*3.3. Descriptive Methods*

Here, we assess the spatial and temporal performance of each GPP against the in-situ records using different statistical techniques. The quantitative statistical indicators, including the root mean square error (RMSE), Pearson correlation coefficient (CC), and standard deviation were applied while using a Taylor diagram, which is a precise technique of measuring the degree of accuracy between GPPs and reference data [60]. The mean error (ME) and relative mean error (RME) were calculated in order to indicate the systematic bias which determines the level of over-or under-estimation of GPPs against in-situ data. Furthermore, the scatter plots were also used to determine the quantitative linear relationship between each GPP against the reference data. Furthermore, the detection and comparison of trends in different GPPs data series were evaluated against the reference data using the non-parametric Mann–Kendall (MK) test. The MK trend test is simple and it has been widely used for the detection of significant trends in hydro-meteorological time series data [61,62]. The trend test is robust against normal distribution, missing values, outliers and is less susceptible to the abrupt change point [63].

Similarly, the Theil and Sen's Slope (TSS) is non-parametric test, which can be used to quantify the slope magnitude in linear trends [64]. The TSS has been widely acceptable and used by many researchers to detect the significant trends in different climate indicators [19]. The test is based on least square regression technique, which is commonly used to estimate the rate of slope in a given time series data [65,66]. Moreover, the abrupt change analysis was performed using the Sequential Mann Kendall (SQMK) test. The SQMK test was proposed by [67] and it has been widely used to identify the abrupt change point in hydro-meteorological time series data [49]. The test sets up two temporal series based on forward and backward process i.e., progressive series (PS) and retrograde series (RS). In this test, the progressive series is a standardized variable with zero mean and unit standard deviation. The nature of the progressive series is same as that of Z values, which range from the initial to last data point. Similarly, the value of the retrograde series is computed backwards, starting from the end point and finishing at the first point of the temporal series. The positive and negative change in time series data indicate increasing and decreasing trends, respectively [67]. Details of the descriptive statistical methods are discussed and reported by many research papers [68–71]
