Improving daily rainfall estimation from NDVI using a wavelet transform

Quantifying rainfall at spatial and temporal scales in regions where meteorological stations are scarce is important for agriculture, natural resource management and land-atmosphere interactions science. We describe a new approach to reconstruct daily rainfall from rain gauge data and the normalized difference vegetation index (NDVI) based on the fact that both signals are periodic and proportional. The procedure combines the Fourier Transform (FT) and the Wavelet Transform (WT). FT was used to estimate the lag time between rainfall and the vegetation response. Subsequently, third level decompositions of both signals with WT were used for the reconstruction process, determined by the entropy difference between levels and R2. The low-frequency NDVI data signal, to which the high frequency signal (noise) extracted from the rainfall data was added, was the base for the reconstruction. The reconstructed and the measured rainfall showed similar entropy levels and better determination coefficients (>0.81) than the estimates with conventional statistical relations reported in the literature where this level of precision is only found for comparisons at the seasonal levels. Cross-validation resulted in 10% entropy differences, compared to more than 45% obtained for the standard method when the NDVI was used to estimate the rainfall in the same pixel where the weather station was located. This methodology based on high resolution NDVI fields and data from a limited number of meteorological stations improves spatial reconstruction of rainfall. 2010 Elsevier Ltd. All rights reserved.