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Table 5

Results of three Copula functions with the constant (A3) parameters and the time-varying (A4) parameters for modeling the dependence between two annual maximum streamflow series

Scenario	Copula	Parameter	K–S statistic indicator^a		AIC value
Scenario	Copula	Parameter	Variable X₁	Variable X₂	Variable X₁	Variable X₂
A3	GH	2.70	0.127	0.131	43	55
	Frank	7.85	0.144	0.157	57	67
	Clayton	3.46	0.172	0.175	71	80
A4	GH	exp(−414+0.56P_h−0.73RI_h)	0.119	0.122	33	39
	Frank	exp(−320+0.18P_h−1.45RI_h)	0.149	0.154	35	49
	Clayton	exp(−257+0.47P_h−0.69RI_h)	0.173	0.171	53	67

Scenario	Copula	Parameter	K–S statistic indicator^a		AIC value
Scenario	Copula	Parameter	Variable X₁	Variable X₂	Variable X₁	Variable X₂
A3	GH	2.70	0.127	0.131	43	55
	Frank	7.85	0.144	0.157	57	67
	Clayton	3.46	0.172	0.175	71	80
A4	GH	exp(−414+0.56P_h−0.73RI_h)	0.119	0.122	33	39
	Frank	exp(−320+0.18P_h−1.45RI_h)	0.149	0.154	35	49
	Clayton	exp(−257+0.47P_h−0.69RI_h)	0.173	0.171	53	67

^aThe K–S test is performed at a significance level of 0.05. The null hypothesis states that the empirical distribution fits the theoretical distribution. If the value of the K–S test indicator is smaller than the value of D(65, 0.05) ⁠, the null hypothesis would not be rejected. The variables X₁ and X₂ are the probability integral transformations for streamflow series Q_a and Q_h at Ankang and Huangzhuang stations, respectively.

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