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

Abstract

Diurnal temperature range is an important variable in climate science that canprovide information regarding climate variability and climate change. Changesindiurnaltemperaturerangecanhaveimplicationsforhydrology,humanhealthand ecology, among others. Yet, the statistical literature on modeling diurnaltemperature range is lacking. In this article we propose to model the distri-bution of diurnal temperature range using the five-parameter lambda (FPL)distribution. Additionally, in order to model diurnal temperature range withexplanatory variables, we propose a distributional quantile regression modelthat combines quantile regression with marginal modeling using the FPL distri-bution. Inference is performed using the method of quantiles. The models arefitted to 30 years of daily observations of diurnal temperature range from 112weather stations in the southern part of Norway. The flexible FPL distributionshows great promise as a model for diurnal temperature range, and performswell against competing models. The distributional quantile regression model isfitted to diurnal temperature range data using geographic, orographic, and cli-matological explanatory variables. It performs well and captures much of thespatial variation in the distribution of diurnal temperature range in Norway.