# Analyzing the Long-Term Phenological Trends of Salt Marsh Ecosystem across Coastal LOUISIANA
## Materials and Methods
### Timesat  
Although the pixels for the time-series analysis were carefully screened using the MODIS quality assurance data, the raw time-series data, as derived from the GBM composites, still showed the presence of residual noise, which was possibly generated from short-term localized environmental disturbances, or tides. However, since the GBM composites were generated using a visible band index (VARI), the tidal effect can be assumed to be minimal. We used the MATLAB-based program TIMESAT to generate a pixel-wise, noise-free time series of GBM. A number of methods have been developed to reduce noise prior to the time series, such as Fourier Series [78; 79], Best Index Slope Extraction (BISE) [47], logistic curve [80], and Savitzky-Golay filtering [48]. TIMESAT provides options to fit a smooth continuous curve to raw time-series data using asymmetric Gaussian (AG), double logistic (DL), and/or Savitzky-Golay (SG) filters. In these methods, local model functions are fitted to data in intervals around maxima and minima in the time series [48; 54]. For the AG smoothing function, the basis function becomes:  
\[g(t;x_{1},\ x_{2},\ldots,\ x_{5})=\left\{\begin{array}{ll}exp\left[-\left( \frac{t-x_{1}}{x_{2}}\right)^{x_{3}}\right],\ if\ t>x_{1}\\ exp\left[-\left(\frac{x_{1}-t}{x_{4}}\right)^{x_{5}}\right],\ if\ t<x_{1} \end{array}\right. \tag{2}\]  
Here, x\({}_{1}\) defines the position of the maximum or minimum with respect to the independent time variable t; x\({}_{2}\) and x\({}_{3}\) determine the width and kurtosis of the right half of the function; and x\({}_{4}\) and x\({}_{5}\) determine the same for the left half of the function.  
The basis function for the DL smoothing function is as follows:  
\[g(t;x_{1},\ldots,x_{4})=\frac{1}{1+exp\left(\frac{x_{1}-t}{x_{2}}\right)}- \frac{1}{1+exp\left(\frac{x_{3}-t}{x_{4}}\right)} \tag{3}\]  
where x\({}_{1}\) and x\({}_{3}\) define the position of the left and right inflection point, respectively, while x\({}_{2}\) and x\({}_{4}\) give the rate of change at x\({}_{1}\) and x\({}_{3}\), respectively. Also, for this function, the parameters are restricted in range to ensure a smooth shape [81].  
The AG and the DL filters have been found to produce similar results, with the AG filter being less sensitive to incomplete baseline time-series data [82]. We tested both filters for generating a noise-free time series, and then extracting seasonality parameters. The SG filter was not considered to be ideal for deriving a smooth time series, as it was too susceptible to localized noise in the raw phenology generated from the time-series images, and hence might provide erroneous estimates of seasonality parameters [83]. We used the Seasonal-Trend Decomposition by LOESS (STL) method to remove spikes and outliers in the time series. The STL method removes outliers by assigning weights to the values in the time series based on STL decomposition. This method does not depend on ancillary data, and is global in nature [84]. Further, we also eliminated any negative or zero values observed in the raw phenology from our analysis. We specified an adaptive upper envelope assuming any noise to be negatively biased [48; 54]. We specified an adaptation strength of two, as a stronger adaptation strength was likely to put too much emphasis on single high-data values, leading to erroneous estimates of seasonality parameters [48; 54].