Proportional discrete Fourier analysis of WaPOR actual evapotranspiration and interception over cropland in Comayagua, Honduras

Abstract

Purpose: Positive agronomic variables are often interpreted using ratios and relative seasonal contrasts. This study examines whether annual seasonality remains dominant when WaPOR actual evapotranspiration and interception (AETI) is centered proportionally rather than additively. Methods: A monthly series was extracted for January 2018–December 2025 from cropland-screened WaPOR version 3 Level 1 cells within Comayagua, Honduras. The screen combined the Food and Agriculture Organization (FAO) Global Administrative Unit Layers (GAUL) 2015 first-level boundary with European Space Agency (ESA) WorldCover 2021 class 40. For each month, dekadal values were averaged with equal weight within each cell, after which the spatial median was calculated across 1,094 valid WaPOR cells. A representative proportional spectrum was computed as the unitary discrete Fourier transform of the centered logarithmic series and compared with the transform of the centered original series. Results: All 96 monthly observations were strictly positive. The geometric mean was 2.4571 mm day^-1. The dominant proportional coefficient occurred at k = 8, the annual bin, with A_p(8) = 1.3549; the semiannual coefficient was A_p(16) = 0.5252. These bins accounted for 72.41% and 10.88% of one-sided proportional power. The direct spectrum was also dominated by k = 8. Conclusions: Proportional spectral analysis provides a unit-invariant characterization of relative AETI variability. It does not represent a different Fourier algorithm, but it distinguishes multiplicative deviations from absolute water-flux amplitudes.