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.