Harmonic regression of Landsat time series for modeling attributes from national forest inventory data

Barry T. Wilson, Joseph F. Knight, Ronald E. McRoberts

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


Imagery from the Landsat Program has been used frequently as a source of auxiliary data for modeling land cover, as well as a variety of attributes associated with tree cover. With ready access to all scenes in the archive since 2008 due to the USGS Landsat Data Policy, new approaches to deriving such auxiliary data from dense Landsat time series are required. Several methods have previously been developed for use with finer temporal resolution imagery (e.g. AVHRR and MODIS), including image compositing and harmonic regression using Fourier series. The manuscript presents a study, using Minnesota, USA during the years 2009–2013 as the study area and timeframe. The study examined the relative predictive power of land cover models, in particular those related to tree cover, using predictor variables based solely on composite imagery versus those using estimated harmonic regression coefficients. The study used two common non-parametric modeling approaches (i.e. k-nearest neighbors and random forests) for fitting classification and regression models of multiple attributes measured on USFS Forest Inventory and Analysis plots using all available Landsat imagery for the study area and timeframe. The estimated Fourier coefficients developed by harmonic regression of tasseled cap transformation time series data were shown to be correlated with land cover, including tree cover. Regression models using estimated Fourier coefficients as predictor variables showed a two- to threefold increase in explained variance for a small set of continuous response variables, relative to comparable models using monthly image composites. Similarly, the overall accuracies of classification models using the estimated Fourier coefficients were approximately 10–20 percentage points higher than the models using the image composites, with corresponding individual class accuracies between six and 45 percentage points higher.

Original languageEnglish (US)
Pages (from-to)29-46
Number of pages18
JournalISPRS Journal of Photogrammetry and Remote Sensing
StatePublished - Mar 2018

Bibliographical note

Funding Information:
This research was supported by the USDA Forest Service, Northern Research Station. The authors are grateful to Mark D. Nelson for helpful comments on an earlier version of this manuscript.

Publisher Copyright:
© 2018


  • Classification models
  • Harmonic regression
  • Image compositing
  • Landsat time series
  • National forest inventory
  • Regression models


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