Time Evolution of Initial Errors in Lorenz’s 05 Chaotic Model

Table 3

Average values over of , calculated from approximations (4)–(7) for all initial conditions and for all prediction time lengths (bold columns), average value over for all prediction time lengths and difference of .

(ND1, (4))	8.3 ± 0.1	−0.1 ± 0.1	8.4 ± 0.3	0.0 ± 0.3	8.1 ± 0.5	−0.3 ± 0.5
(ND1, (5))	9.1 ± 0.4	0.7 ± 0.4	17.0 ± 1.4	8.6 ± 1.4	—	—
(ND1, (6))	8.3 ± 0.1	−0.1 ± 0.1	8.4 ± 0.9	0.0 ± 0.9	8.0 ± 2.1	−0.4 ± 2.1
(ND1, (7))	8.8 ± 0.2	0.4 ± 0.2	12.7 ± 2.4	4.3 ± 2.4	26.8 ± 7.7	18.4 ± 7.7
(ND2, (4))	8.3 ± 0.0	−0.1 ± 0.0	8.3 ± 0.2	−0.1 ± 0.2	8.8 ± 0.7	0.4 ± 0.7
(ND2, (5))	8.9 ± 0	0.5 ± 0.0	10.9 ± 1.0	2.5 ± 1.0	63.4 ± 21.0	55.0 ± 21.0
(ND2, (6))	8.3 ± 0.3	−0.1 ± 0.3	8.2 ± 0.2	−0.2 ± 0.2	7.8 ± 0.7	−0.6 ± 0.7
(ND2, (7))	8.6 ± 0.3	0.2 ± 0.3	10.2 ± 1.0	1.8 ± 1.0	15.9 ± 2.9	7.5 ± 2.9
(ND3, (4))	8.4 ± 0.0	0.0 ± 0.0	8.3 ± 0.1	−0.1 ± 0.1	8.3 ± 0.2	−0.1 ± 0.2
(ND3, (5))	8.8 ± 0.2	0.4 ± 0.2	10.2 ± 0.2	1.8 ± 0.2	18.2 ± 1.7	9.8 ± 1.7
(ND3, (6))	8.3 ± 0.0	−0.1 ± 0.0	8.2 ± 0.2	−0.2 ± 0.2	7.7 ± 0.2	−0.7 ± 0.2
(ND3, (7))	8.5 ± 0.1	0.1 ± 0.1	8.9 ± 0.2	0.5 ± 0.2	9.8 ± 0.3	1.4 ± 0.3
(ND4, (4))	8.4 ± 0.1	0.0 ± 0.1	8.3 ± 0.1	−0.1 ± 0.1	8.7 ± 0.3	0.3 ± 0.3
(ND4, (5))	8.8 ± 0.1	0.4 ± 0.1	9.6 ± 0.2	1.2 ± 0.2	15.3 ± 1.6	6.9 ± 1.6
(ND4, (6))	8.3 ± 0.1	−0.1 ± 0.1	8.2 ± 0.1	−0.2 ± 0.1	8.1 ± 0.2	−0.3 ± 0.2
(ND4, (7))	8.4 ± 0.1	0.0 ± 0.1	8.5 ± 0.1	0.1 ± 0.1	9.3 ± 0.4	0.9 ± 0.4
(ND5, (4))	8.3 ± 0.0	−0.1 ± 0.0	8.3 ± 0.1	−0.1 ± 0.1	8.5 ± 0.1	0.1 ± 0.1
(ND5, (5))	8.7 ± 0.1	0.3 ± 0.1	9.3 ± 0.1	0.9 ± 0.1	11.7 ± 0.5	3.3 ± 0.5
(ND5, (6))	8.3 ± 0.0	−0.1 ± 0.0	8.2 ± 0.1	−0.2 ± 0.1	7.9 ± 0.1	−0.5 ± 0.1
(ND5, (7))	8.4 ± 0.0	0.0 ± 0.0	8.3 ± 0.1	−0.1 ± 0.1	8.4 ± 0.1	0.0 ± 0.1
(, (4))	8.3 ± 0.0	−0.1 ± 0.0	8.3 ± 0.1	−0.1 ± 0.0	8.5 ± 0.2	0.1 ± 0.2
(, (5))	8.9 ± 0.1	0.5 ± 0.1	11.4 ± 2.2	3.0 ± 2.2	27.2 ± 18.1	18.8 ± 18.1
(, (6))	8.3 ± 0.0	−0.1 ± 0.0	8.2 ± 0.1	−0.2 ± 0.1	7.9 ± 0.1	−0.5 ± 0.1
(, (7))	8.5 ± 0.1	0.1 ± 0.1	9.7 ± 1.4	1.3 ± 1.4	14.0 ± 5.9	5.6 ± 5.9