Angular Instability of Daylight Glare in Kinetic Façades: A Climate-Dependent Nonlinear Threshold Framework Across Five Cities

Kinetic louvre façades in high Direct Normal Irradiance (DNI) climates exhibit sharp, non-monotonic transitions in Daylight Glare Probability (DGP) that conventional monotonic models cannot represent. This study introduces the Glare Critical Threshold (GCT), defined as the louvre angle (θ*) at which the absolute angular gradient of DGP (|dDGP/dθ|) is maximized and exceeds the perceptual just-noticeable criterion (δcrit = 0.020/°). A validated predictive framework was developed using approximately 214 Radiance simulations across seven cities spanning the BWh/BSk to Cfb climate gradient. GCT behavior—an abrupt DGP shift from imperceptible (<0.35) to intolerable (>0.45) was identified in five arid-zone cities (Yazd, Tehran, Cairo, Las Vegas, Baghdad; DNI 420–932 W/m²). City-specific threshold angles ranged from 13° to 49°. A four-parameter logistic (4PL) model achieved strong predictive performance (R² = 0.90–0.97), outperforming Gaussian and linear models by 1.5–2.5× in RMSE. Peak angular sensitivities (0.018–0.122 DGP/°), up to six times the perceptual threshold, indicate that typical actuator errors (±2°–5°) can trigger full glare category transitions. GCT positions remained stable within ±2°–3° between 14–28 December, supporting once-per-season calibration. Madrid and London exhibited no GCT behavior (DGP <0.35 at all angles), establishing a climatic boundary at DNI <600 W/m² and latitude >40°N. A polynomial control law (R² = 0.73, RMSE = 8.6°) enables real-time GCT prediction using a single pyranometer, offering a low-complexity, physically interpretable control strategy for kinetic façade automation in high-DNI regions.