Journal of Geographical Sciences

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Evaluating flash flood simulation capability with respect to rainfall temporal variability in a small mountainous catchment

WANG Xuemei, ZHAI Xiaoyan, ZHANG Yongyong, GUO Liang

地理学报(英文版), 2023, 33(12): 2530-2548. DOI: 10.1007/s11442-023-2188-5

Category	Index	Abbreviation	Unit	Equation
Peak	Peak flow modulus	Km	m³/(s·km²)	Km=Q_m/A
	Peak flow occurrence time	Tm	h	Tm=T(Q_m)
	Lag time	Tl	h	Tl=Tm-F_MPI
Dynamics	Average rate of rising limb	RQ	s^-1	$RQ=\frac{3600\left( {{Q}_{m}}-{{Q}_{begin}} \right)}{\left( Tm-{{T}_{begin}} \right)\sum\limits_{t={{T}_{begin}}}^{{{T}_{end}}}{{{Q}_{t}}}}$
	Average rate of declining limb	DQ	s^-1	$DQ=\frac{3600\left( {{Q}_{m}}-{{Q}_{end}} \right)}{\left( {{T}_{end}}-Tm \right)\sum\limits_{t={{T}_{begin}}}^{{{T}_{end}}}{{{Q}_{t}}}}$
	Flood hydrograph kurtosis	K	-	$K=\frac{1}{N}\sum\limits_{t={{T}_{begin}}}^{{{T}_{end}}}{{{\left( \frac{{{Q}_{t}}-\mu }{\sigma } \right)}^{4}}}$

Table 2 Selected flash flood behavior indices at event scale

本文的其它图/表

Figure 1 Spatial distribution of DEM and water system (a), land use (b) and soil texture types (c) in Anhe catchment
Table 1 Selected rainfall characteristic indices at event scale
Figure 2 Correlation coefficients of rainfall characteristic indices
Note: * indicates the correlation coefficient has a significance level p<0.05.
Figure 3 The diagram of total within-cluster variance sum (Var_total) versus cluster number (K)
Notes: The number on the broken line between K=i and K=i+1 (1≤i≤7) represents the decreasing rate of Var_total with K increasing from i to i+1, which is noted as Var_total(i)^*. The number within the bracket represents the difference between Var_total(i+1)^* and Var_total(i)^*, which is noted as Var_total(i+1)^#. The red point represents the optimal cluster number K, which is the elbow inflection point of the curve with the minimum Var_total(K=3)^#.
Figure 4 Distribution of rainfall characteristic indices for three rainfall types
Notes: Boxes represent the ranges from the 25th to the 75th quartiles, whiskers represent the ranges from the minimum to the maximum, and dots and lines in boxes represent the averages and the medians, respectively.
Figure 5 Distribution of normalized flash flood behavior indices induced by three rainfall types
Notes: The flash flood behavior indices are normalized using $Y*=\frac{Y-{{Y}_{\min }}}{{{Y}_{\max }}-{{Y}_{\min }}},$ where Y* and Y are values before and after normalization, respectively; Y_max and Y_min are the maximum and the minimum, respectively. Boxes represent the ranges from the 25th to the 75th quartiles, whiskers represent the ranges from the minimum to the maximum, and dots and lines in boxes represent the averages and the medians, respectively.
Table 3 Evaluation indices for flash flood process simulation
Figure 6 Cumulative frequency distribution of absolute RER and NSE for three rainfall types
Notes: (a) and (c) are the absolute RER and NSE by XAJ, (b) and (d) are the absolute RER and NSE by CNFF.
Figure 7 Observed and simulated flash flood processes of partial events
Figure 8 Observed and simulated flash flood behavior indices for XAJ and CNFF
Table 4 Evaluation indices for flash flood behavior simulations
Figure S1 Correlation coefficients between flash flood behavior indices and rainfall characteristic indices for all events and three rainfall types. * indicates the correlation coefficient has a significance level of p<0.05.

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