The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B6b. Beijing 2008 
UR: urban land; CL: cultivated land; GF: grass and forest land; 
VE: vegetable garden; WA: water; UN: unused land. 
From the table (Table 2Table 2), we can find that during the 
entire study period from 1984 to 2005, the urban land area 
proportion expanded from 25.32% to 47.75% of the study area, 
nearly a double in 21 years, showing a strong trending of 
expansion. And also, we can find a growing in grass and forest 
land area, since the government has taken a policy so-called 
returning farmland to forestry or grass. 
4.1.1 Type of land transferred 
Transfer proportion of land use types was obtained by means of 
Markov model and the principle of algebra in map. The main 
type of land transferred to urban land was cultivated land; while 
other types, for example, water to urban land and gardens to 
urban land are nearly none. 
Figure 4. Land use type change from 1984 to 2005 
UR: urban land; CL: cultivated land; GF: grass and forest land; 
VE: vegetable garden; WA: water; UN: unused land. 
4.1.2 Markov chains and transitional probabilities matrix 
To make trajectory analysis, we need to take random sample of 
a certain number of points in seven classification maps, 
respectively. Then, we examine these samples in six phases on 
the types of land-use changes. According to Liu’s point stability 
of the test results (Liu and Zhou, 2004), when the number of 
random sample reached 1,000 points, its stability will not 
change. So in this study 1,000 randomly were selected sample 
points used for trajectory analysis. And there are 29 types of 
trajectories as followed (Table 3). 
Through analysis of 1000 randomly selected sample, the 
trajectory of urban expansion in the land use change tracked by 
29 series, the proportion of each track as shown in Table (Table 
4Table 4). According to the arrow indicates, the expansion of 
urban in the study area of the track can be divided into three 
groups the following: 
(1) From cultivated land to urban land. Track series of 1 to 17 
belong to this type, as a whole taken for the largest proportion 
of 77.7 percent. For the majority of this type of cultivated land 
to urban land, very small portion from other types into 
cultivated land, and then to urban land. 
(2) From vegetable land to urban land. Track series of 18 to 21 
belong to this type, as a whole taken for the largest proportion 
of 8.8 percent. 
(3) From others to urban land. Track series of 21 to 29 belong to 
this type, as a whole taken for the largest proportion of 10.1 
percent. 
land; 5: water; 6: unused land; arrow (—>): other types of land convert to 
urban land use. 
Table 3. The trajectories of landuse change from 1984 to 2005 
4.2 Spatio-temporal analysis 
From central city to suburb, the land use variation takes on 
strong spatio-temporal change. The extent of urban expansion 
of east is higher than west’s as a whole. The model of urban 
expansion is analyzed by the spatial distribution rules of the 
proportion of urban land and the spatial distribution rules of 
urban expansion. Round-sprawl is the main model of urban 
expansion. The urban expansion models include isolated growth 
and corridor’s growth. Urban expansion cores and traffic are 
two urban expansion spatial influence factors (Figure 5). 
4.2.1 Analysis of maps 
As shown in the expansion map (Figure 5), we can easily find 
that there are one main city-expansion core and four sub 
expansion cores, which is center of Changping, Shunyi & 
Airport, Tongzhou and Daxing, respectively.