Differences in snow-induced radiative forcing estimated from satellite and reanalysis surface albedo datasets over the Northern Hemisphere landmass for the overlapping period of 1982–2012

Surface albedo (a_s) is defined as the ratio of the solar radiation reflected from the Earth's surface to the solar radiation incident upon it, is critical in the regulation of Earth's surface energy budget and characterizing the Earth's radiative regime (Lofgren 1995, Liang et al 2010, Liang et al 2019). Published studies have proved that snow cover extent (SCE) changes are positively correlated with a_s anomalies because of its high reflectance (Qu and Hall 2014, Chen et al 2015, Chen et al 2017, Zhang et al 2019). When the snow cover shrinks, the a_s decreases, with less solar radiation reflected back into the space. Meanwhile, the remaining snow generally has a lower a_s caused by snow metamorphosis (Qu and Hall 2014). The solar radiation perturbation induced by a_s anomalies that are driven by SCE changes is defined as snow-induced radiative forcing (S_nRF) (Flanner et al 2011, Chen et al 2015, Chen et al 2016a), which is vital in measuring the feedback of snow cover to Earth radiation budget (Flanner et al 2011, Singh et al 2015) and climate projections (Perket et al 2014, Qu and Hall 2014) under the climate change background.

To estimate radiative forcing caused by snow cover changes, several studies have estimated the S_nRF at different time spans and spatial scales in recent decades (Flanner et al 2011, Chen et al 2015, Singh et al 2015, Chen et al 2017). For example, Flanner et al (2011) quantified the radiative forcing from the Northern Hemisphere (NH, the half of the Earth that lies north of the equator) cryosphere during 1979–2008 and reported that the cyrospheric cooling declined by 0.45 Wm⁻² during 1979–2008, with nearly equal contributions from changes in land snow cover and sea ice. Chen et al (2015) estimated the SnRF induced by snow cover phenology changes over the NH for the period 2001–2014 and found that the contrasting changes in snow cover phenology led to contrasting anomalies of S_nRF among the NH middle and high latitudes, which accounted for 51% of the total shortwave flux anomalies at the top of the atmosphere (TOA) during 2001–2014. Singh et al (2015) quantified the global land shortwave cryosphere radiative effect during 2001–2013 and reported that the NH land S_nRF estimates from Moderate Resolution Imaging Spectroradiometer (MODIS) were approximately 18% smaller than previous estimates derived from coarse-resolution advanced very high resolution radiometer (AVHRR) data during the overlap period of 2001–2008. However, being limited by the uncertainty of a_s datasets and shortage of long-term a_s datasets, the differences in S_nRF evaluated from longterm satellite and reanalysis a_s datasets are remain unclear.

The a_s is one of the most important parameter in the calculation of S_nRF, which measures the amount of solar radiation reflected back into the space caused by snow cover changes (Groisman et al 1994, Flanner et al 2011, Perket et al 2014, Chen et al 2015, Singh et al 2015). However, a_s is among the main radiative uncertainties in current climate modeling (Liang 2001, Liang et al 2002), which may bring a cumulative error in the S_nRF estimation. For example, Myher and Myher (2003) reported that cropland a_s values is the most important factor yielding the large range in estimated radiative forcings caused by land use changes. Bright and Kvalevåg (2013) confirmed that through perturbations in a_s, land use activities affected shortwave radiative forcing at the TOA. As one of the most notable component of land cover type over the NH, with large spatial coverage and rapid changes, presence of snow cover are largely related with land use changes over the NH. Published studies have proven that SCE in the NH has experienced a well-documented rapid decrease since late 1960s (Déry and Brown 2007, Brown et al 2010, Derksen and Brown 2012, Chen et al 2016a). Moreover, climate projections suggest that the SCE will continue shrinking in the future (Brown and Robinson 2011, IPCC 2013). Thus, to make clear the spatial and temporal differences in S_nRF estimation caused by a_s datasets is necessary to reduce the radiative uncertainties in climate change studies.

Published scholars have reported large differences among current a_s products, e.g., By analyzing the global a_s climatology and spatial-temporal variation during 1981–2010, He et al (2014) showed that at latitudes higher than 50°, the maximum difference in winter zonal albedo ranged from 0.1 to 0.4 among the nine satellite datasets. Assessment of Community Land Model (CLM2) a_s using MODIS data, Oleson et al (2003) reported that in regions with extensive snow cover, the CLM2 overestimated white-sky and black-sky a_s by up to 20%. As the largest single component of the cryosphere in terms of spatial extent, the discrepancy between the satellite-derived and reanalyzed a_s is evident. Although published studies have estimated S_nRF from local to global scales, few of them have provided a comprehensive analysis of the uncertainties in S_nRF estimations induced by a_s datasets.

The objective of the present study is to comprehensively examine the performance of satellite and reanalysis a_s datasets in representing the large scale spatiotemporal variability and long term change in S_nRF over the NH. Additionally, the study aims to understand the differences between reanalysis and satellite a_s in the context of characterizing radiative forcing within the NH climate system, which is crucial for accurately characterizing NH climate patterns and assessing the underlying evolution of the NH climate system.

To calculate S_nRF over the NH and cross-compare S_nRF results from satellite and reanalysis a_s datasets, we first introduce the methodology in calculation of S_nRF. Then, we give a brief introduction of datasets used in this study.

2.1. Methodology

2.1.1. Estimation of S_nRF

To calculated S_nRF over the NH, the radiative kernel approach (Shell et al 2008, Soden et al 2008) was employed in this study. The radiative kernel approach separates the radiative responses to land surface albedo a_s induced by snow cover changes with other climate parameters (such as temperature, water vapor, and CO₂). In this study, the albedo radiative kernels, expressed as the TOA shortwave flux anomalies associated with a 1% change in a_s, were employed to estimate S_nRF driven by snow cover changes. The time (t) dependence of S_nRF (W m⁻²), within a region R (here, the NH) of area A, composed of grid cells r can be expressed as follows (Flanner et al 2011, Chen et al 2015):

$$\begin{eqnarray}&&{S}_{{\rm{n}}}RF(t,R)=\displaystyle \frac{1}{A(R)}\displaystyle {\int }_{R}S(t,r)\displaystyle \frac{\partial {a}_{{\rm{s}}}}{\partial S}(t,r)\displaystyle \frac{\partial F}{\partial {a}_{{\rm{s}}}}(t,r)dA(r)\end{eqnarray} \tag{ 1 }$$

where S (t, r) is the domain of SCE over the NH, ∂α_s/∂S (t, r) is the rate of variation of land surface albedo α_s with snow cover change, and ∂F/∂α_s (t, r) is the response of the TOA net shortwave radiation anomalies to α_s changes. Following Flanner et al (2011), we assumed that the temporally and spatially varying ∂α_s/∂S and ∂F/∂α_s were constant with the snow cover fraction S and α_s, respectively. Therefore, ∂α_s/∂S could be replaced with the mean albedo contrast (Δa_s) induced by the snow cover anomaly and ∂F/∂α_s can obtained from the albedo radiative kernels (Flanner et al 2011, Chen et al 2015).

2.1.2. Z-score definition

To cross-compare S_nRF estimates from satellite and reanalysis a_s datasets consistently, S_nRF over the NH during the period 1982–2012 were converted into corresponding z-score series in the comparison analysis. According Kreyszig (1979), the z-score of a raw S_nRF series x is expressed as

$$\begin{eqnarray}&&z=\displaystyle \frac{x-\mu }{\sigma }\end{eqnarray} \tag{ 2 }$$

where μ and σ are the mean and standard deviation (SD) of S_nRF over the NH for period 1982–2012, respectively.

2.2. Datasets

According equation (1), the snow cover range, albedo contrast Δa_s caused by snow cover presence, and albedo radiative kernels are needed in the calculation of S_nRF. The snow cover range was obtained from SCE dataset. The Δa_s was calculated by subtracting snow-free surface albedo (α_sf) from surface albedo a_s in the corresponding period. The albedo radiative kernels were get from published datasets.

To meet the requirements in S_nRF estimation, the snow cover range from the Climate Data Record (CDR) of NH SCE Version 4 (NHSCE) (Brodzik and Armstrong 2013); two satellite α_s datasets from the global land surface satellite (GLASS) (Liang et al 2013a, 2013b) and the second edition of Climate Monitoring Satellite Application Facility (CM SAF) Cloud, Albedo And Surface Radiation dataset from AVHRR (CLARA-A2) (Karlsson et al 2017); four reanalysis α_s datasets from the European Centre for Medium-Range Weather Forecasts (ECWMF) reanalysis 5 (ERA-5) published by the Copernicus Climate Change Service (C3S) (C3S 2017), the 55-yr Japanese reanalysis project (JRA-55) (Ebita et al 2011), the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) (Gelaro et al 2017), the National Centers for Environmental Prediction (NCEP) climate forecast system reanalysis (CFSR) (Saha et al 2010); a snow-free surface albedo α_sf dataset from the MODIS Terra and Aqua combined Bidirectional Reflectance Distribution Function and Albedo (BRDF/Albedo) Global Gap-Filled, Snow-Free Version 6 (MCD43GF) (Schaaf 2019); and albedo radiative kernels from the community atmosphere model version 3 (CAM3) (Shell et al 2008), atmosphere model 2 (AM2) (Soden et al 2008) and the sixth generation of the atmospheric general circulation model ECHAM (ECHAM6) (Mauritsen et al 2013) were used in this study. Summary of datasets used in this study are listed in table 1.

Table 1. Summary of datasets used in the study.

Variables	Datasets	Horizontal resolution	Temporal resolution	Spatial coverage	Time span	References
Snow cover	NHSCE	25 km	Weekly	NH	1966.10–2018.12	Brodzik and Armstrong (2013)
Satellite-retrieved as	GLASS	0.05°	8-day	Global	1981.06–2017.12	Liang et al (2013a)
	CLARA-A2	0.25°	5-day	Global	1979.06–2015.12	Karlsson et al (2017)
Reanalysis as	ERA-5	0.25°	Monthly	Global	1979.01–2019.10	C3S (2017)
	CFSR	0.50°	Monthly	Global	1979.01–2017.11	Saha et al (2010)
	JRA-55	0.50°	Monthly	Global	1958.01–2012.12	Ebita et al (2011)
	MERRA-2	0.50°	Monthly	Global	1980.01–2017.11	Gelaro et al (2017)
Snow-free as	MCD43GF	0.0083°	Daily	Global (<70°N)	2000.03–2017.12	Schaaf (2019)
Albedo radiative kernels	CAM3	2.81°	Monthly	Global	—	Shell et al (2008)
	AM2	2.50°	Monthly	Global	—	Soden et al (2008)
	ECHAM6	1.88°	Monthly	Global	—	Mauritsen et al (2013)

2.2.1. NHSCE snow cover dataset

To obtain snow cover range used in S_nRF estimation over the NH, the NHSCE Version 4 (https://nsidc.org/data/NSIDC-0046/versions/4) (Brodzik and Armstrong 2013) at weekly intervals for January 1982 through December 2012 at a spatial resolution of 25 km was employed in this study. The NHSCE is developed by Robinson et al (2014), which were derived from the manual interpretation of AVHRR, Geostationary Operational Environmental Satellite (GOES), and other visible-band satellite data (Helfrich et al 2007). The NHSCE is widely used in large-scale snow cover studies (Brown and Robinson 2011, Derksen and Brown 2012, Chen et al 2016a). Uncertainty analysis of NHSCE estimated from regression analysis and an inter-comparison of multiple datasets indicated a 95% confidence interval in NH spring SCE of ±3%–5% for 1966–2010 (Brown and Robinson 2011).

2.2.2. Satellite-retrieved land surface albedo datasets

Two longterm satellite a_s datasets were employed to estimate S_nRF over the NH and to cross-compare with S_nRF estimates from reanalysis a_s for the overlapping period of 1982–2012.

2.2.2.1. CLARA-A2 land surface albedo dataset

The CLARA-A2 dataset provides 5-day black-sky a_s dataset (wavelengths of 0.25–2.5 μm), which is generated based on a homogenized AVHRR radiance time series and is created by using algorithms to separately derive a_s for different land use areas, including snow, sea ice, open water, and vegetation (Karlsson et al 2017). Currently, the CLARA-A2 a_s dataset is the only available longterm a_s product derived from AVHRR imagery. In this study, the CLARA-A2 black-sky a_s over the NH at the spatial resolution of 0.05°, covering from 1982 to 2012 were used to cross-compare S_nRF estimates from GLASS and reanalysis a_s datasets. The CLARA-A2 a_s dataset has been used to estimate sea ice albedo changes (Riihelä et al 2013) and sea ice a_s comparison (Cao et al 2016) over the Arctic regions.

2.2.2.2. GLASS broadband albedo dataset

The GLASS Broadband Albedo Version 40 product is based on the integration of two algorithms through a temporal filter scheme (Liu et al 2013, Zhao et al 2013) using AVHRR and MODIS version 6 radiance data. The GLASS products provide a_s at total shortwave, visible and near-IR under actual atmospheric conditions spectral ranges. To match black-sky a_s obtained from CLARA-A2, the 8-day GLASS total shortwave black-sky a_s at the spatial resolution of 0.05°, covering from 1982 to 2012 were used in this study. The GLASS a_s dataset has been used to quantify the albedo induced radiative forcing of snow melting over Greenland (He et al 2013), forest disturbances over northeastern China (Zhang and Liang 2014) and snow cover phenology changes over the NH (Chen et al 2015, Chen et al 2016a) with high quality and fine spatial resolution.

2.2.3. Reanalysis land surface albedo datasets

Four longterm reanalysis a_s datasets were selected to quantify S_nRF over the NH and to cross-compare with S_nRF estimates from satellite a_s from 1982 to 2012, including JRA-55, CFSR, MERRA-2, and ERA-5.

2.2.3.1. ERA-5 reanalysis land surface albedo datasets

The ERA-5 product is the latest global atmospheric reanalysis dataset produced by the ECMWF (https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5)(C3S 2017). ERA-5 has important changes relative to the former ERA-Interim atmospheric reanalysis, including higher spatial and temporal resolutions with a latest. model and data assimilation system (Albergel et al 2018).

The monthly ERA-5 a_s was calculated with clear sky surface downward and upward shortwave fluxes at a 0.125 spatial resolution from 1979 to present. By using eight independent observations include evapotranspiration, gross primary production, soil moisture, and leaf area index from remote sensing observations and soil moisture, turbulent heat fluxes, river discharges and snow depth from in situ observations, Albergel et al (2018) reported that the ERA-5 showed a consistent improvement over ERA-Interim. To cross-compare S_nRF results from satellite and other reanalysis datasets, the monthly ERA-5 a_s at the spatial resolution of 0.125°, covering NH from 1982 to 2012 were employed in this study.

2.2.3.2. JRA-55 reanalysis land surface albedo datasets

The JRA-55 is the longest reanalysis datasets that uses the full observing system (in contrast, products like ERA-20C and NOAA 20CR assimilate a very limited set of observations while NCEP R1 uses an antiquated model and assimilation scheme) spanning 1958 to present (https://climatedataguide.ucar.edu/climate-data/jra-55). The monthly JRA-55 a_s product is parameterized as functions of solar zenith angle and surface skin temperature (Ebita et al 2011). In this study, the monthly JRA-55 a_s at the spatial resolution of 0.5°, covering NH from 1982 to 2012 were used in quantification of S_nRF over the NH.

2.2.3.3. MERRA-2 reanalysis land surface albedo datasets

The MERRA-2 is a global atmospheric reanalysis derived from the Goddard Earth Observing System atmospheric general circulation model, version 5 (GEOS-5) (Gueymard et al 2019) (https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/). The MERRA-2 is the first satellite-era global reanalysis to assimilate space-based observations of aerosols and represent their interactions with other physical processes in the climate system spans from 1980 to 2017. To cross-compare S_nRF results from satellite and other reanalysis datasets, the monthly MERRA-2 a_s at the spatial resolution of 0.5°, covering NH from 1982 to 2012 were used in this study.

2.2.3.4. CFSR reanalysis land surface albedo datasets

The NCEP CFSR is a global, high resolution, atmosphere–ocean–land surface–sea ice coupled system over the period January 1979 to November 2017 (Saha et al 2010) (https://climatedataguide.ucar.edu/climate-data/climate-forecast-system-reanalysis-cfsr). The CFSR was designed to provide the best estimate of the state of these coupled domains over this period. The monthly NCEP CFSR a_s was calculated using the land model Noah described by Rai et al (2019). To cross-compare S_nRF results from satellite and other reanalysis datasets, the monthly CFSR a_s at the spatial resolution of 0.5°, covering NH from 1982 to 2012 were used in this study.

2.2.4. MCD43GF snow-free land surface albedo dataset

To obtain climatology of monthly-mean snow-free surface albedo α_sf needed in S_nRF calculation, the gap-filled daily MCD43GF α_sf at spatial resolution of 1 km (Schaaf 2019) was used in this study, which representing the a_s after removing the presence of snow cover. The MCD43GFα_sf product are computed for MODIS spectral bands 1 through 7 as well as shortwave-infrared, visible and near-infrared bands from 2001 to 2017. To compare with white-sky a_s from CLARA-A2 and GLASS datasets, the daily shortwave broadband white-sky α_sf from 2001 to 2012 was used in this study.

2.2.5. Albedo radiative kernels datasets

To reduce radiative uncertainty in S_nRF estimation caused by albedo radiative kernels, three monthly albedo radiative kernels: CAM3 gridded at 2.81° horizontal resolution from Shell et al (2008), AM2 gridded at 2.50° horizontal resolution from Soden et al (2008), and ECHAM6 gridded at 1.875° horizontal resolution from Mauritsen et al (2013) were used in this study. The seasonal cycle of albedo radiative kernels from CAM3, AM2 and ECHAM6 over the NH are shown in figure 1.

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2.2.6. Data preparation

Considering the time span and spatial resolution of individual datasets, this study was carried out among the overlapping period of 1982–2012 in 0.5° spatial resolution. Because of missing AVHRR surface reflectance data in 1994, the satellite a_s datasets from CLARA-A2 and GLASS were incomplete in this year. Thus, we excluded 1994 in this study. Due to difficulties in discriminating snow from ice over Greenland, this region was excluded from the analysis.

Before calculation, datasets used in this study in table 1 were regridded and remapped at a spatial resolution of 0.5° with geographic latitude/longitude projection with the help of gdalwarp (http://www.gdal.org/gdalwarp.html). For datasets with spatial resolution greater than 0.5°, we used 'average' in the resampling process, which computed the average of all non-NODATA contributing pixels in the domain of our study. For datasets with spatial resolution lower than 0.5°, we used 'cubic-spline' in the resampling process.

To match the temporal interval of albedo radiative kernels, the weekly NHSCE snow cover dataset, 8-day GLASS, 5-day CLARA-A2, and daily MCD43GF datasets were temporally aggregated to produce a monthly-averaged series in the calculation. To make sure the quality of a_s datasets, the quality control flags of '00' and '01' of the 8-day GLASS a_s, indicating uncertainties of <5% and <10%, were used to generate the monthly mean a_s series. Quality assurance values between '0' and '1' of daily MCD43GF, representing the majority of high-quality and good quality full inversion values, were used to generate the monthly mean snow-free surface albedo and climatology snow-free surface albedo over the NH.

The annual-mean and monthly-mean of S_nRF over the NH for the period 1982–2012 were used to explore the climatology differences between 31-year averaged S_nRF derived from satellite and reanalysis a_s datasets. For S_nRF estimates using a given a_s dataset, we first calculated the monthly S_nRF using CAM3, AM2, and ECHAM6 albedo radiative kernels, respectively. Then, we obtained the annual-mean S_nRF by averaging the monthly-mean S_nRF from January to December. The numbers in parenthesis indicate the SD of averaged annual-mean S_nRF between three S_nRF results.

3.1. Annual-mean S_nRF

The spatial distributions of the 31-year annual-mean S_nRF estimates from two satellite and four reanalysis a_s datasets during 1982–2012 are presented in figure 2. As shown in figure 2(a), S_nRF estimates from both satellite and reanalysis a_s datasets displayed similar spatial distribution over the NH during 1982–2012, with generally larger values in the high latitude areas of Eurasia and North America, and the high elevation Rocky Mountains, Tibetan Plateau, and Stanovoy Range, but smaller values in the low latitude and low elevation regions.

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The annual mean S_nRF over the NH during 1982–2012 was estimated at −1.81 (±0.06) W m⁻², −1.59 (±0.10) W m⁻², −2.30 (±0.15) W m⁻², −1.48 (±0.16) W m⁻², −1.74 (±0.07) W m⁻², and 1.49 (±0.06) W m⁻² using the GLASS, CLARA-A2, ERA-5, CFSR, JRA-55, and MERRA-2 a_s datasets, respectively.

Compared with S_nRF estimates from GLASS a_s (figure 2(a)), the results from CLARA-A2 (figure 2(b)) was minor at high latitudes, especially in regions of Eurasia near the Arctic Ocean. However, compared with S_nRF derived from GLASS and CLARA-A2, most of the S_nRF estimates from reanalysis a_s displayed minor values in high latitude and high elevation regions, especially JRA-55 (figure 2(d)) and MERRA−2 (figure 2(e)). Moreover, as shown in figure 2(c), the S_nRF estimates from ERA-5 a_s displayed higher values in mountainous regions, such as the Rocky Mountains, Tibetan Plateau, and Stanovoy Range. In contrast, S_nRF estimates from CFSR a_s was minor in the high elevation Rocky Mountains, Tibetan Plateau, and Stanovoy Range, which indicate that there are large differences exist between S_nRF results from individual a_s dataset, even among reanalysis a_s datasets.

3.2. Seasonal cycle of the S_nRF

The climatology of monthly-mean S_nRF in each month for a given a_s dataset was calculated by averaging the three S_nRF estimates using CAM3, AM2, and ECHAM6 albedo radiative kernels. The climatology of seasonal S_nRF over the NH for the period 1982–2012 derived from two satellite and four reanalysis a_s datasets are displayed in figure 3. The satellite-based S_nRF in figure 3 were calculated by averaging S_nRFs estimate from GLASS and CLARA-A2 a_s datasets. The reanalysis-based S_nRF in figure 3 were calculated by averaging S_nRFs estimate from JRA-55, CFSR, MERRA-2, and ERA-5 a_s datasets.

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As shown in the seasonal cycle of S_nRF over the NH estimates from six individual a_s dataset during 1982–2012 (figure 3(a)), the S_nRF from both satellite and reanalysis a_s datasets captured the seasonal cycle of S_nRF over the NH. The S_nRF broadly peaked at approximately −5.97 (±0.07) W m⁻² to −4.22 (±0.05) W m⁻² in April because of the high solar radiation and large SCE over the NH in April. Meanwhile, the S_nRF valleys were broad at −0.33 (±0.003) W m⁻² to −0.08 (±0.001) W m⁻² in August because of low SCE and albedo radiative kernels values in August caused by higher cloud optical thickness over the NH. However, there were large differences between seasonal cycles of S_nRF derived from satellite and reanalysis a_s datasets. Compared with the S_nRF estimates from GLASS and CLARA-A2 a_s datasets, S_nRF calculated from the ERA-5 a_s dataset displayed higher values in the entire cycle of S_nRF over the NH from January to December.

The average monthly-mean S_nRF from six a_s datasets are displayed in figure 3(b), in which the largest discrepancies are distributed in May (−1.93 W m⁻²), followed by April (−1.75 W m⁻²) and March (−1.50 W m⁻²). The detailed differences between S_nRF derived from satellite and reanalysis a_s datasets are displayed in figure 3(c). Compared with the averaged satellite-based S_nRF over the NH, the reanalysis-based S_nRF displayed higher values in snow accumulation seasons from October to January, but lower values in snow melting seasons from February to July, which indicated that the reanalysis-based S_nRF could not capture the actual seasonal cycle of S_nRF over the NH during 1982–2012.

Changes in annual-mean and monthly-mean S_nRF were used to explore the ability of S_nRF derived from satellite and reanalysis a_s datasets in capture the radiative feedback of snow cover to Earth climate system for the period 1982–2012. Changes were calculated as linear trends multiplied by the time interval.

4.1. Changes in annual-mean S_nRF

4.1.1. Spatial distribution of changes in annual-mean S_nRF

The spatial distribution of 31-year changes in annual-mean S_nRF estimates from six individual a_s datasets during 1982–2012 are displayed in figure 4.

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As shown in figures 4(a) and (b), the NH experienced weakened cooling effects with a smaller magnitude of S_nRF changes in high latitudes near the Arctic Ocean, but strengthened cooling effects with a larger magnitude of S_nRF changes in the mid-latitudes, including the central United States and Tibetan Plateau during 1982–2012. Compared with S_nRF changes based on satellite a_s datasets, the comparable changes using ERA-5 (figure 4(c)) and JRA-55 (figure 4(d)) displayed general positive anomalies over the NH, except for the TP regions. Moreover, the large scale negative S_nRF changes in the United States and Northern China from satellite-based S_nRF results were not captured in S_nRF estimates from ERA-5 (figure 4(c)), JRA-55 (figure 4(d)), and MERRA-2 (figure 4(e)). Moreover, the CFSR-based S_nRF displayed significant negative changes among most of the NH landmass, except for the high latitudes of Eurasia, which is in conflict with the published findings of rapid snow cover extent reduction in recent decades (Brown et al 2007, Déry and Brown 2007, Chen et al 2016a).

4.1.2. Interannual variability of annual-mean S_nRF over the NH

Detailed comparisons of 31-year annual-mean S_nRF variabilities over the NH calculated from six individual a_s datasets during 1982–2012 are provided in figure 5. The large discrepancies between S_nRFs estimate from two satellites and four reanalysis a_s datasets are clearly displayed in figure 6.

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Both satellite and reanalysis-based S_nRF present generally positive changes with the shrinking of the SCE over the NH during 1982–2012 (figure 5). The peak of annual-mean S_nRF (−1.67 ± 0.03 W m⁻²) occurred in 2012, whereas in the valley, the peak at −1.92 (±0.05) W m⁻² occurred in 2004 in GLASS-based S_nRF estimations. Compared with GLASS-based S_nRF, the magnitude of S_nRF from CLARA-A2 was much smaller, with the peak and valley being −1.38 ± 0.08 W m⁻² in 2000 and −1.83 ± 0.11 W m⁻² in 1992, respectively. For S_nRF estimates from reanalysis a_s datasets, the ERA-5 and JRA-55-based S_nRF series presented peak values in 2007 with −1.99 ± 0.14 W m⁻² and −1.59 ± 0.12 W m⁻², respectively. Moreover, the valleys of the ERA-5 and JRA-55-based S_nRF series occurred in 1985, with −2.60 ± 0.19 W m⁻² and −1.94 ± 0.15 W m⁻².

The S_nRF over the NH declined by 0.39 W m⁻² to 1.25 W m⁻² during 1982–2012 based on series from satellite a_s datasets, which was much smaller than the comparable results calculated from the reanalysis-based S_nRF (2.02 W m⁻² to 2.65 W m⁻²), which may have overestimated the role of snow cover in climate change studies and future climate projections. Thus, the discrepancies between S_nRF estimations from satellite and reanalysis a_s datasets should be considered when evaluating the snow-induced energy budget and climate system anomalies in future studies.

4.2. Changes in seasonal S_nRF

The 31-year linear changes of S_nRF over the NH in each month derived from two satellites and four reanalysis a_s datasets from 1982–2012 are shown in figure 7. Changes in S_nRF in a given month from 1982 to 2012 were calculated as linear trends multiplied by the time interval.

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Driven by the decreased SCE over the NH in spring and summer seasons (Chen et al 2016a), the S_nRF calculated from both GLASS and CLARA-A2 a_s datasets displayed positive changes from April to August, which coincided with the S_nRF changes derived from reanalysis a_s products. However, the negative S_nRF changes calculated from GLASS and CLARA-A2 in the snow accumulation seasons from November to February were largely different from the S_nRF changes derived from reanalysis a_s products, except for CFSR, especially in January. The changes in S_nRF calculated from GLASS (−0.10 ± 0.010 W m⁻²) and CLARA-A2 (−0.41 ± 0.06 W m⁻²) a_s datasets were negative in January, which indicated an enhanced cooling effect caused by snow cover. However, this phenomenon could not be adequately represented by a reanalysis-based S_nRF.

As reported by Chen et al (2016a) and Cohen et al (2012), driven by Arctic Amplification, increasing snow cover and widespread boreal winter cooling occurred from the 1990s onward. With increased snow cover extent and greater albedo contrast, additional solar radiation was reflected to space, which resulted in a strengthened cooling effect of snow cover and negative changes in S_nRF. In contrast, with the rapid decline of spring and summer SCE over the NH (Brown and Robinson 2011, Derksen and Brown 2012, Chen et al 2016a), obviously weakened cooling effects should have been detected from S_nRF. Compared with satellite observations, the reanalysis a_s field captured the S_nRF changes.

The S_nRF is a vital indicator to evaluate the contribution of snow cover to Earth radiation budget under the background of global warming and rapid SCE reduction over the NH in the past few decades. As a key parameter in S_nRF estimation with large bias between satellite and reanalysis products, a comprehensively examine the performance of satellite and reanalysis a_s datasets in representing the large scale spatiotemporal variability and long term change in S_nRF over the NH are necessary. Using two satellite and four reanalysis a_s datasets coupled with several ancillary datasets, this study explored the differences between satellite- and reanalysis-based S_nRFs over the NH for the overlapping period of 1982–2012.

Although both satellite- and reanalysis-based S_nRFs captured the climatology of the annual-mean and seasonal cycle of S_nRF over the NH during 1982–2012, large differences still exist between them. For climatology of annual-mean S_nRF, the reanalysis-based S_nRF displayed lower values in high latitude and high elevation regions compared with satellite-based S_nRF, which may underestimate the radiative forcing and feedback of snow cover to climate change in those regions. For the seasonal cycle, the reanalysis-based S_nRF displayed higher values in snow accumulation seasons from October to January, but a lower value from February to July, compared with satellite-based S_nRF over the NH from 1982 to 2012.

Changes in S_nRF over the NH during 1982–2012 derived from satellite and reanalysis a_s datasets were also cross-compared in this study. The annual-mean S_nRF over the NH declined by 0.39 Wm⁻² to 1.25 Wm⁻² during 1982–2012 from satellite-based S_nRF, which is much smaller than the results calculated from the reanalysis-based S_nRF. In addition, changes in monthly-mean S_nRF from satellite-based S_nRF series displayed an enhance trend in snow accumulation season over the NH from 1982 to 2012, which are largely different with the comparable changes from reanalysis-based S_nRF, indicating that the reanalysis-based S_nRF results cannot capture the actual inter-annual and intra-annual changes of S_nRF over the NH.

Compared with previous research, the present study investigated the spatial and temporal differences between S_nRF over the NH using satellite and reanalysis a_s datasets for the overlapping period of 1982–2012, which is important for current climate change studies and future climate projections. However, several unresolved issues remain in our study. Subjected to the coarse resolution of NHSCE snow range and reanalysis a_s datasets, this study was carried out at 0.5 spatial resolution, which may mixed the radiative forcing induced by snow cover and other land cover types, especially vegetation and permafrost (Johansson et al 2013). As an integral component of the global climate system with rapid changes, more detained evaluation and analysis of radiative forcing and feedback induced by snow cover changes with fine resolution is necessary in future studies. Since CLARA-A2 only provides white-sky surface albedo products, this study used white-sky surface albedo products from satellite observations in the cross-comparisons with reanalysis-based annual-mean and monthly-mean S_nRF results. However, previous studies have reported that the differences between S_nRF with white-sky albedo and black-sky albedo are slightly (Flanner et al 2011, Qu and Hall 2014, Chen et al 2016b), which will not influence the results of this study. Considering the large discrepancies in S_nRF results from different surface albedo datasets, the uncertainties in S_nRF estimations should be considered in future studies.

We would like to thank all people fighting with COVID-19 and the anonymous reviewers for their constructive comments and suggestions. This study was jointly funded by the comprehensive survey of biodiversity over the Mongolian Plateau (2019FY102001), the National Key Research and Development Program of China (NO. 2016YFA0600103) and the National Earth System Science Data Sharing Infrastructure (NO. 2005DKA32300). The Climate Data Record of Northern Hemisphere Snow Cover Extent and MCD43GF land surface albedo products were provided by the https://earthdata.nasa.gov/. The GLASS land surface albedo dataset were available at the national earth system science data center http://www.geodata.cn/. The CLARA-A2 land surface albedo dataset were obtained from the https://wui.cmsaf.eu/safira/. The JRA-55, CFSR and MERRA-2 reanalysis land surface albedo data were obtained from https://rda.ucar.edu/datasets. The ERA5 reanalysis land surface albedo data were obtained from https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5. The albedo radiative kernels were obtained from https://climatedataguide.ucar.edu/climate-data/radiative-kernels-climate-models.