The EarthCARE (Earth Cloud, Aerosol and Radiation Explorer) mission is a collaborative mission between the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA). EarthCARE's primary objective is to enhance our understanding of the processes affecting clouds, aerosols, and radiation in Earth's atmosphere. The mission aims to provide valuable information for improving climate model parameterizations and the understanding of how these components influence the global climate. EarthCARE integrates a suite of instruments including a lidar, radar, and radiometric instruments. Among these instruments, the Broadband Radiometer (BBR) plays the role of providing crucial information for the radiative closure of the mission. This process involves verifying that the radiative transfer simulations, which are fed with atmospheric products from the mission's active sensors, report radiative fluxes within 10 W m-2 of the fluxes derived from the BBR.

The BBR will measure accurate shortwave (SW) (0.25 to 4 µm) and total-wave (TW) radiances (0.25 to >50 µm) at three fixed viewing angles (fore, nadir, and aft) along the EarthCARE track. The very fine spatial resolution of the detector array, 648 m along and across-track in nadir, allows the three views to be integrated over different spatial domains. The radiances measured by the BBR channels are filtered by the spectral response of the instrument, which combines the detector response and the telescope and SW filter throughput. Being directly dependent on the instrument's design, these filtered radiances are of little interest for the science community. They must be converted into (unfiltered) solar and thermal radiances, which are the radiances that would be measured by a perfect instrument, with a flat spectral response, i.e., ϕ(λ)=1 (where λ is the wavelength), that would allow the reflected solar radiation to be accurately separated from the Earth's emitted thermal radiation. In the EarthCARE ground processing, this unfiltering process is performed by the BM-RAD processor. In a later stage, the (unfiltered) radiances are converted into hemispheric fluxes, in a second BBR processor called BMA-FLX .

The BBR instrument (described in ) is composed of three telescopes: a fore view at ±55° forward, a nadir view at ±0°, and an aft view at ±55° backward. Any scene located under the satellite track is therefore observed from three directions almost at the same time (about 3 min between the fore and aft views). Each telescope uses an array of 30 microbolometer detectors, allowing an across-track swath of ∼ 17 km for the nadir view and ∼ 28 km for the two oblique views. The detectors' measurements will be averaged over different spatial domains, namely, standard, small, and full, which are defined by the L1 B-NOM product in the BBR grid with an along-track sampling of 1 km. In addition, an additional configurable domain, the assessment domain (AD), is defined on the Joint Standard Grid (JSG) for the radiative closure assessment of the EarthCARE mission . The main inputs to the BM-RAD processor are the level-1 B-NOM product that gives the filtered shortwave (SW) and longwave (LW) radiances over the standard, small, and full domains, the level-1 B-SNG product that gives the filtered SW/TW radiances at detector level, the MSI cloud mask and cloud phase product from M-CLD , the Joint Standard Grid (X-JSG) and ancillary meteorological data (X-MET) .

The paper is structured as follows. Section  presents the spectral response curves of the BBR instrument and introduces the unfiltering problem. Section  provides an overview of two large databases of radiative transfer computations that are used to design and parameterize the unfiltering algorithm. Section  describes the unfiltering algorithm implemented in the BM-RAD processor. The performances of the algorithm are discussed in Sect. . An end-to-end verification of the algorithm and its implementation in BM-RAD is then presented in Sect.  in which the processor is run on three test scenes of 6200 km each. A final discussion is provided in Sect. .

It is not possible to manufacture a broadband radiometer that has perfectly equal sensitivity to the radiation at all wavelengths. The thermal detector elements show some spectral structure in their response; the throughput of the optics of the instrument also results in spectral variations . The signal provided by the instrument, Lfil, is a radiance filtered by the spectral response ϕ(λ) of the instrument: 1Lfil=∫0∞L(λ)ϕ(λ)dλ, where L(λ) is the input spectral radiance. For the BBR, the spectral responses of the total and shortwave channels are 2ϕTW(λ)=ϕdet(λ)ϕtele(λ),3ϕSW(λ)=ϕdet(λ)ϕtele(λ)ϕquartz(λ), in which ϕdet(λ) is the spectral response of the detectors, ϕtele(λ) is the spectral reflectance of the telescope mirror, and ϕquartz(λ) is the transmittance of the quartz filter used for the SW channel.

Contrary to the SW channel, it is difficult to manufacture an efficient and stable filter to isolate the LW radiation. For this reason, the longwave radiance is obtained by subtracting the SW part in the TW measurement as for the CERES and the GERB instruments. The “synthetic” LW radiance LLW and spectral response ϕLW(λ) are therefore defined as 4LLW=LTW-ALSW,5ϕLW(λ)=ϕTW(λ)-AϕSW(λ), in which the A factor is defined in such a way that the longwave radiance LLW is equal to exactly zero when an idealized black body solar spectrum of 5800 K is observed: 6A=∫0∞L5800K(λ)ϕTW(λ)dλ∫0∞L5800K(λ)ϕSW(λ)dλ, where L5800K is the Planck's emission for a temperature of T=5800 K. As shown in Eq. (), the factor A is not dependent on the observed scene L(λ) but only on the instrument's spectral responses ϕTW(λ) and ϕSW(λ). Figure  shows the SW, TW, and synthetic LW spectral responses of the BBR instrument for the nadir view of the BBR. The curves for the fore and aft telescopes present only marginal difference with the nadir telescope (not shown).

The filtered radiances (LSW, LLW) are dependent on the instrument characteristics such as the number of mirrors in the optics and type of coating of these mirrors, the type of detector and coating, and the thickness of the quartz filter, etc. For this reason, the filtered measurements have limited scientific interest, and they must be converted into unfiltered quantities: 7Lsol=∫0∞Lsol(λ)dλ,8Lth=∫0∞Lth(λ)dλ, where the distinction is not performed in terms of wavelength λ but in terms of type of radiation: Lsol(λ) corresponding to reflection of incoming solar radiation and Lth(λ) to thermal emission in the Earth–atmosphere system. This conversion, called unfiltering, requires an accurate characterization of the instrument spectral response, ϕ(λ) and some assumptions about the spectral signature L(λ) of the observed scene. Furthermore, it is necessary to estimate the contaminations of the SW channel with thermal radiation and of the LW channel with solar radiation. The ratio between the unfiltered and filtered radiances is called either the unfiltering factor or the spectral correction factor, and these are expressed as 9αSW=LsolLSW,sol=∫0∞Lsol(λ)dλ∫0∞Lsol(λ)ϕSW(λ)dλ,10αLW=LthLLW,th=∫0∞Lth(λ)dλ∫0∞Lth(λ)ϕLW(λ)dλ, where SW and LW indicate the BBR spectral channel, and sol and th make reference to the kind of radiation, either solar reflected or thermal emitted. Therefore, “SW,sol” refers to the SW-filtered radiances due to solar radiation, while “LW,th” refers to the LW-filtered radiances due to thermal radiation.

In this work, the unfiltering factors are estimated, offline, from radiative transfer simulations for different scene types on which regressions are derived. These regressions are then used in the BM-RAD processor to infer the unfiltered radiances (Lsol,Lth) from the filtered measurements (LSW, LLW), where the contamination of both the SW channel by thermal radiation and the LW channel by reflected solar radiation needs to be estimated prior to the actual unfiltering process. The mathematical forms of these contaminations are 11LSW,th=∫0∞ϕSW(λ)Lth(λ)dλ,12LLW,sol=∫0∞ϕLW(λ)Lsol(λ)dλ.

The thermal contamination in the SW channel, LSW,th, accounts for the planetary thermal emission in the SW channel, below 5 µm and also beyond 50 µm due to the leak in the quartz filters in the far infrared region. The solar contamination in the LW channel, LLW,sol, is generally negative as the synthetic LW spectral response is, very slightly, negative in shorter wavelengths (below 4 µm). These small quantities should be subtracted from the measured shortwave LSW and longwave LLW radiances before the unfiltering process itself can be realized: 13Lsol=αSWLSW,sol=αSW(LSW-LSW,th),14Lth=αLWLLW,th=αLW(LLW-LLW,sol).

So, the unfiltering process necessitates the estimation of four quantities: the two unfiltering factors (αSW, αLW) and the two contaminations (LSW,th, LLW,sol).

The unfiltering factors and the contaminations are obtained theoretically from two large geophysical databases: one of reflected solar radiances containing 5544 simulations Lsol(λ), i.e. 616 unique scenes simulated at nine solar zenith angles (SZAs), and one of Earth's emitted thermal radiances containing 12 096 simulations Lth(λ). The solar simulations Lsol(λ) are performed for nine SZAs, from 0 to 80° in steps of 10°, and the simulated radiance field is extracted at 18 viewing zenith angles (VZAs), 0 to 85° every 5°, and 19 relative azimuth angles (RAAs), 0 to 180° every 10°. These databases are computed using the libRadtran 1.4 radiative transfer model as described in . The simulations cover a wide range of geophysical conditions, and for this purpose, the scene definition has been done using ancillary models and data, such as surface reflectances from the Aster Spectral Library data and the Optical Properties of Aerosols and Clouds (OPAC) software for the computation of the aerosol optical properties. The aerosols are assumed to be well mixed and defined as being in the mixing layer, between 0 and 6 km for desert aerosols and between 0 and 2 km for continental and maritime aerosols. Given that the Aster Spectral Library contains a large number of spectra, a k-means clustering of 12 clusters has been done for clear-sky scenes. An averaging of the spectra has been done for those scenes with presence of aerosols. The simulations completely cover the illumination and observation geometries of EarthCARE. Various types of clouds have been simulated with optical thickness from 0.3 to 300 and altitudes ranging from 1 to 12 km. The standard profiles used for the simulations are tropical, midlatitude summer, midlatitude winter, subarctic summer, and subarctic winter (Anderson et al., 1986). Scaling (factor between 0.6 and 1.4) of the water vapour profile in the LW simulations is done to take into account the variability of the water vapour.

Solar simulations have been done in the interval of 0.25 to 5 µm, for 833 wavelengths, with the following spectral resolution: from 0.25 to 1.36 µm in steps of 0.002 µm, from 1.36 to 2.5 µm in steps of 0.005 µm, and from 2.5 to 5 µm in steps of 0.05 µm. Thermal simulations have been done in the interval of 2.5 to 100 µm, for 762 wavelengths, with the following spectral resolution: from 2.5 to 14 µm in steps of 0.05 µm, from 14.1 to 50 µm in steps of 0.1 µm, and from 55 to 100 µm in steps of 0.5 µm. The limit at 100 µm for the simulations is due to the fact that ice and water cloud properties are defined up to this wavelength for both the Yang (ice crystals) and Mie (water droplets) parameterizations. As there is still significant radiation beyond 100 µm, the longwave simulations Lth(λ) have been extrapolated up to λ=500 µm using the black body emission curve corresponding to the brightness temperature simulated at λ=100 µm as in .

The simulated radiances L(λ) are convoluted with the SW, TW, and LW spectral responses ϕ(λ) of the BBR for each of the views (fore, nadir, aft) to obtain the filtered radiances for each geometry. The unfiltered radiances are obtained with a perfect constant “filter” ϕ(λ)=1.

An analysis of the unfiltering error is performed for 10 typical scene types covering the full extent in terms of SW and LW radiances. The error combines the one due to the estimation of the contamination and the error due to the estimation of the unfiltering factor. The results are summarized in Table  and provide values averaged over the full range of simulated SZA, VZA, and RAA geometries. For the solar radiation, the relative error on the unfiltered radiances is ≈0.26% for cloudy conditions and increases up to 0.34 % for clear-sky conditions. For the thermal radiation, the relative error is 0.10 ± 0.02 % for all of scene conditions.

In this section, data from the three EarthCARE test frames have been used to verify the performances of the BM-RAD processor. In general a close agreement is found between the unfiltered radiances calculated by the BM-RAD processor and the reference radiances (truth) obtained directly by broadband integration of the radiative transfer computations on the Global Environmental Multiscale Model (GEM) scenes. Table  details the results in terms of bias, rms, and standard deviation, all expressed in Wm-2sr-1; these are for the three telescopes (fore, nadir, aft) and for the three test frames (Halifax, Baja, Hawaii).

Table  summarizes the performances of the stand-alone SW unfiltering, MSI-based SW unfiltering, and stand-alone LW unfiltering procedures for the three test scenes. The error metrics show that the MSI-based shortwave unfiltering provides a small improvement in general. The gaining of including MSI information in the unfiltering process while improving results might not be very large in practice because of parallax effects. Another interesting finding is that the unfiltering of the nadir view is, in general, more accurate than the one of the fore and aft views (with, however, an exception for the stand-alone shortwave unfiltering for the Hawaii scene).

The upper panels of Fig.  show the filtered, unfiltered, and simulated (truth) radiances along the orbit frame for the three test scenes. Differences between filtered and unfiltered radiances can be clearly seen. As expected, the greatest differences are observed over cloudy scenes in the SW regime, while clear-sky scenes present the higher differences in the thermal radiances. Lower panels show the detail of the differences between the unfiltered radiances and the truth radiance. The corresponding mean difference (bias), standard deviation, and RMSE are provided to quantitatively analyse the comparison. The complete summary of results is available in Table . The RMSEs for both SW and LW unfiltered radiances are well within the accuracy requirement for the BBR that is 2.5 Wm-2sr-1 for the SW and 1.5 Wm-2sr-1 for the LW. It is worth mentioning that these metrics are likely an overestimation of the errors because of the simplifications needed in the radiative transfer computations used for the construction of the test scenes.

In this paper, the algorithms used by the unfiltering processor (BM-RAD) for the BBR instrument on board EarthCARE are described. The main output of BM-RAD is the unfiltered solar and thermal radiances for the three BBR views integrated over different spatial domains. These radiances are the main input for the BMA-FLX processor in which the three views are combined to estimate the hemispheric outgoing shortwave and longwave radiative fluxes.

Thanks to its design, the BBR instrument sensitivity shows limited spectral variability, which is a prerequisite for an accurate unfiltering process. The typical stand-alone unfiltering errors are expected to be approximately 0.5 % for the shortwave channel and well below 0.1 % for the longwave channel. The implementation of the algorithm has been successfully verified on the three EarthCARE test scenes (Halifax, Baja, and Hawaii).

Scene information from the MSI radiances (from M-RGR product), MSI cloud retrievals (from M-CLD processor), or snow products (from X-MET product) is useful to further reduce the unfiltering error. So, in addition to the stand-alone unfiltered radiances, the BM-RAD product also contains the MSI-based unfiltered radiance for the shortwave radiation (the improvement for the longwave radiance was considered negligible and therefore not included in the product). However, the MSI-based unfiltering of the fore and aft views might suffer from the parallax effect as the MSI only provides nadir observations. Therefore, a comprehensive evaluation of the MSI-based unfiltering is foreseen to be carried out during the commissioning phase, when the BM-RAD processor can be applied on real BBR and MSI observations. In the meantime, the stand-alone unfiltered radiances should be used.