## 1 Introduction  
The Leaf Area Index (LAI) is defined as one-sided green leaf area per unit ground area in broadleaf canopies, and as the projected needle leaf area in coniferous canopies [1]. LAI is a key parameter in most ecosystem productivity models and global (or regional) models of climate, hydrology, biogeochemistry and ecology [2]. Usually defined as the time evolution of the LAI, leaf phenology depends primarily on the climatic conditions for a given biome [3]. It strongly affects land-surface boundary conditions and the exchange of matter and energy with the atmosphere, influencing the surface albedo, roughness, and dynamics of the terrestrial water cycle [4, 5]. Changes in the phase of LAI may therefore have impacts on climate [6, 7], on the terrestrial carbon cycle [8], and on the atmospheric chemistry through the emission and deposition of several compounds [9, 10, 11, 12]. Therefore, accurate estimates of canopy phenology are critical to quantifying carbon and water exchange between forests and the atmosphere and its response to climate change [8]. Phenology studies based on field observations [13, 14], remote-sensing data [15, 16, 17, 18, 19], atmospheric CO\({}_{2}\) observations [20], and biogeochemical models [21] indicate that the vegetation growing season length (GSL) has significantly increased over the past decades [8]. Specifically, in the temperate and boreal regions of the Northern Hemisphere, the growing season begins in spring with increasing temperatures and solar radiation, the melting of snow, eventual thawing of the soil organic horizons, and the start of photosynthesis [22]. It terminates in autumn as temperatures and solar radiation decrease, soils refreeze, and photosynthesis ceases [23, 24]. Therefore, temperature anomalies in spring and autumn affect the timing and duration of the growing season [8, 25], which in turn control the seasonal onset and ending of the ecosystem carbon uptake period in these regions [8, 26, 27]. Rising temperatures during recent decades have resulted in a widely reported pattern of earlier and longer-lasting growing seasons from local to continental scales [13, 15, 16, 20, 27, 28, 29]. The greater rate of change observed in the beginning of the growing season is thought to be a response to rapid spring warming, and earlier snowmelt and soil thaw [15, 30], while the smaller change in termination date is likely connected with lower rates of autumn warming [31] and the influence of other environmental effects on autumn phenology and growth cessation [23, 32, 33]. The importance of land surface processes in the climate system has mostly been supported by modelling studies on climate sensitivity to albedo [34, 35, 36], soil moisture [37, 38, 39], surface roughness [40], and leaf area index [6, 41, 42, 43, 44, 45, 46]. In the first versions of general circulation models (GCMs) and regional climate models (RCMs) the soil-vegetation-atmosphere transfer (SVAT) schemes [47] were originally designed to simulate exchanges of matter and energy between the land surface and the atmosphere, with vegetation leaf area index as a forcing variable, rather than a prognostic state [6, 44, 48, 49, 50, 51, 52]. In order to improve the representation of the dynamical behaviour of the vegetation, a number of models have recently evolved to include biogeochemical processes [53, 54, 55, 56, 57, 58, 59, 60, 61]. In the last few years a new generation of general circulation models has become available to the scientific community. In comparison to the former model generation, these Earth System Models incorporate additional components describing the atmosphere's interaction with land-use and vegetation, as well as explicitly taking into account atmospheric chemistry, aerosols and the carbon cycle [62]. The inclusion of Earth system components in a climate model has a two-fold benefit. Firstly, it allows a consistent calculation of the impacts of climate change on atmospheric composition or ecosystems [63].