1. Introduction
The top-of-atmosphere (TOA) albedo, which is defined as the fraction of incoming solar irradiance that is scattered back to space by the earth-atmosphere system, is one of the key quantities in determining the global energy balance [
1,
2]. Since a decrease of ~0.01 in the global mean albedo is equivalent to direct radiative forcing at the surface of doubling carbon dioxide in the atmosphere [
3], accurate TOA albedo monitoring is crucial to both the examination of the Earth’s radiation budget (ERB) and in understanding how the Earth’s system is changing. Recently, changes in the Arctic TOA albedo have become a strong focus of research given the rapidly retreating Arctic sea ice extent, which is recognized as one of the most profound climate changes associated with global warming [
4]. During the melt season, the white reflective surfaces of snow-covered ice and bare ice gradually form relatively dark ponded sea ice with some of it ultimately getting replaced by the dark ocean. This change is seen as Arctic darkening as observed from space when uncompensated by other changes, such as an increase in cloudiness. Pistone et al. [
5] argued that the shortwave radiative forcing at the TOA associated with Arctic darkening was equivalent to 25% of the global CO
2 direct forcing during the study period (1979–2011). Such a large sensitivity of the Arctic climate to the ice-albedo feedback raises the importance of obtaining reliable estimates of the Arctic TOA albedo from the Earth-orbiting satellite sensors.
The TOA albedo monitoring systems can be broadly divided into broadband and narrowband sensors, which have been well summarized along with the respective pros and cons in Reference [
6]. As one of the best products in characterizing the Earth’s TOA albedo, the Clouds and the Earth’s Radiant Energy System (CERES) TOA albedo datasets have been widely used in Arctic studies [
5,
7,
8,
9,
10]. However, the quality assessment of the datasets is severely limited by there being few other available TOA albedo datasets available for comparison, particularly datasets that have collocated field-of-views (FOVs) in space and time. Since there are no direct measurements of TOA albedos, but only retrievals from the instantaneous radiances, current CERES TOA instantaneous albedos are mostly evaluated by performing consistency checks between oblique- and nadir-view retrievals, using either CERES along-track observations or spatially and temporally collected MODIS/MISR radiances [
11,
12,
13]. Based on the merged Single Scanner Footprint TOA/Surface Fluxes/Clouds and MISR (SSFM) dataset [
14], for example, Su et al. [
13] found that the CERES SW flux consistency due to ADM uncertainty was ~6% for cloud conditions over snow/ice surfaces. Whether or not these methods provide unbiased error estimates is currently unknown. Comparisons with other independent albedo datasets provide an excellent way of elucidating the quality of and confidence in each dataset, and in understanding the potential areas requiring improvements.
Amongst the other independent TOA albedo datasets, such as the Scanning Radiometer for Radiation Balance (ScaRaB) [
15] and the Geostationary Earth Radiation Budget (GERB) [
16], only the Multi-angle Imaging SpectroRadiometer (MISR) [
17] stands out as an excellent basis to compare against the CERES because it is on board the same
Terra satellite platform as the CERES. Thus, its albedo dataset offers a unique opportunity to evaluate the performance of CERES TOA albedo retrievals using MISR and CERES overlapped near-nadir swaths when the CERES is in its cross-track mode of operations [
11]. An early study by Sun et al. [
18] showed that the CERES cloud albedo is highly consistent with the MISR cloud albedo for the low- and mid-latitude ocean regions. This was in agreement with Zhan and Davies [
19], who showed that zonal trends of low- and mid-latitude albedo from the CERES and MISR corresponded well with each other after accounting for intercalibration differences. Nevertheless, Zhan and Davies [
19] pointed out an unexpectedly large discrepancy between the CERES and MISR zonal albedo trends within the polar regions, suggesting the need to quantitatively compare the CERES and MISR TOA albedo products specifically within the Arctic region.
The objective of this study was to investigate the consistency of instantaneous CERES and MISR TOA albedos within the Arctic. Given that the MISR adopts the CERES angular distribution models (ADMs) for clear-sky albedo retrievals but applies the radiative transfer model (RTM)-based approach for cloud albedo estimates, we focused on quantifying the instruments overcast albedo retrieval differences that were functions of both the surface type and solar zenith angle. In the following assessment, three years (2007, 2015 and 2016) of CERES and MISR Level-2 instantaneous TOA albedo products were collected. This was followed by collocating MISR samples to each CERES FOV, as well as estimating the equivalent MISR operational albedos over the (20 km)2 CERES FOV. Finally, these collocated CERES and MISR TOA albedos were used to examine scene-dependent cloud albedo consistencies and to explore the scene classification performances.
3. Instantaneous Albedo Collocation and Calculation
We chose a large area (poleward of 60° N) covering a long time period to accumulate a sufficient number of valid samples. All the aforementioned datasets (
Table 1) from the CERES and MISR were collected and collocated.
Table 2 summarizes the criteria for data selection, and “n/a” means the parameter was not specified to the particular instrument. Since the MISR uses a different scene identification scheme from the CERES, the collocated samples were further binned by MISR scene type when examining the consistency of the instruments albedo retrieval algorithms as described below. Moreover, the MISR assigns all the measured raw radiances (275 m) to a Reflecting Layer Reference Altitude (RLRA) surface (2.2 km), either to the top or side of a cloudy column [
17]. The pre-processing results from some RLRA surfaces being obscured at oblique views, including in the cross-track direction, and it leads to the redistribution of all the radiance observations. In other words, a high obscuration within the MISR An-camera would indicate a high degree of cloud-top-altitude variability and it may result in a bias in the mean An-camera BRF over a CERES footprint, which would propagate to the MISR-CERES narrow-to-broadband analyses below. Thus, only MISR samples with more than 90% top-unobscured An-camera observations were considered in this study.
Within the Arctic, the data selection criteria given in
Table 2 reduces the sampling significantly, relative to all the CERES retrievals within the broad CERES swath. Only ~17% of the CERES footprints had a VZA < 10°, of which ~40% were overcast. Overcast cloud over a uniform surface type observed by the CERES in the near-nadir (<10°) direction accounted for ~4% of all CERES samples across its full swath. Of these samples, only half passed the >90% unobscured RLRA criterion of the MISR. The analysis below was specific to these particular scene-types and viewing conditions. Issues of representativeness to a broader set of scene types and viewing conditions are discussed in
Section 5.
Since the CERES and MISR are on board the same satellite platform, Terra, some of the footprints are collocated. However, the instantaneous footprints will only intersect in near-nadir directions due to the different operational scan modes between CERES FM1 (which is stuck in the cross-track sampling mode after 2002) and MISR (push-broom sampling). To collocate the samples, we applied an approach similar to the one used by Zhan and Davies [
19], who used the MISR Toolkit (MTK). The MTK was developed by the Jet Propulsion Laboratory and it provides an interface to access the MISR datasets, including geolocation information. Further details on the MTK can be found on the MISR website
https://eosweb.larc.nasa.gov/project/misr/tools/misr_toolkit.
For a CERES near-nadir FOV with a valid shortwave radiance and corresponding reflected flux, an MtkRegion R with CERES center latitude, longitude, that was expanded by 100 km was set by the MTK, which does not handle small region collocation properly. This was followed by using R to collect all the available MISR samples (2.2 km spatial resolution) within the region. Then, the great-circle distances (GD) between each MISR sample and the CERES were calculated. MISR samples with GD ≤ 10 km were then used in the following analysis. For a typical CERES nadir FOV with 20-km spatial resolution, the median number of valid MISR 2.2 km pixels was 64. Thus, any CERES FOV with less than 62 MISR pixels were excluded in the comparison. Although the proposed collocation may have introduced some potential errors, they should have been relatively small because the missing pixels were along the boundary of the CERES FOV.
The collocated MISR spectral radiances were then converted to BRFs and averaged for each CERES FOV. To estimate the corresponding MISR broadband BRF, we developed a set of scene-dependent narrow-to-broadband (NTB) BRF conversions that related the MISR red and Near Infrared (NIR) bands BRF to the CERES unfiltered broadband BRF as follows:
where
,
and
were the CERES broadband BRF, and MISR red and NIR BRF, respectively.
c0,
c1 and
c2 were the regression coefficients from a linear regression analysis, and were a function of both the solar zenith angles and surface types. The solar zenith angles were stratified into 10° bins to match the operational NTB bin size. The surface type, on the other hand, was either 100% ocean or 100% snow/ice (separated for sea ice, fresh snow, and permanent snow) as classified by the CERES. Unlike the previous studies [
14,
18], we did not further bin the samples by viewing the zenith angle, relative viewing azimuth angle, cloud fraction, etc. This is because we inherently chose nadir observations (
≤ 10°) over overcast scenes (
f ≥ 99.9%). Moreover, our results showed that using additional data such as MISR blue and green radiances, precipitable water, or effective cloud top height did not improve the narrow-to-broadband BRF conversion, which was consistent with Sun et al. [
18].
As an example,
Table 3 shows the coefficients, as well as relative RMS differences, of the MISR narrow-to-broadband BRF conversion over the CERES overcast ocean scenes. The coefficients of determination were extremely high for all the solar zenith angle ranges, implying these linear regressions were robust. The overall relative RMS differences in the MISR broadband BRF conversions were ~5% when solar zenith angles were less than 80°, with a slightly larger RMS difference (6.2%) for more oblique sun angles. Note that the reported RMS difference should include both the narrow-to-broadband BRF conversion error and sampling error. Here, the sampling error consisted of both the collocation of the instantaneous FOVs and the mismatched boundary pixels. Compared to the reported RMS difference of ~3% in Sun et al. [
18], the larger integrated error mainly resulted from the larger sampling error caused by both using the coarse resolution MISR BRFs and not accounting for the CERES point spread function.
The relative RMS differences of MISR broadband BRF conversion were smaller for overcast snow/ice scenes.
Table 4 shows the results for the collocated CERES overcast sea ice case. Except for the extremely high solar zenith angles, it was clear that the relative RMS differences were generally less than 5%, which was similar for overcast fresh snow (not shown). For overcast permanent snow scenes (not shown), the RMS difference from both the sampling error and the NTB BRF conversion error was even lower, being ~3% for all solar zenith angles. As we adopted the same methodology to retrieve the collocated samples, the sampling errors should be the same in all cases. Thus, the smaller RMS difference for the overcast snow/ice scenes compared to overcast ocean scenes may be because variations in cloud properties (e.g., optical depth) were more important over dark ocean surfaces than over bright snow/ice surfaces.
For the corresponding MISR broadband restrictive albedo (
), instead of directly using the operational (35.2 km)
2 data, we recalculated the
based on the collocated (2.2 km)
2 samples following the same approach referred to in the MISR Level 2 Top-of-Atmosphere Albedo Algorithm Theoretical Basis Document (ATBD) [
17] and updated by Catherine Moroney [
38] for the narrow-to-broadband conversion strategy. Firstly, we calculated the cosine of the solar zenith angle (
) of all the MISR samples. If any
within the CERES-MISR collocated region was <0.04, the
was not calculated. Following the ATBD, the
can be expressed as:
where
is the sum of the top-leaving contribution calculated from MISR broadband local albedos, which is a linear combination of the red and NIR local albedos (for cloudy scenes).
is the side-leaving contribution that is a solid angle weighted side-leaving BRF of the collocated samples. In the standard MISR product,
is estimated by applying the same narrow-to-broadband conversion coefficients (as the local albedo conversion) to red and NIR side-leaving contributions.
Note that these conversion coefficients only depend on the solar zenith angles and were developed by Sun et al. [
18]. Although the coefficients were derived for overcast ocean scenes within low-/mid-latitudes, the MISR applies them to produce both broadband cloudy local albedos and restrictive/expansive albedos regardless of the surface type. Thus, the reported NTB albedo conversion errors (Table 1 in Reference [
18]) cannot be directly used and the “real” error embedded in the albedo NTB conversion (
) needs to be reformulated. Here we assumed that the difference of the NTB conversion error (
) between BRF and albedo was similar for different surface types and SZA ranges. Bearing this assumption in mind, the scene-dependent NTB albedo conversion can be estimated from
for each surface type (ocean, sea ice, fresh snow, and permanent snow) and solar zenith angle range. According to Sun et al. [
18], approximately 2% and 3% RMS errors have been found for the MISR BRF and albedo NTB conversion, respectively. We then applied the resulting difference (
2.2%) to be subtracted from the scene-dependent BRF NTB conversion error (
Table 3 and
Table 4) to estimate the error of the MISR albedo NTB conversion for different surface types and SZA ranges.
5. Discussion
Compared to previous studies [
11,
12,
13,
18,
42], this study makes an original contribution as follows. Firstly, the accuracy of the CERES instantaneous TOA albedo retrievals has yet to be systematically analyzed. Most of the aforementioned studies focused on examining the regional mean errors [
11,
42]. While providing a general impression of the CERES performance, the studies do little to help further quantify its albedo uncertainties or provide a direction for future improvements, particularly with regard to the known larger errors in the proposed theoretical models and observations [
11,
43,
44]. Secondly, as the first direct comparison of the instantaneous CERES and MISR albedos, Sun et al. [
18] examined the albedo consistency over 1° × 1° overcast ocean regions between 75° S–75° N. However, the results neither included the entire Arctic region nor accounted for the SZA-dependent uncertainties in the estimated zonal RMS errors (the authors
Figure 3c). These early uncertainty estimations addressed the issue of angular inconsistency in the retrieved CERES TOA albedos [
11]. Considering that the largest variation of the CERES anisotropic factor to cloud properties (e.g., cloud optical depth) is found at near-nadir [
45], it remains necessary to examine the performance of the CERES near-nadir albedo retrievals as functions of scene types and solar zenith angles. Thirdly, the MISR has provided its own TOA albedo product that has yet to be fully compared with others. The well-developed radiative transfer simulations and nine-angle configurations led us to believe that the MISR may achieve a comparable or better performance in retrieving cloud albedos, particularly under low sun conditions.
Thus, this study focused on examining the consistency of the instantaneous SW albedo retrieved from the CERES and MISR over the Arctic. Based on features of the two instruments, a set of criteria was firstly applied to select qualified CERES-MISR collocated samples (
Table 2). Owing to the different scanning configurations, we did not include albedo samples from oblique angles in the CERES cross-track sampling mode. We focused on the overcast albedo retrievals, since there are known issues of MISR clear-sky local albedos (fine resolution) that constitute the clear portion in its restrictive albedos (coarse resolution). Furthermore, we excluded CERES mixed-scenes as the ADMs were essentially determined from the single-scene ADMs [
21]. Applying these criteria resulted in 4% of the total CERES FOVs being used, which was further reduced to 2% after collocating with the MISR samples. Despite the small percentage of total data, the samples were carefully selected to ensure that the three uncertainty components (
,
,
) could be quantified from BRF and albedo comparisons. These collocated samples were also representative of the overcast near-nadir CERES samples. Similar sample distributions were found for both the CERES albedos and mean logarithm of cloud optical depths (ln
), for example, the mean (standard deviation) of ln
was 2.3 (0.8) and 2.4 (0.7) for the overcast near-nadir CERES dataset and the CERES-MISR collocated dataset, respectively. Moreover, as the CERES team has examined the consistency of instantaneous TOA albedos estimated from near-nadir and oblique-viewing angles [
11,
12,
13], perhaps the results of this study can be further applied to estimate the CERES overcast albedo uncertainties for off-nadir samples.
To determine the MISR broadband TOA albedos for the collocated CERES FOVs, an updated collocation method using the MisrToolkit was developed. The corresponding MISR broadband restrictive albedos were then retrieved strictly following the operational algorithm. Since the MISR albedo narrow-to-broadband conversion coefficients were designed originally for overcast ocean scenes [
18], the conversion RMS errors cannot be directly used. To have a better estimate of the scene-dependent MISR NTB albedo conversion error, we assumed that the difference between the NTB BRF conversion and NTB albedo conversion (
) was the same for different scene types. The assumption was feasible as we binned the data in the same manner and used the same two MISR spectral bands (i.e., red and NIR) to conduct the linear regression. Whilst
can be calculated (~2.2%) from Sun et al. [
18], the RMS error of the corresponding NTB albedo conversion can be estimated from the NTB BRF conversion errors listed in
Table 3 and
Table 4.
Considering the RMS differences of collocated overcast albedos over consistent scenes (
Table 5), the RMS differences between the CERES and MISR instantaneous overcast albedos purely due to the differential BRF anisotropic correction (
) are shown in
Figure 7 as functions of both surface types and solar zenith angles. The overall relative RMS difference, ranges from 3.2% for overcast sea ice to 8.4% for overcast permanent snow. It should be noted that these values cannot be directly used as the overcast albedo uncertainty due to the significant dependence of the albedo agreement on the solar zenith angles (
Figure 7). The retrieval algorithm differences of overcast scenes were generally less than 5% when the SZA was less than 70° and increased dramatically with the increasing SZA, reaching up to ~14% (~20%) when the SZA exceeded 80° over ocean (snow/ice). In comparison, Sun et al. [
18] found that the ADM difference was ~4% for the overcast ocean albedos between the CERES and MISR for solar zenith angles ≤ 75°. The highly consistent results for the overcast ocean case confirmed the validity of the proposed quantification approach and enhanced our confidence in the overcast snow/ice results. However, the
for solar zenith angles SZA ≥ 70° remain large, suggesting more efforts are needed to improve the TOA albedo retrievals at high solar zenith angles.
Additionally, we showed that the largest discrepancy between CERES overcast albedo samples and MISR albedos for those same samples in the Arctic originated from the MISR scene identification algorithm, which overestimates sea ice coverage and significantly underestimates Arctic low clouds. Whilst using a higher resolution (daily instead of monthly) snow/ice mask with the heritage threshold could largely improve the sea ice misclassification, adopting a Albedo Cloud Designation field from a combination of SDCM, RCCM, and ASCM does improve MISR scene classification by drawing upon the known strengths of the MISR cloud for each underlying surface type. Instead of using the strategy embedded in the current consensus cloud mask (i.e., SDCM + ASCM + RCCM), and certainly in the current Albedo Cloud Designation field (old SDCM only), we separated cloud mask combinations based on the underlying surface types following a much more reasonable logic similar to what was done within the MISR CFbA product (SDCM+ASCM for snow/ice, RCCM for open water). On average, we showed that results from our approach were much more consistent with CERES cloud classifications than all the other MISR standard cloud mask products (
Figure 6). The remaining inconsistencies were mostly over snow/ice surfaces where the CERES also suffers from cloud classification issues. Moreover, a systematic analysis of NR occurrence may provide a more accurate cloud mask for the downstream product such as TOA albedo, as it uses SAW for these samples. Lastly, the misclassified clouds impact the TOA albedo retrievals to different degrees, depending on the difference of anisotropic corrections between the cloudy and clear scenes. Specifically, significant positive biases and negative biases have been observed over ocean and permanent snow, respectively. Both fresh snow and sea ice are not strongly influenced by the cloud misclassification; however, it is because of similar anisotropic corrections for cloudy and clear scenes.