Defense
Student: Ivan de Oliveira Franco
Program: Meteorology
Title: "FORECASTING SURFACE METEOROLOGICAL VARIABLES USING WAVELETS AND NEURAL NETWORKS AT 1-HOUR AND 7-DAY TIME SCALES"
Advisor: Prof. Dr. Humberto Ribeiro da Rocha
Judging Comitee:
- Prof. Dr. Humberto Ribeiro da Rocha - Chair and Advisor (IAG/USP)
- Prof. Dr. Alexandre Cláudio Botazzo Delbem - ICMC/USP (by videoconference)
- Prof. Dr. Rafael Cesario de Abreu - University of Oxford (by videoconference)
Other Members:
- Profa. Dra. Rosmeri Porfírio da Rocha - IAG USP
- Dr. Gabriel Martins Palma Perez - MeteolA
- Dr. Gilvan Sampaio de Oliveira - CPTEC/INPE
Abstract:
Accurate weather forecasting constitutes a fundamental scientific challenge with direct implications for agriculture, renewable energy, water resource management, and civil protection. This dissertation develops and applies multiscale wavelet analysis integrated with LSTM models for spectral characterization and prediction of meteorological variables. The approach is structured in two complementary stages: (i) spectral analysis via Continuous Wavelet Transform (CWT) for identification of characteristic oscillations, cross-relations, and coherence patterns among variables; (ii) predictive modeling using Discrete Wavelet Transform (DWT) coupled with LSTM networks, focusing on approximation coefficients that capture low-frequency components relevant for predictability. A theoretical foundation is established covering harmonic analysis, orthogonal and biorthogonal wavelet theory, Mallat's multiresolution analysis, and recurrent neural networks. The methodology is applied to five meteorological variables — air temperature, wind speed, precipitation, global solar radiation, and relative humidity — using hourly data from INMET automatic stations. Spectral analysis (CWT, WTX, WCOH) uses station A701 (São Paulo/SP) data revealing characteristic oscillations across multiple temporal scales, from diurnal cycles to seasonal variability, identifying wind-solar complementarity patterns and phase relationships among atmospheric variables. Predictive modeling is structured in two horizons: (i) 1-hour prediction (nowcasting) at station A036 (Cristalina/GO), with R² improvements demonstrating wavelet decomposition effectiveness in capturing short-term persistence; (ii) 7-day prediction (synoptic) at station A701 (São Paulo/SP) with daily aggregation, where W-LSTM models operating on approximation components (cA) obtained by DWT with db4, db6, haar, bior2.2, and bior3.3 wavelets demonstrate superiority over conventional LSTM, with improvements up to 666% in KGE for wind and exceptional performance (KGE = 0.888) for solar radiation. Comparative analysis among wavelet families evidences trade-offs among vanishing moments, phase symmetry, and approximation capability, providing variable-specific selection criteria. Contributions include: (i) theoretical-methodological framework for spectral analysis and multiscale prediction in meteorology; (ii) DWT decomposition protocol with principled selection of levels and wavelet families; (iii) identification of optimal temporal scales for weekly predictability; (iv) characterization of complementarity patterns between renewable resources via cross wavelet analysis. [cite: 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34]
Keywords: Wavelets, LSTM, Weather forecasting, Deep learning, Multiscale analysis, Neural networks, Time-frequency transforms [cite: 36]