Improving long-range hydrological forecasts with extended Kalman filters

Figures & data

Fig. 1 Location map of the study areas.

Table 1  Basic descriptive statistics of the data sets used in modelling: all data (January 1960–December 2006), training data (January 1960–December 1993), and test data (January 1994–December 2006) for both streamflow and lake water-level data series, respectively, for the Athabasca River, at Hinton (07AD002), Alberta (Canada) and for Lake Ontario, at Toronto (02HC048), Ontario (Canada)

Hydrological variable	Data partition	Count	Minimum	Maximum	Range	Mean	SD	Skewness
Streamflow	All data	564	48	2130	2082	423	378	1.33
	Training	408	57	2130	2073	433	385	1.36
	Testing	156	48	1560	1512	395	357	1.19
Lake water level	All data	564	73.83	75.74	1.91	74.81	0.29	0.11
	Training	408	73.83	75.74	1.91	74.81	0.31	0.10
	Testing	156	74.29	75.43	1.14	74.80	0.25	0.16
SD: standard deviation.

Table 2  Comparative model performance statistics between the MLP and the RMLP models for forecasting streamflows and lake water levels, respectively, for Athabasca River, at Hinton (07AD002), Alberta (Canada) and for Lake Ontario, at Toronto (02HC048), Ontario (Canada). The testing is based on the test period January 1994–December 2006

Forecast lead (month)	MLP				RMLP
	Bias (%)	RMSE	r	SS (%)	Bias (%)	RMSE	r	SS (%)	SSfor (%)
Streamflow:
1	3.22	169	0.88	77	−0.88	150	0.91	82	21
2	6.43	208	0.82	66	−0.38	174	0.87	76	30
3	0.15	209	0.81	65	−1.45	182	0.86	74	24
4	11.34	220	0.80	62	−0.08	178	0.87	75	35
5	4.79	217	0.80	63	−1.09	181	0.86	74	31
6	13.46	219	0.80	62	0.67	183	0.86	74	30
7	11.41	214	0.81	64	−0.11	183	0.86	74	27
8	10.05	213	0.81	64	−1.11	177	0.87	75	31
9	11.04	210	0.82	65	1.46	179	0.87	75	28
10	12.12	215	0.81	64	1.29	179	0.87	75	31
11	11.58	212	0.81	65	−0.34	178	0.87	75	29
12	14.72	210	0.83	65	−1.96	179	0.87	75	27
Lake water level:
1	0.00	0.11	0.90	81	0.01	0.08	0.95	90	47
2	0.01	0.15	0.80	63	0.04	0.13	0.87	74	25
3	0.01	0.16	0.77	58	0.05	0.15	0.81	63	12
4	0.02	0.18	0.73	51	0.06	0.16	0.79	59	21
5	0.01	0.19	0.68	45	0.07	0.18	0.74	50	10
6	0.03	0.19	0.68	44	0.08	0.18	0.74	49	10
7	0.02	0.19	0.66	40	0.09	0.18	0.74	47	10
8	0.04	0.20	0.65	39	0.08	0.18	0.74	49	19
9	0.03	0.20	0.65	39	0.08	0.18	0.73	48	19
10	0.02	0.20	0.62	36	0.07	0.18	0.73	47	19
11	0.04	0.20	0.63	34	0.07	0.18	0.73	48	19
12	0.02	0.19	0.66	40	0.06	0.18	0.74	50	10

Fig. 2 Observed and simulated 8-month ahead streamflow forecasting using the MLP and the RMLP models for the test period (January 1994–December 2006) for Athabasca River, at Hinton (07AD002), Alberta (Canada).

Fig. 3 Observed and simulated 8-month ahead lake water level forecasting using the MLP and the RMLP models for the test period (January 1994–December 2006) for Lake Ontario, at Toronto (02HC048), Ontario (Canada).