# Incorporating Spatial Autocorrelation into GPP Estimation Using Eigenvector Spatial Filtering
## 1 Introduction  
Terrestrial gross primary productivity (GPP), serving as a vital metric for carbon assimilation through photosynthesis, constitutes a vital component of terrestrial carbon fluxes [1]. It reflects the ability of plants to absorb atmospheric carbon dioxide and transform it into organic matter [2]. Accurately quantifying GPP and evaluating its dynamic changes are essential for assessing the carbon sink potential of terrestrial ecosystems. Therefore, this endeavor contributes to a deeper understanding of carbon balance, greenhouse gas emissions, and the state of climate change [3, 4]. However, the direct observation of GPP poses significant challenges. There are observations obtained from ground-based measurements, spatially scattered sampling, and flux sites, which are only effective within a restricted spatial and time coverage [5]. Therefore, data-driven approaches and simulations facilitated through remote sensing have extended GPP to larger spatial scales. However, whether derived from ground-based observations or data-driven models, the estimation of GPP inevitably faces the influence of environmental variables, the structural complexity of the model, and the diversity of vegetation types. Consequently, in order to mitigate climate change and achieve the aspirations of \"carbon peaking\" and \"carbon neutrality\", enhancingthe performance of GPP estimation and bolstering the applicability of the models remain imperative tasks [6]. Remote sensing estimation models have emerged as a predominant tool for assessing GPP, primarily due to their long temporal scales and extensive spatial monitoring capabilities [7]. These models for estimating GPP can roughly be categorized into statistical models, ecological process models, light use efficiency (LUE) models, and machine learning models [5]. Statistical models utilize various commonly employed statistical methods to establish mathematical relationships between changes in plant biomass and climatic factors, aiming to estimate vegetation productivity. These models have simple structures and few parameters, but lack rigorous physiological foundations, resulting in higher uncertainty in the estimation results [8]. Ecological process models employ mechanistic models based on biogeochemical processes. They estimate GPP by modeling processes such as solar radiation transfer and vegetation photosynthesis [9]. These models require complex parameters and comprehensive data inputs [10; 11]. The LUE model calculates GPP in view of the link between LUE, absorbed photosynthetically active radiation (APAR), and environmental factors, and integrates physiological and ecological processes inherent to vegetation photosynthesis [12; 13; 14]. However, variations in the configuration of model parameters can significantly influence the estimation of GPP [15; 16; 17; 18; 19]. Machine learning algorithms leverage mathematical and statistical methodologies to analyze datasets and establish intricate associations between input and target variables. This iterative process involves training the model to minimize the loss function. Over the past few years, significant advancements have been achieved in GPP estimation by employing machine learning techniques. These methods utilize data-driven techniques to statistically summarize the relationship between GPP and observed variables [20]. Furthermore, in GPP simulation, machine learning methods have demonstrated effectiveness in reducing uncertainty associated with model parameters, the concrete architecture of models, and input variables, which are inherent in other empirical-based and ecological process-based models [21; 22]. Furthermore, the distribution of GPP might be influenced by spatial autocorrelation, where similarities among locations lead to data correlations [23]. When constructing models based on site-level observations, it is often assumed that these sites operate independently, with spatial influences arising from site distribution omitted during modeling.