A new method has been developed for scaling water flow and solute transport during soil water redistribution process. The scaled solutions are invariant for a broad range of soil textures and initial conditions. The invariance of the scaled solutions gives an insight regarding features of the process considered and provides an easy way to obtain approximate solutions of the highly non-linear governing equations.

1. Scaling Solute Transport during the
Soil-Water Redistribution Process
Morteza Sadeghi and Scott B. Jones
Dept. Plants, Soils and Climate,
Utah State University

2. Large amounts of chemicals are applied in
agriculture, industry, and transportation for use
in the topsoil.
Chemicals are transported to greater depths,
leading to contamination of soils and groundwater.

3. Fertilizers & Pesticides
*

4. Accidental chemical spills
*

5. Leakage from corroded tanks
Hanford Site

6. Road Deicing

7. Fertilizers are a main source of Nitrate contamination
Nitrate risk in shallow groundwater

8. USGS: high arsenic concentration in
groundwater associated with landfills and
arsenical pesticides is common.
Arsenic concentration in groundwater

9. To Manage,
Quantifying Solute Transport in soil is of
paramount importance for a wide range of
environmental and agricultural issues.
Solute Transport is one of the most
complex phenomena in vadose zone!!!

10. The System is highly highly nonlinear
( s   r )
  r 
[1  (h) n ]m

R  1

  cR 
t
{1  (h) n1[1  (h) n ] m }2
K  Ks
[1  (h) n ]m / 2
VG models
h
q  K
K
z

q

t
z
D  DL

j
z
Solute flux
c
j   D
 qc
z
c: solute concentration (mass-per-solvent volume)
q

 7/3
w  2
s
 Dw w

11. 
There are analytical solutions only for simplified
cases (simple hydraulic models, neglecting the
dispersion/diffusion process or solute reaction).
 Tedious numerical calculations have to be
repeated for any soils and any initial/boundary
conditions separately.
 TO overcome this complexity,
We introduce a method for scaling different
soils into a unique non-dimensional
medium so that one numerical solution of any
soil can be used for many other soils.

12. One scenario of interest
concentration
 Solutes are incorporated in
irrigation water
 an initial wetted zone is created
 Irrigation water is redistributed
carrying solutes to deeper
depths.
depth
Solution to this case is important
to manage solutes movement to
avoid moving beyond the root
zone for use only by plant roots.

13. Initial and Boundary Conditions:
q=0
θfi
θi
zfi
j=0
qfi
ci
θ
zfi
θ = θi
z
cfi
c = ci
z
Water Flow
Solute Transport
c

14. We propose scaling variables as follows:
Scaled water content:
Scaled depth:
Scaled water flux:
  i
 
 fi   i
*
z
z 
z fi
*
q
q 
q fi
where: q fi 
*

h fi
hi
Scaled concentration:
Scaled time:
Scaled solute flux:
Kdh / z fi  K fi
c  ci
c 
c fi  ci
*
t t
*

q fi
fi
 i  z fi
J
J
J 

J fi q fi
*

15. A scale-invariant system is obtained:


q
 *
*
t
z
*

 c*  *   

J *
 
t *
z*
*
q* (0, t * )  0
J * (0, t * )  0
 * ( , t * )  0
c * ( , t * )  0
1, 0<z < 1
 ( z ,0)   *
0, z > 1
*
*
*
1, 0<z* < 1
c* ( z* , 0)  
0, z* > 1

The only remaining soil-dependent variable is φ
(normalized retardation/exclusion) :
  i

 fi  i
ε: Solute reaction coefficient
θi: Initial water content at dry zone
θfi: Initial water content at wet zone

23. Summary & Conclusions
 A new method is proposed for scaling coupled
water flow and solute transport during soil water
redistribution.
 The scaled solutions are invariant for a wide range
of soils and initial conditions when the scaled
exclusion/retardation term, φ, is identical for all the
cases.
 The invariance of the scaled solutions provides an
insight to the factors influencing solute transport.
 The new method provides opportunities to easily
obtain approximate solutions of the highly nonlinear governing equations.

24. Future Studies
The new scaling method considers a single irrigation
event. It is worthwhile to apply such a method to
frequent applications of irrigation water to track the
solute front in long run.
So far, we have not been able to do so.

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