AIR TEMPERATURE MEASUREMENT BASED ON LIE GROUP SO(3)

Abstract

This study aims to analyze the behaviors of air temperature during the period from 1895(5) to 2021(12) using Lie algebras method. We proposed an alternative method to model air temperature, in which the non-linear structure of temperature is evolved by a stochastic differential equation captured on a curved state space. After expressing stochastic differential equations based on Lie algebras and Lie groups, we tested the non-linear and random behavior of air temperature. This method allow a rich geometric structure. Moreover diffusion processes can easily be built without needing the machinery of stochastic calculus on manifolds.