Roy, DP; Yan, L (2020). Robust Landsat-based crop time series modelling. *REMOTE SENSING OF ENVIRONMENT*, 238, 110810.

**Abstract**

Reliable satellite monitoring of agriculture is often difficult because surface variations occur rapidly compared to the cloud-free satellite observation frequency. Harmonic time series models, i.e., superimposed sequences of sines and cosines, have an established provenance for fitting satellite vegetation index time series to coarse resolution satellite data, but their application to medium resolution Landsat data for crop monitoring has been limited. Non-linear harmonic models have been shown to perform well over agricultural sites using single-year Moderate Resolution Imaging Spectroradiometer (MODIS) time series, but have not been explored with Landsat data. The 2017 availability of Landsat Analysis Ready Data (ARD) over the United States provides the opportunity to investigate the utility of temporally rich Landsat data for 30m pixel-level crop monitoring. In this paper, the capability of 5- and 7-parameter linear harmonic models and a 5-parameter non-linear harmonic model applied to a year of Landsat 5 Thematic Mapper (TM) and Landsat 7 Enhanced Thematic Mapper Plus (ETM+) ARD is investigated. The analysis is undertaken over six sites, each defined by a 5000x5000 30m pixel ARD tile, that together include the major conterminous United States (CONUS) crops identified by inspection of the United States Department of Agriculture (USDA) Cropland Data Layer (CDL). The model fits are evaluated as the root mean square difference (RMSD) between the fitted and the observed Landsat data. Considering locations with at least 21 annual Landsat observations, the 7-parameter linear harmonic model (tile mean crop NDVI RMSD values ranging from 0.052 to 0.072) and the 5-parameter non-linear harmonic model (tile mean crop NDVI RMSD values ranging from 0.054 to 0.074) are shown to be able to fit annual Landsat NDVI time series for most CONUS crops, whereas the 5-parameter linear harmonic model cannot (tile mean crop NDVI RMSD values ranging from 0.072 to 0.099). If there are between 15 and 20 annual Landsat observations, the 5-parameter non-linear harmonic model is recommended for fitting annual NDVI crop time series, and if there are >= 21 observations, then either the 5-parameter non-linear or the 7-parameter linear model can be used. The 7-parameter model had marginally smaller mean NDVI RMSD values but larger standard deviations than the 5-parameter non-linear model, likely due to the relative robustness of the non-linear model to over-fitting and oscillations. None of the models could reliably fit crops with multiple stages, such as alfalfa, that are insufficiently sampled using combined Landsat 5 TM and Landsat 7 ETM+ time series. Given the utility of the growing season peak NDVI for crop yield applications, the date and magnitude of the model fitted peak NDVI are compared to quantify model reporting differences. The differences between the 7-parameter linear and the 5-parameter non-linear harmonic models are not large. For each ARD tile, the mean absolute differences in the estimated peak NDVI days varied from < 2 days in the northern ARD tiles, which had short growing seasons and similar crops, to less than a week for the other tiles except for nearly 10 days for the California tile that had longer growing seasons and more diverse crops including crops with multiple stages. The paper concludes with a discussion and recommendations for future research.

**DOI:**

10.1016/j.rse.2018.06.038

**ISSN:**

0034-4257