Climate change impact assessment on mild and extreme drought events using copulas over Ankara, Turkey

Table 3 The best univariate distribution and copula function that has been selected based on the comparison of chi-squared and RMSE values between theoretical and empirical cumulative probabilities. Ave. Sev., average severity; l, location; s, scale; ml, meanlog; sl, sdlog; sh, shape; r, rate; m, mean; sd, standard deviation; P, parameter

Time period	Dataset	Univariate			Bivariate
Time period	Dataset	Distribution	Parameter	Chi-squared	Copula (P)	RMSE
Reference	Duration	Logistic	l = 17.372; s = 4.671	0.295	Normal (0.47)	0.031
Reference	Ave. Sev.	Logistic	l = 0.886; s = 0.114	0.373	Normal (0.47)	0.031
HadGEM 4.5	Duration	Lognormal	ml = 2.881; sl = 0.669	0.165	Frank (1.93)	0.036
HadGEM 4.5	Ave. Sev.	Logistic	l = 0.799; s = 0.14	0.195	Frank (1.93)	0.036
HadGEM 8.5	Duration	Logistic	l = 15.326; s = 3.156	0.076	Frank (0.18)	0.039
HadGEM 8.5	Ave. Sev.	Gamma	sh = 9.429; r = 10.642	0.056	Frank (0.18)	0.039
MPI 4.5	Duration	Gamma	sh = 3.385; r = 0.193	0.087	Frank (2.95)	0.024
MPI 4.5	Ave. Sev.	Gamma	sh = 8.878; r = 9.825	0.127	Frank (2.95)	0.024
MPI 8.5	Duration	Normal	mean = 15.935; sd = 7.23	0.338	Frank (0.15)	0.03
MPI 8.5	Ave. Sev.	Logistic	l = 0.918; s = 0.168	0.152	Frank (0.15)	0.03
GFDL 4.5	Duration	Gamma	sh = 5.633; rate = 0.288	0.184	Frank (2.93)	0.031
GFDL 4.5	Ave. Sev.	Lognormal	ml = −0.115; sl = 0.271	0.065	Frank (2.93)	0.031
GFDL 8.5	Duration	Gamma	sh = 3.459; r = 0.217	0.074	Normal (0.47)	0.032
GFDL 8.5	Ave. Sev.	Lognormal	ml = −0.152; sl = 0.292	0.123	Normal (0.47)	0.032