## 1 Introduction  
The water cycle and carbon cycle constitute two pivotal components of terrestrial ecosystems, directly influencing vegetation transpiration and photosynthesis, respectively [1]. Evapotranspiration (ET), a crucial component of the water cycle, contributes significantly to returning approximately 60% of precipitation back to the atmosphere [2]. Furthermore, the majority of organic carbon in terrestrial ecosystems is sequestered through vegetation photosynthesis, serving as the primary source of vegetation biomass [3]. Consequently, the precise and efficient monitoring of water and carbon fluxes holds utmost importance in agriculture, ecology, environmental science, and hydrology studies. Instruments such as the eddy covariance system (EC) [4] and large aperture scintillator (LAS) [5] have emerged for use in observing water and carbon fluxes in the field. Despite their ability to cover areas spanning several square kilometers, these instruments cannot provide distributed results or result maps. Remote sensing (RS) offers a remarkable tool for monitoring ecosystem processes at a regional scale. Many RS-based models have been proposed for water and carbon fluxes, broadly categorized into physical and empirical models. The Surface Energy Balance (SEB)-based algorithm stands as a widely accepted physical model for ET estimation. Prominent examples include the Surface Energy Balance Algorithm for Land (SEBAL) [6; 7], Two Source Energy Balance (TSEB) [8], and Surface Energy Balance System (SEBS) [9]. These algorithms have found extensive application in ET estimation across various ecosystems [10; 11; 12; 13; 14]. For carbon flux estimation, the Light Use Efficiency (LUE)-based algorithm is a commonly used physical model for gross primary productivity (GPP) assessment [1; 15; 16; 17; 18; 19]. The LUE model determines GPP by multiplying the photosynthesis-absorbed radiation with the actual LUE to calculate the carbon fixed via photosynthesis [20]. These physical models, be they used for ET or GPP, bridge the gap between remote sensing data and target variables. However, they require a significant number of parameters and computations, adding to their complexity [20; 21]. Furthermore, these models [11; 21] often rely on meteorological data, but the current spatial resolution of such data is often too coarse to align with high-resolution satellite imagery like Landsat (30 m) or Sentinel (10 m). On the other hand, empirical models offer simplicity but with less interpretability. They are typically based on relationships between remote sensing data and in-situ observations of water or carbon fluxes [22; 23; 24; 25; 26]. The advent of machine learning algorithms has facilitated better alignments between remote sensing data and in situ observations [4; 27]. It is worth noting that empirical models often exhibit limited spatial universality; models trained on samples from a specific area might not perform well in other regions [4]. Additionally, semi-empirical equations like Penman-Monteith [28; 29] and Priestley-Taylor [30] have also been employed in remote sensing model development. In summary, both model types possess distinct strengths and weaknesses. Although numerous scholars have delved into the use of the remote sensing model for water or carbon fluxes, most of their investigations into these two flux estimation models have been independent. However, it is crucial to recognize the intricate interaction and coupling between transpiration and photosynthesis, as highlighted by [PERSON] et al. [31]. Photosynthesis and transpiration primarily facilitate the exchange of water and carbon with the atmosphere through leaf stomata. The aperture of these stomata is modulated by various abiotic and biotic factors inherent to plants [32]. For instance, during drought conditions characterized by increased evaporation and decreased precipitation, leaf stomata tend to shrink, thereby impacting carbon exchange. Moreover, soil serves as an additional hub for the exchange of water and carbon within the ecosystem.