## 3 Dasymetric GDP Map Using Nighttime Light Images
### GDP Dnsymetric Map  
A dasymetric map of GDP can reveal the internal differences in a given region in terms of the level of economic development and provide a dataset for analyzing the spatiotemporal process of GDP growth. A number of methods have been used to estimate GDP using nighttime light data, such as linear regression models [21], log-log regression models [22], and second-order regression models [23]. A linear regression model is a relatively accurate and easy tool for estimating GDP using nighttime light data. Therefore, a linear regression model was established in each year at the prefectural level using DN values from the DMSP-OLS dataset as the independent variable  
\[\mathrm{G_{p}}=\mathrm{a}\times\mathrm{D_{p}}+\mathrm{b} \tag{3}\]  
where \(\mathrm{G_{p}}\) is statistical GDP data from each prefecture and \(\mathrm{D_{p}}\) 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  
\[\mathrm{G^{\prime}_{g}}=\mathrm{a}\times\mathrm{D_{g}} \tag{4}\]  
where \(\mathrm{G^{\prime}_{g}}\) and \(\mathrm{D_{g}}\) 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 \(\mathrm{k}\) was used to modify the estimated GDP at the grid level  
\[\mathrm{G_{g}}=\mathrm{k}\times\mathrm{G^{\prime}_{g}}, \tag{5}\] \[\mathrm{k}=\mathrm{G_{p}}/\sum_{P}\mathrm{k}\times\mathrm{G^{ \prime}_{g}}\]  
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.  
where \(\rm G_{g}\) is the final GDP value at the grid level, \(\rm\sum_{P}\,G^{\prime}_{g}\) is the total estimated GDP of each prefecture, and k is the normalization factor.  
The original and corrected NRC data were used to estimate the spatial distribution of the GDP of the Wuhan urban agglomeration from 1992-2012. The regression results are shown in Table 1 at the prefectural level. Comparing NRC and corrected NRC data from 1992 to 2012, the latter exhibited higher determination coefficients (R\({}^{2}\)) 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.  
Dasymetric GDP maps were produced using corrected NRC data from 1992 to 2012. Figure 4 shows the dasymetric GDP map in 2011. This map was estimated from corrected NRC data and prefectural level statistical data.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multicolumn{2}{c}{**NRC DMSP-OLS**} & \multicolumn{2}{c}{**Corrected DMSP-OLS**} \\ \cline{2-5}  & **Regression Model** & **R\({}^{2}\)** & **Regression Model** & **R\({}^{2}\)** \\ \hline  
\hline \hline \end{tabular}
\end{table}
Table 1: Regression models from 1992 to 2012 (GDP unit = 100 million RMB).  
Figure 4: Dasymetric GDP map in 2011.