The Earth Clouds, Aerosol and Radiation Explorer (EarthCARE) satellite’s Broadband Radiometer (BBR) consists of three telescopes and a rotating chopper drum (CD). Together they yield alternating measurements of total wave (TW; 0.25 to >50 μm) and shortwave (SW; 0.25–4 μm) radiances with point spread functions that translate to 0.6-km-diameter pixels. The mission requires that SW and TW radiances be averaged over 100-km2 domains. Correspondingly, the average longwave (LW) radiances are the differences between TW and SW averages. It is shown that impacts on domain-average nadir radiances resulting from alternating samples of TW and SW signals for realistic cloudy atmospheres are sensitive to the variance of cloudy-sky radiances, CD rotation rate, and along-track length of averaging domains. Over domains measuring 5 × 21 km2 and at a 50% rotation rate, uncertainties reached up to 3.2 and 4.1 W m−2 sr−1 for SW and TW radiances, respectively. The BBR’s design allows for in-flight alteration of the CD rate. An approximate method is provided for estimating SW and LW uncertainties resulting from the CD rate. While the nominal rotation rate meets EarthCARE’s mission requirements, reducing below 75% of that rate will lead to uncertainties for domain-average LW radiances that will often exceed mission requirements. This could be mitigated by increasing the size of averaging domains but that would compromise the BBR’s role in EarthCARE’s radiative closure assessment program. Uncertainties for off-nadir radiances are largely free of impacts arising from changes to the CD rotation rate.
The Earth Clouds, Aerosol and Radiation Explorer (EarthCARE) satellite mission is a collaboration between the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA). It will be launched no sooner than the end of 2020, and will yield radar, lidar, and multispectral imager (MSI) measurements for synergistic retrieval of cloud and aerosol properties profiles for 1 km2 nadir columns. EarthCARE’s goal (Poiares Baptista 2001; ESA 2006) is that when broadband radiative transfer models act on retrieved cloud and aerosol properties, estimated top-of-atmosphere (TOA) fluxes for domains with areas 100 km2 will be, on average, within ±10 W m−2 of fluxes inferred from radiances measured by its Broadband Radiometer (BBR; see Illingworth et al. 2015). This “radiative closure assessment” experiment has been a central driver to the overall design of the EarthCARE mission.
The BBR will measure TOA filtered radiances at nadir and two along-track oblique views, with viewing zenith angles of 53°. It consists of three telescopes, each using a linear array of microbolometer detectors with 30 elements (with an element of 0.6-km pixel size), thus covering an area of about 20 km across track and 1 km along track (Wallace et al. 2009). The BBR further consists of a rotating chopper drum mechanism (CDM) and a silica filter to produce SW radiances. As the satellite moves along, radiance measurements alternate between total wave (TW; 0.25 to >50 μm) and shortwave (SW; 0.25–4 μm) with point spread functions that amount to 0.6-km-diameter pixels separated by ground sampling distance . Hence, SW and TW measurements are separated by . The combination of simultaneous across-track and progressive along-track sampling enables constructing larger areas. The telescopes’ characteristics require (mission worthy) radiances to be averaged over (10 km)2 areas. As such, areas used for the radiative closure experiment will be more rectangular but still cover 100 km2. They are referred to as “assessment domains.” Correspondingly, longwave (LW) average radiances are the differences between TW and SW averages.
By design, the CDM rotation rate can be adjusted while in orbit, thereby facilitating possible extensions to the mission’s lifetime (A. Lefebvre 2018, personal communication; Caldwell et al. 2017b). Although standard radiometric performance assessments of the BBR have occurred, uncertainties for assessment domain-average radiances resulting from intermittent sampling of TW and SW radiances have not been quantified. Such uncertainties can be expected when radiances exhibit significant fluctuations at spatial scales near pixel size and are to be averaged over relatively small assessment domains, such as cloud fields within EarthCARE-size assessment domains (e.g., Barker et al. 2017). Given the BBR’s central role in EarthCARE’s radiative closure experiment, it is essential that BBR radiance uncertainties be quantified as well as possible. Moreover, it is useful to know the approximate lower bound on the CDM rotation rate so as not to compromise the closure experiment.
Hence, the primary purpose of this paper is to report on an investigation into the dependence of nadir BBR radiance uncertainties on via the CDM rotation rate. While analyses focus entirely on cloudy atmospheres, the results apply to all scenes that exhibit radiometric variability. Off-nadir radiances, being sufficiently oversampled in the along-track direction, are almost free of CDM-related sampling uncertainties; therefore, they are not addressed here [see Wallace et al. (2009)].
The second section explains the experimental design and simulation of BBR measurements. The third section describes how uncertainties for mean radiances arise as a result of the rotating CDM. Results are presented in the fourth section and conclusions in the final section.
2. Simulation of BBR measurements
To achieve spatially accurate BBR point spread function (PSF) integrations coupled with sampling separation distances, BBR measurements were simulated by averaging high-resolution Landsat-8 imagery. Figure 1a shows the PSF resolved at Landsat-8’s resolution of 0.03 km. At 50% of the PSF’s integrated energy, BBR “pixels” are 0.58 km across, and their centers are separated across track by 0.58 km also. At the CDM’s full (i.e., nominal) rotation rate, one revolution of the CDM takes 0.23 s (Caldwell et al. 2017a). As shown in Fig. 1b, each telescope has four exposures per revolution: two each for the TW and SW bands. Hence, with EarthCARE traveling at 7.21 km s−1, successive nadir-view pixels with the same wavelength will have 0.8 km. Obviously, adjusting the CDM rotation rate will impact . Figure 1c shows conditions at half the CDM’s nominal rate. A detailed description of EarthCARE’s BBR can be found in Wallace et al. (2009).
Landsat-8 bands 5 (0.845–0.885 μm; 0.03-km pixels) and 10 (10.6–11.2 μm; 0.1-km pixels) were used to construct approximate unfiltered BBR SW and LW radiances, thus assuming a perfect spectral response. Broadband SW radiances , at 0.03-km resolution, were approximated by using Landsat-8’s band 5 radiances as a direct proxy for the magnitude of corresponding broadband radiances at TOA. Theoretical considerations—approximating a two-stream radiative transfer by using high-spectral-resolution solar irradiance (Kurucz 2005), atmospheric transmission [based on the high-resolution transmission (HITRAN) 2008 database; Rothman et al. 2009], and spectrally resolved cloud single-scattering albedo and ocean-like surface albedo—indicated that employed approximation underestimated broadband radiances over clouds by 5% and overestimated clear ocean by up to 30% (not shown). Also, radiances were then scaled to correspond to a solar zenith angle of 23° (i.e., multiplication by , with the original solar zenith angle ), which is the smallest for EarthCARE’s orbit, thus providing the highest expectable levels of SW radiation during the mission. Broadband LW radiances , at 0.1-km resolution and brought onto a 0.03-km grid, were approximated by estimating Planck effective temperatures from Landsat-8’s band 10, using them in the Stefan–Boltzmann equation to get broadband fluxes, multiplying them by a broadband effective transmittance of 0.65, and dividing by π to get back to radiance; and are clearly approximations, but what is important here is that once integrated over PSFs, they are close to expected BBR values and exhibit realistic spatial fluctuations. Total wave radiances are defined as .
Mimicking BBR sampling, we spatially integrated and using the BBR PSF. Again, instrument performance affects this sampling, spatially separating same-wavelength samples by . After the integration of and , radiances were interpolated onto a 1-km grid that approximates EarthCARE’s Joint Standard Grid (JSG). The JSG is what most of EarthCARE’s products will be reported on (see Figs. 1d and 1e). Finally, JSG-level BBR radiances are averaged over different assessment domain sizes: a standard resolution of the BBR, that is, (10 km)2; and a size considered for the closure assessment, that is, closer to 5 km across track × 21 km along track (Illingworth et al. 2015; Barker et al. 2015).
3. Definitions and general considerations
Let and be assessment domain-average SW and TW radiances, respectively, as would be measured by the BBR. Their errors are
where and are true domain-averaged SW and TW radiances—arithmetic averages of all and across an assessment domain. Figure 2 provides a graphic example: the top panel presents the basis for , while the BBR perception is shown in the middle panel. Since LW radiances are not measured, domain-average LW BBR radiance is defined as
where the subscript T indicates LW and SW radiances that comprise the TW PSFs; is the difference in mean SW radiances as a result of sampling with the TW and SW bands. Note that in actual operations, the SW channel is slightly contaminated by thermal radiation. This is secondary to the issue at hand and has been neglected here [see Velázquez-Blázquez et al. (2017)]. Figure 2 indicates how and why, in general, . Presented this way it is easy to see that at the nominal rotation rate, are likely to be fairly small, since sampling along track is quite dense. If, however, becomes too large and sampling becomes too sparse, then can be sizable. Hence, the error for is
where represents true domain-averaged LW radiance—the average of all across an assessment domain. When the sun is down, then by definition and . In fact, since fluctuations of LW radiances are usually much smaller than that of SW radiances, even for moderately large values of , it can often be expected that
It can be assumed that and are of the same magnitude, meaning that Eq. (6) can be simplified to
if the errors are independent. When CDM rotation rates are large and are small, it is likely that and that , leading to a deviation from Eq. (7).
This means that uncertainties in estimated mean LW radiances are approximately, though slightly less than, double the magnitude of their SW counterparts, even when LW radiances exhibit no fluctuations at all! This might seem counterintuitive, but it is demonstrated in the next section.
Figure 3 shows 10 Landsat-8 high-resolution images used in this study. These images adequately represent a wide range of cloud types and radiance variability. The BBR sampling process, described above, was applied to these radiances assuming various CDM rotation speeds. Resulting BBR radiance estimates were compared against “true” mean radiances for designated assessment domain sizes.
Intuitively, radiance uncertainties resulting from incomplete sampling should increase as radiances become increasingly heterogeneous across assessment domains. Near-homogeneous fields, such as stratiform decks, where there is little to miss even when sampling is sparse, should present well, while fields of scattered cumulus could be sampled poorly (see Fig. 2). To explore this, N assessment domains measuring 5 × 21 km2 (i.e., one option in EarthCARE’s configurable assessment domain size) were sampled randomly from each tile. To isolate heterogeneity effects, assessment domains were grouped by one-percentile intervals of SW radiance variability , as defined by the standard deviation of SW radiances within an assessment domain. Finally, within each interval, TOA SW, TW, and LW sampling uncertainties, defined as the standard deviation of differences between the sampled mean and true mean radiances, were determined and compared to mission requirements. To address sampling uncertainty during the EarthCARE mission, SW variability was based on radiances resolved at 1 km2 (approximately the size of the EarthCARE’s JSG). Sampling uncertainties for SW and TW radiances are discussed first. This is followed by an assessment for the indirectly measured LW radiances.
a. Uncertainties for SW and TW mean radiances
Figure 4 shows how SW sampling uncertainty increases with reductions to CDM performance for four tiles of very different composition and magnitudes of sampling uncertainty. Tile 3, characterized by weak TOA SW radiance variability (21.8–54.7 W m−2 sr−1; see Table 1), and tile 7, characterized by smooth filaments of high-level clouds (8.3–37.5 W m sr), lead to small SW uncertainties (1.9 and 0.7 W m−2 sr−1, respectively, at the lowest performance), while tiles 4 and 8 have much larger SW uncertainties (2.8 and 3.2 W m−2 sr−1, respectively, at the lowest performance). Tiles with broken low-level cumuli exhibit bright and sharp features that result in large TOA of up to 70.8 W m−2 sr−1 (see Table 1). Hence, SW sampling at the largest would produce an of 3.2 W m−2 sr−1, which when multiplied by π slightly exceeds the mission requirement of 10 W m−2 (tile 8 in Fig. 4).
We believe that the heterogeneity of TOA SW radiances, , explains the varying levels of observed TOA SW nadir radiance sampling uncertainty . Figure 5 shows as a function of and for domains measuring 5 km across track and 21 km along track. SW uncertainty increases almost linearly with .
This linear relationship between and , shown in Fig. 5, grows not only progressively steeper, but also noisier because of progressively larger gaps between BBR along-track SW footprints as increases. To understand the effects of sparser along-track SW footprints, BBR sampling was done repeatedly on the central 50 km × 50 km portion of tile 5 to obtain several values of interpolated SW radiances and SW errors for each 1-km2 cell. The standard interpolation method was used: all overlapping SW footprints and their two-dimensional PSFs resolved at 30 m were considered, each PSF was weighted by the PSF energy overlapping with the cell, and all weighted PSFs were merged onto a horizontal field and normalized to integrate to 1. In addition to interpolating SW radiances, the amount of energy of the normalized PSF falling into each cell was determined. Cell coverage was defined as the integral of normalized PSF values within a cell’s perimeter. Hence, a coverage of “1” translates to BBR sampling only within the cell, while a value of “0” corresponds to no BBR footprint within the grid cell at all. Neither extreme was observed, as dense across-track samples always extended beyond cell perimeters (leading to a coverage <1), and—even at a ground sampling distance of 1.6 km—each cell was partly sampled by at least one SW exposure (a coverage > 0). Similar to , subgrid variability was extracted per grid cell based on 30-m resolved radiances. Figure 6 shows how 1-km2 sampling errors (y axis) grew with subgrid variability (x axis) and with lower coverage (darker colors). At the lowest , coverage varied between 0.6 and 0.7 and errors remained within ±15 W m−2 sr−1 (i.e., the 16th and 84th error percentiles at the highest subgrid variability), while the greatest led to a larger spread in coverage (between 0.1 and 0.7) and produced overall larger errors (±30 W m−2 sr−1). Assembled to domains measuring 21 × 5 km2, such sampling errors can partly compensate as one cell’s overestimation can outweigh a neighboring cell’s underestimation. However, especially at larger , neighboring cells presented a contrast in PSF coverage (not shown) preventing such error compensation: the high coverage (0.7) of one cell (producing a low sampling error) was accompanied by poor coverage (0.1) of along-track neighbors, thereby generating large sampling errors. To conclude, SW errors have shown to grow with more heterogeneous coverage through SW footprints—resulting from increased —and that can be attributed to steeper slopes of radiance uncertainties over domains of 21 × 5 km2 against radiance variability, as well as increased noise around slopes.
Summarizing the aforementioned observations, as BBR SW sampling becomes sparse, radiance uncertainties increase (up to 3.2 W m−2 sr−1), especially for very heterogeneous radiance fields. Thus, only extreme conditions (50% CDM performance and the largest radiance variabilities) led to critical levels of uncertainty that exceed mission requirements of 10 W m−2 when transformed into fluxes. The same goes for TW sampled radiances (not shown) with TW uncertainties reaching 4.1 W m−2 sr−1. As an alternative to a domain size of 5 × 21 km2, domains of 10 × 10 km2 were considered, too. Their SW and TW uncertainties (not shown) were up to 10% larger. For larger solar zenith angles, SW and TW uncertainties would be smaller and their flux equivalents would likely comply with mission requirements at CDM rotation rates between 50% and 100% of the nominal rate.
b. Uncertainties for LW mean radiances
In contrast to the previous subsection, LW radiances are not directly observed, but rather inferred from staggered measurements of TW and SW radiances. In effect, the methodology relies on a dense sampling through both modes. According to Eq. (7), LW uncertainties are expected to be twice as large as , especially, and counterintuitively, when LW radiance heterogeneity is much smaller than its SW counterpart. Figure 4 shows how TOA LW radiance uncertainties generally exceed and follow the rise of SW radiance uncertainties. As a result, sampling at 1.4 km over tiles 4 and 8 produces LW uncertainties that exceed mission requirements when transformed into LW fluxes.
At 1.2 km, LW uncertainty jumps, occasionally accompanied by an abrupt rise in SW uncertainty (e.g., tiles 3 and 4). Figure 7 confirms that the ratio of LW to SW uncertainty increases with , peaking at 1.2 km with ratios near 2. A doubling of SW uncertainties at 1.2 km—or a 33% performance reduction—would result in noncompliant LW uncertainties (see the central panel of Fig. 5), leaving any 1.2 km (i.e., 1.0 km in this study) a safe lower bound to BBR instrument performance. Neither levels of nor can explain error ratio fluctuations (see point size and colors in Fig. 7). Additionally, it was verified that 10 × 10 km2 assessment domains have almost identical relationships (not shown).
Following this, we investigated why the LW inference process (i.e., subtracting sampled SW from TW radiances to gain LW radiances) was sensitive to CDM performance and effectively the along-track distance between subsequent TW and SW footprints. We extracted additional information from the central portion of tile 5 (complementing extracted variables in section 4a) on a 1-km2 grid: we measured the size of SW–TW footprint overlaps, the coherence of SW and TW PSF weights, and the resulting error of BBR-inferred LW radiance. Overlap size is determined through the integral of SW plus TW PSF weights (resolved at 30 m, again each footprint weighted for interpolation, and across both SW and TW PSFs normalized to integrate to 1) of all relevant footprints (i.e., all SW and TW footprints that intersect the grid cell) integrated only within the overlap area (i.e., the area where both SW and TW weights are nonzero). A theoretical maximum of “2” would be reached if SW and TW were sampled simultaneously, while 0 indicated no overlap at all (impossible at ). Observed maximum values of about 1 (at a of 0.8 km) shows that SW and TW PSF effectively overlapped by about 50%. The coherence of SW–TW PSF weights was measured as the covariance of SW and TW PSF weights within the overlap area, denoted as “PSF covariance.” The lowest (negative) covariances were observed for of 1.2 km, and they indicated that locally high SW PSF weights coincided with low TW PSF weights, and vice versa. Figure 8 shows how 1-km2 SW errors (x axis with the same values as the y axis of Fig. 6) corresponded to LW errors (y axis) for different and effectively different levels of PSF overlap size (dot size) and PSF covariance (dot color). For a of 0.8 km, we found the largest overlap sizes (approximately 1) and covariances (about 3 × 10−8). The corresponding slope between LW and SW errors (shown as a magenta line and annotated in the plot) was −0.3. The steepest slopes (approximately −1.2) were found for of 1.2 km and higher. The overlap size was generally smaller (mean < 0.77) and covariances lower (mean < 0). LW errors with the smallest overlap sizes (about 0.2, shown as the smallest points) correspond to even steeper slopes. In conclusion, we showed that SW errors translated into larger LW errors (i.e., a larger LW/SW error ratio) when SW and TW footprints overlapped less and their PSF weights were less coherent—likely eliminating any error covariance between and , as discussed in section 3.
In summary, it has been confirmed that, according to Eq. (7), LW uncertainties are about twice as large as SW uncertainties (at 1.2 km, or a performance reduction ≥ 33%) because of the sensitive nature of LW inferences from staggered SW and TW sampling. To remain within mission requirements and to ensure that LW uncertainties when converted to LW fluxes fall below 10 W m−2, CDM performance should not be reduced beyond 25% (i.e., 1.0 km). Again, smaller LW uncertainties can be expected for smaller SW uncertainties—arising from, for example, large solar zenith angles.
5. Conclusions and discussion
The overall goal of the EarthCARE satellite mission is to retrieve cloud and aerosol properties well enough that when acted upon by radiative transfer models, estimated TOA fluxes for each 100-km2 domain will be within 10 W m−2 of fluxes inferred from BBR measurements (Poiares Baptista 2001; ESA 2006). Similarly, BBR radiances can be used directly in EarthCARE’s radiative closure assessment. For a closure either through fluxes or radiances, it is essential that BBR radiance uncertainties be accounted for. Considering in-orbit adjustable CDM rotation rates, which when reduced will extend instrument lifetime but also decrease along-track sampling rate, it is important to find a compromise between lifetime and required radiometric accuracy. This study analyzed sampling uncertainties arising from both reduced CDM performance and horizontal heterogeneity of radiance fields.
Using high-resolution Landsat-8 scenes, SW, TW, and LW sampling errors were quantified for assessment domains of 5 × 21 km2 and various CDM rotation rates. It was found that SW and TW sampling uncertainties are related approximately linearly to sample heterogeneity and increase with reduced instrument performance (at the lowest performance, SW and TW uncertainties reached 3.2 and 4.1 W m−2 sr−1 for scenes with the greatest radiance variabilities of 70.8 and 65.3 W m−2 sr−1, respectively). LW radiances are inferred from staggered SW and TW radiances, and their uncertainties scaled with SW uncertainties by a factor of 2 for ≥33% performance reductions, even though LW fields exhibited much less variability. It was shown that critical LW uncertainties (exceeding 10 W m−2) were achieved when performance was reduced by more than 25% from the nominal rate.
Previous radiance error assessments focused on radiance unfiltering (Velázquez-Blázquez and Clerbaux 2010). It has been shown here that uncertainties arising from the BBR’s sampling strategy represent a previously unrecognized source of uncertainty. Both unfiltering and sampling errors can reach similar magnitudes. Future research should examine whether these are independent sources of error.
As a final comment, it is interesting to note that had a lens filter been available that allowed LW, rather than SW, radiances to be measured directly, uncertainties for LW radiances would be much reduced with only minor increases in SW uncertainties relative to the BBR’s configuration. Recent payloads [e.g., the Radiation Budget Instrument (RBI) on the Joint Polar Satellite System-2 (JPSS-2)1; Mariani et al. 2016) offer such a filter. Alternatively, LW errors can be mitigated through simultaneous TW and SW measurements (e.g., CERES; Wielicki et al. 1996), thereby avoiding effects caused by staggered measurements of radiances.
This study was supported by a contract (4000112019/14/NL/CT) issued by the European Space Agency, under the EarthCARE component of its Living Planet Programme, to the Freie Universitä Berlin that was subsequently subcontracted to Environment and Climate Change Canada, the Royal Meteorological Institute of Belgium, and GMV. The authors wish to thank Tobias Wehr of ESA for the helpful discussions, and the anonymous reviewers for their constructive and helpful comments.
Earth Science Sensor set cancelled through NASA (www.nasa.gov/feature/nasa-cancels-earth-science-sensor-set-for-2021-launch).