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

Table 1

Average values over of time limits (in days) for model values (EPM), for normal distributions , and for prediction time length (bold rows). Difference between this model values and average values over received from (9)–(11) and NS (7) with parameters , , , , , , , , , and calculated from approximations of (4)–(7) for , , , and (columns , , , , ). Standard deviation of (columns , , , , ).

(Days)
(EPM, )	4.8	0.1	12.9	0.1	16.3	0.1	19.2	0.2	25.8	0.2
(EPM, ) − ((9), )	2.6	0	2.4	0.3	2.4	0.2	2.4	0.3	1.9	0.3
(EPM, ) − ((10), )	3.8	0	6.4	0.3	6.2	0.2	5.6	0.3	5.1	0.9
(EPM, ) − ((11), )	2.2	0.2	2	0.4	1.9	0.3	1.9	0.3	1.4	0.6
(EPM, ) − (NS (7), )	—	—	—	—	—	—	—	—	—	—
(EPM, ) − ((9), )	2.6	0	2.4	0.2	2.4	0.3	2.5	0.3	2.6	1.2
(EPM, ) − ((10), )	3.3	0	4.5	0.2	4.3	0.2	4.5	0.3	8.1	0.2
(EPM, ) − ((11), )	2.1	0.1	1.8	0.1	1.8	0.1	1.9	0.3	2.5	0.6
(EPM, ) − (NS (7), )	—	—	—	—	—	—	—	—	—	—
(EPM, ) − ((9), )	2.5	0.1	2.5	0.1	2.6	0.2	2.8	0.6	5.1	2.9
(EPM, ) − ((10), )	—	—	—	—	—	—	—	—	—	—
(EPM, ) − ((11), )	1.7	0.2	1.5	0.2	1.3	0.4	0.1	0.5	—	—
(EPM, ) − (NS (7), )	1.3	0	1.1	0	1.3	0.1	2	0.3	6.6	0.4
(Days)
(EPM, )	4.9	0.1	10.6	0.1	14	0.2	16.9	0.2	24.3	0.5
(EPM, ) − ((9), )	2.6	0	2.5	0.3	2.6	0.4	2.7	0.4	3	0.4
(EPM, ) − ((10), )	3.6	0	4.6	0.1	5.1	1.1	4.5	0.1	4.4	1
(EPM, ) − ((11), )	1.9	0.4	1.6	0.5	1.6	0.4	1.7	0.4	2.1	0.4
(EPM, ) − (NS (7), )	—	—	—	—	—	—	—	—	—	—
(EPM, ) − ((9), )	2.6	0	2.5	0.2	2.6	0.3	2.6	0.3	2.2	1.4
(EPM, ) − ((10), )	3.5	0.1	4.3	0.2	4	0.3	3.8	0.3	7.2	0.4
(EPM, ) − ((11), )	1.9	0.3	1.6	0.3	1.6	0.3	1.6	0.3	−0.4	2.5
(EPM, ) − (NS (7), )	—	—	—	—	—	—	—	—	—	—
(EPM, ) − ((9), )	2.5	0.1	2.4	0.3	2.5	0.3	2.7	0.3	4.1	3
(EPM, ) − ((10), )	2.9	0.1	2.8	0.2	2.5	0.3	2.6	0.3	7	0.3
(EPM, ) − ((11), )	1.8	0.1	1.5	0.1	1.6	0.3	1.3	0.5	—	—
(EPM, ) − (NS (7), )	1.5	0.2	1.5	0.1	1.5	0.2	1.9	0.4	6.5	0.7
(Days)
(EPM, )	4.9	0.1	8.2	0.2	11.6	0.2	14.4	0.2	21.6	0.4
(EPM, ) − ((9), )	2.6	0.1	2.3	0.1	2.4	0.1	2.1	0.1	2.7	0.2
(EPM, ) − ((10), )	3.5	0.1	4	0.1	3.9	0	3.2	0.2	2.6	0.8
(EPM, ) − ((11), )	2.1	0.1	1.6	0.1	1.6	0.2	1.6	0.2	2.1	0.3
(EPM, ) − (NS (7), )	1	0.2	1.1	0.2	1.3	0.2	1	0.3	1	0.6
(EPM, ) − ((9), )	2.6	0.1	2.4	0.1	2.3	0.1	2.2	0.2	2.4	0.9
(EPM, ) − ((10), )	3.4	0	3.6	0.1	3.3	0.2	2.8	0.2	5	0.2
(EPM, ) − ((11), )	2	0.1	1.5	0.2	1.6	0.2	1.6	0.2	1.2	1.4
(EPM, ) − (NS (7), )	1.5	0.2	1.5	0.2	1.6	0.2	1.4	0.2	2.6	0.6
(EPM, ) − ((9), )	2.7	0	2.3	0.1	2.3	0.1	2.2	0.2	3.4	0.6
(EPM, ) − ((10), )	2.9	0	2.8	0.1	2.5	0.1	2.6	0.1	7	0.2
(EPM, ) − ((11), )	1.8	0.1	1.4	0.2	1.6	0.2	1.4	0.3	—	—
(EPM, ) − (NS (7), )	1.6	0.1	1.5	0.2	1.6	0.2	1.6	0.2	4.1	0.7