PhD Final Defense – Manho Park

On Advancing Computational Efficiency of Atmospheric Tracer Transport

Advisor: Professor Christopher W. Tessum

Abstract

This dissertation explores computational algorithms to improve the Pareto frontier in the speed and accuracy of tracer transport in an air quality model, and the use of an efficient transport model to study the health impacts of PM2.5 transported from wildfires. In search of a faster algorithm, I investigated machine-learned advection operators and improved 3-D modeling architecture to maximize use of flux-form semi-Lagrangian transport. I used a Lagrangian transport model to quantify contributions of individual fire events in total mortality and mortality risk. 

I investigated the potential use of machine-learning to emulate the passive scalar advection. I designed a learned 1-D advection solver that emulates the second-order stencil coefficients to approximate the behavior of a finite volume method. The learned operator has a convolutional neural network inside that reads the stencil scalar and Courant-Friedrich-Lewy (CFL) number and outputs the stencil coefficients that will be multiplied with the cell scalars. The learned solver was capable of reproducing spatiotemporal dynamics in the coarser domain than its fine-scale reference in both space and time. We demonstrated that the 2-D application of the solver survived splitting errors in many tested coarsening scenarios. This was an encouraging result as the learned operator can offer a higher-accuracy simulation in the coarser grid for acceleration than traditional numerical methods. 

However, the solver required a large factor of spatial coarse-graining, which is not ideal in air quality modeling. In addition, the solver was unstable at its original spatial resolution. 

Building on the limitation I found from the first stab, I developed a flux-form learned solver that outputs the numerical fluxes at cell interfaces. To minimize the factor of coarsening required to realize speedup, I used a neural network lighter in parameter space than the first design, and employed SimpleChains.jl, which is a specialized Julia package to efficiently run a small-sized neural network. This design achieved good stability and mass conservation in the 2-D ground-level horizontal advection with the trade-off of $r^2 = 0.24$ for every factor of 10 gained in speed. 

I confirmed the solver design with 4$\times$ coarsening in time successfully emulated 2-D horizontal advection using the wind speed in 72 vertical levels in GEOS-Chem. However, the solvers with larger coarsening factors failed to reproduce stable simulations over the vertical level with high-speed jets. Despite the mass conservation in its design principle of flux exchange, the learned solver does not guarantee monotonicity and produced negative cell scalar values when high-speed wind drives the cell scalar depletion. The negative cell clipping increased overall mass and triggered instability in the worst-case scenario. 

With this partial success, I developed the modifications needed to implement a transport operator with a large temporal coarse-graining factor. I studied ways to minimize the accuracy loss in flux-form semi-Lagrangian transport operator. I implemented a numerical algorithm walking through the cells to find the exact departure location that sends the flux to the receptor cell in the semi-Lagrangian trajectory. Instead of the conventional splitting in horizontal advection, I implemented directional splittings in x ® y and y ® x separately, and took the average tendency to guarantee 2-D monotonicity with the directional bias eliminated. To prevent cell mass depletion, I applied a mass flux limiter. In this 3-D architecture, I found the hybrid use of learned operators in the cell interface reconstruction is useful for temporal coarsening factors ³ 16. Combining these modifications, I demonstrated up to 60´ speedup with R² ³ 0.90 in the transport-only simulation, and 35´ end-to-end speedup with R² ³ 0.68 in the coupled smoke transport simulation. I believe this can have its use rather than staying in a paper, while the operator splitting error needs to be addressed in future study for even better application. 

Finally, I developed a multiscale model pipeline that couples PM2.5 emission from individual fire, plume rise, Lagrangian transport, boundary layer turbulence, Gaussian puff dispersion, and dry and wet deposition. By resolving the emission characteristics at the cluster level, which is the subset of a single fire event, my simulations reveal that death counts per tonne PM2.5 emission vary by two orders of magnitude from the median (0.03 deaths per tonne). My analysis suggests that the population in the surrounding area is a factor driving such a variation. In terms of mortality risk, the modeled PM2.5 concentration is the more important factor than the baseline mortality rate. I performed the validation of the model simulation against the ground-level observed smoke anomaly. The validation score was higher when the longer time window was applied for the time averaging of concentration. This implies that the model has insufficient skill in addressing stochastic processes, which was offset by the longer time window. With the suggested methods to improve the Lagrangian transport model, my framework will open the path to understanding the health implications of wildfire smoke in more detail from individual fire characteristics.