Auxiliary Material
Auxiliary Material 1
Natural strain (ε), also called logarithmic or Hencky strain, is defined as:
i n
 dh
h
  ln
h
h0
i 1
 
(S1)
in which h0 is the initial thickness (m), h is the current thickness (m) and dh is the
change in thickness (m) of layer i.
Auxiliary Material 2
The most important assumptions in Equation 2 are:
1. The initial effective stress (  0 ) is assumed to be 1 kPa, and σ´>1 kPa. This
relatively low value is derived from the assumption that the peat layer was
near full saturation throughout the year during time of formation, and that only
small groundwater table fluctuations occurred. The reference value for t (t0)
was set to 1.
2. Considering the high permeability of recently formed peat, it is assumed that
overpressured pore water is fully dissipated at the end of each time step (in the
calibration dataset on average ~115 years for 5-cm-thick peat layers, in the
model prediction runs usually 50 years).
Auxiliary Material 3
a) The model was run for 125,000 combinations of the parameters b, c and d (50
different values for each parameter; dots in Figure S3). The values of parameter b
ranged from 0 to 0.049, with increments of 0.001, and values of parameters c and d
ranged from 0 to 0.49 with increments of 0.01. Field observations [Van Asselen et al.,
2010] showed that samples used for the calibration of parameters b, c and d were not
much biodegraded, and hence, this process has not much affected the final results.
b) The 95% confidence interval is calculated as model outcomes from parameter sets
lying within the Φmin+ δ contour in parameter space, where Φmin is the lowest
objective function value and δ is [Seber and Wild, 2003; Doherty, 2004]:
  ns 2 F (n, m  n)
(S2)
in which n is the number of parameters, m is the number of observations in the
calibration field dataset, s2 = Φmin/(m-n) and Fα is the F-distribution with probability
interval α = 0.05. For this calibration, Φmin+ δ = 0.00252 + 3·0.00236 / (100-3)·2.7 =
0.00252 + 0.000197 = 0.00256. This range comprises a set of 240 parameter
combinations (Figure S3). For each model scenario, the model is run with this set of
240 parameter combinations. The highest and lowest outcomes of these 240 model
predictions for a particular scenario are the boundaries of the 95% confidence interval
of the prediction for that scenario. The shaded areas in the plots in Figure S3 define
areas in the parameter space where (Φmin+ δ) < 0.00256.
c) The following table presents the lowest objective function resulting from
calibration using the field dataset for different equations relating stress and time with
natural strain, and using the same ranges of parameter values as outlined in Auxiliary
Material 3a.
Compaction equation
ε = a·ln(σ´)+b·ln(t)
ε = a·(σ´)+b·(t)
ε = a·ln(σ´)+ t-b
ε = σ´-a+ t-b
a
0.09·LOI+0.05
0.01·LOI+0.006
0.1·LOI+0.06
0.25
b
0.009
0.00009
0.7
5.6
Φmin
0.00236
0.00382
0.00252
0.04122
Auxiliary Material 4
The effective stress of one layer at a certain moment in time is calculated based on
Terzaghi’s principle of effective stress (σ´= σ-u), in which the total stress (σ; kPa) is
calculated by:
  hsed  s g
(S3)
and the pore water pressure (u; kPa) by:
u  hwater  w g ,
(S4)
with h, the thickness of the overlying sediment (suffix sed) or water (suffix water)
column (m), ρs, saturated density of a texture class (g/cm3), ρw, density of water (=1
g/cm3) and g, the gravity constant (= 9.81 m/s2). The ρs of a texture class is calculated
as:
 s   d  Sw 
(S5)
in which ρd is the dry bulk density (g/cm3), S is the degree of saturation (fraction of 1:
taken 0.98 for peat and clay, 0.99 for loamy deposits and 1.0 for sandy deposits) and
 is the porosity, calculated as  = 1-( ρd / ρmass), where ρmass is the mass density
(g/cm3), calculated using:
 mass 
1
 f org
  f clas f clay
  f clas f silt
   f clas f sand




 

1470
2700
2650
2650
 


 
 
(S6)
in which forg, fclas, fclay, fsilt and fsand, fraction of organics, clastics, clay, silt and sand
respectively, which were estimated from the American soil texture triangle. The ρd of
different texture classes was estimated based on field measurements of the dry bulk
density [Van Asselen et al., 2010], or, if this data was not available, derived from soil
porosity (  ) and soil mass density (ρmass) estimates, using ρd = (1-  )·ρmass [Saxton et
al., 1986].
Auxiliary Material 5
Data from six cores obtained from the Cumberland Marshes (Canada) [Van Asselen et
al., 2010] were used to generate the model calibration dataset. In each of these cores,
the dry bulk density (ρd,i) and LOIi of the compacted peat layer were determined at a
5-cm interval (1 x 1 x 5 cm samples). In addition, the ρd and LOI of different types of
uncompacted surface peat were determined using a new peat sampler [Van Asselen
and Roosendaal, 2009]. Data fitting resulted in exponential relations between ρd and
LOI of different types of uncompacted fen peat. These relations were used to calculate
the decompacted height (h0,i) of each 5-cm-thick compacted peat sample, based on its
LOIi [Van Asselen et al., 2010].
The  i, t of each 5-cm-thick layer in the calibration dataset is derived from the
thickness and texture composition of overlying layers, determined during field
logging of the cores at a 10-cm depth interval [Van Asselen et al., 2010] (Auxiliary
Material 4).
The tdep,i is estimated based on linear interpolation between AMS radiocarbondated peat samples within a core (maximum vertical distance of 20 cm [Van Asselen
et al., 2010]. In the calibration dataset, the deposition time of one 5-cm-thick peat
layer is on average ~115 years. Clastic layers overlying the peat layer accumulated
much faster (<20 yrs).
Auxiliary Material 6
Each model run starts with a time period of peat formation, resulting in a peat
sequence, followed by a time period of overburden (clay) deposition (both in
Situation 1; constant base-level rise). Each time step, a peat or clay layer with an
initial uncompacted thickness of 0.05 m is added to the aggrading sequence. With a
base-level rise of 0.001 m/yr, the accumulation time of one layer becomes 50 years. In
the scenarios presented in this paper, the LOI of the peat sequence has been set to 0.5
or 0.8, and the percentage of intercalated 5-cm-thick clay layers has been set to 0% or
20%, which means that respectively none or every fifth layer within the peat sequence
is clay. The amount of compaction of a peat sequence is calculated as:
compaction 
sp
hp
(S7)
in which sp (m) is the total amount of surface subsidence due to compaction of the
peat sequence and hp is the initial thickness of the peat sequence (m; base level rise
multiplied by duration of accumulation of the peat sequence).
During constant-base-level-rise (Situation 1), the amount of subsidence due to
compaction of one or multiple peat layers is compensated by adding additional (to the
0.05 m) sediment during the next time step (Figure S4). During constant-aggradationrate (Situation 2), a constant amount of sediment is deposited at each time step. If this
amount of sediment is not sufficient to fill up the amount of accommodation space
created by subsidence due to peat compaction and base-level rise, the new surface
elevation is lower than the new base-level height.
Auxiliary Material 7
Symbol List
ai
b
Cint
dhi
δ
εi,t
Fα
fclas
fclay
forg
fsand
fsilt
g
hi,t
h0,i
hc
hi,endtime
hp
hi,obs
hsed
hwater
i
LOIi
m
n
σ
 0
 i, t
calibration parameter (dimensionless)
calibration parameter (dimensionless)
percentage of intercalated 5-cm-thick clay layers (percentage of tp)
change in thickness (m) of layer i
allowed parameter space
natural strain (dimensionless)
F-distribution with probability interval α = 0.05
fraction of clastics (fraction of 1)
fraction of clay (fraction of 1)
fraction of organics (fraction of 1)
fraction of sand (fraction of 1)
fraction of silt (fraction of 1)
gravity constant (9.81 m/s2)
thickness of layer i at timestep t (m)
initial thickness of peat layer i (m)
thickness of clastic sediment layer overlying the peat sequence (m)
modeled final thickness of layer i (m)
initial thickness of the peat sequence (m)
observed final thickness of layer i (m)
thickness of the overlying sediment column (m)
thickness of the overlying water column (m)
5–10 cm thick peat or clay layer
loss on ignition (fraction of 1)
number of observations in the calibration field dataset
number of parameters
total stress (kPa)
initial effective stress (kPa)
effective stress (kPa)

Φ
ρd
ρmass
ρs
ρs,i
ρw
sp
s2
S
porosity (fraction of 1)
objective function value
dry bulk density (g/cm3)
mass density (g/cm3)
saturated density of a texture class (g/cm3)
saturated density of layer i (g/cm3)
density of water (1 g/cm3)
total amount of surface subsidence (m)
variance of observations (=Φmin/(m-n))
degree of saturation (fraction of 1: taken 0.98 for peat and clay, 0.99 for
loamy deposits and 1.0 for sandy deposits)
time (yr)
reference (initial) time (yr)
duration of overburden deposition (yr)
time of deposition of layer i (yr)
duration of peat accumulation (yr)
pore water pressure (kPa)
t
t0
tc
tdep,i
tp
u
Captions Auxiliary Figures
Figure S1
Plot of the calculated decompacted height of each 5-cm-thick peat sample (obtained
from the Cumberlands Marshes) vs. LOI. High-organic peat samples show highest
decompacted thicknesses, indicating that these samples are most compressible. In
general, low-organic samples are less compacted compared to high-organic samples.
It is predicted that pure clay will even be less compressible. The large variation
observed in the scatter plot is mainly due to errors introduced during peat sampling,
the natural variability of peat properties and differences in loading history of the
different samples. The three grey squares represent detritus peat samples, of which the
calculated decompacted height is unreliable because uncompacted detritus peat was
not measured [Van Asselen et al., 2010].
Figure S2
Plot of the modeled vs. observed compaction of all 5-cm-thick peat samples obtained
from the 6 cores (core codes in legend) used for calibration, using the parameter set
c=0.09, d=0.05 and b=0.009.
Figure S3
Combinations of parameters b, c and d (dots), and contours of objective function (see
Auxiliary Material 4). Parameter combinations within contour 0.00256 (shaded area)
are used in model scenarios.
Figure S4
Schematic representation of the constant base-level and the constant aggradation rate
situations. In the constant base-level situation, accommodation space (acc.sp.) created
by compaction of one or more peat layers with thickness h (dark grey) and by a rise of
the base level during a time step (BLt) is filled up by increased sedimentation of clay
(s; grey). In the constant aggradation rate situation a low aggradation rate may lead to
the inability to fill up the created accommodation space during one time step.
Figure S5
Plots of aggradation rate versus the amount of subsidence or rise after 100 years of
constant aggradation, in an 8 (Fig. S5a) and 3 (Fig. S5b) meter thick peat layer (LOI
0.8) covered by clay deposited over different time periods (tc=duration of clay
deposition).
References Auxiliary Material
Doherty, J. (2004), PEST, Model-Independent Parameter Estimation, User Manual
5th Edition, Watermark Numerical Computing, Brisbane.
Saxton, K.E., W.J. Rawls, J.S. Romberger, and R.I. Papendick (1986), Estimating
generalized soil-water characteristics from texture, Soil Sci. Soc. Am. J., 50, 10311036.
Seber, G.A.F., and C.J. Wild (2003), Nonlinear regression, Wiley, New York.
Van Asselen, S., and C. Roosendaal (2009), A new method for determining the bulk
density of uncompacted peat from field settings, J. Sediment. Res., 79, 918-922.
Van Asselen, S., E. Stouthamer, and N.D. Smith (2010), Factors controlling peat
compaction in alluvial floodplains: a case study in the cold-temperate Cumberland
Marshes, Canada, J. Sediment. Res., 80, 155-166.