The MSI L1c products are calibrated and geolocated instrument data. The measurements for solar channels are given in radiance and the three terrestrial channels in brightness temperature. The L1c product is re-sampled onto the grid of a reference TIR channel . Therefore, each channel is mapped on the same pixel, which is important for the M-CLD processor, where we use the combination of all channels. The algorithm starts with the calculation of the reflectances at the top of the atmosphere in the solar channels. The reflectances R(θ0,θ,ϕ) of each channel i are obtained from the following input parameters: the measured radiance (L) and the corresponding inband solar irradiance E0,i as R(θ0,θ,ϕ) = πLi(θ0,θ,ϕ)E0,icos(θ0) and i= VIS, NIR, SWIR1, SWIR2. The measured radiance and brightness temperature for each pixel depends on the solar zenith angle θ0, the viewing zenith angle θ and the relative azimuth angle ϕ, defined by the difference between the sun and instrument viewing azimuth angles.

The retrieval requires further background information on atmospheric and surface conditions. The forward model includes a reflectance term which accounts for backscattered radiation from the underlying surface. For land pixels, we use the long-term albedo climatology from the MODIS science team . We assume that the white-sky albedo product is best suited for cloudy atmospheres since it refers to the reflection of incoming diffuse radiation. MODIS has very similar channel specifications so that these data can be used as they are. Over ocean, the surface albedo is assumed to be 0.05 at both 0.6 and 1.6 µm. For the forward model in the longwave channels, we use the land surface emissivity values provided by the MODIS land surface temperature and emissivity products, which provide per-grid temperature and emissivity values ().

The forward model is an operator that simulates the observed radiance at the sensor based on a known atmospheric state and given auxiliary input parameters. It is strictly channel based, such that the complete operator is composed of independent simulations of the channel i from a set of Fi(x)=y, where x is the state vector of the atmosphere (including the cloud properties) and y the vector of the observations (the measurements). The forward operator F includes the auxiliary data with their uncertainties. The individual components of the equation are separated into the solar spectrum with negligible terrestrial emission (up to 3.5 µ wavelength) and the part of the spectrum where thermal emission dominates the radiative transfer.

The retrieval loop (Fig. ) uses 1D-var optimal estimation inversion techniques to retrieve the cloud optical thickness, effective radius and cloud top heights during daytime, which is defined by the solar zenith angle (θ<84∘). At nighttime the retrieval relies on the infrared channels and only the cloud top height is retrieved.

The derived level 2 cloud properties from the OE retrieval schema are M-COT, M-REF and M-CTT. The M-CTT is further converted to M-CTH and M-CTP using the atmospheric profiles (X-MET) of pressure, temperature and height. These properties are accompanied by uncertainty measures derived from the OE algorithm. Figure  presents the full suite of M-COP products for one EarthCARE test scene, which refers to a realistic EarthCARE frame and MSI swath.

The relation between the cloud optical thickness and the cloud effective radius is used to calculate the cloud water path based on the assumption of a homogeneous cloud. The cloud water path is calculated only indirectly due to the fact that the measurements from the MSI have no water absorption channel. The cloud water path CWP is defined as the integral of the liquid and/or ice water content throughout the profile of an ice or water cloud layer. MSI measurements of solar reflectance in shortwave atmospheric window channels are used to retrieve the cloud phase (water or ice on the top of the cloud; ), cloud optical thickness (τ) and the effective radius (re). The cloud liquid/ice water path is calculated as a function of τ and re. The CWP is derived by using the following equation : CWP=23τreρw,i, where ρw is the density of liquid water 1 g cm-3 and ρi is the density of ice 0.916 g cm-3. The CWP error is estimated from the combination of the error of τ and rw,i as follows: ΔCWP=τΔre+reΔτ.

The M-COP algorithm performance has been tested by applying the M-CLD processor to different atmospheric test scenes created with the EarthCARE simulator. This is an end-to-end simulator for the EarthCARE mission capable to simulate the four instruments configurations for complex realistic scenes. Specific test scenes have been created from model output data (see ). The 6000 km long frames include different types of clouds and aerosols as well as surface and illumination conditions. These synthetic scenes make it possible to evaluate and intercompare the different cloud properties, such as, for example, cloud liquid water path or the cloud effective radius, from active and passive sensors . The synthetic test scenes set up have been considered as the truth (named as such) to better understand and quantify the differences between the retrieved cloud properties based on the different measurement principles. It should be noted that the simulated test scenes are intended to quantify the performance of the different processors, but not to tune the retrievals because the test scenes strongly depend on the assumption made in the EarthCARE simulator. In the following, we present results obtained with the M-CLD processor for the HALIFAX scene (). The scene starts with clouds over the Greenland ice sheet followed by high backscatter and extinction clouds down to 50∘ N. A high ice cloud regime starting over eastern Canada down to 35∘ N is followed by a low-level cumulus cloud regime embedded in a marine aerosol layer below an elevated dirty dust later around 5 km altitude. The results for the M-COP products for the HALIFAX scene are presented in Fig.  with the corresponding optimal estimation uncertainty. The M-COT uncertainty generally increases with increasing M-COT above 50, which is expected as the measurement at the non-absorption channel (VIS) gets saturated with increasing COT. The M-REF error shows clear separation between the detected cloud phase (Fig. ), where ice clouds are associated with higher errors. Note that above 50∘ N the solar zenith angle is higher than 84∘ due to nighttime conditions. Therefore, M-COT/M-REF cannot be retrieved, and only the M-CTH is retrieved for this region. Furthermore, the simple M-CTH nighttime retrieval provides no uncertainty values.

In this evaluation, the 3D dataset input for the test scene (called the truth) is used to define the presence of clouds and to calculate the modelled cloud optical thickness. This is calculated from the extinction profiles of all hydrometeors multiplied by the layer thickness (Fig. ) and compared with the retrieved M-COT. The true cloud optical thickness can also be retrieved in nighttime conditions. Furthermore, the truth includes values below 0.01, which are generally classified as clear sky by the M-CM cloud mask. This has been discussed in . Overall, the comparison with the true cloud optical thickness M-COT (Fig. ) shows a good and promising agreement (Fig. ).

Additionally to the synthetic test scenes, the M-COP cloud algorithm has been tested against realistic satellite observation from MODIS. For that purpose, MODIS Terra L1b calibrated reflectance has been used as input for the M-CLD processor. The MODIS channels 1, 2, 6, 7, 29, 31 and 32 are closed to the seven MSI channels and taken to replace the MSI signal. The meteorological auxiliary data required as input for the M-CLD processor are replaced by the Copernicus Atmosphere Monitoring Service forecast data field. The cloud mask and phase (M-CM) are produced within the M-CLD processor and the results are described in the companion paper by . The three MODIS channels 1, 6 and 31 are used for the M-COP retrieval. The LUTs are not specifically adapted to the MODIS filter function, which will cause some uncertainties. Figure  shows a case study over the Capo Verde islands in the Atlantic Ocean. The right column shows the M-CTT, M-COT and M-REF (at 1.6 µm) results as retrieved by the M-CLD processor. The corresponding MODIS L2 products (MOD06_L2 collection 6.1; ) are given in the left column. The CTT comparisons show an underestimation of the cloud top height for high cirrus clouds, especially multilayer clouds, which will be further investigated if an improvement is possible by using multilayer flags. The COT comparison of M-CLD and MODIS exhibits an almost perfect match, with a correlation factor of 0.95 and a bias of less than 1. The REF comparisons show more differences, such as for ice clouds the M-REF have smaller particle sizes but for water clouds the sizes are slightly higher. It should be noted that different ice particle scattering models are used, which account for some of the variance. Compared with MODIS, the MSI cloud product shows, in general, a good agreement. The robustness of these results could be demonstrated by using longer time periods and also other regions, which is, however, not shown in this study.

The M-CLD cloud products have also been validated within the framework of the CGMS International Cloud Working Group (ICWG; ). The ICWG is a working group aimed at harmonizing and advancing quantitative cloud property retrievals. In support of its mission, the ICWG has assessed a large number of level 2 passive imager cloud parameter retrievals through intercomparison activities. The ICWG cloud assessments have focused on quantifying deterministic differences between level 2 cloud parameters (and their error estimates) and the statistical validation against superior reference datasets. This assessment so far has been limited to geostationary satellites, i.e. MSG with the SEVIRI instrument. SEVIRI provides similar channel settings to MSI except for the 2.2 µm channel, which is missing. The cloud parameters that have been part of the assessment are cloud mask, cloud top temperature, cloud top pressure, cloud top height, cloud phase, cloud optical thickness, effective particle size, cloud liquid water path, and cloud ice water path. As reference datasets, the main sources of information have been the cloud properties obtained from CLOUDSAT and/or CALIPSO observations and cloud liquid water path observations from passive microwave instruments (e.g. AMSR (advanced microwave scanning radiometer)). For a number of “golden days” different scientific institutions have contributed their cloud datasets for intercomparison, e.g. the EUMETSAT central facility, the Nowcasting SAF and the Climate Monitoring SAF, among others. The cloud properties retrieved from all MSG SEVIRI scans collected during 13 June 2008, 19 August 2015 and 21 July 2016 had to be submitted and served as the basis for the intercomparison . It should be noted that the MSI M-CLD algorithm is developed for a polar-orbiting satellite and is adapted to the MSI specification, which leads to uncertainties in the adaptation to SEVIRI due to differences in central wavelength and spectral response function, radiative transfer simulations and generated look-up tables. The M-CLD processor has been directly applied to the SEVIRI observation.

Figure  shows the cloud top pressure obtained by 13 different retrievals for the noon scene of 13 June 2008 and the combined cloud top pressure separated into low, middle and high. The cloud top pressure is separated into three classes for the comparison: low (red), middle (green) and high (blue) based on the ISCCP classification. The zonal distribution of the cloud top pressure is comparable for all datasets. High clouds are present in the intertropical convergence zone. The combined cloud top pressure illustrates the disagreement for the anvil of the convective clouds within the intertropical convergence zone. Adjacent to them, low clouds are most common in the marine stratocumulus region between 30∘ S and 30∘ N and agree well between the algorithms. Note that the cloud masks differ between the algorithms, which also influences the mean cloud top pressure obtained by the algorithm. Some algorithms also limit the domain for retrieval due to large viewing or solar zenith angles and/or sun glint.

Figure  shows the histograms of the cloud top temperature from all the applied retrievals. A common cloud mask is used to calculate the individual CTT histograms. Different cloud occurrence frequencies are observed for the boundary layer clouds. Most histograms show a distribution with two cloud occurrence maxima, one around 230 K and a second one below 280 K. The weakness of M-CTT is the detection of multilayer clouds with high cirrus clouds in the upper troposphere. For example, the anvil of the deep convective storm systems classified as having medium instead of high cloud top height (see Fig. ). This finding is also reflected in the histogram (Fig. , yellow curve) where the second maximum at 230 K is not present. It should be noted that the other algorithms take advantage of the SEVIRI CO2 band, which MSI does not have.

Additionally, the A-Train constellation of earth-observing satellites of the comparison, the CloudSat and MODIS measurement (MYD06_L2; ), are re-gridded onto the SEVIRI grid. Five regions from the SEVIRI disc have been selected to study in more detail specific meteorological conditions. One example is a deep convection cell over West Africa presented in Fig. . On top, the CloudSat measurements on the A-Train track are compared with the M-CTH (Fig. , white crosses) and generally show a good agreement for most of the collocated observations. The M-CLD COT and REF values (red: ice phase; green: water phase) have been also compared to the L2 products from MODIS (Fig. , blue). The COT values between MODIS and MSI are in good agreement, while there is a slight overestimation of M-REF compared with MODIS for water clouds and underestimation for ice clouds. However, one should note that this is only a qualitative comparison for one case study, and a comprehensive assessment of the quality of the M-CLD products will be performed once real MSI observations are available.