2:45 PM - 3:00 PM
[MGI30-05] A Tracer Advection Scheme Based on the Particle-in-Cell Method on the 2-Sphere
Keywords:Global Numerical Modeling, Tracer Advection, HEALPix, Super-Droplet Method
Transport of cloud and aerosol particles is key to understanding the climate on Earth and other planets. To represent such particles in weather and climate models, not only the bulk statistics of these distributions but also detailed information—such as particle trajectories and the amount of dissolved aerosols—is useful for resolving fine-scale processes. However, representing joint distributions of such attributes using a bin method results in computational costs that grow exponentially with the number of attributes. To mitigate these problems, the Particle-in-Cell (PIC) method, which solves the coupled system of Lagrangian super-particles and Eulerian grid information, is promising.
Several examples of such methods are the super-droplet method (Shima et al., 2009, 2020) and the elliptical parcel in cell method (Frey et al., 2023).
Recently, the super-droplet method has already been applied to horizontally 100-km-scale domains in regional models. To understand the interactions between global and long-term climate systems and cloud and aerosol particles, however, it is necessary to apply the PIC method to a global model. To apply the PIC method on the 2-sphere, a key aspect of the grid structure is an equal-area partition of the domain combined with efficient particle-to-cell indexing. To achieve this, we focus on the Hierarchical Equal Area isoLatitude Pixelisation of a sphere (HEALPix; Górski et al., 2005), which has recently been adopted in applications such as the digital twin project in Europe (Destination Earth) and machine learning-based weather forecasting (Karlbauer et al., 2024), and may become a de facto standard for analysis and simulation with machine learning in the future. In this study, we develop a novel tracer scheme and numerical model based on the PIC method on the 2-sphere, utilizing HEALPix, to enable future global simulations with sophisticated analysis and physical processes.
In Matsushima et al. (2023), we developed a numerical model for cloud simulations at meter- to sub-meter scales. In that model, we proposed a method for solving the coupled dynamics of particles and cells, assuming an orthogonal coordinate system and grid. In this study, we extend our method to operate on the 2-sphere domain using HEALPix. To reduce the information per particle, we represent the relative position of each particle using the hierarchical structure of a high-resolution HEALPix. Thanks to its equal-area properties, the sampling and resampling of particles is straightforward, facilitating long-term integration. We employ radial basis functions and polynomials to interpolate non-divergent flow velocities at particle positions. We model the effects of unresolved flow using a Wiener process or an Ornstein–Uhlenbeck process. Finally, we implement the model using a Python-based, multi-platform framework called JAX to leverage automatic differentiation and machine learning, as well as to evaluate performance on AI-based architectures.
To evaluate the numerical accuracy and properties of our method relative to traditional tracer schemes, we conduct the standard suite of tracer advection experiments (Lauritzen et al., 2012) using various parameters, both with and without the effect of unresolved flow. Our scheme eliminates numerical diffusion, and the results demonstrate high accuracy compared with other methods, even when using low-resolution velocity fields.
We will enhance our model in two main directions. One direction is to apply our scheme to analyze cloud patterns on planets and incorporate it into data assimilation frameworks, taking advantage of its differentiability with respect to particle positions. The second direction is to integrate our model into a global framework featuring sophisticated and optimized microphysical processes (Matsushima et al., 2023), enabling simulations in greater detail that better replicate the Earth system using digital twin data to reduce uncertainties in weather and climate predictions.
Several examples of such methods are the super-droplet method (Shima et al., 2009, 2020) and the elliptical parcel in cell method (Frey et al., 2023).
Recently, the super-droplet method has already been applied to horizontally 100-km-scale domains in regional models. To understand the interactions between global and long-term climate systems and cloud and aerosol particles, however, it is necessary to apply the PIC method to a global model. To apply the PIC method on the 2-sphere, a key aspect of the grid structure is an equal-area partition of the domain combined with efficient particle-to-cell indexing. To achieve this, we focus on the Hierarchical Equal Area isoLatitude Pixelisation of a sphere (HEALPix; Górski et al., 2005), which has recently been adopted in applications such as the digital twin project in Europe (Destination Earth) and machine learning-based weather forecasting (Karlbauer et al., 2024), and may become a de facto standard for analysis and simulation with machine learning in the future. In this study, we develop a novel tracer scheme and numerical model based on the PIC method on the 2-sphere, utilizing HEALPix, to enable future global simulations with sophisticated analysis and physical processes.
In Matsushima et al. (2023), we developed a numerical model for cloud simulations at meter- to sub-meter scales. In that model, we proposed a method for solving the coupled dynamics of particles and cells, assuming an orthogonal coordinate system and grid. In this study, we extend our method to operate on the 2-sphere domain using HEALPix. To reduce the information per particle, we represent the relative position of each particle using the hierarchical structure of a high-resolution HEALPix. Thanks to its equal-area properties, the sampling and resampling of particles is straightforward, facilitating long-term integration. We employ radial basis functions and polynomials to interpolate non-divergent flow velocities at particle positions. We model the effects of unresolved flow using a Wiener process or an Ornstein–Uhlenbeck process. Finally, we implement the model using a Python-based, multi-platform framework called JAX to leverage automatic differentiation and machine learning, as well as to evaluate performance on AI-based architectures.
To evaluate the numerical accuracy and properties of our method relative to traditional tracer schemes, we conduct the standard suite of tracer advection experiments (Lauritzen et al., 2012) using various parameters, both with and without the effect of unresolved flow. Our scheme eliminates numerical diffusion, and the results demonstrate high accuracy compared with other methods, even when using low-resolution velocity fields.
We will enhance our model in two main directions. One direction is to apply our scheme to analyze cloud patterns on planets and incorporate it into data assimilation frameworks, taking advantage of its differentiability with respect to particle positions. The second direction is to integrate our model into a global framework featuring sophisticated and optimized microphysical processes (Matsushima et al., 2023), enabling simulations in greater detail that better replicate the Earth system using digital twin data to reduce uncertainties in weather and climate predictions.