Mapping Regional Economic Activity Using DMSP/OLS Nighttime Light Data

Official statistics with only single indicators are difficult to reflect the comprehensive strength of the region. The DMSP/OLS nighttime lighting data contains rich connotations [8,9,10], which can present not only economic aspects (GDP, urban agglomeration, urbanization, etc.), but also social aspects (population distribution, population size, etc.), as well as the ecological aspects (vegetation, energy consumption, CO₂ emissions, etc.). Therefore, the regional scale index based on DMSP/OLS nighttime lighting data can comprehensively express the regional scale. The formula is as follows: (1)Mi=I×B[∑e=gf(Ne×Se)]×AiAo{M_i} = I \times B\left[ {\sum\nolimits_{e = g}^f {\left( {{N_e} \times {S_e}} \right)} } \right] \times {{{A_i}} \over {{A_o}}} where M_i denotes region scale index, N_e denotes gray value of the e-level pixel in the region, that is, DN value of the e-level pixel, S_e denotes the total number of e-level pixel, ∑e=gf(Ne×Se)\sum\nolimits_{e = g}^f {\left( {{N_e} \times {S_e}} \right)} denotes the total night light intensity of the e-level pixel, g and f denotes initial threshold and end threshold respectively, in this paper, g = 1, f = 63; A_i denotes the area between initial threshold and end threshold of the region i pixel gray value, A_o denotes the total area.

Gravity model is based on Newton's classical mechanics. Through the universal gravity formula, it extends and expands continuously to form a complete and simple gravity model [11,12], which is mainly used to analyze and predict the regional interaction. Gravity model is widely used in regional interaction. In general, the gravity model can be simplified as: (2)My=KYiYjDij{M_y} = K{{{Y_i}{Y_j}} \over {{D_{ij}}}} where K denotes constants, which generally represent gravitational coefficients, Y_i and Y_j denote endogenous variables, D_ij denotes spatial distance. The regional interaction model in this paper extends the use of gravity model to analyze the interaction between China and the five central Asian countries. The expanded formula is as follows: (3)Iij=KMiaMjbdijc(i≠j;i∈[1,n];j∈[1,m]){I_{ij}} = K{{M_i^aM_j^b} \over {d_{ij}^c}}\left( {i \ne j;i \in \left[ {1,n} \right];j \in \left[ {1,m} \right]} \right) where I_ij denotes the region interaction index between region i and region j, K denotes proportionality coefficient, in this paper, K=1, M_i denotes the region scale of initial region i, M_j denotes the region scale of end region j. a and b are the potential indexes for cities to generate internal agglomeration and external diffusion of urban factor flows. In this paper, values of a and b are set at 1. cdenotes the damping coefficient of the distance between regions, which is the rate at which the interaction between regions decreases as the distance increases between regions. The damping coefficient cis subject to factors like geographical environment and regional economic development. The damping coefficient is used to describe the scale difference of interaction between regions: when the value is 1, it represents the interaction between regions at the national scale; when the value is 2, it represents the interaction between regions at the regional scale. d denotes the distance between region i and region j.

Based on region interaction index, define region incidence matrix A=[I11I12⋯I1nI21I22⋯I2n⋮⋮⋱⋮In1In2⋯Inn]A = \left[ {\matrix{{{I_{11}}} & {{I_{12}}} & \cdots & {{I_{1n}}} \cr {{I_{21}}} & {{I_{22}}} & \cdots & {{I_{2n}}} \cr \vdots & \vdots & \ddots & \vdots \cr {{I_{n1}}} & {{I_{n2}}} & \cdots & {{I_{nn}}} \cr } } \right] , I_ij denotes the region interaction index of region i and region j. In region incidence matrix, some information is not important, in order to keep important information and filter unimportant information, 0–1 Region Incidence Matrix is needed. The inter-regional association is bounded by the critical value and divided into strong association and weak association. The weak association is set to 0 and the strong association is set to 1. Suppose matrix B is the 0–1 region incidence matrix and suppose α is the critical value. bij={1Iij>α0Iij<α{b_{ij}} = \left\{ {\matrix{1 & {{I_{ij}} > \alpha } \cr 0 & {{I_{ij}} < \alpha } \cr } } \right. [13,14,15]. b_ij=1 denotes that there is strong interaction between region i and region j, b_ij=0 denotes that there is no strong interaction between region i and region j.

DMSP/OLS nighttime light data was obtained by directly averaging the gray values of visible light and NVIR channels throughout the year, and the gray values of the data ranged from 1 to 63. The data used in this paper is downloaded from the web site (https://www.ngdc.noaa.gov/eog/dmsp/downloadV4composites.html). At present, there are six versions of DMSP satellites, F10, F12, F14, F15, F16 and F18, on the website. This paper downloads and uses the latest year's Nighttime Light Data.

To analyze the region network model of China and five Central Asian countries in the Silk Road Economic Belt based on DMSP/OLS nighttime light data, it was necessary to obtain the 0–1 region incidence matrix of China and five central Asian countries based on DMSP/OLS nighttime light data. In this step, strong interaction edges are retained and weak interaction edges are deleted. In this paper, the 0–1 matrix consists of 82 nodes. The incidence structure was visually displayed in the form of black and white grids with the help of Matlab, which vividly shows the relationship between regions. The black grid means that the value of the element in the matrix is “0” and the white grid means the value of the element in the matrix is “1,” as shown in Figure 1.

Fig. 1