# A Map Spectrum-Based Spatiotemporal Clustering Method for GDP Variation Pattern Analysis Using Nighttime Light Images of the Wuhan Urban Agglomeration

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

## 3. Dasymetric GDP Map Using Nighttime Light Images

#### 3.1. DMSP-OLS Data Preprocessing

^{2}and RC DMSP-OLS DN values per km

^{2}for 9 prefectures in 2011. This relationship was similar to those in other years in the Wuhan urban agglomeration area. In the Wuhan urban agglomeration, the GDP of Wuhan is much larger than those of other prefectures. To avoid overestimating the determination coefficient of the regression equation caused by uneven data distributions, the logarithms of the independent and dependent variables were used in the calculation. The NRC DMSP-OLS data can be corrected using the formula

_{total_area}= a × GDP

_{area}+ b

_{total_area}is the logarithm of the corrected total DMSP-OLS DN values per km

^{2}in a prefecture with saturated pixels; GDP

_{area}is the logarithm of the GDP per km

^{2}of the corresponding prefecture; and a and b are regression parameters, which are 0.63615 and −1.27474, respectively, in this study. The corrected values of saturated pixels can be calculated by subtracting the total DN of non-saturated pixels from the total corrected DN of the prefectural area and then dividing this value by the number of saturated pixels in the prefecture [3].

_{t}, b

_{t}, and c

_{t}in each year t were obtained from a study by Liu and Li [20], who used nighttime stable light data from mission F16 in 2007 as a baseline and performed quadratic regressions in invariant areas with little change in actual DNs over time. In addition, the pixels with zero values were excluded from the intercalibration.

_{t}= a

_{t}× DN

^{2}

_{t}+ b

_{t}× DN

_{t}+ c

_{t}

_{t}is the DN of a pixel after calibration in year t; DN

_{t}is the original DN of a pixel in that year; and a

_{t}, b

_{t}and c

_{t}are the corresponding model parameters. Figure 3 shows that the intercalibration improved the continuity of nighttime stable light data in study area from 1992 to 2012.

#### 3.2. GDP Dasymetric Map

_{p}= a × D

_{p}+ b

_{p}is statistical GDP data from each prefecture and D

_{p}is the total DN value of DMSP-OLS data in the corresponding prefecture. Because a negative intercept b could lead to a negative GDP value at the grid level, the above empirical relationship was applied at the grid level as

_{g}= a × D

_{g}

_{g}and D

_{g}are the estimated GDP value and DN value of DMSP-OLS data at the grid level (1 km), respectively. To correct the gridded GDP to best reflect the statistical GDP data from each prefecture, a normalization factor k was used to modify the estimated GDP at the grid level

_{g}= k × G’

_{g},

_{p}/∑

_{p}× G’

_{g}

_{g}is the final GDP value at the grid level, ∑

_{p}G’

_{g}is the total estimated GDP of each prefecture, and k is the normalization factor.

^{2}) than the former. This result indicated that corrected NRC data could be better used to create a dasymetric GDP map than could NRC data. However, the determination coefficient of correct NRC data was lower than that of non-corrected data in four years during the study period. This result occurred because the determination coefficients of the quadratic regression models used for intercalibration were lower in these four years, resulting in a large error associated with corrected NRC data after intercalibration.

## 4. Map Spectrum-Based Spatiotemporal Clustering

#### 4.1. Map Spectrum-Based Spatiotemporal Representation Model

_{x}(∙) is the value of the data within unit x at time t. For effective visualization, GDP distributions of one-column pixels (Figure 5a) from 1992 to 2012 are used as samples to generate a spatiotemporal map spectrum (Figure 5b) based on the model shown in Equation (6). To obtain the GDP trend, min–max normalization was performed for each pixel in the GDP time spectrum. In Figure 5b, the axis labeled “serial number” represents the position of the pixel in the image, and the GDP spectrum represents the normalized GDP value in each year at the same location.

#### 4.2. Similarity Measurement of the Map Spectrum Model

#### 4.3. Extraction of Spatiotemporal Patterns

## 5. Discussion

#### 5.1. Accuracy Assessment of the Dasymetric GDP Map based on County-Level GDP Statistics

#### 5.2. GDP Variation Pattern Analysis based on the Clustering Results

## 6. Conclusions

- (1)
- This study investigated the mapping of statistical GDP data based on spatial location to obtain a dasymetric GDP map using DNs from calibrated night light images. A linear regression model between DN and GDP was constructed at a prefectural level, and normalization factors between grid-level GDP and prefectural GDP statistics were used to produce accurate dasymetric GDP maps.
- (2)
- To investigate GDP growth, this study proposed a method of improved k-means clustering using a map spectrum-based, spatiotemporally integrated model. The proposed spatiotemporal representation model is a 3D model consisting of time, space, and magnitude dimensions. The model provides a solution that simultaneously considers spatial and temporal characteristics in clustering.
- (3)
- This study produced dasymetric maps and obtained the spatiotemporal patterns of GDP growth in the Wuhan urban agglomeration. These findings provide an important basis for economic development, spatial planning, decision making, and management in the region. In addition, the study provides a reference solution for spatial mapping and spatiotemporal pattern extraction using other socioeconomic data.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Sum of DNs in the study area from 1992 to 2012 across all nighttime light satellite missions: (

**a**) before calibration and (

**b**) after calibration. F10, F12, F14, F15, F16, and F18 are the six nighttime light satellite missions in the dataset.

**Figure 5.**Time Spectrum of GDP maps for given column pixels from 1992 to 2012. (

**a**) Position of the column that was used to generate the spatiotemporal map spectrum. (

**b**) Time Spectrum.

**Figure 8.**The statistical results of three land use types for three clustering classes in four years: (

**a**) The first class; (

**b**) The second class; (

**c**) The third class.

Year | NRC DMSP-OLS | Corrected DMSP-OLS | ||
---|---|---|---|---|

Regression Model | R^{2} | Regression Model | R^{2} | |

1992 | y = 0.0045x + 9.6097 | 0.9435 | y = 0.0042x + 11.363 | 0.9630 |

1993 | y = 0.0072x + 5.5751 | 0.9777 | y = 0.0061x + 5.6131 | 0.9768 |

1994 | y = 0.0100x − 2.6774 | 0.9775 | y = 0.0084x − 2.6774 | 0.9775 |

1995 | y = 0.0127x − 11.919 | 0.9764 | y = 0.0123x − 11.952 | 0.9769 |

1996 | y = 0.0153x − 22.355 | 0.9751 | y = 0.0151x − 22.417 | 0.9757 |

1997 | y = 0.0150x − 25.686 | 0.9817 | y = 0.0128x − 21.877 | 0.9740 |

1998 | y = 0.0169x − 29.908 | 0.9810 | y = 0.0144x − 30.016 | 0.9818 |

1999 | y = 0.0160x − 25.013 | 0.9834 | y = 0.0122x − 25.143 | 0.9844 |

2000 | y = 0.0180x − 48.724 | 0.9864 | y = 0.0183x − 48.875 | 0.9873 |

2001 | y = 0.0185x − 49.241 | 0.9921 | y = 0.0168x − 49.412 | 0.9931 |

2002 | y = 0.0206x − 85.218 | 0.9850 | y = 0.0210x − 85.330 | 0.9855 |

2003 | y = 0.0223x − 120.66 | 0.9726 | y = 0.0148x − 120.73 | 0.9728 |

2004 | y = 0.0237x − 155.38 | 0.9584 | y = 0.0204x − 155.41 | 0.9585 |

2005 | y = 0.0248x − 189.32 | 0.9440 | y = 0.0215x − 189.33 | 0.9442 |

2006 | y = 0.0257x − 222.50 | 0.9301 | y = 0.0198x − 222.50 | 0.9301 |

2007 | y = 0.0265x − 254.98 | 0.9170 | y = 0.0246x − 254.96 | 0.9173 |

2008 | y = 0.0289x − 293.35 | 0.9263 | y = 0.0269x − 293.38 | 0.9263 |

2009 | y = 0.0298x − 336.37 | 0.9380 | y = 0.0180x − 336.37 | 0.9382 |

2010 | y = 0.0368x − 317.45 | 0.9517 | y = 0.0234x − 374.60 | 0.9404 |

2011 | y = 0.0444x − 222.38 | 0.9543 | y = 0.0228x − 400.22 | 0.9402 |

2012 | y = 0.0377x − 464.73 | 0.9405 | y = 0.0374x − 464.73 | 0.9405 |

**Table 2.**Three statistical measures based on estimated and actual GDP in the 13 districts/counties of Wuhan (GDP unit = 100 million RMB).

Year | RMSE | MRE | R |
---|---|---|---|

1997 | 4.9614 | 4.5572% | 0.9982 |

1998 | 3.6867 | 3.0326% | 0.9992 |

1999 | 1.8850 | 1.8516% | 0.9988 |

2000 | 4.2335 | 3.3435% | 0.9949 |

2001 | 3.2224 | 2.5797% | 0.9989 |

2002 | 3.3361 | 2.1376% | 0.9995 |

2003 | 10.9458 | 6.1353% | 0.9729 |

2004 | 8.1877 | 4.0032% | 0.9895 |

2005 | 28.8478 | 11.4043% | 0.9649 |

2006 | 14.3577 | 5.1784% | 0.9929 |

2007 | 22.5479 | 7.4647% | 0.9826 |

2008 | 17.6268 | 4.3592% | 0.9934 |

2009 | 12.5426 | 2.8741% | 0.9969 |

2010 | 19.7350 | 3.8184% | 0.9935 |

2011 | 48.0933 | 7.6910% | 0.9694 |

2012 | 68.3982 | 9.3377% | 0.9468 |

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**MDPI and ACS Style**

Zhang, P.; Liu, S.; Du, J. A Map Spectrum-Based Spatiotemporal Clustering Method for GDP Variation Pattern Analysis Using Nighttime Light Images of the Wuhan Urban Agglomeration. *ISPRS Int. J. Geo-Inf.* **2017**, *6*, 160.
https://doi.org/10.3390/ijgi6060160

**AMA Style**

Zhang P, Liu S, Du J. A Map Spectrum-Based Spatiotemporal Clustering Method for GDP Variation Pattern Analysis Using Nighttime Light Images of the Wuhan Urban Agglomeration. *ISPRS International Journal of Geo-Information*. 2017; 6(6):160.
https://doi.org/10.3390/ijgi6060160

**Chicago/Turabian Style**

Zhang, Penglin, Shuaijun Liu, and Juan Du. 2017. "A Map Spectrum-Based Spatiotemporal Clustering Method for GDP Variation Pattern Analysis Using Nighttime Light Images of the Wuhan Urban Agglomeration" *ISPRS International Journal of Geo-Information* 6, no. 6: 160.
https://doi.org/10.3390/ijgi6060160