## 4 Results and Discussion
### Discussion  
#### 4.5.1 Empirical Equations for Ancient Braided Rivers Based on Sedimentary Outcrops  
Defining the edge of a single-channel belt from braided river outcrops is extremely difficult [43], so an empirical relationship with the bankfull channel width (Wb) is usually derived from data collected in modern river systems [5,16]. [PERSON] and [PERSON], based on the data for modern river systems in various climatic environments and tectonic settings, proposed an empirical formula for the reconstruction of paleochannel geometric parameters [5]. [PERSON] and [PERSON] further studied and completed the characterization of geometric parameters of a single braid thread [40]. [PERSON] et al. quantitatively characterized the relationship among A, d, d\({}_{\text{m}}\), Wb, and Q of braided to meandering gravelly rivers by using data from 24 observation sites of modern gravelly rivers in the Kanto region and summarized and compared the previous research results [5,16]. [PERSON] compared the hydrodynamic geometric characteristics of different types of sandy and gravelly rivers based on data from alluvial rivers around the world. However, this paper attempts to use a large number of detailed outcrop data derived from the actual measurement of the trench profiles for research [17]. The data measurement process is different, but the genetic analysis of each element ensures that the same meanings of Wb, d\({}_{\text{m}}\), and d are represented. Therefore, the summary of [PERSON] et al. [16] is compared with the results obtained in the present study (Table 3). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Outcrop** & **No** & **d\({}_{\text{bm}}\) (m)** & **d\({}_{\text{bm}}\)(m)** & **W\({}_{\text{bar}}\) (m)** & **d (m)** & **d\({}_{\text{m}}\) (m)** & **W\({}_{\text{c}}\) (m)** & **W\({}_{\text{b}}\) (m)** \\ \hline \multirow{4}{*}{profile 1} & (1) & 2.34 & 2.62 & 58 & 2.42 & 1.78 & 46.5 & 90 \\ \cline{2-10}  & (2) & 2.78 & 2.85 & 62 & 3.19 & 1.95 & 51.6 & 98 \\ \cline{2-10}  & (3) & 1.43 & 1.78 & 52 & 1.75 & 1.2 & 35 & 84 \\ \cline{2-10}  & (4) & - & - & - & 1.43 & - & - & - \\ \hline \multirow{2}{*}{profile 2} & (4) & 1.64 & 2.94 & 84 & 3.38 & 1.98 & 47.5 & 113 \\ \cline{2-10}  & (5) & 1.35 & 1.95 & - & - & - & - & - \\ \hline \multirow{4}{*}{profile 4} & (6) & 1.31 & 1.86 & 48 & 1.9 & 1.32 & 40 & 72 \\ \cline{2-10}  & (7) & 0.89 & 1.42 & 39 & 1.65 & 0.92 & 23 & 57 \\ \cline{2-10}  & (8) & 4.3 & 5.6 & 156 & 6.45 & 3.82 & 115 & 226 \\ \cline{2-10}  & (9) & - & - & - & - & 89 & - \\ \hline \multirow{4}{*}{profile 6} & (9) & 2.51 & 3.2 & 97 & 3.72 & 2.15 & 70 & 148 \\ \cline{2-10}  & (10) & 2.04 & 2.74 & 75 & 3.22 & 1.89 & 53 & 104 \\ \cline{2-10}  & (11) & 1.65 & 2.2 & 57.5 & 2.04 & 1.66 & 42.5 & 81 \\ \hline \multirow{4}{*}{profile 7} & (12) & 1.67 & 3.32 & 110 & 3.97 & 2.23 & 60 & 157 \\ \cline{2-10}  & (13) & - & - & - & 3.25 & - & - & - \\ \cline{2-10}  & (14) & 1.54 & 2.47 & 90 & 2.76 & 1.65 & 51 & 121 \\ \cline{2-10}  & (13) & - & - & - & 2.6 & - & 47 & - \\ \hline \multirow{4}{*}{profile 10} & (14) & 1.49 & 2.5 & 82 & 2.34 & 1.7 & 43 & 116 \\ \cline{2-10}  & (15) & - & - & - & 2.18 & - & 35 & - \\ \cline{1-1} \cline{2-10}  & (15) & 1.68 & 2.2 & 5.7 & 1.92 & 1.64 & 42 & 118 \\ \cline{1-1} \cline{2-10}  & (15) & - & - & - & 1.85 & - & 57 & - \\ \hline \end{tabular}
\end{table} 
Table 2: Summary data of river course parameters at different scales measured in this study area. The \(d_{m}\) estimated by the \(d_{m}\)-d equation (Equation (1) in Table 3) in the present study is similar to that estimated by the equation of [PERSON] et al. [16] (Equation (2) in Table 3) and is slightly larger than that estimated from the equation of [PERSON] and Mackey and [PERSON] et al.