## 4 Results
### The Direction and Magnitude of LULC Change  
From the late 1970s to the early 1990s, the main manifestations of LULC change in the headwaters of the Yangtze River were in the form of shrinkage of wet- and marshland, showing a decrease of 2.38 km\({}^{2}\), and desertification, showing an increase of 2.59 km\({}^{2}\). The analysis of the transition matrix revealed that 9.36-, 5.11- and 1.28-km\({}^{2}\) water bodies were converted to shoaly land and swamp, desert and low-coverage grassland, respectively; 2.76 km\({}^{2}\) of desert were transformed to water bodies, and 1.63 km\({}^{2}\) of low-coverage grassland were converted to water bodies. The main forms of LULC change in the headwaters of the Yellow River were the expansion of sand, gobi and bare land and a decline of grassland coverage. The transition matrix showed that high-coverage grassland primarily converted to medium-coverage grassland resulted in a 447.13-km\({}^{2}\) loss totally; medium-coverage grassland mainly transformed to low-coverage grassland with 295.92 km\({}^{2}\), and low-coverage grassland primarily converted to sand, gobi and bare land with 93.32 km\({}^{2}\), indicating a gain of 74.68 km\({}^{2}\) in sand, gobi and bare land and a decrease of 83.59 km\({}^{2}\) in the grassland area totally (Table 3). From early 1990s to 2004, expansion of wet- and marshland was the main form of LULC change in the headwaters of the Yangtze River. The transition matrix indicated that the 10.83-km\({}^{2}\) increase in wet- and marshland area mainly resulted from the conversion from desert (6.96 km\({}^{2}\)), grassland (2.58 km\({}^{2}\)), and sand, gobi and bare land (1.28 km\({}^{2}\)). Desert decreased markedly by 7.41 km\({}^{2}\). In the headwaters of the Yellow River, similar patterns of LULC change were found with the magnitude being more dramatic compared to the prior period. A decline of grassland coverage, shrinkage of wet- and marshland and significant expansion in sand, gobi and bare land were noticed. The grassland experienced a dramatic change with 227.46 km\({}^{2}\) high-coverage grassland, 294.94 km\({}^{2}\) medium-coverage grassland and 766.76 km\({}^{2}\) low-coverage grassland transforming to medium-coverage grassland, low-coverage grassland and sand, gobi and bare land, respectively, and the total grassland area decreased by 660.06 km\({}^{2}\). The wet- and marshland decreased 79.81 km\({}^{2}\) with shoaly land and swamp converting to grassland primarily. The sand, gobi and bare land increased by 740.53 km\({}^{2}\), mainly converted from low-coverage grassland (Table 4). From 2004 to 2012, LULC change was more dramatic compared to the prior two periods in the headwaters of the Yangtze River. Expansions of grassland and wet- and marshland, and a decrease of sand, gobi and bare land area were the main forms of LULC change, and glacier retreat occurred in this period. The transition matrix showed that, with the sand, gobi and bare land and desert primarily changing to low-coverage grassland and water bodies, shoaly land and swamp changing to grassland and low-coverage grassland changing to water bodies, the grassland increased by 43.45 km\({}^{2}\), wherein the low-coverage grassland increased by 24.73 km\({}^{2}\), and the wet- and marshland increased by 5.09 km\({}^{2}\), wherein the water bodies increased by 23.94 km\({}^{2}\), and the sand, gobi and bare land decreased by 39.76 km\({}^{2}\). In the headwaters of the Yellow River, an increase of grassland coverage, expansion of wet- and marshland and a decrease of sand, gobi and bare land area were the main LULC change types. With 190.10 km\({}^{2}\) medium-coverage grassland converting to high-coverage grassland, 627.85 km\({}^{2}\) low-coverage grassland converting to medium-coverage grassland and 209.17 km\({}^{2}\) sand, gobi and bare land converting to low-coverage grassland, the grassland coverage increased significantly and the total area increased by 127.51 km\({}^{2}\) and sand, gobi and bare land area decreased markedly by 218.77 km\({}^{2}\).