## 1 Introduction  
Sediments in diverse environments serve as critical agents for recording environmental evolution [1; 2]. Therefore, studying sediment grain size parameters and their variations is fundamental for evaluating changes in sedimentary environments and exploring environmental evolution [1; 2; 3; 4; 5; 6; 7].  
Grain size parameter analysis is key to understanding sedimentary environments and has received substantial attention from sedimentologists and geomorphologists. The graphic method (GM) and moment method (MM) are widely used to analyze sediment grain size parameters in diverse sedimentary environments [1; 8; 9; 10]. Based on statistical methods, the GM allows for the calculation of grain size parameters by taking the grain size at a specific cumulative percentage on the accumulation curve as a variable [1]. This method is straightforward and allows the analysis results to be compared with the grain size accumulation curve [11]. In contrast, the MM involves the calculation of the percentage of all grain sizes and provides insights into the characteristics of the sediment grain size distribution [8]. The MM's computation process is relatively intricate, and its analysis outcomes can be matched with the natural grain size distribution curve [10; 12]. Therefore, the GM and MM have different emphases when characterizing sediment grain size parameters. Consequently, conclusions drawn from the same sedimentary environment information may yield inconsistent results when the aforementioned methods are utilized.  
Previous studies have suggested considerable variations in grain size characteristics across diverse environments [12; 13; 14; 15]. The GM and MM possess unique advantages and limitations when applied. For example, the mean grain size of tidal flat sediments has shown minimal differences when determined using these two methods [12; 16]. However, the sorting coefficient has exhibited discrepancies, and the skewness and kurtosis have exhibited substantial variations [12]. Similar findings have been reported for aeolian sediments, such as Luochuan loess and Qin'an red clay [17; 18]. In contrast, in the analysis of bay and lagoon sediments, the GM is more advantageous than the MM for analyzing grain size parameters owing to the sorting coefficient [19; 20; 21]. Furthermore, comparative analyses of the GM and MM have been conducted using samples from lakes [22]. However, knowledge of the differences in the grain sizes of river flood sediments obtained using the GM and MM is limited. The Yellow River (Huang He) delivers a large amount of terrigenous sediment (with a median grain size of approximately 18 \(\upmu\)m between 1964 and 2020) to its lower reaches and delta area [23]. Some of these sediments are deposited in the lower Yellow River and are classified as fine-grained [23]. It is important to determine which method can effectively reflect the grain size of lower Yellow River flood sediments, as such knowledge is of great importance for identifying paleo-flood sediments and investigating changes in paleo-sedimentary environments.  
Considering the above, a detailed investigation was conducted using 143 modern flood sediment samples collected from the Shandong reach of the lower Yellow River. The main objectives of this study were as follows: (1) to examine the grain size characteristics of modern flood sediments in the lower Yellow River and (2) to assess the applicability of the GM and MM in analyzing the grain size parameters of flood sediments.