Using nighttime DMSP/OLS images of Citylights to Estimate District-level Population Distribution in Developing Countries.
4.2 Result of exponential model applied to each province
(1) Model fitness
Fig.4-2 shows the maximum correlation values of the models as a result of applying exponential model for each province. All provinces were classified to the same categories as in the preceding section.
In fig.4-2, the same tendency as in the former chapter was observed in every group. That is, exponential model fitness for large cities are better than those for other provinces . And, among non-city provinces , this model is over applicable for flat provinces than for mountainous ones.
Fig.4-2 Maximum Correlation Value of each province (Exponential Model)
Fig.4-3 to 4-5 shows detailed fitness of the model for the same provinces as in the former section ; Beijing as a large city, shandong as a flat province , and Ningxia as a mountainous province.

Fig.4-3 Exponential Model fitness on Beijing

Fig.4-4 Exponential Model fitness on Shandong

Fig.4-5 Exponential Model fitness on Ningxia
(2) Effects of Thresholding rate
Fig.4-6 shows the change of fitness of the is model when the thresholding rate varies for few provinces . it can also be observed that the thresholding rate has no strong effects on model fitness using exponential model .

Fig.4-6 Correlation Value with the threshold (Exponential Model)
5. Conclusion and Further research
5.1Conclusion of the analysis
Based on the results of the analysis , the following facts can be concluded on t relationships between night time lights and populations distribution in China.
- Neither the linear model nor the exponential model can be satisfactorily applied to establish only one model for whole of China .
- Both linear ad exponential models can represent the population distribution of large cities in China satisfactorily .
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Both models show better fitness on flat province rather than that on mountainous provinces.
5.2 Further research
To achieve the final purpose of this research , the estimation ability of the model should be improved . for the purpose of this , it is necessary to try to establish a model considering other attributes of the pixels, such as the elevation, vegetation, etc….
To find the key to the new parameters , it should be important t study the reason for the differences in t fitness of the models, which was observed in this research.
Acknowledgement
This research is funded by "Research for the future " Program of Japan society for Promotion of Science .
References :
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Marc L. Imhoff et.al, A Technique for using Composite DMSP/OLS " City Lights " Satellite Data to Map Urban Area , Remote Sens . Environ, 61:pp.361 (1997)
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Paul Suton et.al., A Comparison of Nighttime Satellite Imagery and Population Density for the continental United States , PE&RS 63,11:pp.1303 (1997)
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Mikiyasu NAKAYAMA , Developing Population Database with DMSP/OLS Imagery, Proceedings of International Conference on modeling Geographical and Environmental System with Geographical Information System.