Radiative closure

Demonstration of radiative closure

To demonstrate the concept of radiative closure we consider daytime frames 01752D and 01752E on 18 September 2024, which cover a wide range of cloud and aerosol conditions between Sweden and the Gulf of Guinea as shown in the geostationary satellite composite from 14.00 UTC shown to the right.

The synergistic retrieval algorithm ACM-CAP combines information from the radar, lidar and imager (both solar and thermal-infrared channels) to retrieve the water content and effective radius of liquid and ice clouds, the aerosol extinction coefficient (using the aerosol types provided by the lidar target classification product A-TC) and the rain rate. The figure below shows the total water content (ice plus liquid) where we see cirrus cloud over Sweden centred on 60ºN, nimbostratus over Italy at 45ºN, mixed-phase cloud over Algeria at 30ºN, a large cumulonimbus over Benin at 11ºN and stratocumulus further south over the Gulf of Guinea.

The cloud and aerosol properties from ACM-CAP are passed to ACM-RT, which performs both 1D and 3D solar and thermal-infrared radiative transfer calculations. Calculations are also performed on an additional set of retrievals "ACM-COM" consisting of a composite of the single-instrument retrievals from the radar and lidar. Generally speaking we expect the synergistic retrievals in ACM-CAP to be more accurate, but it is useful to test this radiatively, providing a quantitative measure of the added value of treating the observations synergistically.

The 1D calculation uses a two-stream radiative transfer solver on each column of the ACM-CAP retrievals. The heating rates produced by this calculation are shown in the figure below, where we can see the strong solar heating at cloud top, as well as the weaker heating in clear-sky regions mainly by water vapour. In the thermal-infrared we see mainly cooling by radiative emission to space, except at cloud base that can be heated by absorbing radiation emitted at the surface. 

The 3D radiative transfer calculation is performed on "assessment domains" measuring 5 km across-track and 21 km along-track. Assessment domains are constructed by the ACMB-3D algorithm, which uses the MSI imagery to select columns from the radar-lidar curtain to fill out the 3D domain. A Monte Carlo algorithm is used for the radiative transfer. At the time of writing (February 2025), the 3D calculations are only performed on selected scenes by Environment and Climate Change Canada (ECCC). ESA is currently commissioning additional computational resource to enable these calculations to be carried out on all EarthCARE measurements.

In principle, the 3D calculations are more accurate than 1D and so are compared to BBR measurements. The BBR does not measure fluxes directly, but rather measures broadband radiances in three directions, "fore", "nadir" and "aft", as stored in the BM-RAD product. These are each converted to a top-of-atmosphere upwelling flux (or "irradiance") using an assumed angular distribution model (ADM) for the scene in question, and stored in the BMA-FLX product. The most reliable 1, 2 or 3 fluxes are then averaged into the "effective flux" stored in the same product. For the fairest comparison to the 3D radiative transfer calculations, the radiative transfer calculations are processed in exactly the same way as the observations: that is, the radiances in the three directions are converted to an effective flux using the same ADMs as used in processing the BBR observations. These are stored in the ACMB-DF product.

The figure below compares the measured and computed effective fluxes from this scene in both the solar and thermal-infrared parts of the spectrum. At the time of writing, there is some uncertainty in the BBR calibration: it has been found that the solar measurements are around 10% higher than the CERES flash-flux product, and around 8 W/m2 lower in the thermal-infrared. The grey shading in the figure span this range with the black lines showing the average of the values before and after scaling to match CERES. These will be updated when a final calibration is decided.

The agreement in the thermal-infrared is excellent, with the root-mean-squared difference between observations (without the offset to match CERES) and computations being only 8 W/m2. In the solar the agreement is good, but there is a tendency to underestimate the fluxes particularly in less reflective parts of the scene where the clouds are optically thin or absent. It is believed that this is largely due to an inconsistency in the treatment of surface albedo in the shorwave radiative calculations, but other sources of discrepancy are being investigated. 

It should be stressed that the intial radiative closure comparison did not look as good as this, leading to a number of improvements (and some bug fixes) being made to many of the algorithms. These included (1) fixing an incorrect calculation of radar path-integrated attenuation that led to incorrect retrieval of liquid water path in the Gulf of Guinea, (2) using a consistent ice optical model in the ACM-CAP solar-radiance forward model as used in the ACM-RT radiative transfer calculations, (3) improving the detection of liquid clouds near the ground in the lidar target classification A-TC, and (4) various improvements to the conversion of radinces to fluxes for both the measured and computed fluxes. This work is very much ongoing using a wider range of scenes.