# Modelling Electricity Consumption in Cambodia Based on Remote Sensing Night-Light Images
## 5 Discussion  
### Analysis of Annual Images Synthesised by Different Methods and Modelling Results  
In this work, night-light images of Cambodia from 2012 to 2019 were obtained by processing with three methods. The annual night-light images obtained by the annual average method were heavily influenced by cloud cover and, theoretically, were the least accurate. Although cloud-free months were removed in the annual cloud-free average method, these months varied interannual, which could influence the comparability of images from one year to another. Furthermore, the December night-light images from different years were slightly affected by cloud cover. By taking into account that December is the last month of the year, the annual images obtained by month-specific substitution method possess better continuity between years and, theoretically, produce the best modelling results. Ranking  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Function** & **Regression Equation** & **Adj-\(R^{2}\)** & \(p\) \\ \hline Linear & \(y=17.716x-61,658.739\) & 0.839 & 0.001 \\ Power & \(y=\left(9.702\times 10^{-5}\right)x^{2.262}\) & 0.890 & 0.000 \\ Exponential & \(y=4057.7e^{0.0000x}\) & 0.871 & 0.000 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Modelling results for annual night-light data obtained by the annual average method.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Function** & **Regression Equation** & **Adj-\(R^{2}\)** & \(p\) \\ \hline Linear & \(y=8.802x-26,956.863\) & 0.908 & 0.000 \\ Power & \(y=\left(0.0122\right)x^{1.6652}\) & 0.936 & 0.000 \\ Exponential & \(y=4780.6e^{0.0002x}\) & 0.967 & 0.000 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Modelling results for annual night-light data obtained by the month-specific substitution method.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Function** & **Regression Equation** & **Adj-\(R^{2}\)** & \(p\) \\ \hline Linear & \(y=18.609x-67,046.725\) & 0.840 & 0.001 \\ Power & \(y=\left(7.627\times 10^{-6}\right)x^{2.5451}\) & 0.886 & 0.000 \\ Exponential & \(y=2983.4e^{0.0004x}\) & 0.835 & 0.001 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Modelling results for annual night-light data obtained by the annual average method.  
the quality of different models according to the magnitude of adj-\(R^{2}\)-value and significance, the results confirm these suspicions. The only exception was with the month-specific substitution method, where the linear model had a slightly higher adj-\(R^{2}\)-value than that of the cloud-free averaging method. The adj-\(R^{2}\) values and significance rankings for the other regression methods show that the annual average method < annual cloud-free average method < month-specific substitution method. This conclusion suggests that the three annual night-light image synthesis methods should be ranked as follows: annual average method < annual cloud-free average method < month-specific substitution method. The results of the regression models are shown in Table 8.  
Table 8 indicates that when using data processed by the annual average method, the quality of the regression models is ranked exponential < linear < power. Using data processed by the annual cloud-free average method, the model accuracy is ranked linear < exponential < power. Using data processed by the month-specific substitution method, the model accuracy is ranked linear < power < exponential. The overall quality of the annual images synthesized by different methods is annual average < annual cloud-free average < month-specific substitution. The exponential model was ranked third, second, and first using data from the annual averaging, annual cloud-free averaging, and month-specific substitution methods, respectively. This suggests that as the annual night-light image synthesis method becomes more reasonable, an exponential regression model provides a better fit. Therefore, the relationship between electricity consumption and total night-light values in Cambodia is best expressed using an exponential regression model.