Nonlinear time series temperature modeling based on normal form

¹ NanoTrans solutions - Ruth 8, str., Haifa, Israel
² Financial Engineering Laboratory, Faculty of Industrial Engineering, Technion - Israel Institute of Technology Technion City, Haifa, Israel

^(a) yrosenstein@gmail.com

Received: 8 April 2013
Accepted: 16 January 2014

Abstract

In this work nonlinear modeling of surface temperature is performed. To this end, we derive a simple physical model based on the reduction of Navier-Stokes-Boussinesq equations in rotating coordinates. The model is fit against low-pass embedding filtered real data from 10 stations in Europe and the near East. Using a learning set of 14000 points and forecasting 300 points forward, we obtain a good fit for 300 days ahead. Two key results are the reduction of a weather model to a six-dimensional center manifold that captures the main dynamics, and demonstration of nonlinearity in the time series is established through embedology.