# Assimilation of Earth Observation Data Over Cropland and Grassland Sites into a Simple GPP Model
## 1 Introduction  
Gross primary production (GPP) of crops and rangelands is important for understanding CO\({}_{2}\) uptake of these ecosystems and ultimately for monitoring the provision of services (food, feed, and fibers) [1]. Detailed crop growth models (CGMs) (e.g., WOFOST, [2]; CROPSYST, [3]), describe plant eco-physiological processes such as light interception and absorption, carbon assimilation, as determined by environmental conditions (weather, soil properties, agro-management, etc.) and vegetation characteristics. Nevertheless, the operational use of such detailed models presents important limitations related to the amount and availability of experimental data needed to properly parameterize, calibrate, and evaluate them, especially over large areas. In fact, complex CGMs require a large number of input parameters whose value is often not available and/or highly uncertain. Moreover, the unrealistic spatial and temporal representation of key parameters representing vegetation characteristics and plant functional traits controlling CO\({}_{2}\) uptake was shown to hamper the simulation of GPP at various scales [4; 5]. Uncertainties in model inputs are then transferred into large errors in model estimates [6]. Earth observation (EO) data can provide spatially distributed information to increase the reliability and usefulness of crop models [7]. Various methods have been developed to ingest EO data into thesemodels, ranging from the \"forcing strategy\" (i.e., the direct use of EO as driving variable) to various assimilation techniques. With assimilation, the model does not require EO data as input but the model outputs include some EO variables. For a review of the assimilation techniques see [PERSON] et al. (2018) and [PERSON] et al. (2019). Examples of assimilation of EO data into complex ecosystem models for carbon flux estimation are available for forest ecosystems. [PERSON] et al. (2019) assimilated surface reflectance to improve GPP estimation of a pine forest. [PERSON] et al. (2019) assimilated the fraction of photosynthetically active radiation to estimate the net ecosystem exchange at two forest sites. [PERSON] et al. (2019) assimilated the normalized difference vegetation index to estimate GPP of a poplar plantation. The present study aims at estimating crop and grassland GPP with an approach based on the assimilation of EO observations into a simple process-based model of vegetation growth. In view of the spatial application of the model (and the inherent restriction of data availability to calibrate the model), the crop model is kept as simple as possible (i.e., reduced parameterization). In addition, only publicly and freely available EO data and gridded meteorological variables estimated from global circulation model are employed. The core of the proposed model is composed of a set of equations building on those of the GRAMI model ([PERSON], 1996; [PERSON], 1997; [PERSON], 1998). Specific differences are detailed in Section 3.1. The growth model is coupled with the canopy radiative transfer (RT) model PROSAIL5B ([PERSON], 1998) to translate model estimates of leaf area index (LAI) into Normalized Difference Vegetation Index (NDVI) of the Moderate Resolution Imaging Spectroradiometer (MODIS) at the time of actual satellite overpass (i.e., for actual observation and sun geometry), similarly to ([PERSON], 1998). Besides this coupling, the canopy RT model was used in the growth model to compute the absorbed photosynthetically active radiation (APAR), thus ensuring internal consistency in the definition of the simplified canopy radiative regime. Finally, the coupled model is \"constrained\" by a satellite phenology retrieval model ([PERSON], 1998) that is used to provide a first identification of the likely growth period. For simplicity, we will hereafter refer to such a model scheme as to \"Sim model\". EO data are not used as input (i.e., forcing) but are assimilated into the model to adjust the model parameters and initial conditions.