Identifying Soil and Transport Properties Using a Model
19
by Indelman et al. (1998) to the conditions of the present field test. The model is
applicable when horizontal transfer of fluid and solutes by velocity fluctuations
transverse to the vertical mean flow is negligible. This is bound to happen for
travel distances from the source, which are relatively small compared to the
horizontal integral scales of soil properties. This is the case for the infiltration
cycle at Bet Dagan because the total vertical dimension of the experimental zone
is on the order of one horizontal integral scale of Ks. Therefore, we treat the field
as a collection of independent vertical flow tubes such that each tube samples only
one set of properties in the horizontal plane. The predictive value of this approach
has been supported in field and numerical studies of constant rate transport of
conservative solutes (Butters et al. 1989; Protopapas and Bras 1991; Or and Rubin
1993). The vertical flow model has been applied to study the effects of various
transport processes, for example, local field-scale dispersion (Bresler and Dagan
1981) and heterogeneous kinetic sorption (Cvetkovic and Destouni 1989).
Or and Rubin (1993), Russo et al. (1994), and Russo (1997) tested the ability
of constant-rate vertical column models to predict numerically simulated transport
in soils undergoing transient irrigation. Increased transverse flow during soil
drying limits the depth to which one may apply the vertical column assumption.
Furthermore, the steady-flow assumption models seemed to fail as the length of
the drying periods increased. Indelman et al. (1998) developed a single-cycle
infiltration and redistribution model that is not limited by the assumption of
homogeneous, constant rate flow. Lessoff et al. (2001) extend this model to solve
transport over multiple irrigation cycles and for a finite pulse. Here, we derive an
expression for concentration averaged over a finite sample interval and employ
the model in an inverse mode to estimate soil properties and their confidence
intervals directly from field measurements.
3.1 Solution for a Single Column
3.1.1 Flow
The mass conservation equation of one-dimensional vertical unsaturated flow is
given by
of) + i1j = 0
ot Oz '
(1)
where q is the specific discharge and z is the vertical coordinate, positive
downward. To derive an analytical solution ofEq. (1) valid for a sufficiently long
infiltration period, gravitational flow is assumed. Then, q is equal to the hydraulic
conductivity K, which in turn is given by the Brooks-Corey (1964) constitutive
relationship
19
by Indelman et al. (1998) to the conditions of the present field test. The model is
applicable when horizontal transfer of fluid and solutes by velocity fluctuations
transverse to the vertical mean flow is negligible. This is bound to happen for
travel distances from the source, which are relatively small compared to the
horizontal integral scales of soil properties. This is the case for the infiltration
cycle at Bet Dagan because the total vertical dimension of the experimental zone
is on the order of one horizontal integral scale of Ks. Therefore, we treat the field
as a collection of independent vertical flow tubes such that each tube samples only
one set of properties in the horizontal plane. The predictive value of this approach
has been supported in field and numerical studies of constant rate transport of
conservative solutes (Butters et al. 1989; Protopapas and Bras 1991; Or and Rubin
1993). The vertical flow model has been applied to study the effects of various
transport processes, for example, local field-scale dispersion (Bresler and Dagan
1981) and heterogeneous kinetic sorption (Cvetkovic and Destouni 1989).
Or and Rubin (1993), Russo et al. (1994), and Russo (1997) tested the ability
of constant-rate vertical column models to predict numerically simulated transport
in soils undergoing transient irrigation. Increased transverse flow during soil
drying limits the depth to which one may apply the vertical column assumption.
Furthermore, the steady-flow assumption models seemed to fail as the length of
the drying periods increased. Indelman et al. (1998) developed a single-cycle
infiltration and redistribution model that is not limited by the assumption of
homogeneous, constant rate flow. Lessoff et al. (2001) extend this model to solve
transport over multiple irrigation cycles and for a finite pulse. Here, we derive an
expression for concentration averaged over a finite sample interval and employ
the model in an inverse mode to estimate soil properties and their confidence
intervals directly from field measurements.
3.1 Solution for a Single Column
3.1.1 Flow
The mass conservation equation of one-dimensional vertical unsaturated flow is
given by
of) + i1j = 0
ot Oz '
(1)
where q is the specific discharge and z is the vertical coordinate, positive
downward. To derive an analytical solution ofEq. (1) valid for a sufficiently long
infiltration period, gravitational flow is assumed. Then, q is equal to the hydraulic
conductivity K, which in turn is given by the Brooks-Corey (1964) constitutive
relationship