Spatialization and Analysis of China’s GDP Based on NPP/VIIRS Data from 2013 to 2023

Abstract

The quality of nighttime light (NTL) data is an important factor affecting the estimation of gross domestic product (GDP), but most studies do not use the latest NPP/VIIRS V2 annual composite product, and there is a lack of China’s GDP estimation products in recent years. To address this problem, this paper studies the NPP/VIIRS remote sensing estimation method for the GDP in mainland China from 2013 to 2023. First, the remote sensing data are preprocessed, and the noise masking method is used to remove outliers. The total amount of NTL, average NTL value, and comprehensive NTL index data are extracted. Combined with the GDP data from the Statistical Yearbook, a fitting model of the GDP and NTL index is constructed. The differences between different GDP estimation models are compared and analyzed, and the optimal model is selected as the estimation model. In addition, through the optimal fitting model, GDP spatial estimation products from 2013 to 2023 are produced. Moreover, the spatiotemporal variation characteristics of the GDP in mainland China are analyzed, with a focus on the spatiotemporal variation of GDP decline regions and the changes in the GDP rankings of provinces and cities. The main conclusions include the following: (1) In the time regression analysis, the linear model MNL has a strong correlation with the GDP, with an R² of 0.972. This model is selected as the optimal fitting model to calculate the spatial data of the GDP. (2) The spatial distribution of the GDP in mainland China is high in the east and low in the west, and it shows a characteristic of extending from the provincial capital to the surrounding cities. The connectivity between adjacent high-GDP areas continues to increase. (3) From 2013 to 2023, the GDP in most parts of China showed an upward trend, with 98.56% of pixels growing and only 0.99% of pixels declining. The declining pixels are mainly distributed in heavy industrial cities supported by fossil fuel resources, such as Ordos, Daqing, Aksu, etc. (4) Compared with statistical data, the overall difference of the GDP estimated by NTL data is not large, and the relative error is between 0.04% and 1.95%. From the perspective of the GDP ranking of each province, the ranking of most provinces is not much different, fluctuating between ±2. A small number of provinces have large ranking differences due to reasons such as dominant industries and power supply. By spatializing the GDP data of mainland China in the past 11 years, the spatiotemporal changes of the GDP within mainland China were analyzed. The research results can provide support for government economic decisions such as urban development.

1. Introduction

The GDP is the core indicator of national economic accounting and plays an important role in government decision-making. Traditional GDP data come from government statistical departments and are collected based on administrative divisions. Its statistical method has many limitations: it cannot show the differences within the statistical unit [1], the data update speed is slow, it consumes a certain amount of manpower and material resources, and the statistical measurement standards between different units are different. Therefore, it is difficult for this statistical method to objectively and comprehensively reflect the changes in social and economic activities [2].

NTL is a spatial data closely related to human socio-economic activities. It can realize the observation of global NTL intensity without distinction, and provide new ideas for socio-economic assessment at multiple spatiotemporal scales [3,4,5]. NTL comes from a wide range of sources, such as DMSP-OLS, NPP-VIIRS, Luojia-1, SDGSAT-1, and other satellites/sensors. The temporal and spatial resolutions and the stage of data collection are different. At present, NTL has been widely used in many fields such as urban monitoring [6,7,8,9], socio-economic estimation [10,11,12,13], and disaster assessment [14,15,16,17,18].

In recent years, there have been many research results on GDP estimation using NTL. For example, Zhao et al. spatialized the GDP of Henan Province, China, and analyzed the economic center distribution and development direction of economic connection elements at the provincial and municipal levels [19]; Liang et al. combined multiple data, used multivariate linear regression and random forest algorithms to estimate the GDP of Ningbo City, China, and, following a comparison, concluded that the township estimates were more accurate than county-level estimates [20]; Zijun Chen et al. combined the NPP/VIIRS datasets and Sentinel-2 images to spatialize and analyze the GDP of the secondary and tertiary industries in Zibo City, China, and obtained the GDP change pattern of the city [21]; Xi Chen et al. used the United States as the research area and found that the NPP/VIIRS data predicted the GDP of metropolitan statistical areas better than the GDP prediction results of each state, indicating that NTL is more closely related to cities than to rural areas [22]; Haoyu Liu et al. proposed a learning framework that relies on a convolutional neural network algorithm to use NTL to estimate the county-level GDP in mainland China [23]; Andrew Marx et al. calculated the GDP using DMSP/OLS data and found that, between 2000 and 2012, Panama’s official GDP was 19% higher than the GDP produced by nighttime lights [24]; and Xuantong Wang et al. combined NPP/VIIRS data and population data from the Global Human Settlements to propose a new enhanced light intensity model to capture the spatial heterogeneity in economic activities [25].

Compared with traditional GDP statistics, NTL data have obvious advantages in assessing social and economic indicators: ① they can objectively obtain global NTL data without being affected by administrative boundaries; ② the spatial details within the data are rich and can reflect the internal differences of a certain region [26]; and ③ the periodicity of obtaining data is short and can provide timely support for government decision-making [27]. The quality of NTL remote sensing data is an important factor affecting GDP estimation. The NPP/VIIRS second edition annual NTL data are generated by the average monthly cloud-free radiation, and the data threshold range is based on the multi-year maximum median and multi-year percentage cloud cover grid. This data product has a strong predictive ability for the GDP [12]. Due to the fact that the NPP/VIIRS data are relatively new, and the mainland China region is large and complex, there are fewer studies using the second version of the NPP/VIIRS annual data for GDP estimation, and there is a gap in the spatial data of the GDP for China in recent years. To address this problem, this paper uses the second edition (V2 NTL) annual product data of NPP/VIIRS to study the spatialization method of the GDP, produce NTL remote sensing estimation products for mainland China from 2013 to 2023, and analyze the spatiotemporal variation characteristics of the GDP in the past 11 years.

2. Study Area and Data

2.1. Study Area

China is located in the eastern part of Asia, on the west coast of the Pacific Ocean. It has a vast territory, with a latitude and longitude range between 3.86° N–53.55° N and 73.66° E–135.05° E. Its land area is about 9.6 million square kilometers, ranking third in the world. China is the world’s second largest economy, with a fast GDP growth rate. The land border is 22,800 km long, the coastline is more than 18,000 km long, and there are more than 5000 islands along the coast. China is rich in natural resources, has a superior geographical location, has a long history and culture, and has developed rapidly since the reform and opening up. China has a total of 34 provincial-level administrative regions, including 23 provinces, 4 municipalities, 5 ethnic autonomous regions, and 2 special administrative regions. Due to the lack of statistical data, this study does not include Taiwan, Hong Kong, Macao, and other regions, and only studies the scope of mainland China, as shown in Figure 1.

2.2. Data and Preprocessing

2.2.1. Data

The data for this study mainly include NPP/VIIRS NTL data, geographic information data, and socio-economic statistics. NPP/VIIRS NTL data come from the National Oceanic and Atmospheric Administration (NOAA) of the United States. Its full name is the Visible Near-Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar-orbiting Partnership (Suomi NPP) satellite. The data resolution is about 500 m, and the product types include annual products, monthly products, and daily products. This paper uses the annual average product data from 2013 to 2023 for related research. Geographic information data include China’s administrative boundaries, and provincial, prefectural, and county administrative boundaries; socio-economic data include GDP data, population data, etc., which come from the statistical yearbook published by the Chinese government every year.

2.2.2. Processing of NPP/VIIRS Data

The NPP/VIIRS imagery data downloaded directly have not been denoised, and they contain background noise and the effects of transient light sources such as fires, gas flares, and volcanoes. These effects can increase the intensity of nighttime light, causing abnormally high DN values and reducing the reliability of GDP. Therefore, it is necessary to preprocess the downloaded NPP/VIIRS data to achieve the purpose of eliminating noise. There are many methods to remove the influence of outliers, including the noise mask method [28], the optimal threshold method, the noise threshold method, etc. Because the noise mask method has the advantages of a simple operation and high overall result accuracy, this method is used for noise processing in this paper. For negative DN values in the original NPP/VIIRS image, 0 is assigned; for high outliers, the highest pixel value of Beijing, Shanghai, and Guangzhou, three cities with developed economies and large urban scales in China, is used as the threshold, and the data above the threshold are eliminated, and then the neighborhood operation is performed and smoothing is performed to make it present a reasonable value.

3. Methodology

In order to estimate the GDP of mainland China in the past 11 years using the latest version of NPP/VIIRS second edition annual NTL data, this paper compares the estimation accuracy of different regression models and selects the optimal model to estimate the GDP of mainland China in the past 11 years. The main steps (Figure 2) include the following four aspects: (1) calculation of NTL index; (2) establishment of GDP spatialization model; (3) analysis of spatiotemporal trend; and (4) comparison and analysis of the differences between official GDP and GDP data obtained by NTL.

3.1. Calculation of NTL Index

Using ArcGIS software (v.10.8), we extracted data such as the total amount of NTL, average light intensity, NTL area ratio, average relative light density, and composite light index. The specific calculation formulae for each index are shown in the following

Table 1. NTL indices and economic parameter list [19].

Attribute	Definition
$D{N}_{\mathrm{i}}$	The pixel whose gray value is i in the area.
$D{N}_{\mathrm{M}}$	The pixel with the maximum gray value in the area.
${\mathrm{n}}_{\mathrm{i}}$	The gray value in the area is the number of i pixels.
$N$	The total number of pixels in the area.
$N_{\mathrm{L}}$	The total number of pixels whose gray value is not 0 in the area.
Total nighttime light, TNL	$TNL={\displaystyle \sum _{i=0}^{D{N}_M}D{N}_{\mathrm{i}}{\times \mathrm{n}}_{\mathrm{i}}}$
Mean nighttime light, MNL	$MNL={\displaystyle \frac{1}{n}}\times {\displaystyle \sum _{\mathrm{i}=0}^{D{N}_M}D{N}_{\mathrm{i}}\times n_{\mathrm{i}}}$
Light area ratio, S	$S={\displaystyle \frac{N_L}{N}}$
Average relative light intensity, I	$I={\displaystyle \frac{1}{N_L\times D{N}_M}}\times {\displaystyle \sum _{\mathrm{i}=0}^{D{N}_M}D{N}_{\mathrm{i}}\times n_{\mathrm{i}}}$
Compounded nighttime light index, CNLI	$CNLI=I\times S$

.

3.2. Method for Estimating GDP Using NTL Data

3.2.1. GDP Modeling Methodology

The brightness of NTL reflects the strength of economic development in a certain region. Using NTL data, GDP can be spatialized. In recent years, scholars have constructed many GDP spatialization models [29,30,31], including linear regression models [32], quadratic regression models [33], neural network models [20], and other models. The regression model is simple to operate and relatively accurate. Therefore, this paper selects five models, including linear regression model, quadratic regression model, exponential model, power function model, and logarithmic model, and sets GDP data as dependent variable Y and NTL index as independent variable X for modeling. At the national scale, the accuracy of different regression models is compared and analyzed from time regression and space regression, and the best fitting model is selected to spatialize China’s GDP. In spatial regression analysis, the annual GDP and NTL index data of 31 provincial administrative regions from 2013 to 2023 are used to construct regression models year by year; in temporal regression analysis, the annual GDP and NTL index data of mainland China from 2013 to 2023 are used to construct regression models.

3.2.2. Model Regression Accuracy Evaluation Method

The accuracy evaluation mainly includes three methods: the coefficient of determination of the regression model-R², the root mean square error (RMSE), and the relative error (RE).

The coefficient of determination is also called the goodness of fit, which reflects how much of the fluctuation of y can be described by the fluctuation of x. The greater the goodness of fit, the higher the degree of explanation of the independent variable to the dependent variable. The correlation coefficient R² indicates the correlation between the NTL index and GDP data. The value range of R² is 0 to 1. The closer to 1, the stronger the correlation.

$$R^2=1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^{\mathrm{m}}{(f(x_i)-y_i)}^2}}{{\displaystyle \sum _{i=1}^{\mathrm{m}}{(f(x_i)-{\overline{y}}_i)}^2}}}$$

(1)

where f(x_i) is the true label; $y_i$ is the predicted result; and ${\overline{y}}_i$ is the sample mean. The closer R² is to 1, the better the model fits the data.

RMSE is the square root of the ratio of the square of the deviation between the predicted value and the true value to the number of observations n. It measures the deviation between the predicted value and the true value and is more sensitive to outliers in the data.

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^{\mathrm{n}}{(GD{P}_p-GD{P}_s)}^2}}$$

(2)

Among them, GDP_p is the predicted value of GDP; and GDP_s is the actual value of GDP.

RE refers to the degree of closeness between the predicted value and the statistical value, and the closer the RE value is to 0, the more accurate it is.

$$RE={\displaystyle \frac{GD{P}_{\mathrm{p}}-GD{P}_{\mathrm{s}}}{GD{P}_{\mathrm{s}}}}\times 100\%$$

(3)

3.3. Spatialization of GDP

By comparison, it is found that the linear model of MNL and GDP simulation obtained by time regression analysis at the national scale is the best. Based on this model, the GDP of mainland China in each year is estimated using the MNL from 2013 to 2023, that is, GDP_p estimated based on the NTL index. Then, based on the relationship between MNL and the total NTL value, GDP_p is spatially decomposed into each pixel to obtain the spatial data GDP_i of GDP. The formula for decomposition into each pixel is as follows:

$$GD{P}_i={\displaystyle \frac{D{N}_{\mathrm{i}}}{{\displaystyle \sum _{\mathrm{i}=0}^{D{N}_M}D{N}_i\times n_i}}}•GD{P}_p$$

(4)

Among them, GDP_i is the final GDP simulation value of pixel i, and GDP_p is the total GDP estimated by the NTL index in a certain year, which is calculated by the fitted optimal regression model equation.

3.4. Analysis of GDP Temporal and Spatial Variation Trends

For the changes in continuous data, the direction and trend in the data are often brought to people’s attention. For the dynamic changes in GDP in different years, the Sen trend estimation method [34] is used, and the MK trend test method [35] is used for significance test. The combination of the two methods can improve the accuracy of spatial pixel trends to a certain extent and reduce noise interference [36]. This method does not require the time series to meet most of the assumptions of normal distribution and sequence autocorrelation, and is insensitive to outliers in the time series [37]. It is widely used in scientific research.

Theil–Sen trend estimation method is also known as the Sen slope, which is a robust non-parametric statistical method. By calculating the slope between two pairs of data in the sequence, the median of the slopes of all data pairs is taken as the overall trend in the time series. The calculation formula is as follows:

$$\beta =M\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{n}({\displaystyle \frac{x_j-x_i}{j-i}}), \forall j>\mathrm{i}$$

(5)

In the formula, β is the median of the slope of all data pairs; and x_j and x_i are time-series data, referring to the time-series data of the j year and the i year, respectively; Median is the function used to calculate the median of the data set; β > 0 means that the time series shows an upward trend; β < 0 means that the time series shows a downward trend; and β ≈ 0 means that the data trend does not change much.

The Mann–Kendall trend test method was originally proposed by Mann, and was improved and perfected by Kendall and Sneyers, combined with Theil–Sen; that is, the Sen trend value is calculated first, and then the MK method is used to judge the trend significance. It can more effectively investigate the trend in change and test the significance of long time-series data. The calculation formula is as follows:

$$Z=\left\{\begin{array}{c}{\displaystyle \frac{S-1}{\sqrt{\mathrm{var}(S)}}}, S>1\\ 0,\hspace{1em}S=0\\ {\displaystyle \frac{S+1}{\sqrt{\mathrm{var}(S)}}}, S<1\end{array}\right.$$

(6)

$$S={\displaystyle \sum _{i=1}^{n-1}{\displaystyle \sum _{j=i+1}^n\mathrm{sgn}(x_j-x_i)}}$$

(7)

$$\mathrm{sgn}(x_j-x_i)=\left\{\begin{array}{c}1, x_j-x_i>0\\ 0, x_j-x_i=0\\ -1, x_j-x_i<0\end{array}\right.$$

(8)

$$\mathrm{var}(S)={\displaystyle \frac{n(n-1)(2n+5)-{\displaystyle \sum _{i=1}^m{t}_i(t_i-1)(2t_i+5)}}{18}}$$

(9)

In the formula, Z is the standard normal test statistic; S is the test statistic; var is the variance function; n is the number of data in the time series; sgn represents the sign function; x_j and x_i are the time-series data of the j year and the i year, respectively; m is the number of data groups that appear repeatedly in the sequence; and t_i is the number of repeated data in the i repeated data group. In this study, a bilateral trend test is used. Under a given significance level α, the critical value $Z_{1-\alpha /2}$ is found in the normal distribution table. When $\left|Z\right|\le Z_{1-\alpha /2}$, the null hypothesis is accepted; that is, the trend is not significant. When $\left|Z\right|>Z_{1-\alpha /2}$, the null hypothesis is rejected; that is, the trend is considered significant. In this study, the significance level α = 0.05, then the critical value $Z_{1-\alpha /2}=\pm 1.96$; when the absolute value of Z is greater than 1.65, 1.96 and 2.58, it means that the trend has passed the significance test with a confidence level of 90%, 95%, and 99%, respectively.

4. Results

4.1. Analysis of GDP Modeling Results

4.1.1. Spatial Regression Analysis

Spatial modeling analysis found that the MNL, TNL, and CNLI are not highly correlated with the GDP, but they are highly correlated with the per capita GDP, so we used the NTL index and per capita GDP for modeling analysis.

Table 2. R² values of various function models in 2013.

R2	MNL	TNL	CNLI
Linear model	0.524	0.011	0.512
Logarithmic model	0.684	0.012	0.568
Quadratic function model	0.795	0.015	0.715
Power function model	0.631	0.025	0.517
Exponential model	0.421	0.027	0.408

shows the regression results of five models in 2013, including the linear regression model, quadratic regression model, exponential model, power function model, and logarithmic model, with the NTL index of 31 provinces as the independent variable and the per capita GDP as the dependent variable, taking mainland China as a whole, and taking the per capita GDP as the dependent variable. The results show that the R² of each model of the MNL is between 0.421 and 0.795, with a high correlation; the R² of the TNL is between 0.011 and 0.027, with a very low correlation; and the R² of the CNLI is between 0.408 and 0.715, which is worse than the model of the TNL but not as good as the relevant model of the MNL, so the MNL and per capita GDP data were selected for fitting. From the regression results of each year, among the five function models, the quadratic function regression model has the best fit, and the R² value is the highest in the model, so we choose the quadratic regression model to construct the function model.

As shown in

Table 3. Function equation and error value from 2013 to 2023.

Year	Functional Equation	R2	RMSE
2013	$y=-0.115x^2+1.957x+2.811$	0.795	0.91
2014	$y=-0.122x^2+2.056x+3.158$	0.786	1.00
2015	$y=-0.124x^2+2.151x+3.262$	0.807	1.00
2016	$y=-0.135x^2+2.331x+3.498$	0.842	1.00
2017	$y=-0.12x^2+2.364x+3.209$	0.874	0.96
2018	$y=-0.124x^2+2.433x+3.499$	0.853	1.10
2019	$y=-0.094x^2+2.113x+4.066$	0.722	1.69
2020	$y=-0.082x^2+1.964x+4.172$	0.760	1.51
2021	$y=-0.081x^2+2.051x+4.625$	0.756	1.69
2022	$y=-0.081x^2+2.068x+5.011$	0.737	1.82
2023	$y=-0.075x^2+2.033x+5.259$	0.726	1.95

, the optimal function model constructed from 2013 to 2023, the R² values of the functions are greater than 0.7, and the fitting effect is good. In addition, we calculated the RMSE from 2013 to 2023. The RMSE ranges from 0.91 to 1.95, and the average RMSE is 1.33. Among them, the RMSE of 6 years of data is less than the average. The smallest error is in 2013, the largest error is in 2023, and the error values from 2019 to 2023 are higher than the average. The overall error is within the allowable range, and the fit is higher and better.

4.1.2. Time Regression Analysis

Figure 3 shows the optimal function fitting results with the NTL index of mainland China as the independent variable and the GDP or per capita GDP of mainland China as the dependent variable. The study found that the R² between the GDP and MNL, TNL, and CNLI is higher than the R² between the per capita GDP and MNL, TNL, and CNLI, and the function obtained by fitting the GDP is convenient for constructing a spatial model of the GDP. The R² strength of the regression model of each NTL index is ranked as follows—MNL > TNL > CNLI, and the coefficient values of the linear model and the quadratic regression model are ≥0.97.

After comprehensive consideration, the linear regression model of the MNL and GDP is the optimal model. The regression equation is y = 558592.81x − 53715.7, R² = 0.972, and the fitting effect is very good (Figure 4). Comparing the two regression methods, it is known that the optimal fitting model of the spatial regression method is the quadratic function model obtained by regressing the per capita GDP and MNL, and the optimal model obtained by the time regression method is the linear model obtained by regressing the GDP and MNL. The R² value of the optimal spatial regression model is between 0.722 and 0.874, while the R² value of the time regression model is 0.972. The correlation coefficient of the time regression model is higher than that of the spatial regression model. Therefore, the linear model fitted by the time regression model is selected to invert the GDP data through the MNL value.

4.1.3. Spatialization Results of GDP

The GDP from 2013 to 2023 is spatialized using the best fit regression model to obtain the new NTL estimation value of the GDP for each year. The total GDP data are allocated to each NTL data pixel to obtain the spatialized data of GDP. According to the distribution of GDP, ArcGIS is reclassified and the data (unit: million yuan) are divided into five categories—0–5, 5–10, 10–50, 50–100, and greater than 100—for hierarchical mapping. Figure 5 shows the hierarchical mapping results of the GDP spatialization data in 2013, 2015, 2017, 2019, 2021, and 2023.

4.2. Results of Spatiotemporal Trend Analysis

In order to explore the dynamic changes of GDP in time and space, Sen + MK trend analysis was performed in MATLAB (2023b) to obtain the trend changes from 2013 to 2023, and reclassification and map rendering were performed in ArcGIS. The reclassification results were determined based on β and Z values, that is, based on the slope value of the Sen method and the standard normal test statistic Z value of the MK method, and the proportion of pixels in each category was counted.

Table 4. GDP trend division and pixel statistics.

β	Z	GDP Trends	Pixel Ratio/%
≤−0.01	≤−1.96	Markedly decrease	0.27
≤−0.01	−1.96–1.96	Slightly decrease	0.72
−0.01–0.01	−1.96–1.96	Unchanged	0.46
>0.01	−1.96–1.96	Slightly increase	2.99
>0.01	>1.96	Significantly increase	95.57

shows the classification basis of the change trend and the proportion of each type of pixels. Pixels with a significantly increased GDP accounted for 95.57% of the total pixels, pixels with a slightly increased GDP accounted for 2.99%, and pixels with an increased GDP accounted for 98.56%, indicating that the GDP in most areas of mainland China showed an upward trend, and most of them were significantly increased pixels. Pixels with a significantly decreased GDP accounted for 0.27% of the total pixels, pixels with a slightly decreased GDP accounted for 0.72%, and pixels with a basically unchanged GDP accounted for 0.46%.

5. Discussion

5.1. Comparative Analysis Results of GDP

5.1.1. Overall Accuracy Evaluation

The official GDP data are derived from economic statistical methods, which cannot show the internal differences of statistical units and do not involve rich spatial information. The GDP spatial data calculated by NTL data can directly reflect the distribution of the GDP, and the calculation is simple and the data are objective. Overall, there are differences between the official GDP of the government and the GDP obtained by NTL. The specific situation is shown in

Table 5. GDP data obtained by different statistical methods and their errors.

Year	2013	2015	2018	2021	2023
Official GDP *	630,009.3	722,767.9	914,707.5	1,137,743	1,250,931
NTL GDP *	642,302.06	723,799.48	916,854.55	1,142,995.42	1,251,395.70
Difference	12,292.76	1031.60	2147.08	5252.01	464.39
RE	1.95%	0.14%	0.23%	0.46%	0.04%

* Unit: 100 million yuan.

. It can be seen that the fitting values using light data in 2013, 2015, 2018, 2021, and 2023 are slightly larger than the official GDP values. There are differences in the data, with an RE of 0.04% to 1.95%. The data fitting is good, especially in 2023, with an RE of only 0.04%.

5.1.2. Comparative Analysis of GDP Rankings of Various Provinces

Figure 6 shows the ranking comparison of the official GDP and GDP data obtained by NTL in different provinces in 2013, 2018, and 2023. This ranking result is consistent with the spatial distribution of the GDP, with a high GDP in the east and a low GDP in the west, and large differences between the east and the west.

Among the 31 provincial administrative units, the ranking of most provinces has not changed much, and the ranking change is between ±2, such as in Shanghai, Jiangsu, Zhejiang, Shandong, Guangdong, Tibet, Gansu, Qinghai, Xining, and other provinces. Among them, the GDPs of Shanghai, Jiangsu, Zhejiang, Shandong, Guangdong, and other provinces are the top 10 province GDPs in China, and the GDP of Tibet, Gansu, Qinghai, and other provinces are the bottom 5 province GDPs in China. The ranking of regions with a better and worse GDP is relatively stable; the ranking of a small number of provinces has changed greatly, such as Hunan, Xinjiang, Hubei, and other places. Among them, due to the development of light industry in Hunan and Hubei provinces, factories do not work outdoors or rarely work outdoors, and the NTL values will be low. In addition, due to the insufficient power generation capacity, there are phenomena such as “power outages” during peak power consumption and extreme weather conditions, which will also affect the NTL values. Xinjiang is located in the northwest inland, with rich oil and gas resources and relatively well-developed heavy industry. Mining, transportation, construction, fuel burning, and other phenomena may occur at night, resulting in higher NTL values. In addition, the area is relatively large, and there are many snow-covered mountains, dry riverbeds, or deserts that can reflect strong and weak light, which will also affect the changes in NTL values. In general, the large differences in rankings are caused by factors such as the dominant industry and power generation capacity.

5.2. Dynamic Analysis of GDP Spatial and Temporal Changes

5.2.1. The Overall Spatial and Temporal Characteristics of China’s GDP

From the perspective of spatial changes, the spatial changes in the GDP in mainland China between 2013 and 2023 are characterized by the high-GDP-value areas of provincial capital cities as the center, which continue to extend to the periphery and expand to the surrounding cities, and the spatial continuity between the high-GDP-value areas of adjacent provincial capital cities is gradually increasing. This trend is particularly obvious in the Jiangsu–Zhejiang–Shanghai region, the Guangdong–Guangdong Triangle region, and the Beijing–Tianjin–Hebei region. The development level of each region is relatively consistent with the actual situation.

From the perspective of the spatial distribution pattern, a high-GDP-gathering area consisting of one or more core cities is gradually formed. There are the Yangtze River Delta (Shanghai–Hangzhou–Suzhou–Ningbo–Nanjing–Hefei), the Chengdu–Chongqing region (Chengdu and Chongqing), the Pearl River Delta (Guangzhou–Dongguan–Shenzhen), the Bohai Sea Rim region (Beijing–Tianjin–Qingdao–Dalian–Tangshan), the Central Plains City cluster (Zhengzhou–Luoyang–Kaifeng), the Central South Region (Wuhan–Changsha–Nanchang), Fujian (Fuzhou–Quanzhou–Xiamen), Xi’an, Kunming, etc. These high-GDP-gathering areas are mainly distributed in the eastern coastal areas of China, followed by the central provincial capital cities. This situation is related to the pattern of China’s economic development. The economic development of the southeast coastal areas is relatively fast, while the development speed of the central and western regions is relatively slow due to their proximity to the inland. Different cities have different economic development policies, different leading industries, and different development directions. From the perspective of the overall spatial distribution, the situation is high in the east and low in the west, and the difference between the east and the west is large.

In addition, the area of each category of GDP was counted in ArcGIS, and the proportion of each category was calculated. The situation is shown in

Table 6. The proportion of GDP in different levels.

GDP/Million Yuan	0~5	5~10	10~50	50~100	>100
2013	95.34%	1.88%	2.12%	0.50%	0.16%
2015	95.87%	1.59%	1.84%	0.44%	0.26%
2018	95.34%	1.86%	2.02%	0.50%	0.27%
2021	94.25%	2.39%	2.40%	0.60%	0.35%
2023	94.80%	2.12%	2.18%	0.49%	0.42%

. It is found that the proportion of areas with less than 5 million is getting smaller and smaller, and it is 0.54% less in 2023 than in 2013. The area of other categories has increased. Among them, the area difference of the interval of 5 to 10 million yuan is the largest at 0.8%, and the area of the interval greater than 100 million yuan has continued to increase, increasing by 0.26% during the research period, more than doubling in ten years, and the areas with increased area are mainly in Jiangsu, Zhejiang, Shanghai, Guangdong Triangle, Beijing, and Tianjin. Shanghai, as a leading city in the Jiangsu, Zhejiang, and Shanghai region and even China’s economy, promotes the development of this region. The Guangdong Triangle region is close to Hong Kong and Macao, and there is a special economic zone (Shenzhen). The Chinese government encourages and supports the economic development of this region. Beijing is the capital of China, and the political status is very high, so the economic policy of the region is better, and the economic development is rapid.

5.2.2. Differences in Economic Development of Major Urban Agglomerations

The major urban agglomerations in mainland China include the Beijing–Tianjin–Hebei, Yangtze River Delta, and Pearl River Delta urban agglomerations, as shown in Figure 7, which are economically developed regions. The Beijing–Tianjin–Hebei urban agglomeration includes Beijing, Tianjin, the entire territory of Hebei, and Anyang City in Henan Province. The Yangtze River Delta urban agglomeration includes 27 prefecture-level cities in Shanghai, Jiangsu, Zhejiang, and Anhui. The Pearl River Delta urban agglomeration includes Guangzhou, Foshan, Zhaoqing, Shenzhen, Dongguan, Huizhou, Zhuhai, Zhongshan, and Jiangmen City in Guangdong Province, and is the smallest of the three urban agglomerations.

By calculating the GDP data of the three major urban agglomerations in 2013 and 2023, and obtaining the official GDP data, and comparing them, we obtain

Table 7. GDP of the three major urban agglomerations in 2013 and 2023.

Urban Agglomeration	Official GDP (100 Million Yuan)			NTL GDP (100 Million Yuan)
	2013	2023	Growth Rate	2013	2023	Growth Rate
Jing–Jin–Ji	62,000	104,442	40.64%	53,727.57	112,316.95	48.96%
The Yangtze Delata	97,760	305,045	67.95%	132,275.84	251,827.82	47.47%
Pearl River Delta	53,060.48	110,200	51.85%	47,674.22	87,660.59	45.61%
Total	212,820.48	519,687	59.05%	237,277.63	451,805.36	47.48%

. From the official data, the GDP of the Yangtze River Delta urban agglomeration grew the fastest, with a growth rate of 67.95%; from the NTL data, the GDP growth rate of the Beijing–Tianjin–Hebei urban agglomeration was 1.49% faster than that of the Yangtze River Delta. The Beijing–Tianjin–Hebei urban agglomeration and the Yangtze River Delta urban agglomeration have a large area of more than 200,000 square kilometers, while the Pearl River Delta urban agglomeration covers an area of only 56,000 square kilometers. From the perspective of the unit area, the official GDP of the Pearl River Delta urban agglomeration in 2023 is about 1967.857 billion yuan; the GDP calculated by NTL is about 1565.368 billion yuan; and the GDP of the Beijing–Tianjin–Hebei urban agglomeration is about one-quarter of that of the Pearl River Delta urban agglomeration. The GDP per unit area of the Pearl River Delta urban agglomeration is the highest among the three urban agglomerations, and its economic activities are the most active. Overall, over the past 11 years, the official GDP growth rate has been 11.57% faster than the GDP under NTL. The RE of the total GDP in 2023 is −0.13, which is within the controllable range.

From the overall changes in the high-value-GDP areas (GDP greater than 100 million), between 2013 and 2023, the Beijing–Tianjin–Hebei urban agglomeration added 3557.43 km², the Yangtze River Delta urban agglomeration added 9381.65 km², and the Pearl River Delta urban agglomeration added 4191.24 km². From the expansion rate of the high-value-GDP areas, the Yangtze River Delta region has the fastest expansion rate, which is 852.88 km²/a; and the Beijing–Tianjin–Hebei region has the slowest expansion rate, which is 323.40 km²/a. From the expansion rate per unit area of the high-value-GDP areas, the Pearl River Delta region has the fastest expansion rate, which is about 4.8 times that of the Beijing–Tianjin–Hebei region and 1.8 times that of the Yangtze River Delta region. From the geographical location analysis, the Pearl River Delta region is close to Hong Kong and Macao, and has excellent ports, and foreign trade industry development and prosperity, and, thus, the fastest development rate. The Yangtze Delta, with Shanghai as the center, is located in the plain area, through the Yangtze River; the transport industry is developed, and the industrial characteristics of each city are obvious; the industry is complete, and the development of urban groups is good. The Jing–Jin–Ji region is dominated by the development of heavy industry. Due to China’s attention and protection of the ecological environment in recent years, the economic development of this region has been limited to a certain speed.

In addition, typical cities in each city are selected to analyze the changes in the high-value-GDP areas. As shown in Figure 8, this is a thematic map for spatial expansion research in Beijing, Tianjin, Nanjing, Shanghai, Hangzhou, and Suzhou in the Beijing–Tianjin–Hebei region, and Guangzhou and Shenzhen in the Pearl River Delta region. Taking Beijing as an example, the area of high-GDP-value areas was 1214.52 km² in 2013, and the area of high-GDP-value areas increased by 455.66 km² from 2013 to 2018, and the area of high-GDP-value areas increased by 485.27 km² from 2018 to 2023. The expansion speed of high-GDP-value areas from 2018 to 2023 is faster than that from 2013 to 2018, and high-GDP-value areas continue to expand to the surrounding suburbs.

5.2.3. Regional Differences in Economic Development

According to different cultural customs and regional characteristics, mainland China can be divided into six major regions, as shown in Figure 9, namely, Northeast China, North China, East China, Central South China, Southwest China, and Northwest China. Taiwan is included in the East China region, and Hong Kong and Macao are included in the Central South region, but the statistics of Taiwan, Hong Kong, and Macao are not included. Due to the differences in geographical location, and relevant policies and leading industries in different regions, the economic development conditions of the regions are also different.

Using the results of GDP spatialization, the GDP data of different regions in 2013, 2018, and 2023 were counted, respectively, and the GDP growth rate in the past 11 years was calculated, and

Table 8. GDP of the six major regions in mainland China.

Region	2013	2018	2023	Growth Rate	Area (km2)
North China	94,662.21	121,179.80	175,583.90	46.09%	151.99
Northeast China	58,382.02	66,920.48	78,263.48	25.40%	79.18
East China	222,957.14	338,783.30	468,702	52.43%	80.83
Central–South China	132,708.29	201,902.60	291,331.38	54.45%	102.58
Southwest China	60,688.78	96,966.05	117,082.57	48.17%	233.00
Northwest China	60,610.89	88,955.19	119,967.98	49.48%	301.02

was obtained. In terms of the total GDP, the economic situation in East China is the best in 2023, while the economic situation in Northeast China is relatively poor. In terms of the growth rate, the average GDP growth rate of the country from 2013 to 2023 is 46%, while the growth rate of Northeast China is only 25.40%, which is lower than the GDP growth rate of other regions. The GDP growth rate in Central and South China is the fastest, reaching 54.45%, and the GDP growth rate in East China is slightly lower than that in Central and South China. The GDP in North China, Southwest China, and Northwest China is growing steadily, with a growth rate between 45% and 50%. In terms of land area, the area difference between East China and Northeast China is small, but the GDP gap between the two regions in 2023 is the largest, with a difference of 39,043,852 million yuan.

As shown in Figure 10, from the perspective of the expansion process of the high-value-GDP areas in East China and Northeast China, the Northeast region increased from 3763.48 km² in 2013 to 4830.92 km² in 2023, with an area increase of 1067.45 km². Among them, the expansion area from 2013 to 2018 is 682.02 km², which is 296.59 km² larger than the expansion area from 2018 to 2023. The area of East China’s high-value-GDP area in 203 was 31,313.52 km², an increase of 16,768.38 km² from 2013. The high-value-GDP areas in East China are concentrated in Shanghai, Jiangsu, the Zhejiang coastal areas, Nanchang, Fujian (Fuzhou–Quanzhou–Xiamen), and other places. The high-value-GDP areas in Northeast China are mainly concentrated in Harbin, Changchun, Shenyang, Dalian, and other places. And the scale of East China is larger than that of Northeast China. We analyze the reasons for the huge gap between East China and Northeast China: East China is located on the west coast of the Pacific and the eastern coast of the Eurasian continent, with superior natural conditions. In addition, there are many provinces and cities with a strong GDP in this region, including Jiangsu, Shanghai, Zhejiang, Shandong, and other places. They are rich in products, are economically prosperous, have complete industrial chains and an abundant labor force, and have contributed greatly to the development of China’s economy. The Northeast region has a higher geographical latitude and better natural conditions. It is a high-quality grain-producing area in China. However, the thermal conditions are poor and the winter is long. Although it is located on the border of China, its outlets to the sea are only distributed in Liaoning Province. Coupled with the small reserves of fossil fuel resources, the development of heavy industry is hindered and the population loss is serious. In addition, there are protected areas such as the Greater Khingan Mountains and Lesser Khingan Mountains in the Northeast, whose main functions are ecological protection and water source conservation. The above are factors affecting the slow economic development in Northeast China. East China and Northeast China have similar area sizes, but different leading industries, different economic foundations, and different development strategies, which results in differences in GDP.

5.2.4. Analysis of Cities with Rapid GDP Decline

Figure 11 is a trend chart of GDP temporal and spatial changes. As can be seen from the figure, the GDP data of most parts of mainland China are on an upward trend, and the obvious increase is the general trend in GDP change from 2013 to 2023; only some regions have a more obvious downward trend in GDP, such as Aksu in Xinjiang, Daqing in Heilongjiang, Ordos in Inner Mongolia, Yan’an in Shaanxi, etc.

In order to find the areas with a declining GDP in the figure and explore the law behind the obvious downward trend in the GDP, area tabulation was performed in ArcGIS to obtain data on the obvious decline in the GDP at the prefecture-level city level. The specific situation of the top ten cities with an obvious GDP decline in the absolute area at the prefecture-level city level is shown in

Table 9. Areas and rankings of prefecture-level cities with significant GDP decline.

Rank	Province	City	The Area of Decline/(km2)
1	Shaanxi	Yan’an	1411.25
2	Heilongjiang	Daqing	530.54
3	Shaanxi	Yulin	507.01
4	Xinjiang	Aksu	444.25
5	Hebei	Tangshan	400.75
6	Tianjin	Tianjin	378.75
7	Shanxi	Xinzhou	363.07
8	Inner Mongolia	Ordos	303.22
9	Shanxi	Lvliang	280.90
10	Gansu	Qingyang	266.51

. From the data, it can be seen that most of the areas with an obvious GDP decline are resource-based cities, such as Daqing City, Aksu Prefecture, Tangshan City, Xinzhou City, Ordos City, etc. Among them, the rise and fall of Daqing City in Heilongjiang Province is related to the reserves and production of oil. With the reduction in oil reserves, the development of heavy industry is hindered, and the GDP shows a downward trend. In addition, there is Yan’an City in Shaanxi Province, which is represented by returning farmland to forest and grassland and the relocation of immigrants. Yan’an City is located in the hinterland of the Loess Plateau and the ecological environment is extremely fragile. In recent years, in order to alleviate the phenomenon of soil erosion, Yan’an City has increased its efforts in environmental protection, planted trees and grass reasonably, and reduced the amount of NTL. In general, the regions with a downward trend in GDP are all cities that were mainly developed by heavy industry in the early stage and faced transformation due to the reduction in mineral resource output in the middle and late stages. The damage to the ecological environment and the reduction in mineral resources in these cities have restricted the development of the local urban economy.

5.3. Analysis of Influencing Factors

The preprocessing of the NPP/VIIRS annual average data has a great impact on the estimated GDP, due to the many types of landforms in the world, such as volcanoes, dry riverbeds, deserts, etc., as well as the influence of human activities, such as the exploitation and burning of fossil fuels, major engineering construction, and other factors, resulting in the abnormal enhancement of night lights and the formation of noise values [28]. This paper adopts the noise masking method, taking the highest value of Shanghai, Beijing, and Guangzhou, the three most economically active and developed cities in mainland China, as the threshold, masking the abnormal values above the threshold, and smoothing the image to make it appear as a reasonable value. This method is easy to operate, the DN value obtained is relatively reasonable, and the accuracy of the function regression model is high. However, for abnormally high values in a small part of the area, such as abnormally high values that are lower than the highest threshold but higher than the economic activities of the city that do not conform to the status quo, there is no way to deal with them.

There are many models for estimating the function of the GDP. By comparing the time regression model and the spatial regression model, this paper finds that the time regression model is more suitable for inverting the GDP data within the research period. Therefore, a linear regression model is used to fit the functional relationship between the MNL and GDP, and the new GDP value is calculated and spatially simulated. The results can reflect the spatial information of the GDP in the whole mainland of China and fill the gap in the GDP spatial data. However, considering the large area of mainland China and the complexity of the population, social, economic, and natural conditions, it is difficult to simulate its economic development with a fixed model at a fine spatial scale. Therefore, it is necessary to consider the differences in different research areas according to local conditions, so as to improve and enhance the accuracy of the GDP spatial model [19]. Some scholars also divide the GDP into the first (agriculture), second (industry), and third (service) industries, classify and simulate the GDP of each industry in space, and then obtain the overall GDP data according to the corresponding proportion. However, this method is currently only used for the spatialization of the GDP in cities with a smaller range, and there are certain limitations [38].

In terms of temporal and spatial change trend analysis, we used the Sen + MK trend analysis method. This method combines the Theil–Sen and Mann–Kendall methods, and is suitable for the trend analysis of multi-year time series. It takes into account both linear and nonlinear changes in time-series data, has high computational efficiency, and is insensitive to measurement errors and outliers. This method is more suitable for the spatial simulation of GDP, and is relatively rare in the literature on the spatial simulation of GDP, which is one of the innovations of this paper. NPP/VIIRS began recording NTL data in 2012, and DMSP/OLS recorded NTL data from 1992 to 2013. The two sets of data are not compatible. If a longer time-series GDP spatial simulation is to be performed, it is necessary to clarify the error sources of the two data sources and select the appropriate processing methods to make the two sets of data compatible.

6. Conclusions

This paper uses NPP/VIIRS data and takes mainland China as the research area to calculate NTL indices such as the MNL, TNL, and CNLI, and conducts temporal and spatial regression analysis with GDP-related data. The optimal fitting model is selected to estimate the GDP, and the GDP data are spatialized to produce spatial data products of China’s GDP from 2013 to 2023, analyzing the temporal and spatial variation trend in China’s GDP. The study found the following:

(1)

In spatial regression, the correlation between the MNL and per capita GDP of the quadratic regression function model is the highest combination among the spatial regression models, with correlation coefficient values above 0.7, and the RMSE of the prediction results is between 0.91 and 1.95, with a small error; in temporal regression, the correlation between the MNL and GDP of the linear function model is the highest, with R² = 0.972. Finally, this model was selected for the spatial simulation of the GDP.

(2)

From 2013 to 2023, the spatial distribution of the GDP in mainland China is centered on the high-value-GDP areas of provincial capitals, and continues to extend to the surrounding areas and gradually expand to the surrounding cities. The spatial connectivity between large cities continues to increase, forming multiple urban circles with high-GDP areas. The overall pattern of the GDP distribution is that the southeast coast is much larger than the northwest inland, the east is high, the middle is second, and the west is lowest. From the perspective of changes in various types of GDP areas, the area with a GDP of more than 100 million yuan has more than doubled, while the proportion of areas with an area of less than 5 million yuan has become increasingly smaller, with a decrease of 0.54% in 2023 compared with 2023.

(3)

Pixels with a rising GDP account for 98.56% of the total pixels, while pixels with a falling GDP account for only 0.99%. In addition, through area tabulation, it is found that the spots with a falling GDP are mainly distributed in heavy industrial cities that have developed and concentrated based on rich fossil fuel resources, such as Aksu Prefecture and Daqing City. These cities are facing industrial structure transformation and the contradiction between ecological protection and economic construction.

(4)

The difference between the official GDP data and the GDP obtained using NTL is small, with an RE of 0.04% to 1.95%, and the GDP data obtained using NTL are slightly higher than the official GDP data. From the perspective of provincial rankings, the ranking changes of most provinces are between ±2, such as Jiangsu, Guangdong, Shandong, Gansu, Qinghai, and other provinces; and the rankings of a few provinces fluctuate greatly, such as Hubei, Hunan, Xinjiang, and other provinces. The reasons for the differences are related to the dominant industries, power generation capacity, etc.

To sum up, NTL data can better reflect the spatial changes of the GDP, turn one-dimensional GDP point data into two-dimensional spatial continuous data, improve the readability of the GDP, and reflect the differences between regions. In the future, we will expand our research scope and time series to construct spatial product data of the GDP for Asian and even global NTL data. From the global perspective, the paper analyzes the spatial pattern of the GDP, and expects to forecast the trend in world economic development and make reference to the development orientation.