Potential and Limitations of Machine Learning for Modeling Warm‐Rain Cloud Microphysical Processes

The use of machine learning based on neural networks for cloud microphysical parameterizations is investigated. As an example, we use the warm‐rain formation by collision‐coalescence, that is, the parameterization of autoconversion, accretion, and self‐collection of droplets in a two‐moment framework. Benchmark solutions of the kinetic collection equations are performed using a Monte Carlo superdroplet algorithm. The superdroplet method provides reliable but noisy estimates of the warm‐rain process rates. For each process rate, a neural network is trained using standard machine learning techniques. The resulting models make skillful predictions for the process rates when compared to the testing data. However, when solving the ordinary differential equations, the solutions are not as good as those of an established warm‐rain parameterization. This deficiency can be seen as a limitation of the machine learning methods that are applied, but at the same time, it points toward a fundamental ill‐posedness of the commonly used two‐moment warm‐rain schemes. More advanced machine learning methods that include a notion of time derivatives, therefore, have the potential to overcome these problems.

Plain Language Summary: In our work, we are trying to teach a computer how rain forms in clouds. We show that computer hundreds of cases in the form of data. To be honest, the data are not real data but only results of simulations with a more complicated computer model. This complicated model can track the collisions of 10,000 of droplets, and we save all that data about the growth of the droplets into larger raindrops. This is what we then give to the simpler computer model to teach it something about clouds and rain. Afterward, it can make pretty good predictions about which clouds will rain and how long it will take them to produce the first rain. Unfortunately, the current machine learning methods are still a bit stupid because they only learn from the data but do not understand the mathematics and the physics behind the data. Therefore, the new computer model is still not as good at predicting rain as some clever mathematical formulas that were developed 20 years ago. Maybe we first have to teach the computer model more about calculus before it can learn to predict rain.

Key Points: Machine learning is successfully applied to the warm‐rain parameterization problem. Training and testing data for the warm‐rain kinetic collection equation are provided using the superdroplet method. Standard training methods show some limitations for the resulting ODE system.

Deutsche Forschungsgemeinschaft (DFG) http://dx.doi.org/10.13039/501100001659