# Empirical Approach for Modelling Tree Phenology in Mixed Forests Using Remote Sensing
## 1 Introduction  
Reliable phenological observations, achieved through either direct visual human observations in phenology networks, near-surface measurements using phenology cameras and unmanned aerial vehicles, or remote sensing via satellites [1], are important for anticipating the effects of climate change on tree phenology in forests. In fact, tree phenological phases mirror environmental conditions and thus can respond to variations in climate, making them good indicators of the effects of climate change when long series of phenological observations exist, as they can reveal some trends in the timing of spring and autumn phenological events [2, 3]. Long-term phenological observations in trees, including spring events such as leaf unfolding and autumnal events of leaf colouring, have shown that a rise in global temperature generally leads to earlier timing of spring events [4, 5, 6]. Leaf phenology is a majordeterminant of water and CO\({}_{2}\) fluxes, and several studies clearly showed that growing season length controls net ecosystem primary productivity and that phenological shifts already modified the annual carbon cycle of terrestrial ecosystems [7; 8]. Although many national phenological monitoring networks have their phenological stations equally distributed over altitude, slope, and aspect, most of the stations are either outside the forest or on the forest edge due to accessibility and other practical reasons [4; 9]. This could have implications for the observed tree phenology and the generalisations resulting from these observations at national or regional scales [10]. Direct observations on the ground can provide phenological characteristics of the different plant species present at a given location. However, they are unable to provide continuous phenology characteristics for a given geographic area [11]. On the other hand, satellite data can help estimate and monitor phenological characteristics over extended areas, even though these estimations are always more generalised than direct observations of individual plant phenology [12; 13]. Phenology modelling using remote sensing typically makes use of vegetation indices such as the normalised difference vegetation index (NDVI), the enhanced vegetation index (EVI) and leaf area index (LAI) [1; 14]. The choice of remote sensing data source requires a compromise between their spatial resolution, their temporal resolution, and their time span. Landsat missions provide long records of data with 30 m spatial resolution, but their temporal resolution is around 16 days, making it more challenging to reconstruct continuous data, especially when large data gaps are present. For this reason, several phenology modelling studies turned to moderate and low resolution satellites (>250 m) provided by the advanced very-high-resolution radiometer (AVHRR) and the moderate-resolution imaging spectroradiometer (MODIS) [15; 16; 17]. Some studies demonstrated the adequacy of gross primary production (GPP) for modelling plant phenology [18; 19], making the MODIS GPP product a useful and yet underexplored data source to that end, considering their high temporal resolution of 8 days. To derive phenological characteristics from remote sensing data, seasonality in the satellite data time series is essential. Different factors affect the seasonality observed in the remote sensing data. These factors include noise and extended gaps in the data [20; 21], but also low temporal resolution [22]. It is therefore usual practice to apply mathematical functions to smooth or fit a curve to the time series of remote sensing data and provide continuous data useful for modelling the phenology. These methods include logistic and improved logistic models [23; 24; 25; 26], Gaussian functions [27], quadratic functions and nonlinear spherical models [28; 29], Savitzky-Golay filters [30], polynomial functions [31], discrete Fourier series [11] and machine learning-based algorithms [32].