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.
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