Estimating the impact of radiation transport through cloud sides on the global energy budget is hampered by the lack of a fast radiation scheme suitable for use in global atmospheric models that can represent these effects in both the shortwave and longwave. This two‐part paper describes the development of such a scheme, which we refer to as the Speedy Algorithm for Radiative Transfer through Cloud Sides (SPARTACUS). The principle of the method is to add extra terms to the two‐stream equations to represent lateral transport between clear and cloudy regions, which vary in proportion to the length of cloud edge as a function of height. The present paper describes a robust and accurate method for solving the coupled system of equations in both the shortwave and longwave in terms of matrix exponentials. This solver has been coupled to a correlated‐k model for gas absorption. We then confirm the accuracy of SPARTACUS by performing broadband comparisons with fully 3‐D radiation calculations by the Monte Carlo model “MYSTIC” for a cumulus cloud field, examining particularly the percentage change in cloud radiative effect (CRE) when 3‐D effects are introduced. In the shortwave, SPARTACUS correctly captures this change to CRE, which varies with solar zenith angle between −25% and +120%. In the longwave, SPARTACUS captures well the increase in radiative cooling of the cloud, although it is only able to correctly simulate the 30% increase in surface CRE (around 4 W m−2) if an approximate correction is made for cloud clustering.

Several mechanisms have previously been proposed to explain differences between the shortwave reflectance of realistic cloud scenes computed using the 1D independent column approximation (ICA) and 3D solutions of the radiative transfer equation. When the sun is low in the sky, interception of sunlight by cloud sides tends to increase reflectance relative to ICA estimates that neglect this effect. When the sun is high, 3D radiative transfer tends to make clouds less reflective, which we argue is explained by the mechanism of “entrapment” whereby horizontal transport of radiation beneath a cloud layer increases the chances, relative to the ICA, of light being absorbed by cloud or the surface. It is especially important for multilayered cloud scenes. We describe modifications to the previously described Speedy Algorithm for Radiative Transfer through Cloud Sides (SPARTACUS) to represent different entrapment assumptions, and test their impact on 65 contrasting scenes from a cloud-resolving model. When entrapment is represented explicitly via a calculation of the mean horizontal distance traveled by reflected light, SPARTACUS predicts a mean “3D radiative effect” (the difference in top-of-atmosphere irradiances between 3D and ICA calculations) of 8.1 W m−2 for overhead sun. This is within 2% of broadband Monte Carlo calculations on the same scenes. The importance of entrapment is highlighted by the finding that the extreme assumptions in SPARTACUS of “zero entrapment” and “maximum entrapment” lead to corresponding mean 3D radiative effects of 1.7 and 19.6 W m−2, respectively.

Cold-pool-driven convective initiation is investigated in high-resolution, convection-permitting simulations with a focus on the diurnal cycle and organization of convection and the sensitivity to grid size. Simulations of four different days over Germany were performed using the ICON-LEM model with grid sizes from 156 to 625 m. In these simulations, we identify cold pools, cold-pool boundaries and initiated convection. Convection is triggered much more efficiently in the vicinity of cold pools than in other regions and can provide as much as 50% of total convective initiation, in particular in the late afternoon. By comparing different model resolutions, we find that cold pools are more frequent, smaller and less intense in lower-resolution simulations. Furthermore, their gust fronts are weaker and less likely to trigger new convection. To identify how model resolution affects this triggering probability, we use a linear causal graph analysis.In doing so, we postulate a graph structure with potential causal pathways and then apply multi-linear regression accordingly. We find a dominant, systematic effect: reducing grid sizes directly reduces upward mass flux at the gust front, which causes weaker triggering probabilities. These findings are expected to be even more relevant for km-scale, numerical weather prediction models. We thus expect that a better representation of cold-pool-driven convective initiation will improve forecasts of convective precipitation. K E Y W O R D S causal effect estimation, numerical weather prediction, convection organization INTRODUCTIONConvection-permitting models have become increasingly prominent for numerical weather prediction in recent years (Baldauf et al., 2011;Clark et al., 2016). Such models have a grid size of several hectometres to a few kilometres which is sufficient to run without the use of a convection parametrization. Due to the many underlying approximations and systematic biases of convection schemes (e.g., Gentine et al., 2018), being able to simulateThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Current weather and climate models neglect 3‐D radiative transfer through cloud sides, which can change the cloud radiative effect (CRE) significantly. This two‐part paper describes the development of the SPeedy Algorithm for Radiative TrAnsfer through CloUd Sides (SPARTACUS) to capture these effects efficiently in a two‐stream radiation scheme for use in global models. The present paper concerns the longwave spectral region, where not much work has been done previously, although the limited previous work has suggested that radiative transfer through cloud sides increases the longwave surface CRE of shallow cumulus by around 30%. To assist the development of a longwave capability for SPARTACUS, we use a reference case of an isolated, isothermal, optically thick, cubic cloud in vacuum, for which 3‐D effects increase CRE by exactly 200%. It is shown that for any cloud shape, the 3‐D effect can be represented in SPARTACUS provided that correct account is made for (1) the effective zenith angle of diffuse radiation emitted from a cloud, (2) the spatial distribution of fluxes in the cloud, (3) cloud clustering that enhances the interception of emitted radiation by neighboring clouds, and (4) radiative smoothing leading to the effective cloud edge length being less than the measured value. We find empirically that the circumference of an ellipse fitted to a horizontal cross section through a cumulus cloud provides a good estimate of the radiatively effective cloud edge length, which provides some guidance to how cloud observations could be analyzed to extract their most important properties for radiation.

Midlatitude cyclones are strongly affected by diabatic processes. While the importance of latent heating is well established, the role of radiation has received little attention. Here we address this question for idealized cyclones by performing baroclinic life cycle simulations in the global atmosphere model ICON with and without radiation, and with transparent clouds. Radiation substantially weakens the simulated cyclone: peak eddy kinetic energy reduces by 50%, and minimum storm central pressure increases by 17 hPa. An analysis of the Lorenz energy cycle shows that the radiative weakening is not due to changes in the large‐scale environment alone but involves radiative processes within the cyclone. In fact, radiation warms the lower tropospheric part of the cyclone's warm conveyor belt and cools the upper tropospheric part. We hypothesize that radiation weakens the cyclone by destroying midtropospheric potential vorticity in the warm conveyor belt.

To represent the effects of unresolved cloud processes in numerical weather prediction and climate models, parametrizations of the subgrid properties of clouds are required. In this paper, we describe a method for specifying the “cloud‐edge length” within a model grid‐box, which is an important parameter for approximating the subgrid mixing of air at cloud boundaries. We begin by proposing three conceptual models that predict the cloud‐edge length using the grid‐box cloud fraction and a length‐scale to be derived empirically. The conceptual models are then evaluated using a wide range of observations and cloud‐resolving models. Based on the finding that the “effective cloud spacing” approach fits both these data best, we parametrize the effective cloud spacing as a function of pressure and model resolution. An application of this parametrization to the cloud erosion scheme in the ECMWF forecast model is then demonstrated. The effective cloud spacing approach is compared to the “effective cloud scale” approach and is shown to increase cloud fraction in stratocumulus regions, while decreasing cloud fraction in cumulus regions. These cloud changes have the overall effect of decreasing the error of the modelled top‐of‐atmosphere net short‐wave irradiance when compared to CERES observations by around 3%. Additionally, the cloud‐edge length is an important parameter for approximating subgrid radiative transfer and it is hoped that this parametrization will be useful to quantify the effect of representing 3D cloud radiative transfer in global models.

The single-column mode (SCM) of the ICON (ICOsahedral Nonhydrostatic) modeling framework is presented. The primary purpose of the ICON SCM is to use it as a tool for research, model evaluation and development. Thanks to the simplified geometry of the ICON SCM, various aspects of the ICON model, in particular the model physics, can be studied in a well-controlled environment. Additionally, the ICON SCM has a reduced computational cost and a low data storage demand. The ICON SCM can be utilized for idealized cases—several well-established cases are already included—or for semi-realistic cases based on analyses or model forecasts. As the case setup is defined by a single NetCDF file, new cases can be prepared easily by the modification of this file. We demonstrate the usage of the ICON SCM for different idealized cases such as shallow convection, stratocumulus clouds, and radiative transfer. Additionally, the ICON SCM is tested for a semi-realistic case together with an equivalent three-dimensional setup and the large eddy simulation mode of ICON. Such consistent comparisons across the hierarchy of ICON configurations are very helpful for model development. The ICON SCM will be implemented into the operational ICON model and will serve as an additional tool for advancing the development of the ICON model.

<p>Radiation in the atmosphere provides the energy that drives atmospheric dynamics and physics on all scales, from cloud particle growth to global weather and climate. Radiation schemes in global weather and climate models make assumptions to simplify the complex interaction of radiation with the Earth system. Capturing cloud-radiation interactions is particularly challenging since clouds vary strongly on small spatial and temporal scales not resolved in the models, and interact strongly with radiation. Uncertainties in these assumptions in the radiation scheme and the cloud, aerosol, gas and surface inputs lead to uncertainties in multiple weather and climate processes, such as energy balance, cloud development and dynamics.</p><p> </p><p>The modular radiation scheme ecRad (Hogan and Bozzo, 2018, Rieger et al. 2019) is operational in ICON at DWD since April 2021 and provides the opportunity to vary parametrisations and assumptions individually to determine their impact. Several options are available for the radiation solver, cloud vertical overlap and horizontal inhomogeneity treatment and cloud hydrometeor optical property parametrisations. The solver SPARTACUS is the only radiation solver in a global model that can treat 3D radiative effects.</p><p> </p><p>Using global satellite and surface data and high-resolution surface radiation measurements gathered during the FESSTVaL campaign (https://fesstval.de), we evaluate the radiation and cloud parametrisations on local to global scales and investigate the sensitivity of radiation results to model assumptions and cloud properties and the role of cloud-radiation interactions. In ICON, ecRad improves the global radiation balance, model physics and forecast performance as evaluated against observations.</p><p>References: </p><p>Hogan, R. J., & Bozzo, A. (2018), A flexible and efficient radiation scheme for the ECMWF model. <em>Journal of Advances in Modeling Earth Systems</em>, 10, 1990-2008. https://doi.org/10.1029/2018MS001364</p><p>Rieger, Daniel, Martin Köhler, Robin J. Hogan, Sophia A. K. Schäfer, Axel Seifert, Alberto de Lozar and Günther Zängl (2019). ecRad in ICON - Implementation Overview, <em>Reports on ICON</em></p>