Climatic efficiency index (CEI): a multi-scale diagnostic for energy–water–climate interactions in semi-arid regions

Abstract Climate change and increasing demand for energy require the use of comprehensive indicators that consider atmospheric, hydrological, and energy system dynamics. Degree-day indices, such as Cooling Degree Days (CDD) and Heating Degree Days (HDD), have long been used to estimate energy demand in response to climatic variability. However, because CDD and HDD only consider near-surface air temperature, they ignore critical processes like radiative forcing, evaporative cooling, and surface energy balance, limiting their ability to fully represent climatic constraints on energy efficiency. In this study, we created and used the Climatic Efficiency Index (CEI), a compound index that combines three important components: thermal penalty, Bowen ratio, and evaporative fraction. CEI was calculated at multiple timescales (CEI-1 (monthly), CEI-3 (three-monthly), CEI-6 (semi-annual), and CEI-12 (annual) and compared to degree-day indicators using data from Southeastern Anatolia (1950–2024). The results show a strong positive correlation between CEI and CDD (ρ > 0.90) and a strong negative correlation with HDD (ρ < −0.85) at short timescales (CEI-1). However, the magnitude of these correlations decreases at longer time scales, reflecting the smoothing of climatic variability over multi-month periods. Despite this attenuation, significant associations persist at all scales, confirming CEI's robustness as an energy-climate indicator. From an energy standpoint, CEI is a more comprehensive and mechanistic measure than CDD alone, as it explains why and under what climatic conditions energy stress occurs. By combining evaporative and radiative dynamics, CEI can capture both immediate thermal stress and long-term climatic inefficiencies, connecting energy demand to drought processes and climate change impacts. This makes CEI an important addition to the water-energy-climate nexus, providing new insights into energy system planning and adaptation in semi-arid areas.