Figure 8 is here.
Fig. 8 Graphical hydrograph separation method: For the Gōno River catchmentN \(\ \approx\) 4 days.
In the case of flood assessment, information and complexity measures should be customized in such a way that describe the patterns of floods in terms of occurrence, frequency, etc., moreover, it should be emphasized that it is very important to define the appropriate value forQthreshold . In this work, we adapted the corresponding discharge value of the designated maximum water level introduced by the MLIT for each gauging station as a threshold and we used the maximum daily discharge data. According to the MLIT, this level is used as a guide for municipal mayors to issue evacuation warns, also is used as a reference for evacuation decisions by the local residents, etc.
We believe that employing two characters as a word length is, therefore, suitable for the assessment of different future flood scenarios. Increasing the word length to describe flood patterns, is not useful in our opinion, because we assume that having high floods for more than two days means a great natural and national disaster, bearing in mind that we are considering the maximum daily discharge in our analyses. The proposed analyses in this work suggest that the characterizing system patterns by means of information and complexity measures could be customized to be used in different ranges of applications.
In the case of flood assessment, one of the most important applications of considering different word patterns is to propose new contour inundation maps and/or hazard maps for the different discharge gauging stations, to support policy makers to improve their understanding and choose better decisions and alternatives for the related issues and future projects.

Inferences from low and high frequency analyses

Quantifying streamflow patterns by means of information and complexity metrics and addressing different aggregation lengths revealed various interesting behaviors of streamflow during low and high frequencies. Regarding low frequency findings, it can be seen that using different aggregation lengths, the information metrics (metric entropy and mean information gain) for streamflow data recorded at the studied stations have obviously two scaling regimes. The first one with steep slope for shorter AL ranges, and the other one for longer AL ranges. In fact, this finding matches with the results of Al Sawaf et al., (2017) who studied the discharge fluctuations in the Gōno River by means of Detrended Fluctuation Analysis (DFA) and reported of the presence of two scaling regimes of the river discharge fluctuations separated by a crossover time observed around 3-5 days. To compare, it can be noticed in Fig. 5(a & b) the long AL ranges (i.e. AL greater than 20 has a mild slope which is similar to the outcomes of DFA results indicating that this range may reveal the long-memory characteristics of the river flow fluctuations. Of interest, both information and complexity contents evaluated for the studied stations showed similar crossover times detected roughly at AL\(\approx\) 20 hours equivalent to 80 hours (see Fig. 7(c&d)). However, one of the challenging tasks in DFA or spectral analyses is to find the crossover time accurately. In the case of these approaches, the crossover time is usually estimated by performing a linear regression fit to the suspected regimes separately, thus, the intersection point of the two fitting lines composes the crossover time. Nevertheless, the findings revealed that crossover times may be estimated from the corresponding aggregation length time where the fluctuation complexity value reaches its peak according to the information-complexity diagram as can be seen in Fig. 6 (Also, refer to the Table 1 in the supplementary materials). In the case of the Ozekiyama station, the crossover time observed at AL= 14 hours equivalent to 56 hours, i.e. the crossover time (56 hours) = aggregation length (14) * word length (4 characters). Therefore, further investigations are still required to interpret and decipher the nested relationships between the information metrics and fractal analysis.
Regarding the high frequency analyses, an interesting phenomenon was observed namely the presence of an extra scaling regime that occurs during sub-daily scales captured by FAT records can be observed at AL\(\leq\ 4\) equivalent to 16 hours. To verify the existence of this scale, we estimated the power spectrum for the discharge records obtained by both Ozekiyama and FAT stations using the proposed model by Dolgonosov et al., (2008), presented in Fig. 9. As can be distinguished, the spectral analysis shows that both RC and FAT data have two main scaling denoted by S1 for long ranges that are roughly quite similar, and S2 for mid ranges (Fig. 9) with a crossover time around 60 hours which is very near to AL=14 (i.e. 56 hours). Nevertheless, it can also be realized that the presence of a specific slope captured by FAT data namely S3 which is somehow near to AL=4 (i.e. 16 hours). This finding seems to confirm our hypothesis about the existence of an additional scaling regime happens within very short time scales and can be captured by FAT as can be seen in Fig. 7a. However, the slight variation may be confirmed by comparing with another scaling method (fractal analysis) or considering shorter word length for high frequency analysis (e.g. 3 characters per word).
The last remaining question is why there is an additional regime that was captured by means of FAT. Though it needs further exploration to clearly describe this phenomenon, it can be said that the FAT system measures the discharge according to the fundamental discharge equation as given in Eq (2). Unlike discharge estimated by means of the RC method, the velocity and area (depth) terms are embedded directly in streamflow estimates and hence FAT can clearly show the high resolution of discharge estimate.