(1. Zhenhai Branch of Ningbo Municipal Bureau of Land and Resources, Ningbo, 3 15 1202. School of Civil Engineering, Ningbo University, Ningbo, 3 15 120)

Abstract: Urban land price is a multidimensional concept with space-time nature, which has strong relevance and particularity in spatial distribution. Taking the downtown area of Ningbo as the research area and the land price information as the research object, this paper probes into the principles and methods of how to study the spatial distribution characteristics and laws of land price based on geostatistics and GIS.

Keywords: urban land price; Spatial analysis; Geostatistics; Ningbo urban area

1 Basic concepts of geostatistics

Geostatistics was put forward and founded in 1963 by Professor G Marcelon, a famous French mathematician, on the basis of studying the work of South African geological engineer D·G· Crick. Geostatistics is a set of theories and methods to analyze spatially related variables based on geological analysis and statistical analysis. It is based on the theory of regionalized variables and takes variogram as the main tool to study those natural phenomena which are both random and structural in spatial distribution. Geostatistics can make full use of all kinds of information provided by field investigation, such as sample position, sample value and sample bearing size. Sparse or irregular spatial data can be used. Geostatistics has been paid more and more attention because it can accurately describe the randomness and structural changes of regionalized variables. It has been successfully applied to natural resources, and also widely used in environmental science, agriculture and forestry science, water conservancy science and land science.

In the field of land price research, the application of geostatistics is mainly reflected in three aspects: one is to quantify the spatial correlation of regionalized variables, the other is to interpolate the survey data, and the third is to analyze the temporal and spatial regularity of spatial data. Relatively speaking, spatial interpolation is widely used. In the usual land price survey, because the data obtained from the field survey can not completely cover the required area, it is necessary to interpolate and interpolate the discrete sampling point data into a continuous data surface by geostatistics.

The biggest advantage of applying geostatistics is that it can use sparse and irregular survey data on the basis of spatial correlation analysis to reveal the spatial information provided by these data to the maximum extent. However, the application of geostatistics in land price research has just begun, and there are still some problems, such as the collaborative analysis of space and time, the design of sample number, sampling position, direction and size, etc. These are all worthy of further improvement and improvement.

2. Basic functions of geological statistical analysis

Geostatistics, the functions used in spatial correlation analysis mainly include semi-variance function, covariance function and correlation function, among which semi-variance function is the most commonly used tool in geostatistics. In addition, there are general relative variance function, cross variance function, paired relative variance function, logarithmic variance function, generalized variance function, characteristic variance function (or index variance function) and scatter chart. , but rarely used, generally not suitable for spatial analysis of land prices.

The semi-variance function is defined as the mathematical expectation of the square of the increments of the regionalized variables z (xi) and Z (Xi+H), that is, the variance of the increments of the regionalized variables. Semi-variance function is not only a function of distance h, but also a function of direction α. The calculation formula is as follows:

Innovation of Land Information Technology and Development of Land Science and Technology: Proceedings of the 2006 Annual Conference of china land science Institution.

Where, γ(h) is the value of semi-variance function, and the semi-variance function graph is the coordinate graph of semi-variance function γ(h) versus distance h, N (h) is the number of separated data pairs, z (xi) and z (xi+h) are the measured values of samples at points xi and xi+h respectively, and h is the distance between two separated sample points.

For a typical spatial aggregation distribution, the semi-variance function generally increases with the increase of distance, that is, the spatial variation of regionalized variables becomes larger and larger, and the spatial correlation gradually decreases. However, when it increases to a certain value, the semi-variance function no longer increases but remains stable, which indicates that there is no spatial correlation between sampling points. The distance when the semi-variance function value no longer increases is called spatial correlation range, which is referred to as range or correlation range for short, and is represented by A. At this time, the semi-variance function value is called abutment value, which is represented by C0+C. The intercept of the semi-variance function curve on the Y axis is called regional discontinuity value, also called Nugget coefficient or kernel variance, which is represented by C0. The size of C0 can reflect the local randomness of regionalized variables. (Abutment is a piece of gold)/abutment size (that is, C/(C0+C)) can reflect the proportion of spatial variation in the total variation, or the size of randomness (lump of gold/abutment, that is, C0/(C0+C)) can reflect the variation proportion in the total variation caused by the spatial autocorrelation of non-land price within the research scope, that is, the randomness and structure of land price.

3 Geostatistical analysis of land price in Ningbo

3. 1 Geostatistical analysis scope and sample distribution of land price in Ningbo

The urban land grading in Ningbo includes six districts in Ningbo, and there are great differences in land use mode and land market development level, especially in mountainous areas, where land transactions are scarce and land price samples are scarce. According to the requirements of geostatistics for sample points, although regular sampling of land price sample points is not required, the scarcity of sample points in a large area will greatly affect the reliability of the analysis results. At the same time, considering that the land transactions in Ningbo urban area are mainly concentrated in a radiation circle with Sanjiang area as the core, the geostatistical analysis of land price in Ningbo urban area is defined as the area where Sanjiang area of Ningbo City expands outward. See fig. 1 ~ fig. 3 for valence samples within the analysis range and scope.

Figure 1 Distribution of commercial land price samples within the analysis scope

Figure 2 Distribution of residential land price sample points within the analysis scope

Figure 3 Distribution map of industrial land price sample points within the analysis scope

3.2 Analysis of land price changes under anisotropic conditions

As a regionalized variable, land price changes in all directions. If a regionalized variable changes in different directions, it is said to be isotropic when the variation function r (h) changes in all directions, and vice versa. Figures 4 ~ 6 show the change curves of different land price types in four directions: 0, 45, 90 and135.

(1) Industrial land price does not show anisotropic structural characteristics. The semi-variance function values in different directions and distances can not fit a suitable model, which shows that the development axis of industrial land in Ningbo urban area is unclear and the policy factors of industrial land price are also large, resulting in poor land price regularity.

(2) Both residential and commercial land prices show certain anisotropic structural characteristics. In different directions, the nugget value, adjacent value and range are different, which has the characteristics of zonal anisotropy. In the direction of 135 (northwest-southeast), the fitting effect of semi-variance function value of land price at different distances is good, which shows that the construction of Yinzhou District has had a significant impact on the distribution pattern of commercial and residential functions in Ningbo in recent years. A large number of residential areas have been built in the west and south of Sanjiang in Ningbo, forming new commercial centers such as Trust-Mart and Metro.

3.3 Analysis of land price changes under isotropic conditions

In order to compare different land prices and analyze land price diffusion, it is often necessary to transform anisotropic structures into isotropic structures through linear transformation and matrix transformation. The principle is that by changing the distance h in different directions, the change of γ(h) in all directions is the same. Geostatistics software GS+ provides this tool, which can transform anisotropic regionalized variables into isotropic structures for research. Figures 7 ~ 9 show the change curves of different land price types under isotropy, and Figure 10 ~ 12 shows the planes and corresponding three-dimensional surfaces of different land price types after kriging space interpolation. Table 1 gives the parameters of the change curve simulation formula under the isotropy of different land price types.

Table 1 Parameter isotropy of simulation formula of change curve under different land price types

Fig. 4 Variation curves of industrial land price in four directions of 0, 45, 90, 135 (exponential model).

Fig. 5 Variation curves of residential land price in four directions of 0, 45, 90, 135 (exponential model).

Fig. 6 Variation curves of industrial land price in four directions of 0, 45, 90 and 135 (spherical model)

The simulation equation of industrial land price change curve is:

Innovation of Land Information Technology and Development of Land Science and Technology: Proceedings of the 2006 Annual Conference of china land science Institution.

Fig. 7 curve of industrial land price change (spherical model)

The simulation equation of residential land price change curve is:

Innovation of Land Information Technology and Development of Land Science and Technology: Proceedings of the 2006 Annual Conference of china land science Institution.

The simulation equation of commercial land price change curve is:

Innovation of Land Information Technology and Development of Land Science and Technology: Proceedings of the 2006 Annual Conference of china land science Institution.

Fig. 8 residential land price change curve (spherical model)

Fig. 9 Variation curve of commercial land price (spherical model)

The plane of industrial land price and its corresponding three-dimensional surface after interpolation in figure 10 kriging space.

The residential land price plane and its corresponding three-dimensional surface after interpolation in figure 1 1 kriging space.

Commercial land price plane and its corresponding three-dimensional surface after interpolation in figure 12 kriging space.

4 conclusion

(1) The three land prices have spatial correlation in a certain spatial range, and the spatial correlation distance is 18 10 ~ 3925m. The spatial correlation distance of industrial land price is the largest, which is 3925m；; ; The second place is residence, which is 2914m; ; The lowest commercial value is 18 10 m, which shows that the gradient of spatial change of land price is that commercial land is larger than residential land, and residential land is larger than industrial land.

(2) In the total variance of the three spatial variations of land price, the proportion of structural variance (C) is greater than that of nugget effect (C0). This shows certain factors (traffic conditions, infrastructure, environmental conditions, etc. ) The influence on land price is greater than that caused by random factors, and the composition of land price is relatively reasonable.

(3) Nugget effect (C0) is residential land price > commercial land price > industrial land price, which shows that among the three land prices, residential land price is the most vulnerable to uncertain factors, with the largest price change and the most stable industrial land price. This is consistent with the obvious increase in housing prices in Ningbo real estate market and the macro-control policies introduced by the government from time to time in recent years.

Figure 13 Price Distribution Map of Commercial Land in Ningbo

Figure 14 Distribution Map of Residential Land Price in Ningbo

(4) The spatial variability coefficient C/C0+C, the commercial land price is 0.659, the residential land price is 0.807, and the industrial land price is 0.874, indicating that the industrial land price has the strongest spatial variability and is most affected by the surrounding land prices. In recent years, the commercial land price and residential land price in Ningbo have been affected by the adjustment of urban planning. With the construction of the newly planned urban center (such as the eastern new city) and sub-center (the central area of Yinzhou), it presents the characteristics of discontinuity and mutation in space.

(5) From the spatial interpolation of the land price distribution map of downtown Ningbo (Sanjiang area), adding the controlling basic factors such as roads and rivers (Figure 13 ~ Figure 15), it can be seen that the regional differentiation law of commercial land price in Ningbo is obvious, not only the land price in the built-up area of the old city in the original central city is higher, but also the whole city develops eastward, Jiangbei District develops northward and Haishu District develops westward. The changing law of residential land price and industrial land price in Ningbo urban area has also been very intuitive.

Figure 15 Distribution Map of Industrial Land Price in Ningbo City

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