# Analysis of the Spatial and Temporal Evolution of the GDP in Henan Province Based on Nighttime Light Data

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}resolution in 11 countries in the United States and the European Union [21]. Ghosh et al. established regression models between NTL spatial patterns and regional economic activity data in the United States and Mexico. A comparison between the estimated gross state income and official economic data showed that the impact of the informal economy and remittance inflows was greater in Mexico than in the official formal economy [22]. Then, Nordhaus corrected the global GDP grid product using remote nighttime light sensing data from 1992 to 2008, and found that NTL data can play a significant role in estimating the GDP of countries with missing statistics [23]. In the same year, Zhao et al. constructed Chinese GDP images for 1996 and 2000 based on the provincial relationship between NTL and GDP [24].

## 2. Study Area and Data

#### 2.1. Study Area

#### 2.2. Data

## 3. Methodology

#### 3.1. Modeling of GDP Spatialization

^{2}value can represent the correlation between the NTL indices and the GDP data. The values of R

^{2}range from 0 to 1, with larger values representing better model fitting accuracy.

#### 3.2. GDP Spatialization Data Connectivity Analysis

_{min}..., t

_{i}..., t

_{max}} is a finite set. A threshold can be set by setting t

_{i}to generate the connected components for multitemporal and multilevel GDP spatialization data, and thresholding G at the t

_{i}level to generate a binary image Q of G [39], which is represented as:

#### 3.3. Tree Construction of the Connected Components and Derivation of the Node Attributes

#### 3.4. Standard Deviation Ellipse and Economic Center

_{i}and y

_{i}are the spatial location coordinates of each element, $\overline{\mathrm{X}}$ and $\overline{\mathrm{Y}}$ are the arithmetic mean centers, and SDEx and SDEy are the centers of the ellipses. The formulas for calculating the arithmetic mean center are as follows:

## 4. Results

#### 4.1. Analysis of Henan Province GDP Spatialization Results

^{2}) values, which were between 0.75 and 0.92; the second-best fitting effect was that of the regression model of S; and the GDP R

^{2}values were between 0.65 and 0.91. The fitting relationships between I, CNLI, and GDP were poor, with R

^{2}values of approximately 0.5. Regarding the selection of the regression model for GDP spatialization, the quadratic regression model of MNL and MGDP had the best fit (R

^{2}= 0.9107), which is why it was selected in this study as the model for the GDP spatialization in Henan Province. The model for the spatialized modeling of the GDP is as follows:

^{2}) of the GDP simulation values and the GDP true values is 0.9147. The experimental results show that the NPP-VIIRS-like NTL data fit well with the GDP data, and the quadratic regression model constructed using the MNL and MGDP of the NPP-VIIRS-like NTL data with long time series fit the GDP spatialization of Henan Province better. However, when the regression model is used to spatialize the GDP, the GDP simulation value will be refined to each pixel of NTL, resulting in some pixel cumulative errors. Therefore, it was necessary to use Formula (4) to correct the accumulated pixel errors generated after the GDP simulation by the regression model. As shown in Figure 8b, through the regression analysis of the GDP spatialized values and GDP true values obtained after correction, we can determine that the spatialized GDP of Henan Province from 2001 to 2020 is basically consistent with the GDP in the statistical yearbook, which again verifies that the pixel-level GDP spatialization can accurately reflect the real situation of the Henan economy in 20 years. Then, we generated the pixel-level (500 m × 500 m) GDP spatialized density maps of Henan Province from 2001 to 2020 using the corrected GDP spatialization data.

#### 4.2. GDP Spatialization Data Connectivity Analysis

#### 4.2.1. Henan Province GDP Spatialization Data Connectivity Analysis

#### 4.2.2. Urban GDP Spatialization Data Connectivity Analysis

#### 4.3. Changing Trends in Economic Center Analysis

#### 4.3.1. Henan Province Economic Center Changes

#### 4.3.2. Zhengzhou Economic Center Changes

## 5. Discussion

#### 5.1. GDP Spatial and Temporal Changes

#### 5.2. Shortcomings and Prospects

## 6. Conclusions

- The NPP-VIIRS-like NTL data are highly correlated with the GDP statistics, and they were used for the construction of a GDP spatialization data model. The five NTL indices I, S, CNLI, MNL, and TNL extracted from the NPP-VIIRS-like NTL data were regressed with the GDP parameters of Henan Province using four models: a linear regression model, a quadratic regression model, an exponential model, and a power function model. The results show that the quadratic regression model has the highest correlation between the MNL and MGDP (R
^{2}= 0.9107). The model can simulate the GDP spatialization data well, without any overall bias, and the relative error of the GDP simulation value is 15%, accounting for more than half of the errors. The results of the GDP spatialization obtained by modeling the NPP-VIIRS-like NTL indices and the GDP parameters of Henan Province are reliable. - The GDP spatialization data can intuitively show the economic distribution of Henan Province. With increasing time, the overall economic level of Henan Province has been on the rise. The regional economy in Henan Province has been developed to different degrees, but the degrees of the economic development between the regions are quite different. Overall, Zhengzhou, as the capital city of Henan Province and the center of the Central Plains city cluster, has been in a leading position in the economy for 20 years, followed by Luoyang and Kaifeng. The economic distribution in Henan Province is centered on Zhengzhou and spreads outwardly in a radial pattern; the peripheral economic level has gradually declined, and the western and southwestern regions have a lower level of economic development. It can be clearly seen that Anyang, Hebi, Xinxiang, Xuchang, Luohe, Zhumadian, and Xinyang have formed a strip economic belt along the Beijing-Guangzhou Railway.
- We conducted multitemporal and multilevel economic connectivity analyses of the GDP spatialization data and constructed an urban economic tree structure. From 2001 to 2007, the number of connected components in Henan Province increased significantly, and the areas of the connected components did not change significantly; the number of economically connected components in eight cities increased significantly, and there were 44 more in 2007 than in 2001. The depth of the tree structure of urban connected components is shallow, and the urban economic center is single. From 2007 to 2014, the number of connected components in Henan increased slowly, and the areas of the connected components increased significantly; the number of high-level connected components in cities increased to a certain extent, the depth of the tree structure of connected components in each city increased significantly, and there was a development trend of multicity economic centers. From 2014 to 2020, there were no significant changes in the number of connected components, and the areas of the connected components increased significantly. The areas around the city center have linked the development, and the number of connected components between cities has increased. The depth of the urban tree structure has increased, the number of high-level connected components has increased, and the development trend of multicity economic centers has become more obvious.
- Standard deviation ellipses were used to analyze the distribution ranges and development directions of the economic center of Henan Province and the cities, and to analyze the spatial and temporal evolution of the economy. From 2001 to 2020, the economy of Henan Province developed rapidly, and the overall economic center was relatively stable. The economic center of Henan Province has always been located in Zhengzhou City, the direction of economic development in Henan Province is clear, and the economic center generally shows a trend of moving to the southeast. The economic center of Zhengzhou is also relatively stable as a whole. The economic development trend of Zhengzhou is roughly the same as the overall development trend of Henan Province, and the economic center also generally shows a trend toward the southeast. In the past 20 years, the cohesion of Henan Province’s economic development has gradually become stronger. The economy of Henan Province is centered on Zhengzhou City, which drives the common development of the surrounding cities, and the economic center shows a trend of southward development.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The location and nighttime light from the NPP-VIIRS-like NTL data (2018) of the study area.

**Figure 2.**The comparison with density between 2012 for the composited NPP-VIIRS NTL data and extended NPP-VIIRS-like NTL data in Henan: (

**a**) the pixel-level and (

**b**) the city-level. The solid line denotes the 1:1 line, and N is the number of sample points (cities).

**Figure 3.**Evaluation of temporal consistency of the NPP-VIIRS-like NTL data in Henan Province. (

**a**) Correlation between NPP-VIIRS-like NTL total intensity data and GDP data in Henan, and (

**b**) variation trends of NPP-VIIRS annual synthetic NTL data and NPP-VIIRS-like NTL data sets in 2012 in Henan Province.

**Figure 4.**Technical flow chart of the study: (1) modeling GDP spatialization; (2) GDP spatialization data connectivity analyses; (3) tree construction of connected components and derivation of the node attributes; (4) standard deviation ellipse and economic center.

**Figure 5.**Contraction-based connectivity of Zhengzhou and Xuchang in 2020: (

**a**,

**c**) are the previously weakly connected regions, (

**b**,

**d**) are the regions after contraction-based connectivity analysis. The different colors in (

**a**), (

**b**–

**d**) represent different connected components.

**Figure 6.**Tree construction of the connected components in Zhengzhou in 2020: (

**a**) first level of connected connectivity analysis results, (

**b**) the second level of connectivity, (

**c**) third level of connectivity, (

**d**) fourth level of connectivity, and (

**e**) constructed tree structure. The different colors in (

**a**), (

**b**–

**d**) represent different connected components, and the numbers in (

**a**), (

**b**–

**d**) represent the labels of connected components corresponding to the numbers in (

**e**), respectively. The red and blue dashed rectangles in (

**e**) represent “retrieving crosswise” and “retrieving lengthwise” of the tree structure, respectively.

**Figure 7.**Regression models of the NTL indices and GDP parameters: (

**a**) MNL and MGDP, (

**b**) I and GDP, (

**c**) S and GDP, and (

**d**) CNLI and MGDP.

**Figure 8.**Relationships between GDP simulation values, GDP spatialized values, and GDP true values in Henan Province from 2001 to 2020: (

**a**) GDP simulation values and GDP true values, (

**b**) GDP spatialized values and GDP true values.

**Figure 9.**The pixel-level (500 m × 500 m) spatialized density maps of Henan Province GDP: (

**a**) 2001, (

**b**) 2004, (

**c**) 2008, (

**d**) 2012, (

**e**) 2016, and (

**f**) 2020.

**Figure 10.**Henan Province level 1 connected components: (

**a**) 2001, (

**b**) 2007, (

**c**) 2014, and (

**d**) 2020. The different colors in (

**a**), (

**b**–

**d**) represent different connected components.

**Figure 11.**Henan attribute information for the level 1 connected components: (

**a**) number of connected components, (

**b**) total area, (

**c**) maximum area, and (

**d**) area standard deviation.

**Figure 12.**Histograms of tree structure information in eight cities in Henan Province: (

**a**) 2001, (

**b**) 2007, (

**c**) 2014, and (

**d**) 2020.

**Figure 13.**Total areas of the different levels of connected components in eight cities: (

**a**) Anyang, (

**b**) Hebi, (

**c**) Kaifeng, (

**d**) Luoyang, (

**e**) Pingdingshan, (

**f**) Zhengzhou, (

**g**) Zhoukou, and (

**h**) Zhumadian.

**Figure 14.**Henan weighted standard deviation ellipses, economic centers, and trends in economic center change, for GDP spatialization data.

**Figure 15.**Henan Province 2001–2020 standard deviation ellipse parameters: (

**a**) oblateness, (

**b**) long and short axes, and (

**c**) shift of direction cosine.

**Figure 16.**Zhengzhou weighted standard deviation ellipses, economic centers, and trends in economic center changes for GDP spatialization data.

**Figure 17.**Zhengzhou data from 2001–2020 standard deviation ellipse parameters: (

**a**) oblateness, (

**b**) long and short axes, and (

**c**) shift of cosine direction.

Attribute | Definition |
---|---|

${\mathrm{DN}}_{\mathrm{i}}$ | The pixel whose gray value is i in the area. |

${\mathrm{DN}}_{\mathrm{M}}$ | 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. |

${\mathrm{N}}_{\mathrm{L}}$ | The total number of pixels whose gray value is not 0 in the area. |

Total nighttime light (TNL) | $\mathrm{TNL}={{\displaystyle \sum}}_{\mathrm{i}=0}^{{\mathrm{DN}}_{\mathrm{M}}}{\mathrm{DN}}_{\mathrm{i}}\times {\mathrm{n}}_{\mathrm{i}}$ |

Mean nighttime light (MNL) | ${\mathrm{DN}}_{\mathrm{mean}}=\frac{1}{\mathrm{n}}\times {{\displaystyle \sum}}_{\mathrm{i}=0}^{{\mathrm{DN}}_{\mathrm{M}}}{\mathrm{DN}}_{\mathrm{i}}\times {\mathrm{n}}_{\mathrm{i}}$ |

Average relative light intensity (I) | $\mathrm{I}=\frac{1}{{\mathrm{N}}_{\mathrm{L}}\times {\mathrm{DN}}_{\mathrm{M}}}\times {{\displaystyle \sum}}_{\mathrm{i}=\mathrm{P}}^{{\mathrm{DN}}_{\mathrm{M}}}{\mathrm{DN}}_{\mathrm{i}}\times {\mathrm{n}}_{\mathrm{i}}$ |

Light area ratio (S) | $\mathrm{S}=\frac{{\mathrm{N}}_{\mathrm{L}}}{\mathrm{N}}$ |

Compounded nighttime light index (CNLI) | $\mathrm{CNLI}=\mathrm{I}\times \mathrm{S}$ |

Mean gross domestic product (MGDP) | $\mathrm{MGDP}=\frac{\mathrm{GDP}}{\mathrm{N}}$ |

Attribute | Definition |
---|---|

Nj | Nj is the number of connected components at level 1. |

Maximum area (MAXA) | $\mathrm{MAXA}={\mathrm{max}}_{\mathrm{i}=1}^{\mathrm{Nj}}\left\{\mathrm{ai}*\right\}$ |

Total area (TA) | $\mathrm{TA}={{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{Nj}}\mathrm{ai}$ |

Average area (AVA) | $\mathrm{AVA}=\frac{\mathrm{TA}}{\mathrm{Nj}}$ |

Area standard deviation (ASTD) | $\mathrm{ASTD}=\sqrt{\frac{1}{\mathrm{N}}{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{Nj}}{\left(\mathrm{ai}-\mathrm{AVA}\right)}^{2}}$ |

Level number (LN) | LN is the level number of a tree structure for the urban center. |

Maximum node number (MNN) | MNN is the max node number of a tree for the urban center. |

Total node number (TNN) | TNN is the total node number of a tree for the urban center. |

Year | Longitude | Latitude | Migration Distance (km) | Direction |
---|---|---|---|---|

2001 | 113°44′1″ E | 34°42′47″ N | - | - |

2002 | 113°44′45″ E | 34°34′1″ N | 15.96 | Southeast |

2003 | 113°40′34″ E | 34°37′19″ N | 8.70 | Northwest |

2004 | 113°39′59″ E | 34°31′16″ N | 11.01 | Southeast |

2005 | 113°38′32″ E | 34°31′57″ N | 2.53 | Northwest |

2006 | 113°37′7″ E | 34°27′52″ N | 7.72 | Southwest |

2007 | 113°37′27″ E | 34°28′56″ N | 1.98 | Northeast |

2008 | 113°38′19″ E | 34°28′44″ N | 1.35 | Southeast |

2009 | 113°39′36″ E | 34°33′11″ N | 8.31 | Northeast |

2010 | 113°39′3″ E | 34°31′31″ N | 3.14 | Southwest |

2011 | 113°42′6″ E | 34°28′37″ N | 7.00 | Southeast |

2012 | 113°41′58″ E | 34°33′43″ N | 9.26 | Northwest |

2013 | 113°41′6″ E | 34°30′54″ N | 5.27 | Southwest |

2014 | 113°41′37″ E | 34°29′12″ N | 3.17 | Southeast |

2015 | 113°43′16″ E | 34°29′48″ N | 2.71 | Northeast |

2016 | 113°44′39″ E | 34°27′42″ N | 4.34 | Southeast |

2017 | 113°43′28″ E | 34°26′36″ N | 2.70 | Southwest |

2018 | 113°42′55″ E | 34°27′0″ N | 1.11 | Northwest |

2019 | 113°43′20″ E | 34°23′33″ N | 6.30 | Southeast |

2020 | 113°44′2″ E | 34°23′11″ N | 1.24 | Southeast |

Year | Longitude | Latitude | Migration Distance (km) | Direction |
---|---|---|---|---|

2001 | 113°37′29″ E | 34°46′22″ N | - | - |

2002 | 113°37′54″ E | 34°44′57″ N | 2.63 | Southeast |

2003 | 113°37′24″ E | 34°45′17″ N | 0.95 | Northwest |

2004 | 113°35′15″ E | 34°43′52″ N | 4.13 | Southwest |

2005 | 113°35′42″ E | 34°44′35″ N | 1.48 | Northeast |

2006 | 113°36′21″ E | 34°45′15″ N | 1.56 | Northeast |

2007 | 113°36′18″ E | 34°44′54″ N | 0.64 | Southeast |

2008 | 113°33′58″ E | 34°44′33″ N | 3.56 | Southwest |

2009 | 113°36′35″ E | 34°43′30″ N | 4.37 | Southeast |

2010 | 113°36′44″ E | 34°42′50″ N | 1.22 | Southeast |

2011 | 113°38′30″ E | 34°42′40″ N | 2.67 | Southeast |

2012 | 113°37′53″ E | 34°42′33″ N | 0.95 | Southwest |

2013 | 113°38′25″ E | 34°41′23″ N | 2.27 | Southeast |

2014 | 113°38′33″ E | 34°41′33″ N | 0.37 | Northeast |

2015 | 113°38′46″ E | 34°41′30″ N | 0.34 | Southeast |

2016 | 113°40′2″ E | 34°40′56″ N | 2.17 | Southeast |

2017 | 113°38′33″ E | 34°40′32″ N | 2.36 | Southwest |

2018 | 113°37′58″ E | 34°40′9″ N | 1.11 | Southwest |

2019 | 113°38′25″ E | 34°39′38″ N | 1.17 | Southeast |

2020 | 113°38′7″ E | 34°39′42″ N | 0.45 | Northwest |

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## Share and Cite

**MDPI and ACS Style**

Zhao, Z.; Tang, X.; Wang, C.; Cheng, G.; Ma, C.; Wang, H.; Sun, B. Analysis of the Spatial and Temporal Evolution of the GDP in Henan Province Based on Nighttime Light Data. *Remote Sens.* **2023**, *15*, 716.
https://doi.org/10.3390/rs15030716

**AMA Style**

Zhao Z, Tang X, Wang C, Cheng G, Ma C, Wang H, Sun B. Analysis of the Spatial and Temporal Evolution of the GDP in Henan Province Based on Nighttime Light Data. *Remote Sensing*. 2023; 15(3):716.
https://doi.org/10.3390/rs15030716

**Chicago/Turabian Style**

Zhao, Zongze, Xiaojie Tang, Cheng Wang, Gang Cheng, Chao Ma, Hongtao Wang, and Bingke Sun. 2023. "Analysis of the Spatial and Temporal Evolution of the GDP in Henan Province Based on Nighttime Light Data" *Remote Sensing* 15, no. 3: 716.
https://doi.org/10.3390/rs15030716