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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 123 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. 123 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 123 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 123 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 123 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. 123 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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