## 3 Results and Discussion
### Correlations between Bulk Optical Properties and PNSDs  
The scattering and extinction coefficients (Mm\({}^{-1}\)) would be changed with particle number concentrations of smoke. \(SSA\) is near 1 for smoldering smoke, which means light scattering is much stronger than light absorption. Therefore, the bulk optical properties of smoldering smoke are also related to the particle sizes for different kinds of smoke [21; 52]. To set up the relationship between optical properties and PNSDs, the PCCs of bulk optical properties (extinction and scattering coefficients) and particle number concentrations of different sizes were analyzed. We show the correlation coefficients between extinction coefficients/scattering coefficients and particle number concentrations of different sizes for smoldering smoke from biomass burning in Figure 5. For soya, the extinction coefficient has strong correlations with particle number concentrations of sizes from 87 nm to 316 nm (PCC \(>\) 0.8). The size ranges of strong correlation are from 154 nm to 365 nm for wheat (PCC \(>\) 0.8), from 205 nm to 487 nm for corn (PCC \(>\) 0.8), and from 205 nm to 316 nm for rice (PCC \(>\) 0.8), respectively. The size ranges of strong correlation are changed from 154 nm to 422 nm for Ph (PCC \(>\) 0.8), from 178 nm to 649 nm for Po (PCC \(>\) 0.8), and from 205 nm to 316 nm for P2 (PCC \(>\) 0.8), respectively. The extinction coefficient has relative strong correlations with particle number concentrations of sizes from 274 nm to 422 nm for Pi (PCC \(>\) 0.6), and from 237 nm to 365 nm for P1(PCC \(>\) 0.5). The scattering and extinction coefficients showed similar trends for smoldering smoke. Therefore, the correlation of the scattering coefficient and particle number concentrations of different sizes is similar to that of the extinction coefficient. The flow rate of DMS was changed in the measurements of smoldering smoke of P3, and the relationship between extinction coefficients/scattering coefficients and particle number concentrations was not matched, so the results of P3 are not displayed in Figure 5. As a conclusion, the bulk optical properties  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Biomass Samples**} & \multicolumn{3}{c}{**Mode 1**} & \multicolumn{3}{c}{**Mode 2**} & \multicolumn{3}{c}{**Mode 3**} \\ \cline{2-7}  & \(D_{g}\) (nm) & \(\sigma_{g}\) & \(D_{g}\) (nm) & \(\sigma_{g}\) & \(D_{g}\) (nm) & \(\sigma_{g}\) \\ \hline Soya & 12.17 & 1.391 & 68.61 & 1.565 & / & / \\ Wheat & 13.74 & 1.398 & 51.28 & 1.622 & / & / \\ Corn & 12.30 & 1.376 & 62.58 & 1.811 & / & / \\ Rice & 12.63 & 1.416 & 51.22 & 1.535 & / & / \\
**Average** & **12.71** & **1.395** & **58.42** & **1.633** & / & / \\
**SD** & **0.71** & **0.017** & **8.64** & **0.124** & / & / \\ Ph & 7.93 & 1.185 & 20.26 & 1.558 & 56.21 & 1.679 \\ Po & 7.32 & 1.150 & 12.29 & 1.310 & 66.52 & 1.804 \\ Pi & 10.71 & 1.193 & 20.16 & 1.280 & 87.99 & 1.630 \\ P1 & 12.98 & 1.271 & 28.93 & 1.459 & 67.18 & 1.229 \\ P2 & 11.35 & 1.164 & 20.65 & 1.194 & 61.50 & 1.721 \\ P3 & 11.20 & 1.169 & 16.59 & 1.284 & 60.83 & 2.282 \\
**Average** & **10.25** & **1.189** & **19.81** & **1.348** & **66.70** & **1.724** \\
**SD** & **2.18** & **0.043** & **5.50** & **0.134** & **11.18** & **0.339** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Lognormal fit parameters of particle number size distribution for smoldering smoke from biomass burning.  
of smoldering smoke have strong correlations with particle number concentrations of sizes bigger than 100 nm.