多种机器学习模型对不同洪水类型特征指标模拟效果评估

doi:10.18306/dlkxjz.2022.07.008

Abstract

Abstract:

The characteristic indicators of flood process include not only flood magnitude, but also flood duration, dynamics, and so on. The existing models and methods focus on the simulation of flood magnitude indicators, but the simulation of other indicators remains insufficient. In this study, four machine learning models — multiple linear regression, multi-layer perceptron, random forest, and support vector machine — were used to simulate seven characteristic indicators — total flood volume, peak flow, flood duration, time deviation of flood peak, proportion of high flow duration, flood rise and fall rates — of 59 rainfall-flood events in the Changtaiguan Basin in the upper reaches of the Huaihe River. The simulation performance of the models for different flood types and characteristic indicators were evaluated. The results show that: 1) The flood process in the Changtaiguan Basin can be divided into three categories. The first category is characterized by moderate flood volume, long duration, and earlier peak time (16 fields); the second type has low flood volume, short and fat shape, and the flood peak appears later (34 fields); the third type has large flood volume, sharp and thin shape, and flood rises and falls rapidly (9 fields). 2) Time indicator simulation performed the best and dynamic indicator simulation performed the worst; the performance of multiple linear regression and random forest simulation increased with the increase of all characteristic indicator values. The simulation performance of support vector machine decreased with the increase of flood duration, and increased with the increase of value of the remaining characteristic indicators. The simulation performance of multi-layer perceptron increased with the increase of value of four indicators, namely, total flood volume, peak flow, proportion of high flow duration, and flood rise rate. 3) With regard to the simulation accuracy of characteristic indicators of various types of floods, the four models performed the best for the simulation of the third type of floods, but the worst for the second type; random forest showed the best simulation performance for the first and third types of floods, and support vector machine showed better simulation performance for the second type of floods. 4) According to the comprehensive simulation accuracy, the support vector machine model performed the best, followed by random forest, multi-layer perceptron, and multiple linear regression. Relative errors for the calibration and validation periods were 23% and 98%, 21% and 109%, 37% and 75%, and 41% and 102%, respectively. The study results may provide some references for flood type simulation and countermeasures in the Huaihe River Basin.

Key words: flood process, characteristic indicators, machine learning, model comparison, Huaihe River Basin

ZHANG Fan, ZHANG Yongyong, CHEN Junxu, ZHAI Xiaoyan, HU Qingfang. Performance of multiple machine learning model simulation of process characteristic indicators of different flood types[J].PROGRESS IN GEOGRAPHY, 2022, 41(7): 1239-1250.

Figures/Tables 10

Fig.1

Tab.1

Flood process characteristic indicators

类别	指标	简写	单位	计算公式	备注
量级	洪水总量	Flow	mm	$F l o w = ∑ t b e g i n t e n d Q t / A$	反映洪水总量级。 $Q t$ 为某时刻洪水流量,A为流域面积, $t b e g i n$ 、 $t e n d$ 分别表示洪水开始和结束的时刻
量级	洪峰流量	Qpk		$Q p k = m a x Q t / s u m Q t$	反映洪峰量级。除以总流量以消除量纲的影响
时间	洪水历时	Dur	d	$D u r = t e n d - t b e g i n$	反映总时间特征。指标含义同上
时间	洪峰时间偏度	FT		$F T = Q t p k - t b e g i n / D u r$	反映洪峰出现时间。 $Q t p k$ 为洪峰出现时刻
形态	高流量历时占比	HT		$H T = t 75 % / D u r$	反映洪峰形态。 $t 75 %$ 表示大于洪峰流量75%的流量持续时间
动力学	涨洪速率	Inr	m³∙s^-1∙h^-1	$I n r = m a x Q t - Q t b e g i n Q t p k - t b e g i n × 24$	反映洪水过程的变化率。 $Q t b e g i n$ 为洪水开始时刻的流量
动力学	落洪速率	Der	m³∙s^-1∙h^-1	$D e r = m a x Q t - Q t e n d t e n d - Q t p k × 24$	反映洪水过程的变化率。 $Q t e n d$ 为洪水结束时刻的流量

Tab.1

Tab.2

Key precipitation indicators affecting flood process

类别	指标	计算方式	说明
量级	平均雨量	$P a v e = 1 T ∑ i = 1 n α i P i$	反映流域降雨强度。T为降水总历时, $α i$ 为泰森多边形面积权重因子, $P i$ 为第i个雨量站的累积降雨量,n为雨量站的个数
	最大雨强	$P m a x = m a x P m, t$	反映流域降雨强度。 $P m, t$ 为t个时间点的面降雨量
	面降雨量	$P m = ∑ i = 1 n α i P i$	反映流域降雨量级情况。指标含义同上
	峰前雨量	$P r = ∑ t = 1 T m a x P m, t$	反映降水中前期状况。 $T m a x$ 为面降雨量中最大值出现的时间, $P m, t$ 为t个时间点的面降雨量
时间	雨峰系数	$R c = T m a x T$	反映流域降水峰值出现时间。T为降水总历时
	时间变差系数	$T c = 1 n - 1 ∑ i = 1 n K i - 1 2$	反映流域降水在时间上的均匀度。 $K i$ 表示降雨过程中第i个时刻降雨量与该场次暴雨雨强的比值。 $T c$ 越大表示时间上分布越不均匀,反之亦然
	降水集中度	$D c = R x t 2 + R y t 2 P m$ $R x t = ∑ i = 1 n r t, i × s i n θ i$ , $R y t = ∑ i = 1 n r t, i × c o s θ i$	反映流域降水在时间上的集中度。 $P m$ 为研究时间段内的降雨总量; $r t, i$ 为研究时间段内某小时降水量; $θ i$ 表示第i个时间段的方向,即将研究时间段视为一个圆周,按小时时段进行平均分配
空间	雨量极大值比	$σ = P m H m a x$	反映流域降雨空间均匀度。 $P m$ 为面降雨量, $H m a x$ 为点最大雨量。该值越接近于1表示流域降雨越均匀
空间	暴雨相对中心	$C p = ∑ i = 1 n P i d i ∑ i = 1 n P i$	反映流域降雨中心到流域出口的距离。 $d i$ 表示第i个雨量站到流域出口的直线距离
	起始流量		反映流域降雨前期含水情况

Tab.2

Fig.2

Fig.3

Tab.3

Tab.4

Fig.4

Fig.5

Fig.6

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模型	相对误差/%			相关系数			均方根对数误差
模型	率定集	验证集	综合	率定集	验证集	综合	率定集	验证集	综合
多元线性回归	41	102	60	0.90	0.68	0.82	0.14	0.18	0.16
多层感知器	37	75	49	0.91	0.77	0.88	0.11	0.14	0.12
随机森林	21	109	48	0.98	0.75	0.93	0.06	0.17	0.11
支持向量机	23	98	45	0.92	0.67	0.87	0.04	0.16	0.10

评价指标	模型	洪水类型
评价指标	模型	1类	2类	3类
相对误差/%	多元线性回归	37	81	24
	多层感知器	30	64	24
	随机森林	23	69	12
	支持向量机	33	57	18
相关系数	多元线性回归	0.80	0.60	0.87
	多层感知器	0.83	0.74	0.84
	随机森林	0.90	0.74	0.97
	支持向量机	0.76	0.77	0.92
均方根对数误差	多元线性回归	0.10	0.18	0.07
	多层感知器	0.11	0.13	0.10
	随机森林	0.07	0.14	0.03
	支持向量机	0.07	0.12	0.04

Performance of multiple machine learning model simulation of process characteristic indicators of different flood types

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