# Mapping Paddy Rice in China in 2002, 2005, 2010 and 2014 with MODIS Time Series
## 3 Data and Methods
### Time Series Creation and Feature Extraction  
The two MODIS 16-day composites are delivered with an eight-day shift between them, which we used to combine both into synthetic time series with eight-day intervals spanning 46 observations and alternating MOD13Q1 and MYD13Q1 data. This approach introduces the issue that pixel values from one scene might be from a later day of the year than the one of the following scene. With the compositing algorithm used to generate the MODIS products, this is seldom the case; however, we still decided to derive metrics from the time series that are mostly independent of these possible temporal overlaps. Calculation of the local extrema is influenced by this error source; therefore, we decided to use only their sum as a feature in our classification and disregard their temporal position in the time series. This approach is different to most time series-based rice classifications, which capitalize on the temporal position of distinctive water or vegetation index peaks. Each layer has been stored in its own Time Series (TS), denoted as TS\({}_{\text{NDVI}}\), TS\({}_{\text{EVI}}\), TS\({}_{\text{Fed}}\), TS\({}_{\text{NIR}}\), TS\({}_{\text{blue}}\), TS\({}_{\text{MIR}}\) and TS\({}_{\text{LSWI2130}}\). From these time series, we extracted the following features as the input of our classification (Table 1).  
All features were calculated along the temporal axis of the time series. The percentiles were defined as the value in the time series below which the given percentage of observations fall. The amplitude was calculated as the difference between the largest and the smallest value in a time series. Prior to the calculation of the local maxima and minima, the gaps in the time series, resulting from the pixel reliability mask, have been linearly interpolated. Should the temporal gap exceed three consecutive values, no interpolation and smoothing were applied. In the next step, TS\({}_{\text{EVI}}\) was  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Feature** & **Input Time Series** \\ \hline
10 th percentile & TS\({}_{\text{EVI}}\)1, TS\({}_{\text{Fed}}\)2, TS\({}_{\text{NIR}}\)3, TS\({}_{\text{blue}}\)4, TS\({}_{\text{MIR}}\)5, TS\({}_{\text{LSWI2130}}\)6 \\
25 th percentile & TS\({}_{\text{EVI}}\), TS\({}_{\text{Fed}}\), TS\({}_{\text{NIR}}\), TS\({}_{\text{blue}}\), TS\({}_{\text{MIR}}\), TS\({}_{\text{ISWI2130}}\)50 th percentile/median & TS\({}_{\text{EVI}}\), TS\({}_{\text{Fed}}\), TS\({}_{\text{NIR}}\), TS\({}_{\text{blue}}\), TS  
smoothed with a Savitzky-Golay filter with a window length of five (including the center value) and a second order polynomial, which is commonly applied in time series analysis of vegetation indices [62]. The interpolated time series were used as input for the local extrema calculation. Local maxima have been defined as the values in the time series that are larger than the three observations prior and the three observations after them while also exceeding the given threshold. Local minima are the inverse and have to be below the given threshold. The amount of observations along the temporal axis that fulfill these criteria was then counted. The EVI and LSWI\({}_{2130}\) inversions have been defined as the amount of observations where the value of the TS\({}_{\text{EVI}}\) exceeds 0.45 and double the value of TS\({}_{\text{LSWI2130}}\). This feature is similar to the EVI-LSWI inversion rice classification approach employed by [PERSON] _et al._[13; 23; 24], although they calculated LSWI with the short-wave-infrared band with a wavelength from 1628 nm-1652 nm, which is not available in the MOD13Q1/MYD13Q1 datasets. In total, we calculated 64 features from our input time series giving special consideration to the features being robust in regard to the possible temporal overlap in our synthetic eight-day time series.