## 3 Results
### Relationship between the Total Imperviousness and Population Density  
Total imperviousness and population density values for the 154 selected suburbs ranged from 5% to 62%, and 343 to 4430 (persons/km\({}^{2}\)) in this study. The data range in this study was larger than that (total imperviousness: 1-24% and population density: 70-950 persons/km\({}^{2}\)) in recent previous studies over large areas (county scale) in China [10]. Different linear and nonlinear regression models were created between population density (PD) and total imperviousness (TI) (Table 2). Capability of the models was assessed using three criteria of R\({}^{2}\), MAE, and RMSE. Among them, the linear regression model showed the highest accuracy with determination of coefficient (R2), mean absolute error (MAE), and root mean absolute error (RMSE) of 0.52, 6.77, and 9.06, respectively. Power regression also showed good accuracy compared to the linear regression. The values for the three criteria are approximately similar to corresponding values from the linear model. Other regression models (exponential and logarithmic) demonstrated lower accuracy. Totally, the linear model can more accurately represent the relationship between population density and total imperviousness at suburb scale than nonlinear models in \begin{table}
\begin{tabular}{c c c c} \hline \hline
**References** & **R\({}^{2}\)** & **MAE (\%)** & **RMSE (\%)** \\ \hline This study & 0.87 & 7 & 9 \\ [PERSON] et al. [44] & 0.7 & NA & 10 \\ [PERSON] et al. [49] & NA & NA & 9 \\ [PERSON] and [PERSON] [10] & NA & 10 & NA \\ [PERSON] et al. [50] & NA & 12.90 & NA \\ \hline \hline \end{tabular}  
NA: not available.  
\end{table} 
Table 1: Evaluation results of imperviousness estimation using LSMA approach at Landsat pixel in this study and previous studies. Figure 4: Accuracy assessment of estimated imperviousness for 300 selected pixels from Landsat. this study (Figure 5). Predicted total imperviousness for the 154 suburbs by the linear regression model versus observed data is shown in Figure 5.  
This result is corresponding to the result shown by [PERSON] et al. (2016). They also demonstrated that the linear regression model is the best model to explore the relationship between population density and total imperviousness compared to the nonlinear regressions over a large area. However, [PERSON] and [PERSON] (2010) indicated that their relationship can be expressed with an exponential equation. In comparison with this study, [PERSON] et al. (2016) and [PERSON] and [PERSON] (2010) showed a stronger relationship between population density and total imperviousness with R\({}^{2}\) of 0.85 and 0.88, respectively. Both of these previous studies, however, have developed regression models between the population density and total imperviousness at a scale much larger than that in this study. For example, [PERSON] and [PERSON] (2010) developed the regression model at the county scale (>1000 km\({}^{2}\)) in China, which was significantly larger than the suburb scale (1-26 km\({}^{2}\)) considered in this study. The relationship between population density and total imperviousness in this study is poor because there are some significant outliers in data. As shown in Figure 5, there are some outliers which refer to suburbs with low population density and high total imperviousness. It is found that they are mostly associated with suburbs where non-residential imperviousness (e.g., industrial areas, shopping areas and public services) is a significant component of the total imperviousness. For example, three of the outliers shown by red color are suburbs with imperviousness of more than 80%. In contrast, two of the outliers shown by blue color are suburbs with residential imperviousness of more than 90%.