Comparing Two Approaches of Characterizing Soil Map Unit Behaviorin Solute Transport

P. A. Finke,* J. H. M. Wosten, and J. G. Kroes

ABSTRACTSoil maps can be used in different ways to characterize spatial

patterns of soil behavior. A first approach is to establish the behaviorof a pedogenetically representative profile from each soil map unit(SMU); a second is to subsample each SMU and select from the samplea characteristic profile by its behavior with respect to water and solutetransport. The first approach was tested against the second withdata from a SMU in the Netherlands. The use of pedogeneticallyrepresentative profiles resulted in biased estimations of five studiedfunctional properties related to water and solute transport. Theseproperties were (i) the number of days with good workability; (ii) thenumber of days with sufficient aeration; (iii) the elapsed time to 10%breakthrough of an inert tracer (Cl~); (iv) the percentage break-through after 1 yr of an adsorbing, inert contaminant (Cd); (v) thepercentage breakthrough after 1 yr of an adsorbing, degrading herbi-cide (isoproturon [N-(4-isopropylphenyl)-N', N'-dimethylurea]). Soilprofiles that did not fit the definition of the SMU (impurities) wereresponsible for the occurrence of extreme values for four out of fiveproperties, which implies that impurities must be sampled when riskassessments have to be made. In this case, probability sampling offersa valid approach.

SOIL MAPS are increasingly used to obtain an impressionof the spatial patterns of soil behavior (Breeuwsma

et al., 1986; Bregt and Beemster, 1989). Usually, thebehavior of a RP is established and attached to the corre-sponding SMU (e.g., Van Lanen et al., 1992). The underly-ing assumption in this type of study is that the RP, usuallydefined by a soil surveyor from a pedogenetic standpoint,shows a representative, typical behavior for the SMU.An instrument frequently used to establish the behaviorof a soil profile is a simulation model. Since simulationmodels are usually nonlinear in their response to valuesof soil characteristics, an average profile may not showaverage behavior at all. The RP approach is disputablealso when the vulnerability of a SMU to an environmentalhazard, say pesticide leaching, is to be established. Theuse of only a RP gives no information on the variabilitywithin SMUs, which may have consequences when mak-ing risk assessments, in which case one is not so muchinterested in average behavior but in the occurrence ofextreme values. Also, the RP approach will only describesoil behavior in the pure part of the SMU, i.e., the partwhere the soils meet the definition of the SMU withrespect to dominant subgroup and inclusions. This isusually not the case everywhere in the SMU (e.g., Mars-man and De Gruijter, 1986; Foussereau et al., 1993).The consequence is that an impure part of the SMU,which may have an altogether different vulnerability, isignored completely in the analysis. Taking into accountthe variability within a SMU, inclusive of impurities,

DLO Winand Staring Centre for Integrated Land, Soil and Water Research(SC-DLO), P.O. Box 125, NL-6700 AC Wageningen, the Netherlands.Received 8 Apr. 1994. "Corresponding author (p.a.finke@sc.agro.nl).

Published in Soil Sci. Soc. Am. J. 60:200-205 (1996).

would thus seem a better approach. This can be achievedby using randomly sampled profile descriptions from theSMU to characterize the SMU.

This study aims at a comparison of the RP and therandomly sampled profiles approaches. The behavior ofan SMU in the Netherlands was evaluated, with twosimulation models to calculate five properties related towater and solute transport. A period of 18 mo wassimulated between 1 Oct. 1979 and 1 Apr. 1981. Theyear 1980 was chosen because the analysis should bevalid for meteorological circumstances that are commonin the Netherlands, and 1980 is a median year for itsprecipitation surplus. The studied properties were (i) thenumber of days the soil had a good workability, assessedby the number of days between 15 Mar. and 15 Maywhere the pressure at 5 cm depth is < -7.0 MPa;(ii) the number of days the soil had sufficient aeration,assessed by the number of days in the same period withan air-filled porosity at 5-cm depth >0.1 m3 m~3; (iii)the elapsed time to 10% breakthrough of an inert tracer(Cl~); (iv) the percentage breakthrough after 1 yr of anadsorbing, inert contaminant (Cd); (v) the percentagebreakthrough after 1 yr of an adsorbing, degrading herbi-cide (isoproturon).

Properties (iii) to (v) apply to a plane at 40-cm depth,below which solutes are considered lost for plant uptake.Two options of characterizing SMU behavior were com-pared: First, by using the available RP, second by usinga number of profiles located in the SMU accordingto a statistical sampling design. The purpose of thecomparison was to determine if it is necessary to imple-ment the second, more costly option. Furthermore, amethod will be presented to select profiles with a behaviorcharacteristic of the SMU and its internal variability.

MATERIALS AND METHODSSoils and Soil Sampling

The study focused on an SMU in the northeastern part ofthe Netherlands on the 1:50000 soil map (Fig. 1). The SMUHn21-V/V*, occupying 115 km2, is denned as field Podsolsoils in sand and loamy sand. This definition includes sandy,siliceous, mesic Aquic Haplorthods, some Typic Placorthods,and some Histic Endoaquods (Soil Survey Staff, 1994). Thegroundwater regime is described by a MHW shallower than40 cm and a MLW deeper than 120 cm. During the soilsurveys, a RP fitting the definition of the SMU was selectedon each of three different map sheets by an experienced soilsurveyor (RP set). These profiles were sampled and described

Abbreviations: SMU, soil map unit; MHW, mean highest water table,the mean value of the highest three measured values of the water tablein 1 yr, averaged across at least 8 yr; MLW, mean lowest water table,the mean value of the lowest three measured values of the water table in1 yr, averaged across at least 8 yr; STS, stratified two-stage sampling;OM, organic matter; M50, median of the sand fraction; RP, representativeprofile; SEM, standard error of the mean.

200

FINKE ET AL.: SOIL MAP UNIT BEHAVIOR CHARACTERIZATION IN SOLUTE TRANSPORT 201

equation written in terms of soil water pressure head h (Eq. [1])by explicit linearization with the so-called Thomas algorithm:

\ Unpublished map sheet

Sampling stratum

0 20 40 60 80 100km

Fig. 1. Location of sampling strata in the Netherlands.

It""" Sampling stratum withrepresentative profile

to characterize the SMU as it occurs in these map sheets, soeach RP is intended to be valid for one map sheet only.

Currently, a nationwide soil sampling program is in progressin the Netherlands to upgrade the SMUs of the nationwide1:50 000 soil map by determining spatial distribution parame-ters of several soil characteristics in the SMU. The data setanalyzed in this study is connected to the first SMU sampledin this program. This data set was obtained following a stratifiedtwo-stage random sampling design (Cochran, 1977). Elevenmap sheets, some of them extended for practical purposes withadjoining areas in which the SMU occurs (Fig. 1), served assampling strata. In each stratum, two map polygons belongingto the SMU were drawn at random with replacement, wherethe drawing probability of a polygon was proportional to itsacreage. In each polygon, four sampling locations were allo-cated randomly. The resulting data set, referred to as the STSset comprised (11 X 2 X 4) 88 profile descriptions. Becauseof the design, distribution parameters such as mean, standarddeviation, and percentiles of any measured soil characteristicand the acreage occupied by map impurities could be estimatedeasily and with quantified precision.

Soil data available were profile descriptions consisting ofgeneral characteristics such as rootable depth, MHW andMLW, and for each soil horizon, its depths, clay content,(clay + silt) content, OM content, and the median of the sandfraction (M50). All soil characteristics were field estimatescorrected by a regression equation that was fitted on a dataset with both estimated and analyzed values. The MHW andMLW were estimated in two steps. First, a regression was donebetween the MHW (and MLW) and the depth to groundwater ona certain day t in piezometers. These piezometers had beensampled biweekly for a period of more than 8 yr prior to1980, which is necessary to calculate the MHW and MLW(see the definition). Second, the regression equation was appliedto the measured depth to groundwater on day t at each of thedescribed soil profiles.

Simulation Models and Needed DataWater flow was simulated with the SWACROP model (Fed-

des et al., 1988). The SWACROP model solves the Richard's

dhdt W(h) [1]

where W = differential soil water capacity dQ/dh (cm2 cm"3),6 is volumetric water content (cm3 cm'3), t = time (d), h =soil water pressure head (cm), z = depth (cm), K = hydraulicconductivity (cm d"1), 5 = sink term representing water lostby transpiration (cm3 cm"3 d"1).

In this study, a bare soil is assumed, so S = 0. The requiredfunctions between K, 0, and h were described by the closedform equations from van Genuchten (1980). Output of thismodel comprises, for example, water balances at small timeintervals (usually 1 d) for each soil compartment of 0.05-mthickness.

Transport of solutes was simulated with the TRANSOLmodel (Rijtema and Kroes, 1991). The water balances forchosen time and depth intervals, as computed by SWACROP,were used for the water • quality calculations. The generaladvection-dispersion transport equation describing one-dimensional, nonsteady water and solute flow is

dQ+ Pb —— =dt dt

- it.OC [2]

where pb = soil dry bulk density (kg m"3), q = volumetricwater flux (m3 d"1), <?t = volumetric transpiration flux (m3

d~') ,D = apparent diffusion coefficient (m2d~'), 2 = adsorbedconcentration (kg kg"1), C = concentration in solution (kgm"3), 8 = selectivity-constant for crop uptake (kg m"3 d"1),and ki = transformation rate (d"1).

In the TRANSOL model, Eq. [2] was solved for finitecompartments with thickness L and assuming complete mixingin each identified soil compartment. Discretization of the spatialterms to finite differences according to a backward calculationscheme yields the following differential equation:

dt

where n = compartment number (—) , 9n(?) = volumetricwater content in compartment n at time t (m3 m"3), Cn-i(f) =average concentration in compartment n — I during timestept (kg m~3), Cn(f) = concentration in compartment n at time t(kg m"3), Qn(t) ^quantity adsorbed in compartment n at timet (kg kg"1), 2^Cn-i(0 = total incoming mass flow of solute(kg m"2 d"1), XfFoC.JX) = total outgoing mass flow of solute(kg m"2 d"1), T = transpiration water flux density (m3 m~2

d"1), k\<a — transformation rate for the amount adsorbed (d"1),ki.i, = transformation rate for the amount of solute (d"1), andL = compartment thickness (m).

Equation [3] was solved analytically for each time step andeach compartment. The calculation procedure followed thedirection of the water flow with the concentration of the incom-ing flux (F{) as input. Physical diffusion and dispersion werenot simulated through the input of a dispersion length but byusing compartment thicknesses to set numerical dispersionaccording to Ldis = 0.5L, where Ldis is the dispersion length (m).The transformation of a solute was described as a first-orderprocess. The transformation rates (Jki,a, k\j,) were calculatedas a function of temperature, depth, and moisture content. The

202 SOIL SCI. SOC. AM. J., VOL. 60, JANUARY-FEBRUARY 1996

250

50 100 150Measured depth to water table (cm)

200 250

Fig. 2. Relation between measured and estimated depths to watertable between 1 Oct. 1979 and 1 Apr. 1981 at five locations in thestudy area.

adsorbed amount of solute (Q) depends on the concentrationin solution according to linear sorption or a Freundlich iso-therm. In this case, Freundlich sorption was used for isopro-turon and a modified Freundlich sorption, including the effectof pH (Van der Zee and Van Riemsdijk, 1987; Boekhold andVan der Zee, 1992), was used for Cd.

Model input data needs can be divided into two parts: profileproperties and boundary conditions. In the present study, profileproperties needed by the models comprise the starting andending depths of soil horizons and a number of physical andchemical properties of each horizon. Physical properties arethe values of the dry bulk density for TRANSOL and of the vanGenuchten parameters for SWACROP. Recently, nonlinearregression functions were established and parameterized forsoils in the Netherlands (Wosten et al., 1995) to estimate thevalues of the van Genuchten parameters from clay content,(clay + silt) content, OM, M50, bulk density, and the qualita-tive variable topsoil or subsoil. The resulting functions, calledcontinuous pedotransfer functions in the terminology of Boumaand Van Lanen (1987), were applied in this study. Dry bulkdensities were estimated with linear regression functions be-tween type of horizon and OM as established by Krabbenborget al. (1983). Chemical properties needed by the TRANSOLmodel are the organic matter fraction, the pH (estimated fromtype of soil horizon), and sorption and decomposition parame-ters. Sorption parameters (Raman and Reddy, 1987; Boekholdand Van der Zee, 1992) and decomposition parameters (Blairet al., 1990) were derived from the literature.

Boundary conditions for SWACROP were daily values ofpotential evapotranspiration, precipitation, and water tabledepth. Potential evapotranspiration and precipitation were mea-sured daily at a weather station in the central part of the studyarea. A biweekly value of the water table depth at each locationwas estimated with the MHW, the MLW, and a measuredvalue from a characteristic time series. This relation has thegeneral form

where Dxo,t = depth to the water table at location jcO and timet and DXJ = measured depth to water table at time t andlocation x.

The quality of this relation was tested with five measuredtime series in the study area. Daily values were derived byinterpolation from biweekly values. Chemical upper boundaryconditions for TRANSOL were satisfied by surface applicationsat the first simulation day of Cr (1.0 kg ha"1), Cd (0.3 kg ha"1),and isoproturon (1.5 kg ha"1). The Cd dosage corresponds toreported annual deposition levels in industrialized areas in theNetherlands, and the isoproturon dosage is recommended bythe manufacturer. Initial concentrations were set to 0.

Statistical MethodsOne research question was, "Can the RP data set provide

an accurate estimate of the mean (of a simulated soil property)for the SMU or is there a significant bias?" We assumed thatany soil surveyor would have chosen the same RPs in theinvestigated strata, so the RP data set is treated as not uncertain.The STS data set was used as a test set. For each stratumwhere both one RP and eight STS profiles were available, wecalculated the difference between the RP model result and theSTS model results. When the RP data set gives an unbiasedestimate for the stratum mean, the mean difference in thisstratum will not differ significantly from 0. We repeated thisapproach for all strata and combined strata results, weightingfor the acreage of each stratum, to calculate the bias for theSMU. We tested the significance of the bias with the one-sampleMest, adjusted for the specific sampling design used. First,the mean difference is estimated by

L

y = S Whyh/!=!

[5]

where Wh = AhIA, the relative acreage of stratum h, Ah =acreage stratum h, A = acreage of all strata, yh = mean

Table 1. Simulation results. Range and distribution characteristics for stratified two-stage sampling (STS) data set and values forrepresentative profile (RP) data set.

Dataset

STSSTSSTSSTSSTS

RPRPRPRPRP

Number of

Variable

workabilityaerationCl~ breakthroughCd breakthroughisoproturon

breakthroughworkabilityaerationCl" breakthroughCd breakthroughisoproturon

breakthrough

Unit

dddlog (%)

log (%)dddlog (%)

log (%)

Strata11111111

113333

3

Samples

88888888

883333

3

Min.

310

36-9.85

-5.70

ValueMax.

626275

-2.69

1.45

Mean

585441

-5.98

-3.47

SEMt

1210.12

0.06

Value 1

590

39-6.50

-4.22

Value 2

575043

-6.99

-4.40

Value 3

610

42-8.10

-5.00

t SEM = standard error of the mean.

FINKE ET AL.: SOIL MAP UNIT BEHAVIOR CHARACTERIZATION IN SOLUTE TRANSPORT 203

difference in stratum h,L = number of strata where both STSand RP data were sampled (L = 3).

Second, the variance s2(y) of the estimatory is calculated from

Wlsl[6]

where nh is the number of drawn polygons in stratum h(nh =2) and si is the sample variance between polygon means instratum h, calculated by

(ya, -MA - 1

[7]

If |y| > t-s(y), where l is the critical value for the f-testat a certain confidence, then it is concluded that the RP dataset yields a biased estimate of average SMU behavior.

To enable the identification of the role of map impuritieson the distributions of model outcomes, empirical distributionsof each simulated soil property Z for the SMU were constructedin five steps: (i) a sequence of 500 cutoff values Zc at regularintervals is defined, which covers the full range of the 88observed values of Z; (ii) an indicator variable 7C is defined,which yields the value 1 if the soil property Z < z,, and 0otherwise; (iii) the SMU mean of Ic is estimated for each cutoffvalue Zc. This SMU mean, calculated with Eq. [5] where y isreplaced by Ic, is equal to both the area fraction of the SMUand the cumulative probability for which Z < Zc', (iv) an

70

60

50

I4 0

caCD< 30

20

10

0

70

60

50

I 40

coflj< 30

20

10

0

I I puregroundwater regime impuresoil impure

30 35 40 45 50 55 60 65Workable days

I I pureIHJgroundwater regime impure^3 soil impure

35 40 45 50 55 60 65 70 75Days until 10% chloride breakthrough

60

SO

40

go 30oj

20

10

0

60

50

40

1a 302?

20

10

0

I I pure- [HIgroundwater regime impure

§3 soil impure

0 10 20 30 40 50 60 70Days with good aeration

HU groundwater regime impure[§2j soil impure

-10 -9 -8 -7 -6 -5 -4log (Cadmium breakthrough % after 1 year)

Drinking water concentrationexceeded?

-3 -2

-*u

35

30

25

20

15

10

5

e

~m

'•i-Kj-K'-i'v.

x£&£^

'CRxiixx

mililif

CH pureHI groundwater regime impure^§ soil impure

SssSSsss.s;. ;.;<;. vX^,;.

•11XXX^^1 mm

30

?co 20

10

n

f

111

&£§&

;:::>:: :;:;:::;::::

no

•

yesCH Pure13 groundwater regime impurej%*|soil impure

:S:K:-x:̂

9SS3SS

-5 -4 -3 -2 -1 0log (Isoproturon breakthrough % after 1 year)

-8 -7 -6 -5 -4 -3 -2 -1log (Isoproturon leaching concentration over one year, mg.l )

Fig. 3. Frequency distribution in the soil map units of (a) days with a good workability between 15 Mar. and 15 May 1980; (b) days with agood aeration between 15 Mar. and 15 May 1980; (c) days until 10% breakthrough of a Cl~ tracer in the period after application (1 Oct.1979); (d) the logarithm of the percentage cadmium breakthrough 1 yr after application on 1 Oct. 1979; (e) the logarithm of the percentageIsoproturon breakthrough 1 yr after application on 1 Oct. 1979; and (f) the Isoproturon leaching concentration during the first year afterapplication on 1 Oct. 1979. Impure means that the soil or groundwater regime does not fit the definition of the soil map unit.

204 SOIL SCI. SOC. AM. J., VOL. 60, JANUARY-FEBRUARY 1996

Table 2. Results of the test that combining weighted values fromthe representative profile (RP) data set yields a good estimateof the soil map unit mean.

Table 3. Profile numbers of the stratified two-stage sampling dataset of 88 profiles showing behavior corresponding to the 5, 50,and 95% points of the areal distribution.

Difference fromRP values

Variable

workability, daeration, dCl" breakthrough, dCd breakthrough, log(%)isoproturon

breakthrough, log(%)

Mean

219

-3.11.26

1.4

SEMt1.104.730.600.09

0.45

(-value

1.964.005.1

14.00

3.20

Significance(%, df -

2)t<10<5<2.5<0.5

<5

t SEM = standard error of the mean,t df = degrees of freedom.

empirical cumulative distribution is calculated for Z from allSMU estimates of Ic; and (v) an empirical distribution isobtained by dividing the cumulative distribution into classesand calculating increments between two adjacent classes.

RESULTS AND DISCUSSIONThe estimation of the time series of depth to the water

table with Eq. [4] was evaluated by comparing estimateswith measurements at five locations in the study area.Results are presented in Fig. 2. The relation explained87% of the total variance, and the root mean squarederror was 15.4 cm, which was thought to be preciseenough to allow use of this relation to predict time seriesof depths to water table at locations where only MLWand MHW estimates were available.

Simulation results are summarized in Table 1. Proba-bility distributions giving the area percentage of theSMU occupied by a data value class of a simulatedcharacteristic are given in Fig. 3a to 3f. Distributionsof Cd and isoproturon breakthrough values were stronglyskewed and therefore log-transformed. The three RPshave lower values for the characteristic aeration daysand Cd and isoproturon breakthrough than the averagevalues from the STS data set (Table 1). The results oftesting whether the RP data set yielded unbiased estimatesof SMU mean values (for Cd and isoproturon, thesemeans are geometrical means, otherwise they are arith-metic means) are given in Table 2. For all consideredcharacteristics but the number of days with good work-ability, the RP data set yielded a significantly (at 5%confidence) biased estimate for the SMU means. TheRP values overestimated the number of days to Cl~breakthrough and underestimated the number of dayswith good workability and aeration and the percentagesof Cd and isoproturon breakthrough. An advantage ofusing the STS data set is that acreages can be estimatedwhere threshold values are exceeded. Figure 3f shows theprobability distribution in the SMU for the isoproturonleaching expressed as a yearly concentration in the pre-cipitation surplus. It shows that in 18% of the area (SEM= 8%), the drinking water standard of 0.1 ng L~' isexceeded, when considering the leaching concentrationat 40-cm depth. No such risk was identified with the RPsimulation results.

In Fig. 3a to 3f, the role of map impurities is indicatedby crosshatched areas. Only 39% (SEM = 8%) of thearea satisfied the definition for the SMU, including that

Profile number

Variable 5% profile 50% profile 95% profileworkabilityaerationCl" breakthroughCd breakthroughisoproturon

breakthrough

1141146486

108

103103103107

107

6464

114113

113

for the groundwater regime. When considering only thesoil part of the definition of the SMU at the subgrouplevel of the Dutch classification system (De Bakker andSchelling, 1986), a purity of 93% (SEM = 3%) isachieved. Human-induced drought has caused the actualgroundwater regime to deviate from that found duringmapping. Map impurities, especially groundwater re-gime impurities, are responsible for extreme values forall characteristics but aeration days. This phenomenonprovides added evidence that using only profile descrip-tions related to the pure part of the SMU will underesti-mate risks related to the occurrence of extreme values.

Since SMU behavior cannot be characterized ade-quately with the RP data set, an attempt was made toselect from the 88 member STS data set profiles with acharacteristic behavior. Profiles were selected showingsimulation results corresponding most closely to the 5,50, and 95% points of the empirical cumulative distribu-tions. Results are given in Table 3. It appeared thatfor the characteristics workability, aeration, and Cl~breakthrough, the same three profiles describe the threepoints from the areal distributions. In all three cases,Profile 103 described the 50% behavior. Profile 114,which is characterized by a wet groundwater regime,corresponded to the 5% point of the workability andaeration distributions and to the 95% point of the Cl~breakthrough distribution. The opposite holds for Profile64, which is characterized by a dry groundwater regime.The 50 and 95% points of both the Cd and isoproturonbreakthrough distributions corresponded to Profiles 107and 113, whereas the 5% points corresponded to twodifferent profiles. As a result, it is concluded that inthis SMU, seven profiles can be used to describe threecharacteristic points of the distributions of five simulatedsoil properties reflecting a wide range of soil behavior.

CONCLUSIONSTwo major conclusions can be drawn from this study.

First, the use of RP to describe SMU behavior may yieldbiased estimates of mean values for a SMU. Second,map impurities are responsible for the occurrence ofextreme values and should therefore not be disregardedwhen making risk assessments for a SMU. These conclu-sions support the current strategy to upgrade the soilmap of the Netherlands by stratified random sampling,because this strategy enables both the characterizationof SMU behavior and the recognition of the occurrenceof extremes. Thus, the use of upgraded soil maps canfacilitate the use of existing knowledge for risk assess-

FINKE ET AL.: SOIL MAP UNIT BEHAVIOR CHARACTERIZATION IN SOLUTE TRANSPORT 205

ments. Since it appeared that a few soil profiles character-ized the distributions of several characteristics describingsoil behavior, these profiles may serve as benchmarkprofiles for further studies in this SMU, greatly reducingfurther simulation efforts. The method we proposed toselect characteristic profiles, with STS sampling and aset of standard simulations, can be extended to otherSMUs.

ACKNOWLEDGMENTSThe authors acknowledge fruitful discussions with Dr. J.J.

De Gruijter concerning the statistical techniques and wish tothank R. Visschers for collecting the soil data.