## 3 Data and Methods  
### Data Sets  
The GIMMS3g NDVI data set was used in this study, which has a spatial resolution of about 8 km and a temporal resolution of 15 days. This data set was previously developed by the Global Inventory  
Figure 1: Geographical location of the study area. Inset map shows the location of the Okavango, Kwando, and upper Zambezi (OKZ) catchment in southern Africa. The white lines show the contours of mean annual precipitation (MAP) with an interval of 100 mm, which illustrates that MAP increases from south to north. Modeling and Mapping Studies (GIMMS) group, and is currently available from July 1981 to December 2011 generated in the framework of the Global Inventory Monitoring and Modeling System (GIMMS) project at NASA Goddard Space Flight Center. No atmospheric correction is applied to the GIMMS data except for volcanic stratospheric aerosol periods (1982-1984 and 1991-1994) [22]. A satellite orbital drift correction is performed using the empirical decomposition/reconstruction methods, minimizing effects of orbital drift by removing common trends between time series Solar Zenith Angle and NDVI [17]. Additionally, this data set has been corrected for factors that do not relate to changes in vegetation greenness, and applies an improved cloud masking as compared to older versions of the GIMMS NDVI data set. The GIMMS3g NDVI data use the maximum NDVI value over a 15-day period to represent each 15-day interval to minimize corruption of vegetation signals from atmospheric effects, cloud contamination, scan angle effects and so on at the time of measurement [28]. The maximum value composite (MVC) method was used to obtain monthly NDVI from January 1982 to December 2010 to further reduce cloud effects, and the pixels with mean annual NDVI value less than 0.2 were removed to reduce the effect of non-vegetation cover. Overall, the GIMMS3g archive is considered the best dataset available for long-term trend analysis of vegetation greenness. A second satellite based dataset, overlapping for 11 years with the AVHRR data was also utilized in this research, the monthly MODIS NPP product (MOD17A2), which spans from January 2000 to December 2010 at a 1-km spatial resolution [5, 24]. It is the first regular, near-real-time data set for repeated monitoring of NPP over vegetated land [29]. The principle of the MOD17 algorithm is the application of the radiation conversion efficiency logic to predictions of daily GPP and the subsequent estimation of maintenance and growth respiration terms that are subtracted from GPP to arrive at NPP [24, 25]. These data are freely available to the public from the Numerical Terradynamic Simulation Group (NTSG) at the University of Montana. The study area covers three tiles: h19v10, h20v10, and h20v11. Based on the QA information, only the pixels of good quality (labeled with \"0\") were considered. To match the grid cell size of MODIS NPP data with other data sets, we adopted a simple but frequently used way to resample. The values of each \(9\times 9\) grid block were average to create a single pixel, if the values with \"good quality\" were more than 80% of the total after the values out of 2-time standard deviation were removed. We chose the Matsuura and Willmott data set of monthly precipitation (1982-2010) which has a spatial resolution of 0.5 degree by 0.5 degree with grid nodes centered on 0.25 degree. These datasets improve upon a previous global mean monthly dataset with a refined Shepard interpolation algorithm and an increased number of neighboring station points included in the analysis [30]. Based on the grid nodes included in the three catchments we interpolated the datasets into continuous surfaces with a spatial resolution of about 0.08 degrees using inverse distance weighted interpolation. A land cover map of Africa derived by the Global Land Cover (2000) project was used, which has a spatial resolution of 1-km [31]. The map is based on daily observations made from November 1999 to December 2000 by the VEGETATION sensor on the SPOT4 satellite.