Inverse Method to Determine Soil Hyd Raul Ic Properties

7/27/2019 Inverse Method to Determine Soil Hyd Raul Ic Properties

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Table 1 　 Final optimized parameters with diff erent a uxiliary variables in t he objective f unction f or one2step outflow

experiments

Parameter

Final parameter

Q H Q + H

　　 30 0cm

r (cm3

cm- 3 ) 0 0 . 0038 0 . 08

α (cm- 1) 0 . 004 0 . 001 0 . 00 1

n ( - ) 1 . 19 1 . 33 1 . 44

　　 40 0cm

r (cm3

cm- 3 ) 0 0 . 018 0

α (cm- 1) 0 . 003 0 . 001 0 . 00 2

n ( - ) 1 . 90 2 . 04 2 . 04

　　 60 0cm

r (cm3

cm- 3 ) 0 . 08 0 0 . 00 8

α (cm- 1) 0 . 003 0 . 004 0 . 00 5

n ( - ) 1 . 68 2 . 84 1 . 55

Table 2 　 Final optimized parameters with diff erent a uxiliary variables in t he objective f unction f or mult i2step outflo w

experiments

ParameterFinal parameter

Q H Q + H

r (cm3

cm- 3 ) 0 . 051 0 . 002 0

α (cm- 1) 0 . 0026 0 . 0033 0 . 0032

n ( - ) 1 . 55 1 . 70 1 . 64

(600cm ) t h a n i n l o w e r p r e s s u r e ( 300cm ) i n m o s t

c as es , w h i h i n d ic a t es t h a t t h e n o n2uniqueness of

in v e rs e me th o d w o uld re d u ce if w e ra is e p ress u re .

Fig. 4 　 Optimized water retention curves from different vari2

ables at pressure 30 0cm

Fig. 5 　 Optimized water retention curves f rom different vari2ables at pressure 40 0cm

　　 A n d w e f i n d t h a t r s h o w s a la rg e r v a ria b il i ty

t ha n t he o t he r t wo p a ra met ers a nd n , w h ic h

c o ul d be d ue t o t h e f a c t t h a t r was not sensitive to

o u tflo w v a ria bles . T he C V s b e c o me s ma lle r w h e n

876



Table 3 　 RMSE f or all experiments

Experiment

RMSE(cm3

cm- 3 )

Q H Q + H

One2step 300 cm 0 . 108 0 . 151 0 . 14 1

One2step 400 cm 0 . 037 0 . 122 0 . 06 3

One2step 600 cm 0 . 060 0 . 118 0 . 02 0

Multi2step 0 . 084 0 . 037 0 . 04 1

Table 4 　 Coeff icients of variation f or parameters computed from t hree diff erent initial parameters

ParameterCoefficients of variation

Q H Q + H

　　 OSO300 cm

r (cm3

cm- 3 ) 1 . 4 0 . 681 0 . 57 2

α (cm- 1) 0 . 41 0 . 032 0 . 07 9

n ( - ) 0 . 128 0 . 004 0 . 03 6

　　 OSO400 cm

r (cm3

cm- 3 ) 0 . 77 0 . 642 1 . 13

α (cm- 1) 0 . 015 0 . 188 0 . 00 3

n ( - ) 0 . 015 0 . 177 0

　　 OSO600 cm

r (cm3

cm- 3 ) 0 . 48 0 . 572 0

α (cm- 1) 0 . 022 0 . 001 0 . 02 5

n ( - ) 0 . 006 0 . 003 0 . 01 4

　　 MSO

r (cm3

cm- 3 ) 0 . 317 1 . 48 0 . 91 6

α (cm- 1) 0 . 106 0 . 071 0 . 02 7

n ( - ) 0 . 039 0 . 054 0 . 02 8

b o th o u tflo w a n d p re s s u re h e a d a re in c lu d e d in th e

o bj ec t i ve f u n c t i o n e xc e p t p r e ss u r e is a t 6 00 c m ,

w h ic h c oul d b e d ue t o t h e e x p e r i me n t al e r r o r . I nMSO experi ments , r also shows a larger variability

a n d t h e C Vs a r e s m al le r w h e n b ot h o ut f l ow a n d

p r e ss u r e h e a d a r e i n c l ud e d i n t h e o b j e ct i ve f u n c2

t i o n .

5 . 　 CONCL USION

T r a ns ie n t o ut f l o w m e t h o d c o m b i n e d w i t h i n2

v e rs e m e t h o d is a t t r a c ti ve t o d et e r m i n e h y d r a ul icp r o p e r t i es . I n o u r e x p e ri m e n ts , w e h a ve f o u n d i n

th e O SO e x p e rime n t th a t th e in c re me n t o f p re s s u re

will i ncrease the uniqueness of the i nverse solution ,

a n d in th e M SO e x p e rime n t a d d itio n a l in fo rma tio n

i n t h e o b j e c t i v e f u n c t i o n ( s uc h a s p r ess u re h e a d )

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Inverse Method to Determine Soil Hyd Raul Ic Properties