Annual Mean Temperature and Rain Precipitation in North America Using NHPP to Detect Climate Changes
Jorge Alberto Achcar
Ribeir ˜ao Preto Medical School, University of S˜ao Paulo, Ribeir ˜ao Preto - S˜ao Paulo, Brazil.
Eliane R. Rodrigues
Instituto de Matem´ aticas, Universidad Nacional Autonoma de Mexico, Area de la Investigacion Cientifica, Circuito Exterior - Ciudad Universitaria, Ciudad de Mexico 04510, Mexico.
Ricardo Puziol de Oliveira
State University of Maring ´ a, Maring ´ a, Paran´ a, Brazil.
Emerson Barili *
Ribeir ˜ao Preto Medical School, University of S˜ao Paulo, Ribeir ˜ao Preto - S˜ao Paulo, Brazil.
*Author to whom correspondence should be addressed.
Abstract
In this study, non-homogeneous Poisson processes (NHPP) are assumed to analyze annual average temperatures and rain precipitations, considering climate data for some regions of North America reported for a long period. A power law process (PLP) is assumed for the intensity function (derivative of the mean value function) or rate \(\lambda\) (t), t \(\ge\) 0 of the NHPP which the Poisson events occur considering data (accumulated number of years in a given time interval [0,t) where the climate measure is above a threshould given by the overal average in the assumed period) in presence or not of a change-point. The parameters of the assumed model are estimated under a Bayesian approach and using MCMC (Markov Chain Monte Carlo) methods. Alternatively to the use of a PLP process, we also assume a polynomial parametrical form for the mean value function of the NHPP process where a simple Bayesian inference approach is proposed to get better fit for the intensity and mean value functions of the NHPP process. From the fitted models it was possible to to detect the years where climate changes occurred.
Keywords: Climate change, non-homogeneous poisson processes, PLP process, polynomial mean value function, bayesian inference, change-point, MCMC methods