Radial Basis Function Finite Difference Methods
RBF-FD Methods are an extension of spectral methods which solve partial differential equations but return to principles of standard finite difference methods for inspiration. The principle appeal of RBF-FD Methods is that they are meshless and easily scalable on supercomputing systems. In particular, they feature applications to geophysical flow problems, relevent to my interests in climate modeling and numerical weather prediction, but still applicable to many other issues from porous flow modeling to machine learning.

Monsoon Dynamics and Intraseasonal Oscillations
Numerical weather predition and climate models rely on complex interconnected models which solve for the present and future atmospheric and oceanic states. Despite the many decades of work improving these models, monsoons remain largely unpredictable compared to other disaster relevent events like hurricanes. Considering the significance seasonal monsoons have on people's livelihoods and agriculture production, further studying the monsoon is of upmost importance. An observed phenonema that could shed some light on complex monsoon dynamics include the Monsoon Intraseasonal Oscillations (MISO). Weather data and satellite imagery highilght a wave like propogation pattern measurable in the Indian subcontinent which follows the active-break cycle throughout the monsoon season. However, the cause of these atmospheric waves are not fully understood but are hypothesized to result from interactions of Rossby and Kelvin waves. Other influences on these wave dynamics which remain to be fully understood include complex mountainous orography and air-sea interactions. A goal of my research is to recreate this MISO phenomena in cutting edge atmospheric Numerical Weather Prediction (NWP) computational models. Then, with the use of these models, we could more accurately pinpoint the factors contributing to monsoon variability, perhaps paving the way for relaible seasonal forecasts of monsoon precipitation. From there it remains to incorporate this understanding into coordinating improved response systems for policy makers and governments.