3.1. Coordination Degree
The study used the improved Equation (1) to obtain the CD of the PT-IT-LT (Figure 2
). It used the quartering method to analyze the result in different periods: the first stage was the lower-level coordinate whose degree was from 0.0 to 0.25; the second stage was the low-level coordinate whose degree was from 0.25 to 0.50; the third stage was the middle-level coordinate whose degree was from 0.50 to 0.75; the last stage was the high-level coordinate whose degree was from 0.75 to 1.0.
In time, the CD of the PT-IT-LT changed to high-level from low-level, and the mean value of the CD was 0.14, 0.20, 0.26 and 0.28 from 1990 to 2015. From 1990 to 2015, the CD was generally lower-level, but the proportions accounting for the total counties decreased gradually, and the values were 83.44%, 70.70%, 61.78% and 56.69%. The proportions of the low-level, middle-level and high-level CD accounting for the total counties increased from 1990 to 2015, which showed that the CD of rural PT-IT-LT in the Beijing-Tianjin-Hebei region continuously improved. With the economic development, ever more farmers gave up agriculture and left rural areas to work in factories; the demand for land increased, and the government had to take measures to alleviate the conflict between population and land.
In terms of space, most counties belonged to the lower-level CD from 1990 to 2015, but they had great spatial differences. The high-level CD of PT-IT-LT applied to Beijing and Tianjin; few counties occurred in the center of the Beijing-Tianjin-Hebei region (Figure 3
). A circle structure from southeast to northwest Beijing-Tianjin-Hebei was clear; the CD of coastal counties was greater than for those far from the sea, which reflected the order of socioeconomic development in the region. The CD of some southeastern counties had reached the middle-level in 2015, while the northwestern counties were still at the lower-level, compared with 1990, because the economic development in the southeast with more advantages was faster than for the northwest, and its economy promoted the rural areas to develop in a more coordinated manner.
3.2. Transformation Degree
The study obtained the rural TD of different counties by the linear weighting of three indicators from 1990 to 2015. According to the value of the TD, the study divided rural transformation into four types: lower-level transformation (0–0.25), low-level transformation (0.25–0.50), middle-level transformation (0.50–0.75), and high-level transformation (0.75–1.0). From Figure 4
, no counties in the region achieved the high-level transformation, and most of the counties remained at the lower-level transformation (52.86%) in 1990. The proportion of high-level transformations increased, and the proportion of lower-level transformations decreased from 1990 to 2015; there were 10 counties with high-level transformation in 2015, while the number with lower-level transformation was only 3, accounting for 1.91% of the total counties. The result reflected that the level of the TD in the Beijing-Tianjin-Hebei region gradually became better from 1990 to 2015, and there was a great difference in these counties because of their different bases in different periods.
In terms of space, there was a spatial development trend similar to that of the CD from 1990 to 2015. Beijing and Tianjin were the cores of this region, and the TD of their counties was always higher than for other counties, reaching high-level transformation in 2015 (Figure 4
). However, the northwestern area of the Beijing–Tianjin–Hebei region was at the lower-level from 1990 to 2015. This shows that regional differences were a serious problem that hindered the development of urban and rural integration.
To analyze the differences in the TD, this study obtained the speed of transformation for the periods of 1990–2000, 2000–2010 and 2010–2015 (Figure 5
). The speed for 1990–2000 was higher than that for 2000–2010 and 2010–2015, and the speed for 1990–2000 and 2000–2010 did not follow an obvious trend, but the speed for 2010–2015 in the southeast of the Beijing-Tianjin-Hebei region was faster than for other regions. However, the speed decreased gradually from 1990 to 2015, and its change trend was opposite to that of the TD. Thus, the higher the transformation level was, the lower its speed.
3.3. Rural Transformation—Coordination Development
The study obtained the fitting curves of the PT-IT-LT, CT and TD by disturbance translation with 18 iterations, which avoided the volatility of the sample counties’ data. Then, according to the coupling results of all the factors, the rural transformation–coordination development was divided into five types: fast industry lower-level coordination and transformation development (A), fast industry and population lower-level coordination and low-level transformation development (B), high factors lower-level coordination and low-level transformation development (C), fast population low-level coordination and middle-level transformation development (D) and fast land middle- and high-level coordination and transformation development (E) (Figure 6
(1) The fast industry lower-level coordination and transformation development (A) described the industry transformation increasing continuously with rapid growth and was higher than the population and land transformation. The CD and land transformation had lower-level stability, and the TD was lower-level but increased slowly. This reflected that the industry transformation had an influence on the rural TD but had no effect on the rural CD.
(2) The fast industry and population lower-level coordination and low-level transformation development (B) described the industry and population transformation growing quickly, but the land transformation and CD increasing very slowly. The TD was low-level and improved with the change of industry and population transformation. Thus, this showed that the industry and population had a larger impact on the rural TD than the land but a smaller function for the rural CD.
(3) The high factors lower-level coordination and low-level transformation development (C) was a type for which the population, industry and land were relatively stable and without significant change. However, the coordination was still lower-level and it had a high volatility similar to the change of the land transformation. It is clear that the land transformation was promoting the change of the rural CD, and the rural TD was affected by population, land and industry together in these counties.
(4) The fast population low-level coordination and middle-level transformation development (D) showed that the TD was middle-level and increased rapidly with the change of population. Meanwhile, the CD had reached the lower-level and its growth was slower than that of the TD. The amplitude for the land transformation and industry was also lesser than that of the population transformation. Thus, the population was the main factor influencing the rural transformation in the regions.
(5) The fast land middle- and high-level coordination and transformation development (E) was the most highly developed type, whose TD and CD were middle- or high-level and whose population transformation and industry transformation were also high-level in these regions. However, the increase of land transformation was more than other types and arrived at the high-level, as for the population and industry in the previous sample points. Accordingly, land was the most important factor for the rural transformation in these counties.
According to the characteristics of different rural transformation types, we found the developing state of different counties from 1990 to 2015, and detected the leading factors influencing the TD and CD, which would provide support for the functional subzones of the rural transformation development in the Beijing-Tianjin-Hebei region and greatly enlighten the study of rural development.