Published online May 26, 2006

Estimation of the Unsaturated Hydraulic Conductivity of Peat Soils:
Laboratory versus Field Data
K. Schwärzel,* J. Šimůnek, H. Stoffregen, G. Wessolek, and M. Th. van Genuchten
retention and unsaturated hydraulic conductivity functions (Dane and Topp, 2002). In addition to these direct
methods, inverse solution techniques are now also
increasingly used to determine the hydraulic properties
from transient field or laboratory measurements (e.g.,
Dane and Hruska, 1983; Parker et al., 1985; Eching andHopmans, 1993; Šimůnek et al., 1998b; Abbaspour et al.,
2000; Jacques et al., 2002; Sonnleitner et al., 2003). The
application of inverse methods assumes a certain parametric model for the hydraulic properties with as yet unknown parameters. A flow experiment is then typicallyconducted to estimate these parameters by minimizationof deviations between measured and predicted flow variables (Kool and Parker, 1987). An excellent review ofthe principles and advantages of inverse methods wasgiven by Hopmans et al. (2002). In this study we use
inverse procedures to determine the unsaturated hydraulic properties of peat soils.
In general, laboratory measurements are quick andprecise, but often lead to soil hydraulic properties that are
not representative of field conditions. Differences between laboratory and field measurements have long been
noted for mineral soils (e.g., Sonnleitner et al., 2003), butsuch differences may be especially important for peatsoils because of their unique physical properties. Moreover, standard field methods such as the instantaneous
profile method (Vachaud and Dane, 2002) or the planeof-zero-flux method (Arya, 2002) are generally notapplicable to peat soils, which are usually situated inareas with relatively shallow water tables. While the useof lysimeters may overcome some of these limitations,
their installation and operation is often very expensive. In
contrast to conventional lysimeters, we developed arelatively low-cost lysimeter that can be installed moreeasily, and with minimal technical effort (Schwärzel andBohl, 2003). Field lysimeters of this type, without vegetation, were used in the Schwärzel and Bohl (2003) study
to determine the unsaturated soil hydraulic functionsof peat soils using traditional direct methods. Results
showed that direct estimation of the hydraulic conductivities from the lysimeter data was very tedious, uncertain (due to very small pressure head gradients), andlimited to a relatively small pressure head interval. In
contrast, measurements of the hydraulic properties in thelaboratory were quicker and more accurate over a muchwider range of water contents. Still, questions arose as
to what extent the relatively small size of the laboratory
samples and soil disturbance during sample collection
affected the hydraulic properties of the peat soils.
The objectives of this study hence were to use parameter inverse estimation methods to determine the

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

ABSTRACTAs compared with mineral soils, there are few in situ measurementsof the unsaturated hydraulic properties of peat soils available. We usedparameter estimation (inverse) methods to estimate the water retention
and hydraulic conductivity functions of drained peat soils from both laboratory and field data. The laboratory data were obtained on small cores
using the traditional evaporation method, while the field data wereobtained by means of evaporation experiments using groundwater
lysimeters with and without vegetation. The field experiments without
vegetation produced highly uncertain parameters and were limited to a
relatively small pressure head range. Better results were obtained for thelysimeter with a grass cover that caused the peat soil to dry out more.
However, a physically realistic minimum in the objective function for theplant-coveredlysimetercouldbefoundonlywhenpriorinformationabout
severalparameters wasincluded intheoptimization.Goodagreementwas
obtained between the laboratory and field measurements. The hydraulicfunctions were subsequently tested by comparing forward simulations
with independently measured pressure heads and water contents of anadditional lysimeter experiment under grass. The dynamics of the drying
process was described well using the optimized soil hydraulic properties.

U

NDERSTANDING the processes that control the reten-tion and flow of water in peat soils is critical toeffective management of such soils from both agricultural and ecological perspectives. In contrast to mineralsoils, much less is known about the unsaturated soil hydraulic properties of peat soils, especially the hydraulicconductivity. This is in part due to the unique nature of
the physical and hydraulic properties of peat soils, suchas volume changes during dewatering (Schwärzel et al.,
2002; Price, 2003). Only a relatively few measurementsof the unsaturated hydraulic conductivity of peat soils
have been reported in the literature (e.g., Rijtema, 1965;
Renger et al., 1976; Loxham and Burghardt, 1986;
Schouwenaars and Vink, 1992; Baird, 1997; Silins andRothwell, 1998; Schlotzhauer and Price, 1999; Schindler
et al., 2003; Naasz et al., 2005). Most of these studies
involved direct laboratory measurements of the unsaturated hydraulic conductivity using steady-state methods on small core samples.
Many laboratory and field methods are currently
available for direct determination of the soil water
K. Schwärzel, Institute of Soil Science and Site Ecology, Univ. of Technology, Dresden, Germany; J. Šimůnek, Dep. of Environmental
Sciences, Univ. of California, Riverside, CA 92521 USA; H. Stoffregenand G. Wessolek, Institute of Ecology, Dep. of Soil Science and Soil
Protection, Technical Univ. of Berlin, Germany; M.Th. van Genuchten,
USDA-ARS, George E. Brown, Jr. Salinity Lab., Riverside, CA 92521,
USA. Received 10 May 2005. *Corresponding author (Kai.Schwaerzel@
Forst.TU-Dresden.de).
Published in Vadose Zone Journal 5:628–640 (2006).
Original Researchdoi:10.2136/vzj2005.0061ª Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

Abbreviations: VGM, van Genuchten–Mualem; WRC, water retention curve.

628

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www.vadosezonejournal.org

hydraulic properties of peat soils and to investigate possible differences between laboratory and in situ fieldmeasurements. Transient evaporation experiments were
for this purpose performed on small laboratory soilcores and using field lysimeters with and without a grasscover. An important aspect of this study was to investigate the suitability of transient evaporation experimentson lysimeters with a grass cover. The estimated hydraulic functions were subsequently tested by comparing
predictions with measured pressure heads and water contents of an additional lysimeter experiment under grass.

THEORY
Governing Equations
Water flow simulations were conducted with theHydrus-1D model (Šimůnek et al., 1998a), which numerically solves the Richards equation:
]u
]
]h
5
1K 2S
K
]t
]z
]z

1

2

[1]

where u is the volumetric water content (L3 L23), t is
time (T), z is the vertical coordinate (positive upward)(L), h is the pressure head (L), K is the hydraulicconductivity (L T21), and S represents the root water
uptake rate (T21). Solving Eq. [1] requires a set of initialand boundary conditions. The initial condition in ourstudy was given in terms of measured pressure head, hi:h(z,t) 5 hi (z)

t50

[2]

An atmospheric boundary condition was specified at
the soil surface:2K ]h 2 K # E at z 5 0
[3]


]z
and
hA # h # hSat z 5 0[4]where E is the maximum potential rate of infiltration orevaporation under the current atmospheric conditions(L T21), and hA and hS are the minimum and maximum
pressure heads, respectively, allowed at the soil surface(L). Following Šimůnek et al. (1998a) values for hA andhS were assumed to be 21.0 3 106 and 0 cm, respectively. We additionally applied a zero flux condition to
the bottom boundary of the lysimeter:]h12K ]z 2 K25 0

at z 5 2 L[5]m 5 1 2 1/nn.1

Soil Hydraulic Properties
The unsaturated soil hydraulic properties were described with the van Genuchten–Mualem (VGM) model(van Genuchten, 1980; Mualem, 1976):
for h # 0

[6]

[8]
[9]

where Q is effective saturation, uR is the residual volumetric water content, uS is the saturated volumetric watercontent, KS (L T21) is the saturated hydraulic conductivity, and a (L21), n, m, and l are empirical parameters.
Weiss et al. (1998) previously demonstrated the flexibility of the VGM model in describing the water retention
data of peat soils. They obtained optimal results using
only three VGM parameters (uS, a, and n), with uR being
fixed at zero. In our preliminary studies we could not find
improvements in predictions of K(h) by varying the lparameter in Eq. [8]. The use of alternative parametricexpressions (Burdine, 1953; Brooks and Corey, 1964) also
did not lead to better optimization results. For thesereasons we reduced the number of unknown parametersin Eq. [6] by fixing the values of uR and l to zero and 0.5,
respectively, thus enhancing the likelihood of uniquenessand stability of the inverse solution. We note that in our
inverse analysis we considered all parameters (including
KS and uS) to be fitting parameters that define the scale
and the shape of the soil hydraulic functions without any
clear physical meaning. Their mutual correlation andpossible nonidentifiability hence were not a major concern to us, as long as they reproduced the measured data
used for calibration and subsequent validation.

Root Water Uptake
In this study the sink term, S, in Eq. [1] is defined as
the volume of water removed from a unit volume of soil
per unit time due to plant water uptake. Feddes et al.
(1978) defined S as
S(h) 5 b(h)Sp[10]where b (0 # b # 1) is a prescribed dimensionless function
representing root water uptake in response to water stress,
and Sp is the potential root water uptake rate distribution(T21). When the potential root water uptake rate isuniformly distributed over the root zone, Sp becomesSp 5 (1/Lr )Tp[11]

where Lr is the depth (L) of the root zone and Tp is thepotential transpiration rate (L T21). Equation [11] may
be generalized by introducing a nonuniform distributionof the potential root water uptake rate over a root zone ofarbitrary shape (Fig. 1):
Sp 5 b(z)Tp

where L is the depth of the lysimeter.

u 2 uR1
Q5
5nuS 2 uR(1 1 |ah| ÞmK(Q) 5 KS Ql [1 2 (1 2 Q1/m )m ]2[12]

where b(z) is the normalized water uptake distribution(L21). The spatial variation of the potential extraction
term, Sp, over the root zone is obtained by normalizing
any arbitrarily measured or prescribed root distributionfunction, b9(z), as follows
b(z) 5b9(z)#b9(z)dz

[13]

Lr

Q51

for h . 0

[7]where Lr is the region occupied by the root zone (L).

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630

VADOSE ZONE J., VOL. 5, MAY 2006

Fig. 1. Schematic of the potential root water uptake distribution function.

The potential root-water uptake function Sp (Eq. [11])corresponds to the transpiration rate Tp of a growing
canopy (Fig. 1) such that

# S dx 5 T
p

[14]

p

Lr

in which Tp depends on weather conditions, plant height,
and canopy resistance against water loss. The actual root
water uptake rate S is obtained by substituting Eq. [12]into Eq. [10], while the actual transpiration rate Ta(L T21) follows by integrating S over the root zone:
Ta 5 Tp# b(h)b(z)dz

[15]

Lr

Inverse Parameter Estimation Procedure
Parameter estimation in this study was accomplishedby minimizing the following objective function, F(Šimůnek et al., 1998a):nqj

mq

F(b,q,p) 5

O r O w [q *(z,t ) 2 q (z,t ,b)]
1 O y O w 9[ p *(u ) 2 p (u ,b)]
1 O v̂ [b * 2 b 
2

j51

j

i51

j

i

j

i

npj

mp

j51

ij

j

i51

ij

j

i

j

2

i

npj

2

i51

j

j

j

[16]

in which the first term represents deviations between
measured, qj*, and calculated, qj, space–time variables,such as pressure heads or water contents. In this term
mq is the number of different sets of measurements, nqi
the number of measurements in a particular measurement set, qj*(z, ti) represents a specific measurement attime ti for the jth measurement set, qj(z,ti,b) are thecorresponding model predictions for the vector of estimated parameters b(uR, uS, a, n, KS, l), and ri and wij
are weights associated with a particular measurement
set or data point, respectively. The second term of Eq.
[16] represents differences between independently
measured, pj*, and predicted, pj, soil hydraulic properties, such as retention or conductivity data at particular pressure heads. The terms variables, mp, npj, pj*(ui),pj(ui,b), y9j and w9ij, in this second term have similar
meanings as in the first term, but now for the soil
hydraulic properties. The last term of Eq. [16] represents a penalty function for deviations between priorknowledge of the soil hydraulic parameters, bj*, andtheir final estimates, bj, with nj being the number ofparameters with prior knowledge and r̂j representing
preassigned weights.
In this study we assume that the weighting coefficientswij and w9ij in Eq. [16] are equal to 1. The weighting coefficients ri and y9j that equalize the contribution of different data types to the objective function F are given by
rj 5

1
nj s2j[17]

which normalizes the objective function in terms of thevariances s j2 of measurement type j.
Minimization of the objective function F was accomplished using the Levenberg–Marquardt nonlinear
optimization method (Marquardt, 1963; Šimůnek et al.,1998a). Since the Levenberg–Marquardt method is alocal search method, the final optimized parameters may
depend on the initial parameter values (e.g., Abbaspour
et al., 2004). The use of a well-defined flow problem
combined with prior information about the optimized
parameters generally enhances the likelihood of uniqueness of the inverse solution (Russo et al., 1991).
Although uniqueness of the inverse problem cannot
always be guaranteed, solving the problem several times
with different initial parameter estimates should ensurethat the search algorithm locates the global minimum of
the objective function.
Compared with global optimization methods (e.g.,
the genetic algorithm method used by Vrugt et al., 2001)
in conjunction with Hydrus) that have been used recently to determine empirical parameters of lumped
hydrological (Vrugt et al., 2002) or other black box
models (e.g., Barhen et al., 1997), the Levenberg–
Marquardt method provides useful statistical information about the optimized parameters, such as theirmutual correlation and confidence intervals. This information should be indicative whether or not the experimental data have enough information content for uniquedetermination of the optimized parameters (Šimůnek
and Hopmans, 2002).

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Forward Simulations
Based on an additional lysimeter experiment undergrass, forward simulations were conducted to test theaccuracy of estimated hydraulic functions. Differences
between various simulations were quantified by comparing predicted results Pi with the observed data Oi
using the RMSE given by (Loague and Green, 1991):
sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
N2
i51 ðPi 2Oi Þ 100[18]
RMSE 5N
O
where N is the number of values and O is the arithmetic
average of the N measurements.

O

MATERIALS AND METHODSThe Rhinluch Field Site
Field measurements were performed in Rhinluch, a fen areaof about 87 000 ha, 60 km northwest of Berlin, Germany. Peatsoils in the area, drained more than 250 yr ago, are characterized as a Eutri Folic Histosol, with an average thickness ofabout 120 cm. Below the peats are glacifluvial sands (mostly
fine sand) and limnic sediments such as detritus or calcareous
mud. The upper peat layers are strongly decomposed and altered pedogenically because of intensive land use and drainage. Humified and very humified peats are mostly present near
the soil surface. Deeper layers consist primarily of sedge(Carex spp.) or reed-peats (Phragmites spp.), or of a mixture ofthese two peats. Vegetation at the study site was dominated byreed canary grass (Phalaris arundinacea L.).

Laboratory Methods
The unsaturated soil hydraulic properties were determined in
the laboratory during transient conditions using the evaporation
method (Wendroth et al., 1993) and during steady state conditions using the hanging water column method and a pressure
apparatus (Dane and Topp, 2002). Undisturbed cores (3 replicates from each layer) with a height of 10 cm and an inside
diameter of 5.64 cm were used for the evaporation method. Fivetensiometers with cups of 4 cm length and 0.3 cm outside
diameter were installed at depths of 1, 3, 5, 7, and 9 cm andconnected to pressure transducers with a precision of 61 cm.
Once placed on a ceramic plate, a hanging water column (withdeionized water) was used to create a negative pressure equal
to the initial soil water pressure head of 220 cm at the bottomof the cores. After hydraulic equilibrium was reached, the lidcovered samples were moved from the ceramic onto impermeable plates for the evaporation experiments. After an additional
day of equilibration, immediately before the evaporation experiments, tensiometer readings were compared and corrected,
assuming that hydraulic equilibrium had been reached. The
evaporation process was then started, with pressure heads
recorded every 30 min. Water losses with time were measured byweighing the cores several times each day. We also estimatedwater losses from water contents determined with five mini
TDR probes (Easy Test, Lublin, Poland, 1993) consisting of two
wires (5.3 cm long and spaced 0.6 cm apart) installed at depths of
1, 3, 5, 7, and 9 cm. The error of the laboratory TDR probes formeasuring water content was about 0.01 m3 m23 (Plagge et al.,1994). At the end of the experiments, tensiometers and TDR
probes were removed and residual water contents determinedby oven drying the samples at 1058C and weighing.
The water content was determined by using a site-specificcalibration between the dielectric constant, e, and the watercontent (standard error of calibration 5 0.022 m3 m23,
Schwärzel and Bohl, 2003):

u 5 0:0393 1 0:0284e 2 0:000419e2 1 0:00000277e3 [19]Unsaturated hydraulic conductivities were estimated fromthe evaporation experiments in two ways. First, when TDR
measurements were available, water fluxes were calculated
from the water content changes and pressure head gradients.
For these calculations, water contents for each TDR probe
were fitted with a quadratic polynomial function of time, andmeasured pressure heads with a quadratic polynomial functionof depth at each measurement time. Hydraulic conductivities
as a function of the pressure head were next calculated using
Darcy’s Law. Second, when TDR measurements were notavailable, hydraulic conductivities were calculated using theapproach of Wind (1968). In this approach, water contents
were first calculated from measured pressure heads using aretention curve (the VGM model in our case) that was optimized such that water content changes in the soil column
became equal to the measured total water losses. These watercontents were subsequently used to calculate hydraulic conductivities as described above.
In addition to the above direct methods for estimating thesoil hydraulic functions, an inverse parameter optimization
method (Šimůnek et al., 1998b) was applied to all laboratory
measurements. The tensiometer readings as a function of time
and the total water volume at the end of the experiment wereused for the calibration. Water volume measurements wereused to calculate evaporation rates needed for the upperboundary condition. A zero-flux condition was used as the bottom boundary condition. As the initial condition we assumed
hydraulic equilibrium with the initially imposed pressure head(220 cm) at the bottom of the soil sample. No prior information was used in the inverse analysis of the laboratory evaporation data.
Undisturbed soil core samples (5 replicates from each layer)with a height of 4 cm and a diameter of 5.5 cm were used todetermine retention curves assuming steady-state conditions.
Samples were first placed on a ceramic plate and saturated. The
dewatering process (desorption) was performed using ceramic
plates connected to a hanging water column down to a pressureof 2100 cm. A pressure apparatus was used below this pressure.
Volume changes during the dewatering process were quantified
with a caliper rule at the end of every pressure step. The peatsoils used in our study started to noticeably shrink at pressure
heads below 230 m (5% loss of volume). More details about
this problem were given by Schwärzel et al. (2002).

Field Methods
Three nonweighing groundwater table lysimeters (1 by 1 by1 m) were installed in two replicates and equipped with fully
automated tensiometers using pressure transducers with a
precision of 61 cm and manually operated TDR probes (Easy
Test, Lublin, Poland, 1993), made from two wires (10 cm longand spaced 1.6 cm apart, and having measurement precision of
0.01 m3 m23), at depths of 10, 20, 30, 40, 50, 60, 70, and 80 cm.
All sensors were horizontally installed. TDR readings wereconverted into water content values using the site-specificcalibration equation (Eq. [19]). Groundwater levels in thelysimeters and the surrounding soil were monitored using
slotted PVC pipes connected via a flexible tube to a differential pressure transducer a precision of 1 cm. Following theapproach of Feddes (1971), the water level in the lysimeter waseither adjusted to the surrounding groundwater level (the reference level) or fixed at a certain depth. Water level differences recorded by the control unit either triggered a bilge

632

VADOSE ZONE J., VOL. 5, MAY 2006

t2

t2

L t2

# ET dt 5 # (P 1 Q)dt 2 # # ]u]t dzdt
a

t1

t1

[20]

0 t1

21

3
K/Kmin and K/Kmax

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

pump in the lysimeter pipe, or released a valve in a water supply container. The volume of water automatically added or
removed from the lysimeter was manually measured by recording water levels in the container. Hysteresis in the imposed groundwater level was observed to be at most 2 cm.
The average actual evapotranspiration rate, ETa, (LT21) for acertain time interval between t1 and t2 was calculated as follows:2
upper limit
1lower limit

21

where P (L T ) is the precipitation rate, Q (L T ) is the net
inflow rate (inflow minus outflow) into the lysimeter needed
to keep the groundwater table at the same level, and L (L)is the depth of the lysimeter. Additional information about
the groundwater lysimeters and the field site was given in
Schwärzel and Bohl (2003).
Two of the three lysimeters were operated with a grass cover.
One of these was used for parameter estimation and the otherone to test the estimated parameter in forward simulations. The
third lysimeter was operated in 1994 and 1995 without plants
and with roofing for rain protection. This third lysimeter was
fully saturated at the beginning of the vegetation period, atwhich time the water level control mechanism was disabled bydisconnecting the control unit. As a result, the soil monolithslowly dried out in about 70 d, similarly to the laboratory
evaporation experiment. Bare lysimeter data were analyzed
using the standard evaporation method (Hillel et al., 1972; Arya,
2002), as well as inverse procedures. For the latter approach, theevaporation rate, q0, (LT21) from the soil surface was calculated
from TDR-measured soil water content changes in the soil
profile as follows:

dW
]h
q0 5
5 2K(h)
11
dt
]z
z50

1

2

[21]

where W (L) is the total depth of water in the soil profile given by
L

W5

# udz

[22]

0

Experimental Limitations
The accuracy of the directly calculated unsaturated hydraulic conductivities and the inversely estimated hydraulic parameters depends on the precision of the measurement devices(i.e., on the instrumental error). The calculated unsaturated
hydraulic conductivities are especially sensitive to hydraulicpressure gradients close to 21 cm cm21. The influence of themeasurement precision of the tensiometers on the calculated
hydraulic gradients, ]h/]z (L L21), and consequently on the unsaturated hydraulic conductivities, were quantified as follows(Stoffregen, 1998):]h(h1 6 dh 1 z1 ) 2 (h2 6 dh 1 z2 )5]z
z1 2 z 2[23]

where dh is the measurement precision of the pressure transducer (61 cm), and h1 and h2 are measured pressure heads at
depths of z1 and z2, respectively. Upper and lower limits of thecalculated hydraulic conductivity at a particular pressure
gradient may be determined using Eq. [21] and [23]. Figure 2
shows the ratios of the calculated unsaturated hydraulic conductivity (K) without considering the measurement error, toeither the upper limit (Kmax) or the lower limit (Kmin) of theunsaturated hydraulic conductivities with the measurement

0
0

-25

-50

-75

-100

Hydraulic gradient [cm cm-1]
Fig. 2. Effect of tensiometer measurement precision on calculated
unsaturated hydraulic conductivities.

error. The actual value of the hydraulic conductivity should belocated between the upper and lower curves. Figure 2 demonstrates that tensiometer measurement errors can have a large
effect on the calculated hydraulic conductivities, especiallywhen small hydraulic gradients are present.
Another source of error may be due to imprecise estimates ofthe evaporation rate as calculated from the TDR readings. The
influence of this error on the accuracy of the unsaturated hydraulic conductivity was quantified as follows (Stoffregen, 1998):

K(h) 5

2q0 6 dq0
grad H[24]

where dq0 is the measurement error in the calculated evaporation
rate. Equation [24] shows that a relative error in the calculated
flux leads to the same relative error in calculated unsaturated
hydraulic conductivity. The smaller the water content change, thehigher the relative error will be in the evaporative flux, and hence
the higher the errors in the hydraulic conductivity.

RESULTS AND DISCUSSION
Laboratory Measurements
Directly measured and inversely estimated laboratorywater retention and hydraulic conductivity functionsof the peat soil are compared in Fig. 3. Final optimized
parameters obtained from the inverse approach arelisted in Table 1. Since unsaturated hydraulic conductivities were calculated directly at various measurement
locations within the soil core, the analysis leads to several data sets, as shown in Fig. 3. By comparison, theinverse method leads to only one effective conductivity
function for the entire column. Notice the relatively good
agreement in Fig. 3 between the directly and inversely
estimated hydraulic conductivities for pressure heads lessthan 2100 cm. Deviations between the direct and inverse
estimates at the higher pressure heads are most likely due
to the very small pressure head gradients during the earlystages of the experiments (as discussed above). These
small pressure gradients caused relatively high uncertainty in the directly estimated hydraulic conductivities
near saturation (Šimůnek et al., 1998b) (Fig. 2).
Despite the high correlation between the measured
and simulated flow variables (Table 1), much uncertainty was found for the parameters KS and a because

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0.9< 15 cm depth-6
0.5

Direct-1
Direct-2
Direct-3
Inverse-1
Inverse-2
Inverse-3
Fit static WRC
2< 15 cm depth
Volumetric water content

-2

-4

0.7

0.5

0.3

0.1
0.5

3.5

log |h| [cm]

2.0

3.5

log |h| [cm]0.9

15 to 25 cm depth

-2

-4

-6
0.5

Direct-1
Direct-2
Direct-3
Inverse-1
Inverse-2
Inverse-3
Fit static WRC

15 to 25 cm depth
Volumetric water content

log K [cm/d]

0

0.7

0.5

0.3

0.1
0.5

2
3.5
log |h| [cm]2
3.5
log |h| [cm]0.9
22 to 32 cm depth

0

-2

-4

-6
0.5

Direct-1
Direct-2
Direct-3
Inverse-1
Inverse-2
Inverse-3
Fit static WRC
2
3.5
log |h| [cm]Volumetric Water content

22 to 32 cm depth

log K [cm/d]

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

log K [cm/d]

0

0.7

0.5

0.3

0.1
0.5

2
3.5
log |h| [cm]Fig. 3. Hydraulic conductivity (left) and water retention (right) functions for the peat soil as determined in the laboratory (3 replicates for eachhorizon) using inverse parameter estimation and direct methods. Open circles represent directly estimated hydraulic conductivities, squares are
directly measured retention data, u(h); solid lines represent inversely estimated K(h) and u(h) functions; and dashed lines are u(h) functions fitted
to directly measured retention data and K(h) functions predicted from the fitted retention curves and the directly measured KS.

of their considerable mutual correlation (0.959–0.991).
The uncertainties in KS and a were caused mainly bysmall pressure head gradients at the beginning of thetransient evaporation experiment. Our findings are
consistent with those by Romano and Santini (1999),
who performed numerical evaporation experiments
to explore the sensitivity of pressure heads to selectedsoil hydraulic parameters. Romano and Santini (1999)
concluded that measurements of the pressure headlater during the experiments produce steeper hydraulic gradients and hence better identifiable soil hydraulic parameters.
Variability in hydraulic conductivities was found to
be relatively small within each of the three soil layers,
while being in a relatively narrow range at intermediate and high tensions. The K(h) curves of the various
horizons deviated only in the near-saturated region.
Major differences in conductivities among the different

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VADOSE ZONE J., VOL. 5, MAY 2006

Table 1. Inverse parameter estimation results for the laboratory experiments. ‘‘No.’’ indicates replicate number (soil core), while Fh and Fu
are the minimized values of the pressure head and water content terms of the objective function, respectively.†
Depth

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

cm
,15

No.

rb‡

Peat type

23

15–25

1
2
3
1

22–32

2
3
1

X§

very humified

g cm
0.312

%
77

very humified

0.371

76

humified

0.386

77

Characteristic of horizon

Fh

Fu

2

R

us

a

n

KS

21

crumb or fine subangular structure
crumb or fine subangular structure,compacted
crumb or fine subangular structure,compacted

2321

5.6e-25.0e-2
1.4e-24.3e-34.4e-45.9e-42.0e-24.5e-3

0.98
0.99
0.99
0.99

0.880
0.802
0.796
0.730

cm
0.026
0.020
0.0094
0.012

1.19
1.23
1.23
1.12

cm d
33.5
14.0
4.17
3.78

2.7e-2
1.3e-2
1.1e-22.7e-37.e-6
9.0e-5

0.99
0.99
0.99

0.730
0.744
0.684

0.013
0.015
0.0021

1.12
1.11
1.48

6.69
6.65
0.041

1.4e-2
1.6e-22.3e-55.5e-5

0.99
0.99

0.790
0.741

0.00250.0051

1.26
1.15

0.25
0.92

† For all cases uR 5 0.0 and l 5 0.5.
‡ rb, bulk density.
§ X, ignition loss.

horizons occurred for pressure heads larger than about2100 cm. Unsaturated hydraulic conductivities nearsaturation decreased with increasing depth. Conductivities of the third horizon were up to an order ofmagnitude smaller than those of the first horizon. Thismay have been due to the use of heavy machinery
during tillage, leading to compaction of layers below theroot zone, as well as due to natural peat compression
often observed for peat soil profiles (e.g., Price, 2003).
Figure 3 shows that the reduced unsaturated hydraulicconductivities correspond with lower saturated watercontents and that the compacted subsurface layers
exhibit more variability in both u(h) and K(h). Figure 3
also shows that soil compaction affects the shape ofthe soil water retention curve (WRC), with the measured curve acquiring a bimodal-type distribution especially at the 15- to 25-cm soil layer. The retention
curve of this layer could not be described with the standard VGM model.
Results in the right column of Fig. 3 also show thatwithin the measurement range of the tensiometers, retention data points obtained from the steady-state measurements agree reasonably well with retention curves
obtained using the inverse parameter estimation technique. However, differences between the directly measured retention data and inversely estimated retention
curves increased substantially at lower water contents.
Extrapolation of the optimized WRCs beyond the measurement range covered by the experiment hence produced, as expected, a high level of uncertainty. Some
overestimation of the directly measured retention data
at lower pressure heads may have been caused by shrinkage during dewatering of the peat soil. Schwärzel et al.
(2002) compared WRCs of slightly decomposed peatsoils with and without considering shrinkage. They
found substantially higher volumetric water contents atlow (more negative) pressure heads when shrinkage wastaken into account.
The independently measured retention data points
fitted with the van Genuchten (1980) analytical modeland the KS value measured in the laboratory with theconstant head method were used to predict the unsaturated hydraulic conductivity function (Fig. 3). Even
though the shapes of the K(h) curves were quite similar,
the predicted K(h) curves (dashed lines in Fig. 3) did notcorrespond well with the other (direct and inverse) results, mostly because of a KS value that was too high.
Good agreement between measured and estimated hydraulic conductivity curves was found only for the
top layer.
The VGM parameters listed in Table 1 differ fromthose of Weiss et al. (1998) and Naasz et al. (2005). Thisis due to the fact that our peat soils were much more
influenced by drainage processes, and hence pedogenetic changes, than the peat material of the other studies.

Field Measurements
Only very small changes in pressure heads and watercontents were recorded during the later stages of theevaporation experiment for the bare lysimeter (see also
Schwärzel and Bohl, 2003). The topsoil layer at that time
was air dry with a very low hydraulic conductivity, which
prevented further evaporation. Actual soil evaporation
rates were calculated from weekly measured water content values. While pressure heads were measured
hourly, only daily averages were used in the inverse parameter optimization. Figure 4 shows that the measured
pressure heads and water contents of the bare lysimeters
decreased substantially only in the upper parts of the
profile in 1994 (top plots). Similar results were also
found for 1995 (not shown).
The evaporation experiments of the bare lysimeter
were first analyzed using the direct approach. Because
water contents varied very little, we could only calculate
unsaturated hydraulic conductivities of the first two
major soil horizons between 10 and 20 cm and between
20 and 30 cm. For 1994 and 1995 we obtained 61 and 54
K(h) data pairs, respectively (Fig. 5). Because of verysmall hydraulic gradients and flow rates, the calculated
values are quite scattered, causing much uncertainty inthe directly determined K(h) data.
To obtain more information about the hydraulicproperties in the dry range, we used another lysimetercovered with vegetation. This lysimeter was operated
during the unusually dry summer of 1994. Although at
the beginning of the experiment the groundwater levelin the lysimeter was 60 cm below the soil surface, after
2 wk the lysimeter was already without groundwater(below the measurement depth) because of the highReproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

www.vadosezonejournal.org

635

Fig. 4. Measured (open circles) and fitted (dashed lines) pressure heads (left) and water contents (right) for the lysimeter experiments without (top)and with (bottom) plants.

evaporative demand. Figure 4 (bottom plots) shows thatthe decrease in pressure heads and water contents, especially in the two surface layers, was much more significant than for the bare lysimeter. The experiment withvegetation produced three weekly measured evapotranspiration rates that were scaled to 22 daily values
using the calculated potential evapotranspiration, 24
water content values (again measured weekly), and 150
pressure head values (measured hourly and used asdaily averages in numerical inversions) for use with theinverse method.
We next used inverse methods to determine the soil
hydraulic parameters from both the bare and vegetatedlysimeters. The soil profile in the numerical calculations
was for this purpose divided into two different soil layers(0–30 cm and below 30 cm). A zero flux condition was
imposed at the bottom of the soil profile in all cases.
Measured evaporation fluxes were used as the upperboundary condition for the bare lysimeter, while evaporation from the lysimeters with plants was considered
to be negligible because of the presence of complete
plant cover. For the lysimeters with plants, root water
uptake was calculated from weekly measured evapotranspiration rates, which were scaled to daily values
using calculated daily grass reference evaporation rates(Allen et al., 1994). The initial condition was given interms of measured pressure heads for all runs.
The VGM soil hydraulic parameters of the two soil
horizons were fitted simultaneously to all available data.
The residual water content uR and the pore-connectivity
exponent l in Eq. [8] were fixed at zero and 0.5, respectively. Hence, only eight parameters were optimized
simultaneously for the two horizons. Three sets of initial
estimates of the parameters were used to identify the
global minimum.
Figure 4 compares measured and fitted tensiometer
and TDR readings for the lysimeters with and without plants. We obtained an excellent fit of the tensiometer readings in both cases and for all depths.
Deviations between measured and fitted TDR readings were somewhat higher, especially at depths of 10
and 20 cm, for the plant-covered lysimeter. Notice thatthe measured water contents at the 10-cm depth wereslightly overestimated and at the 20-cm depth underestimated. We believe that these deviations were most
likely due to the use of a simplified potential root water
uptake distribution function with a constant rooting
depth of 30 cm. A better fit to the measured watercontents may have been possible using a root uptake
function that accounts for root growth into the subsoil

636

VADOSE ZONE J., VOL. 5, MAY 2006

Table 2. Parameter estimation results obtained with three different initial estimates of the optimized parameters (Runs 1–3) for the field
lysimeter experiments in 1994 and 1995 with and without plants. Fh and Fu are the minimized values of the pressure head and watercontent terms of the objective function, respectively.
Year

1994
1995
1994
1994
1995

1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3

Comment

DepthWith plants

cm
10–30

Without plants

10–30

Without plants

10–30

With plants.30

Without plants.30

Without plants

.30

Fh

Fu

R

2

us

a

n

KS

0.99
0.98

0.783
0.789

cm
0.015
0.0088

1.17
1.24

cm d
0.83
0.001

0.97
0.97
0.95
0.99
0.99
0.99
0.99
0.98

0.762
0.762
0.765
0.749
0.749
0.749
0.850
0.839

0.00560.00560.013
0.00540.00540.00540.018
0.0042

1.31
1.31
1.13
1.42
1.43
1.42
1.11
1.56

0.10
0.10
0.74
0.10
0.10
0.10
13.7
0.08

0.97
0.97
0.95
0.99
0.99
0.99

0.780
0.780
0.779
0.765
0.765
0.765

0.00770.00740.014
0.00160.00120.0023

2.47
2.36
5.00
1.73
1.39
1.07

0.00590.0063
55.5
0.015
0.025
0.530

21

1.28e-2
8.24e-2
3.29e-2
1.00e-1
No successful run
5.70e-2
1.92e-2
5.69e-2
1.93e-2
9.74e-2
1.62e-2
1.63e-2
8.54e-2
1.59e-2
8.81e-2
1.81e-2
8.81e-2
2.88e-2
7.64e-2
3.29e-2
1.00e-1
No successful run
5.70e-2
1.92e-2
5.69e-2
1.93e-2
9.74e-2
1.62e-2
1.63e-2
8.54e-2
1.59e-2
8.81e-2
1.81e-2
8.81e-2

21† Different initial parameter values. For all cases uR 5 0.0 and l 5 0.5.

20Direct-94-without plants
Direct-95-without plants
Inverse-94-without plants
Inverse-95-without plants
Inverse-under grass-2-4
10 to 30 cm depth
-6
0.5
2
3.5
log |h| [cm]optimized parameters, which suggests that local minima were present in the objective function F (Table 2).
This difficulty occurred for both 1994 and 1995. These
relatively poor results reflect the fact that soil moisture variations in the subsoil were very small and hence
did not provide enough resolution to permit a uniqueparameter optimization process. The parameter n, in particular, produced a wide range of values when different
sets of initial parameter values were used. As opposedto the topsoil, estimated parameters for the subsoil were
only weakly correlated to each other. The large confidence intervals of the estimated parameters indicate thatthe optimized parameters are highly uncertain (data notshown). Despite the large confidence intervals for thesoil hydraulic parameters of the bare lysimeter, differences between the unsaturated hydraulic conductivity
functions obtained from the different experiments wererelatively small. This is shown in Fig. 5, which compares
the hydraulic conductivity and water retention functionsof the topsoil for all successful optimizations.
Tables 1 and 2 indicate relatively good agreement between the laboratory and field estimates of the param0.9
10 to 30 cm depth

0.7
Water content [-]and increased root intensity in the topsoil. We did not
pursue this possibility because of a lack of independent
root growth data.
Final results of the parameter optimization for bothlysimeters and both years are presented in Table 2. The
different sets of initial parameter estimates always generated the same set of optimized parameters for the topsoil of the bare lysimeter. Also, only small differenceswere found between the parameter values of the barelysimeter for years 1994 and 1995. Despite the good fitof data and the small differences between parametervalues for years 1994 and 1995, we found a high levelof uncertainty for the parameters of the bare lysimeter.
We always obtained strong correlations between theparameters n and a (20.990 to 20.992), n and KS(20.989 to 20.992), and a and KS (0.990–0.992). Thesestrong correlations are a consequence of the much narrower range of measured pressure heads and watercontents and suggest that the parameters a, n, and KS
should not be identified simultaneously in such cases.
The inverse simulations for the subsoil of the lysimeter without plants did not always converge to the samelog K [cm/d]

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

1994

Run†

0.5

0.3

0.1
0.5

2
3.5
log |h| [cm]Fig. 5. Hydraulic conductivity (left) and water retention (right) functions of the peat soil as determined from the lysimeter experiments using inverse
parameter estimation and direct methods.

637

www.vadosezonejournal.org

Table 3. Various scenarios and associated parameter sets used in forward calculations of the additional field lysimeter experiment withvegetation.†
Scenario

Comment

Field

m
,30
.30
,20
20–25
25–30
.30‡
,20
20–25
25–30
.30‡
,20
20–25
25–30
.30‡
,20
20–25
25–30
.30‡

parameters obtained from the lysimeter
experiment with plant coverparameters obtained from different laboratory
evaporation experiments

Lab 1

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

Depth

Lab 2

parameters obtained from different laboratory
evaporation experiments

Lab 3parameter obtained from different laboratory
evaporation evaporation experiments

WRCparameters obtained by fitting the measured
water retention curve

us

a

n

KS

1.17
1.11
1.19
1.12
1.48
1.16
1.23
1.11
1.26
1.16
1.23
1.11
1.15
1.16
1.14
1.25
1.16
1.26

cm d
0.83
13.7
33.5
3.78
0.04
104
14.0
6.69
0.25
104
4.17
6.65
0.92
104
25.0
15.0
15.0
40.0

21

21

cm
0.015
0.018
0.026
0.012
0.00210.00320.020
0.013
0.00310.00320.00940.015
0.00510.00320.025
0.00190.00570.0048

0.783
0.850
0.880
0.730
0.684
0.891
0.797
0.730
0.794
0.891
0.796
0.744
0.741
0.891
0.816
0.698
0.767
0.831

† For all cases uR 5 0.0 and l 5 0.5.
‡ Data from Bohl et al. (1994) for weakly humified peat.

eters a and n. However, the saturated hydraulic conductivity, KS, estimated from the field data differed significantly from the laboratory estimates. This is attributed
to the very narrow range of the field data as comparedto the laboratory data, particularly a lack of information to define the field hydraulic properties at ornear saturation.
For the plant-covered lysimeter, a minimum in theobjective function was found only when prior information about several subsoil parameters, estimated from theindependent laboratory water retention measurements
and from field borehole tests (Bohl et al., 1994), wasincorporated into the optimization process (Table 2).
One reason for this is the fact that the soil was alreadyslightly unsaturated at the beginning of the experiment,
and hence little or no information was available about thenear-saturated hydraulic properties. Consequently, theglobal minimum of the objective function was difficult or
impossible to locate when different initial parametervalues were used. Our findings are consistent with thoseof Russo et al. (1991), who reported that uniqueness andstability of the inverse solution often depend on thequality of prior information about the model parameters.
Sonnleitner et al. (2003) similarly found ill-defined
hydraulic properties close to saturation when full saturation was not reached at the beginning of their lysimeter experiments.
In contrast to the hydraulic conductivity functions, thewater retention functions obtained from the different
lysimeter experiments were similar only within the measurement range (Fig. 5). With increasing pressure heads,

differences between the different retention functions
increased significantly. This shows that the optimized
soil hydraulic functions should be used only for the conditions and measurement range of the experiment. Extrapolation of results, especially toward lower pressure
heads (drier conditions), could quickly lead to incorrect predictions.
Contrary to the transient evaporation experiments
conducted in the laboratory, application of the inverse
method to the transient field evaporation data was subject to several experimental difficulties. Nonuniquenessand nonidentifiability problems were especially evident
for the evaporation experiment performed on the barelysimeter. This was primarily due to the limited range inthe experimental pressure head and water content data.
Soil moisture and pressure head variations were simply
too small to produce a well-defined global minimum inthe objective function (Fig. 4).
An important source of error in field studies may
result when the evaporation flux is estimated from TDR
readings. Flow rates calculated from the water content
data of the bare lysimeter were very small and wellwithin the range of the measurement precision of the
TDR probes (Fig. 4). Romano and Santini (1999) performed numerical evaporation experiments to explore
the influence of the imposed evaporation rate on illposedness of the inverse problem. They suggested thatthe inverse method for fine-textured soils subject tohigher evaporation rates might experience problems of
ill-posedness. For coarse-textured soils higher evaporation rates did lead to better identifiability of the un-

Table 4. The RMSE values in percentage of observed versus predicted pressure heads at different depths for the various forward simulations listed in Table 3.

Table 5. The RMSE values in percentage of observed versus predicted water contents at different depths for the various forward simulations listed in Table 3.

Depth

WRC

Depth

52
44
133
302

cm
10
20
30
40

cm
10
20
30
40

Field
26
32
13
17

Lab 1

Lab 2

49
118
54
18

%
10
67
29
29

Lab 3
49
95
36
36

Field
14
15
5
2

Lab 1

Lab 2

Lab 3

WRC

15
14
14
5

%
9
12
1
5

14
13
8
5

37
9
10
9

638

VADOSE ZONE J., VOL. 5, MAY 2006

Water content [m3 m-3]

0.9

-h [cm]

10

0.5

0.3
10 cm depth
0.1

0

7

14
21
Time [d]

28

0

7

14
21
Time [d]1020 cm depth
028

20 cm depth

0.9
Water content [m3 m-3]

-h [cm]

1000

0.7

0.5

0.3

Obs
Lab 1
Lab 3

Field
Lab 2
WRC

0.1
0

7

14
21
Time [d]

0

28

1000

7

14
21
Time [d]1030 cm depth
028

30 cm depth

0.9
Water content [m3 m-3]

-h [cm]

Field
Lab 2
WRC

0.7

10 cm depth
0

0.7

0.5

0.3

Obs
Lab 1
Lab 3

Field
Lab 2
WRC

0.1
0

7

14
21
Time [d]

28

0

1000

7

14
21
Time [d]1040 cm depth
0
0

7

14
21
Time [d]2828

40 cm depth

1.1
Water content [m3 m-3]

-h [cm]Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

1000

Obs
Lab 1
Lab 3

0.9
0.7
0.5
Obs
Lab 1
Lab 3

0.3
0.1

0

7

14
21
Time [d]

Field
Lab 2
WRC
28

Fig. 6. Observed (circles) and predicted (lines) pressure heads (left) and water contents (right) for the additional evaporation experiment using alysimeter with plants. The different simulation scenarios are explained in Table 3.

known parameters. Peat soils behave more similarly tocoarse- rather than to fine-textured soils. Higher evaporation rates hence should produce a wider range inwater contents and pressure heads. The wider measurement range can be achieved also when the lysimeteris covered with grass. However, to find the global

639

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www.vadosezonejournal.org

minimum of the objective function, prior information forthe subsoil still needed to be incorporated in the objective function. A well-defined global minimum without
prior information is much more likely when the watercontent data show more resolution, especially in the
topsoil. Figure 4 illustrates that much more water is lostto evaporation from the upper part of the soil profile,with soil water depletion being very low deeper inthe profile. Additional TDR probes in the upper part ofthe profile hence would have provided more useful
information for the inverse estimation procedure. This
would have enabled better definition of the evaporation
rate needed as an upper boundary condition for the inverse simulations.

Forward Predictions
The accuracy of the estimated hydraulic parameters
was tested by simulating pressure heads and water contents at different depths for a second plant-covered
lysimeter during an extended drying period. The groundwater level in the lysimeter for this experiment was adjusted to the water table of the surrounding area. Within
28 d of the experiment the groundwater level had declined from 30 to 70 cm below the soil surface. Water
contents during the experiment at the 10-cm depth
decreased from 0.70 to 0.29, at the 30-cm depth from0.80 to 0.75, and at the 60-cm depth from 0.87 to 0.83.
Pressure heads similarly decreased from 220 to below
2700 cm at the 10-cm depth (i.e., below the measurement limit of the tensiometers), and from 32 to 212 cm
at the 60-cm depth. Forward simulations were conducted with both the directly determined and inversely
estimated soil hydraulic parameter sets. Table 3 gives
details about the different simulation scenarios andinvoked parameter sets.
Tables 4 and 5 summarize the RMSE between predicted and observed variables for different scenarios.
Figure 6 presents time series of simulated and measured
pressure head and water content values. Simulations
with parameter values obtained from the various inverse
estimates reproduced the measured pressure heads
reasonably well. Relatively large differences between
observed and predicted values were found only for the
20-cm depth. Inspection of Fig. 6 shows that the WRCparameter set (Table 3) produced substantially lower(negative) pressure heads than the 30- and 40-cm depth
data, and much higher water contents than the 10-cm
depth data when the peat soil dried out. The RMSE for
the WRC set was in most cases the highest as comparedwith the other scenarios (Table 4), except for the depthof 20 cm. The best agreement between measured andpredicted pressure heads at all depths was found withthe parameter set determined under field conditions(see “Field” in Tables 4 and 5).
The hydraulic properties for the Lab 1, Lab 2, andLab 3 scenarios were obtained from transient laboratory
measurements with three replicates. Only minor differences between predicted pressure heads were observed
when different laboratory parameter values were used.
An exception is the 20-cm depth, where the simulatedpressure heads for the three scenarios diverged morefrom the data than at other depths. This is mostly likely
due to the variability in the hydraulic properties of theunderlying layer (Fig. 3, 22–32 cm).
Simulations with different parameter sets also matched
the dynamics of water contents reasonably well, especially for the 10-cm depth. Only the WRC scenario forthe 10-cm depth showed relatively large deviations during the drier conditions, while the other parameter sets
closely matched the drying process. Large differences
between observed and predicted water content values
were found only at the 20-cm depth. The poor agreement between the predicted and observed water contents at the 20-cm depth could have been due to the useof inaccurate root distribution and/or root growth functions. In general, simulations with different parameter
sets led to similar values of the water content. Table 5shows that the RMSE values were about the same for allcases and all depths.

CONCLUSIONSInverse analysis of the unsaturated hydraulic parameters of the peat soils using both field and laboratory
experiments produced reliable results. Compared withthe field, measurements in the laboratory allowed forquicker and more cost-effective estimation of the soil
hydraulic properties across a much wider range of soil
water contents. Considerable parameter uncertainty forthe bare field lysimeters was due to the narrow range insoil moisture conditions of that lysimeter. This uncertainty was reduced substantially by using a vegetative
cover to produce a much broader range of pressure
heads and water contents. Prediction of the unsaturated
hydraulic conductivity function from retention data andthe saturated hydraulic conductivity, KS, produced
unsatisfactory results, mostly because of estimates ofKS that were too high.
The accuracy of the estimated hydraulic functions was
further tested by comparing forward predictions using
data from an additional evapotranspiration experimenton a different lysimeter. The dynamics of the drying process were very well described using hydraulic properties determined from the transient field and laboratory
experiments. In contrast, predictions obtained from measured retention data and KS overestimated the drying process. Our results showed only little difference
between the laboratory and field data. Hence, for peatsoils of the type used in our study we recommend measurements of the unsaturated hydraulic conductivity
in the laboratory in combination with inverse parameter optimization.
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