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Journal of Geographical Sciences >

2023 , Vol. 33 >Issue 12: 2530 - 2548

DOI: https://doi.org/10.1007/s11442-023-2188-5

Research Articles

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

  • WANG Xuemei , 1 ,
  • ZHAI Xiaoyan , 1, * ,
  • ZHANG Yongyong 2 ,
  • GUO Liang 1
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  • 1. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, Research Center on Flood and Drought Disaster Reduction, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
  • 2. Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China
* Zhai Xiaoyan (1989-), Associate Professor, specialized in hydrology and water resources. E-mail:

Wang Xuemei (1998-), PhD Candidate, specialized in hydrology and water resources. E-mail:

Received date: 2022-12-27

  Accepted date: 2023-09-26

  Online published: 2023-12-14

Supported by

National Natural Science Foundation of China(42171047)

National Natural Science Foundation of China(42071041)

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Abstract

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.

Key words： rainfall characteristic indices; flash flood behavior indices; hydrological model; mountainous catchment

Cite this article

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/s11442-023-2188-5

1 Introduction

Flash floods are defined as the intense catchment responses to rainfall storms in mountainous catchments, which are characterized by extremely sudden onset, rapid flood response, and highly concentrated flood energy (Ritter et al., 2020; Leal et al., 2022; Habibi et al., 2023). They are recognized as the main flood disasters causing grave losses of life and property (Khajehei et al., 2020). Globally, property losses caused by flash flood disasters is the most prominent among natural disasters (Borga et al., 2011; Yin et al., 2023), and 40%-90% of flood-related casualties are owing to flash floods (Barredo, 2007; Ashley and Ashley, 2008; Zhai et al., 2021a). China is one of the countries seriously affected by flash flood disasters worldwide. Flash floods accounts for more than 70% of the flood-related casualties, and the annual direct economic losses have exceeded 120 billion CNY from 2000 to 2017 (Zhang et al., 2019; Zhai et al., 2021a). Identifying rainfall-flood response regularities and developing effective flash flood forecasting techniques can provide scientific supports for decision making of flash flood disaster prevention, as well as timely release of flash flood warning information.
Short-duration heavy rainfall is widely accepted as the direct inducing force of flash floods (Garambois et al., 2014; Lompi et al., 2022). Catchment hydrological responses involving runoff generation and concentration processes are sensitive to the temporal structure of rainfall forcing, which can be reflected by the variations of flood characteristics (e.g., timing, magnitude, and shape) (Batisani, 2011; Zhang et al., 2020; Liu et al., 2022). Series of studies have been conducted to investigate the relationships between flood characteristics and rainfall temporal distributions. Brunner et al. (2018) analyzed event-scale rainfall and flood processes in 163 catchments in Switzerland, and found that flash floods with steep rising and falling limbs of hydrographs were generally triggered by high total rainfall amount and maximum hourly rainfall. Fischer et al. (2019) compared flood-inducing rainfall characteristics between distinct flood types based on timescales (i.e., ratio between flood volume and flood peak) in Mulde River basin in eastern Germany, and noticed that flash floods are induced by rainfall processes with high intensity. Zheng et al. (2022) assessed effects of rainfall peak characteristics on flood hydrographs in Daqinghe catchment in China, and found that rainfall peak occurrence moment and rainfall peak number affected time to flood peak and shape of flood peak hydrographs, respectively. Present studies focus on certain rainfall temporal characteristics (e.g., rainfall amount and peak), while the attention on overall rainfall temporal distribution is insufficient. It is crucial to focus on the overall rainfall temporal structures (e.g., magnitude, intensity, time, and concentration), which can provide an effective approach to explore the generation and evolution mechanisms of flash floods.
Hydrological models, which usually adopt generalized mathematical equations to describe natural rainfall-flood processes, are powerful tools to probe the regularities of rainfall-runoff conversion and flood propagation (Wagener et al., 2001; Song et al., 2011; Zhang et al., 2021; Chen et al., 2023; Gao et al., 2023). Considering the accumulation of hydro-climatic and geomorphologic data as well as the concurrent maturation of computing power, hydrological models have been widely employed to develop effective flash flood hazard prediction plans (Liu and Liu, 2001; Meresa et al., 2021). The rigorous evaluation of model performance is useful for facilitating the applicability and effectiveness of hydrological models in operational forecasting and warning of flash floods. Rozalis et al. (2010) used an uncalibrated hydrological model, which was based on SCS curve number method and kinematic wave method, to simulate 20 flood events in Merhavia catchment in Israel, and found good model performances for flood events with high magnitudes and poor model performances for events with medium and low magnitudes. Orth et al. (2015) assessed simulation performances of HBV, PREVAH, and SWBM in eight well-observed catchments in Switzerland, and found that all the three models fitted slightly better with observations at low altitude sites than those at high altitudes, and each model had its own unique advantages in flood simulation. McMillan et al. (2016) adopted TopNet to simulate daily rainfall-flood events in 485 catchments in New Zealand, and found better performances in larger and medium-wet catchments with smaller seasonal variations. To date, many studies have been conducted to assess model simulation capabilities with respect to catchments with different hydrological conditions or flood events with different characteristics. Whereas, the effects of rainfall temporal variability, which serves as the key factor inducing flash floods, on flash flood modelling are still ambiguous.
This study aims to identify the rainfall temporal patterns and associated flash flood behaviors in small mountainous catchments, and assess their effects on flash flood simulation performances. Two widely used hydrological models (i.e., XAJ and CNFF) in China are adopted for exploration. The specific objectives of this study include: (1) cluster typical rainfall types based on six rainfall temporal characteristic indices measuring magnitude, intensity, time, and concentration by principal component analysis and dynamic K-means cluster analysis; (2) identify flash flood process variations from perspective of six behavior indices induced by different rainfall temporal patterns; (3) assess model simulation capability under various rainfall types in reproducing water balances and flood hydrographs, as well as flash flood peak and dynamics behavior indices.

2 Study area and data sources

Anhe catchment (114°17′E-114°32′E, 25°56′N-26°70′N) located in southeastern China is selected for study with a drainage area of 251 km2 (Figure 1). The study area belongs to a subtropical humid monsoon climate. The annual average rainfall is 1400 mm, 70% of which falls between April and September. The altitude decreases from northwest to southeast, with an average elevation of 492 m. The main land use types are forest (78.81%) and farmland (12.43%), and main soil texture types are sandy clay (80.24%) and sandy loam (10.12%).
Figure 1 Spatial distribution of DEM and water system (a), land use (b) and soil texture types (c) in Anhe catchment
The collected dataset includes geographic information system (GIS) data as well as rainfall and water discharge observations. GIS data including digital elevation model (DEM, 1:50,000), river system (1:100,000), land use (1:250,000) and soil texture types (1:500,000), is used for the delineation and attribute extraction of sub-catchments, all of which are collected from the National Geomatics Center of China (http://www.ngcc.cn/). The hourly rainfall and water discharge observations from 1978 to 2012 are collected from eight rainfall stations and Anhe hydrological station, and are used for rainfall type identification and model performance evaluation.

3 Methods

3.1 Rainfall type identification

3.1.1 Rainfall characteristic indices and flash flood behavior indices

A rainfall event is determined with its total rainfall amount threshold being 12.70 mm and the inter-event time threshold being 6 hours (Huff, 1967; Fan, 2012). Six rainfall characteristic indices are selected to describe the magnitude, intensity, time, and concentration of rainfall events (dos Santos et al., 2017; Park et al., 2019) (Table 1). Specifically, the peak rainfall moment coefficient (RMPI) ranging from 0 to 1, describes the occurrence moment of peak rainfall, and a great value of RMPI indicates a late occurrence moment of peak rainfall. The rainfall concentration (PCI) ranging from 0 to 1, describes the temporal distribution of hourly rainfall amounts, and a great value of PCI indicates high concentration of a rainfall temporal process.
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(Pt)
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: pt is the rainfall amount at time t, mm; Fbegin and Fend are the time when a rainfall event begins and ends, respectively, h; FMPI is the occurrence time of the maximum rainfall intensity, h.

Rainfall variability strongly impacts runoff generation and confluence processes of natural catchments. A flood event corresponding to the rainfall event is determined with its flood peak higher than the annual average water discharge and the inter-event time threshold being 6 hours. Six flash flood behavior indices, which are categorized into flood peak and dynamics indices, are used to characterize flood process variations induced by a certain rainfall pattern (Table 2) (Zhai et al., 2021a). Specifically, the average rates of rising and declining limbs (i.e. RQ and DQ) are used to quantify the change rates of flood discharges, and great values of RQ and DQ indicate quick onset and recession of a flood process, respectively. The flood hydrograph kurtosis (K) is used to quantify the shape of a flood hydrograph, and a great value of K indicates a thin flood hydrograph.
Table 2 Selected flash flood behavior indices at event scale
Category Index Abbreviation Unit Equation
Peak Peak flow modulus Km m3/(s·km2) Km=Qm/A
Peak flow occurrence time Tm h Tm=T(Qm)
Lag time Tl h Tl=Tm-FMPI
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: Qm is the peak flow, m3/s; A is the catchment area, km2; Qbegin, Qend and Qt are the flood flows at time Tbegin, Tend and t, respectively, m3/s; Tbegin and Tend 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.

3.1.2 Principal component analysis

Rainfall characteristics indices might be correlated with each other, which may result in information overlapping. Pearson correlation analysis is performed in advance to test their relationships, and the principal component analysis (PCA) is adopted to reduce the dimensionality of six rainfall characteristic indices. The p rainfall characteristic indices from n rainfall events constitute the initial matrix X={xij}n×p, and is normalized into the matrix X*={$x_{ij}^{*}$}n×p and correlation matrix R={rkt}p×p. The eigenvalues (λ1≥λ2≥…≥λp) of matrix R are determined by resolving Equation 1 and the corresponding eigenvector is ${{\mu }_{j}}={{\left( {{\mu }_{1j}},{{\mu }_{2j}},...,{{\mu }_{pj}} \right)}^{\text{T}}}\left( j=1,2,...,p \right)$.
$\left| \left( \begin{matrix} {{r}_{11}} & {{r}_{12}} &... & {{r}_{1p}} \\ {{r}_{21}} & {{r}_{22}} &... & {{r}_{2p}} \\... &... &... &... \\ {{r}_{p1}} & {{r}_{p2}} &... & {{r}_{pp}} \\ \end{matrix} \right) \right|-\left| \left( \begin{matrix} {{\lambda }_{1}} & 0 &... & 0 \\ 0 & {{\lambda }_{2}} &... & 0 \\... &... &... &... \\ 0 & 0 &... & {{\lambda }_{p}} \\ \end{matrix} \right) \right|=0$
where rkt is the correlation coefficient between the kth and tth rainfall characteristic indices, k=1, 2,…, p, t=1, 2,…, p.
The objective function J is to preserve the variance information of original rainfall indices in maximum, and is expressed as Equation 2. The m PCA components are further determined if the cumulative variance $\left( \sum\limits_{u=1}^{m}{{{\lambda }_{u}}}/\sum\limits_{u=1}^{p}{{{\lambda }_{u}}} \right)$ is over 85%, and the PCA component matrix P*={zij}n×m is obtained by Equation 3.
$J\left( {{P}^{*}} \right)=\max \left[ \sum\limits_{u=1}^{m}{Var\left( {{P}_{u}} \right)} \right]$
${{z}_{ij}}=\sum\limits_{t=1}^{p}{x_{it}^{*}{{\mu }_{tj}}}$
where Pu is the uth PCA component; Var(Pu) is the variance of Pu; m is the number of selected PCA components; zij is the jth PCA component value of the ith rainfall event; $x_{it}^{*}$ is the tth normalized rainfall characteristic index value of the ith rainfall event; μtj is the tth element of the jth eigenvector.

3.1.3 Dynamic K-means cluster analysis

The dynamic K-means cluster algorithm is implemented on the m PCA components to identify typical rainfall types. To minimize the total within-cluster variance sum (Vartotal), the objective function Jc is denoted as Equation 4. Specifically, the similarities between rainfall events and cluster centroids are quantified using Euclidean distance d. Rainfall events are assigned into the cluster with the smallest d, and the averages of rainfall events within K clusters are considered as the new K cluster centroids to drive the next reassignment. The assignment calculation proceeds iteratively until the values of cluster centroids no longer change or change within a permitted narrow range, and all rainfall events are finally clustered into K typical rainfall types.
$\left\{ \begin{align} & {{J}_{c}}\left( {{U}^{\mathbf{*}}},{{C}^{\mathbf{*}}} \right)=\min \left( \sum\limits_{i=1}^{n}{\sum\limits_{r=1}^{K}{{{\eta }_{ir}}d_{ir}^{2}}} \right) \\ & {{d}_{ir}}=\sqrt{\sum\limits_{j=1}^{m}{{{\left( {{z}_{ij}}-{{c}_{rj}} \right)}^{2}}}} \\ \end{align} \right.$
where U* and C* are the optimal partition matrix and the optimal cluster centroid matrix, respectively; K is the number of clusters; n is the number of rainfall-flood events; ${{\eta }_{ir}}$ is the membership coefficient, ${{\eta }_{ir}}=\left\{ \begin{align} & 0\text{, }{{Z}_{i}}\notin r\text{th cluster} \\ & 1\text{, }{{Z}_{i}}\in r\text{th cluster} \\ \end{align} \right.$; dir is the Euclidean distance between the ith rainfall event ${{Z}_{i}}=\left( {{z}_{i1}},{{z}_{i2}},...,{{z}_{im}} \right)$ and the rth cluster centroid ${{C}_{r}}=\left( {{c}_{r1}},{{c}_{r2}},...,{{c}_{rm}} \right)$; crj is the jth feature of Cr, ${{c}_{rj}}=\frac{\sum\limits_{i=1}^{n}{{{\eta }_{ir}}{{z}_{ij}}}}{\sum\limits_{i=1}^{n}{{{\eta }_{ir}}}}$.
The elbow method is adopted to assess the cluster performance (Thorndike, 1953). Both the value and the decreasing rate of Vartotal decrease along with the increase of cluster number K, revealing that for a greater K the total within-cluster cohesion is improved and the cohesion improvement efficiency decreases simultaneously. The optimal cluster number K is determined based on the cohesion improvement efficiency. If the decreasing rate of Vartotal decreases considerably beyond a certain cluster number, the number is considered to be a good choice, which occurs at the elbow inflection point of the curve between Vartotal and K. Moreover, the Kruskal-Wallis test is adopted to examine whether the differences among the identified rainfall types are significant in terms of six rainfall characteristic indices (Theodorsson-Norheim, 1986).

3.2 Flash flood simulation

3.2.1 XAJ hydrological model

Xinanjiang hydrological model (XAJ) is developed by Professor Zhao Renjun of Hohai University (Zhao, 1992), and has been widely applied in humid and semi-humid regions for rainfall-runoff simulation and forecasting in China (Jie et al., 2018; Gong et al., 2021; Jiang et al., 2023). The tension and free water storage capacity curves are used to calculate runoff generation shown as Equation 5, and the linear reservoir method and the segmental Muskingum method are used to simulate overland runoff concentration and flood routing, respectively.
$\left\{ \begin{align} & \alpha =1-{{\left( 1-\frac{WM}{WMM} \right)}^{B}} \\ & \beta =1-{{\left( 1-\frac{SM}{SMM} \right)}^{EX}} \\ \end{align} \right.$
where α is the proportion of the area with tension water storage capacity no greater than WM; β is the proportion of the area with free water storage capacity no greater than SM; WM and WMM are the tension water storage capacity within the study area and its maximum, respectively; SM and SMM are the free water storage capacity within the study area and its maximum, respectively; B and EX are the exponents.

3.2.2 CNFF hydrological model

China Flash Flood hydrological Model (CNFF) is developed by China Institute of Water Resources and Hydropower Research, and has been widely used in the simulation and early-warning of flash floods over China (Zhai et al., 2018; 2021b). In this study, the excess saturation runoff method is used to calculate runoff generation, the modified distributed unit hydrograph method and the dynamic Muskingum method are used to simulate overland runoff concentration and flood routing, respectively. The flow velocity and flow time of overland runoff are calculated as follows:
$\left\{ \begin{align} & V=K{{S}^{0.5}}{{i}^{0.4}} \\ & {{T}_{j}}=\sum\limits_{m=1}^{{{M}_{j}}}{\frac{c{{L}_{m}}}{{{V}_{m}}}} \\ \end{align} \right.$
where V is the flow velocity at a grid cell (25 m×25 m); K is the flow velocity coefficient, mainly affected by land use conditions (Soil Conservation Service, 1972); S is the hydraulic slope; i is the dimensionless rainfall intensity; Tj is the flow time from grid cell j to catchment outlet; Lm is the flow path length of water drops at the mth grid cell; c=1 or $\sqrt{2}$; Mj is the grid cell numbers along the flow path at grid cell j.

3.2.3 Model performance evaluation

The study area was divided into 19 sub-catchments, with an average drainage area of 13.16 km2. The study period was evenly divided into three sub-periods: the first sub-period from 1978 to 1993 (36 rainfall-flood events in total) and last sub-period from 2001 to 2010 (36 rainfall-flood events in total) were set as model calibration period, and the second sub-period from 1994 to 2001 (35 rainfall-flood events in total) was set as model validation period. The objective function for parameter optimization was to minimize the average relative error of runoff volume (RER) and maximize the average Nash-Sutcliffe efficiency coefficient (NSE). The equations were expressed as follows. A small value of absolute RER indicates a well-obtained water balance between simulated and observed runoff volume, and a great value of NSE indicates a close agreement between simulated and observed flood hydrographs.
$RER=\frac{1}{n}\sum\limits_{j=1}^{n}{\left( \frac{{{\overline{R}}_{s,j}}-{{\overline{R}}_{o,j}}}{{{\overline{R}}_{o,j}}} \right)}$
$NSE=\frac{1}{n}\sum\limits_{j=1}^{n}{\left( 1-\frac{\sum\limits_{t=1}^{{{N}_{j}}}{{{\left( {{Q}_{t,s,j}}-{{Q}_{t,o,j}} \right)}^{2}}}}{\sum\limits_{t=1}^{{{N}_{j}}}{{{\left( {{Q}_{t,o,j}}-{{\overline{Q}}_{o,j}} \right)}^{2}}}} \right)}$
where ${{\bar{R}}_{o,j}}$ and ${{\bar{R}}_{s,j}}$ are the average observed and simulated runoff volume for the jth rainfall-flood event, respectively; Qt,o,j and Qt,s,j are the observed and simulated flood discharge at time t for the jth rainfall-flood event, respectively; ${{\bar{Q}}_{o,j}}$ is the average observed flood discharge for the jth rainfall-flood event; n is the number of rainfall-flood events; Nj is the length of jth rainfall-flood event.
Moreover, model performances on flash flood behavior indices are evaluated using the relative root mean square error (RMSEr) and linear correlation coefficient (r) with the optimal values of zero and one, respectively. A smaller RMSEr and a greater r indicate a better model performance on flash flood behavior indices. The evaluation indices are calculated as follows:
$RMSEr=\sqrt{\frac{\sum\limits_{i=1}^{n}{{{({{O}_{i}}-{{S}_{i}})}^{2}}}}{n\cdot {{{\bar{O}}}^{2}}}}$
$r=\frac{\sum\limits_{i=1}^{n}{\left( {{O}_{i}}-\bar{O} \right)\left( {{S}_{i}}-\bar{S} \right)}}{\sqrt{\sum\limits_{i=1}^{n}{{{\left( {{O}_{i}}-\bar{O} \right)}^{2}}\sum\limits_{i=1}^{n}{{{\left( {{S}_{i}}-\bar{S} \right)}^{2}}}}}}$
where Oi and Si are the observed and simulated flash flood behavior indices of the ith flood event; $\bar{O}$ and $\bar{S}$ are the average observed and simulated flash flood behavior indices for all events.

4 Results

4.1 Rainfall temporal pattern and associated flash flood behavior identification

There were 107 rainfall-flood events determined for rainfall type identification with total rainfall amount and inter-event time greater than 12.70 mm and 6 hours, respectively. Significant linear correlations existed between most of the rainfall characteristic indices (Figure 2). P was significantly and linearly correlated with T (r≥0.50, p<0.05), AP was significantly and linearly correlated with MPI, T, and PCI (|r|≥0.50, p<0.05), and PCI was also significantly and linearly correlated with MPI and T (|r|≥0.50, p<0.05).
Figure 2 Correlation coefficients of rainfall characteristic indices

Note: * indicates the correlation coefficient has a significance level p<0.05.

Six rainfall characteristic indices were composited into three independent PCA components, which could explain 88.17% of the total rainfall characteristic variations. The first PCA component mainly included AP, MPI, T and PCI, the second PCA component mainly included P, and the third PCA component mainly included RMPI. Specifically, these PCA components could explain 46.64%, 25.11% and 16.42% of the total variability, respectively. Dynamic K-means cluster analysis was then performed with cluster numbers ranging from one to eight. As shown in Figure 3, the total within-cluster variance sum (Vartotal) decreased along with the increase of cluster number K, and the decreasing rate change of Vartotal reached the maximum of -85.81 at K=3, after which the cohesion improvement efficiency began to decrease considerably. Thus, all rainfall events were clustered into three types, noted as Type 1, Type 2, and Type 3, with 14, 65, and 28 rainfall events, respectively. Furthermore, the Kruskal-Wallis test showed that the distributions of six rainfall characteristic indices existed significant differences among three rainfall types at a level of p<0.01, revealing that the identified rainfall types were significantly different.
Figure 3 The diagram of total within-cluster variance sum (Vartotal) 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 Vartotal with K increasing from i to i+1, which is noted as Vartotal(i)*. The number within the bracket represents the difference between Vartotal(i+1)* and Vartotal(i)*, which is noted as Vartotal(i+1)#. The red point represents the optimal cluster number K, which is the elbow inflection point of the curve with the minimum Vartotal(K=3)#.

The characteristics of three rainfall types were distinct from each other (Figure 4). The average values of P, AP, MPI, T, RMPI and PCI were 56.94 mm, 8.09 mm, 30.14 mm/h, 7.93 h, 0.39, and 0.55, respectively for Type 1; 50.19 mm, 2.84 mm, 12.24 mm/h, 21.06 h, 0.46, and 0.27, respectively for Type 2; 115.68 mm, 2.32 mm, 12.43 mm/h, 54.04 h, 0.49, and 0.10, respectively for Type 3. 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 relatively uniform hourly distribution. The characteristics of Type 2 laid between those of Type 1 and Type 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.

As for the flash floods induced by the three rainfall types, flash flood behavior indices were closely related with rainfall characteristic indices (Figure S1) and varied greatly among type to type (Figure 5). Specifically, Km showed significant correlations with RMPI and PCI for Type 1, with P for Type 2, and with P, AP and MPI for Type 3 (|r|≥0.50, p<0.05). Tm showed significant correlation with RMPI for Type 1 (r≥0.50, p<0.05). Tl showed significant correlation with MPI for Type 1 (r≤-0.50, p<0.05). RQ showed significant correlations with MPI for Type 1, with AP for Type 2, and with AP, MPI and PCI for Type 3 (r≥0.50, p<0.05). DQ showed significant correlations with AP and MPI for Type 3 (r≥0.50, p<0.05). K showed significant correlations with P and PCI for Type 1 (|r|≥0.50, p<0.05). The average values of Km, Tm, Tl, RQ, DQ and K were 0.48 m3/(s·km2), 4.99 h, 3.71 h, 41.54 s-1, 13.52 s-1, and 3.37, respectively for Type 1; 0.37 m3/(s·km2), 9.13 h, 5.10 h, 21.76 s-1, 8.64 s-1, and 3.56, respectively for Type 2; 0.71 m3/(s·km2), 15.26 h, 5.44 h, 5.15 s-1, 2.82 s-1, and 3.23, respectively for Type 3. The flash floods induced by Type 1 were characterized by small peak flow magnitude, early peak flow occurrence time, short lag time, rapid flood rising and declining rates, and thin flood hydrographs. The flash flood processes induced by Type 3 were characterized by great peak flow magnitude, late peak flow occurrence time, long lag time, slow flood rising and declining rates, and fat flood hydrographs. Similarly, the characteristics of Type 2 laid between those of Type 1 and Type 3.
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; Ymax and Ymin 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.

4.2 Flash flood process simulation evaluation

The evaluation indices for flash flood simulations at event scale were shown in Table 3. As for XAJ, RER varied between -20.64% and 50.27% with an average absolute value of 6.89% in calibration period, and varied between -42.37% and 19.56% with an average absolute value of 10.62% in validation period. NSE varied between -0.22 and 0.97 with an average value of 0.78 in calibration period, and varied between 0.03 and 0.97 with an average value of 0.72 in validation period. As for CNFF, RER varied between -29.80% and 24.10% with an average absolute value of 7.58% in calibration period, and varied between -33.90% and 49.20% with an average absolute value of 18.58% in validation period. NSE varied between 0.44 and 0.98 with an average value of 0.87 in calibration period, and varied between 0.20 and 0.96 with an average value of 0.70 in validation period. Overall, model performances were consistent for XAJ and CNFF, both of which could well simulate water balances and flood hydrographs in the study area.
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
The cumulative frequency distribution of absolute RER and NSE for three rainfall types is displayed in Figure 6, and the simulated and observed flash flood processes are displayed in Figure 7. XAJ and CNFF provided similar simulation performances for three rainfall types on water balances as well as flood hydrographs. For water balances, absolute RERs for most Type 1 events were greater than those for Type 2 and Type 3 events, and the average absolute RERs for both Type 2 and Type 3 were within 8.00% for XAJ and within 11.00% for CNFF (Table 3). Thus, the two models can better simulate water balances for Type 2 and Type 3 events than those for Type 1 events. For flood hydrographs, NSEs for Type 3 events were overall greater than those for Type 1 and Type 2 events, and hence both models could well capture flood hydrograph variations for Type 3 events with the average NSE reaching 0.85. Comparably, the agreement between observed and simulated hydrographs was the worst obtained by XAJ for Type 2 events (NSE=0.71) and by CNFF for Type 1 events (NSE=0.76), respectively. In addition, it was noted that CNFF generally over-estimated the flood recession rates of Type 1 events (e.g. events 19940503 and 20080524 in Figure 7), suggesting that CNFF was insufficient in reproducing the declining limb shape for quick-developing flood hydrographs.
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

4.3 Flash flood behavior simulation evaluation

Both XAJ and CNFF reasonably reproduced the flash flood behaviors of 107 events in study area, with most of the observed and simulated behavior indices fitting the 1:1 line well (Figure 8). Table 4 listed the evaluation indices for flash flood behavior simulation.
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
For all flash flood behavior indices, the average RMSEr and r ranged from 0.29 (Type 3) to 0.38 (Type 2) and from 0.67 (Type 1) to 0.90 (Type 3), respectively for XAJ, and ranged from 0.24 (Type 3) to 0.31 (Type 1 and Type 2) and from 0.68 (Type 1) to 0.95 (Type 3), respectively for CNFF. The model performances of XAJ and CNFF shared a similarity in simulating flood behaviors for three rainfall types. All flash flood behavior indices for Type 3 were the best simulated with the smallest deviation and strongest linear correlation, while those for Type 1 were simulated with the weakest linear correlation and those for Type 2 were simulated with the greatest deviation.
For flood peak indices, the average RMSEr and r ranged from 0.26 (Type 1) to 0.28 (Type 2 and Type 3) and from 0.85 (Type 1) to 0.90 (Type 2 and Type 3), respectively for XAJ, and ranged from 0.20 (Type 2 and Type 3) to 0.23 (Type 1) and from 0.85 (Type 1) to 0.95 (Type 2 and Type 3), respectively for CNFF. As for XAJ, flood peak indices for Type 1 were simulated with smaller deviation but weaker linear correlation than those for Type 2 and Type 3. As for CNFF, flood peak indices for Type 2 and Type 3 were simulated with smaller deviation and stronger linear correlation than those for Type 1. Therefore, XAJ competitively simulated flood peak indices induced by three rainfall types, and CNFF better simulated those induced by Type 2 and Type 3.
Compared with flood peak indices, the simulation performances of both XAJ and CNFF declined for flood dynamics indices (Figure 8). The average RMSEr and r of flood dynamics indices ranged from 0.30 (Type 3) to 0.47(Type 2) and from 0.49 (Type 1) to 0.90 (Type 3), respectively for XAJ, and ranged from 0.28 (Type 3) to 0.42 (Type 2) and from 0.52 (Type 1) to 0.94 (Type 3), respectively for CNFF. XAJ and CNFF also shared a similar performance pattern for three rainfall types in terms of flood dynamics behavior simulation like the simulation for all flood behaviors. Flood dynamics indices for Type 3 were the best simulated with the smallest deviation and the strongest linear correlation, while those for Type 1 were simulated with the weakest linear correlation and those for Type 2 were simulated with the greatest deviation.

5 Discussion

Rainfall temporal characteristics play a dominant role in runoff generation and concentration processes. It is of considerable interest for regional flash flood management to identify flash flood behavior characteristics and evaluate model simulation capability with respect to different rainfall temporal patterns. This study proposes a rainfall temporal pattern identification method taking the magnitude, intensity, time, and concentration features of rainfall processes all into account, which not only is operable and feasible for practical implementation and is generalizable for catchments with massive rainfall-flood events, but also thoroughly considers rainfall characteristics probably affecting flood behaviors.
The defined 107 rainfall events in Anhe catchment were identified into three typical rainfall types (Type 1, Type 2, and Type 3), and the temporal variability of rainfall types and inducing flash flood behaviors shared great consistency. Type 1 rainfall events, which mainly occur in May (nearly 40% of rainfall events), are mainly generated in convective rainfall weather systems (Zhang et al., 2011). Although the total rainfall amount is small, Type 1 rainfall events with short duration, heavy intensity, and concentrated hourly distribution tend to induce flash floods with rapid flood rising and declining rates as well as thin flood hydrographs. These conspicuous flash flood behavior characteristics imply that Type 1 rainfall-flood events are of strong instantaneous destructive power and pose great challenges for flash flood warning and forecasting, which may result in poor timeliness of flood warning information, insufficient time to coordinate flood response measures, and damages to human lives and properties (Ruiz-Villanueva et al., 2012; Archer and Fowler, 2018). Type 3 rainfall events, which occur throughout the year, are mainly generated in frontal rainfall weather systems (Zhang and Hall, 2004). Although the rainfall intensity is low, this rainfall type with great total amount, long duration and relatively uniform hourly distribution generally induces flash floods with great peak magnitude and runoff volume, which is likely to cause inundation risks to riparian villages. The inducing weather systems of Type 2 are the couple of those of Type 1 and Type 3, rather than a single dominant weather system type. The temporal characteristics of both rainfall events and corresponding flash floods for Type 2 lie between those of Type 1 and Type 3, as well as the hazard and destructiveness of flood events. Therefore, flood management strategies should be formulated considering rainfall processes with different temporal structures to implement timely and effective flash flood disaster prevention actions.
XAJ and CNFF both well reproduce the hourly variability of flood process in the study area and provide similar simulation performances for three rainfall types. Comparably, Type 3 events are the best simulated for both flood processes and flood behaviors, while Type 1 and Type 2 events are simulated less satisfactorily. The simulation differences reveal that both XAJ and CNFF show superiority in capturing variations of flood process induced by rainfall with long duration and relatively uniform hourly distribution, while they are still insufficient for floods induced by rainfall with short duration and concentrated hourly distribution. In mountainous catchments, rainfall with high intensity that exceeds infiltration capacity of soil can cause overland flow even though soil moistures are not saturated (Uhlenbrook and Leibundgut, 2002; Berghuijs et al., 2016), which is referred to as the excess infiltration runoff generation. As for Type 1 characterized by relatively high intensity and concentration, the existence of excess infiltration runoff mechanism, which is inconsistent with the underlying theories of XAJ and CNFF, might result in the discrepancy between calculated and actual runoff yielding (Zhai et al., 2021b), and subsequently affect model capability for reproducing flood hydrograph variability (e.g., flood hydrograph kurtosis). Besides, Type 1 and Type 2 events are both of short durations and great variations in temporal distributions, and the hourly rainfall observations are deficient in describing the temporal rainfall variability in detail (Bonaccorso et al., 2020). It may be inferred that lack of precise rainfall forcing may also be the key factor restricting the simulation performances of two models for quick flood responses induced by Type 1 and Type 2. In order to further improve model simulation capability especially for Type 1 and Type 2, accurate rainfall forcing in both space and time should be collected to well depict the magnitude, intensity, time, and temporal distribution of rainfall processes, and runoff generation modules of both XAJ and CNFF should be improved to well capture variations of thin flood hydrographs generated under rainfall events with high intensity and concentration. Model parameters might be optimized for various rainfall temporal patterns to further improve flash flood simulation accuracy. Furthermore, it is remarkable that CNFF outperforms XAJ in simulating flood hydrographs for Type 2 and Type 3, as well as most flood behaviors for three rainfall types. This phenomenon can be ascribed to the use of modified distributed unit hydrograph method for runoff concentration calculation in CNFF, which has advantages in portraying the nonlinear characteristics of runoff confluence processes in mountainous catchments. However, CNFF needs to be improved to better obtain water balances induced by rainfall with different temporal variability, and reproduce overall flood hydrographs induced by short-duration heavy rainfall. Moreover, more events should be collected from various mountainous catchments with diverse rainfall characteristics in further studies to validate the flash flood simulation capability with respect to rainfall temporal variability.

6 Conclusions

In this study, the multivariate statistical analysis and hydrological simulations were combined to identify typical rainfall types and simulate flash flood processes from perspective of rainfall characteristic indices and flash flood behavior indices. The results showed that:
(1) Three typical rainfall types were identified from 107 rainfall events. 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 relatively uniform hourly distribution. The characteristics of Type 2 laid between those of Type 1 and Type 3.
(2) Both XAJ and CNFF showed satisfactory performances in simulating flash flood processes with average absolute RER within 19% and average NSE over 0.70 in both calibration and validation periods. Water balances and flood hydrographs were better reproduced by both models for Type 3 with average absolute RER within 11.00% and average NSE reaching 0.85.
(3) Both XAJ and CNFF reasonably reproduced most flash flood behavior indices for three rainfall types with average RMSEr within 0.40 and average r over 0.67. All the indices and flood dynamics indices were the best simulated by both models for Type 3 with average RMSEr within 0.30 and average r over 0.90. The flood peak indices were competitively simulated for all the three rainfall types by XAJ and except Type 1 by CNFF.
Evaluating flash flood simulation capability with respect to rainfall temporal variability in a small mountainous catchment
WANG Xuemei1, *ZHAI Xiaoyan1, ZHANG Yongyong2, GUO Liang1
1. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, Research Center on Flood and Drought Disaster Reduction, China Institute of Water Resources and Hydropower Research, Beijing 100038, China;2. Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Science and Natural Resources Research, CAS, Beijing 100101, China

Supplementary figure

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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