Abstract: This study presents a multi-temporal analysis of displacement data from Sentinel-1 Synthetic Aperture Radar data at Hurst Castle with datasets sourced from the European Ground Motion Service, and temperature records from Ventnor Park and Otterbourne, with datasets sourced from the CEDA archive. To reduce speckle noise inherent in Synthetic Aperture Radar time series, three speckle filtering techniques, Boxcar, Lee, and Frost, were applied. The filtered displacement and temperature data were modelled using a range of mathematical functions, linear, quadratic, sinusoidal, step function, phenomenological, exponential, Lagrangian, and higher-order polynomial models. Model performance was evaluated using a comprehensive set of error metrics, including Root Mean Squared Error, Least Mean Squares, Sum of Squared Errors, Akaike Information Criterion, and Bayesian Information Criterion. Further regression analysis involved Median Absolute Error, Mean Absolute Percentage Error, Symmetric Mean Absolute Percentage Error, coefficient of determination, adjusted coefficient of determination, and the Durbin–Watson statistic to assess autocorrelation in residuals. The best fitting models were determined based on the coefficient of determination and Durbin– Watson values to evaluate the robustness of model selection across different filters and data sources. The study underscores the importance of integrating displacement and temperature time series modelling for environmental monitoring and structural risk assessment at heritage sites.

Keywords: Remote satellite sensing, Synthetic Aperture Radar, time series analysis, speckle filtering, multi-temporal monitoring, coastal heritage, mathematical modelling

Pages: 1343-1359