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In the original Predicted Particle Properties (P3) bulk microphysics scheme, all ice-phase hydrometeors are represented by one or more “free” ice categories, where the physical properties evolve smoothly through changes to the four prognostic variables (per category), and with a two-moment representation of the particle size distribution. As such, the spectral dispersion cannot evolve independently, which thus results in limitations in representation of ice—in particular, hail—due to necessary constraints in the scheme to prevent excessive gravitational size sorting. To overcome this, P3 has been modified to include a three-moment representation of the size distribution of each ice category through the addition of a fifth prognostic variable, the sixth moment of the size distribution. The details of the three-moment ice parameterization in P3 are provided. The behavior of the modified scheme, with the single-ice-category configuration, is illustrated through simulations in a simple 1D kinematic model framework as well as with near large-eddy-resolving (250-m grid spacing) 3D simulations of a hail-producing supercell. It is shown that the three-moment ice configuration controls size sorting in a physically based way and leads to an improved capacity to simulate large, heavily rimed ice (hail), including mean and maximum sizes and reflectivity, and thus an overall improvement in the representation of ice-phase particles in the P3 scheme.

There are more uncertainties with ice hydrometeor representations and related processes than liquid hydrometeors within microphysics parameterization (MP) schemes because of their complicated geometries and physical properties. Idealized supercell simulations are produced using the WRF model coupled with “full” Hebrew University spectral bin MP (HU-SBM), and NSSL and Thompson bulk MP (BMP) schemes. HU-SBM downdrafts are typically weaker than those of the NSSL and Thompson simulations, accompanied by less rain evaporation. HU-SBM produces more cloud ice (plates), graupel, and hail than the BMPs, yet precipitates less at the surface. The limiting mass bins (and subsequently, particle size) of rimed ice in HU-SBM and slower rimed ice fall speeds lead to smaller melting-level net rimed ice fluxes than those of the BMPs. Aggregation from plates in HU-SBM, together with snow–graupel collisions, leads to a greater snow contribution to rain than those of the BMPs. Replacing HU-SBM’s fall speeds using the formulations of the BMPs after aggregating the discrete bin values to mass mixing ratios and total number concentrations increases net rain and rimed ice fluxes. Still, they are smaller in magnitude than bulk rain, NSSL hail, and Thompson graupel net fluxes near the surface. Conversely, the melting-layer net rimed ice fluxes are reduced when the fall speeds for the NSSL and Thompson simulations are calculated using HU-SBM fall speed formulations after discretizing the bulk particle size distributions (PSDs) into spectral bins. The results highlight precipitation sensitivity to storm dynamics, fall speed, hydrometeor evolution governed by process rates, and MP PSD design.

Cloud microphysics—the collection of processes that govern the small‐scale formation, evolution, and interactions of liquid droplets and ice crystals in clouds and precipitation—remains a major source of uncertainty in weather and climate models. Although too small in scale to be explicitly resolved in any large‐eddy simulation, weather, or climate model, the representation of cloud microphysical processes has significant impact at the climate scale. Current microphysical schemes are limited by both parametric uncertainty, linked to uncertainty in physical parameter values, and structural uncertainty, arising from incomplete physical understanding of the processes at play or approximations made for computational efficiency. Recent advances in the application of machine learning (ML) to the physical sciences show significant potential for minimizing these limitations by leveraging high‐fidelity simulations and observations. Here we outline the challenges that must be addressed to apply ML toward cloud microphysics scheme development. This perspectives paper synthesizes recent progress in using data‐driven methods, including ML, to improve cloud microphysics parameterizations and highlights opportunities to address key uncertainties. We discuss the roles of aleatoric (irreducible, or statistical) and epistemic (reducible, or systematic) errors in contributing to microphysics parameterization uncertainty. ML can leverage observations to improve microphysical schemes via bottom‐up and top‐down constraints. Methods such as differentiable programming and ML‐enhanced sampling strategies and the creation of large scale benchmark data sets promise to bridge the gap between observations and models and to improve the consistency of cloud microphysical representation across temporal and spatial scales. Plain Language Summary Cloud microphysics refers to the microscale processes that impact liquid droplets and ice crystals in clouds and precipitation. Though small in scale, these processes need to be represented in weather and climate models because they impact the large‐scale evolution of clouds, precipitation, and the Earth's energy balance. Because of uncertainty in both cloud microphysical processes and in how these processes should be represented in models, they are a major source of uncertainty in current weather and climate models. The recent application of machine learning (ML) methods to atmospheric model development holds significant promise to address current limitations in modeling cloud microphysics, and thus improve atmospheric models. Here we discuss both the challenges and opportunities in applying ML methods to cloud microphysics. Key Points Cloud microphysics remains a major source of uncertainty in weather and climate models, and new paradigms are needed to address this challenge Machine learning (ML) holds promise for both bottom‐up and top‐down microphysics scheme development ML can address physical process and model representation uncertainty, but some uncertainty is inherently irreducible

A new, complete three‐moment bulk microphysics approach is proposed that includes the effects of all relevant microphysical processes on the evolution of ice particle size distribution (PSD) width. This extends the three‐moment approach that was originally implemented in the Predicted Particle Properties (P3) scheme that assumed sedimentation and advection dominate and neglected the effects of most microphysical processes on PSD width. The new approach (FULL) is tested in idealized one‐dimensional kinematic updraft and three‐dimensional supercell simulations and compared to results using the original approach (ORIG). Although tendencies of the gamma PSD width parameter (μ) from several microphysical processes using FULL are large in magnitude relative to the sedimentation and advection tendencies, they have only minor impacts on the overall spatiotemporal patterns of μ; PSDs are narrower using FULL in regions with relatively narrow PSDs using ORIG and slightly wider in regions with relatively wide PSDs. The processes driving these impacts using FULL are ice‐rain collection near convective cores and sublimation in the far forward flank, both leading to PSD narrowing, and broadening from aggregation in the near forward flank. A general theoretical expression is derived to explain whether a process broadens or narrows PSDs based in part on the ice particle mass‐size relationship. However, the effects on bulk cloud and precipitation properties are limited, with only a 7%–8% decrease in mean surface precipitation using FULL compared to ORIG. Although overall impacts are modest in the tests conducted, the full approach improves physical realism with a negligible increase in computational cost. Plain Language Summary In atmospheric models, cloud and precipitation processes are represented by a microphysics scheme. In this study, we improve the Predicted Particle Properties (P3) microphysics scheme. The previous version of P3 made simplifying assumptions about how the ice particle size/mass distribution in a model grid volume changes from microphysical processes such as riming (collection of liquid drop by ice), sublimation, and aggregation. Specifically, it assumed that the relative spread of the distributions did not change from these processes. In the new version of P3, we explicitly calculate how the spread of particle sizes is affected by all relevant processes. In idealized simulations of a type of thunderstorm called a supercell, we show that the new approach produces narrower ice particle size distributions in parts of the storm where the distributions are relatively narrow, and slightly wider distributions where they are relatively wide, compared to the original approach. Despite these changes to the particle size distributions, the impacts on overall cloud and precipitation properties are modest. For example, the new approach produces 7%–8% less surface precipitation than the original version. Although bulk impacts are modest, the new scheme improves physical realism with little increase in computational cost. Key Points A new, complete 3‐moment approach to represent ice particles is proposed and implemented in the P3 bulk microphysics scheme Compared to the original 3‐moment closure in P3, size distribution width is altered by all microphysical processes in the new approach The new approach improves physical realism but impacts on cloud and precipitation properties are modest for a simulated supercell storm

Bin and bulk schemes are the two primary methods to parameterize cloud microphysical processes. This study attempts to reveal how their structural differences (size‐resolved vs. moment‐resolved) manifest in terms of cloud and precipitation properties. We use a bulk scheme, the Arbitrary Moment Predictor (AMP), which uses process parameterizations identical to those in a bin scheme but predicts only moments of the size distribution like a bulk scheme. As such, differences between simulations using AMP's bin scheme and simulations using AMP itself must come from their structural differences. In one‐dimensional kinematic simulations, the overall difference between AMP (bulk) and bin schemes is found to be small. Full‐microphysics AMP and bin simulations have similar mean liquid water path (mean percent difference <4%), but AMP simulates significantly lower mean precipitation rate (−35%) than the bin scheme due to slower precipitation onset. Individual processes are also tested. Condensation is represented almost perfectly with AMP, and only small AMP‐bin differences emerge due to nucleation, evaporation, and sedimentation. Collision‐coalescence is the single biggest reason for AMP‐bin divergence. Closer inspection shows that this divergence is primarily a result of autoconversion and not of accretion. In full microphysics simulations, lowering the diameter threshold separating cloud and rain category in AMP from 80$80$to 50μm$50\\,\\mu \\mathrm{m}$reduces the largest AMP‐bin difference to ∼10%, making the effect of structural differences between AMP (and perhaps triple‐moment bulk schemes generally) and bin even smaller than the parameterization differences between the two bin schemes. Plain Language Summary There are two primary ways to predict how clouds form and evolve. In a model grid box, bulk schemes typically predict the evolution of just the total number and mass of cloud droplets, whereas bin schemes not only keep track of total amount but also the number of droplets of different sizes. Bulk schemes are more computationally efficient than bin schemes, but bin schemes are usually assumed to be more accurate. This study aims to reveal how such differences affect their prediction of clouds. Our results show that small droplets colliding and combining to form raindrops is the only process that leads to large differences between bin and bulk schemes. Other individual processes, including droplet activation, condensation, evaporation, and sedimentation, contribute substantially less to differences between the two schemes. These results suggest that the advantages of using a bin scheme may not be as large as previously thought. Key Points Bulk and bin microphysics schemes with the same parameterizations simulate clouds more similarly than those simulated by two bin schemes Substantial differences between bin and bulk schemes are found only for collisions; they are reduced with a lower cloud‐rain size boundary The advantages of using a bin scheme rather than a bulk scheme for microphysics may not be as large as previously thought

Bulk microphysics schemes continue to face challenges due in part to the necessary simplification of hydrometeor properties and processes that is inherent to any parameterization. In all operational bulk schemes, one such simplification is the division of liquid water into two subcategories (cloud and rain) when predicting the evolution of warm clouds. It was previously found that biases in collisional growth in a bulk scheme with these separate liquid water categories can be mitigated with a unified liquid water category in which cloud and rain are contained within the same category. In this study, we examine the effect of artificially separating the liquid water category on other microphysical processes and in more realistic settings. Both our idealized 1D and 3D results show that a unified category bulk scheme is fundamentally better at predicting the timing and intensity of rain from warm‐phase cumulus clouds compared to a traditional (separate) category bulk scheme. This is because a unified category bulk scheme allows a bimodal distribution to exist within one traditional “rain” category, whereas separate category bulk scheme only have one mode per category. This advantage allows the unified bulk scheme to retain the information of the largest droplets even as they fall through a layer of small raindrops. A separate category bulk scheme fails to represent this bimodal feature in comparison. Plain Language Summary Bulk microphysics schemes are fast enough for simulating the evolution of clouds in weather and climate prediction, but they also face problems when calculating the collision and falling of water droplets. Some of the problems might not come from our lack of cloud physics knowledge but how the schemes are designed. For example, bulk schemes artificially divide the liquid water category into smaller droplets (“cloud”) and larger droplets (“rain”). It was found that the biases typically produced by a separate category bulk scheme can be fixed with a unified category bulk scheme. In this study, we look into how a unified category bulk scheme compares to a separate category one under more physical processes and model settings. We find that a unified category bulk scheme consistently outperforms a separate category one, especially when predicting the timing and heaviness of rainfall. This is because collision and falling of water droplets can create droplet size distributions with two peaks in the traditional cloud or rain category, which cannot be modeled with a separate category bulk scheme. Key Points A unified category bulk scheme accurately predicts rainfall timing and intensity far better than a traditional separate category scheme Sedimentation of bimodal rain distributions is poorly captured by a separate category scheme but well captured by a unified category one The improvement arises from more flexibility in size distributions despite the same number of total predicted moments in both schemes

Warm rain collision-coalescence has been persistently difficult to parameterize in bulk microphysics schemes. We use a flexible bulk microphysics scheme with bin scheme process parameterizations, called AMP, to investigate reasons for the difficulty. AMP is configured in a variety of ways to mimic bulk schemes and is compared to simulations with the bin scheme upon which AMP is built. We find that an important limitation in traditional bulk schemes is the use of separate cloud and rain categories. When the drop size distribution is instead represented by a continuous distribution, the simulation of cloud-to-rain conversion is substantially improved. We also find large sensitivity to the threshold size to distinguish cloud and rain in traditional schemes; substantial improvement is found by decreasing the threshold from 40 to 25 μm. Neither the use of an assumed functional form for the size distribution nor the choice of predicted distribution moments has a large impact on the ability of AMP to simulate rain production. When predicting four total moments of the liquid drop size distribution, either with a traditional two-category, two-moment scheme with a reduced size threshold, or a four-moment single-category scheme, errors in the evolution of mass and the cloud size distribution are similar, but the single-category scheme has a substantially better representation of the rain size distribution. Optimal moment combinations for the single-category approach are investigated and appear to be linked more to the information content they provide for constraining the size distributions than to their correlation with collision-coalescence rates.

Using the Weather Research and Forecasting model coupled with a spectral‐bin microphysics (“SBM”) and measurements from the Atmospheric Radiation Measurement Mobile Facility field campaign in China (AMF‐China), the authors examine aerosol indirect effects (AIE) in the typical cloud regimes of the warm and cold seasons in Southeast China: deep convective clouds (DCC) and stratus clouds (SC), respectively. Comparisons with a two‐moment bulk microphysics (“Bulk”) are performed to gain insights for improving bulk schemes in estimating AIE in weather and climate simulations. For the first time, measurements of aerosol and cloud properties acquired in China are used to evaluate model simulations to better understand aerosol impact on clouds in the southeast of China. It is found that changes in cloud condensation nuclei (CCN) concentration significantly change the timing of storms, the spatial and temporal distributions of precipitation, the frequency distribution of precipitation rate, as well as cloud base and top heights for the DCC, but not for the SC. Increasing CCN increases cloud droplet number (Nc) and mass concentrations, decreases raindrop number concentration, and delays the onset of precipitation. Compared with SBM, Bulk predicts much higher Ncand the opposite CCN effects on convection and heavy rain, stemming from the fixed CCN prescribed in Bulk. CCN have a significant effect on ice microphysical properties with SBM but not Bulk and different condensation/deposition freezing parameterizations employed could be the main reason. This study provided insights to further improve the bulk scheme to better account for aerosol‐cloud interactions in regional and global climate simulations, which will be the focus for a follow‐on paper. Key Points Aerosols significantly change the timing of storms and precipitation Fixed CCN prescribed in Bulk is the reason for the suppressed convection by CCN Suggestions for improving bulk microphsycis are provided

A bulk three‐moment representation for rain microphysics is developed and implemented in the Predicted Particle Properties (P3) microphysics scheme. In addition, a new parameterization for rain self‐collection and collisional breakup (RSCB) is presented using a lookup table approach, based on the Spectral‐Bin Model (SBM). To quantify the impacts of sedimentation, evaporation, and RSCB on drop size distributions (DSDs), a rain shaft model is applied to a wide range of atmospheric scenarios (i.e., initial conditions and regimes) and compared against results from the SBM. DSD shapes are mainly determined by both sedimentation and evaporation, except in heavy rain where the impact of RSCB on DSD shape becomes more important than evaporation. The new parameterization for RSCB has a considerable impact on the mean drop size, improving the agreement between P3 and SBM. Only 4% of the original two‐moment rainshaft simulations have mean drop sizes and rain rates within ±20% of the SBM results, but this increases to more than 95% agreement when the three‐moment rain representation is used together with the new parameterization for RSCB. Generally, the improvement is more significant for heavy rain than for light drizzle. Remaining differences between bin and bulk model are attributable to treatments of evaporation, and the restriction to gamma DSDs in P3. Plain Language Summary We improve the representation of rain for numerical models of the atmosphere. This is achieved by adding an additional predicted variable to allow for a more physically based prediction of raindrop sizes evolving from various microphysical processes, such as gravitational settling, evaporation, and growth and breakup upon drop‐drop collisions. Key Points The three‐moment rain scheme yields highly improved simulations of precipitation, compared to the original two‐moment representation The relative contributions of sedimentation, evaporation, and breakup to the shapes of drop size distributions depend on the rain regime A new parameterization of self‐collection and breakup based on lookup tables yields drop mean sizes comparable to a spectral bin scheme

A new spectral bin microphysical scheme (SBM) was implemented into the Weather Research and Forecasting model referred to as Fast‐SBM, which uses a smaller number of size distribution functions than the original version of the scheme referred to as Exact‐SBM. It was shown that both schemes produced similar dynamical and microphysical structure of a squall line simulated. An excellent agreement in the simulated precipitation amounts between the schemes was found within a range of cloud condensation nuclei concentrations from 100 to 3000 cm−3. The Fast‐SBM requires about 40% of the computing power of the Exact‐SBM, allowing it to be used for “real‐time” simulations over limited domains. The results obtained using the SBM simulations have been compared with those using a modified version of the Thompson bulk parameterization scheme. The main extension of the bulk scheme was the implementation of the process of drop nucleation, so that drop concentration is no longer prescribed a priori but rather calculated using the prescribed aerosol concentration. This scheme is referred to as the Drop scheme. A large set of sensitivity studies have been performed, in which microphysical parameters and precipitation, droplet nucleation above cloud base, etc., have been compared with those obtained from SBM. The SBM scheme produces more realistic dynamical and microphysical structure of the squall line. The Drop scheme did relatively little to change the cloud structures simulated by the bulk scheme. Unlike the SBM simulations that show different precipitation sensitivities to aerosol concentrations in relatively dry and humid environments, the Drop scheme indicates monotonic decrease in precipitation with increasing aerosol concentrations.