The ACM-COM process begins by simply extracting, from X-MET files, information about atmospheric state, as needed by all BB RT models. This includes profiles of pressure, temperature, humidity, and ozone concentration. Regarding aerosols, their classification information is provided by the AC-TC (TC: target classification) processor (Irbah et al., 2023a) with extinction profiles at 0.355 µm obtained from the A-EBD (EBD: extinction backscatter depolarization) product (Donovan et al., 2023). Six types of aerosols are considered: dust, sea salt, continental pollution, smoke, dusty smoke, and dusty mix. Grid cells in AC-TC that are classed as cloudy, uncertain, missing, or noisy are considered to be aerosol-free.

Additionally, ACM-COM adds the following minor molecular species to X-MET profiles: CO2, CH4, N2O, CFC-11, CFC-12, CFC-22, and CCL4. These profiles come from climatologies generated by Jean-Jacques Morcrette and Alessio Bozzo (Robin Hogan personal communication, 2013). Values are functions of month, pressure, and latitude.

This subsection describes the algorithm that produces the alternative to ACM-CAP's synergistic L2b best estimates. It is based on compositing L2a cloud microphysical property retrievals from A-ICE (ICE: ice microphysical estimation) (Donovan et al., 2023a) and C-CLD (CLD: cloud) (Mroz et al., 2023) products.

The L2a composite's cloud properties depend on an indication of columnar cloudiness from the M-COP (COP: cloud optical properties) processor (Hünerbein et al., 2023). If a grid cell in a column has either A-ICE or C-CLD cloud water content greater than zero, the reported cloud properties enter directly into the L2a composite. If, however, both A-ICE and C-CLD report valid cloud properties with ice water content IWC >0, aggregated normalized uncertainties for IWC and crystal effective radius reff are computed, respectively, as 1σA-ICE=σIWCA-ICEIWCA-ICE2+σreffA-ICEreffA-ICE2andσC-CLD=σIWCC-CLDIWCC-CLD2+σreffC-CLDreffC-CLD2, where σIWCA-ICE, σIWCC-CLD, σreffA-ICE, and σreffC-CLD are processor-specific 1σ uncertainties. Ice cloud properties for the product with min⁡σA-ICE,σC-CLD enter into the L2a composite. For grid cells designated to contain only liquid clouds, C-CLD properties are used. Hence, L2a composites resemble NASA's CloudSat–CALIPSO–CERES (C3M) product (Kato et al., 2010), though it is simpler in that active-sensor-derived water content is not constrained, as it is in ACM-CAP, by MSI passive radiances.

Figure 3 shows an example of this compositing process for a column from a simulated frame (Qu et al., 2022). Only ice clouds were present, so both A-ICE and C-CLD reported hydrometeors. Above ∼ 3.4 km ATLID's estimates have the least uncertainty, meaning that A-ICE values enter into the composite. At ∼ 3.3 km the CPR value is least uncertain, and so C-CLD's estimate is used. As ATLID failed to return useable signals at lower altitudes, CPR values fill the remainder of ACM-COM's profile.

In this example, the “reference values”, as simulated by the Global Environmental Multiscale (GEM) model (Qu et al., 2022), generally match ACM-COM's better than ACM-CAP's. This, however, does not mean that ACM-COM profiles will be used by the RT models. First, during the mission reference values are, of course, unknown, so a plot like Fig. 3 cannot be made or used. Second, if and when ACM-CAP profiles exist, they are used by default.

Snow-free surface albedo over land for visible (0.3–0.7 µm) and infrared (0.7–5.0 µm) SW bands was calculated from climatological bidirectional-reflection distribution function parameters for 16 d periods based on 12 years (2002–2013) of MODIS MCD43GF data (Schaaf et al., 2002). Terrestrial snow albedo data for the same spectral bands are based on Moody et al. (2007), whose calculations were, in turn, based on 5 years (2000–2004) of climatological statistics of Northern Hemisphere white-sky albedos for 16 International Geosphere–Biosphere Programme (IGBP) ecosystem classes when accompanied by the presence of snow on the ground. For ice-covered land or water surfaces, BB-averaged albedos over 16 000–50 000 cm-1 are provided by X-MET (via ECMWF).

Ideally, the 3D RT models should include bidirectional-reflection and bidirectional-emission functions, such as the land surface model of Rahman et al. (1993), which is in EarthCARE's SW 3D RT code, but global parameters are lacking. Hence, spectral albedos, as just described, and the Lambertian assumption are used.

For open water surfaces, spectrally independent ocean albedo is approximated by 11αsfc=0.021+x2(0.0421+x(0.128+x(-0.04+x3.125.68+w+0.074x21+3w))), where x=1-cos⁡θi, θi is zenith angle of an incident photon, and w is surface wind speed (m s-1) (Hansen et al., 1983). The 3D SW model uses Eq. (11) for all photons arriving at a water surface. Additionally, it uses the ergodic wave model of Cox and Munk (1956) to describe the probability of a SW photon incident at the surface being reflected, with the probability defined by Eq. (11), toward a BBR telescope. As such, simulated radiances capture some semblance of sun glint, the effects of which are tempered by EarthCARE's orbit (Illingworth et al., 2015).

While the 1D SW model uses Eq. (11), with θ0 replacing θi, to describe direct-beam albedo, its diffuse-beam albedo is 12αsfc=0.03815+0.14865.68+w+0.00261+3w, which is just the integral of Eq. (11) assuming isotropic irradiance, regardless of sky condition. Last, hemispheric spectral emissivities for land and sea surfaces, for each RRTMG_LW band, are based on Huang et al. (2016). Like albedo, emissivity is assumed to be Lambertian.

The 1D RT models in RRTMG are meant to be applied to layered atmospheres with optical properties varying only in the vertical. As RRTMG was designed for use in large-scale models, it comes with algorithms that address unresolved horizontal fluctuations in cloud water content and cloud overlap. These algorithms are not needed for EarthCARE because RRTMG will be applied to individual JSG columns resolved at ∼1 km resolution with homogeneous layers.

The LW transport solver in RRTMG performs flux calculations for a single diffusivity angle with an adjustment for profiles that contain large H2O vapour content. It is an emissivity model that neglects scattering by all atmospheric constituents. Its SW solver employs the multi-layer delta-Eddington two-stream approximation (Wiscombe, 1977), which accounts for multiple scattering but, as with the LW solver, has well-documented conditional limitations for aerosol and cloud conditions (e.g., Li and Ramaswamy, 1996; Barker et al., 2015a). Nevertheless, due to RRTMG's widespread use at the time of writing, it is used for EarthCARE with a minimum of alterations so as to be consistent with other current applications.

There are three applications of the 1D SW and LW RT models to each valid JSG column along the retrieved cross-section. The first, denoted as “all-sky”, uses the full retrieved profiles. The second is “clear-sky”, where clouds are removed, leaving molecules and aerosols. The third application is “pristine-sky”, in which clouds and aerosols are removed, leaving just the molecular atmosphere.

Monte Carlo solutions of the 3D RT equation are used to calculate both SW and LW fluxes and radiances. This represents a break from, and advancement over, previous satellite missions that have been limited to the use of 1D RT solvers. The 3D RT models are discussed in the following subsections.

As discussed in Sect. 2, broadband flux and heating rate profiles for all admissible L2 columns are computed by RRTMG's SW and LW 1D RT models. The left column of Fig. 5 shows ∼ 2200 km of cloud and aerosol properties retrieved by ACM-CAP's synergistic algorithm (Mason et al., 2023). These results pertain to 21 km long non-overlapping assessment domains near the centre of the Halifax test frame. The middle column shows corresponding SW all-sky HRs and differences between all-sky HRs and clear-sky HRs (CRE: cloud radiative effect) as well as clear-sky HRs and pristine-sky HRs (ADE: aerosol direct effect). Aside from the usual 1D RT features, such as large SW heating near the cloud top and much smaller values below relative to clear sky, the only peculiarity is the fairly strong heating at ∼ 5 km altitude at the southern end. This is due to an elevated layer of water vapour. The vast majority of minor heating due to aerosol is from continental pollution that overrides sea salt.

The rightmost column in Fig. 5 is like the middle column, but it shows results for LW HRs. As expected, there is strong cooling in the upper 1–2 km or so of clouds, little net heating or cooling below, and general cooling from cloudless skies. LW CREs are generally stronger than in the SW and exhibit strong cooling near all cloud tops and warming in clouds when they are of sufficient vertical extent. LW ADEs are an order of magnitude smaller than their SW counterparts and manifest themselves as cooling just beneath their SW warming counterparts.

To demonstrate what will be available in the ACM-RT archive, Fig. 6 shows TOA CRE, ADE, and some integrated cloud and aerosol properties that correspond to Fig. 5. Some noteworthy points here are SW CRE reaching ∼ 300 W m-2 at μ0≈0.3 due to clouds near 41∘ N with large cloud water paths (CWPs), LW CRE reaching 100 W m-2 near 37∘ N due to supercooled liquid aloft, and weak ADE (∼ -10 W m-2 in the SW and less than 1 in the LW) stemming from aerosol optical depth at 0.355 µm being at most 0.2. Aside from this, there is very little to comment on in these plots; they serve to demonstrate what will be available in the ACM-RT archive.

As mentioned above, one of EarthCARE's notable advancements over prior alike missions is operational use of both 1D and 3D RT models. The decision to use 3D RT models was fuelled by myriad studies that show systematic differences between 1D and 3D treatments of RT, especially for cloudy atmospheres at solar wavelengths. Results shown in this subsection help justify the computational expense of using 3D RT models operationally.

Before getting to results that apply strictly to EarthCARE, consider a detailed view of the impact of neglecting multi-dimensional RT. Figure 7 shows nadir SW radiances simulated by a Monte Carlo RT model (Villefranque et al., 2019) for two stretches of the Hawaii test frame, each measuring 128 km along-track by 20.25 km across-track (Qu et al., 2022). The 3D RT simulation used horizontal grid spacing Δx=0.25 km, while its 1D rendition used Δx set arbitrarily large. Hence, differences in their radiances stem entirely from the dimensionality of the RT solution. For this demonstration, the number of photons per column was 4096, which is, on an areal density basis, several times larger than what will be used operationally for the EarthCARE mission.

These images display the varied and complicated ramifications for radiances when 1D RT modelling theory is assumed to apply. For sample 1, 1D radiances show much variability and sharp contrasts relative to their 3D counterparts; off-nadir views (not shown) look much the same. This region is blanketed by thick overcast ice clouds, which at Δx=0.25 km act to diffuse upwelling radiation, thus blurring localized reflection from low-level intermittent liquid clouds (e.g., Diner and Martonchik, 1984). When 1D RT is affected by setting Δx large, however, flow of radiation is confined to the vertical, and the sharp features of liquid clouds remain intact regardless of altitude.

On the other hand, sample 2 has mostly low- to mid-level liquid clouds and shows, due in part to large θ0, more familiar differences between 3D and 1D RT (e.g., Barker et al., 2017). In particular, 1D radiances lack texture, whilst their 3D counterparts exhibit much contrast due to shadowing and cloud-side illumination. Note, however, that imagery for thin liquid clouds at the northern edge of the sample depends little on Δx. This is because reflected photons undergo small numbers of scattering events and thus tend to exit clouds close to where they enter.

Consider now differences one can encounter in applications to EarthCARE retrievals. Figure 8 shows differences between 3D and 1D RT modelled SW broadband upwelling fluxes at 20 km and surface irradiances for 5×21 km assessment domains across the Hawaii frame using ACM-CAP cloud properties. Values for 3D and 1D RT are from the Monte Carlo model using Δx=1 km and arbitrarily large Δx, respectively. Each simulation used 2.5×106 photons, which is likely much larger than what will be used operationally throughout the mission. For almost cloud-free skies, thin ice clouds only with ice water path IWP <0.01 kg m-2, and very thick clouds with CWP >0.5 kg m-2, differences are well within ±10 W m-2 for fluxes at both levels. Clearly, under these conditions SW photon trajectories are characterized by either extremely small or large numbers of scattering events with cloud particles for both 1D and 3D RT. For the majority of other cloud conditions, however, especially with CWP in the vicinity of ∼ 0.1 kg m-2, differences can be much larger than ±30 W m-2, which far exceeds EarthCARE's goal (ESA, 2001; Illingworth et al., 2015; Eisinger et al., 2023), the implication being that many attempts to perform a radiative closure assessment on EarthCARE's retrievals will be doomed to failure if 1D RT models are adhered to.

Figure 9 shows cumulative frequency distributions of the differences shown in Fig. 8 for several ranges of total cloud fraction Ac. For upwelling fluxes at 20 km with Ac<0.25, median differences are all close to zero. The same goes for 3D–1D mean bias errors (MBEs), as listed in Table 2. Differences tend to be distributed more or less symmetrically about zero with occasional large differences, exceeding ±50 W m-2, enhancing root mean square errors (RMSEs) as Ac increases (see Table 2) relative to the 16th and 84th percentiles of the distributions, which can be gleaned from the graphs.

There are at least two interesting points to these plots that involve extreme cloud conditions. First, 3D–1D can be expected to be maximized for overcast domains, which implies that the geometry of overcast clouds is often anything but approximately plane-parallel and homogeneous (cf. Hogan et al., 2019). Second, for assessment domains (D's) with Ac=0, 3D–1D values for upwelling flux at 20 km show a tendency to be positive on account of contributions from clouds in the surrounding buffer zone (see Fig. 2).

Figure 10 shows that SW HR differences between 3D and 1D RT for the Hawaii frame's 5×21 km assessment domains are much less dramatic than those seen in Figs. 8 and 9 for boundary fluxes. At all altitudes and ranges of Ac, MBEs are essentially zero and close in magnitude to Monte Carlo uncertainties for 2.5×106 photons. There are several reasons why RMSE values are ∼10 times larger than Monte Carlo uncertainties and only increase slightly as Ac increases. There are the obvious differences due to cloud-side illumination, shadowing, and photon entrapment (Hogan et al., 2019), as well as impacts on flux profiles for 3D RT due to out-of-domain sources and sinks of photons, i.e., clouds outside D, but still in D+, that cast shadows or scatter radiation into D.

There is the possibility that radiative closure assessments of cloud and aerosol retrievals could (i.e., should) use broadband radiances rather than fluxes. There are reasons both for and against this. For instance, off-nadir BBR radiances offer powerful assessments due to their weak correlation, relative to nadir BBR radiances, with MSI radiances that are used for some retrievals. They can, however, arise from attenuators outside the domain being assessed (see Barker et al., 2015b). On the other hand, all of EarthCARE's performance goals are in terms of BBR fluxes, which will be estimated regularly by tailor-made algorithms (Velázquez-Blázquez et al., 2023a) despite adding at times substantial uncertainty at the last step of EarthCARE's processing chain.

Regardless, SW BBR radiances will be estimated throughout the mission. Figure 11 shows nadir values for the Hawaii frame's assessment domains using 2.5×106 photons per assessment domain and Δx=1 km. It also shows relative Monte Carlo uncertainties for NMie=4 and NMie→∞. As 2.5×106 photons per domain is likely to be more than routine operations can afford, uncertainties for NMie→∞ could be substantially larger than those shown here. This would render them useless for most assessments. While use of NMie=4 will help, as is evident for the thick clouds between 0 and 10∘ N and near 20∘ S, it will foster errors in radiances themselves. Two options are being considered: (i) using radiances instead of fluxes for assessments when their relative Monte Carlo uncertainties are less than some specified value (e.g., 0.01; see Fig. 11) and (ii) unbiased variance reduction methods (e.g., Iwabuchi, 2006).

As is well known, flux and radiance differences between 3D and 1D treatments of RT for LW radiation are usually much smaller than those for SW radiation (e.g., Ellingson and Takara, 2005; Cole et al., 2005; Hogan et al., 2016; Fauchez et al., 2017). Figure 12 shows the LW counterpart of the upper panel in Fig. 8. When differences go beyond ±10 W m-2, they do so along with corresponding large differences in SW fluxes, typically for overcast skies with CWP ∼ 0.1 kg m-2. As shown in Fig. 13, ∼ 5 % of overcast cases exhibit 3D fluxes that are less than their 1D counterparts by more than 10 W m-2. For these domains, CWPs are small relative to their neighbouring domains. This demonstrates a difficulty when interpreting “fluxes” for 5×21 km domains: at 20 km altitude, fluxes for 3D RT can be influenced substantially by adjacent cloudier domains. Table 3, however, shows that 3D and 1D fluxes usually differ by less than ±1 W m-2, which is on the order of the Monte Carlo uncertainty for these calculations, roughly 0.2 W m-2.