680 SSSAJ: Volume 74: Number 2 • March–April 2010

Soil Sci. Soc. Am. J. 74:680–694Published online 21 Jan. 2010doi:10.2136/sssaj2009.0148Received 20 Apr. 2009.*Corresponding author (Dimitre.Dimitrov@NRCan-RNCan.gc.ca).© Soil Science Society of America, 677 S. Segoe Rd., Madison WI 53711 USAAll rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.

Modeling the Subsurface Hydrology of Mer Bleue Bog

Wetland Soils

The water balance in peatlands has long been considered a key control on physical, chemical, and biological processes in peat (Lafl eur et al., 2005a,b,

2003; Clymo, 1983; Ingram, 1983), which makes understanding peat subsurface hydrology of great importance. Peat is classifi ed from the surface to the bottom as fi bric, hemic, and sapric (Letts et al., 2000; Clymo, 1983) on the basis of hydro-logic properties, texture, and degree of decomposition and compression. Although the entire peat profi le is characterized by extremely high porosities ≥0.85 m3 m−3 (Lafl eur et al., 2005a,b), near-surface fi bric peat has a low water holding capacity and rapid infi ltration rates, as most of the incoming water drains immediately to the water table (WT), while hemic and sapric peat below have high water holding capacities and low infi ltration rates (Lafl eur et al., 2005b; Fraser et al., 2001; Letts et al., 2000).

Macroporosity and Its Implication for Peat HydrologyTh e rapid infi ltration and drainage of fi bric peat (Schwarzel et al., 2002; Silins

and Rothwell, 1998; Baird, 1997; Zeitz, 1992; Boelter, 1964; Romanov, 1961) causes rapid changes in near-surface water contents, possibly because of the large spaces between the remains of dead plants (Clymo, 1983; Ingram, 1983), i.e., macropores, which may serve as major pathways for gravitational water infi ltra-tion and drainage, and aeration. Th e intraaggregate spaces of the peat matrix, i.e., micropores, are responsible for water retention (Hillel, 1982). Peat macroporosity

Dimitre D. Dimitrov*Canadian Forest ServiceNorthern Forestry Centre5320 122nd StreetEdmonton, AB, CanadaT6H 355

Robert F. GrantDep. of Renewable ResourcesUniv. of AlbertaEdmonton, AB, Canada, T6G 2H1

Peter M. Lafl eurGeography Dep.Trent Univ.Peterborough, ON, Canada, K9J 7B8

Elyn R. HumphreysDep. of Geography and Environmental StudiesCarleton Univ.Ottawa, ON, Canada, K1S 5B6

In this study, the ecosys model was used to simulate the hydrology of the Mer Bleue bog, Ontario, Canada, with seasonally varying water tables in the upper 1 m. Th e soil profi le was divided into three zones of peat (fi bric, hemic, and sapric). In the model, large, readily drained macropore fractions in the fi bric peat caused low water-holding capacity and high infi ltration rates, in contrast to hemic and sapric peat, with small macropore fractions, high water-holding capacities, and low infi ltration rates. Model results for peat water contents, θ, and water table depths, Z, were tested with continuous hourly measurements from 2000 to 2004 using time domain refl ectometry probes and piezometers. Within the zone of pronounced water table variation, the θ and Z modeled with the Hagen–Poiseuille equation for macropore fl ow and Richards’ equation for peat matrix fl ow corresponded better to the measured θ and Z (regression slopes between 0.62 and 1.03, intercepts between −0.05 and 0.02 m3 m−3, and R2 between 0.40 and 0.56), than did the modeled θ and Z with Richards’ equation alone (regression slopes between 0.33 and 1.43, intercepts between 0.11 and 0.22 m3 m−3, and R2 between 0.27 and 0.41). Th e Richards equation alone, even when parameterized with extremely high or low bulk saturated hydraulic conductivities of fi bric peat, modeled slower infi ltration, greater water retention, and lower Z than measured. Th e implications of macropore fl ow might be of great importance for peatland hydrology, therefore this experimental and modeling work should be extended to other wetlands as well.

Abbreviations: DOY, day of the year; EC, eddy covariance; ET, evapotranspiration; TDR, time domain refl ectometry; WT, water table.

SSSAJ: Volume 74: Number 2 • March–April 2010 681

decreases with depth, eventually becoming negligible, while at the same time the peat matrix fraction increases as peat decom-poses and compresses, and transforms to hemic and sapric forms (Price, 2003; Nungesser, 2003; Blodau and Moore, 2002; Ingram, 1983; Ivanov, 1981; Romanov, 1961; Price and Schlotzhauer, 1999). Th ese changes are associated with sharp increases in water retention with depth compared with water retention in the near-surface peat (Lafl eur et al., 2005a,b).

Quantifying macropore fl ow in fi bric peat requires estimates of macropore volumetric fractions. Classifying macropores solely by size is arbitrary, however, as their diameters are reported to vary widely, from 30 μm to >1 mm in mineral soils (Holden et al., 2001; Liu et al., 2001; Drzal et al., 1999; Watson and Luxmoore, 1986; Luxmoore, 1981; Puustjarvi, 1974) and in peat (Quinton et al., 2008; Carey et al., 2007; Schwarzel et al., 2002; Silins and Rothwell, 1998; Baird, 1997; Zeitz, 1992; Levesque et al., 1980). Th us, plausible defi nitions describe macropores as pores that pro-vide preferential gravitational fl ow so that mixing and transfer of water between them and smaller pores is limited (Skopp, 1981). Although macropores in peat and preferential water fl ow have been investigated in various studies (Blodau and Moore, 2002; Holden et al., 2001), few data are available concerning macro-pore volumetric fractions to help better understand the role of macropore fl ow in peat hydrology. Schwarzel et al. (2002) and Zeitz (1992) investigated upper peat horizons in German fens and published percentages of pore fractions by diameter: 3 to10, 10 to 50, and >50 μm. To our knowledge, their study is one of the very few that has attempted to quantify the macropore fraction in peat. Other detailed reviews of peat pore fractions and their distributions with depth have been given by Silins and Rothwell (1998) for the upper 40 cm of peat in a forested peatland in west-ern Canada, and by Quinton et al. (2008, 2000) and Carey et al. (2007) for arctic and subarctic peats.

Previous Modeling of Peat HydrologyTo date, most models of coupled peatland hydrology and

C cycling, such as the McGill Wetland Model (St-Hilaire et al., 2008), InTEC V3.0 ( Ju et al., 2006), the Peat Carbon Simulator (Frolking et al., 2002), COUP (Kellner, 2001; Jansson and Karlberg, 2001), and the Peat Accumulation Model (Hilbert et al., 2000), do not account for macropore fl ow. InTEC V3.0 and the Peat Accumulation Model simulate θ by the Richards equa-tion (Hillel, 1982) but do not resolve landscape microtopog-raphy. Th ese models therefore cannot properly reference their simulated θ to depth, which makes them incapable of simulating peatland hydrology on the microscale of hummocks and hol-lows. On the other hand, Z in the McGill Wetland Model and the Peat Carbon Simulator are prescribed to model hydrologic eff ects on C fl uxes, so that these models inherently do not fully simulate peatland hydrology. Th erefore, to consider the com-plexity of the peat profi le, a model is needed that accounts for microtopographic variations and simulates the soil hydrology and ecosystem processes.

OBJECTIVES AND HYPOTHESESTh e main objective of this study was to understand whether

the rapid infi ltration and limited retention of water by fi bric peat and the rapid changes in Z observed in peatlands can be explained by macropore fl ow in fi bric peat cavities plus micro-pore fl ow in the peat matrix, or by micropore fl ow alone through the bulk peat with no explicit representation of macropores. Th e conceptual hypothesis was that the high macropore frac-tions in fi bric peat determine its low water holding capacity and rapid gravitational discharge of infi ltrating water. Macroporosity sharply decreases to negligible values as peat changes from fi bric to hemic and sapric below, which is refl ected in slower infi ltra-tion and greater water retention. Th us, the macropore fl ow de-termines how Z and θ change in the peat profi le.

Th e classical soil hydrology models, based solely on the Richards equation, may be inappropriate for modeling soil wa-ter movement in organic soils because they do not represent preferential water fl ow through highly macroporous fi bric peat (Baird, 1997). Instead, a model is needed that partitions the fl ow between the matrix domain where soil water is driven by suction and gravitation, i.e., Richards-type fl ow, and the macropore do-main where soil water is driven by gravity alone (Baird, 1997). Th e modeling hypothesis tested in this study (Fig. 1a) was that both (i) the Hagen–Poiseuille equation for gravitational macro-pore fl ow and (ii) Richards’ equation for unsaturated and satu-rated micropore fl ow in the peat matrix function in parallel to explain peat subsurface hydrology. An alternative hypothesis (Fig. 1b) was that Richards’ equation alone, parameterized with hydraulic conductivities of bulk peat including macropore frac-tions, and without accounting separately for macropore fl ow, can explain peat subsurface hydrology. Th ese two hypotheses were tested by applying the ecosys model (Grant, 2001), parameterized for peat, at the Mer Bleue bog in southern Canada.

MODEL DEVELOPMENT: SOIL WATER TRANSPORT

Th e ecosys model is a detailed, process-based, three-dimen-sional model that couples soil physics, water transport, and heat transfer to biologically driven C and energy fl uxes of ecosystems through (i) soil–plant–atmosphere energy exchange and water relations, (ii) canopy C fi xation, (iii) canopy and root respiration and senescence, (iv) plant growth and phenology, and (v) soil microbial activity (Grant, 2001). A comprehensive description of the theory and algorithms on which ecosys is based was given by Grant (2004, 2001), Grant and Roulet (2002), and Grant et al. (2007, 2004). In this study, the model represented for the fi rst time a complex terrain microtopography of alternating hum-mocks and hollows, and solved for hummock and hollow θ and Z on an hourly time scale. A general description of the theory and equations that govern surface overland fl ow, subsurface ma-trix fl ow, and subsurface macropore fl ow is given below. Th e model parameters are defi ned in the Appendix and their values are given in Fig. 1.

682 SSSAJ: Volume 74: Number 2 • March–April 2010

Fig.

1. G

raph

ical

sch

eme

of t

he h

ypot

heti

cal p

eat

profi

le a

t M

er B

leue

bog

: (a)

mac

ropo

rosi

ty h

ypot

hesi

s w

ith

Hag

en–P

oise

uille

(H

-P)

fl ow

thr

ough

the

mac

ropo

re f

ract

ion

of t

he fi

bric

pea

t an

d R

icha

rds

(R)

fl ow

thr

ough

the

pea

t m

icro

pore

(m

atri

x) f

ract

ion

of fi

bri

c pe

at, a

nd t

hrou

gh h

emic

and

sap

ric

peat

wit

h no

mac

ropo

rosi

ty, w

ith

the

hori

zont

al s

atur

ated

hyd

raul

ic c

ondu

ctiv

ity

for

the

peat

mat

rix

(Ksa

t,h,

mm

h−

1 ),

assu

med

to

be fi

ve

tim

es t

he v

erti

cal

satu

rate

d hy

drau

lic c

ondu

ctiv

ity

(Ksa

t,v)

(R

eeve

et

al.,

2000

); a

nd (

b) a

lter

nati

ve h

ypot

hesi

s w

ith

Ric

hard

s (R

) fl

ow a

lone

and

wit

h no

exp

licit

re

pres

enta

tion

of m

acro

pore

fl ow

thr

ough

the

fi br

ic p

eat

(pea

t vo

lum

etri

c m

acro

pore

frac

tion

[Sc

hwar

zel e

t al

., 20

02]

MF

= 0

m3

m−

3 ), b

ut w

ith

Ksa

t,v

(mm

h−

1 ) (

Lett

s et

al.,

200

0), w

ater

con

tent

at

fi el

d ca

paci

ty fo

r pe

at m

atri

x (N

. Rou

let,

per

sona

l com

mun

icat

ion,

200

5) (θ F

C, m

3 m

−3 )

, and

wat

er c

onte

nt a

t w

iltin

g po

int

for

peat

mat

rix

(N. R

oule

t, p

erso

nal c

omm

unic

atio

n, 2

005)

(θ W

P, m

3 m

−3 )

ref

erri

ng

to b

ulk

fi br

ic p

eat

that

incl

udes

mic

ropo

res

and

mac

ropo

res;

N is

the

num

ber

of s

oil l

ayer

s, s

tart

ing

from

the

hum

moc

k su

rfac

e; S

LTk

(cm

) an

d SL

T w (

cm)

are

the

soil

laye

r de

pths

fro

m t

he h

umm

ock

and

hollo

w s

urfa

ces,

res

pect

ivel

y; B

D (

Mg

m−

3 ) is

the

bul

k de

nsit

y of

pea

t w

ith

mac

ropo

res

for

Laye

rs 1

to

10 (

Blo

dau

and

Moo

re, 2

002)

and

11

to 1

5 (F

rolk

ing

et a

l., 2

002,

200

1); a

nd ε

t (m

3 m

−3 )

is t

he s

oil

laye

r to

tal p

oros

ity,

cal

cula

ted

from

the

cor

resp

ondi

ng B

D.

SSSAJ: Volume 74: Number 2 • March–April 2010 683

Surface FlowSurface fl ow, Qr (m3 m−2 h−1), is calculated as the product

of the runoff velocity v (m h−1), the depth of mobile surface water, dm (m), and the width of fl ow paths, Lp (m), in west to east x and north to south y directions for each landscape posi-tion x,y:

( ) ( , ) , ( , )r , , x x y x y y x yx x yQ v d L= [1a]

( ) ( , ) , ( , )r , , y x y x y x x yy x yQ v d L= [1b]

w ( , )r , ( , ) r , 1( , ) r , ( , ) r , 1( , )

x yx x y x x y y x y y x y

dQ Q Q Q

tΔ

Δ + += − + − [1c]

where dw is the depth of the water (m) and Δt is the time step. Th ese equations implement the kinematic wave theory in which changes in horizontal overland fl ow plus changes in surface wa-ter depth equal the diff erence between rainfall and infi ltration. Further details about calculating Qr are given in Grant (2004).

Matrix FlowWater fl uxes in the soil matrix, Qm (m3 m−2 h−1), are a prod-

uct of the water potential, ψ (MPa), diff erences and hydraulic con-ductances, Km′ (m MPa−1 h−1), in west to east x, north to south y, and vertical z directions for each landscape position x,y,z:

( ) ( )m , , 1, ,m, , , x x y z x y zx x y zQ K ψ ψ += ′ − [2.1a]

( ) ( )m , , , 1,m, , , y x y z x y zy x y zQ K ψ ψ += ′ − [2.1b]

( ) ( )m , , , , 1m, , , z x y z x y zz x y zQ K ψ ψ += ′ − [2.1c]

Values of ψ are sums of matric, ψm (MPa), osmotic, ψo (MPa), and gravimetric, ψg (MPa), components calculated from θ (m3 m−3), solute concentrations (mol m−3), and relative topo-graphic elevations in the soil profi le (m), respectively. Hydraulic conductances (Km′) are calculated from hydraulic conductivi-ties, Kθ (m2 MPa−1 h−1), of adjacent landscape positions in the x, y, and z directions. Th e Kθ values are calculated according to Green and Corey (1971) for each landscape position:

( ) ( ) ,

2, , , , sat 2 1 2

j i m

x y z x y z jK CK j iθ θ ψ=

−⎡ ⎤= + −⎣ ⎦∑ [2.2]

from an input value of the saturated hydraulic conductivity of the soil matrix, Ksat (mm h−1), in the horizontal (Ksat,h) and ver-tical (Ksat,v) directions (Fig. 1). With negligible macroporosity or without accounting separately for macropore fl ow in soils, the parameters Ksat,h and Ksat,v are assumed to be numerically equal to the bulk saturated hydraulic conductivities in the horizontal and vertical directions reported in the literature. Th e other terms in Eq. [2.2] are m (dimensionless), the total number of pore classes in the soil matrix; i (dimensionless), the last water content class on the wet end of the soil matrix (i = 1 identifi es saturation); ψj (MPa), the water potential for the jth class (1 ≤ j ≤ m) of

water-fi lled pores; and C (g s−2), a coeffi cient that summarize the eff ects of m, the surface tension and viscosity of water, and total soil porosity (Green and Corey, 1971).

Th e value of Km′ is calculated in the x, y, z directions (Eq. [2.3a], [2.4a], and [2.5a]):

, , 1, ,m

, , ,( 1, , ) 1, , ,( , , )

, , e( , , ) 1, , e( 1, , )

, , e( , , ) 1, , e( 1, , )

2

;

;

x y z x y zx

x y z x x y z x y z x x y z

x y z x y z x y z x y z

x y z x y z x y z x y z

K KK

K l K lθ θ

θ θ

ψ ψ ψ ψ

ψ ψ ψ ψ

+

+ +

+ +

+ +

′=+

⎡ ⎤< <⎣ ⎦⎡ ⎤> >⎣ ⎦

[2.3a]

, ,m

( 1, , ) ( , , )

, , e( , , ) 1, ,z e( 1,y , )

2

;

x y zx

x x y z x x y z

x y z x y z x y x z

KK

l lθ

ψ ψ ψ ψ+

+ +

′=+

⎡ ⎤> <⎣ ⎦

[2.3b]

1, ,m

( 1, , ) ( , , )

, , e( , , ) 1, , e( 1, , )

2

;

x y zx

x x y z x x y z

x y z x y z x y z x y z

KK

l lθ

ψ ψ ψ ψ

+

+

+ +

′=+

⎡ ⎤< >⎣ ⎦

[2.3c]

, , , 1,m

, , ( , 1, ) , 1, ( , , )

, , e( , , ) , 1, e( ,y 1, )

, , e( , , ) , 1, e( , 1, )

2

;

;

x y z x y zy

x y z y x y z x y z y x y z

x y z x y z x y z x z

x y z x y z x y z x y z

K KK

K l K lθ θ

θ θ

ψ ψ ψ ψ

ψ ψ ψ ψ

+

+ +

+ +

+ +

′=+

⎡ ⎤< <⎣ ⎦⎡ ⎤> >⎣ ⎦

[2.4a]

, ,m

( , 1, ) ( , , )

, , e( , , ) , 1, e( , 1, )

2

;

x y zy

y x y z y x y z

x y z x y z x y z x y z

KK

l lθ

ψ ψ ψ ψ+

+ +

′=+

⎡ ⎤> <⎣ ⎦

[2.4b]

, 1,m

( , 1, ) ( , , )

, , e( , , ) , 1, e( , 1, )

2

;

x y zy

y x y z y x y z

x y z x y z x y z x y z

KK

l lθ

ψ ψ ψ ψ

+

+

+ +

′=+

⎡ ⎤< >⎣ ⎦

[2.4c]

, , , , 1m

, , ( ,y , 1) , , 1 ( , , )

, ,z e( , ,z) , ,z 1 e( , , 1)

, , e( , , ) , , 1 e( , , 1)

2

;

;

x y z x y zz

x y z z x z x y z z x y z

x y x y x y x y z

x y z x y z x y z x y z

K KK

K l K lθ θ

θ θ

ψ ψ ψ ψ

ψ ψ ψ ψ

+

+ +

+ +

+ +

′=+

⎡ ⎤< <⎣ ⎦⎡ ⎤> >⎣ ⎦

[2.5a]

,y ,m

( , , 1) ( , , )

, , e( , , ) , , 1 e( , , 1)

2

;

x zz

z x y z z x y z

x y z x y z x y z x y z

KK

l lθ

ψ ψ ψ ψ+

+ +

′=+

⎡ ⎤> <⎣ ⎦

[2.5b]

684 SSSAJ: Volume 74: Number 2 • March–April 2010

, , 1m

( , , 1) ( , , )

, , e( , , ) , , 1 e( , , 1)

2

;

x y zz

z x y z z x y z

x y z x y z x y z x y z

KK

l lθ

ψ ψ ψ ψ

+

+

+ +

′=+

⎡ ⎤< >⎣ ⎦

[2.5c]

unless ψ of one of the positions exceeds its air-entry potential, ψe. Th e lx (m), ly (m), and lz (m) are the model cell sizes. In these cases, Km′ is calculated from Kθ of the saturated position only (Eq. [2.3b], [2.3c], [2.4b], [2.4c], [2.5b], and [2.5c]), and ψ of the unsaturated position is calculated from a θ that excludes wa-ter added while ψ of the fi rst position is >ψe, thereby simulating a wetting front during Green–Ampt infi ltration (Grant, 2004). Water movement between adjacent positions thus alternates be-tween Richards and Green–Ampt fl ow, depending on ψ vs. ψe in each position. Changes in θ at each time step Δt arise from dif-ferences in subsurface fl ow among adjacent landscape elements:

m , ,m ( , ) m 1( , ) m ( , )

m 1( , ) m ( , ) m 1( , )

x y zx x y x x y y x y

y x y z x y z x y

Q Q Qt

Q Q Q

ΔθΔ +

+ +

= − +

− + −

[2.6]

Macropore FlowWater macropore fl ux, QM (m3 m−2 h−1) moves in the

x, y, and z directions for each landscape position according to Poiseuille–Hagen theory for laminar fl ow in tubes, driven by diff erences in ψg (MPa) and macropore conductances KM′ (m MPa−1 h−1)

( ) ( )M g , , g , , 1M, , , x y z x y zz x y zQ K ψ ψ += ′ − [3.1]

Values of ψg are calculated from relative topographic elevations in the soil profi le. Values of KM′ are calculated from macropore hydraulic conductivities KM (m2 MPa−1 h−1) of each two adja-cent positions in the soil profi le:

M , , M , , 1M

M , , ( , , 1) M , , 1 ( , , )

2K

x y z x y z

x y z z x y z x y z z x y z

K KK

l K l+

+ +

′=+

[3.2]

Values of KM are calculated from individual macropore hydrau-lic conductivities KM* (m4 MPa−1 h−1 pore−1) and macropore density, NM (number of macropore channels m−2):

M , , M M , , *x y z x y zK N K= [3.3]

Th e KM* values are calculated from the average macropore radi-us, RM (m), and the dynamic viscosity of water, ηw (g cm−1 s−1):

4M

M, , ,w

*8x y z

RK πη

= [3.4]

Values of NM are calculated from the macropore volume, VM (m3 m−3), within the model cell, the model cell thickness, lz (m), and the individual pore surface area, SM* (m2):

MM

M

/*

zV lNS

= [3.5]

Values of VM are calculated from the preset macropore fraction fM (m3 m−3), specifi c for each soil type:

M M

M z x y zV f l l l

f l=

= [3.6]

Values of SM* are calculated from RM:

2M M*S Rπ= [3.7]

SITE DESCRIPTION AND KEY SITE CHARACTERISTICS

Mer Bleue bog is a large, ombrotrophic bog, located about 15 km east of Ottawa in the Ottawa Valley, Ontario, Canada, with a surface area of approximately 2800 ha. Th e groundcover is mainly Sphagnum mosses and the overstory vegetation is domi-nated by a low shrub canopy (20–30-cm height), with sparse sedges and herbaceous plants and some discontinuous patches of coniferous trees (Lafl eur et al., 2005a; Frolking et al., 2002; Moore et al., 2002). Peat depth increases from 2 to 6 m from the periphery toward the center and averages about 4 to 5 m. Th e bog surface has an expressed hummock–hollow microtopogra-phy, dominated by hummocks with an average diameter of 1 m that comprise about 70% of the surface. Th e average relief be-tween hummocks and hollows is 25 cm (Lafl eur et al., 2005a). On a macrotopographical scale, the bog is almost fl at, with a very slight north–south slope of 0.005° and even slighter east–west slope of 0.0008° (Fraser et al., 2001; Fraser, 1999). Th e latter is assumed to be negligible for the microscale of this modeling work. Mer Bleue is a dry peatland, with a WT varying between ?20 and ?70 cm below the hummock surface (Lafl eur et al., 2005a,b). Based on peat texture and the Von Post degree of hu-mifi cation, fi bric peat occupies the top 0 to 35 cm, followed by hemic peat at 35 to 45 cm, then sapric peat at depths >45 cm in hummocks, and the top 0 to 10, 10 to 20, and >20 cm, respec-tively, in the hollows (Lafl eur et al., 2005b; S. Admiral, personal communication, 2005).

Micropore and macropore fractions of the fi bric peat at Mer Bleue bog are 0.15 and 0.8 m3 m−3, respectively, estimated from micropore and macropore fractions and the peat bulk den-sity of the near-surface peat in German peatlands (Schwarzel et al., 2002; Zeitz, 1992). Th is high macroporosity of 0.8 m3 m−3 is supported by studies for boreal, arctic, and subarctic peat-lands. Silins and Rothwell (1998) found, for boreal peatlands of western Canada, that macropores with diameters >30 μm were ~0.75 m3 m−3, and those with diameters >600 μm were ~57 m3 m−3 in near-surface peat. Carey et al. (2007) reported pore diameter distributions for subarctic organic soils at 4-, 6-, and 15-cm depths, according to which the macroporosity of di-ameters >30 μm should comprise ?75% of the total peat poror-sity, even though they considered as macropores only pores with

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diameters >1000 μm. Although not distinguishing macropores in peat, Quinton et al. (2008, 2000) reported high active poror-sity, defi ned as “relatively large, interparticle pores that actively transmit water”, that reached ?0.8 m3 m−3 in the top active layer of arctic and subarctic peatlands, thus implying high macropore fractions there.

Slower drainage and greater retention of water at 40- and 50-cm depths in Mer Bleue hummocks (S. Admiral, personal communication, 2005) implies small or absent macropore frac-tions in the hemic and sapric peat. Quinton et al. (2008) and Silins and Rothwell (1998) also reported a decrease in macropore fractions with depth. A reduction of macroporosity with depth is consistent with the advanced decomposition and compression of hemic and sapric peat, in comparison to fi bric peat (Quinton et al., 2008, 2000; Clymo 1983). Th erefore, no macropore fractions were modeled in hemic or sapric peat.

METHODSTh e ecosys model (Grant, 2001) was run with and without macro-

pores to simulate the presence and absence of macropore fl ow for testing the hypotheses above by comparing simulated θ vs. θ measured by time do-main refl ectometry (TDR) at various depths in hummocks and hollows, and simulated Z vs. Z measured by potentiometers at Mer Bleue bog.

Measurements of Water Content and Water Table Depth

Continuous in situ TDR measurements of θ, potentiometric mea-surements of Z, and eddy covariance (EC) measurements of C and en-ergy fl uxes have been conducted at Mer Bleue bog since 1998 (Lafl eur et al., 2001). Values of θ were measured at 10-, 20-, 30-, 40-, and 50-cm depths below the hummock surface, and at 3 and 15 cm below the hol-low surface. All the TDR readings were linearly normalized to fall be-tween 0.07 and 0.93 m3 m−3, i.e., between the θ of the air-dried peat and the porosity of moss. Normalizing was done so that observations would show saturation when the WT was above the sensor location and would also approximate the results from gravimetric measurements. Values of Z were measured, with respect to the hummock surface, in wells be-neath hummocks and hollows using a fl oat and counterweight system attached to a potentiometer, and complementary manual measurements were made to check the potentiometers.

Key soil parameters and their sources used to initialize ecosys for the Mer Bleue bog are given in Fig. 1 for hummocks and hollows, with depths referenced to the hummock surface. Peat parameters measured

or derived at Mer Bleue bog are explicitly stated in Fig. 1. Water contents at fi eld capacity and the wilting point, measured when the macropores are drained, were attributed entirely to the fi bric peat micropore frac-tion (0.2 in Fig. 1a and 1.0 in Fig. 1b). Bulk soil attributes were, there-fore, the same in both model formulations. Th e peat ψ at fi eld capacity and the wilting point were set at −0.03 MPa (Levesque et al., 1980) and at −1.5 MPa (Clymo, 1983), respectively, as generalized and representa-tive values for peat.

To drive ecosys, half-hourly continuous input was provided during the period 1998 to 2004 for incoming shortwave radiation above the canopy, RSW (W m−2), air temperature at 2 m above the canopy, Ta (°C), relative humidity at 2 m above the canopy, RH (%), wind speed at 2 m above the canopy, U (m s−1), and precipitation, P (mm Δt−1), where Δt is the model time step; measurements were described in de-tail in Lafl eur et al. (2005a,b, 2003). Th e winter precipitation for the days with snow cover was calculated from the positive increments of the snow cover, corrected by the snow bulk density ρsn of 0.11 Mg m−3. Th en every 30-min precipitation measurement from the periods January to March and October to December each year was corrected by the ratio between the total 3-mo precipitation measured at Macdonald–Cartier Ottawa Airport (?15 km from Mer Bleue bog) and the total 3-mo pre-cipitation measured at Mer Bleue bog for those periods.

Th e latent heat (LE) fl ux was measured by the EC technique (Lafl eur et al., 2005a, 2003). Values of LE were integrated across time to calculate the daily evapotranspiration, ET (mm d−1) (Lafl eur et al., 2005a), which was compared with the simulated ET.

Th e quality of the LE measurements was ensured by fi rst screen-ing for erroneous values of half-hour water vapor, wind, air temperature, and pressure due to sensor malfunction or during periods with rainfall >0.4 mm h−1. Th en, all the data beyond ±3 standard deviations from the monthly daytime and monthly nighttime means were also fi ltered out. Gaps in the RSW, Ta, RH, W, and P data were fi lled by (i) average neighboring values, if no more than four missing 30-min values occurred in a sequence, or by (ii) projecting the corresponding period of time from the previous or the next day with available data across the missing values, should more than four of them occur in a sequence. Th e entire period 1 Jan.–30 May 1998 was missing and was substituted with data from the same period in 1999 to complete the yearly meteorological records for 1998 to drive the ecosys model. Th erefore, output from 1998 and 1999 were not used in model testing to avoid artifacts in the simulations.

Model ExperimentA two-dimensional model transect of six grid cells, three hum-

mocks and three hollows, was designed to represent the microtopog-raphy of Mer Bleue bog in actual size and proportions (Fig. 2), as de-scribed above. All transect cells were allowed to freely exchange soil water, heat, gases, and solutes with adjacent cells, and through northern and southern boundaries of the transect (Fig. 2) following the preset north–south slope of ?0.005°. No fl ux exchange was allowed in the model through the eastern and western boundaries of the transect due to the negligible east–west slope that was set to zero for the microscale of this research. Th e bottom soil layer (Fig. 1) of each grid cell was con-sidered as the lower boundary through which no fl uxes were allowed, thus representing the impermeable marine clay at the bottom of Mer Fig. 2. Model two-dimensional transect with microtopography at Mer

Bleue bog, as represented in ecosys; GC is grid cell.

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Bleue basin (Mott and Camfi eld 1969). Th e fi rst and second and the fi ft h and sixth cells were considered boundary cells, so that the θ of the third and fourth cells used in comparisons were not directly aff ected by assumptions of water movement through boundaries. Th e third and fourth cells were used to generate hourly and daily output in model test-ing for bog hummocks and hollows.

To test the macroporosity hypothesis, ecosys was run with macropore fractions of 0.8, 0, and 0 m3 m−3 for fi bric, hemic, and sapric peat, respec-tively (Fig. 1a). Th e model needed to be parameterized with the generally unknown Ksat of the fi bric peat micropore (matrix) fraction, which was set equal to the known value for hemic peat with no macroporosity (Fig. 1a). To test the alternative hypothesis, ecosys was run with macropore frac-tions of 0 m3 m−3 for fi bric, hemic, and sapric peat, and with the represen-tative bulk Ksat of fi bric peat, as given in Fig. 1b (Letts et al. 2000; Fraser et al. 2001; Fraser, 1999), based on combined matrix and macropore fl ow. Values of Ksat for hemic and sapric peat were the same in both runs be-cause no macropore fractions were assumed there (Fig. 1).

Th e ecosys model was run for 106 yr, with moss and shrubs seed-ed in the very fi rst model year, and then spun up by repeating the 7-yr weather period of 1998 to 2004, available at the time of writing, 15 times. Equilibrium during the model spin-up was attained aft er 60 to 70 yr, when changes in simulated C sequestration in the soil humic pool became stable with time ( Ju et al., 2006). Model output for θ at various depths was generated for both hummocks and hollows. Th e ecosys model simulates Z within discrete soil layers, so the modeled WT was consid-ered to include any soil layer with a water-fi lled pore space >0.9 m3 m−3, calculated from the layer’s bulk density, thus accounting for ?10% en-trapped gas in the peat water on a volumetric basis, as reported in the lit-erature for northern bogs (Rosenberry et al., 2006; Kellner et al., 2004).

Sensitivity of the simulated micropore fl ow to widely varying bulk fi bric Ksat values found in the literature (Letts et al., 2000) was inves-tigated to better understand whether water infi ltration and retention in the near-surface peat could be explained by extreme bulk hydraulic conductivities rather than by macropore fl ow.

Model Test and StatisticsTh e ability of the model with and without macropore fl ow to

simulate short-term infi ltration and water retention in hummocks and hollows was fi rst tested against measurements of θ, Z, and ET follow-ing an extreme rainfall event in 2004. Th e ability of the two model ver-sions to simulate the seasonal dynamics of θ, Z, and ET were then tested against measurements in 2001, a drier year with relatively low precipita-tion. Changes in Z modeled and measured in 2001 were then contrasted with those during 2004, which was a wetter year. Discrepancies between model output and measurements for the two model runs were evaluated by the RMSD. Th e relative discrepancies between measurements and model output were evaluated by Willmott’s index of agreement (d), d = 1 − [Σ(Pi − Oi)

2/Σ(|Pi − O*| + | Oi − O*|)2], with 0 ≤ d ≤ 1 be-cause the smaller the relative discrepancies, the higher the d value, where i is the number of all measurements, Oi are the measured values, Pi are the modeled values, and O* is the standard deviation of the measure-ments (Willmott, 1982, 1981; Davies, 1981; Powell, 1980; Willmott and Wicks, 1980). To evaluate the goodness-of-fi t and predictive power for the two model runs, coeffi cients of determination (R2), slopes, and

intercepts, were obtained from linear regressions between the modeled θ and the TDR data at 10-, 20-, 30-, 40-, and 50-cm depths in hummocks, and between the modeled and potentiometric Z values.

RESULTSShort-Term Peat Hydrology during Rainfall Events

Th e year 2004 was wet and cool, with high peat θ and WT, thus providing an opportunity to test the alternative model hypotheses with and without macropore fl ow under wet conditions. Th e most intensive rainfall event during the study period occurred on day of the year (DOY) 253, when 124.5 mm of precipitation occurred in a 24-h period. Th e TDR measurements indicated rapid infi ltration and low water retention, associated with small changes in θ, in the fi bric peat at 10- and 20-cm depths under hummocks (Fig. 3a and 3b). Rapid infi ltration and low retention caused saturation at the 30-cm depth under hummocks and a rapid rise of the WT during and immediately aft er the rainfall event (Fig. 3c and 4a). Values of Z remained above the 25-cm depth in the hummocks, saturating the hollows (Fig. 4), for several days aft er the rainfall (Fig. 5), following which the WT fell as the rainwater drained, indicated by a rapid decline in θ.

Fig. 3. Hourly simulated and measured (using time domain refl ectometry) soil water content (θ) at (a) 10-cm, (b) 20-cm, and (c) 30-cm depths in hummocks, Mer Bleue bog, following a 124.5-mm rainfall on day of the year (DOY) 253 in 2004.

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Simulating Short-Term Infi ltration, Retention,and Water Table with Macropore Flow

Simulated preferential fl ow through the large macropore fraction (Eq. [3.1–3.7]), and low water holding capacity of the small micropore fraction (Fig. 1a), caused rapid water infi ltra-tion (Fig. 3a and 3b) and WT rise (Fig. 5), followed by rapid lateral drainage (Fig. 3c) and WT fall (Fig. 5), and low water retention aft er drainage (Fig. 3c) in hummocks. Simulated θ declined more slowly than did TDR θ at 30 cm (Fig. 3c), in-dicating lower lateral hydraulic conductivity and consequently slower drainage in the model. A prolonged WT rise close to the hollow surface in the model compared with the TDR records (Fig. 4) also suggested slower lateral drainage, probably due to

lower fi bric Ksat in the model (Fig. 1a) than in the fi eld, and possibly a smaller slope in the model (Fig. 2) than at the TDR locations. Slower simulated drainage might have also been an artifact of presetting no exchange through the east and west boundaries, thus preventing surface fl ow around hummocks when the hollows were saturated.

During the extreme rainfall event, the large amount of in-coming rainwater raised θx,y,z in the model grid cells. Th is rise consisted of one in matrix (micropore) water content, Δθmx,y,z (Eq. [2.2]), and, if the grid cell was within the fi bric peat zone and below the WT (Fig. 1a), of one in macropore water con-tent, ΔθMx,y,z. With a macroporosity of 0.8 m3 m−3 (Fig. 1a), Δθmx,y,z remained small (Fig. 3a and 3b), while ΔθMx,y,z was large (Fig. 3c). Th e latter was not subject to retention by the soil but rose rapidly when infi ltration exceeded drainage and declined rapidly when drainage exceeded infi ltration. Drainage was hastened by rapid macropore fl uxes QM,z (Eq. [3.1]) through the fi bric peat zone to the uppermost saturated layer. Th is layer was below the fi bric zone, however, where Ksat was smaller (Fig. 1a), so that macropore drainage was constrained by slow infi ltration and lateral transport, causing the rapid rise in the WT to 25-cm depth in the hummocks (Fig. 3c) and 3-cm depth in the hollows (Fig. 4a). Th is rise closely tracked the measured rise in the WT so that the run with macropore fl ow adequately simulated the WT dynamics (Fig. 5).

Capillary rise, simulated by upward Green–Ampt wetting (Eq. [2.1c]), maintained θm near saturation in the peat matrix at all depths above the WT during and aft er the rainfall event (Fig. 3 and 4a). Saturation and low Ksat of the micropore frac-tion caused Qm to be driven by a relatively small Δψ (Eq. [2.1a], [2.1b], and [2.1c]) and Kθ (Eq. [2.3]) and Km′ (Eq. [2.4a], [2.5a], and [2.6a]), slowing Qm through adjacent layers and boundaries and maintaining a high θm. Th e steeper initial rise of the TDR θ right aft er the rainfall (Fig. 3) possibly implied slightly higher hydraulic conductivities than simulated for the fi bric peat ma-trix. Matrix-only fl uxes Qm (Eq. [2.1a], [2.1b], and [2.1c]) in the hemic and sapric peat below the fi bric peat (Fig. 1a) slowed the drainage of the fi bric peat above.

Simulating Short-Term Infi ltration, Retention,and Water Table without Macropore Flow

Th e model run without macropore fl ow failed to adequately simulate the infi ltration, lateral drainage, and water retention in fi bric peat. In each model cell, the rainfall caused a sharp initial increase of θm above the WT (Fig. 3 and 4) due to the larger micropore water holding capacity (Fig. 1b). Th is increase delayed the rise in the WT compared with the measurements (Fig. 5). High bulk fi bric Ksat for the combined matrix and macropore fractions (Fig. 1b) and an initial increase of θm for peat layers above the WT aft er the start of the rainfall event caused high Kθ and K′ values and hence rapid infi ltration aft er the rainfall ceased. Th e decrease in θm during drainage caused rapid declines of Kθ and K′, however, and although the lower θm caused a larg-er Δψ, Qm declined (Eq. [2.1a], [2.1b], and [2.1c]) so that θm

Fig. 4. Hourly simulated and measured (using time domain refl ectometry) soil water content (θ) at (a) 3-cm and (b) 15-cm depths in hollows, Mer Bleue bog, following a 124.5-mm rainfall on day of the year (DOY) 253 in 2004.

Fig. 5. Hourly simulated and measured (potentiometric) water table (WT) depth below the hummock surface, Mer Bleue bog, 2004, following a 124.5-mm rainfall on day of the year (DOY) 253 in 2004.

688 SSSAJ: Volume 74: Number 2 • March–April 2010

tended to equilibrate at ?0.3 m3 m−3 in hummocks (Fig. 3) and hollows (Fig. 4a), well above the fi eld capacity of 0.1 m3 m−3 in bulk fi bric peat (T. Moore, personal communication, 2005). Higher θm, compared with macropore fl ow, caused faster lateral exchange through the model boundaries, which resulted in a lower WT and slower WT dynamics compared with macropore fl ow (Fig. 5).

Simulating Short-Term Evapotranspiration withand without Macropore Flow

Both model runs, with and without macropore fl ow, had the same meteorological input drivers, so diff erences between their daily ET rates (Fig. 6) were caused by diff erences in near-surface θ and hence vapor pressure arising from diff erences in subsurface water transport. Th e run without macropore fl ow simulated more rapid ET during the fi rst 10 d aft er the rainfall, oft en exceeding the measured values, due to slower matrix in-fi ltration and higher water retention modeled in the fi bric peat with no macroporosity.

Seasonal Peat HydrologyTh e relatively hot and dry year 2001 with a high ET/P

(evapotranspiration/precipitation) ratio of 0.88 (Lafl eur et al., 2005a) caused pronounced seasonal changes in the TDR θ and potentiometric WT, which gave an opportunity to test the alter-native model hypotheses with and without macropore fl ow dur-ing the spring thawing with WT rise, summer drying with WT decline, and autumn rewetting with WT rise.

Simulating Seasonal Hydrology with Macropore Flow

During 2001, the run with macropore fl ow better simu-lated θ peaks above the 30-cm depth in hummocks with early-spring thawing (Fig. 7a, 7b, and 7c) and θ declines below the 30-cm depth with summer drying (Fig. 7d and 7e), θ peaks at the 3-cm depth in hollows with early-spring thawing (Fig. 8a) and θ declines below the 3-cm depth with summer drying (Fig. 8b), and WT rise in late fall (Fig. 9a). In the model, summer dry-ing between DOYs 160 and 260 (Fig. 9a) reduced the surface θ, which equilibrated at ?0.03 m3 m−3 (?30% of the fi bric peat micropore fraction), in the surface 5 cm in hummocks and slight-ly below 0.11 m3 m−3 in the surface 1 cm in hollows (data not shown). Drying of the hummock surface occurred in the model because upward Qm from the WT through the small micropore fraction of the thicker fi bric peat did not maintain the surface θ under the high ET demand in summer. Wetness of the hollow surface was maintained in the model by more rapid upward Qm from the WT through the shallower fi bric peat. Values of θ in fi bric peat increased to ?0.11 m3 m−3 (?80% of the fi bric peat micropore fraction) between 5- and 35-cm depths in hummocks (Fig. 7a, 7b, and 7c) and between 1- and 10-cm depths in hol-lows (Fig. 8a). Upward Qm was maintained by Green–Ampt fl ux in the near-saturated zone just above the WT and by Richards fl ux farther up the unsaturated profi le (Eq. [2.1c]).

In the run with macropore fl ow, precipitation plus lateral re-charge (Eq. [2.1a–2.1b]) did not fully replace the water removed by rapid ET during summer, forcing upward Qm from the WT surface and thereby lowering the WT (Fig. 7d, 7e, and 9a). Th is WT decline in the course of 2001 was contrasted with that dur-ing the wetter year 2004 (Fig. 9b) to test the performance of the run with macropore fl ow under diff erent hydrologic boundary conditions. Th e lower ET/P ratio of 0.44 during 2004 (Lafl eur et al., 2005a) enabled the model to maintain higher θ values through the fi bric peat zone, with little surface desiccation and lower Z (Fig. 9b).

Simulating Seasonal Hydrology without Macropore Flow

Th e run without macropore fl ow simulated seasonal chang-es in peat θ and Z less satisfactorily than did the run with mac-ropore fl ow. Simulated θ without macropore fl ow responded excessively to rainfall in the upper soil layers (Fig. 7a, 7b, 7c. and 8a) and inadequately in lower layers (Fig. 7d, 7e, and 8b) of both hummocks and hollows, while the simulated Z fell deeper with drying than the observed Z (Fig. 9a). Th ese responses were caused by slower infi ltration and drainage, and greater water re-tention in fi bric peat, as observed above.

Both model runs simulated similar annual ET (547 and 540 mm for the non-macropore and macropore runs, respectively), larger than the 457 mm derived from the EC measurements. Th e diff erence may have been due to incomplete energy balance clo-sure of ?90% (Lafl eur et al. 2005a) aff ecting the EC-measured LE fl ux (see above) and accelerated plant productivity in both model runs in early May. Larger ET rates modeled without macropore fl ow in the summer (not shown) were due to larger simulated near-surface θ (Fig. 7a).

Agreement between Modeled and Measured Water Content and Water Table Depth with and without Macropore Flow

Linear regressions between θ and Z measured and simu-lated with and without macropore fl ow during 2000 to 2004 at Mer Bleue were highly signifi cant (P < 0.0001) (Tables 1 and 2). Regression statistics for both model runs, however, demonstrated

Fig. 6. Daily evapotranspiration simulated by the ecosys model and derived by eddy covariance during and after heavy rainfall on day of the year (DOY) 253 in 2004.

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varying levels of agreement with the measured θ at diff erent depths (Tables 1 and 2). Agreement was low for both runs at 10- and 50-cm depths due to low variability in the measured θ and Z above and below the zone of WT movement (Fig. 7a, 7e, and 9b). Agreement for both runs improved at the 20-, 30-, and 40-cm depths as variability in θ increased in the soil zone through which the WT rose and fell (Fig. 7b, 7c, 7d, and 9b). Th e R2 and slopes were closer to one, and intercepts closer to zero, for the run with macropores than for the run without macropores (Table 1 vs. Table 2), indicating better model performance with preferential macropore fl ow. Similar RMSDs suggested similar discrepancies between simulated and measured θ for both model runs, but higher, closer to 1, Willmott’s d values with macropore fl ow suggested smaller relative discrepancies and better model performance with macropores.

We recognize that there are potential problems with apply-ing the TDR technique in peat because TDR is sensitive to high organic contents in soil, its degree of humifi cation, and its tem-perature (Myllys and Simojoki, 1996; Pepin et al., 1992; Topp and Davis, 1985). Th ese sensitivities may have infl uenced agreement between the modeled and measured θ values. Nonetheless, the

TDR measurements represent at least the dynamics of the hydro-logic patterns, if not the exact θ values (Kellner and Lundin, 2001).

Discrepancies between modeled and measured Z for both runs (Table 1 and 2) were to some extent artifacts of the soil layer discretization in the model because Z in ecosys was allo-cated to the midpoint of the uppermost saturated soil layer (see above). Instead, the primary focus of this modeling eff ort was to simulate θ at depth reasonably well. Yet, within the range of WT variation at Mer Bleue bog, the RMSD of 6.6 cm for Z with macropore fl ow (Table 1) indicated a comparatively smaller discrepancy than that expressed by the RMSD for Z without macropore fl ow (Table 2).

DISCUSSIONIn this study, the ecosys model (Grant, 2001) was shown to

explicitly simulate water infi ltration and retention, and θ dynam-ics in the unsaturated near-surface peat in both hummocks and hollows with an hourly time step at diff erent depths. Recent detailed measurements in peatlands allowed us to generate rep-resentative sets of values for the peat hydraulic properties at depth (Fig. 1) that could be used to parameterize complex pro-cess-based models, such as ecosys. Th e model output was tested

Fig. 7. Hourly simulated and measured (using time domain refl ectometry) soil water content (θ) at (a) 10-cm, (b) 20-cm, (c) 30-cm (d) 40-cm, and (e) 50-cm depths in hummocks, Mer Bleue bog, during 2001. DOY is day of the year.

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against continuous measurements of hourly TDR θ for several years at various depths in hummocks and hollows and against hourly measurements of Z below the hummock surface. To our knowledge, this is one of the most detailed model–data com-parisons in peatland hydrology, allowing our alternative model hypotheses to be subjected to better testing than most earlier model studies (e.g., Kluge et al., 2008; Schwarzel et al., 2006; Kennedy and Price, 2004; McKenzie et al., 2002; Kellner, 2001; Jansson and Karlberg, 2001; Šimůnek et al., 1998; Garnier et al., 1997; Harbaugh and McDonald, 1996; Jarvis, 1994; Oostindie and Bronswijk, 1992; Bronswijk, 1989, 1988; McDonald and Harbaugh, 1988; Hoogmoed and Bouma, 1980). Th is testing clearly indicated the need to simulate macropore fl ow explicitly to represent the eff ects of highly porous upper peat on water fl ows in peatlands.

Importance of the Macropore Flow and Microtopography for Modeling Peatland Hydrology

Th e ecosys model without macropore fl ow, even when pa-rameterized with a representative bulk Ksat of fi bric peat of 1.008 m h−1 (Letts et al., 2000), which refl ected the contribu-tion to water transport from both macropores and the peat ma-trix, failed to accurately simulate the dynamics of the peat θ and Z. Similarly, the diffi culty for many existing models to simu-late hydrologic processes properly in the unsaturated peat zone was partially due to their limitations in simulating macropore fl ow in the near-surface peat (Baird, 1997). Models such as FLOCR (Bronswijk, 1989, 1988), FLOCR 2.0 (Oostindie and

Bronswijk, 1992), MODEFLOW (Harbaugh and McDonald, 1996; McDonald and Harbaugh, 1988), ECOUL (Garnier et al., 1997), COUP (Kellner, 2001; Jansson and Karlberg, 2001), Visual MODEFLOW (McKenzie et al. 2002), FLOCOPS (Kennedy and Price, 2004), and HYDRUS (Kluge et al., 2008, Schwarzel et al., 2006, Šimůnek et al., 1998) describe soil subsurface hydrology in the unsaturated zone through the Richards equation, continuity equation, and various hydrau-lic conductivity functions, and equations for water retention curves, some of them especially parameterized for peat (Letts et al., 2000, Weiss et al., 1998). To our knowledge, however, these models do not explicitly account for possible macropore fl ow in the fi bric peat zone.

Other models ( Jarvis, 1994; Hoogmoed and Bouma, 1980) partition water fl ow between the matrix domain and the mac-ropore domain in soil, but to our knowledge do not explicitly simulate hummock–hollow microtopography, which is a gen-eral limitation to refer properly simulated θ to soil depth. Th e MACRO model ( Jarvis, 1994) is a one-dimensional, dual-po-rosity model describing water fl ow in layered macroporous soil. Unlike in ecosys, however, where the Hagen–Poiseuille equation determines the rate of macropore fl ow as a function of the water viscosity and average macropore radius in the soil, the macropore fl ow in MACRO is a function of macropore saturation ( Jarvis et al., 1999) and not explicitly connected to the macropore radii.

Fig. 8. Hourly simulated and measured (using time domain refl ectometry) soil water content (θ) at (a) 3-cm and (b) 15-cm depths in hollows, Mer Bleue bog, during 2001. DOY is day of the year.

Fig. 9. (a) Hourly simulated and measured (potentiometric) water table (WT) positions below the hummock surface, Mer Bleue bog during the growing season in 2001; and (b) contrasting water tables during the later growing season in 2001 and 2004. DOY is day of the year.

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Th e hydrologic model of Hoogmoed and Bouma (1980) as-sumes that the water in macropores is subject to lateral absorp-tion through their walls into a homogenous soil matrix, through which the water drains vertically (Booltink and Bouma, 1993). Th us, unlike ecosys, where the macropore fl ow is driven by grav-ity in the vertical direction, their model simulates predominantly horizontal macropore fl ow with no explicit vertical component. If part of the simulated water in the ecosys macropores had been absorbed laterally through their walls, it might have resulted in slower macropore infi ltration and lower saturation of the hemic

and sapric peat in the model in both hummocks (Fig. 7d and 7e) and hollows (Fig. 8b).

Another limitation in many previous models is the scarcity of data on the various hydraulic properties of the unsaturated peat (Baird, 1997). In most cases, model hypotheses for water fl ow based on these properties have not been tested against mea-surements of θ and Z at the highly resolved temporal and spatial scales at which these fl ows occur.

Table 1. Run with macropore fl ow: Statistics for regressions of simulated on measured hourly volumetric soil water contents (θ) at 10, 20, 30, 40, and 50 cm in hummocks, and simulated on hourly potentiometric water table depth (Z) below the hum-mock surface at Mer Bleue bog for the period 2000 to 2004.

Statistic Value (signifi cance)θ, m3 m−3

10 cm hummock (n† = 20,058) Slope (b)‡ 0.28 (P < 0.0001)§ Intercept (a)‡, m3 m−3 0.06 (P < 0.0001)¶ R2 0.15 (P < 0.0001)# Willmott’s d 0.66 RMSD††, m3 m−3 0.0120 cm hummock (n = 31,803) Slope (b) 0.62 (P < 0.0001) Intercept (a), m3 m−3 0.02 (P < 0.0001) R2 0.40 (P < 0.0001) Willmott’s d 0.82 RMSD, m3 m−3 0.0330 cm hummock (n = 29,149) Slope (b) 0.73 (P < 0.0001) Intercept (a), m3 m−3 0.05 (P < 0.0001) R2 0.56 (P < 0.0001) Willmott’s d 0.88 RMSD, m3 m−3 0.1640 cm hummock (n = 29,170) Slope (b) 1.03 (P < 0.0001) Intercept (a), m3 m−3 −0.05 (P < 0.0001) R2 0.45 (P < 0.0001) Willmott’s d 0.88 RMSD, m3 m−3 0.1350 cm hummock (n = 21,050) Slope (b) 0.53 (P < 0.0001) Intercept (a), m3 m−3 0.41 (P < 0.0001) R2 0.11 (P < 0.0001) Willmott’s d 0.85 RMSD, m3 m−3 0.06

Z, cm (n = 28,044) Slope (b) 0.78 (P < 0.0001) Intercept (a), cm 14.36 (P < 0.0001) R2 0.72 (P < 0.0001) Willmott’s d 0.99 RMSD, cm 6.55

† n, number of daily values in regression; ‡ Y = a + bX, where Y is the modeled fl ux and X is the eddy covariance (EC) fl ux.§ Signifi cance of the slope b.¶ Signifi cance of the intercept a.# Signifi cance of the linear regression.†† Y = a + bX, where Y is the eddy covariance (EC) fl ux and X is the modeled fl ux.

Table 2. Run without macropore fl ow: Statistics for regressions of simulated on measured hourly volumetric soil water contents (θ) at 10, 20, 30, 40, and 50 cm in hummocks, and simulated on hourly potentiometric water table depth (Z) below hummock surface, at Mer Bleue bog for the period 2000 to 2004.

Statistic Value (signifi cance)θ, m3 m−3

10 cm hummock (n† = 20,058) Slope (b)‡ 5.59 (P < 0.0001)§ Intercept (a)‡, m3 m−3 −0.29 (P < 0.0001)¶ R2 0.25 (P < 0.0001)# Willmott’s d 0.33 RMSD††, m3 m−3 0.0120 cm hummock (n = 31,803) Slope (b) 1.43 (P < 0.0001) Intercept (a), m3 m−3 0.11 (P < 0.0001) R2 0.27 (P < 0.0001) Willmott’s d 0.51 RMSD, m3 m−3 0.0330 cm hummock (n = 29,149) Slope (b) 0.33 (P < 0.0001) Intercept (a), m3 m−3 0.22 (P < 0.0001) R2 0.40 (P < 0.0001) Willmott’s d 0.92 RMSD, m3 m−3 0.1840 cm hummock (n = 29,170) Slope (b) 0.44 (P < 0.0001) Intercept (a), m3 m−3 0.16 (P < 0.0001) R2 0.41 (P < 0.0001) Willmott’s d 0.83 RMSD, m3 m−3 0.1450 cm hummock (n = 21,050) Slope (b) 0.35 (P < 0.0001) Intercept (a), m3 m−3 0.45 (P < 0.0001) R2 0.11 (P < 0.0001) Willmott’s d 0.72 RMSD, m3 m−3 0.06

Z, cm(n = 28,044) Slope (b) 4.40 (P < 0.0001) Intercept (a), cm −82.85 (P < 0.0001) R2 0.38 (P < 0.0001) Willmott’s d 0.92 RMSD, cm 9.73

† n, number of daily values in regression; ‡ Y = a + bX, where Y is the modeled fl ux and X is the eddy covariance (EC) fl ux.§ Signifi cance of the slope b.¶ Signifi cance of the intercept a.# Signifi cance of the linear regression.†† Y = a + bX, where Y is the eddy covariance (EC) fl ux and X is the modeled fl ux.

692 SSSAJ: Volume 74: Number 2 • March–April 2010

Sensitivity of Micropore Flow to Bulk Saturated Hydraulic Conductivity of Fibric Peat Based on Combined Matrix and Macropore Flow

Th ere remains the possibility that slower drainage and great-er water retention simulated without macropore fl ow (Fig. 7) were caused by underestimates of the bulk Ksat in fi bric peat. Th is value is reported to vary by orders of magnitudes, e.g., from 10−7 to 10−3 m s−1 (Letts et al., 2000; Gafni, 1986; Boelter, 1968; Baird, 1997). Fraser (1999) estimated that in Mer Bleue peat the surface bulk Ksat varied between 10−5 and 10−3 m s−1, possibly due to local diff erences in vegetation composition. Th ree addi-tional runs without macropore fl ow were therefore conducted to test the sensitivity of the modeled water transport to variations in the bulk Ksat. Th e fi rst run was parameterized with vertical bulk Ksat,v = 4.5 × 10−3 m s−1 and horizontal bulk Ksat,h = 22.5 × 10−3 m s−1, representing the maximum probable values of the bulk Ksat (Letts et al., 2000; Magnussen, 1994). Th e second run was parameterized with bulk Ksat,v = 2 × 10−6 m s−1 and bulk Ksat,h = 1 × 10−5 m s−1, representing the minimum probable val-ues of the bulk Ksat (Letts et al., 2000; Magnussen, 1994). In con-trast to the assumption that Ksat,h is fi ve times higher than Ksat,v (Reeve et al., 2000), the third run was parameterized with bulk Ksat,h = Ksat,v = 2.8 × 10−4 m s−1, equal to Ksat,v of the original run without macropore fl ow (Fig. 1b). All other parameters for these three runs remained the same as those in the original model run without macropore fl ow.

All of the three runs without macropore fl ow underesti-mated infi ltration and overestimated retention of the water from rainfall on DOY 253 in 2004 (Fig. 10). Th e maximum probable bulk Ksat resulted in the fastest infi ltration and least water re-tention among the three runs, allowing θ to approach measured values aft er 2 d. Th e intermediate bulk Ksat caused greater wa-ter retention, while the minimum probable bulk Ksat resulted in prolonged saturation (Fig. 10). None of these runs simulated θ as accurately (compared with the measured values) as did the run with macropores, clearly indicating that it was not the parameter values but the process that had been misrepresented by modeling peatland hydrology solely from the Richards equation.

Evaluating the Implications of Uncertainty in Modeled Water Table with Macropore Flow

As subsurface hydrology and biochemical cycling are tight-ly linked in peatlands (Waddington et al., 2001; Silvola et al., 1996), the accuracy with which peatland hydrology is simulated is likely to aff ect the accuracy with which peatland C exchange is simulated. To evaluate this likelihood at Mer Bleue, we estimated the eff ect on ecosystem respiration (ER) of uncertainty in mod-eled Z from a regression of EC-measured CO2 effl uxes on Z by Lafl eur et al. (2005b). Th e changes in ER caused by changes in Z of 6.55 and 9.73 cm (RMSD for Z modeled with and without macropore fl ow vs. measured Z, Tables 1 and 2) were 0.30 and 0.45 μmol m−2 s−1. Th ese changes were less than the random er-ror of 0.74 μmol m−2 s−1 for EC-measured ER at Mer Bleue esti-mated by Richardson et al. (2006). If modeled and measured ER

have similar sensitivities to Z (to be tested in another study), this comparison indicates that the uncertainty in modeled Z would be unlikely to introduce signifi cant uncertainty in modeled ER; however, the uncertainty in ER caused by the uncertainty in Z modeled with macropore fl ow would be smaller than that caused by Z modeled without it. Th e caveat here is that this evaluation of the uncertainty applies only to Mer Bleue bog, which has a relatively deep average WT (Lafl eur et al., 2005a,b). More re-search is needed to evaluate this uncertainty for other peatlands.

CONCLUSIONSTh e fi ndings of this study suggest that preferential macro-

pore fl ow in fi bric peat is an important mechanism that, when modeled in parallel with matrix fl ow, improves the simulation of bog subsurface hydrology, as also suggested by Baird (1997). For modeling purposes, the Richards and Hagen–Poiseuille equations should be applied to simulate parallel matrix and mac-ropore fl ows, respectively, in fi bric peat, instead of the Richards equation alone. Th e unknown matrix hydraulic conductivity of highly macroporous fi bric peat can be substituted in the models by the bulk hydraulic conductivity of hemic peat (mainly matrix with negligible macroporosity) that can be retrieved from the lit-erature (Letts et al., 2000) and therefore easily used in the mod-els. Although demonstrated only for the Mer Bleue bog in this study, we believe that the implications of macropore fl ow might be of great importance in the hydrology of other peatlands, for which further experimental and modeling work is needed.

Fig. 10. Hourly soil water content (θ) measured using time domain refl ectometry (TDR) and simulated with different values of the saturated hydraulic conductivity Ksat of bulk fi bric peat at 10-cm depth in hummocks, Mer Bleue bog, following 124.5 mm of rainfall on day of the year (DOY) 253 in 2004; Kmax is the maximum probable values of Ksat in bulk fi bric peat (Letts et al., 2000; Magnussen, 1994), e.g., 4.5 × 10−3 m s−1 in the vertical direction and 22.5 × 10−3 m s−1 in the horizontal direction, on the assumption that the latter is fi ve times higher than the former in peat (Reeve et al. 2000); Kmin is the minimum probable values of Ksat in bulk fi bric peat (Letts et al., 2000; Magnussen, 1994), e.g., 2 × 10−6 m s−1 m s−1 in the vertical direction and 1 × 10−5 m s−1 in the horizontal direction, on the assumption that the latter is fi ve times higher than the former in peat (Reeve et al. 2000); Kh and Kv are equal, intermediate probable values of Ksat in bulk fi bric peat in vertical and horizontal directions (Letts et al., 2000; Magnussen, 1994), e.g., 2.8 × 10−4 m s−1.

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ACKNOWLEDGMENTSFunding was provided by Fluxnet Canada Research Network (FCRN). Computational facilities were provided by Westgrid Canada, University of Bristish Columbia. Data were collected with funding from FCRN through its major sponsors Natural Science and Engineering Council of Canada, Canadian Foundation for Climate and Atmospheric Sciences, and Biocap Canada. Special thanks to Prof. Tim Moore and Prof. Nigel Roulet, McGill University; Prof. Christian Blodau, University of Bayreuth, Germany; Dr. Staurt Admiral, Trent University; and Prof. Yongsheng Feng and Prof. Dennis Gignac, University of Alberta.

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APPENDIXVariables in Hydrologic Equations

fM macropore fraction (m3 m−3)

KM macropore hydraulic conductivity (m2 MPa−1 h−1)

Ksat saturated hydraulic conductivity of the soil matrix (mm h−1)

Ksat,h horizontal saturated hydraulic conductivity of the soil matrix (mm h−1)

Ksat,v vertical saturated hydraulic conductivity of the soil matrix (mm h−1)

Kθ unsaturated hydraulic conductivity (m2 MPa−1 h−1)

KM* individual macropore hydraulic conductivity (m4 MPa−1 h−1 pore−1)

Km′ hydraulic conductance of the soil matrix (m MPa−1 h−1)

KM′ macropore hydraulic conductance (m MPa−1 h−1)

Lp width of fl ow paths (m)

lx model cell size, horizontal length (m)

ly model cell size, horizontal length perpendicular to lx (m)

lz model cell size, vertical thickness (m)

m number of pore classes in the soil matrix (dimensionless)

NM macropore density (number of macropore channels m−2)

QM water macropore fl ux (m3 m−2 h−1)

Qr surface water fl ux (m3 m−2 h−1)

Qm subsurface water fl ux through the soil matrix (m3 m−2 h−1)

RM average macropore radius (m)

Ta atmospheric temperature (°C)

Δt time step (e.g., 30 min, 1 h, 1 d, etc.)

VM macropore volume within the model cell (m3 m−3)

v runoff velocity (m h−1)

εt total soil porosity (m3 m−3)

ηw dynamic viscosity of water (g cm−1 s−1)

θ soil water content (m3 m−3)

ψ water potential (MPa)w

ψe air-entry potential (MPa)

ψg gravimetric water potential (MPa)

ψj water potential for the jth class of water-fi lled pores (cm)

ψm matric water potential (MPa)

ψo osmotic water potential (MPa)

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