A nonlinear harmonic model for fitting satellite image time series: Analysis and prediction of land cover dynamics

Hugo Carrão, Paulo Gonçalves, Mário Caetano

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)


Numerous efforts have been made to develop models to fit multispectral reflectance and vegetation index (VI) time series from satellite images for diverse land cover classes. The common objective of these models is to derive a set of measurable parameters that are able to characterize and to reproduce the land cover dynamics of natural-and human-induced ecosystems. Good-fitting models should therefore match different waveforms and be insensitive to sharp and localized variations, generally due to atmospheric disturbances. In this paper, we propose a modelbased approach to identify and predict important dynamics for indiscriminate land cover classes. Our method relies on an original nonlinear harmonic model that remarkably matches intraannual time series of multispectral reflectances and VIs obtained from satellite images. The proposed model is characterized by the following: 1) parsimonious, comprising only five parameters; 2) readily identifiable (in the maximum likelihood sense) from only few observations; 3) robust to noise; and 4) versatile, since it can reproduce a wide variety of intra-annual land cover dynamics as a deterministic function of time. To demonstrate the relevance of our approach, we use a time series of Moderate Resolution Imaging Spectroradiometer eight-day composite images acquired in Portugal over a one-year period at a 500-m nominal spatial resolution. For 13 different land cover classes, which are representatives of Mediterranean landscapes, we evaluate the data-model adequacy of our model and compare it with several other approaches. We then address a particularly interesting and promising application of our method using rice crops and shrublands as case studies. We not only show that phenological attributes can be accurately estimated from the fitted time series, but we also demonstrate that it is possible to make early predictions of phenological attribute dates and magnitudes from our expected model adjusted to only few anterior observations.

Original languageEnglish
Article number5345879
Pages (from-to)1919-1930
Number of pages12
JournalIeee Transactions On Geoscience And Remote Sensing
Issue number4 PART 2
Publication statusPublished - 1 Jan 2010


  • Curve fitting
  • Intra-annual dynamics
  • Land cover
  • Nonlinear harmonic model
  • Phenology
  • Prediction
  • Remote sensing
  • Time series


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