused by heterogeneous vegetation and
107
orography21 (Figure S1). The largest ∆αsnow variability occurs over shrublands, grasslands, and
108
sparsely vegetated terrain (Table S1). Although pre-melt sea-ice albedo varies little because of
109
snow cover19 , melt-season albedo also becomes quite variable (Figure S3) and depends on ice
110
thickness, pond area and depth19 , bubble and ice grain size, and content of sediment, algae, and
111
light absorbing impurities. We account for this variability implicitly, through liberal ∆αice ranges,
112
and acknowledge that a more constrained assessment could be produced with improved knowledge
113
of the ice state. This study differentiates only between MYI and FYI, the latter of which is darker
114
because of greater morphological susceptibility to ponding and tendency to be thinner. The range
115
of ∆αice represents variability observed along a line that included a variety of ponded, bare, and
116
snow-covered ice19 . These June–September albedos are, however, ∼ 15% lower than 40-year
117
means measured at a Soviet drifting station19 , illuminating a potential source of low bias in our
118
CrRFice estimates.
119
Figures 2b and S6 show spatial distributions of annual-mean and seasonal ∆CrRF with the
120
CAM3 kernel. ∆CrRF is large and positive over Eurasian land during March–May and over much
121
7
of the Arctic Ocean during June–August. Autumn anomalies are large in the Chukchi Sea, where
122
September ice has diminished2 . Large portions of North America and Eurasia show slightly nega-
123
tive ∆CrRF during September–November, associated with increased snow cover1 .
124
Thirty-year ∆CrRF by month is depicted in Figure 1b. Sea-ice ∆CrRF peaks distinctly in
125
June, with a smooth seasonal cycle. Thus, although sea-ice loss has been largest in September2 ,
126
April–August ice changes, facilitated by stronger insolation, have driven greater change in CrRFice .
127
∆CrRFsnow is statistically significant (p = 0.01) during March–April and June–August, whereas
128
∆CrRFice is significant in all months (though very small during winter). Our technique distin-
129
guishes between FYI and MYI and thus includes changes in CrRF caused by ice age changes, in
130
addition to the dominant influence of ice concentration changes. We estimate that 14% of ∆CrRFice
131
was caused by transitions from MYI to FYI. A weakness of our approach, however, is applying
132
fixed annual cycles of FYI and MYI albedo, meaning we neglect contributions to ∆CrRFice of
133
altered sea-ice albedo associated with (e.g.,) changes in timing of melt onset and freezup. Sea-ice
134
absorbed solar flux is especially sensitive to timing of melt onset, which decreases albedo coinci-
135
dentally with near-maximal insolation. At one site, melt onset ranged by 16 days over six years26 ,
136
and it has become earlier by about 8 days over the Arctic Ocean since 197927 . Fixed ∆αsnow cycles
137
similarly fail to capture interannual changes in albedo of snow-covered regions (e.g., as caused by
138
altered snow metamorphism, vegetation, or aerosol deposition)6, 23 . If snow has darkened with
139
warmer spring temperatures in recent years, ∆CrRF estimates would be further biased low. Ad-
140
ditionally, we show no change in CrRF over Greenland (Figure 2b), but melt area has increased
141
significantly since 197928 , contributing to some decrease in albedo. We discuss other potential
142
8
sources of bias and comparisons with previous analyses in Supplementary Material.
Estimates of 1979–2008 NH warming obtained from the GISS Surface Temperature Analysis29
143
144
and Hadley Centre / Climate Research Unit HadCRUT3v dataset30 are 0.79 and 0.67◦ C, respec-
145
tively. Ranges of ∆CrRF combined with these warmings yield NH cryosphere albedo feedback
146
(∆Fcryo /∆Ts ) of 0.62 (0.33 − 1.07) W m−2 K−1 , where the range indicates the extreme mini-
147
mum/maximum combinations of ∆T and ∆CrRF (Table 2). Using models from the CMIP3 multi-
148
model dataset, we quantify a 1980–2010 NH model feedback of only 0.25 ± 0.17 W m−2 K−1 .
149
The large range is likely due to the spread of albedo feedbacks in climate models and the relatively
150
short period of differencing. This discrepancy with our estimate indicates that either other surface
151
processes are driving negative albedo feedback in models that offset strong cryosphere feedback,
152
or the cryosphere is responding more sensitively to, and driving stronger climate warming than
153
models indicate. Future analyses can inform on the relative importance of the two possibilities.
154
In support of the later, recent work determined that NH sea-ice is declining faster than models
155
simulate31 . Although 30-year feedback strengths may be strongly affected by climate variability,
156
we believe our range provides a conservative lower bound on the present feedback because of
157
∆CrRF biases described earlier. Thus, we conclude that CMIP3 models likely underestimate the
158
recent surface albedo feedback. In summary, these estimates of CrRF evolution will help 1) ascribe
159
causes of observed increases and variability in net TOA solar flux13 , 2) evaluate model cryosphere
160
processes, and 3) constrain one determinant of Earth’s climate sensitivity.
161
9
Methods
162
We utilize monthly binary snow cover data (89 × 89 gridcells, projected on a polar stereographic
163
grid) from the National Oceanic and Atmospheric Administration (NOAA), maintained by Rutgers
164
University14 (http://climate.rutgers.edu/snowcover), and derived from Advanced
165
Very High Resolution Radiometer (AVHRR) observations. We use monthly gridded sea-ice con-
166
centrations derived from microwave retrievals with the NASA Team algorithm15 and fill the pole-
167
centered data void using a nearest-neighbor algorithm.
168
We derive land albedo contrast primarily from the MODIS MCD43C3 collection 5 dataset
169
(0.05◦ × 0.05◦ resolution). We determine monthly snow-covered albedo climatologies of all
170
NOAA/Rutgers gridcells defined binarily as snow-covered at any time during 1979–2008 using
171
the following priority of filling: 1) monthly-resolved mean MODIS white-sky albedo of all co-
172
incident times during 2000–2008 when at least 50% of the “snow-covered” gridcell is defined
173
with quality flag 2 or better, 2) annual-mean (quality-filtered) MODIS albedo, averaged only dur-
174
ing times of snow cover, 3–4) methods (1) and (2) repeated with 1982–2004 Advanced Polar
175
Pathfinder (APP-x) albedo data16 , which has greater temporal overlap with NOAA/Rutgers snow
176
cover, but which has limited mid-latitude spatial coverage and is derived from lower fidelity ob-
177
servations, and 5) annual-mean MODIS snow-covered albedo by land classification (Table S1),
178
defined with University of Maryland / MODIS land cover product MCD12C1. We derive a sim-
179
ilar dataset using APP-x priority over MODIS (i.e., filling priority order 3,4,1,2,5), but find that
180
it changes our CrRF and ∆CrRF estimates by less than 3%. Furthermore, using only method 5,
181
we obtain CrRF and ∆CrRF estimates that differ by only 3% from the methods described above.
182
10
We determine monthly-resolved snow-free albedo entirely from MODIS product MCD43C3, us-
183
ing its accompanying snow-cover filter and quality flag for strict prevention of snow contami-
184
nation. Central estimates of CrRFsnow and ∆CrRFsnow increased very slightly (3% and 2%, re-
185
spectively) when we applied MODIS black-sky albedo instead of white-sky albedo. We derive
186
maximum/minimum estimates of ∆αsnow (Figure S2) by adding/subtracting the combined stan-
187
dard deviations of snow-free and snow-covered albedos grouped by land classification (Table S1).
188
These mean snow-covered albedos are lower than maximum snow-covered albedos21 because they
189
are averaged over NOAA/Rutgers gridcells that are partially snow-free. Thus, our ∆αsnow range
190
includes variability caused both by 1) unresolved snow cover variability within the binary snow
191
product, and 2) variability in the influence of vegetation (within each land class) on albedo con-
192
trast.
193
Sea-ice concentrations were partitioned into first-year ice (FYI) and multi-year ice (MYI) us-
194
ing ice motion vectors derived from microwave and AVHRR remote sensing products, combined
195
with Lagrangian parcel tracking at weekly resolution17, 18 . We use seasonally-dependent ranges of
196
MYI albedo derived from ground measurements over heterogeneous ice terrain (snow-covered ice,
197
various morphologies of bare ice, and ponded ice)19 , and derive FYI albedo from 1) unpublished
198
ground measurements made by Perovich during April–June, and 2) APP-x albedo16 averaged over
199
FYI parcels determined with the Lagrangian tracking method during July–September20 . Lacking
200
reliable statistics on FYI albedo variability, we apply the MYI albedo variance to FYI (Figure S3).
201
Winter values are filled with typical snow-covered ice albedo and have negligible impact on solar
202
CrRF. Although open-water albedo can vary slightly, depending (e.g.,) on solar angle and phyto-
203
11
plankton content, we assume a constant value of 0.0719 .
204
We derive annually-varying estimates of ∂F/∂α using 1984–2008 2.5◦ × 2.5◦ resolution
205
ISCCP-D222 and 1982–2004 25 × 25 km resolution APP-x16 cloud optical depth, filled with mean
206
annual cycles to achieve continuous 1979–2008 data, and ISCCP-D2 cloud fractions for weighting
207
with clear-sky fluxes. We prescribe these properties, along with 0.01 perturbations to surface
208
albedo9, 10 , in a radiative transfer model32 with profiles of atmospheric gases and aerosols typical
209
of mid-latitude summer and winter, sub-Arctic summer, and tropical environments. Thus, ∂F/∂α
210
variability caused by gas and aerosol concentration changes is poorly captured in these radiative
211
kernels, although such variability is likely much smaller than that generated by (optically thicker)
212
clouds. The model-derived CAM3 and AM2 monthly ∂F/∂α products are described elsewhere9, 10 .
213
All products are mapped with conservative area regridding from their native resolutions to
214
1◦ × 1◦ for analysis. Linear trends and statistical significance are determined, respectively, with
215
the Mann–Kendall and Theil–Sen techniques, including trend-free pre-whitening to account for
216
autocorrelation1 .
217
For the CMIP3 models, we use the CAM3 radiative kernel9 to determine albedo feedback
218
between years 2001–2010 of 21st century SRES-A1B simulations and years 1981–1990 simulated
219
by the same model, but for the 20th century case. The 18 models used are listed in Table S2.
220
The feedback calculation technique requires a multi-year average, and the time period considered
221
is short. Using ten years offers a compromise between maximizing the climate change signal
222
and reducing noise from natural climate variability. We use 2001-2010 rather than 1999-2008 for
223
12
simplicity since the SRES-A1B scenarios start at year 2000. The specific start date is unlikely to
224
alter the feedback estimates.
225
1
227
226
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32. Zender, C. S. et al. Atmospheric absorption during the Atmospheric Radiation Measure-
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ment (ARM) Enhanced Shortwave Experiment (ARESE). J. Geophys. Res. 102, 29901–29915
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(1997).
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17
Acknowledgements We thank Chuck Fowler and Jim Maslanik for providing multi-year sea-ice data,
299
Thomas Estilow and Mary Jo Brodzik for providing snow and sea-ice data and advice, and Steve Warren for
300
reviewing the manuscript. MODIS data are distributed by the Land Processes Distributed Active Archive
301
Center, located at the U.S. Geological Survey Earth Resources Observation and Science Center (lpdaac.
302
usgs.gov). The ISCCP D2 data were obtained from the International Satellite Cloud Climatology Project
303
web site (http://isccp.giss.nasa.gov) maintained by the ISCCP research group at NASA GISS.
304
We acknowledge the modeling groups, the Program for Climate Model Diagnosis and Intercomparison and
305
the WCRP’s Working Group on Coupled Modelling for their roles in making available the WCRP CMIP3
306
multi-model dataset. Research was supported by NSF ATM-0852775 (MGF) and ATM-0904092 (KMS).
307
Author contributions MGF wrote the manuscript and combined all datasets to quantify CrRF. KMS pro-
308
vided radiative kernel data, quantified CMIP3 model feedbacks, and helped write the manuscript. MB
309
provided land snow covered albedo data. DKP and MAT provided, respectively, field-measured and remote
310
sensing sea-ice albedo data.
311
Competing Financial Interests The authors declare that they have no competing financial interests.
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Correspondence Correspondence and requests for materials should be addressed to M.G. Flanner (email:
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[email protected]).
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18
N. Hemisphere TOA Forcing (W m−2)
Mean Monthly Cryosphere Forcing (1979−2008)
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
−11
−12
Land Snow
Sea−Ice
Snow+Ice
a
J
F
M
A
M
J
J
A
S
O
N
D
J
N. Hemisphere TOA Forcing (W m−2)
Change in Cryosphere Forcing from 1979 to 2008
2
1.8
Land Snow
Sea−Ice
Snow+Ice
b
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1
2
3
4
5
6
7
8
9
10
11
12
13
J
F
M
A
M
J
J
A
S
O
N
D
J
Figure 1
315
Seasonal cycle of northern hemisphere cryosphere radiative forcing and
316
changes in forcing from 1979 to 2008. Contributions to top-of-atmosphere forcing
317
are shown for land-based snowpack (green, squares), sea-ice (blue, diamonds), and
318
combined snow+sea-ice (black, circles). Panel (a) shows the mean influence of the
319
cryosphere during 1979–2008 and panel (b) shows 30-year changes calculated from lin-
320
ear trends. Whiskers depict full ranges of snow+sea-ice cryosphere forcing from the 12
321
all-sky albedo contrast and radiative kernel scenarios listed in Tables 1 and 2. X’s in panel
322
(b) indicate months of statistically significant change at p = 0.01.
323
19
324
Figure 2
Figure 2: Annual-mean cryosphere radiative forcing during 1979–2008
325
and change in forcing from 1979 to 2008. Negative cryosphere forcing in panel (a)
326
indicates that snow and ice decrease the net TOA solar energy flux, and positive changes
327
in panel (b) indicate that the cryospheric cooling effect has decreased since 1979. These
328
data were derived with central estimates of albedo contrast and the CAM3 radiative
329
kernel9 . 30-year changes in (b) were derived from linear trend analysis at each gridcell.
330
20
Table 1: Northern Hemisphere cryosphere radiative forcing (W m−2 ) averaged over 1979–
2008 for all albedo contrast (∆α) and radiative kernel (∂F/∂α) combinations. Numbers in
parenthesis indicate the percent of CrRF caused by land-based snow.
Kernel (∂F/∂α)
Albedo contrast (∆α)
Low
Central
High
CAM3
–2.3 (51)
–3.1 (57)
–3.9 (61)
AM2
–2.7 (52)
–3.6 (59)
–4.4 (63)
ISCCP
–2.2 (58)
–3.1 (63)
–4.0 (66)
APP-x
–2.6 (55)
–3.6 (61)
–4.6 (63)
CAM3 clear-sky –4.5 (53)
–6.1 (59)
–7.7 (62)
AM2 clear-sky
–5.7 (59)
–7.1 (62)
–4.3 (55)
21
Table 2: Change in Northern Hemisphere CrRF (W m−2 ) from 1979 to 2008 for all albedo
contrast (∆α) and radiative kernel (∂F/∂α) combinations. Numbers in parenthesis indicate the percent of change due to land-based snow.
Kernel (∂F/∂α)
Albedo Contrast (∆α)
Low
Central
High
CAM3
+0.26 (42)
+0.38 (50)
+0.48 (53)
AM2
+0.29 (41)
+0.40 (49)
+0.49 (52)
ISCCP
+0.40 (48)
+0.57 (54)
+0.72 (56)
APP-x
+0.31 (41)
+0.48 (49)
+0.59 (49)
CAM3 clear-sky +0.58 (38)
+0.82 (45)
+1.00 (48)
AM2 clear-sky
+0.77 (46)
+0.97 (49)
+0.58 (41)
22