Robust doubly censored Weibull modelling of NDVI-based burn-scar persistence in satellite time series

Abstract. Burn-scar persistence in satellite imagery is treated as a lifetime process and modelled within a doubly censored Weibull framework arising from the finite temporal extent of satellite archives. Episodes may appear doubly censored in calendar time because the Landsat record spans a limited analysis window, so that for some pixels neither the true ignition time nor the full recovery are directly observed. On the persistence-time scale used for inference, incomplete episodes contribute as right-censored lifetimes within a unified likelihood formulation. A robust weighted-likelihood estimator with Huber-type influence weights downweights atypically long-lived scars without excluding any observations, thereby limiting the impact of outliers while preserving the central structure of the persistence distribution. The framework is applied to NDVI-based burn-scar persistence derived from Landsat surface-reflectance time series at Monitoring Trends in Burn Severity (MTBS) sampling locations within a large interior-Alaska fire scar, yielding a sample of 90 persistence episodes comprising fully observed and right-censored lifetimes. Weibull parameters are estimated under both maximum likelihood and weighted likelihood, with parametric bootstrap resampling used to obtain confidence intervals. Agreement between model-based and empirical survival behavior is assessed using Kaplan–Meier and Turnbull estimators and a Weibull probability plot. The fitted model indicates a median persistence of approximately 2.7–2.9 years and a 90th-percentile persistence of roughly five to six years, with the Weibull shape parameter consistently exceeding one, indicating an increasing recovery hazard over time. The proposed framework combines interpretability and robustness under censoring and generalizes naturally to other persistence-type environmental processes observed under incomplete monitoring.