# Estimation of Time-Series Forest Leaf Area Index (LAI) Based on Sentinel-2 and MODIS
## 1 Introduction  
The forest ecosystem is the main component of the terrestrial ecosystem [1; 2]. Estimating the distribution and change of carbon storage in forest ecosystems is helpful for understanding the relationship between carbon sources and sinks [3; 4; 5]. The leaf area index is an important parameter for describing vegetation growth and one of the main parameters in ecological and climate models. It is defined as the sum of the one-sided area of green leaves per unit ground area [6; 7]. The leaf area index is closely related to ecophysiological processes such as photosynthesis, transpiration, respiration and the productivity of vegetation [8; 9; 10; 11]. It is an essential driving parameter in the carbon and water cycle of forest ecosystems at regional and global scales [12; 13]. The time-series LAI characterizes the growth dynamics of vegetation, and obtaining the regional time-series LAI becomes an important data preparation step in the study of carbon and water cycle mechanism models at the regional scale [14; 15]. How to quickly obtain a high spatial-temporal resolution sequence LAI has become a research focus. At present, the estimation of the regional scale LAI mainly adopts the remote sensing inversion method [16; 17], which is divided into two types of models--the statistical estimation model and the physical inversion model--according to whether it involves physical physiological processes. Physical inversion models [18; 19; 20] have clear physical meaning and require the input of the biochemical and structural parameters of leaves. They also have the shortcomings of large uncertainty, large computation and time consumption. Statistical estimation models [21; 22; 23; 24] estimate the leaf area index by establishing linear ornonlinear relationships between the LAI and vegetation index, which have the advantages of few parameters and easy implementation. They are often applied to LAI estimation in smaller areas [25; 26; 27; 28]. At present, a number of world-wide LAI products have been produced from many different types of satellite remote sensing data [29; 30]. These products use multifarious methods for retrieval and have their own spatio-temporal resolutions. Table 1 lists the major LAI products in the world. It can be seen from Table 1 that the MODIS LAI has the highest spatial-temporal resolution (4 days, 500 m) in the system that is still running. Because of frequent clouds and other factors, the existing LAI products may be provided with anomalous time-series characteristics. In order to break through these difficulties, a few reconstruction methods, according to the principles of the statistical filtering and the data assimilation, have been put forward [31; 32; 33]. The reconstruction method based on the dynamic change mechanism model can restructure time-series LAI data by attaching additional data [34]. By attaching the radiative transfer model to the dual logic LAI time model, the time-series MODIS reflection data are used to restructure the time sequent LAI product [35]. At present, high time resolution LAI products are widely available in vegetation phenology dynamic monitoring, as well as crop yield prediction. [PERSON] et al. [36] characterized the baseline phenology of the vegetation at the global scale from the GEO-CLIM climatology of the LAI estimated from the 1-km SPOT-VEGFATION time series for 1999-2010. [PERSON] et al. [37] proposed a method that combines sparse representation and harmonic characteristics derived from the time-series MODIS LAI to identify crop planting areas to the north of the Yellow River in the North China Plain, where winter wheat and maize are widely cultivated. Although the current MODIS has provided LAI data products on a global scale time-series, which provides a good data source for studying the temporal variation pattern of the LAI, the spatial resolution of the products is not high enough (500-1000 m) and is too rough to satisfy the demand of the high spatial resolution remote sensing requirements.