## 4 Discussions  
### The Differences between the Results of the Graphic Method (GM) and Moment Method (MM)  
Numerous studies have investigated the differences between the GM and MM, focusing on estuarine, coastal beach, and marine sediments [12; 15; 27; 28]. However, our understanding of how to effectively reflect the grain size parameters of flood events in the lower Yellow River using the GM and MM is limited. To resolve this, we compared and analyzed 143 fresh flood sediment samples collected from six sites in the Shandong section of the lower Yellow River using the GM and MM and evaluated their applicability for analyzing flood sediments. The results indicated a remarkable correlation between the mean grain size and sorting coefficient (Figures 2 and 3), whereas significant differences were observed in the skewness and kurtosis values (Figure 3). The differences between the two methods were intrinsically linked to the calculation formulas employed [12; 27]. The GM considers seven specific grain sizes (\(D_{5}\), \(D_{16}\), \(D_{25}\), \(D_{50}\), \(D_{75}\), \(D_{84}\), and \(D_{95}\)) when computing grain size parameters [29], whereas the MM performs calculations for all grain sizes [8]. Although both methods consider grain sizes in the range of 5-95% of the cumulative probability curve, the MM not only accounts for the influences of grain sizes ranging from 5% to 95% but also for the influences of grain sizes <5% and >95% on the curve, resulting in more accurate and comprehensive characterizations of differences between sediments than the GM [15]. If a sediment grain size frequency distribution curve conforms to a standard normal distribution, a strong correlation can be observed between the results obtained using the GM and MM. However, if the distribution curve does not follow a normal distribution, the difference between the two methods increases with an increase in the number of moments. Hence, the MM is more sensitive to grain size components both below 5% and above 95% [12; 27; 30]. The skewness of the 143 samples was calculated using the GM and MM. The results can be classified into five categories: strongly positive vs. strongly positive, positive vs. strongly positive, nearly symmetrical vs. strongly positive, positive vs. positive, and nearly symmetrical vs. positive (the former and latter refer to the results obtained using the GM and MM, respectively, as shown in Figure 4). For most of the samples analyzed, the qualitative outcomes were consistent, achieving 79.17% agreement (Figures 3b and 4a,c). However, 30 samples exhibited inconsistent results, with 28 (19.44%) showing positive outcomes using the GM and strongly positive outcomes using the MM (Figure 4b), indicating that the MM's results were more strongly positive than those based on the GM. Similarly, one sample exhibited nearly symmetrical vs. strongly positive outcomes, and one sample exhibited nearly symmetrical vs. positive outcomes (Figure 4c,e), and the results based on the MM were more positive or more strongly positive than those obtained using the GM. In the natural distribution curves of the samples, all samples exhibited a visible tail (Figure 4), leading to the MM producing more positive or more strongly positive results, as it could comprehensively and accurately reflect the grain size information. Similarly, the kurtosis of the 143 samples was calculated using the GM and MM. The results could be classified into seven categories: very sharp vs. moderate, very sharp vs. flat, sharp vs. flat, moderate vs. flat vs. flat, sharp vs. very flat, and moderate vs. very flat (the former and latter denote the outcomes of the GM and MM, respectively, as illustrated in Figure 5). The results indicated that most of the samples analyzed (97.9%) yielded inconsistent outcomes, with the MM tending to classify the samples as moderate, flat, or very flat. On the other hand, the GM generated sharper kurtosis results than the MM and was better able to highlight the dynamic sedimentary information of flood events.