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Instituto de Ingeniería Matemática

Facultad de Ingeniería

Ingeniería Civil Matemática certificada por 3 años hasta Diciembre de 2026

Alonso Nicolás Lagos Orellana


Thesis Advisor

  • Karine Bertin

Co-Advisor

  • Lisandro Fermín
  • Andrea Jiménez

Resumen

The increasing frequency of extreme weather events, fire rates, and energy demand in recent decades has led to the need to study climate variables in local spatial areas to generate solutions to these problems. This work seeks to implement a statistical downscaling scheme for wind intensity fields in the Valparaíso region, which integrates a space-time weighted regression (GTWR) model to estimate nested grids of Weather Research and Forecasting (WRF) models (3 km → 1 km → 1/3 km). The method relies on local assumptions of spatial regularity, spatial homogeneity, spatial self-similarity, and stationarity of the residuals. To this end, non-parametric scaling factors are calibrated using weighted least squares (WLS) with a space-distributional kernel. Next, real-world wind intensity fields at 3 km and 1 km resolutions, obtained from WRF models (73 hourly time measurements between September 2, 2023, and September 5, 2023) with a spatial domain in the Valparaíso region (East-West latitude coordinates −33.43985 and −32.88078, and North-South longitude −71.89282 and −70.93353), were considered. For the real-world data, the topographic zones of sea, valley, and mountain were classified using a Farthest Neighbor (FPC) algorithm based on the distributional distances of the absolute difference in variations. Then, the GTWR model was applied between 3 km and 1 km fields to recover the scale factors, obtaining excellent predictive capacity in the sea and valley zones (low MSE and high coefficients of determination for space and time). However, the GTWR model shows difficulties adapting to local topography in mountainous areas (high mean square error and low-to-intermediate coefficient of determination for both space and time). The scheme is finalized by applying scaling factors to obtain the target wind field at 1/3 km, where the prediction improves spatial resolution at 1/3 km by capturing changes in wind intensity, from slight local increases in areas of greater homogeneity (sea and valley) to large increases in areas of greater topographic variability (mountains). It is concluded that the GTWR model is computationally efficient and shows high predictive capacity for spatial areas where the topography is of slight or medium variation, while in areas of high topographic variability, the model overfits the change in scale in the time series. This behavior is possibly due to the increased spatial heterogeneity when applying spatial downscaling in mountainous areas. To improve the effectiveness of the GTWR model, it is recommended to: implement a model by topographic zones, calibrate window widths by cluster and/or by a spatio-temporal method, and study the incorporation of new covariates into the model (wind direction, temperature, height variable, among others).