Hybrid mssa-geostatistical approach to spatio-temporal interpolation of meteorological variables: The case of the Meric-Ergene Basin

Abstract

This thesis examines the critical challenge of obtaining accurate and continuous climate records, which are essential for hydrological modeling, disaster management, and sustainable water resource planning in regions such as the Meriç-Ergene Basin. The primary issue arises from the inherent difficulties of meteorological observation, including sparse monitoring networks and the complex spatio-temporal characteristics of variables such as daily maximum and minimum temperatures and total daily precipitation. Traditional interpolation methods are limited because they treat simultaneous measurements independently and do not account for natural temporal evolution, long-term trends, or seasonal fluctuations within climate data. This research develops and evaluates a robust hybrid statistical framework for spatio-temporal interpolation of point meteorological measurements. The primary methodological innovation integrates the time-series analysis capabilities of Multivariate Singular Spectrum Analysis (MSSA) with the spatial estimation strengths of geostatistical techniques, including Inverse Distance Weighting (IDW), Radial Basis Function (RBF), and Kriging. The approach is systematic: MSSA is first applied to decompose multivariate time-series data from 20 stations in the Meriç-Ergene Basin, extracting dominant temporal patterns such as nonlinear trends and periodicities. Subsequently, the spatial distribution of the resulting eigenvectors is modeled using the selected geostatistical methods. This process enables reconstruction of underlying signals through Reconstructed Components (RCs), which are then used to generate synthetic time series and accurately fill missing data at locations without measurement stations, such as test station 18096 in Lalapaşa. The efficacy of this combined approach is rigorously evaluated using performance metrics, including Root Mean Square Error (RMSE), to demonstrate a more robust spatio-temporal predictive model compared to existing methods. Additionally, Cluster Analysis (CA) is employed to identify homogeneous climatic regions within the basin, supporting network design and regionalization. The research produced three principal conclusions regarding the performance of the hybrid model: Efficacy of the Hybrid Model: The integration of MSSA's temporal pattern extraction with geostatistical methods for spatial modeling demonstrates a powerful, data-adaptive alternative to static interpolation. This framework effectively reconstructs the continuous spatio-temporal field of the meteorological variables. Model performance varies according to the type of meteorological variable: Continuous Variables (Temperature): For daily maximum and minimum temperatures, the hybrid approach achieved high success, with spatial interpolation rates exceeding 90% using only two nearby stations. Notably, the Root Mean Square Error (RMSE) for temperature decreased as the MSSA sliding window size (M) was varied, confirming the effectiveness of temporal decomposition for continuous data. Discontinuous Variables (Precipitation): Precipitation, characterized by its intermittent and non-continuous structure, presented greater challenges. Reliable spatial representation required a denser monitoring network, with six to seven nearby stations necessary to maintain high logical success. Unlike temperature, the RMSE for precipitation increased with variations in M, indicating greater difficulty in modeling its complex temporal structure. Framework, by isolating and filtering stochastic noise to reconstruct dominant signals, failed to accurately capture extreme meteorological values (both peaks and troughs). This constraint inherently limits the model's direct applicability in specific high-stakes fields, such as flood and drought risk assessment, where the fidelity of extreme-event simulation is a paramount requirement. In summary, the thesis validates the hybrid MSSA-Geostatistical framework as a viable method for enhancing the integrity of basin-level climate records. It also provides data-driven recommendations for optimal parameter selection and monitoring network density, tailored to the distinct spatio-temporal behavior of continuous and discontinuous meteorological variables.