2.6 Computational metrics and results interpretation
A set of computational metrics are selected for this study. The binary assessment comparing the scenarios with and without re-infiltration is considered with True Positives (TP), False Negatives (FN), and False Positives (FP). The rationale behind this is that flood extent observations, e.g., witness reports, watermark, satellite-derived flood extent, and insurance claims, are still uncertain without ground truth (Bates, 2004; Chen et al., 2021). For flood magnitude, the depth, area, and volume are calculated as a basin-integrated ratio. For flood dynamics, we inspect the initial inundation timings and total inundation duration that are often factored in flood risk assessments (Merz, Kreibich, Schwarze, & Thieken, 2010). The first six metrics listed in Table 3 are calculated at the maximum flood depth across the simulation period. In the real case study, we verify the performance of two schemes against stream gauge measurements, which is so far the most conventional and trustworthy source. During the verification, the Nash-Sutcliffe Efficiency (NSE) and Correlation Coefficient (CC) are the primary evaluation scores with each indicating the best value of 1. The detailed formulas for calculating these variables are listed in Table 3, as well as their ranges.
[INSERT TABLE 3 HERE]
The RMSE can be further decomposed to reveal the systematic error and random error (Tang et al., 2020). First, we assume an additive error model by fitting a linear regression to our simulated stage to determine regression coefficients a and b . We assign the new variable as F . Then the residual is calculated by the difference of observed river stage O and fitted river stage F .
\begin{equation} F=a\times S+b\nonumber \\ \end{equation}\begin{equation} \text{RMSE}_{S}=\sqrt[2]{\frac{1}{n}\sum_{i=1}^{n}{(S-F)}^{2}}\nonumber \\ \end{equation}\begin{equation} \text{RMSE}_{R}=\sqrt[2]{\frac{1}{n}\sum_{i=1}^{n}{(F-O)}^{2}}\nonumber \\ \end{equation}
, where S is denoted as the simulated river stage and O is the observed.
In the results section, we present it in two parts: sensitivity analysis and real case study. The former includes basin-wise difference in an integral to reveal general differences (Section 3.1.1) and spatiotemporal relations to uncover the importance of re-infiltration with time and space (Section 3.1.2). In the real case study, we focus on the efficacy of re-infiltration scheme by comparing to river stage observations (Section 3.2.1), and the High Water Marks surveyed in the aftermath of the event (Section 3.2.2). In Section 3.2.3, we investigate the importance of re-infiltration scheme in real case study by cross-comparing it to the synthetic results.