## 1 Introduction  
Gross primary productivity (GPP) represents the carbon taken up by the biosphere that can be used for biotic processes. Understanding its changes across space and time is crucial in understanding our changing planet, as it is the largest component of the global carbon budget [1]. GPP has been increasing across much of the globe due, in large part, to global greening [2, 3] and CO\({}_{2}\) fertilization [4], and it is predicted to increase further throughout the 21 st century [5]. Simultaneously, water limitation is playing an increasing role in controlling GPP at interannual to decadal time scales [6], often dampening its response to otherwise favorable climatic conditions [7]. Satellite remote sensing has revolutionized our ability to estimate GPP [8, 9, 10] and is particularly important for understanding its changes in areas where ground observations are sparse. Interpreting GPP from space can be difficult because different interpretations can result from different GPP data products [11, 12, 13] and from different statistical methods for time series analysis [14, 15, 16, 17]. Multi-method comparisons can help reduce uncertainties, critique methods, and lend confidence that results are robust [18]. Doing so across diverse regions can further help understand how, why, and where GPP is changing, and where our interpretations of changes are insensitive to a chosen satellite product or methodological approach, thereby requiring additional study for more robust inference. The calculation of trends over time for any natural phenomenon can employ parametric or non-parametric methods (or both). Among the parametric methods, linear regression is the most frequently used. Despite numerous studies predicting the trend of GPP values using linear regression [19; 20; 21; 22], researchers tend to prefer non-parametric methods such as the Mann-Kendall, Sen's Slope, and Spearman's Rho due to the preconditions of linear regression, including the assumption of normal distributions, homoscedasticity, and the absence of multicollinearity [4; 23; 24]. Certain details, which conventional methods struggle to elucidate, can be examined through graphical methods such as Innovative Trend Analysis (ITA) and Empirical Mode Decomposition (EMD). Contrary to conventional methods, ITA and EMD provide detailed information on the fluctuations of the trend over time and, in our case, the tendencies of trends at low, medium, and high GPP values. Utilizing over-simplified methods to deduce the trend in GPP values may omit significant details. GPP varies dynamically across multiple scales in time, but studies tend to conduct trend analyses of annual GPP values. For example, the annual trend of GPP values has been investigated in studies where the entire Earth is considered as the study area [25; 26], in studies for China [27; 28; 29; 30], in studies for India [21; 31] and in studies for Australia [32]. While this may provide acceptable results for the study at hand, the trend of monthly GPP values over time is important in natural areas, and especially in cultivated agricultural areas, for understanding trends in productivity and investigating changes in seasonal patterns that may have management implications [33]. Annual GPP values represent the whole year after a single value has been obtained by averaging or summing, and do not explicitly consider variations during periods that are sensitive to plant growth including agricultural activity. The second innovation in this study, in addition to the multi-trend analysis, is the trend analysis of monthly GPP values. Here, we compare multiple satellite-based GPP estimates and multiple approaches for time series analysis to interpret decadal-scale GPP trends, using the diverse geography and vegetation of the Republic of Turkiye as a case study.