I study the physics of clouds, which is one of the most complex processes to accurately simulate in a global weather model. I applied mathematical tools to reproduce the physical processes in a cost effective way to avoid running expensive models. I have developed a novel forecast system, which has the ability to run low cost simulations and quantify the model uncertainties in a seamless fashion.
A more technical description of my PhD research:
I focus on quantifying the uncertainties of model cloud physics with the tools : stochastic spectral
method (i.e., Polynomial Chaos Expansion (PCE) with Dimension Adaptive Sparse Quadrature (DASQ) rules), Bayesian inference
(using Delayed Rejection Adaptive Metropolis (DRAM) MCMC), Sobol global sensitivity analysis, clustering method (e.g., Heirarchi-
cal Cluster Analysis (HCA), k-means/k-medoids clustering, etc), spectral methods (e.g., PCA, Rotated EOF, FFT, discrete Chebyshev
transform, etc), and stochastic process parameterization.