## 1 Introduction  
Carbon uptake through the photosynthesis process by a terrestrial ecosystem termed gross primary productivity (GPP) [1; 2] is the way CO\({}_{2}\) enters into the biosphere from the atmosphere [3; 4]. GPP not only drives the ecosystem functioning but also takes part in terrestrial carbon sequestration through phenological and physiological processes [5].  
During the few past decades, some research has indicated that the accumulation rate of atmospheric CO\({}_{2}\) has significantly increased and land and ocean sinks have exhibited a higher inter-annual variability. These changes in CO\({}_{2}\) and sinks were significantly associated with the continuous major global climate change [1; 2]. However, different diagnostic and prognostic models were developed and operated to estimate the spatial and temporal patterns of GPP variability [1; 5; 6; 7].  
These models are grouped into four categories based on their fundamental theories: enzymes kinetic process-based model, the light-use efficiency (LUE) or production efficiency models, machine learning models based on eddy covariance (EC), and other measurements statistically based on sun-induced chlorophyll fluorescence (SIF) models, respectively [7; 8; 9; 10]. Among these approaches (models), the LUE models are widely used because of their simplicity of using the satellite-based production efficiency models (PEMs) and the capability of offering a relative balance at different spatial-temporal scales (hourly, daily, 8 days, 16 days, monthly and yearly; 250, 500 and 1000 m) [11; 12; 13].  
LUE models are well understood at the leaf level and defined as the slope of the photosynthesis curve in the light-limited section [10]; hence, their initialization depends on variations from fractional photosynthesis active radiation (FPAR) through canopy and chlorophyll processes [6]. However, an accurate GPP estimation itself cannot provide accurate information about the ecosystem services to extreme climatic events but can help to predict future carbon cycle dynamics and their relationship to climate change [2; 14]. Although the LUE models proved to be indispensable in GPP estimation, the comparison of different GPP-based models is more important to indicate the more reliable and higher accurate models for GPP simulations [15; 16].  
The application of GPP-based LUE models, especially in well-watered areas, provides a good understanding of how photosynthetic processes are regulated by ecosystem factors (biotic and abiotic) and climate factors, i.e., water availability (rainfall), temperature and other climate factors [6; 7; 16; 17].  
Over the past decades, multiple observations on the enhancement of seasonal and annual exchanges of CO\({}_{2}\) and GPP variations, especially in the ecosystems induced by CO\({}_{2}\) fertilization and with a limited extent of the growing season, were carried out from global to local scales. These variations of GPP indicated distinctive spatial pattern changes with climate in the hotspot ecosystems such as arid and grassland ecosystems [5; 18; 19]. Several research studies associated these changes with gradual variations in water availability and precipitation patterns [20; 21].  
However, the interactions between climate characteristics and GPP variations, particularly in humid and semi-humid climates, remain unclear. This study aimed at: (i) examining the spatial and temporal variation of GPP based on different LUE models and evaluating their stability on GPP simulations; (ii) evaluating the seasonal and inter-annual variations of GPP in different vegetation function types; and (iii) investigating the impacts of climate characteristics on GPP dynamics over the Great Lakes region of Sub-Saharan Africa (GLR-SSA).