Appropriate Copula Investigation for Modeling Dependence Structure of Troposperic Delay Data in the Mountainous Area of Central Europe

Abstract

Troposphere is the lowest and one of the most complex layers of the Earth's atmosphere from the electromagnetic signal travelling point of view. Electromagnetic signals in travelling through this medium are affected and received by a delay in receivers. In GNSS applications, regardless of treating the impact as a signal or noise, it has to be modeled efficiently. To this end, the problem is firstly discretized in space and time.To adopt an appropriate time and spatial resolution for the model, a-priori information on the dependence structure of the input data is inevitable. This study applies Copula as a mathematical tool for modeling the dependence structure of the Zenith Tropospheric Delays (ZTD). For this purpose, four of the most common Archimedean Copulas, i.e. Frank, Clayton, Gumbel and Ali-Mikhail-Haq (AMH) are used. In this research, south-east of Germany together with the neighboring areas in Czech Republic and Austria are selected as the study region. For this evaluation, hourly time series of ZTDs from April to October 2016 are calculated using three dimensional meteorological parameters extracted from the Weather Research and Forecast (WRF) model. Appropriate Copula is detected by two common criteria, i.e. Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The obtained results in most cases suggest Gumbel Copula for the test field. This Copula is asymmetric and exhibits tail dependence, especially the upper form within the input data. This implies tropospheric delays are more associated when approaching the larger values. Moreover, the results approve that the Pearson correlation is not always an appropriate measure for analyzing the dependence structure in the local scale troposphere modeling. Also, the obtained results emphasize on the necessity of applying a dynamic model based on the dependence structure of tropospheric delays.