A copula based bi-variate model for temperature and rainfall processes

Abstract

Rainfall and temperature remain the two major climatic parameters influencing agriculture productivity, meteorology and weather related industries. It is known that accurate analysis and simulation of temperature and rainfall processes is difficult due to the interdependence between them. This study provides an alternative approach by modeling rainfall and temperature processes using Frank copula from Archimedean family to derive a bi-variate model and measure the dependence between them. The copula approach is flexible in that it enables independent modeling of marginal behavior and dependence between the variables besides providing information on both the structure and degree of dependence. The study used historical daily rainfall and daily average temperature data for 20 years covering the period from 1995 to 2015 collected by Malawi’s meteorological services for Balaka district. Results of the study indicate that temperature and rainfall are positively correlated based on Kendall tau correlation test. Using the derived bi-variate model we simulated daily average temperature and daily rainfall data which behaved same way as the actual data.

Keywords

• Rainfall
• Temperature
• Dependence
• Copula
• Frank copula
• Archimedean family