Journal of Geographical Sciences >
Evaluating flash flood simulation capability with respect to rainfall temporal variability in a small mountainous catchment
Wang Xuemei (1998), PhD Candidate, specialized in hydrology and water resources. Email: wang_xmww@163.com 
Received date: 20221227
Accepted date: 20230926
Online published: 20231214
Supported by
National Natural Science Foundation of China(42171047)
National Natural Science Foundation of China(42071041)
Rainfall temporal patterns significantly affect variability of flash flood behaviors, and further act on hydrological model performances in operational flash flood forecasting and warning. In this study, multivariate statistical analysis and hydrological simulations (XAJ and CNFF models) were combined to identify typical rainfall temporal patterns and evaluate model simulation capability for water balances, hydrographs, and flash flood behaviors under various rainfall patterns. Results showed that all the rainfall events were clustered into three types (Type 1, Type 2, and Type 3) in Anhe catchment in southeastern China. Type 1 was characterized by small total amount, high intensity, short duration, early peak moment, and concentrated hourly distribution. Type 3 was characterized by great total amount, low intensity, long duration, late peak moment, and uniform hourly distribution. Characteristics of Type 2 laid between those of Type 1 and Type 3. XAJ and CNFF better simulated water balances and hydrographs for Type 3, as well as all flash flood behavior indices and flood dynamics indices. Flood peak indices were competitively simulated for all the types by XAJ and except Type 1 by CNFF. The study is of significance for understanding relationships between rainfall and flash flood behaviors and accurately evaluating flash flood simulations.
WANG Xuemei , ZHAI Xiaoyan , ZHANG Yongyong , GUO Liang . Evaluating flash flood simulation capability with respect to rainfall temporal variability in a small mountainous catchment[J]. Journal of Geographical Sciences, 2023 , 33(12) : 2530 2548 . DOI: 10.1007/s1144202321885
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 
Category  Index  Abbreviation  Unit  Equation 

Magnitude  Total rainfall amount  P  mm  $P=\sum\limits_{t={{F}_{begin}}}^{{{F}_{end}}}{{{p}_{t}}}$ 
Average rainfall amount  AP  mm  AP=P/T  
Intensity  Maximum rainfall intensity  MPI  mm/h  MPI = max(P_{t}) 
Time  Rainfall duration  T  h  $T={{F}_{end}}{{F}_{begin}}+1$ 
Peak rainfall moment coefficient  ${{R}_{MPI}}$    ${{R}_{MPI}}={{{F}_{MP}}_{I}}/{T}\;$  
Concentration  Rainfall concentration  PCI    PCI=MPI/P 
Notes: p_{t} is the rainfall amount at time t, mm; F_{begin} and F_{end} are the time when a rainfall event begins and ends, respectively, h; F_{MPI} is the occurrence time of the maximum rainfall intensity, h. 
Table 2 Selected flash flood behavior indices at event scale 
Category  Index  Abbreviation  Unit  Equation 

Peak  Peak flow modulus  Km  m^{3}/(s·km^{2})  Km=Q_{m}/A 
Peak flow occurrence time  Tm  h  Tm=T(Q_{m})  
Lag time  Tl  h  Tl=TmF_{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    $K=\frac{1}{N}\sum\limits_{t={{T}_{begin}}}^{{{T}_{end}}}{{{\left( \frac{{{Q}_{t}}\mu }{\sigma } \right)}^{4}}}$ 
Notes: Q_{m} is the peak flow, m^{3}/s; A is the catchment area, km^{2}; Q_{begin}, Q_{end} and Q_{t} are the flood flows at time T_{begin}, T_{end} and t, respectively, m^{3}/s; T_{begin} and T_{end} are the time when a flood process begins and ends, respectively, h; μ and σ are the average value and standard deviation value of a flood process, respectively. 
Figure 2 Correlation coefficients of rainfall characteristic indicesNote: * indicates the correlation coefficient has a significance level p<0.05. 
Figure 3 The diagram of total withincluster 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 typesNotes: 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 typesNotes: 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 
Model  Evaluation indices  Period  Type  

Calibration  Validation  Type 1  Type 2  Type 3  
XAJ  Absolute RER (%)  6.89  10.62  10.73  7.67  7.81 
NSE  0.78  0.72  0.79  0.71  0.85  
CNFF  Absolute RER (%)  7.58  18.58  13.17  11.00  10.60 
NSE  0.87  0.70  0.76  0.81  0.85 
Figure 6 Cumulative frequency distribution of absolute RER and NSE for three rainfall typesNotes: (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 
Model  Evaluation indices  Type  Flash flood behavior indices  

Km  Tm  Tl  RQ  DQ  K  
XAJ  RMSEr  Type 1  0.15  0.26  0.35  0.27  0.44  0.35 
Type 2  0.33  0.18  0.33  0.43  0.55  0.43  
Type 3  0.18  0.18  0.49  0.23  0.33  0.33  
r  Type 1  0.96  0.89  0.70  0.79  0.46  0.23  
Type 2  0.90  0.96  0.85  0.85  0.85  0.39  
Type 3  0.97  0.98  0.73  0.96  0.97  0.75  
CNFF  RMSEr  Type 1  0.11  0.25  0.34  0.30  0.44  0.40 
Type 2  0.12  0.16  0.29  0.36  0.55  0.36  
Type 3  0.18  0.11  0.31  0.20  0.40  0.24  
r  Type 1  0.99  0.86  0.69  0.67  0.56  0.32  
Type 2  0.99  0.97  0.90  0.93  0.89  0.61  
Type 3  0.98  0.99  0.88  0.98  0.99  0.86 
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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