Conclusions

• The states of the surface and root zoon soil moisture are considered as key variables controlling surface water and energy balances. Force-restore method (FRM) is widely used to estimate the soil moisture variations near the surface based on meteorological data for the prediction of climate changes. The applicability of the method seems to be insufficient from a soil physical view. • The difficulty to estimate the variations could be partly ascribed to the hardness of accurate evaluation of soil water flux through the bottom of a root zone under various conditions.

• We investigated the soil water flux during drainage based on numerical solutions and developed approximate solutions. • The variation of the flux in a root zone was approximately described by a product of two functions: one is a time function expressing the flux through a deep reference layer where soil moisture substantially remains constant, and the other is a depth function. Matric flux potential, which was convertible into water content, was also approximated in a similar manner. • On these processes, we found a stationary flux could be treated separately, and simply be added to an unsteady one even for the soil with nonlinear hydraulic properties (like a Brooks and Corey type).

• Evapotranspiration influenced the moisture distribution, especially in an upper layer of a root zone. According to the numerical solutions, however, the estimation of gravity drainage using the average water content of the root zone seemed to be rational except in an advanced dry phase, when the flux at the bottom of a root zone was upward.

• Incorporating the stationary flux, we could expand the application of FRM to more dry area.

• For further improvement of FRM, precipitation effects in a root zone have to be examined. In addition, the investigation in the thin surface layer are important to predict the moisture variation near the soil surface.

Efficient prediction of root zone soil moisture content with improved force-restore method Hideki KIYOSAWA

Graduate school of Bioresources, Mie University, Tsu, Japan kiyosawa@bio.mie-u.ac.jp

Bibliography

Bakker, M., and J.L. Nieber. 2009. Damping of sinusoidal surface flux fluctuations with soil depth. Vadose Zone J. 8:119-126.Kiyosawa, H. 1996. Approximate solutions for the soil water movement during drainage under a high groundwater table condition. Trans. JSIDRE 185, 755-765 (in Japanese).Mathias, S.A., and A.P. Butler. 2006. Linearized Richards’ equation approach to pumping test analysis in compressible aquifers. Water Resour. Res. 42:W06408, doi:10.1029/ 2005WR004680.Montaldo, N., J.D. Albertson, M.Mancini, and G. Kiely. 2001. Robust simulation of root zone soil moisture with assimilation of surface soil moisture. Water Resour. Res. 37, 2889-2900.

Abstract

Objectives• To analyze drainage processes in a vadose zone to clarify the structure of flux profiles and the characteristics of the flux through the bottom of a root zone.• To seek a method to estimate the soil water content and the flux at the bottom of a root zone.

Installation of stationary fluxApproximate solutions for drainage

• Beneath a root zone, we assume the existence of a layer (depth L) in which soil moisture is kept nearly constant through an intended period.

• The approximate solution of eq.1 was obtained using the separation of variables. It consists of a steady term f s and an unsteady one (Kiyosawa 1996).

[3]

[4]

where, r(t), f L: unsteady flux and f at z=L.

• The flux derived from the solution is,

[5]

If L is large compared to a root zone depth and a>>m ( in that case f u

>>f s and D is proportional to f), the function z(z) and h(z) become,

[6]

( ) ( )Lztrqtzqqtzq sus hh )(),(),(

( ) ( ) affff /)(),()( ztrzztz sus

( ) ( ) ( ) ( ) ( )LzLLzz aaaa exp11

( ) zz h

( ) ( ) ( ) ( ) zLqzLz sLs aaaff exp1exp

• The variation range of soil water is narrow at the lower part of a root zone and beneath it. Gardner-Kozeny model (Mathias and Butler 2006) should be applicable to the hydraulic properties of soil.

Hydraulic conductivity: he: air entry pressure

Water retention curve: n0: porosity

• Matric flux potential ( ) :

• Richards equation: [1]

• Soil water diffusivity: [2]

( ) es hhKK aexp

( ) ehhn m exp0

hKdhf

zztD

faff

2

21

amaaf

mf

m

Kn

K

d

dD

m

s

s ,0

( ) ( ) maaaf 0nKK s

Problem preparation( ) ( ) ( )( )mrrs

nes nKhhKK

0/

5

q/r

qs=0n=5, m=5, L=200cm, he=20cm, Ks=5*10-3cm/sn0 =0.45, r =0.1

• For the distribution of f, integrate the approximate equation,

( ) ( ) see hLzathLztrKz

ffff

:)/(

dtrt

0(cm)

• For the variation of drainage rate,

LS

SdzS

r

dst

0,

0

lines: numerical solution, dots: approximate solutions

Example (Brooks & Corey type)

Drainage rate from a root zone • The conventional force-restore method considers the near-surface and total root zone soil layers. The water content of the total root zone 2 evolves according to the water balance of this zone (depth d2), Pg: Precipitation

Eg: Evaporation Et: Transpiration

( )22

2 1qEEP

dt tggw

q2 is the drainage rate from the root zone, and often evaluated using the unit gradient assumption of gravity drainage and the hydraulic conductivity for

the average water content (Montaldo, et al. 2001). • Using numerical solutions, we found the assumption applicable in many cases with the slight correction of water content, except in an advanced evapotranspiration case when the flux at the bottom of the root zone was upward.

• The soil water flux for drainage was described as the sum of a steady term and an unsteady one. The unsteady term approximated as the product of a time function which indicates the drainage rate and a function of depth.

• Incorporating the stationary upward flux, FRM could be applicable to more dry situation.

1E+0

1E+2

1E+4

1E+6

1E+8

0 0.1 0.2 0.3 0.4 0.5

1E-10

1E-8

1E-6

1E-4

1E-2

Ma

tric

su

ctio

n (

cm)

Co

nd

uct

ivity

(cm

/s)

Water content (volumetric)

1E+0

1E+2

1E+4

1E+6

1E+8

0 0.1 0.2 0.3 0.4 0.5

1E-10

1E-8

1E-6

1E-4

1E-2

Ma

tric

su

ctio

n (

cm)

Co

nd

uct

ivity

(cm

/s)

Water content (volumetric)

Depth(cm)

00.20.40.60.8

1

0 20 40

absorption power of the root system

Depth(cm)

00.20.40.60.8

1

0 20 40

absorption power of the root system

Groundwater level 150cm

Totally saturated at t=0

1: Drainage only (D)

2: D+E (Ep = 6mm/day)

3: D+ET (ETp = 6mm/day)

4: D+ET (ETp = 12mm/day)

5: Hydraulic conductivity

Average water content of RZ (40cm)

Dra

inag

e ra

te (c

m/s

)

1E-10

1E-8

1E-6

1E-4

1E-2

0.0 0.1 0.2 0.3 0.4 0.5

123

4K

Average water content of RZ (40cm)

Dra

inag

e ra

te (c

m/s

)

1E-10

1E-8

1E-6

1E-4

1E-2

0.0 0.1 0.2 0.3 0.4 0.5

123

4K

• Using eqs. 5,3, we can estimate the flux and the water content at the bottom of the root zone. The availability of these equations to FRM depends on the fitness of the linearization and the induced parameters.

• Eqs. 3 and 5 show the independence of the stationary flux and the unsteady one. If the hydraulic conductivity approximates mainly the unsteady one, the total flux q2 is,

q

q2=qs+K()

• When evapotranspiration is dominant, q2 become negative and the variation of upward flux could be approximated.

-1.0E-6

0.0E+0

1.0E-6

2.0E-6

3.0E-6

4.0E-6

5.0E-6

6.0E-6

0 10000 20000 30000 40000

q2

Case 3 (D+ET)

Dra

inag

e ra

te (

cm/s

)

K()+qs