Modeling Moisture Retention in Peat Soils

Modeling Moisture Retention in Peat SoilsR. Weiss, J. Aim,* R. Laiho, and J. Laine

ABSTRACTSoil moisture governs many biogeochemical processes in peatlands.

Modeling of those processes relative to climate and anthropogenicinfluences requires knowledge of the basic hydraulic properties ofdifferent peat soils in a function form. Water retention of undisturbedsurface peat samples, collected at four depths at each of 38 undrainedand drained pine {Pinna sylvestris L.) mire sites, was measured forsuction pressures of -0.98, -3.10, -6.19, -9.81, -98.1, and -1554.25kPa. The obtained data were used to test several well-known waterretention models commonly applied to mineral soils. The most suitablemodel was found to be van Genuchten's model if the residual watercontent was omitted. Peat characteristics were used to explain thevariation in the model's shape parameters. Accounting for the remainsof Sphagnum, Carex, Eriophorum, and lignin and the distinction be-tween shallow and deep peat layers considerably improved the mois-ture retention predictions compared with using bulk density only. Thedifferent behavior of the shallow vs. the deep peat layers was mainlyattributed to the Sphagnum and lignin residues, but not to the Carexresidues. We developed a semiempirical model with only one shapeparameter, which was clearly better explained by the peat characteris-tics than the two shape parameters of the van Genuchten model.We recommend that for statistical investigations or investigationsrequiring a robust model, the semiempirical model be used. The vanGenuchten model is to be preferred in predicting the moisture condi-tions near saturation.

PEAT SOIL, as a matrix for hydrophysical phenomena,is characterized by a high proportion of small pores

(e.g., Paivanen, 1973) and a very heterogeneous porestructure derived from plant residues in various stages ofdecomposition. According to Loxham (1980), differentpore categories can be identified: large multiple andsimply connected open pores, dead-end pores, com-pletely isolated pores, and pores in cell structures. Thestructure of the peat matrix thus elicits a hydrophysical

R. Weiss and J. Aim, Dep. of Biology, Univ. of Joensuu, P.O. Box111, FIN-80101 Joensuu, Finland; R. Laiho and J. Laine, Dep. ofForest Ecology, Univ. of Helsinki, P.O. Box 24, FIN-00014 Helsinki,Finland. Received 29 July 1996. *Corresponding author (jukka.alm®joensuu.fi).

Published in Soil Sci. Soc. Am. J. 62:305-313 (1998).

response different from that of the granular geologicalporous media (Hoag and Price, 1985).

Knowledge of the water content profile of peat rela-tive to the level of the water table is a prerequisite formodeling processes related to soil moisture conditionsof peatlands. Most models of water content in porousmedia make intensive use of a moisture retention curve,which describes the moisture conditions at differentpressure heads. The relationship between soil perme-ability or hydraulic conductivity and soil water contentis also in a key position in considering water movement,and is often directly related to the moisture retentioncurve. Both physical characteristics, however, are sel-dom available, especially in the case of peat soils andwhen operating on a regional scale. Fortunately, basicpeat soil characteristics are often available for peatlandresearch sites, or are monitored during soil survey cam-paigns. Equations describing relationships between peatsoil characteristics and hydraulic properties could im-prove the use and interpretation of peat soil maps andincrease the applicability of simulation models at boththe local and regional scale.

For peat soils, very few attempts have been made toestimate water retention from certain peat properties.Boelter (1969) and Paivanen (1973) used multiple re-gressions to relate the water content at certain pressurehead values to the bulk density of peat. The disadvan-tage of these models is that they provide data in tabularform, which makes mathematical and statistical opera-tions difficult. A continuous function to better describethe water retention characteristics is preferred. Thiswould enable the generation of complete curves andfacilitate both mathematical and statistical operations.Romanov (1968), who dealt with the physical interpreta-tion of pore geometry and capillary rise of water in peat,pointed out that the water retention of peat at staticequilibrium could be hyperbolically related to the heightof the water table and therefore to the matric suction.Although hyperbolic curves have, to a limited extent,been published for peat samples by Romanov (1968)and Vorobev (cited by Ivanov, 1981), they were notrelated to other peat properties.

306 SOIL SCI. SOC. AM. J., VOL. 62, MARCH-APRIL 1998

The water retention characteristics of mineral soilshave been modeled quite intensively, and several mod-els have been presented in the last 25 yr (e.g., Brooksand Corey, 1964; Brutsaert, 1966; van Genuchten, 1980;Ross and Smettem, 1993; Zhang and van Genuchten,1994). Some of these models could also be calibratedfor peat soils, and some will be investigated here. Mostof the water retention models for mineral soils allowfor analytical solutions of the hydraulic conductivity orpermeability function. Unfortunately, these analyticalmodels contain curve shape parameters that were origi-nally determined for large sets of mineral soil samples(e.g., Mualem, 1976). Consequently, they should not beused for peat soils without refitting the shape parame-ters (Loxham and Burghardt, 1986).

MATERIALS AND METHODSUndisturbed volumetric peat samples were collected at 38

peatland sites, both undrained and drained, which belong tothe following peatland site types in the Finnish classificationsystem (Cajander, 1913; see Laine et al., 1986, for currentterminology): (i) herb-rich sedge birch-pine fen, (ii) tall-sedgepine fen, (iii) cottongrass-sedge pine fen, (iv) low-sedgeSphagnum papillosum pine fen, and (v) cottongrass pine bog.Brief site type descriptions are also given in Laiho and Laine(1994), where the selection of the material is described indetail. The oldest drainage areas sampled had been drained55 yr before. Of the nearly 5.3 million ha of peatland drainedfor forestry in Finland, about 35% consists of these peatlandsite types (Keltikangas et al., 1986). They form a continuumfrom mesotrophy to oligotrophy and ultimately ombrotrophy.The surface peat is Carex dominated in the meso- and meso-oligotrophic sites, but the proportion of Sphagnum residuesincreases along the gradient toward ombrotrophy. The peat-lands studied are located in southern Finland in a region from61°35' to 62°05'N and 23°50' to 24°55'E.

Three series of peat samples (289 or 250 cm3, sample height69 or 63 mm) were taken from four depths: 0 to 10, 10 to 20,25 to 35, and 50 to 60 cm. Zero level was taken as the upperlevel of the rooting zone, which often corresponded to thelower level of the green moss layer. The samples were deepfrozen and stored until further treatment, a standard preserva-tion technique, which is assumed to cause only minimal alter-ations in the flexible organic matter pore structures.

For the determination of the water retention, about 1.5-cm-thick subsamples were taken from the top and bottom ofthe samples. This was done to ensure a reasonable measuringtime, because the time needed to reach static equilibriumincreases more than linearly with increasing sample thickness,especially in organic soil with pore-size distribution dominatedby small-diameter, and partly "dead-end", pores.

The water content of the subsamples was determined gravi-metrically at suction levels 0.98, 3.10, 6.19, 9.81, 98.1, and1554.25 kPa (corresponding to pF values 1.0,1.5,1.8, 2.0, 3.0,and 4.2, and pressure heads of 10,30,60,100,1000, and 15 850cm H2O, respectively) obtained using pressure plate extractors(Catalog no. 1500 and 1600, SoilMoisture Equipment Corp.,Santa Barbara, CA). The pressure applied was ensured byincluding a hydrostatic pressure buffering system. The watercontent of each sample was calculated as the mean of the topand bottom subsample values. After extraction at all pressures,the subsamples were dried at 105°C (standard temperaturefor organic soils) to constant mass. Their dry masses were thenadded to the dry masses of the sample's remnants determinedearlier, and the bulk densities of the whole original sample

were used to transform the gravimetric water contents to volu-metric ones. The botanical composition of each sample wasdetermined microscopically after a short digestion in a 10%KOH solution and staining with safranine (e.g., Heikurainenand Huikari, 1952). One hundred points were counted on eachslide prepared, and the object closest to the center of eachpoint was classified into one of the following classes: Carex,Sphagnum, Eriophorum, lignin (including both tree and shrubremains), unrecognizable plant residues, and amorphous mass(see Table 1).

Model Identification and Parameter Estimation

Basic ModelsThree basic equations for describing the water retention

curves were tested:1. The equation proposed by van Genuchten (1980):

e = er + (es - er)[i + (ah)"]-'" [i]2. The bimodal equation proposed by Zhang and van Gen-

uchten (1994):

0 = 6, + (9S - 6r) [1 + C!(a/z)]/[l + (ah) + C2(ah)2]

[2]3. A semi-empirical equation derived in this study (Appen-

dix I):6 = exP{ln(6s) - [ln(6s) - [3]where 0 is the water content (m3 m~3) of peat, 6r is the residualwater content (m3 m^3), 6wii, is the wilting-point water content(m3 m~3 at 1.554 MPa), h is the pressure head in cm H2O(15 850 cm H2O, loglo(h) = 4.2 at the wilting point), 6S is thesaturated water content (m3 m""3); a, n, m are parametersdefining the van Genuchten curve shape; a, c\, and c2 areparameters defining the Zhang and van Genuchten curveshape; and k is a single parameter defining the semiempiri-cal curve.

The model parameters were obtained as follows:Water Content at Saturation. A sensitivity study by Ver-

eecken et al. (1989) showed that models like those above aremost sensitive to errors in 6S. The value of 6S for the modelswas therefore not obtained from parameter-fitting valueswhen fitting the models to the data, but from the total porosityof peat as a fixed value for 6S. This value can be obtainedphysically from the bulk density of the peat sample, p, andthe density of solids or specific gravity, g, (e.g., Paivanen,1973):

= (gs - [4]The values of density of solids in Finnish peats (here = gs)have been reported to vary between 1.4 and 1.6 g cm~3 (e.g.,Puustjarvi, 1970). In this connection, gs was fixed as an averagevalue of 1.5 g cm~3. Gas content of saturated peat, whichranges from 0 to 10% (Paivanen and Laine, 1982), was alsoignored in our approach.

Water Content at Permanent Wilting Point. The volumetricwater content at wilting point h = 15 850 cm H2O, 6wat, wasestimated separately for that pressure head by linear regres-sions of the measurements. Using only bulk density polynomi-als (p, p2) as parameters, we obtained Eq. [5]. Adding botanicalresidues to the regression parameters somewhat improved theregression performance, and we obtained Eq. [6]. The notationS, L, C, and Er denote here the Sphagnum, lignin, Carex, andEriophorum content as percentages:

= 4.3 + 67p R2adi = 0.28 [5]

WEISS ET AL.: MODELING MOISTURE RETENTION IN PEAT SOILS 307

Table 1. Value range and sample distributions of the 152 peatcores analyzed.

Bulkdensity Sphagnum

(P) (S)

MeanSDMax.Min.

g cm 3 -0.1020.030.180.04

3429970

Carex(C)

2024890

Lignin Eriophorum(L) (Er)

2010582

1410490

Amorphousmass

(Amor)

1112580

6wilt(p,S,L,C,Er) = 5.3 + 87p - 0.050C - 0.11L/&i = 0.38 [6]

The coefficients of determination are not high (parameterswere significant), but the equations are considered sufficientbecause of the small water content at the wilting point. Addingdepth or interaction parameters presented below did not im-prove these equations.

Residual Water Content. The residual volumetric watercontent, 6r, is a measure more general than 6wilt defined at thepermanent wilting point of the plants. The parameter 6r wasused in Models 1 and 2, but was not obtained from the mea-surements. Mualem (1976) suggested an extrapolation proce-dure to obtain 6r from other matric suction measurementpoints. However, this extrapolation procedure estimated 9r :£0 for 82% of all peat samples in this work. Therefore, 6r wasestimated by the model-fitting procedures.

Curve Shape Parameters. The values of curve shape param-eters of Models 1 to 3 were estimated by applying the Leven-berg-Marquardt algorithm (Marquardt 1963; SPSS, Inc., 1988;Press et al., 1992). The estimates of the parameters are furtherexplained using peat characteristics.

Model SelectionA model identification test was performed to compare the

performance of the equations and to check the need for allparameters in the equations. In this test, full and reducedversions of Eq. [1] to [3] were samplewise fitted to the observedwater retention data of a subset of 25 peat samples with dif-fering peat characteristics or originating from different depths.Very high correlations were found to exist between the curveshape parameters in Eq. [1] and [2]. The full models werethus overdefined for our data set and could be reduced. Toobtain a sufficient degree of freedom with respect to ourpressure head measurements, the number of fitting parametershad to be restricted to one or two. In the case of Eq. [1], vanGenuchten (1980) suggested m = 1 - 1/n, which does notmuch affect the flexibility in describing the water retentioncurve. The restriction n > 1 follows from the restriction 0 <m < 1, both due to the fact that diffusion is >0 at saturation(van Genuchten and Nielsen, 1985). Setting m = 1 reduces Eq.[1] to a model proposed by Brutsaert (1966) and Endelmann etal. (1974). In the case of Eq. [2], setting c, = 1 results in agenuinely s-shaped curve (Zhang and van Genuchten, 1994).When fitting both full and restricted versions of Eq. [1] and[2], the value of 6r still became negative for several samples,forcing us to restrict 6r 3: 0. However, Vereecken et al. (1989)pointed out that 6r is the least important parameter in Eq. [1],which allowed us to assume 6r = 0 for all samples. Similary,Eq. [3] was reduced and tested with 6wii, obtained from Eq.[6] and with 6wii, = 0 (Table 2).

We performed an F-test (Pindyck and Rubinfeld, 1991) tocheck if a reduced model could be used without a significantloss of fit. When comparing the reduced versions of Eq. [1] to[3], we used Akaike's information criteria, the final prediction

Table 2. Model selection and parameter reduction results. (SSE[sum of squared errors of the model], F test for reduction of theparameters, see Pindyck and Rubinfeld [1991]. For informationcriteria averages AIC [Akaike's information criteria] and FPE[final prediction error] see Soderstrom and Stoica [1989]. ForMDL [minimum description length] see Rissanen [1983].)

Model 1a e = er +b e = e, + (e, - e,)[i +c o = e, + (e, - e,)[i +d e = e«[i +e 0 = 0,[1 =f e = e,[i =

Model 2a 0 = 6, + (0, - 6r)[l + d(aA)]/[l = (aA) + c2(aA)2

b 0 = 0, + (0, - 6r)[l + (aA)]/[l + (aA) + c2(aA)2]c 0 = Os[l + C!(aA)]/[l + (aA) + c2(aA)2]d 0 = 8,[1 + (aA)]/[l + (aA) + c2(aA)2]

Model 3a 6 = exp(ln(0s) - [ln(6.) - ln(Orf,)][log10(A)/4.2]'£lb 0 = exp[ln(0,)] - (ln(6,) - ln[0»i,,(p,l,c)]) [log,0(A )/4.2]*c e = 0,exP{l-[log10(A)/4.2]*)

error criterion (Soderstrom and Stoica, 1989), and the criterionof minimum description length (Rissanen, 1983), see Table 2.According to these criteria, the model reduced from Eq. [1]:

e = es[i + (ah)n]- [7]performed best. This model is related to the theories andphysical soil properties presented by van Genuchten (1980),but requires two fitting parameters {a,n}. If only one fittingparameter is allowed, Eq. [3] performed best with 6wfl, fromEq. [5] or [6] and [k] as the shape parameter.

Sensitivity Analysis and Parameter DistributionsA sensitivity analysis was performed to evaluate the relative

importance of the value parameters. The core of the analysiswas similar to Vereecken et al. (1989) but we extended thecalculations to all pressure heads. Close to saturation, at apressure head of 10 cm H2O, both models were most sensitiveto changes in 6S, then to those in n, k, and a (in descendingorder), whereas 6wat had only a small effect. The order ofimportance was gradually reversed with the pressure headincreasing to 15 850 cm H2O. Since the groundwater table isvery close to the surface in most natural peat soils, we canconclude that n should be more precisely modeled than a or k.

When the models where separately fitted to each of the152 sample measurement series, the parameter n followed anormal distribution quite well. Parameter a, however, hada skewed distribution, but fortunately Iog10(ot) was closer tonormal and was used in the regressions (see below). The shapeparameter distribution characteristics and the correspondingresponses of the selected van Genuchten model (Eq. [7]) areshown in Fig. la and Ib. The figures indicate that the modelis sensitive to changes in log,o(a) very close to saturation,whereas the slope is greatly affected by n after 10 cm H2O.For the selected semiempirical model Eq. [3], shape parameterk followed a normal distribution relatively well (Fig. Ic). Fig-ures la to Ic show clearly that k combines the patterns of nand a quite well.

RESULTSConstruction of the Final Models

Linear ordinary least square (OLS) regression wasapplied to explain the variation in the model shape


10 100100

0

100

80 -

1- 60 -u>

8\_03a

40 -

20 -

o

100

1000 10000• I • • • • I

—— n = 1.28 (average)—— n - 1.28 ± SD—+-+-+-1 i i i i | i i i -t-H-

iog10(«) =(max)

Iog10(a) = -0.91 (average)Ioq10(a) = -0.91 ± SD

k = 1.66 (average)k = 1.66 ± SD

-1 I i i i i I i i I i i i i I

B

10 100 1000 10000

Pressure head (cm H20)Fig. 1. Peat water content as predicted by (A, B) the van Genuchten

model (Eq. [7]) and (C) our semiempirical model (Eq. [3]) withdistribution of shape parameters (A) n, (B) logio(a), and (C) k.Functions are evaluated at minimum (min), maximum (max), aver-age, and standard deviation (SD) values of the parameters.

parameters (n, Iog10(a) in Eq. [7] and k in Eq. [3]) fromthe distributions of the peat characteristics (Table 1).The resulting significant peat characteristic variableswere then used in the nonlinear regressions, which wereused to derive the final models from the entire empiricalset. Five different peat character sets were used in theregression analysis (Table 3). The first set consisted only

Table 3. Peat character sets. Peat layers: Layer 1 = 0 to 10 cmbelow the peat surface, Layer 2 = 10 to 20 cm, Layer 3 = 25to 35 cm, and Layer 4 = 50 to 60 cm. The layer variables aredummy variables in the models; they are set to 1 in the depthconsidered, else to zero. Slay 1 to Slay 4 and Llay 1 to Llay 4denote the interaction of Sphagnum (S) or lignin (L) remainsand peat layer so that, e.g., Slay 1 = S x Layer 1 and Day 2= L x Layer 2, respectively.

Set 1: p (bulk density), p2

Set 2: p, p2, S (Sphagnum), C (Carer), Er (Eriophorum),L (lignin), Amor (amorphous mass)

Set 3: p, p2, Layer 1, Layer 2, Layer 3, Layer 4 (Layer 1 = 1 ifit is in current layer, 0 otherwise, etc.)

Set 4: p, p2, S, C, Er, L, Amor, Layer 1, Layer 2, Layer 3,Layer 4

Set 5: p, p2, S, C, Er, L, Amor, Layer 1, Layer 2, Layer 3, Layer 4________Slay 1, Slay 2, Slay 3, Slay 4, Llay 1, Llay 2..._____

of the polynomial terms of bulk density. Botanical peatcomponents were added to the second set whereas depthby the sampling layer numbers was added to the thirdset, and both term groups were added to the fourth set.Interaction terms (botanical components with samplinglayer) were finally included in the fifth set.

Before running regression analysis, a preliminary dataanalysis using correlation and principal factor analysiswas performed to detect linear relationships betweenthe peat characteristics and to examine the data struc-ture. Most of the botanical components and the bulkdensity correlated significantly with each other (Table4). The bulk density p correlated strongly with the bo-tanical components Sphagnum (S, negative) and amor-phous mass (Amor, positive), and quite strongly withlignin (L) and Eriophorum (Er). The strong negativecorrelation between Sphagnum and Carex (C) could beexplained by the observation that peat soils in Finlandhave mostly S or C as their main component. The posi-tive correlation between the uppermost sample layer(0-10 cm, Layer 1) and S and the negative correlationbetween Layer 1 and C can be explained by the differ-ences between the respective peat formation processes.Carex peat consists mainly of root and rhizome residues,a continuous input of which takes place mainly at adepth of 10 to 30 cm. The uppermost =10 cm are typi-cally dominated by Sphagnum residues also on sites withCarac-dominated peat lower down. The high positivecorrelation between Amor and p results from the corre-lation of humification with these variables. The correla-tions between the botanical components can also partlybe explained by the fact that they are given as percent-ages. Therefore, an angular transformation x' = arcsin(x) was tested (Ranta et al., 1989, p. 46), but was rejectedbecause of poor performance in the final equations.Also the principal factor model had to be rejected, leav-ing all the peat characteristics in the final models.

A lack-of-fit test, similar to that performed for min-eral soil water retention curve parameters by Vereeckenet al. (1989), was used to verify the adequacy of themodels in Eq. [3] and [7]. Due to deviations from someof the assumptions of this test in our data, the resultscan only be taken as indicative, and no significanceprobabilities are displayed in Table 5. To test whethera larger, unrestricted set of independent variables (UR)is significant compared with a restricted set of variables(R) (Table 5), we used the common F statistic (Pindyckand Rubinfeld, 1991).


Table 4. Correlation coefficients of the peat characteristics! considered.

pcErLSAmorLayer 1Layer 2Layer 3Layer 4

P1.000.120.37***0.45***

-0.66***0.58***

-0.21**0.22**0.06

-0.06

C

1.00-0.25**-0.16*-0.62***-0.13-0.32***

0.020.150.14

Er

1.000.14

-0.30***0.24**

-0.17**-0.01

0.110.07

L

1.00-0.39***

0.23**0.17*

-0.20*-0.02

0.06

S

1.00-0.49***

0.36**0.09

-0.18*-0.27**

Amor

1.00-0.24**-0.05

0.070.22**

Layer 1

1.00-0.33***-0.33***-0.33***

Layer 2

1.00-0.33***-0.33***

Layer 3 Layer 4

1.00-0.33*** 1.00

*,**, and *** Significant at the 0.05, 0.01, and 0.001 probability levels, respectively.t p = bulk density, C = Carex, Er = Eriophorum, L = lignin. S = Sphagnum, Amor = amorphous mass, Layer 1 = 0-10 cm below peat surface, Layer

2 = 10-20 cm, Layer 3 = 25-35 cm, Layer 4 = 50-60 cm.

The parameters n and Iogi0(a) defining the shape ofEq. [7] can be estimated with coefficients of determina-tion of 38 and 61%, respectively. The most importantpeat soil properties controlling both parameters werethe bulk density and the separation between the shallowpeat layer (0-10 cm) and the deeper layers.

The parameter k defining the shape model Eq. [3]was estimated with a coefficient of determination of70%. Bulk density, the Sphagnum content, and the sepa-ration between the shallow peat layer and the deeperlayers were the most important factors controlling theparameter k. The lignin content was not clearly statisti-cally significant when added (sign, t = 0.04). Addinginteraction terms between the sample layer and the bo-tanical components, the Sphagnum and lignin contentsclearly showed statistically significant differences in wa-ter retention between top layers and deeper layers. Thisdifference was more significant for the Sphagnum con-tent than for the lignin content. However, since theresulting increase in the coefficient of determinationwas not clearly significant, Set 4 (Table 3) was the mostreliable variable set for the shape parameter k.

According to the sensitivity analysis, n should be moreaccurately determined than k. This goal was notachieved. The lack-of-fit test also showed that there wasnot much more to be explained in the variations of n,indicating high fitting errors in the distribution of n.Consequently, the van Genuchten model Eq. [7] wastoo sensitive to be well defined by the regressions above,

Table 5. Shape parameter regression results.

while the semiempirical model Eq. [3] gave a slightly lessaccurate but more robust estimate of the water content.

The final models were obtained by nonlinear regres-sion, using the Levenberg-Marquardt algorithm (Mar-quardt, 1963; SPSS, Inc., 1988, p. B35-B47). The linearlyobtained parameter values were used as initial valuesfor the iterations. As a final result, the semiempiricalmodel Eq. [3] has its parameter functions for differentsets of peat characteristics listed in Table 6. The bestvan Genuchten-type model (Eq. [7]) has its parameterfunctions listed in Table 7. A one-parameter version ofEq. [7] was tested, with a as shape parameter and nfitted to an optimal average value. The resulting modelperformed quite well (R2 = 0.920) but clearly not aswell as the semiempirical model. We must also pointout that simple linear regressions reached only R2 =0.809 for our water retention data.

Model Validation and EvaluationWe applied a double cross-validation method by

which we tested the suitability of the partial regressioncoefficients and the reliability of the coefficient of deter-mination. This method splits the observations randomlyinto two halves. A nonlinear regression is fitted to eachof these sets using the variables retained by the modelfor the complete set of observations. One can calculatethe coefficient of determination R2 between observedand predicted values by applying the nonlinear regres-

Model,parameter

3b, k

le, n

le, logio(a)

Variableset

122A344L51234512345

Significant regression variables!

constant, p, p2

constant, p2, S, Cconstant, p2, Er, L, Amorconstant, p2, Layer 1, Layer 2constant, p2, S, C, Layer 1constant, p2, S, C, L, Layer 1constant, p!, S, C, L, Slay 1, Llay 1constant, p, p2

constant, p, p2, Cconstant, p, p2, Layer 1constant, p, p2, C, Layer 1same result as for Set 4constant, p, p2

constant, p, p2, L, C, Sconstant, p, p2, Layer 1p2, S, C, Layer 1same results as for Set 4

K2

adjusted

0.4730.5580.5450.6020.6960.7030.7090.2320.2930.3600.377

0.2950.3910.5190.613

Lack-of-fittest

(test limit = 1.3)37.731.031.827.219.619.019.42.82.21.21.3

68.458.345.135.2

Significance test,^(^significance)

1—2: <0.0011— 2A: <0.0011—3: <0.0012—4, 3—4: <0.0014— 4L: 0.034—5, 4L— 5: 0.13

1—2: <0.0011—3: <0.0012—4: <0.001; 3—4: 0.03

1—2: <0.0011—3: <0.0012—4, 3—4: <0.001

t p = bulk density, C = Carex, Er = Eriophorum, L = lignin, S = Sphagnum, Amor = amorphous mass, Layer 1 = 0-10 cm below peat surface, Layer2 = 10-20 cm, Layer 3 = 25-35 cm, Layer 4 = 50-60 cm.


Table 6. Parameter functions of the semiempirical model (Eq. [3]).

VariablesetSet 4

Set5

Set 3

Set 2

Setl

Set 0*

Parameter

e,erf,ke,, erflk6,

wiltk

e,, ertl,Ae,, 0*,,kese.«,h

Estimated parameter functions!

100 — 66.7 p (peat sample porosity, Eq. [4])5.3 - 87.7 p - 0.11 L - 0.05 C (Eq. [6])0.71(±0.10) + 54.0(±4.8) p2 + 0.0060(± 0.0012) C + 0.0088(± 0.0012) S - 0.38(±0.04) Layer 1same as for Set 40.48(±0.14) + 52.5(±4.8) p2 + 0.0077(± 0.0014) C + 0.0111(±0.0015) S + 0.0078(± 0.0031) L -

0.0045(±0.0010) Slayl - 0.0090(± 0.0026) Llaylsame as for Set 44.3 - 67p (Eq. [5])1.33(±0.05) + 28.6(±3.9) p1 - 0.28(±0.05) Layer 1 + 0.21(±0.06) Layer 2same as for Set 40.61(±0.11) + 54.0(±5.5) p2 + 0.0076(±0.0014) C + 0.0077(± 0.0014) Ssame as for Set 31.91(±0.24) - 14.3(±5.1) p + 104(±13) p2

102.7(±8.0)11.4(±1.3)1.42(±0.15)

R\tall data

0.940

0.942

0.922

0.919

0.902

0.836

«2§valid,

part 1, 2

0.9330.944

0.9320.944

0.9110.931

0.9110.9260.8880.9130.8300.841

t p = bulk density, C = Carer, Er = Eriophorum, L = lignin, S = Sphagnum, Amor = amorphous mass, Layer 1 = 0-10 cm below peat surface, Layer2 = 10-20 cm, Layer 3 = 25-35 cm, Layer 4 = 50-60 cm, Slay 1 = S x Layer 1, Llay 1 = L x Layer 1.

IR2 is for the complete model (must not be compared with R2 in Table 5). Set 0 = parameters 0,, 0,vii,, and k estimated directly from water retentiondata, not explained by peat characteristics.

§ The right-hand column displays the results (R2 valid) of the cross-validation.

sion model obtained from the first set to the second oneand vice versa. The validation test for both sets of soilproperties indicated that all the signs of the regressionparameters in the models (Eq. [3] with Table 6, Eq. [7]with Table 7) are stable, and that the parameter valuesdid not change significantly. The cross-validated regres-sion models show an R2 for the independent observationsets comparable to both the R2 obtained on the identifi-cation data set and the R2 for the complete data set(last columns in Tables 6 and 7). This indicates stableprediction levels, the semiempirical model Eq. [3] yield-ing slightly more stable predictions than the van Gen-uchten model Eq. [7].

Cross-validation performed on the peat characteristicparameter selection results from the linear regressionprocedure (Table 5) indicated that most of the peatproperty parameters in sets 1 through 5 remain stableand do not show major changes in their degree of signifi-cance. The parameters p2, S, C, and Layer 1 obtainedfrom Set 4 were especially stable. However, the lignincontent (L) of Sets 4L and 5 was not always significant.Also, in Set 3 of Model [3], the parameter Layer 2became uncertain.

To be able to evaluate the model performance atdifferent pressure heads, coefficients of determinationof the model predictions at the local pressure head levelsare shown in Fig. 2. Regressions through local measure-ment points depending on the bulk density or its polyno-mials, i.e., models of the same structure and type as

Table 7. Parameter functions of the optimal van Genuchten model.

those presented by Boelter (1969) and Paivanen (1973),are also shown. The results in Fig. 2 clearly show thata major increase in fit has been achieved by the continu-ous models presented here, especially in the regionsclose to saturation. For the optimal peat character set(Set 4), the fit of the Models [3] and [7] were only slightlylower than those for the best possible local multipleregressions, but more usable by being continuous. How-ever, the maximum fit limits of the models due to thesingle sample curve fitting errors show that the predic-tions could be much better still, especially at lower pres-sure heads of 0.98 to 6.19 kPa (10-60 cm H2O).

Examples of observed values and estimated waterretention curves (Eq. [3], Sets 4 and 5) and (Eq. [7], Set4) of some Sphagnum, Carex, lignin, and Eriophorumpeat samples are given in Fig. 3a through 3h. The exam-ples illustrate the quite good performance of the reten-tion curves, as well as showing the obvious differencein moisture retention between the top layer and thedeeper peat layers.

Figures Ib and 3a to 3h illustrate clearly, that Model[7] for some parameter combinations gives a curve that,close to saturation, has exaggerated slope that can causeproblems in numerical studies. The problem can beavoided by a simple linear interpolation from the realsaturation point to some threshold point at the retentioncurve (we recommend the curve point at a thresholdpressure head of 3-10 cm H2O). In this way, it is alsopossible to use empirical models for the water content

Variableset

Set 4

Parameter

e,n

logio(a)

Estimated parameter functions!

100 - 66.7 p (peat sample porosity, Eq. [4])1.49(±0.05) - 3.56(±0.90) p + 13.2(±4.0) p2 +

0.00027(±0.00034) C - 0.037(±0.018) Layer 1-51.8(±3.0) p2 - 0.0057(±0.0012) C - 0.0100(±0.0007) S + 0.53(±0.09) Layer 1

R'.t all data

0.944

R2 validjpart 1, 2

0.930

0.953

t p = bulk density, C = Carex, Layer 1 = 0-10 cm below the peat surface, S = Sphagnum.t R2 is for the complete model (must not be compared to R~ in Table 5).§ The right-hand column (R: valid) displays the results of the cross-validation.


200

50

Change in parameter value, %Fig. 2. Model performance indicated by coefficient of determination

(K2) at the local soil water suction levels where the measurementswere made. Local point regressions with the shape parametersexplained by peat Character Sets 1 and 4 (see Table 3), semiempiri-cal model (Eq. [3]) with Set 4, and van Genuchten model (Eq.[7]) with Set 4 are compared with their maximum fit limit andtheoretical maximum limit values.

at saturation (e.g., Paivanen, 1973) with Models [3] and[7]. This makes it possible to account for the 0 to 10%gas content in peat at saturation or to use gs valuesdeviating significantly from the assumed average gs =1.5 g cm"3.

DISCUSSION AND CONCLUSIONSThe models developed and tested in this research

show that continuous water retention models apply well

100

80 -

to peat soils. A reduced version (Eq. [7]) of the vanGenuchten model proved to be optimal for the availablemeasurement intensity (number of suction points). Op-timal model parameters were the water content at satu-ration 9S, determined from sample porosity, and twoshape parameters, n and a. The residual water contentof peat, 6r, was thus left out of this model.

The n and a shape parameter distributions, whichwere obtained by fitting the van Genuchten (1980)model Eq. [7] separately to each peat sample waterretention measurement series, could be partly explainedby bulk density. Addition of the percentage of the bo-tanical components Sphagnum and Carex increased thedetermination rate considerably, and these variablesproved to be clearly statistically significant. This indi-cates that the difference in water retention betweendifferent peat types can be explained not only by differ-ences in peat characteristics related to bulk density, butalso by differences in plant residue cell structure andpeat pore geometry (cf., Romanov, 1968).

A distinction between the top sample layer (0-10 cmfrom the lower level of the green moss layer) and thedeeper sample layers (10-60 cm from the referencelevel) also proved to be a clearly statistically significantvariable. The inclusion of this variable considerably in-creased the determination degree of peat water reten-tion, but could not be further explained by investigatingthe shape parameters n and a of the reduced van Gen-uchten model (Eq. [7]). Fortunately, the distribution ofthe single shape parameter k in the semiempirical model

100

60 -ca>coom 40 -

20 -

oc

ffl<B

Layer = 1p = 0.058S = 65c = oL = 20Er = 25

Layer = 1p = 0.087S = 28

Layer = 1p = 0.110S = 51C = 0L = 22Er = 20

Layer = 4p = 0.099s = oC = 75L = 15Er =

Layer = 2p = 0.057

= 87C = 0L = 8Er = 6

100

Log,0(/i) Log,0(h) Log10(/7) Log10(/i)Fig. 3. Examples of peat water content as predicted by model Eq. [7] (solid line) and 3b (dotted line, see Table 1) with the shape parameters

explained by peat Character Set 4 (see Table 3) and Model [3] with peat Character Set 5 (dashed line). Measured water content (dots) andmeasured sample characteristics (sample origins in peat depth profile = Layer, bulk density = p, botanical components S, C, L and Er) aregiven for each sample. Approximate (6%) error bars due to potential measurement errors in water content are also indicated. Samples arenamed by the dominant botanical peat component (Sphagnum, Carex, or lignin) followed by the visual field characterization of the peat(combination of symbols S, C, L, and Er). Nomenclature of the botanical components as in Table 1.


Eq. [3] could be better explained. The distribution of krevealed that the top vs. deeper layer distinction ismainly due to layer differences in the water retentioncharacteristics of Sphagnum (clearly significant) and lig-nin (less significant), but not due to layer differences inCarex (clearly not significant) residues. Physically, thelayer dependence of the moisture retention of Sphag-num could be explained by differences in pore structurein the shallow vs. deep peat layers. Logically, Sphagnumwater retention should be influenced in the same way.The layer dependence of the moisture retention of lignincould be due to a correlation between macropores andlignin content in the top peat layers, or due to a lowerdegree of humification of the lignin residues in the toplayers. The different behavior of Carex is in agreementwith the reasoning of Romanov (1968), who pointedout that "grass bogs" do not display a predominantlyvertically orientated pore structure in the top layers,and thus have markedly smaller layer differences inwater movement than Sphagnum bogs.

Because of the higher degree of freedom, Model [7]performs better than Model [3] close to saturation (ata pressure of 0.98 kPa). Where the suction region nearsaturation (0.5-10 kPa) is of major interest, the bestpredictions of moisture retention (R2 = 0.942) are givenby the final van Genuchten model (Eq. [7], Table 7). Infurther statistical analyses or general tasks, for instancewater retention questions related to ditching, the semi-empirical model (Eq. [3], Table 6) provides a morerobust structure with an almost as good overall predic-tion level (R2 = 0.940). However, this is achieved at thecost of a lower prediction rate in the region aroundIkPa.

Some improvement in the models could perhaps beachieved if the air-entry pressure in situ could be takeninto account, which requires denser measurement inten-sity at low pressure head values (below 3.10 kPa). Thesensitivity analyses suggest that some progress in thesemodels could be made by determining the peat Os moreaccurately. Paivanen (1973) and Paivanen and Laine(1982) pointed out that the theoretical value of 6S ob-tained from porosity, as in these models, is slightly toolarge since peat soil even at saturation contains a certainamount of gas, mostly <10% (Paivanen and Laine,1982). For laboratory samples, porosity (Eq. [4]) stillhas the advantage of giving a clear, robust estimate for6S, and it was therefore kept among the retention curveparameters. Corrections in the water retention curvesdue to large gas content at saturation or due to devia-tions of density of solids from the assumed average valuecan be made afterward by the interpolation correctionproposed above, and will thus not affect the water reten-tion curve outside the interpolation interval (0 to 0.5—0.98 kPa).

One should be aware that the models presented heredescribe the desorption curve (i.e., falling water table).Adsorption (i.e., rising water table) will probably havedifferent moisture retention characteristics. Hysteresiseffects (e.g., Poulavassilis and Childs, 1971; Ilnicki, 1982)were not taken into account. Peat matrix swelling andshrinking are not accounted for either, but could bedetermined at a more coarse level from bulk density

and peat type according to the results by Paivanen(1982). The range of seasonal water table in natural anddrained peatlands corresponds to pressure heads from0 to 100 kPa, thus reducing the potential error in predic-tions caused by shrinkage.

ACKNOWLEDGMENTSThis work was a part of the Finnish Research Programme

on Climate Change (SILMU) and was funded by the Academyof Finland.

APPENDIXDerivation of the Semiempirical Moisture

Retention EquationIn several studies of mineral soil hydrology, the water reten-

tion curve is based on the effective saturation of the soil, whichis defined as follows:

"Self =e -e,- o > 5eff > i [Al]

Mathematically, this expression is most sensitive to mea-surement errors at water content near saturation. This is usu-ally not important in upland mineral soils because most calcu-lations deal in this field with the lack of water caused by deepgroundwater tables. In peat soil studies, the opposite generallyoccurs. The water table is often very close to the peat surface,and the water retention near saturation is far more interestingthan the water retention near the residual point. We thereforefocused on the opposite expression, the effective saturationdeficit Z)eff:

£>eff = e s - e ro < Da < i [A2]

In field and laboratory measurements of peat, Or is rarelydetermined. It is more convenient to use 0wi,t, which necessi-tates redefining the expression above. Still, we assumed someclear relation between the redefined effective saturation defi-cit and corresponding matric suction values, 4>, which gives:

D* = es - e i|>. - $ _ i|ies - Swat >K - «l»wiit io42 [A3]

We used an empirical approach in this study to obtain thisphysical relationship. For the whole data set, the mean mea-sured moisture retention values, Om£.anij, for each pressure mea-surement point were calculated. A clear nonlinear relationshipwas found between the effective saturation deficit calculatedfrom 6meanj and their corresponding matric suction values, \\it.To find a mathematical form of this relationship, the watercontents emean,j were changed to their natural logarithms,ln(0mean,j), and the matric suction values to corresponding loga-rithms, log10(iK). Taking one more logarithmic step, we finallygot a very strong linear relationship through the origin:

ln[ »l(emean,) ~ m(9meanj) 1 = ^ Jiogio(ft)j r^l

Lln(6mean,s) - ln(emean,wilt)J L 4.2 JAll data calculated from 6meanj are situated close to this straightline, giving R2^ = 0.996. Rearranging the expression above inrespect to 6meanj and changing emean to 6, we obtained the semi-empirical water retention curve presented here (Eq. [3]).Clearly, the shape parameter (k\ is the slope of the line ob-tained from logarithmic transformations.


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Modeling Moisture Retention in Peat Soils