Spatially and temporally complete Landsat reflectance time series modelling: The fill-and-fit approach

Statistical time series models are increasingly being used to fit medium resolution time series provided by satellite sensors, such as Landsat, for terrestrial monitoring. Cloud and shadows, combined with low satellite repeat cycles, reduce surface observation availability. In addition, only a single year of data can be used where there is high inter-annual variation, for example, over many croplands. These factors reduce the ability to fit time series models and reduce model fitting accuracy. In solution, we propose a novel fill-and-fit (FF) approach for application to medium resolution satellite time series. In the 'fill' step, gaps are filled using a recently published algorithm developed to fill large-area gaps in satellite time series using no other satellite data. In the 'fit' step, a linear harmonic model is fitted to the gap-filled time series. The FF approach, and the conventional harmonic model fitting without gap filling, termed the F approach, are demonstrated using seven months of Landsat-7 and -8 surface reflectance Analysis Ready Data (ARD) over agricultural regions in North Dakota, Minnesota, Michigan, and Kansas. Synthetic model-predicted reflectance for days through the growing season are examined, and assessed quantitatively by comparison with an independent Landsat surface reflectance data set. The six Landsat reflective band root-mean-square difference (RMSD) between the predicted and the independent reflectance, considering millions of pixel observations for each ARD tile, show that the FF approach is more accurate than the F approach. The mean FF RMSD values varied from 0.025 to 0.026 for the four tiles, whereas the mean F RMSD values varied from 0.026 to 0.047. These mean FF RMSD values are< 0.03 which is comparable to the uncertainty specification for the Landsat 8 OLI TOA reflectance, but greater than the atmospheric correction uncertainty in any Landsat 8 OLI band. The greatest RMSD values were found over the Minnesota tile and occurred due to a long period of missing data early in the growing season, and the smallest RMSD values were found for the Kansas tile because of the high availability of clear surface observations. The F approach could not be applied where there were insufficient clear surface observations to fit the model, and where the model was applied, the fitting was often sensitive to issues including gaps in the Landsat time series and the presence of undetected cloud- and shadow-contaminated observations. The FF approach could be applied to every ARD tile pixel location and the predicted reflectance was spatially-coherent and natural looking. Examples are shown that illustrate the potential of using FF predicted synthetic reflectance time series for land surface monitoring.