Joint Modeling of Precipitation and Temperature Using Copula Theory for Current and Future Prediction under Climate Change Scenarios in Arid Lands (Case Study, Kerman Province, Iran)

Table 9

Selection criteria of the best fit of copula functions for historical and future periods.

	Copula functions	Parametric					Nonparametric
		AIC	BIC	NRMSE	NSE	Parameter	AIC	BIC	NRMSE	NSE	Parameter
Historical	Gaussian	−17.1	−15.3	0.039	0.93	−0.589	−17	−15.2	0.038	0.91	−0.597
	Frank	−18.8	−17.7	0.038	0.94	−4.84	−18.8	−17	0.037	0.93	−4.613
	Rotated Clayton	−10.6	−8.87	0.041	0.92	−0.918	−7.37	−5.57	0.043	0.90	−1.518
	Rotated Gumbel	−14.9	−13.1	0.039	0.93	−1.61	−14.3	−12.5	0.038	0.91	−1.759
	Rotated Joe	−10.5	−8.73	0.043	0.92	−1.74	−5.95	−4.41	0.045	0.89	−2.395
RCP2.6	Gaussian	−41.3	−40.1	0.032	0.96	−0.602	−41.2	−39.2	0.035	0.94	−0.578
	Frank	−44.6	−42.3	0.027	0.97	−3.99	−44.5	−42.2	0.032	0.95	−4.06
	Rotated Clayton	−32.5	−30.1	0.043	0.95	−0.992	−21.5	−19.8	0.048	0.91	−1.29
	Rotated Gumbel	−37.9	−35.4	0.044	0.95	−1.56	−36.8	−33.1	.0.05	0.90	−1.64
	Rotated Joe	−26.9	−23.1	0.069	0.92	1.674	−17.7	−15.6	0.078	0.91	−2.18
RCP4.5	Gaussian	−17.7	−15.3	0.020	0.9	−0.524	−17.2	−16.8	0.022	0.9	−0.517
	Frank	−16.1	−14.8	0.022	0.97	−3.40	−16.4	−15.2	0.024	0.95	−3.45
	Rotated Clayton	−10.6	−10.6	0.028	0.96	−0.851	−10.4	−7.53	0.032	0.94	−1.057
	Rotated Gumbel	−14.3	−14.4	0.021	0.97	−1.46	−14.7	−13	0.031	0.92	−1.52
	Rotated Joe	−9.95	−8.15	0.032	0.95	−1.54	−9.98	−6.55	0.038	0.91	−1.95
RCP8.5	Gaussian	−19	−18.1	0.023	0.95	−0.463	−19	−17.8	0.024	0.94	−0.469
	Frank	−15.2	−13.2	0.024	0.94	−2.8	−14.9	−12.3	0.024	0.92	−3.04
	Rotated Clayton	−14.1	−11.1	0.025	0.91	−0.548	−9.64	−8.12	0.025	0.9	−0.903
	Rotated Gumbel	−16.2	−14.3	0.026	0.93	−1.39	−15.9	−13.5	0.027	0.91	−1.45
	Rotated Joe	−11.7	−9.8	0.031	0.87	−1.53	−9.32	−8.5	0.032	0.84	−1.81