## 1 Introduction  
Vegetation gross primary productivity (GPP), the total carbon assimilation rate of vegetation in unit area in unit time, plays a key role in driving terrestrial ecosystem processes [1]. Quantifying and modeling terrestrial GPP is crucial to understand the massive carbon exchanges between the land surface and the atmosphere and, hence, the global carbon cycle [2; 3; 4]. Satellite remote sensing that provides synoptic observational data of the land surface has become an attractive tool for large-scale studies on terrestrial carbon cycles [5; 6]. As the carbon fluxes between the land surface and the atmosphere are not directly measureable over large areas, various methods--mostly modeling methods such as the light use efficiency models, the process-based models, and the data-driven models--have been developed to simulate terrestrial GPP using remote sensing data [7]. The underlying idea of these methods is to simulate vegetation productivity based on satellite-derived leaf area index (LAI) and/or fraction of photosynthetically active radiation (FPAR), given that solar radiation absorption of vegetation leaves is closely related to plant carbon assimilation [8; 9]. These models largely differ from each other in terms of model sophistication and consideration for the impacts of environmental factors (e.g., temperature, vapor pressure deficit, and soil water content) that regulate leaf photosynthetic rates [10; 11; 12; 13; 14]. Given that various satellite-based vegetation productivity models have become available, the model performance is key for applications in land surface studies. At the site scale, continuous ground measurements of the net energy and material exchanges between ecosystems and the atmosphere at eddy covariance flux towers have been found to be particularly useful in the study of terrestrial ecosystem carbon cycles [15; 16; 17]. As such, most studies developed GPP models based on in situ observations from flux tower sites and further applied the developed models to characterize the spatiotemporal pattern of terrestrial GPP at regional to global scales [18]. The model performance over large areas is less clearly understood than that at the site scale as there is a lack of appropriate large-scale reference data. A comparison of the model results is useful to identify and understand where current models need improvements. For example, comparisons among multiple models are found to deviate largely in specific regions like the Amazon basin and Africa, where ground observations are also limited [19]. Most existing studies focus on modeling and assessing GPP on the intra-annual (i.e., subdaily, daily, and/or weekly) basis rather than on the interannual basis, likely because evaluating the modeling results needs abundant long-term ground observations that are often unavailable. Deciduous broadleaf forest is one of the most extensively studied biomes given the abundant eddy covariance flux towers established in the midlatitude temperate region, of which the modeling is generally considered accurate with low uncertainties in land surface studies as compared with other biomes [20; 21]. Studies have reported that the modeled GPP of deciduous broadleaf forest well agrees with flux tower measurements on the intra-annual basis [22; 23]. Data accumulation from flux towers now allows assessment and examination of model performance at yearly time scale, which is still largely a knowledge gap in existing studies. Given that modeling vegetation productivity on the yearly basis is one key to understanding the long-term dynamics of the land surface, this study compares and evaluates multiple models that use satellite data to simulate GPP of deciduous broadleaf forest across the eastern United States. The study would help improve our knowledge on (1) how current models agree with each other in an extensively studied biome and region and (2) how current models perform on the yearly basis as evaluated using site-level data.