Uncertainty Analysis of Multiple Hydrologic Models Using the Bayesian Model Averaging Method

Table 2

Results of BMA(9) and its 9 individual models in the mean prediction and 90% uncertainty interval for the whole flow series.

Objective function	Models	Mean prediction			90% uncertainty interval
		𝑅^2 (%)	DRMS	RE (%)	CR (%)	𝐵 (m^3/s)	𝐷 (m^3/s)
Calibration period
OF2 (MSEST)	XAJ	85.45	34.89	30.24	17.89	29.43	21.46
	SMAR	84.61	35.89	6.96	31.67	36.51	19.30
	SIM	80.73	40.17	31.51	15.39	28.47	22.67
OF3 (MSESRT)	XAJ	89.78	29.25	10.44	68.06	33.37	11.75
	SMAR	80.25	40.66	10.13	44.17	35.37	17.39
	SIM	72.42	48.05	−5.82	47.72	42.57	21.26
OF4 (MSELT)	XAJ	79.99	40.93	12.39	63.94	33.92	14.75
	SMAR	58.01	59.29	−9.22	42.28	43.45	28.32
	SIM	52.71	62.92	−41.07	38.89	55.51	26.93
BMA(9)		90.49	28.22	21.40	91.11	70.98	14.54
Validation period
OF2 (MSEST)	XAJ	82.70	32.21	31.92	14.79	21.56	18.20
	SMAR	80.05	34.59	0.66	30.23	29.52	16.64
	SIM	69.81	42.56	39.48	20.84	24.43	22.32
OF3 (MSESRT)	XAJ	88.52	26.25	4.54	68.56	26.95	9.62
	SMAR	78.26	36.11	7.48	44.56	27.59	14.53
	SIM	71.09	41.64	8.98	53.86	27.69	16.47
OF4 (MSELT)	XAJ	77.25	36.94	8.74	63.07	26.68	11.85
	SMAR	43.43	58.25	−18.79	35.53	35.76	27.36
	SIM	72.27	40.79	−21.69	34.05	36.22	18.96
BMA(9)		84.54	30.46	25.42	90.23	55.91	13.20

Note: bolded values represent the best results.