## 3 Dasymetric GDP Map Using Nighttime Light Images  
### DMSP-OLS Data Preprocessing  
NRC DMSP-OLS saturation data can underestimate the GDP values of saturated pixels and overestimate the values of non-saturated pixels. [PERSON] (1988) and [PERSON] et al. (2006) found that GDP is related to DMSP-OLS data in China. In the NRC DMSP-OLS dataset collected over the Wuhan urban agglomeration from 1992 to 2012, saturated pixels only existed in the data from 2010 to 2012. Therefore, the saturated pixels in NRC DMSP-OLS data were corrected by adopting the method developed by [PERSON] et al. (2006), RC DMSP-OLS data and prefectural GDP statistical data from the Wuhan urban agglomeration in 2011.  
Figure 2 shows the linear relationship between GDP per km\({}^{2}\) 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  
\[\mathrm{D_{total\_area}=a\times GDP_{area}+b} \tag{1}\]  
where \(\mathrm{D_{total\_area}}\) is the logarithm of the corrected total DMSP-OLS DN values per km\({}^{2}\) in a prefecture with saturated pixels; \(\mathrm{GDP_{area}}\) 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 ([PERSON] et al., 2006).  
Due to a lack of on-board calibration and intercalibration, the inconsistencies between DMSP-OLS nighttime stable light data are obstacles in time series analysis. Therefore, the annual nighttime stable light data from different satellite missions were intercalibrated using the quadratic regression model (Equation (2)) proposed by [PERSON] et al. (2009). The model parameters \(\mathrm{a_{t}}\), \(\mathrm{b_{t}}\), and \(\mathrm{c_{t}}\) in each year t were obtained from a study by [PERSON] and [PERSON] (2010), 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.  
\[\mathrm{DN^{\prime}_{t}=a_{t}\times DN^{2}t+b_{t}\times DN_{t}+c_{t}} \tag{2}\]  
where \(\mathrm{DN^{\prime}_{t}}\) is the DN of a pixel after calibration in year t; \(\mathrm{DN_{t}}\) is the original DN of a pixel in that year; and \(\mathrm{a_{t}}\), \(\mathrm{b_{t}}\) and \(\mathrm{c_{t}}\) 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.  
Figure 2: Relationship between GDP per km\({}^{2}\) and total RC DMSP-OLS per km\({}^{2}\) in 2011.