Mechanical and Thermal Forcing for Upslope Flows and Cumulus Convection over the Sierras de Córdoba
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High resolution extended-range cloud condensation nuclei (CCN) spectral comparisons with cloud microphysics and drizzle of the Physics of Stratocumulus Tops (POST) field experiment confirmed results in the Marine Stratus/Stratocumulus Experiment (MASE). Both of these stratus cloud projects demonstrated that bimodal CCN spectra typically caused by cloud processing were associated with clouds that exhibited higher concentrations of smaller droplets with narrower distributions and less drizzle than clouds associated with unimodal CCN spectra. Resulting brighter clouds and increased cloudiness could enhance both indirect aerosol effects (IAE). These stratus findings are opposite of analogous measurements in two cumulus cloud projects, which showed bimodal CCN associated with fewer larger droplets more broadly distributed and with more drizzle than clouds associated with unimodal CCN. Resulting reduced cumulus brightness and cloudiness could reduce both IAE. Physics of Stratocumulus Tops (POST) flights in air masses with higher CCN concentrations, N CCN , showed more extremes of the stratus characteristics. However, POST flights with lower N CCN showed opposite droplet characteristics similar to the cumulus clouds, yet still showed less drizzle in clouds associated with bimodal CCN, but not as much less as the flights with higher N CCN . Since all MASE clouds were in polluted air masses, while the two cumulus projects were in clean air masses we deduce from these four projects that both the dynamic stratus/cumulus differences (vertical wind) and N CCN are responsible for the microphysics and drizzle differences among these projects. This is because the clean POST characteristics are a hybrid between MASE/POST high N CCN and the two cumulus projects.
Recent observational and large eddy simulation (LES) modeling studies have nearly unanimously supported the view of deep cumulus convection being composed of a series of quasi-spherical bubbles of buoyant air, known as moist thermals. Despite the prevalence of moist thermals in deep convection, a comprehensive theory for the dynamics of these structures is lacking. Most current conceptual models for cumulus convection are based on canonical scaling theories for dry thermals or plumes; however, there is considerable evidence that the behavior of moist thermals differs markedly from these theories. Furthermore, the theoretical basis for most cumulus parameterizations originates from the plume conceptual model, and therefore these parameterizations are inconsistent with the real structure of moist convection. Motivated by the aforementioned knowledge gaps, this “end-to-end” research effort use theory, observations, numerical simulations, and direct improvements to the Zhang-McFarlane (ZM) convection scheme in the global climate Community Atmosphere Model (CAM) to address the following research questions: What key environmental parameters determine whether or not shallow convection will transition into deep convection, in the context of thermal-like updrafts? What factors regulate the size of thermals within cumulus updrafts? How does vertical wind shear influence thermal behavior, and as a consequence, vertical velocity and mass flux profiles and the shallow-to-deep convective transition? What are the critical processes that determine updraft vertical velocities and their connection to the vertical mass flux profile for thermal-like updrafts? Idealized LES modeling will be used in conjunction with theoretical models for the core properties of thermal-like updrafts to better understand key processes that regulate thermal ascent rates and entrainment properties. Thermal-tracking procedures will be used to characterize the behavior of thermals within the LES, and recently developed direct measures of entrainment and detrainment will be used to quantify entrainment/detrainment rates. Building from these results, we will analyze the structure of moist thermals from hemispheric range-height indicator scans taken during the Atmospheric Radiation Measurement Cloud, Aerosol, and Complex Terrain Interactions (CACTI) field campaign, and from “real case” LES of CACTI events. This combined modeling and observational analysis will provide essential validation for the existing body of research on moist thermal dynamics, which is based primarily on modeling studies. With the insight gained from the aforementioned activities, we will modify the Zhang-McFarlane convection scheme to improve its representation of updraft vertical velocity and entrainment rate profiles. These process-level changes will be tested in the Community Atmosphere Model to assess the impact on global climate simulations.
Entrainment and detrainment rates (ε and δ) constitute the most critical free parameters in mass flux schemes commonly employed for cumulus parameterizations. Recently, Zhu et al. (2021) introduced a new approach that utilizes aircraft observations to simultaneously estimate ε and δ for cumulus clouds, overcoming the limitation of other observation-based approaches that solely yield ε without offering insights into δ. This study aims to comprehensively evaluate the reliability of this new approach. First, evaluation using an Explicit Mixing Parcel Model demonstrates the capability of the new approach to back-calculate predetermined ε and δ based on the physical properties before and after the entrainment mixing. Second, evaluation using large-eddy simulations illustrates that the new approach yields consistent ε and δ profiles compared to the traditional approach. Sensitivity tests indicate a weak sensitivity of the estimated δ with the new approach to the entrained air source. A decrease in the proportion of cloudy air in the assumed detrained air leads to a reduction in the estimated δ, while ε remains unaffected. Finally, the most appropriate assumptions for entrained and detrained air are discussed. Estimating ε for cumulus parameterizations involves acquiring ambient air more than 500 m away from the cloud edge as entrained air. Due to implicit mean field approximations in the traditional approach, determining the optimal assumption for detrained air properties proves challenging. Finally, this study confirms the reliability of the new approach in estimating ε and δ, providing confidence in its application to extensive observational data and advancement in parameterization.
Rain formation is a critical factor governing the lifecycle and radiative forcing of clouds and therefore it is a key element of weather and climate. Cloud microphysics–turbulence interactions occur across a wide range of scales and are challenging to represent in atmospheric models with limited resolution. Based on past experiments and idealized numerical simulations, it has been postulated that cloud turbulence accelerates rain formation by enhancing drop collision–coalescence. We provide substantial evidence for significant impacts of turbulence on the evolution of cloud droplet size distributions and rain formation by comparing high-resolution observations of cumulus congestus clouds with state-of-the-art large-eddy simulations coupled with a Lagrangian particle-based microphysics scheme. Turbulent coalescence must be included in the model to accurately represent the observed drop size distributions, especially for drizzle drop sizes at lower heights in the cloud. Turbulence causes earlier rain formation and greater rain accumulation compared to simulations with gravitational coalescence only. The observed rain size distribution tail just above cloud base follows a power law scaling that deviates from theoretical scalings considering either a purely gravitation collision kernel or a turbulent kernel neglecting droplet inertial effects, providing additional evidence for turbulent coalescence in clouds. In contrast, large aerosols acting as cloud condensation nuclei (“giant CCN”) do not significantly impact rain formation owing to their long timescale to reach equilibrium wet size relative to the lifetime of rising cumulus thermals. Overall, turbulent drop coalescence exerts a dominant influence on rain initiation in warm cumulus clouds, with limited impacts of giant CCN.
Following methods outlined in Remillard et al. (2012), we classify seven cloud types using radar reflectivity, best-estimated cloud base, and cloud-layer product from the Active Remotely Sensed Cloud Locations (ARSCL) product (Kollias et al. 2007). A cloud mask is created based on the detectable radar reflectivity (>-40 dBZ) combined with the best-estimated cloud base height. Each cloud object is analyzed individually as contiguous cloudy pixels, and its type is determined based on the cloud’s boundaries and duration. Focusing on marine boundary-layer clouds, low clouds are further classified into four types: shallow cumulus, broken stratocumulus (Sc) or cumulus clouds, single-layer Sc, and multi-layer Sc or Sc coupled with cumulus. The remaining three categories are middle clouds, high clouds, and deep convective clouds. For detailed definition of each cloud type, please refer to Zheng et al. (2024).
This study investigates the microphysical and thermodynamic influences on North Atlantic trade-cumulus rain evaporation in the sub-cloud layer over Barbados from January to November 2020. Using radar observations and a 1-D model, the results reveal that microphysical properties, namely geometric mean diameter (D g ) and raindrop concentration, primarily control evaporation processes under conditions of limited thermodynamic variability. Thermodynamic factors like cloud base height and relative humidity exert a smaller influence due to their narrow observed ranges. Small D g leads to rapid increases in rain evaporation fraction (REF), as small drops evaporate completely, while larger D g yields slower, more gradual REF changes. Frequent weak-rain cases reduce the mean evaporation flux, whereas infrequent intense-rain events substantially enhance it. These findings highlight the pivotal role of microphysical variability in shaping sub-cloud evaporation in this trade cumulus regime, while thermodynamic effects may be more important in other environments.
Aerosol-cloud-precipitation interactions are a leading source of uncertainty in estimating climate sensitivity. Remote marine boundary layers where accumulation mode (~100–400 nm diameter) aerosol concentrations are relatively low are very susceptible to aerosol changes. These regions also experience heightened Aitken mode aerosol (~10–100 nm) concentrations associated with ocean biology. Aitken aerosols may significantly influence cloud properties and evolution by replenishing cloud condensation nuclei and droplet number lost through precipitation (i.e., Aitken buffering). We use a large-eddy simulation with an Aitken-mode enabled microphysics scheme to examine the role of Aitken buffering in a mid-latitude decoupled boundary layer cloud regime observed on 15 July 2017 during the Aerosol and Cloud Experiments in the Eastern North Atlantic flight campaign: cumulus rising into stratocumulus under elevated Aitken concentrations (~100–200 mg -1 ). In situ measurements are used to constrain and evaluate this case study. Our simulation accurately captures observed aerosol-cloud-precipitation interactions and reveals time-evolving processes driving regime development and evolution. Aitken activation into the accumulation mode in the cumulus layer provides a reservoir for turbulence and convection to carry accumulation aerosols into the drizzling stratocumulus layer above. Further Aitken activation occurs aloft in the stratocumulus layer. Together, these activation events buffer this cloud regime against precipitation removal, reducing cloud break-up and associated increases in heterogeneity. We examine cloud evolution sensitivity to initial aerosol conditions. With halved accumulation number, Aitken aerosols restore accumulation concentrations, maintain droplet number similar to original values, and prevent cloud break-up. Without Aitken aerosols, precipitation-driven cloud break-up occurs rapidly. In this regime, Aitken buffering sustains brighter, more homogeneous clouds for longer.
Abstract This study estimates the meteorological covariations of aerosol and marine boundary layer (MBL) cloud properties in the eastern North Atlantic (ENA) region, characterized by diverse synoptic conditions. Using a deep‐learning‐based clustering model with mid‐level and surface daily meteorological data, we identify seven distinct synoptic regimes during the summer from 2016 to 2021. Our analysis, incorporating reanalysis data and satellite retrievals, shows that surface aerosols and MBL clouds exhibit clear regime‐dependent characteristics, whereas lower tropospheric aerosols do not. This discrepancy likely arises from synoptic regimes determined by daily large‐scale conditions, which may overlook air mass histories that predominantly dictate lower tropospheric aerosol conditions. Focusing on three regimes dominated by northerly winds, we analyze the Atmospheric Radiation Measurement Program (ARM) ENA observations on Graciosa Island in the Azores. In the subtropical anticyclone regime, fewer cumulus clouds and more single‐layer stratocumulus clouds with light drizzle are observed, along with the highest cloud droplet number concentration (Nd), surface cloud condensation nuclei (CCN) and surface aerosol levels. The post‐trough regime features more broken or multi‐layer stratocumulus clouds with slightly higher surface rain rate, and lower Nd and surface CCN levels. The weak trough regime is characterized by the deepest MBL clouds, primarily cumulus and broken stratocumulus clouds, with the strongest surface rain rate and the lowest Nd, surface CCN and surface aerosol levels, indicating strong wet scavenging. These findings highlight the importance of considering the covariation of cloud and aerosol properties driven by large‐scale regimes when assessing aerosol indirect effects using observations.
High-resolution hemispheric camera images at a meteorological site in western Germany are used to analyze the multi-dimensional spatial characteristics of continental cumulus cloud fields, and to evaluate Large-Eddy Simulations on this aspect. Traditional non-hemispheric cloud-detecting instruments provide additional reference data. The main model-observation comparison focuses on cloud size distributions (CSDs), employing two methods: (a) directly using three-dimensional model fields, direct CSDs, and (b) using rendered hemispheric images of the model fields as produced by a camera simulator based on path-tracing. In the latter method, both the real and rendered images are used to three-dimensionally reconstruct the cloud fields, yielding hemispheric CSDs. Advantages of hemispheric comparisons over more classic approaches include (a) fair comparisons between model and data, and (b) full use of the enhanced resolutions and hemispheric spatial coverage of the camera imagery. Basic evaluation of the simulations demonstrates good agreement on thermodynamic structure and its diurnal cycle. Cloud heights and cloud cover are intercompared between the model, camera data and other instrumentation, providing insight into their structural differences. A consistent alignment is found between the hemispheric CSDs from both the model and the cameras. Power law fits reveal structurally lower exponents in hemispheric CSDs compared to non-hemispheric CSDs, which particularly caution against directly comparing hemispheric CSDs to non-hemispheric distributions. This result is robust for sample size and fitting method. These findings inform future use of hemispheric camera systems for studying cumulus cloud field morphology and model evaluation.
Large-eddy simulations (LESs) are conducted for each day of the intensive observation periods (IOPs) of the Green Ocean Amazon (GoAmazon) field campaign to characterize the updrafts and microphysics within deep convective cores while contrasting those properties between Amazon wet and dry seasons. Mean Doppler velocity (V dop ) values simulated using LESs are compared with 2-year measurements from a radar wind profiler (RWP) as viewed by statistical composites separated according to wet- and dry-season conditions. In the observed RWP and simulated LES V dop composites, we find more intense low-level updraft velocity, vigorous graupel generation, and intense surface rain during the dry periods compared with the wet periods. To investigate coupled updraft–microphysical processes further, single-day golden cases are selected from the wet and dry periods to conduct detailed cumulus thermal tracking analysis. Tracking analysis reveals that simulated dry-season environments generate more droplet-loaded low-level thermals than wet-season environments. This tendency correlates with seasonal contrasts in buoyancy and vertical moisture advection profiles in large-scale forcing. Employing a normalized time series of mean thermal microphysics, the simulated cumulus thermals appear to be the primary generator of cloud droplets. When subsequent thermals penetrate the ice crystal layer, droplets within the thermals interact with entrained ice crystals, which enhances riming in the thermals. This appears to be a production pathway of graupel/hail particles within simulated deep convective cores. In addition, less-diluted dry-case thermals tend to be elevated higher, and graupel grows further during sedimentation after spilling out from thermals. Therefore, greater concentrations of low-level moist thermals likely result in more graupel/hail production and associated dry-season convective vigor.
In cumulus clouds, aerosol concentrations control cloud droplet concentrations, modifying cloud radiative properties, precipitation processes, and cloud electrification. However, mechanisms of aerosol-deep convection interactions are not well understood due to complex cloud dynamics and microphysics. We investigate the interaction of aerosols with isolated deep convection using Large Eddy Simulations of two cases during the TRacking Aerosol Convection interactions ExpeRiment (TRACER) near Houston, Texas, using a joint cell-thermal tracking algorithm. Cumulus thermals are droplet generators, since supersaturation and droplet nucleation coincide with thermal centers, where the strongest updrafts occur. Primary ice crystal formation does not take place inside thermals, but at layers where previous thermals detrained moisture. As subsequent thermals containing supercooled droplets penetrate these layers, hail and graupel form at or near these thermals. Higher aerosol concentrations result in higher droplet concentrations that suppress drizzle, delay warm rain processes, and transport more moisture aloft. This increases snow and ice amount, as well as graupel and hail, leading to more lightning. Polluted thermals initiate at slightly higher altitudes, and are slightly larger and faster, suggesting a weak invigoration. We also find more thermals per cell, but fewer isolated cells, since convection is more aggregated and intense, especially near the end of the 24 h simulation. Non-linear mesoscale feedback likely triggered by temperature and moisture responses to aerosol-thermal interactions causes the aggregation. Time-lagged aerosol-reinitialization experiments show that the mesoscale response is the predominant forcing for the invigoration. These changes happen within one day, on a smaller scale than previously suggested.
An analysis of stereo-camera data from the Tracking Aerosol Convection Interactions Experiment (TRACER) campaign in Houston, Texas, reveals the existence of pinned clouds sitting atop industrial heat sources. These are not plumes of vapor and condensate emanating from stacks: The pinned shallow cumuli have cloud bases at about the lifting condensation of near-surface air. On many mornings, the pinned clouds are the only shallow cumuli in the field of view of the stereo cameras, persisting by themselves for at least an hour. On those mornings, the lower atmosphere straddles the boundary between stable and unstable, and the waste heat from industrial facilities is able to pin moist convection overhead. When solar heating of the surface becomes sufficient later in the morning, those mornings transition to having widespread shallow moist convection. Occurring within the field of view of the stereo cameras and other TRACER instruments, these pinned clouds represent steady plume-like moist convection triggered by known heat sources in a well-characterized atmosphere, making them a rich target for further study. Significance Statement This article introduces steady-state cumulus clouds observed during the Tracking Aerosol Convection Interactions Experiment (TRACER) campaign that were pinned to industrial heat sources. These pinned clouds were present in the early morning only when conditions were primed for moist convection, but for which there was not yet enough solar heating to trigger widespread convection. They persist in a statistical steady state and therefore provide a natural setting to explore the mechanisms controlling convective dynamics, which play a central role in Earth’s atmospheric circulation and radiative balance.
The initiation of deep moist convection is governed in part by the horizontal width of updrafts near cloud base, which limits the deleterious effects of entrainment-driven dilution on buoyant thermals ascending through the free troposphere. However, the factors controlling cloud-base updraft width, which in turn dictates cloud depth, are not well understood. We track the evolving three-dimensional structure of the mesoscale subcloud forcing for vertical motion and near-cloud thermodynamic ingredients within a high-resolution ensemble of simulations of seven realistic daytime orographic convection initiation events to determine their relative roles in controlling cloud width and depth. Statistical analysis of approximately 5000 cloudy updraft samples indicates that the most important contributors to the width of cloudy updrafts across the ensemble are the depth and magnitude of the subcloud mesoscale ascent. However, the depth achieved by clouds is more consistently predicted by the near-cloud ambient relative humidity within the lower to middle free troposphere and convective available potential energy. Therefore, although the width of cloudy updrafts may be partly set at low levels by the mesoscale vertical mass and moisture flux, the likelihood of deep moist convection is governed by the generation of positive buoyancy within cumulus thermals and entrainment-driven dilution that reduces it. The persistence of the low-level mesoscale vertical forcing locally consolidates and vertically transports boundary layer moisture, helping to reduce updraft dilution. However, these factors vary in relative impacts on cloudy updrafts across individual cases, indicating multiple pathways for deep convection initiation.
Climate models often face challenges in accurately simulating the daily precipitation cycle over tropical land areas, particularly in the Amazon. One contributing factor may be the incomplete representation of the diurnal evolution of shallow cumulus (ShCu) clouds. This study aimed to enhance the understanding of the diurnal cycles of ShCu clouds—from formation to maturation and dissipation—over the Central Amazon (CAMZ). Using observational data from the Green Ocean Amazon 2014 (GoAmazon) campaign and large eddy simulation (LES) modeling, we analyzed the diurnal cycles of six selected pure ShCu cases and their composite behavior. Our results revealed a well-defined cycle, with cloud formation occurring between 10 and 11 local time (LT), maturity from 13 to 15 LT, and dissipation by 17–18 LT. The vertical extent of the liquid water mixing ratio and the intensity of the updraft mass flux were closely associated with increases in turbulent kinetic energy (TKE), enhanced buoyancy flux within the cloud layer, and reduced large-scale subsidence. We further analyzed the diurnal cycles of the convective available potential energy (CAPE), the convective inhibition (CIN), the Bowen ratio (BR), and the vertically integrated TKE in the mixed layer (ITKE-ML), exploring their relationships with the cloud base mass flux (Mb) and cloud depth across the six ShCu cases. ITKE-ML and Mb exhibited similar diurnal trends, peaking at approximately 14–15 LT. However, no consistent relationships were found between CAPE (or BR) and Mb. Similarly, comparisons of the cloud depth with CAPE, BR, ITKE-ML, CIN, and Mb revealed no clear relationships. Smaller ShCu clouds were sometimes linked to higher CAPE and lower CIN. It is important to emphasize that these findings are preliminary and based on a limited sample of ShCu cases. Further research involving an expanded dataset and more detailed analyses of the TKE budget and synoptic conditions is necessary. Such efforts would yield a more comprehensive understanding of the factors influencing ShCu clouds’ vertical development.
This study demonstrates a specific application of the hierarchical system development (HSD) approach to investigate, analyze, and attribute model issues within the Unified Forecast System (UFS), with a focus on process isolation. By evaluating a non‐precipitating, shallow cumulus case at the Atmospheric Radiation Measurement Southern Great Plains site in the UFS global forecast against the observation, the investigation identifies a warmer and deeper daytime convective planetary boundary layer (PBL) and misrepresented nocturnal PBL transition. Hypothesis testing, which employs the Common Community Physics Package (CCPP) single‐column model (SCM) and uses the same physics as the UFS global model, confirms that these issues are attributed to the model physics and initialization. Specifically, misrepresented PBL processes are linked to problematic surface condition and a lack of cloud formation, which may stem from deficiencies in PBL and cloud microphysics parameterizations and their interactions. The UFS initial condition contributes to an earlier, excessively collapsed daytime convective boundary layer and a lack of decoupling between the stable boundary layer and residual layer late in the afternoon. This work introduces an avenue for the community to engage with the application of HSD, along with the CCPP and CCPP SCM, to understand the interplay of model physics, disentangle the roles of model components, as well as facilitate model and forecast improvement.
The sources of the magmas that formed the Rustenburg Layered Suite of the Bushveld Complex in South Africa remain debated, despite decades of research. Vertical and lateral variation in bulk rock and mineral separate Sr-Nd isotopic compositions, which generally indicate enriched sources, demonstrate that the layered sequence was formed by the emplacement of multiple batches of magma, crucially resulting in episodes of PGE-Cr-V mineralisation. The Lu-Hf isotope compositions of zircon are, however, at odds with the bulk rock Sr-Nd isotopic heterogeneity as they show near homogeneous compositions throughout the layered sequence (εHf (2.06 Ga) =−8). This lack of variation in Hf isotope composition has been attributed to deep, continental lithospheric mantle-related and/or crustal contamination of plume-derived Bushveld magmas. In this study, we analysed the major, trace element and Sr-Nd isotope geochemistry of apatite in the Rustenburg Layered Suite. Apatite occurs as an intercumulus mineral in the lowermost regions and a cumulus mineral in the uppermost regions of the layered sequence and can therefore be used to test existing models for the isotopic disequilibrium between bulk rock Sr-Nd and zircon Hf isotopic compositions. Apatite is largely chlorapatite in the lowermost regions and fluorapatite in the uppermost regions of the layered sequence. The Merensky Reef is unusual in that it comprises both chlorapatite and fluorapatite. Apatite throughout the layered sequence is generally unzoned and shows no evidence of late-stage alteration. Trace element data show that apatite is enriched in L/HREE, with common negative Eu-Sr anomalies. These trace element signatures are consistent with a magmatic origin for the apatite grains, with prior, or concurrent, plagioclase crystallization from the same melt. Variability in in situ Sr and Nd isotope compositions of apatite is recorded throughout the layered sequence with εNd (2.06 Ga) compositions varying between −2.5 and − 10.2 and initial 87 Sr/ 86 Sr compositions varying between 0.7079 and 0.7103 (for the Marikana dikes only). The variability in Sr-Nd isotope compositions of apatite is consistent with the bulk rock (and mineral separate) variation in Sr-Nd isotope compositions, suggesting apatite preserves primary magmatic compositions in the Rustenburg Layered Suite.
Cloud-type impacts present a great challenge to solar forecasting due to diverse and complex cloud-radiation interactions. This third part of our paper sequence seeks to address this challenge by quantifying the forecast accuracies under eight cloud types: cumulus (Cu), stratified clouds (St), altocumulus (Ac), altostratus (As), cirrostratus/anvil (Cr), cirrus (Ci), congestus (Co), deep convective clouds (Dc) across four physics-informed persistence models reported in Part I. To generalize the cloud impacts, the eight cloud types are further grouped into three cloud categories based on their common features: weak convective clouds, stratiform clouds, and strong convective clouds. Here, the decade-long (2001 ~ 2014) collocated measurements of irradiances and cloud types at the U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Program South Great Plain (SGP) Central Facility site are used for model evaluation. Results reveal a clear performance hierarchy for global horizontal irradiance (GHI) and direct normal irradiance (DNI): best for weak convective clouds and cirrus, intermediate for stratiform clouds, and worst for strong convective clouds. Performance for diffuse horizontal irradiance (DHI) is less influenced by cloud types. Cloud albedo dominates all three irradiances for Dc, while both cloud albedo and cloud fraction are influential for other cloud types. A 12 %~33 % improvement in accuracy at 6-hour lead time compared to the benchmark smart model confirms the effectiveness of incorporating physics into the models for various cloud types; further improvements are expected by directly integrating cloud type information into forecasting models by modifying the physical formulation of cloud-radiation interaction, and/or using more advanced machine learning models.