Multi scale copula analysis of hot–dry dependence across Australia

Compound hot–dry events can strongly affect water resources, agriculture and ecosystems, yet their stochastic structure and dependence on time-scale remain incompletely understood in many regions. This study develops a copula-based framework to quantify multiscale dependence between temperature, precipitation and a simple water-balance deficit across Australia using high quality station observations. Daily maximum and minimum temperatures from the ACORN-SAT network, daily precipitation from the Australian high quality rainfall network and annual evaporation from selected high quality pan stations are aggregated to annual, seasonal and monthly indices. Station‑level dependence is first explored using Kendall’s tau between temperature and precipitation and, where available, between temperature and a precipitation–evaporation‑based water‑balance deficit. Bivariate copulas are then fitted to pseudo observations of (), (and, at evaporation sites, (and (at each time-scale, with families selected by information criteria and uncertainty evaluated via nonparametric bootstrap. Annual τ() is moderately negative at most stations (median ≈ − 0.33), whereas annual τ() is near zero, indicating much weaker coupling of night-time temperature and rainfall. At seasonal and monthly scales, median τ() weakens and often spans zero, while τ() becomes weakly positive on average, revealing pronounced time-scale and diurnal asymmetry. At two dry, water limited case-study sites, copula-based probabilities of annual hot–dry years (90th-percentile and 10th-percentile precipitation) are around 4–5%, whereas probabilities of joint hot and high‑deficit years (90th‑percentile temperature and 90th‑percentile precipitation–evaporation‑based deficit) are below 1%, quantifying the rarity of truly hot–dry–high demand combinations under present-day climatology.