Modeling Peat Thermal Regime of an Ombrotrophic

Wetland Soils
Modeling Peat Thermal Regime of an Ombrotrophic
Peatland with Hummock–Hollow Microtopography
Dimitre D. Dimitrov*
Canadian Forest Service
Northern Forestry Centre
5320-122nd Street
Edmonton, AB, Canada T6H3S5
Robert F. Grant
Dep. of Renewable Resources
Univ. of Alberta
Edmonton, AB, Canada T6G 2H1
Peter M. Lafleur
Geography Dep.
Trent Univ.
Peterborough, ON, Canada K9J 7B8
Elyn R. Humphreys
Dep. of Geography and Environ. Studies
Carleton Univ.
Ottawa, ON, Canada, K1S 5B6
The theory of conductive heat transfer cannot explain different attenuations of the daily amplitude of peat
temperatures (TS) in hummocks (detectable below the 20-cm depth) and hollows (disappearing above the 10cm depth). Large readily drained macropores in the upper fibric peat determine a large air permeability and
hence may enhance heat transfer by air convection in porous media, driven by temperature gradients between
hummock sides and interiors. In this study, the ecosys model was used to simulate a peat thermal regime at Mer
Bleue peatland, Ontario, Canada. It was hypothesized that adding the air-convective heat transfer to conductive
plus water-convective heat transfers would improve simulations of TS. The results for TS, ground heat fluxes, G,
and sensible heat fluxes, H, modeled with and without air-convective heat transfer were tested with continuous
hourly measurements from 2000 to 2004 using thermocouples, heat flux plates, and eddy covariance. Simulated
air-convective heat transfer caused an average increase in G and a corresponding decrease in H of ?20 W m−2
from the simulated conductive plus water-convective heat transfer. Hastened soil warming in hummocks resulted
in better agreement between measured and simulated hummock TS values with (RMSD of 2.23°C) than without
air-convective heat (RMSD of 2.54°C). Enhanced hummock TS caused an indirect increase in hollow TS in the
model with (RMSD of 1.68°C) compared to without air-convective heat (RMSD of 1.82°C). Our results suggest
that air convection is probably an important mechanism of heat transfer in peat hummocks and should be included
in peatland biogeochemical models.
Abbreviations: DOY, day of the year; EC, eddy covariance; ER, ecosystem respiration; MAE, mean
absolute error.
S
oil temperature, Ts, is an important environmental control on soil respiration and thus on ecosystem respiration (ER) in mineral soils (Reichstein et al.,
2003) and peatlands (Lafleur et al., 2005b; Bubier et al., 2003a, 2003b; Scanlon
and Moore, 2000; Silvola et al. 1996a, 1996b). The Ts is known to control rates
of biological processes that drive soil respiration, such as hydrolysis and redox
reactions (Grant, 2004; Brock and Madigan, 1991). The TS also affects physical
processes that control soil respiration, such as gaseous and aqueous diffusion, and
solubilization (Grant, 2001), thus affecting O2 supply for redox reactions (Clymo,
1983). Therefore, the ability to predict temporal and spatial patterns in TS is an
important concern for biogeochemical models. Yet little consideration has been
given to this issue for peatland environments, where many models use soil heat
transfer parameterizations developed for mineral soils, with little regard for the
unique characteristics of peat properties at depth, variations of water table, and
peatland surface microtopography.
Heat transfer in soil has long been considered to occur mainly by conductive
heat flow, combined with some vapor-convective and water-convective heat flows
(Côté and Konrad, 2005; Grant, 2001; Farouki, 1982; de Vries, 1963; Mickley,
1951). However, the classical theory of conductive heat transfer and storage in soil,
which describes attenuation of diurnal TS variation and delay of maxima and minima with depth (Campbell, 1977; Monteith, 1973), has not always worked properly
Soil Sci. Soc. Am. J. 74:1406–1425
Published online 9 Apr. 2010
doi:10.2136/sssaj2009.0288
Received 5 Aug 2009.
*Corresponding author ([email protected]).
© Soil Science Society of America, 677 S. Segoe Rd., Madison WI 53711 USA
All 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.
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SSSAJ: Volume 74: Number 4 • July–August 2010
for peat. According to this theory, the damping depth of the diurnal TS amplitude (the depth at which the diurnal TS amplitude is reduced to e−1 = 0.37 of its surface magnitude) should be
about 5 cm in peat (Clymo, 1983; Campbell, 1977). Therefore,
below the 15-cm depth TS in peat should be approaching the
average daily temperature at the surface and the diurnal TS amplitude should disappear. Although this may be true for some
peatlands (Clymo, 1983) and especially for hollows, it is definitely not so in hummocks. Measurements show that diurnal TS
fluctuations are clearly and consistently detectable at 1, 5, 10, and
20 cm below the hummock surface at Mer Bleue bog, and only
disappear well below the 20-cm depth (Lafleur et al., 2005b).
Kellner (2001) also measured higher diurnal TS amplitudes at
corresponding depths in hummocks than in hollows in a mire in
central Sweden.
These large TS amplitudes at depth may be due to air–convective heat transfer in peat. Unlike mineral soils, where low airfilled porosities (Kutilek and Nielsen, 1994) cause low permeability to air (Ingham and Pop, 2002), the large and well-drained
macropore fractions of fibric peat (Dimitrov, 2009; Schwärzel et
al., 2002; Silins and Rothwell, 1998; Baird, 1997) cause greater
air-filled porosity and hence permeability to air (Dullien, 1979).
The latter may cause internal air circulation and air-convective
heat transfer in fibric peat as in other porous media (Ingham and
Pop, 2002; Nield and Bejan, 1992) that supplements the conductive heat transfer.
Detailed process-based modeling, complementing measurements of TS and heat fluxes can help in studying the thermal
regime in peat. However, we are not aware of any successful attempts so far to model TS at depth in field peat profiles by applying the classical theory of conductive heat transfer. Kellner
(2001) attempted to model peat TS at depth, but even though
his model adequately described TS in hollows, there was a poor
agreement between modeled and measured TS in hummocks. A
possible reason for the poor simulation in the hummock environments is that the large porosity within the fibric peat allowed
for air-convective heating.
Objectives and Hypotheses
Air-convective heat transfer can be generated in hummocky microtopography by temperature gradients within hummocks which,
combined with high air permeability of fibric peat (Dullien, 1979),
should cause air density gradients and hence air movement (Ingham and
Pop, 2002). This movement should hasten heat transfer in hummocks
and thereby increase diurnal amplitudes in hummock TS at depth. The
main objective of this study was to investigate whether TS at various
depths under peat hummocks and hollows, as well as ground heat flux
G and sensible heat flux H at the peat surface, can be better simulated
by adding the air-convective heat transfer to conductive and vapor- and
water-convective heat transfers than by conductive and vapor- and
water-convective heat transfers alone. No air-convective heat transfer is
hypothesized in hollows, due to their concave shape and shallow fibric
peat that limits air convection (Ingham and Pop, 2002; Nield and Bejan,
SSSAJ: Volume 74: Number 4 • July–August 2010
1992). However, lateral conduction of air-convective heat in hummocks
is hypothesized to hasten the heat transfer in adjacent hollows too.
The modeling hypothesis is that air-convective heat transfer in
hummocks can be simulated by enhancing the soil thermal conductivity
term (de Vries, 1963) by a heat convection term, resulting from natural
heating-from-the-side air convection in porous media (Bejan and Tien,
1978), as described in Fig. 1. This hypothesis was implemented by adding a module with the formulae for heating-from-the-side air convection in porous media (Nield and Bejan, 1992) to algorithms for conductive heat transfer in the source code of the ecosys model (Grant, 2001).
The alternative hypothesis is that modeling heat transfer in peat does
not require an air-convective component (Fig. 1).
MODEL DEVELOPMENT
Ecosys is a detailed process-based three-dimensional model that
couples soil hydrology and heat transfer to biologically driven C and
energy fluxes of ecosystems (Grant, 2001). The model can represent
complex microtopography of alternating hummocks and hollows, and
can solve for G, H, and TS in hummocks and hollows on an hourly time
scale. Rationale of the theory and partial differential equations that
govern conductive, and vapor- and water-convective heat transfers in
the original ecosys, and newly added air-convective enhancement of the
conductive heat transfer in hummocks, are given below. Numerical solutions of these differential equations and other model equations that
describe the soil heat transfer in ecosys are given in Appendix 1, their
parameter values in Appendix 2.
Rationale of Modeling Soil Heat Transfer
Net radiation, Rn (MJ m−2 h−1), reaching the terrestrial surface is
redistributed among sensible heat flux, H (MJ m−2 h−1), latent heat flux,
LE (MJ m−2 h−1), between the ground surface and the atmosphere, and
ground heat flux at terrestrial surface (soil, surface residue, or snowpack),
GTS (MJ m−2 h−1) (Grant et al., 1990). For simplicity and relevance to
the objectives of this research only the equations that govern GTS in the
soil are considered here; as the equations governing GTS through snowpack and surface residue are similar and comply with the same principles
(Grant, 1992). The GTS is cumulative and calculated from the ground
heat fluxes between adjacent model cells GMC (MJ m−2 h−1). With upper
boundary conditions of current weather at soil surface and lower boundary conditions of constant TS at the 10-m depth that is equal to the average annual TS at soil surface, and on the assumption for homogeneity of
each model cell, the following general set of partial differential equations
describes ∂E/∂t and TS of each model cell:
GMC G V W
TS
x
G
V
V
[1]
TS
y
c WTS Lv
W c WTS k
[2]
TS
z
S
x
CV
x
S
y
CV
y
S
z
CV
z
[3]
[4]
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E
t
TS
t
G MC
x
G MC
y
G MC
z
Lf
E t
cS
[5]
[6]
The term G (MJ m−2 h−1) is that part of GMC that is transferred
through the soil by conduction. The term V (MJ m−2 h−1) is that part
of GMC that is transferred as vapor-convective heat with vapor fluxes in
soil. The term W (MJ m−2 h−1) is that part of GMC that is transferred
as water-convective heat with water fluxes in soil. The term E (MJ m−3)
is the energy storage in the model cell. The other quantities in this set
of equations are the soil thermal conductivity, λ (MJ h−1 m-1 oC−1);
time, t (h); distances, x (m), y (m), and z (m) in the x, y, and z directions, respectively; vapor concentration, CV (g m−3); vapor diffusivity, σV (m2 h−1); specific heat capacity of water, cW (MJ kg-1 oC−1);
latent heat of vaporization, Lv (MJ m−3); hydraulic conductivity, kθ
(m2 MPa−1 h−1); soil water potential, ψS (MPa); latent heat of freezing and thawing, Lf (MJ m−3); and soil volumetric heat capacity, cS
(MJ m-3 oC−1). Thus, heat fluxes in ecosys are tightly coupled to precipitation, overland flow, subsurface drainage, and evapotranspiration.
To account for the effect of internal air circulation on enhancing G
and TS through enhancing λ (Ingham and Pop, 2002) in highly macroporous and well-drained hummocks, Eq. [2] was modified as
G Nu
TS
x
TS
y
TS
z
[7]
where Nu (dimensionless) is the Nusselt number, that is, the ratio between heat transfer with convection and without (Nield and Bejan,
1992), which depends on peat air-filled porosities and fiber diameters
(Dullien, 1979). In the case of no convective effects on heat transfer, Nu
= 1; in the case of heat convection, Nu > 1.
Integration of Eq. [1–7] is generally difficult because they involve
more than one variable (time and space) and are tightly coupled to other
Fig. 1. Graphical schemes of the convection hypothesis and
the alternative hypothesis.
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SSSAJ: Volume 74: Number 4 • July–August 2010
simulated quantities, for example, precipitation, overland flow, subsurface drainage, and evapotranspiration. However, these differential
equations were solved in ecosys numerically, by explicit finite difference
approximations at an hourly time step (Grant, 2001, 1992; Grant et al.,
1990), as described below.
Conductive and Vapor- and Water-Convective
Heat Transfers in Soil
The conductive heat flux G between each two adjacent model
cells, in the x, y, z directions is calculated from thermal conductances
λ′ (MJ h−1 m–2 oC−1) and temperature differences (K) (Eq. [A1.1a,
A1.1b, A1.1c] in Appendix 1). The λ′ in the x, y, z directions are calculated as geometric means of the thermal conductivities λ in each two
adjacent model cells (Eq. [A1.2a, A1.2b, A1.2c] in Appendix 1), and are
additionally enhanced by a wind-driven effect UW of heat diffusivity
through soil surface boundary layers. The UW depends on wind speed
(m h−1) at the surface, and exponentially attenuates with soil depth,
d (m) (Eq. [A1.2d] in Appendix 1). Soil depth d is accumulated from
summing the thicknesses of all the soil layers l (Eq. [A1.2e] in Appendix
1). The λ is calculated for each model cell by de Vries (1963), assuming
water as the continuous medium in which the granules of other materials, such as air, ice, organic and mineral soil particles, sand, and rocks are
located. Equation [A1.3] in Appendix 1 describes λ (MJ h−1 m-1 oC−1)
as a function of the thermal conductivities λwtr, λair, λice, λorg , λmin,
λsnd, λrck (MJ h−1 m−2 oC−1) of each of the above materials, weighted
by their volumetric fractions (m3 m−3) fwtr, fair, fice, forg , fmin, fsnd, frck
(de Vries, 1963). The material-specific quantities κwtr, κair, κice, κorg ,
κmin, κsnd, κrck (dimensionless) in Eq. [A1.3] are the ratios between the
average temperature gradients in the granules of each material and the
average temperature gradient in the medium (de Vries, 1963); κwtr = 1
and the rest are given in Appendix 1.
The vapor-convective heat flux, V, between two adjacent model
cells in soil, in the x, y, and z directions, is calculated from vapor flux
QV (m h−1), soil temperature TS (°C) of the originating cell, cW and Lv
(Eq. [A1.4a, A1.4b, A1.4c] in Appendix 1). The QV between two adjacent model cells in soil, in the x, y, and z directions, is calculated from
vapor conductances σV′ (m h−1) and CV (Eq. [A1.5a, A1.5b, A1.5c] in
Appendix 1). The σ’ V in the x, y, and z directions are calculated from lx,
ly, lz (Eq. [A1.6a, A1.6b, A1.6c] in Appendix 1). The σV is calculated
from the diffusivity of water vapor in open air at 0°C σV,o (m2 h−1),
air-filled soil porosity εa (m3 m−3), total soil porosity εt (m3 m−3), and
TS (°K) (Eq. [A1.7] in Appendix 1). The CV is calculated from TS (°C)
of the originating cell and ambient vapor pressure e (kPa) (Eq. [A1.8]
in Appendix 1). The latter is calculated from saturation vapor pressure
e’sat (kPa) at a given soil temperature, molecular mass of water MW (g
mol−1), soil matric and osmotic potentials (ψm + ψo) (kPa), TS (°C) of
the originating cell, and gas constant R ( J mol−1 m−3) (Eq. [A1.9] in
Appendix 1). The e’sat is calculated from saturation vapor pressure at 0°C
esat and TS (Eq. [A1.10] in Appendix 1).
The water-convective heat flux W between two adjacent model
cells in soil, in the x, y, and z directions, is calculated from the soil
matrix water flux QW,x (m h−1), QW,y (m h−1), and QW,z (m h−1), soil
macropore water flux QM,z (m h−1), precipitation QP,z (m h−1), and
snowmelt Qsn,z (m h−1), and cW and TS (°C) (Eq. [A1.11a, A1.11b,
SSSAJ: Volume 74: Number 4 • July–August 2010
A1.11c, A1.12, A1.13, A1.14, A1.15] in Appendix 1). Soil water fluxes
are calculated from hydraulic conductances and water potential differences; equations described in detail in Grant (2001). Also, ecosys calculates for the latent heat of freezing and thawing, which controls the
timing of spring warming and autumn cooling of the soil in the model
(Grant, 2001).
Change in energy storage of a given model cell, ΔE (MJ m−3),
during a time step, Δt (Eq. [A1.16] in Appendix 1), is calculated from
balancing incoming and outgoing G, V and W to and from that cell (Eq.
[A1.17, A1.18, A1.19] in Appendix 1), and the incoming and outgoing
heat flux through the model boundaries, B (MJ h−1 m−2), (Eq. [A1.20]
in Appendix 1) (Grant, 2001; Grant, 1992). Soil temperature of that
cell at the beginning of the next time step, TS,Δt (°C), is calculated from
TS (°C) at the beginning of the current time step, Δt, and soil temperature change, ΔTS (°C), during the current Δt (Eq. [A1.21] in Appendix
1). The ΔTS is calculated from ΔE divided by soil volumetric heat capacity cS (MJ m-3 oC−1) (Eq. [A1.22] in Appendix 1). The cS is calculated
(Eq. [A1.23a, A1.23b] in Appendix 1) by material-specific heat capacities (Appendix 2), weighted by volumetric fractions (m3 m−3) of water
and ice in soil matrix fWμ and fIμ, and in soil macropores fWM and fIM,
and by volumetric fractions (m3 m−3) of organic, mineral, sand, and
rock particles forg , fmin, fsnd, and frck.
Air-Convective Heat Transfer in Peat as Porous Media
The case of “Shallow Layer” regime of Heating-from-the-Side natural convection of a fluid in a porous medium (Nield and Bejan, 1992;
Bejan, 1984) was projected over hummocks of highly macroporous fibric peat, given the order of the ratio between hummock heights Hhmk
(m) above neighboring hollow surface and hummock diameters, L (m).
Bejan and Tien (1978) and Walker and Homsy (1978) described the
shallow-layer convection by horizontal fluid counterflow (in this case
air counterflow) through a large porous space, referred as the “core”,
with vertical fluid (air) movement only through thin end layers next to
the inner and outer sides (Fig. 1). Temperature gradients between hummock sides and interiors drive the horizontal Heating-from-the-Side air
convection in hummocks (Fig. 1). This convection can cause heat transfer rates that are considerably greater than the heat transfer rate of conduction alone (Nield and Bejan, 1992). The condition of impermeable
upper and lower walls usually holds during daytime hours, or whenever
peat stays warmest on hummock surfaces and coolest at the bottom of
the fibric layer. Vertical end walls (hummock sides) are assumed to be
permeable, following Bejan and Tien (1978).
The basic equations from Bejan and Tien (1978) and Nield and
Bejan (1992) were used to calculate for each model cell the overall heat
transfer coefficient h (MJ h−1 m-1 oC−1), which equals λ enhanced by
Nu (Eq. [A2.1a, A2.1b] in Appendix 1). The Nu is calculated from
Rayleigh number Ra and an axial temperature gradient constant, C1
(Eq. [A2.2a, A2.2b] in Appendix 1), calculated from hummock effective height, H*hmk (m), horizontal depth of convection from hummock
side to interior, L* (m), and Ra (Eq. [A2.3a, A2.3b] in Appendix 1). The
H*hmk is calculated at every time step Δt as a cumulative thickness of all
the top hummock layers q with air-filled porosities εa (m3 m−3) greater
than water-filled porosities εw (m3 m−3) (Eq. [A2.4] in Appendix 2);
H*hmk is always less than or equal to the distance between the average
1409
Fig. 2. Complex microtopography at Mer Bleue bog with alternating
hummocks and hollows.
hummock surface and the average hollow surface, Hhmk (m). The L* is
calculated from H*hmk and Ra (Eq. [A2.5] in Appendix 1) and is always
equal to or less than the maximum possible horizontal depth of air convection, L (m).
The Rayleigh number, Ra, is dimensionless and associated with the
heat transfer within the porous media (Ingham and Pop, 2002). When
Ra is less than a critical value Racr (Appendix 2), the heat transfer is in
the form of conduction alone (Nu = 1) and when Ra > Racr, the heat
transfer is by convection (Nu > 1) in addition to conduction (Pestov,
2000). The Ra is calculated from earth acceleration, g (m s−2), thermal
expansion coefficient of air, βair (°C−1), kinematic viscosity of air, υair
(m2 s−1), thermal diffusivity of peat, αp (m2 s−1), permeability of peat to
air, kp, (m2), temperature at hummock side, Tout (°C), and temperature
inside hummock, Tin (°C), and H*hmk (Eq. [A2.6] in Appendix 1). It
is assumed that the simulated Tout of the lateral hummock sides (Fig.
1) equals the temperature at the horizontal hummock surface, although
hummock sides have different solar angles. The Tin is calculated as average from the temperatures of all the hummock layers, from the surface to
depth H*hmk, with air-filled porosities greater than water-filled porosities at a given time step Δt (Eq. [A2.7] in Appendix 1). Thus, although
a simplification, the above way to estimate Tout and Tin is a convenient
one to calculate the difference Tout–Tin, which drives the Heating-fromthe-Side air convection.
Permeability of a porous medium is independent of the nature of
the fluid flowing through it, but rather depends on the geometry of the
medium (Kutilek and Nielsen, 1994; Nield and Bejan, 1992; Dullien,
1979). For the purposes of this research, peat and the water content in
peat matrix are considered as the porous medium, and air as the fluid
flowing through. The permeability of peat to air kp is calculated for fibrous beds as stable structures of extremely high porosities, up to 0.99
on a volumetric basis (Dullien, 1979). The kp is calculated from the average diameter of fibers, Df (μm), average air-filled porosity ε’a (m3 m−3)
of all the top hummock layers q with εa > εw, multiplied by π and the
constants c’ and c” (Eq. [A2.8] in Appendix 1). The ε’a is calculated at
every time step Δt as a weighted average from εa and layer thickness Lz
(m) of the top portion of each layer of the hummock with εa > εw (Eq.
[A2.9] in Appendix 1), where εa is the air-filled porosity and εw is the
water-filled porosity of a given layer.
Penetration of the Heating-from-the-Side air convection inside
hummocks depends on the temperature difference, through Ra. Thus, at
1410
Fig. 3. A three-dimensional transect from the ecosys model
representing the specific surface microtopography at Mer Bleue
bog and depth intervals of fibric, hemic, and sapric peat; GC is
grid cell. Modeled heat, gases, water, and solutes were allowed to
freely exchange between adjacent grid cells or through the transect
boundaries in the north–south direction following the main slope of
the terrain, given that the east–west slope was negligible.
Fig. 4. Cross-section in the north–south direction of the simulated
peat profile at Mer Bleue bog; N is the number of soil layers in the
ecosys model, starting from the hummock surface; SLTk (cm) and
SLTw (cm) are the soil layer depths in ecosys from the hummock
and hollow surfaces, respectively; ρb (Mg m−3) is the bulk density of
peat with macropores for Layers 1 to 10 (measured by Blodau and
Moore, 2002) and Layers 11 to 15 (taken from Frolking et al., 2002,
2001); εt (m3 m−3) is the soil layer total porosity, calculated from the
corresponding ρb; MF (m3 m−3) is the peat volumetric macropore
fraction (determined by Dimitrov, 2009). Wavy lines depict the
range in water table variation, e.g., from ?23 to ?70 cm below the
hummock surface for the period 1998 to 2004.
SSSAJ: Volume 74: Number 4 • July–August 2010
any time step Δt, there may be a central region inside hummock mounds
where air-convective heat wouldn’t have penetrated and heat conduction would act alone. Therefore, the effective heat transfer coefficient h*
is calculated (Eq. [A2.10] in Appendix 1) for the hummock periphery,
subject to heat conduction and convection (h term in Eq. [A2.10]), and
the hummock interior subject to heat conduction alone (λ term in Eq.
[A2.10]). Finally, h* is substituted for λ in further calculations of heat
and soil temperatures within the same time step, thus incorporating the
effect of possible air convection in the overall heat transfer mechanism
of ecosys.
Simulated air-convective heat transfer ceases when cooling of
the near-surface peat causes the warmest temperature to “move” vertically and laterally into the hummock mounds. This movement splits
the core zone and minimizes the air-convective heat transfer that depends directly on the height of the porous core zone (Nield and Bejan,
1992). Furthermore, given time delays in developing large convective
buoyant cells able to cause vertical air instability and buoyant convection (Rappoldt et al., 2003), it is assumed that there is no air convection whenever the warmest peat is inside the hummock mounds, as during nighttime. Whenever the warmest temperature “moves” below the
hummock mounds during prolonged periods of cooling in fall and winter, cooler temperatures at peat surface may eventually induce vertical
instability of air density and onsetting of buoyant convection (Ingham
and Pop, 2002; Nield and Bejan, 1992). However, the latter can be
shown to increase h roughly by one third to one half of the h increased
by Heating-from-the-Side air convection, with small Ra values as is the
case of the “Shallow Layer” regime (Bejan and Tien, 1978). Thus, the
effect of air-convective heat transfer on cooling in the fall and winter is
expected to be much smaller than that on warming in spring and summer. Furthermore, the insulation properties of snow may minimize the
difference between the temperatures at hummock surface and interior,
such that Ra becomes close to or less than Racr and no air-convective
effects occur. Therefore in the model, air-convective heat transfer occurs
only when Tout–Tin > 0, that is, mainly during daytime, and in spring
and summer, and no air-convective heat transfer occurs when Tout–Tin
< 0, that is, mainly during nighttime, and in fall and winter. However,
even when Tout–Tin < 0, the overall heat transfer in the model is indirectly affected by the air-convection through the temperature gradients
in previously warmed peat.
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 surface area
of approximately 2800 ha. The groundcover is mainly Sphagnum mosses
and overstory vegetation is dominated by a low shrub canopy (20–30 cm
height), with sparse sedges and herbaceous plants and some discontinuous patches of coniferous trees (Lafleur et al. 2005a, Frolking et al. 2002,
Moore et al. 2002). The bog surface has expressed hummock-hollow microtopography, dominated by hummocks with an average diameter of 1
m that comprise about 70% of the surface, and an average relief between
hummocks and hollows of 25 cm (Lafleur et al., 2005a, 2005b) (Fig. 2).
Mer Bleue is a dry peatland with a water table varying between ~20 and
~70 cm below the hummock surface (Lafleur et al. 2005a, 2005b). Peat
SSSAJ: Volume 74: Number 4 • July–August 2010
depth increases from 2 to 6 m, from the periphery toward the center
and is on average 4 to 5 m. Based on peat texture and Von Post degree of
humification, fibric peat occupies the top 0 to 35 cm, then hemic peat at
35 to 45 cm, and sapric peat at >45 cm in hummocks, and respectively at
0 to 10 cm, 10 to 20 cm, and >20 cm in hollows (Lafleur et al. 2005b; S.
Admiral, personal communication, 2005) Macroporosity of fibric peat
is estimated to be 0.8 m3 m−3 (Dimitrov, 2009).
METHODS
The ecosys model was run with and without air-convective heat
transfer to test the hypotheses above by comparing simulated vs. measured TS at various depths, G, H, LE, and Rn.
Field Measurements of Model Drivers, Soil
Temperature, and Energy Fluxes
To drive ecosys, half-hour continuous measurements were provided
during the period 1998 through 2004 for incoming short-wave radiation RSW (W m−2), air temperature at 2 m above canopy Ta (°C), relative humidity at 2 m above canopy RH (%), wind speed at 2 m above
canopy U (m s−1), and precipitation P (mm Δt−1), where Δt is the model time step (Lafleur et al., 2005a, 2005b, 2003). Gap-filling for RSW,
Ta, RH, W, and P and corrections of winter precipitation at Mer Bleue
from an Environment Canada weather station at Macdonald-Cartier
Ottawa Airport (~15 km away) are described in detail in Dimitrov
(2009). Screening and gap-filling procedures for energy fluxes were
done by Priestley–Taylor relationship or energy budget adjusted to lack
typical energy closure, and are quite similar to those described in detail
in Lafleur et al. (2005a) and Admiral and Lafleur (2007).
Continuous in situ measurements of TS with thermocouples (copper constantan) at the 5-, 10-, 20-, 40-cm depths in hummocks and at
the 5- and 10-cm depths in hollows, G with heat flux plates, Rn with a
net radiometer, and H, LE via the eddy covariance method have been
made at Mer Bleue since 1998 (Lafleur et al. 2005a, 2005b, 2003, 2001).
Model Experiment
The hummocky microtopography of Mer Bleue bog (Fig. 2) was
represented by a simple three-dimensional model transect of six grid
cells, consisting of three hummocks and three hollows, with their proportions and depth intervals as described above (Fig. 3). Each hummock
grid cell was subdivided into 15 soil layers starting from hummock surface and each hollow grid cell was subdivided into 11 soil layers starting
from hollow surface (Fig. 4). Each soil layer was parameterized with a
macropore fraction determined for Mer Bleue and a bulk density value
either measured for Mer Bleue or taken from the literature, as explained
on Fig. 4. Low bulk densities determined extremely high total porosities
in peat layers (Fig. 4) and high air-filled porosities in well-drained hummock mounds that resulted in high permeability to air.
Thus, the entire peat profile in ecosys consisted of 78 model cells,
that is, 3 × 15 in hummocks + 3 × 11 in hollows. Each model cell was
allowed to freely exchange soil, heat, gasses, water, and solutes with its
adjacent subcells or through the transect boundaries in north-south direction following the main slope of the terrain (Fig. 3), given that the
east-west slope was negligible. The first and second, and the fifth and
sixth grid cells were considered as boundary grid cells so that simulated
1411
TS, G, and H of the third and fourth grid cells, used in comparisons
with measured data for hummocks and hollows respectively, were not
directly affected by assumptions of heat movement through the transect
boundaries (Fig. 3).
To test the hypothesis with air-convective heat, the modified ecosys was run with the module accounting for enhanced heat transfer in
hummocks (Eq. [A2.1–2.10] in Appendix 1). To test the hypothesis
without air-convective heat, the original ecosys was run without Eq.
[A2.1–A2.10]. Both modified and original model versions were run for
106 yr, starting with a planting year, in which the model was initialized
with the biological properties of bush and moss, and spun up by repeating 15 times the 7-yr weather period of 1998 through 2004 available at
the time of writing. Equilibrium during the model spin up was attained
after 60 to 70 yr, when simulated C sequestration in the soil humic pool
became stable over time ( Ju et al., 2006).
Model Test and Statistics
The ability of the two model versions to simulate short-term diurnal variation in TS, G, and H with and without air-convective heat transfer was first tested for a dry period in early July (Day of the Year [DOY]
181–187) 2002 during which warming was followed by cooling, and
for a wet period in mid-September (DOY 259–266) 2004 during which
cooling was followed by warming. The ability of the two model versions
to simulate seasonal increase of TS during spring and decrease during fall
was then tested in the warm year 2002 and the cool year 2004. Finally,
the ability of ecosys with air-convective heat transfer to simulate rapid reduction of TS at depth under conditions not favoring air-convection in
hummocks was tested following an extreme rainfall in September 2004.
Discrepancies between model output and measurements for the
two model runs were evaluated by the root mean square deviations
(RMSDs) and mean absolute errors (MAEs) and relative discrepancies by Willmott’s index of agreement between measurements and
model output (Willmott, 1982, 1981; Davies, 1981; Powell, 1980;
Willmott and Wicks, 1980). To evaluate goodness of fit and predictive power for the two model runs, coefficients of determination,
slopes and intercepts were obtained from linear regressions between
modeled and measured values.
RESULTS
Diurnal Heat Transfer in Peat
The dry period DOY 181 through DOY 187 in 2002 was
characterized by low water contents (θ) in the fibric peat matrix
above the water table, compared with the wet period DOY 259 to
DOY 266 in 2004. The water table for both periods was ~30 cm
below the hummock surface, thus confining air-convective heat
transfer to the upper 25 cm in hummocks. In the comparisons
of modeled and measured G, H, and TS, positive and negative
values for H represent downward (toward the ecosystem) and
upward (toward the atmosphere) fluxes respectively, while those
for G represent cooling and heating respectively (Fig. 5 and 6).
Diurnal Heat Transfer without Air-Convective Heat
Ecosys simulated thermal conductivities λ (Eq. [A1.3]
in Appendix 1) for Mer Bleue bog that corresponded well
1412
to experimentally determined values between 0.000144 and
0.00018 MJ h−1 m-1 oC reported by Côté and Konrad (2005)
for peat with average total porosity of ~0.96 m3 m−3. However
simulated λ caused G (Eq. [A1.1a, A1.1b, A1.1c] in Appendix
1), and hence |ΔG| (Eq. [A1.17] in Appendix 1), to be underestimated (Fig. 5b and 6b), so that TS and its diurnal variation
in the modeled hummocks were smaller than those measured at
10 cm (Fig. 5e and 6e), and 20 cm (Fig. 5f and 6f ). A smaller G
in the model delayed both warming and cooling with respect to
measurements (Fig. 5e).
Diurnal Heat Transfer with Air-Convective Heat
In the model, hummock side-interior temperature differences Tout– Tin and the large air-filled porosity εa of fibric peat
(Eq. [A2.9] in Appendix 1) caused Ra to exceed Racr (Eq. [A2.6,
A2.7, A2.8] in Appendix 1) and therefore Nu to exceed 1 (Eq.
[A2.2a, A2.2b, A2.3.a, A2.3b, A2.5] in Appendix 1) in hummock
mounds. These Ra and Nu resulted in enhancement of peat thermal conductivity, λ (through h* in Eq. [A2.10] in Appendix 1),
by 5 to 15 times compared with measured values as noted above.
The enhanced λs resulted in enhanced thermal conductances λ’
(Eq. [A1.2a, A1.2b, A1.2c] in Appendix 1), which caused greater
G (Eq. [A1.1a, A1.1b, A1.1c] in Appendix 1) and hence greater
|ΔG| (Eq. [A1.17] in Appendix 1), bringing them closer to measured values in both the 2002 and 2004 periods (Fig. 5b and 6b).
Sharp negative peaks in modeled G on DOY 260 and 264, 2004
(Fig. 6b) were caused by incoming water-convective heat with
some light rainfalls, while the heat flux plates detect conductive
heat only (Kellner 2001).
An increase in G of ~ 20 W m−2 modeled with air-convective heat transfer (Fig. 5b and 6b) caused a corresponding decrease in H (Fig. 5c and 6c), compared with G and H modeled
without air-convective heat transfer. Larger modeled vs. measured H in both years could be partially attributed to an average
energy balance closure (EBC) of 90% in eddy covariance (EC)
measurements at Mer Bleue bog (Lafleur et al., 2005a, 2003).
Slightly lower EBC of 93% during DOY 180 to 187 in 2002
could help in explaining slightly higher discrepancies between
measured and simulated H and G for this period, compared with
those for DOY 259 to 266 in 2004 (Fig. 5b, 5c, 6b, and 6c) with
EBC of 97%.
The larger |ΔG| modeled with air-convective heat transfer caused larger changes in energy storage ΔE (Eq. [A1.16]
in Appendix 1) and hence larger ΔTS in each model cell (Eq.
[A1.22] in Appendix 1). These larger ΔTS resulted in hummock TS (Eq. [A1.21] in Appendix 1) and in time courses of
warming and cooling at the 5-, 10-, and 20-cm depths that were
closer to measured values in both years (Fig. 5d, 5e, 5f, 6d, 6e,
and 6f ). The improved simulation of warming and cooling
with air-convective heat transfer was attributed in the model to
more rapid changes of Tout than Tin (Eq. [A2.7] in Appendix
1) when calculating Ra. A more rapid decrease of Tout than Tin
with cooling during DOY 184 to 186 in 2002 caused a decline
in negative G (Fig. 5b) and hence a decrease of simulated TS
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SSSAJ: Volume 74: Number 4 • July–August 2010
1413
Fig. 5. Short-term dynamics of (a) hourly air temperature, (b) ground heat flux, and (c) sensible
heat flux modeled with and without air-convective heat transfer; hourly simulated and measured
(thermocouple) soil temperatures at the (d) 5- and (e) 10-cm depths in hummocks, showing how
diurnal amplitudes in soil temperatures increase when air-convective heat transfer is included.
Fig. 5 continued. Short-term dynamics of the (f) 20-, and (g) 40-cm depths in hummocks, showing how diurnal amplitudes in soil temperatures increase when air-convective heat transfer is included;
and hourly simulated and measured (thermocouple) soil temperatures at (h) 5 and (i) 10 cm in hollows, showing increasing temperatures with air-convective heat transfer in adjacent hummocks,
Mer Bleue bog, 2002; DOY is Day of the Year.
1414
and its diurnal variation (Fig.
5d, 5e, and 5f ). Conversely, a
more rapid increase of Tout than
Tin with warming during DOY
264 to 266 in 2004 caused a
rise in negative G (Fig. 6b) and
hence an increase of simulated
TS and its diurnal variation (Fig.
6d, 6e, and 6f ).
Larger modeled G and TS
in the hummock mounds drove
greater vertical and lateral G below the hummock mounds (Eq.
[A1.1a, A1.1b] in Appendix 1)
that increased TS modeled at
40 cm under hummocks (Fig.
5g and 6g), and at 5 and 10 cm
under hollows (Fig. 5h, 5i, 6h,
and 6i), bringing them closer to
measured values.
Seasonal Heat
Transfer in Peat
Interannual performance
of ecosys with and without airconvective heat transfer was
compared during the periods
of pronounced spring warming in 2002 (DOY 120–180)
and fall cooling in 2004 (DOY
260–320) at the 10- and 20-cm
depths in hummocks (Fig. 7 and
8). Lower simulated G by the
run without air-convective heat
transfer (Fig. 5b and 6b) caused
underestimation of the rise in TS
during the spring of 2002 at both
depths (Fig. 7). Underestimated
TS in spring of 2004 resulted in
lower gradients between TS at
adjacent soil model cells (Eq.
[A1.1] in Appendix 1) and in
underestimated decline in TS
during the fall in 2004 (Fig. 8).
Seasonal rises and declines in
TS were better simulated with
air-convective heat transfer in
the spring (Fig. 7), due to the cumulative enhancement of G, and
in the fall (Fig. 8), due to higher
TS gradients between previously warmed soil model cells in
hummock interior and already
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SSSAJ: Volume 74: Number 4 • July–August 2010
1415
Fig. 6. Short-term dynamics of (a) hourly air temperature, (b) ground heat flux, and (c) sensible heat flux; hourly simulated and measured (thermocouple) soil temperatures at (d) 5- and (e) 10-cm depths
in hummocks, , showing how diurnal amplitudes in soil temperatures increase when air-convective heat transfer is included; DOY, is Day of the Year.
Fig. 6. Continued. Short-term dynamics of hourly simulated and measured (thermocouple) soil temperatures at (f) 20- and (g) 40-cm depths in hummocks, , showing how diurnal amplitudes in soil
temperatures increase when air-convective heat transfer is included;and at (h) 5 cm and (i) 10 cm in hollows, showing soil temperatures increasing with air-convective heat transfer in adjacent hummocks,
Mer Bleue bog, 2004; DOY is Day of the Year.
1416
cooled soil model cells close to
hummock surface.
Heat Transfer in Peat
under Conditions not
Favoring Air Convection
Day of year 249 to 256 in
2004 were selected to demonstrate how TS was affected by
a temporary cessation of airconvective heat transfer in the
model during a heavy rainfall
event on DOY 253. During this
period G was driven within the
saturated peat matrix by conduction plus water-convection
alone as the air-convective heat
transfer in well-drained macropores of the hummock mounds
(Dimitrov, 2009) was minimized with small Tout – Tin. This
difference remained <4°C as the
Tout, assumed to be equal to the
hummock surface temperature,
dropped faster than the Tin (Eq.
[A2.7] in Appendix 1). Thus, Ra
< Racr (Eq. [A2.6]) and Nu =
1 (Eq. [A2.1a] in Appendix 1),
which caused h* = λ (Eq. [A2.10]
in Appendix 1) so that G was
only conductive plus water-convective, causing low simulated TS
at 5-, 10-, and 20-cm depths in
hummocks on DOY 253. The TS
modeled without air convection
corresponded well with the measured values on that day (Fig. 9).
As soon as Tout – Tin rose on the
next day, h* rose above λ so that
air convection enhanced G, causing the run with air-convective
heat to increase diurnal variation
of TS, following that in the thermocouple measurements. The
run without air-convective heat
transfer increased diurnal variation in TS inadequately (Fig. 9).
Improved agreement between measured and simulated
TS and G with and without airconvective heat transfer under
decreasing Tout − Tin was also
apparent during DOY 262 to
264, 2004 (Fig. 6e, 6f, and 6g).
SSSAJ: Volume 74: Number 4 • July–August 2010
Agreement between
Modeled and Measured Soil
Temperature, Ground Heat
Flux, Sensible Heat Flux,
Latent Heat Flux, and Net
Radiation With and Without
Air-Convective Heat Transfer
Linear regressions between
measured TS, G, H, LE, and Rn and
those simulated with and without
air-convective heat transfer during
the period 2000 to 2004 at Mer
Bleue, were highly significant (p <
0.0001) (Table 1). The coefficients
of determination (R2) indicated
good predictive power for both
model runs. However, declining
slopes and rising intercepts for TS
simulated without air-convective
heat transfer at the 5-, 10-, and 20cm depths in hummocks clearly indicated a progressive decline in simulated TS from the thermocouple
measurements with increasing depth
(Table 1). That decline was also
reflected in simulated G patterns
without air-convective heat transfer
(Fig. 5b and 6b). Regression slopes
close to unity and intercepts around
1°C for the simulated TS indicated
improved model performance with
air-convective heat transfer (Table
1). Willmott’s index of agreement d
indicated small relative discrepancy
Fig. 7. Daily-averaged soil temperatures measured (dots) vs. modeled with (solid line) and without between modeled and measured
(dashed line) air-convective heating during spring warming at the (a) 10- and (b) 20-cm depths in TS for both runs (Willmott, 1982,
hummocks at Mer Bleue bog in 2002; DOY is Day of the Year.
1981; Willmott and Wicks, 1980).
However, the RMSDs and MAEs inLower Tout − Tin brought performance of the run with airdicated that discrepancy between measured and simulated TS was
convective heat closer to that of the run without during coolsmaller with air-convective heat transfer than without (Table 1).
er years 2004 (Fig. 6) and 2000 (data not shown). However,
Statistics for Rn, LE, H, and G for the run without aircompared with simulated TS and G without air-convective
convective heat are not given here, as they did not differ much
heat transfer, higher Tout – Tin brought simulated TS and G
from those for the run with air-convective heat subject to the
with air-convective heat transfer much closer to those measame weather (Table 1). Statistics for G should be treated with
sured during warm years 2002 (Fig. 5) and 2001 (data not
caution, given the limited area that heat flux plates represent on
shown). In addition, the energy storage ΔE (Eq. [A1.16] in
a microtopographical scale, their inability to capture convective
Appendix 1) in the model during the wetter years 2004 and
heat with incoming rain water, and that they were reported to
2000 was more influenced by vapor- and water-convective
give less accurate G values in peat soils (Kellner, 2001; Halliwell
heat fluxes ΔV and ΔW (Eq. [A1.18, A1.19] in Appendix 1),
and Rouse, 1987). Yet, the slope and intercept for G simulated
than was ΔE during the drier years 2002 and 2001. Increased
with air-convective heat (Table 1) indicated less discrepancy
importance of ΔV and ΔW during periods of precipitation
with measurements, compared with those for G simulated withpartially compensated for the missing air-convective heat in
out (respectively, slope = 0.41 and intercept = −2.85 W m−2,
the original ecosys and explained its relatively better fit to
not given in Table 1). In addition, lower simulated than meameasurements during the wetter than during the drier years.
sured G (Fig. 6a and 6b) is consistant with higher simulated than
SSSAJ: Volume 74: Number 4 • July–August 2010
1417
measured H (Table 1) for the run
with air-convective heat.
We recognize that the general
inability of the model with air-convective heat to reproduce the extremes in diurnal temperature cycles
in the dry year 2002 (Fig. 5d and
5e) might be due to improper parameterization. Due to peat vertical
stratigraphy (Frolking et al. 2001)
possible gradients of peat fiber diameters (Levesque et al., 1980) and
air-filled macroprorsities (Silins and
Rothwell, 1998) with depth might
have determined vertical gradients
in air permeability of fibric peat in
the field. Therefore, simulated hummock TS with average air permeability kp might need to be further
corrected, so that those near the
surface (at ?5 cm) with higher kp
should further increase and those
at depth (at ~ 20 cm) with lower kp
should further decrease (Poulikakos
and Bejan, 1983; McKibbin and
Tyvand, 1982). This possible underestimation of the simulated
TS at near-surface, together with
some nighttime air-convective heat
enhancement that was not simulated at this stage, might explain
pronounced nighttime underestimation of the hummock TS at the
5-cm depth (Fig. 6a and 9a). Still,
the Heating-from-the-Side air-convective heat transfer appears to be a
key mechanism of the peat thermal
regime, captured reasonably well by
Eq. [A2.1–A2.10] in Appendix 1 in
the modified ecosys.
Fig. 8. Daily-averaged soil temperatures measured (dots) vs. modeled with (solid line) and without
(dashed line) air-convective heating during autumn cooling at the (a) 10- and (b) 20-cm depths in
hummocks at Mer Bleue bog in 2004; DOY is Day of the Year.
DISCUSSION
We have shown that a complex model such as ecosys can simulate soil thermal regime in a peatland ecosystem at the scale of the
local microtopography. The highly macroporous, well-drained,
and aerated fibric peat in hummock mounds required simulation
of air convective heat transfer, in addition to the conductive plus
water- and vapor-convective transfers, to achieve this result and to
give improved results over the model without air-convective heat
transfer. In addition to improved simulation of the dynamics and
diurnal amplitudes of TS at depth in hummocks and hollows, the
air-convective heat transfer mechanism also improved simulation
of G and H bog energy balance components.
1418
Air-Convective vs. Alternative Heat Transfer in Peat
Alternative heat transfer mechanisms could be hypothesized to act complementary to the ground heat conduction. The
most probable mechanisms are (i) heat transfer enhancement
within near-surface peat with air moved by wind-induced pressure drops, and (ii) lateral conductive ground heat flux through
hummock sides (Kellner, 2001).
Ecosys already incorporates formulae to calculate the effects on heat transfer from wind-driven pressure drops in surface
residue layer (Grant, 2004; Grant et al., 2004; Tanner and Shen,
1990). However, the model has not been programmed to account
for such effects deeper in soil profiles, as the original code was
designed for mineral soils with low air permeabilities, where air
convection is not an issue. Yet, at present this mechanism cannot
be supported as a significant source of heat transfer in near-surface peat for the following reasons. First, it is controversial how
SSSAJ: Volume 74: Number 4 • July–August 2010
between hummock surfaces and
hollow surfaces, determined such a
zero plane displacement height that
was not significantly different from
zero at both hummock and hollow
surfaces. However, in contrast to
hummocks, the hollows maintain
much more rapid temperature attenuation in depth, although they
both are subject to the same winds
at the same time, and that the same
large and well-drained macropore
fraction occur within the top 10
cm of the hollow peat (Dimitrov,
2009; Lafleur et al., 2005b). Third,
the strong winds required to induce
pressure drops do not blow continuously to maintain the enhanced heat
transfer that seems to occur within
hummocks at Mer Bleue. Moreover,
the air-convective heat enhancement of G in the model and high
TS at depth occur even at low wind
speed (figures not given here). Yet, it
is possible that the wind-driven heat
enhancement may act complementary to hypothesized air-convective
heat enhancement, whenever strong
winds blow over the bog surface.
Such conditions may help to explain
partially some peaks in diurnal TS
that were not captured by the modified ecosys.
Kellner (2001) attributed failure to model TS in hummocks to
omitting significant conductive
heat through the hummock sides,
thus also recognizing that the local
microtopography should be considered in modeling the complex
heat transfer in peat. However, this
Fig. 9. Hourly soil temperature at (a) 5-, (b) 10-, and (c) 20-cm depths in a hummock at Mer Bleue bog, lateral conduction alone was insuf2004, showing attenuation of the air-convective heat transfer with attenuating temperature differences
ficient to explain the diurnal variabetween the peat surface and the interior on Days of the Year (DOY) 253 to 254 when a massive rainfall
tion of TS below hummock surface
of 125 mm occurred.
at Mer Bleue bog. During the cool
strong such possible pressure drops would be within the surface
and rainy DOY 253 in 2004, the
peat, and whether they could affect the air in hummocks up to
Tout– Tin was insufficient to drive the air-convective heat in
~40 cm below surface. This is the depth to which diurnal variahummock mounds and conductive plus water-convective G oction in TS is still detectable by in situ thermocouples, and greater
curred in hummocks and hollows. If the horizontal component
than that expected from conduction alone. Second, it is still dubiof G really mattered, the horizontal and vertical G at hummocks
ous how the rigid, shrubby hummock-hollow bog surface would
should result in hummock TS with prominently larger diurnal
affect such potential pressure drops in depth. Kellner (2001)
variation compared to those in hollows determined by vertical
analyzed wind profiles of Swedish mires and found that low and
G only. However, the thermocouple TS at the 5-, 10-, and 20sparse vegetation canopy and insufficient differences in elevation
cm depths in hummocks and hollows converged within ~1.5°C
SSSAJ: Volume 74: Number 4 • July–August 2010
1419
difference on DOY 253 (Fig. 10). So, the lateral conductive plus
water- and vapor-convective G could not explain properly the
overall hummock G and TS.
Limitations to the Hypothetical Air-Convective
Heat Transfer
The air-convective effect modeled here would decrease
if fibric peat thickness became shallower than the hummock
heights and hemic or sapric peat partially occupied hummock
mounds above the hollow surfaces. There are two main reasons
for such a decrease. First, the high water retention in hemic and
sapric peat, and their high water-filled porosities would result in
lower air-filled porosities and insufficient permeabilities to air kp
(Eq. [A2.8] in Appendix 1) resulting in Ra < Racr (Eq. [A2.6]
in Appendix 1), so that air circulation would not commence.
Second, decreasing height of the fibric peat would result in lower
Ra (Eq. [A2.6] in Appendix 1) and lower Nu (Eq. [A2.2a, A2.2b]
in Appendix 1), and even though there still might be some air
convection in shallower fibric peat, it would be less intensive.
Therefore, it is not only the hummocky microtopography and
Table 1. Statistics for regressions of simulated on measured (thermocouples) hourly soil temperatures at 5, 10, 20, and 40 cm in
hummocks and at 5 and 10 cm in hollows for Mer Bleue bog for 2000 to 2004.
Statistic
Value
Soil temperatures, run without air-convective heat transfer
5 cm, hummock (n† = 43,299)
Slope b‡
0.93 (P < 0.0001)
Intercept a‡, °C
−1.10 (P < 0.0001)
R2
0.91 (P < 0.0001)
Willmott’s index of agreement, d
0.98
RMSD§, °C
2.80
Mean Absolute Error (MAE)§, °C
2.27
10 cm, hummock (n = 43,316)
Slope b
0.81 (P < 0.0001)
Intercept a, °C
−0.31 (P < 0.0001)
R2
0.90 (P < 0.0001)
Willmott’s d
0.98
RMSD, °C
2.71
MAE, °C
2.29
20 cm, hummock (n = 43,279)
Slope b
0.76 (P < 0.0001)
Intercept a, °C
0.26 (P < 0.0001)
R2
0.91 (P < 0.0001)
Willmott’s d
0.98
RMSD, °C
2.25
MAE, °C
2.04
40 cm, hummock (n = 43,201)
Slope b
0.69 (P < 0.0001)
Intercept a, °C
1.02 (P < 0.0001)
R2
0.92 (P < 0.0001)
Willmott’s d
0.99
RMSD, °C
1.54
MAE, °C
1.79
5 cm, hollow (n = 40,724)
Slope b
1.03 (P < 0.0001)
Intercept a, °C
−1.04 (P < 0.0001)
R2
0.87 (P < 0.0001)
Willmott’s d
0.97
RMSD, °C
2.43
MAE, °C
1.86
10 cm, hollow (n = 40,701)
Slope b
Intercept a, °C
R2
Willmott’s d
RMSD, °C
MAE, °C
1420
0.83 (P < 0.0001)
0.22 (P < 0.0001)
0.91 (P < 0.0001)
0.98
1.67
1.53
Statistic
Value
Soil temperatures, run with air-convective heat transfer
5 cm, hummock (n = 43,210)
Slope b
0.98 (P < 0.0001)
Intercept a, °C
−0.59 (P < 0.0001)
R2
0.91 (P < 0.0001)
Willmott’s d
0.98
RMSD, °C
2.80
MAE, °C
2.00
10 cm, hummock (n = 43,002)
Slope b
0.99 (P < 0.0001)
Intercept a, °C
0.66 (P < 0.0001)
R2
0.93 (P < 0.0001)
Willmott’s d
0.98
RMSD, °C
2.37
MAE, °C
1.74
20 cm, hummock (n = 42,450)
Slope b
1.02 (P < 0.0001)
Intercept a, °C
1.19 (P < 0.0001)
R2
0.94 (P < 0.0001)
Willmott’s d
0.98
RMSD, °C
1.80
MAE, °C
1.65
40 cm, hummock (n = 43,201)
Slope b
0.89 (P < 0.0001)
Intercept a, °C
2.03 (P < 0.0001)
R2
0.96 (P < 0.0001)
Willmott’s d
0.99
RMSD, °C
1.07
MAE, °C
1.37
5 cm, hollow (n = 37,786)
Slope b
1.08 (P < 0.0001)
Intercept a, °C
−0.70 (P < 0.0001)
R2
0.86 (P < 0.0001)
Willmott’s d
0.96
RMSD, °C
2.24
MAE, °C
1.99
10 cm, hollow (n = 37,979)
Slope b
0.90 (P < 0.0001)
Intercept a, °C
1.11 (P < 0.0001)
R2
0.92 (P < 0.0001)
Willmott’s d
0.99
RMSD, °C
1.54
MAE, °C
1.04
SSSAJ: Volume 74: Number 4 • July–August 2010
Table 1 continued. Statistics for regressions of simulated on
measured (thermocouples) hourly soil temperatures simulated on eddy-covariance (EC)-measured hourly ground heat
flux, sensible heat flux, latent heat flux, and net radiation for
Mer Bleue bog for 2000 to 2004.
Statistic
Value
Surface energy fluxes, run with air-convective heat transfer
Ground heat flux (n = 16,631)
Slope b
0.47 (P < 0.0001)
Intercept a, W m−2
−0.87 (P < 0.0001)
R2
0.22 (P < 0.0001)
Willmott’s d
0.80
RMSD, W m−2
13.47
MAE, W m−2
11.79
Sensible heat flux (n = 23,126)
Slope b
1.24 (P < 0.0001)
Intercept a, W m−2
−10.48 (P < 0.0001)
R2
0.71 (P < 0.0001)
Willmott’s d
0.87
RMSD, W m−2
39.40
MAE, W m−2
44.68
Latent heat flux (n = 16,631)
Slope b
0.98 (P < 0.0001)
Intercept a, W m−2
−3.85 (P < 0.0001)
R2
0.81 (P < 0.0001)
Willmott’s d
0.95
RMSD, W m−2
34.87
MAE, W m−2
25.24
Net radiation (n = 22,204)
Slope b
0.95 (P < 0.0001)
Intercept a, W m−2
15.78 (P < 0.0001)
R2
0.94 (P < 0.0001)
Willmott’s d
0.98
RMSD, W m−2
44.19
MAE, W m−2
32.86
† n, number of hourly values in regressions.
‡ y = a + bx, where y is the modeled flux and x is the EC-derived flux.
§ y = a + bx, where y is the EC-derived flux and x is the modeled flux.
the large kp caused by large macroporosity, but also the thickness
of the fibric peat that would determine the air-convective effect
on heat transfer in peat. Thus, if the air-convective heat transfer
is to be tested geographically to find whether it would occur in
other peatlands, one would need to know the magnitude of fibric
peat thickness, in addition to the average hummock height above
the hollow surface.
Evaluating the Impacts of Uncertainty in Modeled
Soil Temperature
Accurate simulation of peat thermal regime is important
for simulation of other peatland processes such as C exchange
and ER, which depend on TS (Grant, 2004; Bubier et al., 2003a,
2003b; Reichstein et al., 2003). To evaluate the accuracy with
which peat thermal regime is simulated at Mer Bleue, we estimated the effect on ER of uncertainty in modeled TS from a regression of EC-measured CO2 effluxes on TS by Lafleur et al.
(2005b). Uncertainty in TS (RMSD at the 5-, 10-, 20-cm depths
in hummocks and at the 5- and 10-cm depths in hollows from
Table 1) modeled with air-convective heat transfer caused uncertainty in ER that varied between 0.49 and 0.68 μmol m−2 s−1.
This was less than the random error for EC-measured ER of 0.74
μmol m−2 s−1 estimated by Richardson et al. (2006). Uncertainty
in TS modeled without air-convective heat transfer caused uncertainty in ER > 0.74 μmol m−2 s−1. Although a simple test,
this exercise suggests that the introduction of air-convective heat
transfer is likely to have a significant influence on improving the
accuracy of other simulated processes.
CONCLUSIONS
Although a simplification at this stage, findings of this
study suggest that the air-convective heat transfer in hummock
mounds, driven by the temperature gradients between hummock sides and interior, is an important mechanism that improves the
simulation of peat thermal regime.
This mechanism complements heat
transfer by conduction plus vapor- and water-convection in peat,
and could explain the differences
in attenuating patterns of daily soil
temperatures in hummocks and hollows. Because it is dependent on bog
microtopography and fibric peat
thickness and macroporosity, the
air-convective enhancement of the
conductive ground heat might vary
among different peatlands.
At present, air-convective heat
transfer in hummocks is hypothesized
and has not been demonstrated in the
field experimentally. The potential sigFig. 10. Hourly measured (thermocouple) soil temperatures at 5-, 10-, and 20-cm depths in hummocks nificance of this mechanism, however,
and hollows at Mer Bleue bog, 2004, showing convergence of the soil temperatures at various depths
for improving peat thermal simulain both hummocks and hollows with a drop in air temperature on Days of the Year (DOY) 253 to 254.
SSSAJ: Volume 74: Number 4 • July–August 2010
1421
tions and the other ecosystem processes that rely on accurate soil
temperture estimation warrants a call for such experiments. With
current technology, it may not be possible to directly measure air
convection within hummocks, but careful instrumentation of the
three-dimensional thermal regime within peatland hummocks may
indirectly support the hypothesis. In addition, it may be possible to
conduct simulations with ecosys for peatlands exhibiting sufficiently
different microtopographic structure where the importance of the
air-convection mechanism would probably vary. In any case, we believe that this mechanism represents an improvement in our understanding of peatland thermal processes and their modeling.
APPENDIX 1:Soil Heat Transfer Equations
Soil heat transfer equations of the existing ecosys code: conductive
ground heat flux, vapor-convective heat flux, water-convective heat flux,
energy storage, and soil temperatures.
V, y
V ,z
′
′
V ,x , y ,z
l x , y ,z
V , x , y 1, z
V ,x , y ,z
l x , y ,z
V ,x , y,z
V ,x , y,z 1
l x , y ,z
V ,x , y ,z 1
[A1.6c]
V ,x , y ,z
1
1.75
TSx , y , z
2
a
2/3
t
V ,x , y ,z
[A1.6b]
l x , y 1, z
V , x , y 1, z
V ,o
0.002173
e x , y ,z
TSx , y , z
C V ,x , y ,z
e x , y , z esat ′exp
M
m
[A1.8]
[A1.9]
o
RTS
1
TS
esat ′ esat exp 5360 0.003661
Ground heat flux
*[
[
′ 7s[ , \ , ] 7S[
1, \ , ]
[A1.1a]
1, ]
[A1.1b]
*\
′
7S[ , \
\ 7s[ , \ , ]
*]
′
] 7S[ , \ , ] 7S[ , \ , ] 1
[
28 W
′
O[ , \ , ]
G
O[ , \ , ]
[ 1, \ , ]
O[
1, \ , ]
[, \, ]
[A1.2a]
[, \,]
[, \, ]
1, ]
100 0.01YW exp
[, \,]
[, \,] 1
O[ , \ , ]
[, \,] 1
[A1.2b]
[ , \ 1, ]
O[ , \
[ , \ 1, ]
28 W
′
8W
[, \, ]
[ 1, \ , ]
28 W
′
\
]
O[ , \ , ]
[A1.1c]
[A1.2c]
1
[A1.2d]
O
f wtr
x , y ,z
wtr
[A1.2e]
f air c air
f wtr
air
f ice c ice
f air c air
f org c org
ice
f ice c ice
f min c min
org
f org c org
f min c min
min
f snd c snd
f snd c snd
snd
f rck c rck
f rck c rck
rck
[A1.3]
Vapor-convective heat flux
Vx
c WTSx , y , z Lv Q V , x
Vy
c WTSx , y , z Lv Q V , y
[A1.4b]
Vz
Q V ,x
Q V, y
Q V ,z
′
V ,x
1422
c WTSx , y , z Lv Q V , z
′ C Vx , y , z C Vx
V ,x
V, y
[A1.4c]
1, y , z
′ C Vx , y , z C Vx , y 1, z
V ,z
′ C Vx , y , z C Vx , y , z
V ,x , y ,z
l x , y ,z
V , x 1, y , z
1, y , z
[A1.5a]
[A1.5b]
1
V , x 1, y , z
lx
W x c WTSx , y , z Q W , x
[A1.11a]
W y c WTSx , y , z Q W , y
[A1.11b]
Wm, z c WTSx , y , z Q W , z
[A1.11c]
WM, z c WTSx , y , z Q M, z
[A1.12]
WP, z c WTair Q P, z
[A1.13]
Wsn, z c WTsn Q sn, z
[A1.14]
Wz Wm, z WM, z WP, z Wsn, z
[A1.15]
Energy Storage
G x , y ,z
E x , y ,z
[A1.5c]
[A1.6a]
Vx , y ,z
Wx , y ,z
Bx , y , z
l x , y ,z
G x , y ,z
x , y ,z
G in
cell
G out
cell
Vx , y ,z
x , y ,z
Vin
cell
Vout
cell
Wx , y ,z
Bx , y , z
[A1.4a]
[A1.10]
Water-convective heat flux
[, \,]
G
[A1.7]
273.15
Win
x , y ,z
Bin
x , y ,z
cell
cell
Wout
Bout
Lf [A1.16]
[A1.17]
[A1.18]
[A1.19]
cell
[A1.20]
cell
Soil Temperature
TSx , y , z ,
TSx , y , z
t
TSx,y ,z
[A1.21]
E x , y ,z
[A1.22]
c Sx , y ,z
c Sx , y , z c Mx , y , z
f I,
c Mx , y , z
TSx , y , z
c
I I
f org c M,org
f rck c M,rck
f W,
c
W W
f W ,M
c
W W
f I,M I c I
f min c M,min
f snd c M,snd
[A1.23a]
[A1.23b]
Soil heat transfer equations of the newly developed module
in ecosys code: air-convective effect on thermal conductivity
V ,x , y,z
SSSAJ: Volume 74: Number 4 • July–August 2010
hx , y , z
x , y,z
hx , y , z Nu
, Nu 1, no convection: Ra Ra cr [A2.1a]
x , y ,z
, Nu 1, convection: Ra Ra cr [A2.1.b]
Ra 2C13
120
Nu C1
4.39
0.71Ra 0.5
Ra 0.5
Nu
*
L* H hmk
C1
[A2.2a]
[A2.2b]
2
*
L* H hmk
Df
esat
Lf
Lv
M
R
Racr
p
air
0.5
Ra 15
[A2.3a]
Ra 30
air
ice
C1
4.39
Ra 0.5
[A2.3b]
min
org
if Eq. [2.5] is substituted into Eq. [2.3a]
rck
*
H hmk
*
H i , 0 H hmk
H hmk ; q:
i 1, q
a
w
[A2.4]
snd
air
L* 0.158 H *Ra
g
Ra
p
air
[A2.5]
kp Tout
Tin H *
[A2.6]
Ti
q
Df a ′ln c ′′ 1
4c′ 1
′
a
i 1, q
a
a
′
wtr
[A2.8]
′
V,o
air
APPENDIX 3
l z ,i a ,i
l z ,i
L*
Nu
L
snd
2
[A2.9]
where q is the deepest soil layers where εa > εw
hx , y , z *
min
rck
[A2.7]
where q is the deepest soil layers where εa > εw
kp
ice
org
air
i 1, q
Tin
0.5
average fiber diameter in fibric peat, 75 μm
(Levesque et al., 1980)
saturation vapor pressure at 0oC, 0.6108 kPa
(de Vries, 1963)
latent heat of freezing, 3.33 MJ m−3 (de Vries, 1963)
latent heat of vaporization, 2460 MJ m−3 (de Vries, 1963)
molecular mass of water, 18 g mol−1 (Campbell, 1977)
gas constant, 8.3145 J mol−1 m−3 (Campbell, 1977)
critical Rayleigh number for side-to-side natural air convection,
66.2 (Kwok and Chen, 1987)
dry and wet peat thermal diffusivity, 1.0 × 10−7 m2 s−1,
(Campbell, 1977)
thermal expansion coefficient of air at 20oC, 0.00343 oC−1
(Nield and Bejan, 1992)
ratio between the average temperature gradients of air and water,
1.609 (de Vries, 1963)
ratio between the average temperature gradients of ice and water,
0.611 (de Vries, 1963)
ratio between the average temperature gradients of mineral soil
particles and water, 0.514 (de Vries, 1963)
ratio between the average temperature gradients of organic
particles and water, 1.253 (de Vries, 1963)
thermal conductivity coefficient of rock, 0.259
(de Vries, 1963)
thermal conductivity coefficient of sand, 0.259 (de Vries, 1963)
thermal conductivity of air, 9.050 × 10−5 MJ h−1 m−1 oC-1 (de
Vries, 1963)
thermal conductivity of ice, 7.844 × 10−3 MJ h−1 m−1 oC−1 }
(de Vries,1963)
thermal conductivity of mineral soil particles,
1.056 × 10−2 MJ h−1 m−1 oC−1 (de Vries, 1963)
thermal conductivity of organic soil particles,
9.050 × 10−4 MJ h−1 m−1 oC−1 (de Vries, 1963)
thermal conductivity of rock, 3.076 × 10−2 MJ h−1 m-1 oC−1
(de Vries, 1963)
thermal conductivity of sand, 3.076 × 10−2 MJ h−1 m−1 oC−1
(de Vries, 1963)
thermal conductivity of water, 2.067 × 10−3 MJ h−1 m−1 oC−1
(de Vries, 1963)
vapor diffusivity in open air at 0oC, 0.077 m2 h−1
(Millington and Quirk, 1960)
kinematic viscosity of air at 20oC, 15.11 × 10−6 m2 s−1 (Nield and
Bejan, 1992)
x , y ,z
L L*
L
x , y ,z
[A2.10]
h* substitutes λ (Eq. [A1.2a–A1.2c]) for further heat and soil T
calculations within the same time step Δt.
Appendix 2: General Heat Transfer and Soil
Physics Parameters
c′
c″
cI
cM,min
fibrous beds permeability function parameter, 6.1 (Dullien, 1979)
fibrous beds permeability function parameter, 0.64 (Dullien, 1979)
specific heat capacity of ice, 1.927 MJ kg−1 oC−1 (de Vries, 1963)
volumetric heat capacity of soil mineral particles,
2.385 MJ m−3 oC−1 (Campbell, 1977)
cM,org volumetric heat capacity of soil organic particles,
2.496 MJ m−3 oC−1 (Campbell, 1977)
cM,rck volumetric heat capacity of rock, 2.128 MJ m−3 oC−1 (Campbell, 1977)
cM,snd volumetric heat capacity of sand, 2.128 MJ m−3 oC−1
(Campbell,1977)
cW
specific heat capacity of water, 4.187 MJ kg−1 oC−1 (de Vries, 1963)
SSSAJ: Volume 74: Number 4 • July–August 2010
Definitions of Variables and Parameters
bulk density of peat with macropores (Mg m−3)
soil volumetric heat capacity (MJ m−3 oC−1)
vapor concentration (g m−3)
ρb
cS
CV
cW
d
Df
e
E
ΔE
specific heat capacity of water (MJ kg−1 oC−1)
soil depth (m)
average diameter of peat fibers (μm)
ambient vapor pressure (kPa)
energy storage in the soil (MJ m−3)
change in energy storage of a given model cell (MJ m−3)
esat′
fIμ
fmin
forg
frck
fsnd
fWM
fWμ
g
G
GMC
GTS
saturation vapor pressure (kPa) at a given soil temperature
volumetric fraction of ice in the soil matrix (m3 m−3)
volumetric fraction of mineral particles in the soil matrix (m3 m−3)
volumetric fraction of organic particles in the soil matrix (m3 m−3)
volumetric fraction of rock particles in the soil matrix (m3 m−3)
volumetric fraction of sand particles in the soil matrix (m3 m−3)
volumetric fraction of water in soil macropores (m3 m−3)
volumetric fraction of water in the soil matrix (m3 m−3)
gravity (cm s−2)
conductive ground heat flux (MJ m−2 h−1)
ground heat flux between adjacent model cells (MJ m−2 h−1)
ground heat flux at the terrestrial surface (MJ m−2 h−1)
1423
h
H
Hhmk
h*
H*hmk
kp
kθ
L
L*
LE
Lf
Lv
lx
ly
lz
Nu
QV
QW
Ra
Rn
SLTk
SLTw
t
Δt
T″
T0–1
Ta
Tin
Tl
Tout
TS
TS,Δt
UW
V
W
x
y
z
αp
εa
εa′
εt
εw
ηw
λ
λ′
σV
σV′
ψS
overall heat transfer rate
sensible heat flux (MJ m−2 h−1)
hummock height (m)
effective heat transfer coefficient
hummock effective height (m)
permeability of peat to air (m2)
unsaturated hydraulic conductivity (m2 MPa−1 h−1)
hummock diameter (m)
horizontal depth of air convection from hummock side to interior (m)
latent heat flux (MJ m−2 h−1)
latent heat of freezing and thawing (MJ m−3)
latent heat of vaporization (MJ m−3)
model cell size, horizontal length (m)
model cell size, horizontal length (m)
model cell size, vertical thickness (m)
Nusselt number
vapor flux (m h−1)
subsurface water flux through the soil (matrix) (m3 m−2 h−1)
Rayleigh number
net radiation (MJ m−2 h−1)
soil layer depth from the hummock surface (cm)
soil layer depth from the hollow surface (cm)
time (h)
time step (e.g., 30 min, 1 h, 1 d, etc.)
warmest temperature inside the peat profile at night (°C)
temperature of the horizontal hummock surface layer (0–1 cm) (°C)
atmospheric temperature (°C)
temperature inside hummock (°C)
temperature at each soil layer l (°C, K)
temperature at hummock side (°C)
soil temperature (°C, K)
soil temperature of a model cell at the beginning of the next time step (K)
wind-driven effect of heat diffusivity through the soil surface
vapor-convective heat flux in the soil (MJ m−2 h−1)
water-convective heat flux in the soil (MJ m−2 h−1)
distance in the x direction (m)
distance in the y direction (m)
distance in the z direction (m)
thermal diffusivity of peat (m2 s−1)
air-filled soil porosity (m3 m−3)
average air-filled porosity (m3 m−3)
total soil porosity (m3 m−3)
water-filled porosity (m3 m−3)
dynamic viscosity of water (g cm−1 s−1)
thermal conductivity (MJ h−1 m−1 °C−1)
thermal conductance (MJ h−1 m−2 °C−1)
vapor diffusivity (m2 h−1)
vapor conductance (m h−1)
soil water potential (MPa)
ACKNOWLEDGMENTS
Funding 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.
1424
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