## 4 Results and Discussion
### Discussion
#### 4.5.1 Empirical Equations for Ancient Braided Rivers Based on Sedimentary Outcrops
[5,55] (Equations (3) and (4) in Table 3) for a given value of d. Compared with other studies (Equations (3) and (4) in Table 3) [5,55], the \(d_{m}\) value predicted by the \(d_{m}\)-d equation in the present study is relatively large, which is related to the relatively flat bottom shape of the channels in this study area and the lack of deeper thanweg. This situation may reflect the higher average annual discharge in the region, consistent with that in the Kanto region [56]. Under the influence of regional climate (seasonal precipitation), more than 70% of the annual discharge is concentrated in the rainy season from June to September (the peak is in July and August) [44], while the icebound period lasts from November to April, which means that high discharge is maintained from May to October. At the same time, due to the influence of a cohesive riverbank in a vegetation-covered area, the lateral migration rate of a mid-channel downstream accreting coarse sand-conglomerate bar is lower, and a bank-attached laterally accreting bar in this study area is usually not the result of secondary helical circulation, resulting in the relatively stable and flat fluvial channel. \begin{table}
\begin{tabular}{c c c c} \hline
**Equation** & **Reference** & **Applicable Range** & **Remarks** \\ \hline \(d_{m}\)-d relationships & & & \\ \hline \((1)\)\(d_{m}\) = 0.617 d & Present study & \(1.5\leq d\leq 6.5\) m & Coarse sandy-gravelly braided rivers in the Songyuan region (present study) \\ \hline \((2)\)\(d_{m}\) = 0.62 d & [PERSON] et al. (2018) [16] & \(2.3\leq d\leq 9.4\) m & Gravelly rivers between braided and meandering rivers \\ \hline \((3)\)\(d_{m}\) = 0.57 d & [PERSON] (1993) [5] & - & Combined equation [4] \\ \hline \((4)\)\(d_{m}\) = 0.5819 d & [PERSON] et al. (2003) [55] & \(0.2\leq d\leq 2.6\) m & Gravelly and sandy ephemeral and perennial streams \\ \hline \(W_{b}\)-\(d_{m}\) relationships & & & \\ \hline \((5)\)\(W_{b}\) = 56.025 \(d_{m}\)\({}^{0.9656}\) & Present study & \(0.8\leq d_{m}\leq 4.5\) m & Coarse sandy-gravelly braided rivers in the Songyuan region (present study) \\ \hline \((6)\)\(W_{b}\) = 49.16 \(d_{m}\)\({}^{0.67}\) & [PERSON] et al. (2018) [16] & \(1.0\leq d_{m}\leq 6.7\) m & Gravelly rivers between braided and meandering rivers (g,b-m.) \\ \hline \((7)\)\(W_{b}\) = 8.8 \(d_{m}\)\({}^{1.82}\) & [PERSON] (1993) [5] & - & Widely used equation for paleochannel Reconstructions (\(W\)) \\ \hline \((8)\)\(W_{b}\) = 242.4 \(d_{m}\)\({}^{2.19}\) & [PERSON] (2004) [17] & \(0.4<d_{m}<3\) m & Gravelly braided rivers in various tectonic and climatic settings (g,b.) \\ \hline \((9)\)\(W_{b}\) = 340.4 \(d_{m}\)\({}^{1.94}\) & [PERSON] (2004) [17] & \(1.5<d_{m}<15\) m & Sandy braided rivers in various tectonic and climatic settings (s,b.) \\ \hline \((10)\)\(W_{b}\) = 2.36 \(d_{m}\)\({}^{2.53}\) & [PERSON] (2004) [17] & \(0.7<d_{m}<15\) m & Sandy meandering rivers in various tectonic and climatic settings (s,m.) \\ \hline \((11)\)\(W_{b_{\rm{min}}}\) = 59.9 \(d_{m}\)\({}^{1.8}\) & [PERSON] (2000) [40] & - & Widely used equation for the extent of the single braided belts (W,s) \\ \hline \end{tabular} Annotations: (A) the meaning of each parameter is detailed in Section 3; (B) error margins: thickness measurements (\(\pm 5\) cm), width (\(\pm 2\) m), and paleocurrent direction (\(\pm 3\)?), based on triplicate measurements of 20% of outcrops; (C) quality control: the 10/9 corrections for diagenetic compaction were applied uniformly; (D) uncertainty sources clarification that missing data (e.g., \(W_{\rm{bar}}\) in profile 2) resulted from poor outcrop exposure.  
\end{table} 
Table 3: Empirical equations derived from this study area and previous studies on the relationship between the river bankfull channel depth d, mean bankfull channel depth d\({}_{m}\), and bankfull channel width \(W_{b}\). Modified after [PERSON] et al. (2018) [16].