Quantile based modelling of diurnal temperature range with the five-parameter lambda distribution

Diurnal temperature range is an important variable in climate science that can provide information regarding climate variability and climate change. Changes in diurnal temperature range can have implications for hydrology, human health and ecology, among others. Yet, the statistical literature on modelling diurnal temperature range is lacking. In this paper we propose to model the distribution of diurnal temperature range using the five-parameter lambda (FPL) distribution. Additionally, in order to model diurnal temperature range with explanatory variables, we propose a distributional quantile regression model that combines quantile regression with marginal modelling using the FPL distribution. Inference is performed using the method of quantiles. The models are fitted to 30 years of daily observations of diurnal temperature range from 112 weather stations in the southern part of Norway. The flexible FPL distribution shows great promise as a model for diurnal temperature range, and performs well against competing models. The distributional quantile regression model is fitted to diurnal temperature range data using geographic, orographic and climatological explanatory variables. It performs well and captures much of the spatial variation in the distribution of diurnal temperature range in Norway.