Analysing Tail Dependencies of Temperature in Agriculturally Active Regions Across South Africa.

V. N. Masingi${}^a$, G. L. Grobler${}^b$ and S. C. Liebenberg${}^a$

${}^a$Focus Area for Pure and Applied Analytics, North-West University, ${}^b$ Unit for Data Science and Computing, North-West University

Extreme temperature events pose significant risks to perennial crops, such as citrus, by reducing flowering at low temperatures and impairing fruit development at high temperatures. Reliable meteorological data are therefore essential for agricultural risk management. However, such datasets are often affected by missing values, measurement errors, and outliers due to technical and environmental factors, especially in agriculturally active areas. The estimation of missing extreme observations and the detection of anomalies rely on a strong dependence in the tails. However, using methods that capture dependence over the full distribution may not produce accuracy in the tails. Therefore, this study investigates the tail dependence between temperature extremes derived from agriculturally active areas in South Africa that produce citrus and other fruits. Specifically, reference temperatures measured at weather stations within these areas are compared with auxiliary observations from ERA5 and neighbouring weather stations. These comparisons are used to assess their suitability for extreme value imputation and outlier detection. This study employed two methods to analyse tail dependence, namely a naive estimation method of tail dependence coefficients and estimates from several fitted Copula models. Goodness-of-fit was assessed using likelihood-based measures computed on observations exceeding high thresholds, thereby focusing on the tails of the distribution. The study findings reveal that, for maximum temperatures, the reference observations show a considerably higher upper-tail dependence with ERA5 observations compared to the estimated lower tail dependence, suggesting an asymmetry in the dependence structure. However, this asymmetry is not as evident when comparing the estimated upper and lower tail dependencies of the reference and auxiliary weather stations. Furthermore, the results show that, where there is a strong tail dependence in the tail, the BB1 and BB7 copulas provide a good fit in the tails. This work lays the foundation for the use of copula methods to detect outliers and impute missing meteorological data.

Keywords: Tail dependence, Copulas, extreme temperature.