## 1 Introduction  
The terrestrial biosphere plays a vital role in the global carbon, water, and energy cycles [1; 2]. Exchanges of carbon between the land surface and the atmosphere directly influence atmospheric carbon dioxide concentrations. The interactions of these three cycles result in a climate-carbon cycle feedback, which is a major source of uncertainty in climate change projections [2]. Large uncertainties exist in estimates of the terrestrial carbon balance both in observations and in model simulations [2; 3; 4; 5]. Therefore, a better understanding of the response of the terrestrial biosphere to climate variability is both necessary and fundamental for improving projections of future climate change. Several land data assimilation systems (LDASs) have been developed recently to assimilate various observations into land surface models, such as the carbon cycle data assimilation system (CCDAS) [6], the global land data assimilation system (GLDAS) [7], the coupled land vegetation LDAS (CLVLDAS) [8], and the LDAS-Monde [9]. These LDASs either optimize state variables or process parameters of the land surface model. CCDAS is an ideal tool to infer carbon exchanges both within the terrestrial biosphere and with the atmosphere by combining observations (remotely sensed or in-situ data) with process information as represented in models [6; 10; 11] to constrain model process parameters. A terrestrial biosphere model, in our case, the Biosphere Energy Transfer HYdrology (BETHY) model [12], parameterizes relevant processes in the terrestrial biosphere, from water and energy balance to photosynthesis. The actual values of the parameters used in these process-based models are often badly constrained by a limited set of observations taken on small scales with limited plant types and soil textures as well as climates. The typical spatial and temporal heterogeneity of various ecosystems can cause large uncertainties in modeling the global response of the terrestrial biosphere [2; 13]. Also, the many nonlinear processes implemented in terrestrial biosphere models result in more complicated relationships between chosen parameters and modeled carbon fluxes at different temporal and spatial scales [3; 14]. Assimilating observations into terrestrial biosphere models has been shown to be a powerful and efficient tool in constraining model parameters [10; 11; 15; 16; 17; 18; 19]. One of the observational datasets most used within the CCDAS, either as the unique observational constrain or jointly with others, is the Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) [11; 15; 16; 17; 18; 20; 21]. Work has been done to assimilate FAPAR into the BETHY model, which was modified by an improved phenology scheme coupled to the model's two-flux representation of the radiative transfer in the canopy-soil system [16]. They found that most of the uncertainty reduction could be seen in parameters related to leaf phenology. The simultaneous assimilation of FAPAR with other datasets has also been shown to be promising. In a study by [22], FAPAR together with atmospheric CO\({}_{2}\) concentrations were assimilated into BETHY, and the model's hydrology could be significantly constrained in a global simulation. Another work was done by assimilating latent heat flux and FAPAR for a woodland site in Botswana [18]. The study demonstrated that the model parameter controlling the maximum water uptake was efficiently constrained, but its optimal value was sensitive to the choice of the observational data used in the assimilation procedure. This leads to the probable conclusion that different observational constraints are connected to different processes in the terrestrial biosphere model. Recently, a comparison of assimilations with two FAPAR products using the ORCHIDEE model (Organising Carbon and Hydrology In Dynamic Ecosystems) [23] in an assimilation system was performed, with a simplified observation operator that employs the Lambert-Beer law to simulate FAPAR as a function of LAI (Leaf Area Index) [20].