Improving bulk cloud microphysics modeling: the role of super-droplet simulations

Cloud microphysics refers to the complex processes that govern the formation, evolution, and interactions of particles within clouds. These processes significantly influence the Earth’s climate system by regulating precipitation patterns and cloud cover. Understanding the intricacies of cloud microphysics is therefore essential for accurate climate modeling. Yet, the precise modeling of these complex microphysical processes remains one of the most challenging aspects of climate research. Traditional cloud microphysics modeling within climate models, known as bulk methods, aims to simplify the physics governing the vast range of processes occurring within clouds. While these methods have enabled more efficient climate simulations, their inherent simplifications introduce limitations that could affect the overall accuracy of climate models.

The challenge of simplification

Clouds are composed of hydrometeors—cloud droplets, ice crystals, raindrops, etc.—each engaging in intricate and varied interactions and evolutionary processes. Bulk methods simplify these complex interactions into more manageable, aggregated representations. While computationally efficient, this approach tends to oversimplify the representation of particle size distributions and the dynamic processes affecting them, introducing significant errors and uncertainties. As the climate modeling community strives for greater accuracy, the need to mitigate these errors and uncertainties becomes increasingly apparent.

**Figure 1:** Results from the one-dimensional simulations with the SDM. Contours of (a) maximum cloud water path \(CWP_{max}\), (b) maximum rainwater path \(RWP_{max}\), (c) maximum surface rain rate \(RR_{max}\), and (d) rain initiation time for varying updraft speed and aerosol concentration. The results are averaged over 100 simulations.

Bridging the gap with super-droplet simulations

Recent advances in computational capabilities and numerical methods have opened new avenues to refine cloud microphysics modeling. At the forefront of these advances is the super-droplet method (SDM), a particle-based approach that offers a more detailed and physically based representation of cloud processes. Unlike traditional bulk methods, which approximate the size distribution of hydrometeors through parameterization, SDM is capable of resolving these distributions through ‘super-droplets’—virtual droplets that each represent a collection of real particles. By simulating super-droplets, SDM provides detailed insights into the micro-scale interactions within clouds. The potential of super-droplet simulations to inform bulk methods is immense, offering a pathway to significantly improve the accuracy of bulk methods.

In our latest research, we used SDM (implemented in the python-based code PySDM) to produce an extensive library of one-dimensional rain-shaft simulations with varying updraft speeds, aerosol concentrations, surface pressures, and other variables. Figure 1 provides a visual representation of the variations of the maximum cloud-water path, the maximum rainwater path, the maximum surface precipitation rate, and the rain initiation time for varying updraft speed and aerosol concentration. This figure shows that higher updraft speeds facilitate the condensation of more cloud water, leading to increased rain production. Conversely, a rise in aerosol concentration tends to reduce rain formation due to the formation of smaller droplets that are less likely to collide and coalesce into rain. Moreover, an increase in updraft speed and a reduction in aerosol concentration result in earlier precipitation. This library of SDM simulations can be used to evaluate and calibrate bulk schemes to enhance their accuracy.

**Figure 2:** Comparison of one-dimensional simulations using the SDM and the bulk method. Height-time contours of specific cloud water content \(q_c\) (left panels) and specific rainwater content \(q_r\) (right panels) are compared for the simulations using the SDM (a and b), the bulk method with the initial parameters (c and d), and the calibrated bulk method (e and f). Black lines compare a single contour level for the SDM (dashed) and the bulk method (solid).

Calibrating for accuracy

In our research, we exploit the SDM simulations to calibrate and enhance bulk microphysics schemes. This calibration employs ensemble Kalman methods (implemented in the Julia-based package EnsembleKalmanProcesses.jl), enabling an efficient and robust optimization of model parameters against the detailed physics captured by super-droplet simulations. By minimizing mismatches in statistics such as the mean values of cloud and rainwater contents over spatial and temporal intervals simulated by bulk methods and by the detailed particle-based simulations, we refine parameters in the bulk methods, such as those governing rain formation, sedimentation and evaporation. This calibration process improves the accuracy of the bulk methods and provides insights into cloud microphysics processes. To illustrate the efficacy of this calibration, Figure 2 compares the results of the SDM, a simple bulk method with prior parameters, and the calibrated bulk method. It demonstrates how calibration markedly improves the accuracy of the bulk microphysics scheme.

The path forward

Integrating super-droplet simulations into the development of bulk microphysics models marks an advance toward achieving more accurate and reliable climate predictions. This approach bridges the gap between the micro-scale complexities inherent in cloud processes and the macro-scale representations of bulk models. Modeling cloud microphysics with the necessary accuracy presents a significant challenge. Yet, we are progressively moving toward improved microphysics representations through methods such as calibrating bulk models using SDM simulations. The results above focus on warm clouds, that is, clouds without ice. But work improving ice clouds and mixed-phase clouds is also underway.