Flood Hydrograph Coincidence Analysis of the Upper Yangtze River and Dongting Lake, China

doi:10.21203/rs.3.rs-277815/v1

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Research Article

Flood Hydrograph Coincidence Analysis of the Upper Yangtze River and Dongting Lake, China

https://doi.org/10.21203/rs.3.rs-277815/v1

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Journal Publication

published 05 Sep, 2021

Read the published version in Natural Hazards →

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In hydrological research, flood events can be analyzed by flood hydrograph coincidence. Existing flood hydrograph coincidence research mostly focuses on the analysis of the coincidence risk probability of the annual maximum flood event using the 15-day maximum annual flood volume; the actual duration of the flood hydrograph is neglected. The duration of the flood hydrograph is a key variable in (1) determining whether flood hydrograph coincidence occurs, and (2) accurately calculating the flood hydrograph coincidence risk probability. This paper creatively proposes a novel method to analyze the flood hydrograph coincidence risk probability by establishing a five-dimensional joint distribution of flood volumes, durations and interval time for two hydrologic stations. More specifically, using the annual maximum flood of the upper Yangtze River and input from Dongting Lake as an example, the Pearson Type III and the mixed von Mises distributions were used to establish the marginal distribution of flood volumes, flood duration and interval time. Subsequently, the five-dimensional joint distribution based on vine copula was established to analyze the flood hydrograph coincidence risk probability. The results were verified by comparison with a historical flood sequence. The flood hydrograph coincidence volume-risk probability curve was also obtained, providing theoretical support for flood control safety and risk management in the middle and lower Yangtze River. This study also demonstrates the significant beneficial role of regulation by the Three Gorges Water Conservancy Project in mitigating flood risk of the Yangtze River.

Environmental Engineering

Environmental Policy

Flood hydrograph coincidence

Hydrological extremes

Joint distribution

Vine copula

Risk probability

Yangtze River Basin

Table 1

The P-III distribution parameter estimation results and the distribution fitting test results for AMF volumes

Station	Period				χ² test	K-S test
Yingchang Station	Period 1	5.67	2.07	1.37	2.070(5.991)	0.004(0.189)
Yingchang Station	Period 2	5.28	2.41	1.10	0.158(5.991)	0.009(0.349)
Chenglingji Station	Period 1	2.78	1.84	0.76	0.419(5.991)	0.004(0.189)
Chenglingji Station	Period 2	3.25	3.08	0.53	1.082(5.991)	0.028(0.349)
Notes: The critical values are in parentheses.

Table 2

The mixed von Mises distributions parameter estimation results and the distribution fitting test results for AMF durations and interval times

Variable	Station	Period				χ² test	K-S test
AMF duration	Yichang Station	Period 1	0.29	1.80	16.74	4.063(12.592)	0.023(0.189)
		Period 1	0.71	2.72	2.51	4.063(12.592)	0.023(0.189)
		Period 2	0.25	1.21	37.97	0.214(5.991)	0.011(0.349)
		Period 2	0.75	2.36	2.61	0.214(5.991)	0.011(0.349)
	Chenglingji Station	Period 1	0.40	0.78	16.29	3.791(9.488)	0.016(0.189)
			0.51	2.09	2.13
			0.09	5.21	30.99
		Period 2	0.28	0.37	700.87	1.345(3.841)	0.040(0.349)
			0.51	1.60	8.43
			0.21	2.58	26.44
AMF interval time	Between the two stations	Period 1	0.45	2.60	9.39	0.449(7.815)	0.005(0.189)
		Period 1	0.55	3.52	1.68	0.449(7.815)	0.005(0.189)
		Period 2	1	3.35	1.35	0.002(9.488)	0.015(0.349)
Notes: The critical values are in parentheses.

Table 3

Vine copula structures of the five-dimensional joint distributions of AMF hydrograph coincidence for the two studied periods

	Period 1 (R-Vine)			Period 2 (R-Vine）
	Variable	Copula function	Parameter	Variable	Copula function	Parameter
Tree1	T_d, d₂	Independence		T_d, d₂	Gaussian	par = −0.44
	d₂, d₁	Tawn type 2	par 1= 20.00 par 2= 0.08	d₂, V₂	Tawn type 1	par 1= 20.00 par 2= 0.31
	d₁, V₁	Frank	par = 6.20	d₂, V₁	Clayton	par = 0.80
	d₂, V₂	Joe–Frank	par 1 = 3.60 par 2 = 0.93	V₁, d₁	Survival Clayton	par = 2.04
Tree2	T_d, d₁; d₂	Independence		T_d, V₂; d₂	Rotated Tawn type 1 180 degrees	par 1 = 20.00 par 2 = 0.20
	d₂, V₁; d₁	Independence		T_d, V₁; d₂	Independence
	d₁, V₂; d₂	Rotated Tawn type 1 90 degrees	par 1 = −3.86 par 2 = 0.10	d₂, d₁; V₁	Tawn type 2	par 1 = 20.00 par 2 = 0.31
Tree3	T_d, V₁; d₂, d₁	Rotated Tawn type 1 90 degrees	par 1 = −6.68 par 2 = 0.11	V₂, V₁; T_d, d₂	Rotated Tawn type 1 90 degrees	par 1 = −3.21 par 2 = 0.42
Tree3	V₁, V₂; d₁, d₂	Student t	par 1 = 0.39 par 2 = 2.96	T_d, d₁; d₂, V₁	Independence
Tree4	T_d, V₂; V₁, d₁, d₂	Tawn type 2	par 1 = 20.00 par 2 = 0.01	V₂, d₁; T_d, d₂, V₁	Rotated Tawn type 1 90 degrees	par 1 = −2.70 par 2 = 0.58

Table 4

AMF hydrograph coincidence risk probability for different return period combinations

Risk probability		Station	Yichang
station	R₀₂	Period\R₀₁	1000	500	100	50	10	5
Chenglingji	1000	Period 1	3.00 × 10⁻⁵	3.00 × 10⁻⁵	4.00 × 10⁻⁵	6.00 × 10⁻⁵	1.10 × 10⁻⁴	1.70 × 10⁻⁴
	1000	Period 2	<1.00 × 10⁻⁵	<1.00 × 10⁻⁵	<1.00 × 10⁻⁵	<1.00 × 10⁻⁵	3.00 × 10⁻⁵	7.00 × 10⁻⁵
	500	Period 1	3.00 × 10⁻⁵	4.00 × 10⁻⁵	8.00 × 10⁻⁵	1.40 × 10⁻⁴	2.00 × 10⁻⁴	2.90 × 10⁻⁴
	500	Period 2	<1.00 × 10⁻⁵	<1.00 × 10⁻⁵	<1.00 × 10⁻⁵	<1.00 × 10⁻⁵	5.00 × 10⁻⁵	1.10 × 10⁻⁴
	100	Period 1	7.00 × 10⁻⁵	1.00 × 10⁻⁴	2.70 × 10⁻⁴	4.50 × 10⁻⁴	1.05 × 10⁻³	1.59 × 10⁻³
	100	Period 2	<1.00 × 10⁻⁵	<1.00 × 10⁻⁵	2.00 × 10⁻⁵	4.00 × 10⁻⁵	2.60 × 10⁻⁴	4.60 × 10⁻⁴
	50	Period 1	7.00 × 10⁻⁵	1.00 × 10⁻⁴	3.50 × 10⁻⁴	5.80 × 10⁻⁴	1.75 × 10⁻³	2.73 × 10⁻³
	50	Period 2	<1.00 × 10⁻⁵	<1.00 × 10⁻⁵	5.00 × 10⁻⁵	7.00 × 10⁻⁵	4.80 × 10⁻⁴	8.50 × 10⁻⁴
	10	Period 1	1.10 × 10⁻⁴	1.70 × 10⁻⁴	7.50 × 10⁻⁴	1.31 × 10⁻³	5.26 × 10⁻³	9.35 × 10⁻³
	10	Period 2	3.00 × 10⁻⁵	5.00 × 10⁻⁵	2.70 × 10⁻⁴	3.80 × 10⁻⁴	1.81 × 10⁻³	3.36 × 10⁻³
	5	Period 1	1.20 × 10⁻⁴	2.20 × 10⁻⁴	1.11 × 10⁻³	1.89 × 10⁻³	7.68 × 10⁻³	1.41 × 10⁻²
	5	Period 2	7.00 × 10⁻⁵	1.10 × 10⁻⁴	4.30 × 10⁻⁴	7.00 × 10⁻⁴	3.17 × 10⁻³	5.70 × 10⁻³

Table 5

AMF hydrograph coincidence volumes for different return period combinations

Volume (m³)		Station	Yichang
Station	R₀₂	Period\R₀₁	1000	500	100	50	10	5
Chenglingji	1000	Period 1	1.57 × 10¹¹	1.52 × 10¹¹	1.41 × 10¹¹	1.36 × 10¹¹	1.23 × 10¹¹	1.16 × 10¹¹
	1000	Period 2	1.18 × 10¹¹	1.14 × 10¹¹	1.04 × 10¹¹	9.98 × 10¹⁰	8.89 × 10¹⁰	8.35 × 10¹⁰
	500	Period 1	1.52 × 10¹¹	1.48 × 10¹¹	1.36 × 10¹¹	1.31 × 10¹¹	1.18 × 10¹¹	1.12 × 10¹¹
	500	Period 2	1.15 × 10¹¹	1.11 × 10¹¹	1.01 × 10¹¹	9.71 × 10¹⁰	8.62 × 10¹⁰	8.08 × 10¹⁰
	100	Period 1	1.42 × 10¹¹	1.37 × 10¹¹	1.26 × 10¹¹	1.21 × 10¹¹	1.08 × 10¹¹	1.01 × 10¹¹
	100	Period 2	1.08 × 10¹¹	1.04 × 10¹¹	9.48 × 10¹⁰	9.05 × 10¹⁰	7.96 × 10¹⁰	7.42 × 10¹⁰
	50	Period 1	1.37 × 10¹¹	1.32 × 10¹¹	1.21 × 10¹¹	1.16 × 10¹¹	1.03 × 10¹¹	9.64 × 10¹⁰
	50	Period 2	1.05 × 10¹¹	1.01 × 10¹¹	9.18 × 10¹⁰	8.75 × 10¹⁰	7.66 × 10¹⁰	7.12 × 10¹⁰
	10	Period 1	1.25 × 10¹¹	1.21 × 10¹¹	1.09 × 10¹¹	1.04 × 10¹¹	9.13 × 10¹⁰	8.48 × 10¹⁰
	10	Period 2	9.80 × 10¹⁰	9.40 × 10¹⁰	8.45 × 10¹⁰	8.02 × 10¹⁰	6.93 × 10¹⁰	6.39 × 10¹⁰
	5	Period 1	1.20 × 10¹¹	1.15 × 10¹¹	1.04 × 10¹¹	9.88 × 10¹⁰	8.58 × 10¹⁰	7.93 × 10¹⁰
	5	Period 2	9.46 × 10¹⁰	9.06 × 10¹⁰	8.11 × 10¹⁰	7.68 × 10¹⁰	6.59 × 10¹⁰	6.05 × 10¹⁰

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Journal Publication

published 05 Sep, 2021

Read the published version in Natural Hazards →

Editorial decision: Minor revisions
27 Jun, 2021
Reviews received at journal
01 Mar, 2021
Editor assigned by journal
28 Feb, 2021
Reviewers invited by journal
28 Feb, 2021
First submitted to journal
25 Feb, 2021

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Flood Hydrograph Coincidence Analysis of the Upper Yangtze River and Dongting Lake, China

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