The role of antecedent temperature in controlling extreme rainfall statistics: multi-temporal and geomorphic patterns across Northern Italy

Convective storms frequently trigger flash floods, debris flows, and urban flooding, making robust sub-hourly precipitation statistics essential for risk assessment and infrastructure design. The TENAX model (TEmperature-dependent Non-Asymptotic statistical model for eXtreme return levels) offers a physically-based framework to estimate future extreme rainfall by linking precipitation intensity to near-surface air temperature. Its standard configuration adopts a 24-hour temperature window with zero offset preceding the rainfall event, which is mainly driven by compatibility with daily climate model outputs rather than empirical optimization. Yet, its sensitivity to alternative configurations remains largely unexplored. We hereby analyze 145 rain gauges from Arpae Emilia-Romagna (106) and ARPA Lombardia (39), from the Po plains to the Alpine forelands, spanning 2003–2024, each with at least 15 years of precipitation records at 10- to 15-minute resolution. Temperature data come from VHR-REA_IT reanalysis at 2.2 km resolution. We test twelve model configurations obtained by combining three alternative window durations (1, 12, and 24 h) with four temporal offsets (0, 1, 5, and 12 h). The analysis is performed both at the annual and at the seasonal levels, and model performance is assessed through repeated split-sample validation (50–50 random temporal splits), where the optimal configuration is selected by minimizing the mean squared error with respect to empirical return levels derived using Weibull plotting positions. Our annual analysis shows that the 24 h window with 12 h offset consistently outperforms the default configuration. In contrast, seasonal analyses reveal marked differences: summer extremes show a clear preference for short (1-h) temperature windows, consistent with convective storm dynamics, whereas autumn and winter exhibit higher variability with no single dominant configuration. Moreover, we identify a statistically significant relationship (p < 0.05) between the optimal temperature window configuration and station elevation, suggesting that elevation-dependent thermodynamic and convective processes modulate the temperature–precipitation link. The findings provide practical guidance for calibrating TENAX in data-rich regions and support more physically consistent applications to future climate projections.