Introduction
Soil moisture is the main driver of temporal changes in values of the soil
thermal conductivity (Sourbeer and Loheide II, 2015). The latter is a key
variable in land surface models (LSMs) used in hydrometeorology or in climate
models for the simulation of the vertical profile of soil temperature in
relation to soil moisture (Subin et al., 2013). Shortcomings in soil thermal
conductivity models tend to limit the impact of improving the simulation of
soil moisture and snowpack in LSMs (Lawrence and Slater, 2008; Decharme et
al., 2016). Models of the thermal conductivity of soils are affected by
uncertainties, especially in the representation of the impact of soil
properties such as the volumetric fraction of quartz (fq), soil
organic matter and gravels (Farouki, 1986; Chen et al., 2012). As soil
organic matter (SOM) and gravels are often neglected in LSMs, the soil
thermal conductivity models used in most LSMs represent the mineral fine
earth, only. Nowadays, fq estimates are not given in global
digital soil maps, and it is often assumed that this quantity is equal to the
fraction of sand (Peters-Lidard et al., 1998).
Soil thermal properties are characterized by two key variables: the soil
volumetric heat capacity (Ch) and the soil thermal conductivity
(λ), in J m-3 K-1 and W m-1 K-1,
respectively. Provided the volumetric fractions of moisture, minerals and
organic matter are known, Ch can be calculated easily. The
estimation of λ relies on empirical models and is affected by
uncertainties (Peters-Lidard et al., 1998; Tarnawski et al., 2012). The
construction and the verification of the λ models is not easy. The
λ values of undisturbed soils are difficult to observe directly.
They are often measured in the lab on perturbed soil samples (Abu-Hamdeh and
Reeder, 2000; Lu et al., 2007). Although recent advances in line-source probe
and heat pulse methods have made it easier to monitor soil thermal
conductivity in the field (Bristow et al., 1994; Zhang et al., 2014), such
measurements are currently not made in operational meteorological networks.
Moreover, for given soil moisture conditions, λ depends to a large
extent on the fraction of soil minerals presenting high thermal
conductivities such as quartz, hematite, dolomite or pyrite (Côté and
Konrad, 2005). In midlatitude regions of the world, quartz is the main driver
of λ. The information on quartz fraction in a soil is usually
unavailable as it can only be measured using X-ray diffraction (XRD) or X-ray
fluorescence (XRF) techniques. These techniques are difficult to implement
because the sensitivity to quartz is low. In practise, using XRD and XRF
together is necessary to improve the accuracy of the measurements
(Schönenberger et al., 2012). This lack of observations has a major
effect on the accuracy of thermal conductivity models and their applications
(Bristow, 1998).
Most of the land surface models (LSMs) currently used in meteorology and
hydrometeorology simulate λ following the approach proposed by
Peters-Lidard et al. (1998). This approach consists of an updated version of
the Johansen (1975) model and assumes that the gravimetric fraction of quartz
(Q) is equal to the gravimetric fraction of sand within mineral fine earth.
This is a strong assumption, as some sandy soils (e.g., calcareous sands) may
contain little quartz and as quartz may be found in the silt and clay
fractions of the soil minerals (Schönenberger et al., 2012). Moreover,
the λ models used in most LSMs represent only the mineral fine
earth. Yang et al. (2005) and Chen et al. (2012) have shown the importance of
accounting for SOM and gravels in λ models for organic top soil
layers of grasslands of the Tibetan plateau.
The main goals of this study are to (1) assess the feasibility of using
routine automatic soil temperature profile sub-hourly measurements (one
observation every 12 min) to retrieve instantaneous soil thermal diffusivity
values at a depth of 0.10 m; (2) retrieve instantaneous
λ values from the soil thermal diffusivity
estimates, accounting for the impact of soil vertical heterogeneities;
(3) obtain, from reverse modeling, the quartz fraction together with soil
thermal conductivity at saturation (λsat); (4) assess the
impact of gravels and SOM on λsat; (5) derive pedotransfer
functions for the soil quartz fraction.
For this purpose, we use the data from 21 weather stations of the Soil
Moisture Observing System – Meteorological Automatic Network Integrated
Application (SMOSMANIA) network (Calvet et al., 2007) in southern France. The
soil temperature and the soil moisture probes are buried in the enclosure
around each weather station. Most of these stations are located in
agricultural areas. However, the vegetation cover in the enclosure around the
stations consists of grass. Along the Atlantic–Mediterranean transect formed
by the SMOSMANIA network (Fig. 1), the grassland cover fraction ranges
between 10 and 40 % (Zakharova et al., 2012). Various mineral soil types
can be found along this transect, ranging from sand to clay and silt loam
(see Supplement 1). During the installation of the probes, we collected soil
samples which were used to determine soil characteristics: soil texture, soil
gravel content, soil organic matter and bulk density.
Location of the 21 SMOSMANIA stations in southern France (see
station names in Supplement 1).
Using this information together with soil moisture, λ values are
derived from soil thermal diffusivity and heat capacity. The response of
λ to soil moisture is investigated. The feasibility of modeling the
λ value at saturation (λsat) with or without using
SOM and gravel fraction observations is assessed using a geometric mean
empirical thermal conductivity model based on Lu et al. (2007). The
volumetric fraction of quartz, fq, is retrieved by reverse
modeling together with Q. Pedotransfer functions are further proposed for
estimating quartz content from soil texture information.
The field data and the method to retrieve λ values are presented in
Sect. 2. The λ and fq retrievals are presented in Sect. 3
together with a sensitivity analysis of λsat to SOM and
gravel fractions. Finally, the results are discussed in Sect. 4, and the main
conclusions are summarized in Sect. 5. Technical details are given in
Supplement.
Data and methods
The SMOSMANIA data
The SMOSMANIA network was developed by Calvet et al. (2007) in southern
France. The main purposes of SMOSMANIA are to (1) validate satellite-derived
soil moisture products (Parrens et al., 2012); (2) assess land surface models
used in hydrological models (Draper et al., 2011) and in meteorological
models (Albergel et al., 2010); and (3) monitor the impact of climate change
on water resources and droughts (Laanaia et al., 2016). The station network
forms a transect between the Atlantic coast and the Mediterranean sea
(Fig. 1). It consists of preexisting automatic weather stations operated by
Météo-France, upgraded with four soil moisture probes at four depths:
0.05, 0.10, 0.20 and 0.30 m. Twelve SMOSMANIA stations were activated in
2006 in southwestern France. In 2008, nine more stations were installed along
the Mediterranean coast, and the whole network (21 stations) was gradually
equipped with temperature sensors at the same depths as soil moisture probes.
The soil moisture and soil temperature probes consisted of ThetaProbe ML2X
and PT100 sensors, respectively. Soil moisture and soil temperature
observations were made every 12 min at four depths. The soil temperature
observations were recorded with a resolution of 0.1 ∘C.
In this study, the sub-hourly measurements of soil temperature and soil
moisture at a depth of 0.10 m were used, together with soil temperature
measurements at 0.05 and 0.20 m from 1 January 2008 to 30 September 2015.
Soil characteristics at 10 cm for the 21 stations of the SMOSMANIA
network. Porosity values are derived from Eq. (1). Solid fraction values
higher than 0.3 are in bold. The stations are listed from west to east (from
top to bottom). ρd, θsat, f and m stand for
soil bulk density, porosity, volumetric fractions and gravimetric fractions,
respectively. Soil particle fractions larger than 0.3 are in bold. Full
station names are given in Supplement 1 (Table S1.1).
Station
ρd
θsat
fsand
fclay
fsilt
fgravel
fSOM
msand
mclay
msilt
mgravel
mSOM
(kg m-3)
(m3 m-3)
(m3 m-3)
(m3 m-3)
(m3 m-3)
(m3 m-3)
(m3 m-3)
(kg kg-1)
(kg kg-1)
(kg kg-1)
(kg kg-1)
(kg kg-1)
SBR
1680
0.352
0.576
0.026
0.013
0.002
0.032
0.911
0.041
0.020
0.003
0.024
URG
1365
0.474
0.076
0.078
0.341
0.005
0.025
0.149
0.153
0.665
0.009
0.024
CRD
1435
0.438
0.457
0.027
0.033
0.000
0.045
0.848
0.051
0.060
0.000
0.041
PRG
1476
0.431
0.051
0.138
0.138
0.214
0.028
0.092
0.250
0.248
0.385
0.025
CDM
1522
0.413
0.073
0.241
0.231
0.012
0.030
0.128
0.422
0.404
0.020
0.026
LHS
1500
0.416
0.102
0.202
0.189
0.051
0.039
0.181
0.359
0.335
0.091
0.034
SVN
1453
0.445
0.127
0.073
0.176
0.162
0.017
0.233
0.133
0.322
0.296
0.015
MNT
1444
0.447
0.135
0.066
0.230
0.102
0.020
0.248
0.121
0.424
0.188
0.018
SFL
1533
0.413
0.127
0.071
0.118
0.250
0.021
0.221
0.123
0.205
0.434
0.018
MTM
1540
0.405
0.110
0.081
0.076
0.297
0.032
0.189
0.140
0.131
0.512
0.027
LZC
1498
0.429
0.129
0.066
0.068
0.292
0.015
0.229
0.117
0.121
0.519
0.013
NBN
1545
0.401
0.063
0.135
0.075
0.290
0.035
0.109
0.232
0.130
0.499
0.030
PZN
1311
0.495
0.222
0.074
0.131
0.054
0.023
0.450
0.151
0.266
0.111
0.023
PRD
1317
0.494
0.038
0.052
0.069
0.326
0.021
0.076
0.105
0.139
0.659
0.021
LGC
1496
0.428
0.253
0.044
0.042
0.214
0.019
0.451
0.078
0.074
0.380
0.017
MZN
1104
0.560
0.212
0.037
0.045
0.097
0.049
0.510
0.089
0.109
0.234
0.057
VLV
1274
0.506
0.294
0.054
0.086
0.031
0.029
0.614
0.112
0.179
0.064
0.030
BRN
1630
0.379
0.105
0.009
0.016
0.474
0.016
0.171
0.015
0.027
0.774
0.013
MJN
1276
0.506
0.064
0.029
0.056
0.317
0.028
0.133
0.060
0.118
0.661
0.029
BRZ
1280
0.508
0.097
0.074
0.109
0.190
0.020
0.202
0.154
0.228
0.396
0.021
CBR
1310
0.501
0.120
0.057
0.068
0.241
0.013
0.243
0.116
0.139
0.489
0.013
The ThetaProbe soil moisture sensors provide a voltage signal (V). In order
to convert the voltage signal into volumetric soil moisture content
(m3 m-3), site-specific calibration curves were developed using in
situ gravimetric soil samples for all stations and for all depths (Albergel
et al., 2008). We revised the calibration in order to avoid spurious high
soil moisture values during intense precipitation events. Logistics curves
were used (see Supplement 1) instead of exponential curves in the previous
version of the data set.
The observations from the soil moisture (48) and from the temperature (48)
probes are automatically recorded every 12 min. The data are available to
the research community through the International Soil Moisture Network web
site (https://ismn.geo.tuwien.ac.at/).
Figure 2 shows soil temperature time series in wet conditions at various soil
depths for a station presenting an intermediate value of
λsat (Table 2) and of soil texture (see Fig. S1.1 in
Supplement 1). The impact of recording temperature with a resolution of
0.1 ∘C is clearly visible at all depths as this causes a leveling
of the curves.
Soil temperature measured in wet conditions at the
St-Félix-Lauragais (SFL) station on 23 February 2015 at depths of 0.05,
0.10, 0.20 and 0.30 m. Leveling is due to the low resolution of the
temperature records (0.1 ∘C).
Soil characteristics
In general, the stations are located on formerly cultivated fields and the
soil in the enclosure around the stations is covered with grass. Soil
properties were measured at each station by an independent laboratory we
contracted (INRA-Arras) from soil samples we collected during the
installation of the probes. The 21 stations cover a very large range of soil
texture characteristics. For example, SBR is located on a sandy soil, PRD on
a clay loam, and MNT on a silt loam (Table 1 and Supplement 1). Other
properties such as the gravimetric fraction of SOM and of gravels were
determined from the soil samples. Table 1 shows that 12 soils present a
volumetric gravel content (fgravel) larger than 15 %. Among
these, three soils (at PRD, BRN and MJN) have fgravel values larger
than 30 %.
In addition, we measured bulk density (ρd) using undisturbed
oven-dried soil samples we collected using metal cylinders of known volume
(about 7×10-4 m3; see Fig. S1.10 in the Supplement).
The porosity values at a depth of 0.10 m are listed in Table 1 together with
gravimetric and volumetric fractions of soil particle-size ranges (sand,
clay, silt, gravel) and SOM. The porosity, or soil volumetric moisture at
saturation (θsat), is derived from the bulk dry density
ρd, with soil texture and soil organic matter observations as
θsat=1-ρdmsand+mclay+msilt+mgravelρmin+mSOMρSOM
or
θsat=1-fsand-fclay-fsilt-fgravel-fSOM,
where mx (fx) represents the gravimetric (volumetric) fraction of
the soil component x. The fx values are derived from the measured
gravimetric fractions, multiplied by the ratio of ρd
observations to ρx, the density of each soil component x. Values of
ρSOM=1300 kg m-3 and ρmin=2660 kg m-3 are used for soil organic matter and soil minerals,
respectively.
Retrieval of soil thermal diffusivity
The soil thermal diffusivity (Dh) is expressed in m2 s-1
and is defined as
Dh=λCh.
We used a numerical method to retrieve instantaneous values of Dh
at a depth of 0.10 m using three soil temperature observations at 0.05 m,
0.10 and 0.20 m, performed every 12 min, by solving the Fourier thermal
diffusion equation. The latter can be written as
Ch∂T∂t=∂∂zλ∂T∂z.
Given that soil properties are relatively homogeneous in the vertical
(Sect. 2.1), values of Dh can be derived from the Fourier
one-dimensional law:
∂T∂t=Dh∂2T∂z2.
However, large differences in soil bulk density, from the top soil layer to
deeper soil layers, were observed for some soils (see Supplement 1). In order
to limit this effect as much as possible, we only used the soil temperature
data presenting a relatively low vertical gradient close to the soil surface,
where most differences with deeper layers are found. This data sorting
procedure is described in Supplement 2.
Given that three soil temperatures Ti (i ranging from 1 to 3) are
measured at depths z1=-0.05 m, z2=-0.10 m and z3=-0.20 m, the soil diffusivity Dhi at zi=z2=-0.10 m
can be obtained by solving the one-dimensional heat equation, using a
finite-difference method based on the implicit Crank–Nicolson scheme (Crank
and Nicolson, 1996). When three soil depths are considered (zi-1,
zi, zi+1), the change in soil temperature Ti at depth zi,
from time tn-1 to time tn, within the time interval Δt=tn-tn-1, can be written as
Tin-Tin-1Δt=Dhi[12γi+1n-γinΔzm+12γi+1n-1-γin-1Δzm],withγin=Tin-Ti-1nΔzi,Δzm=Δzi+Δzi+12andΔzi=zi-zi-1.
In this study, Δzi=-0.05 m, Δzi+1=-0.10 m and a
value of Δt=2880 s (48 min) are used.
It is important to ensure that Dh retrievals are related to
diffusion processes only and not to the transport of heat by water
infiltration or evaporation (Parlange et al., 1998; Schelde et al., 1998).
Therefore, only situations for which changes in soil moisture at all depths
do not exceed 0.001 m3 m-3 within the Δt time interval
are considered.
From soil diffusivity to soil thermal conductivity
The observed soil properties and volumetric soil moisture are used to
calculate the soil volumetric heat capacity Ch at a depth of
0.10 m, using the de Vries (1963) mixing model. The Ch values,
in units of J m-3 K-1, are calculated as
Ch=θChwater+fminChmin+fSOMChSOM,
where θ and fmin represent the volumetric soil moisture and the
volumetric fraction of soil minerals, respectively. Values of
4.2 × 106, 2.0×106 and 2.5×106 J m-3 K-1 are used for Chwater,
Chmin and ChSOM, respectively.
The λ values at 0.10 m are then derived from the Dh and
Ch estimates (Eq. 2).
Soil thermal conductivity model
Various approaches can be used to simulate thermal conductivity of
unsaturated soils (Dong et al., 2015). We used an empirical approach based
on thermal conductivity values in dry conditions and at saturation.
In dry conditions, soils present low thermal conductivity values
(λdry). Experimental evidence shows that
λdry is negatively correlated with porosity. For
example, Lu et al. (2007) give
λdry=0.51-0.56×θsat(inWm-1K-1).
When soil pores are gradually filled with water, λ tends to increase
towards a maximum value at saturation (λsat). Between dry
and saturation conditions, λ is expressed as
λ=λdry+Keλsat-λdry,
where Ke is the Kersten number (Kersten, 1949). The latter is
related to the volumetric soil moisture, θ, i.e., to the degree of
saturation (Sd). We used the formula recommended by Lu et
al. (2007):
Ke=expα1-Sd(α-1.33),
with α=0.96 for Mnsand≥0.4 kg kg-1, α=0.27 for Mnsand<0.4 kg kg-1 and
Sd=θ/θsat.
Mnsand represents the sand mass fraction of mineral fine earth
(values are given in Supplement 1).
The geometric mean equation for λsat proposed by
Johansen (1975) for the mineral components of the soil can be generalized to
include the SOM thermal conductivity (Chen et al., 2012) as
lnλsat=fqlnλq+fotherlnλother+θsatlnλwater+fSOMlnλSOM,
where fq is the volumetric fraction of quartz, and
λq=7.7 W m-1 K-1, λwater=0.594 W m-1 K-1 and λSOM=0.25 W m-1 K-1 are the thermal conductivities of quartz, water
and SOM, respectively. The λother term corresponds to the
thermal conductivity of soil minerals other than quartz. Following
Peters-Lidard et al. (1998), λother is taken as
2.0 W m-1 K-1 for soils with
Mnsand > 0.2 kg kg-1 and as 3.0 W m-1 K-1
otherwise. In this study, Mnsand > 0.2 kg kg-1 for all
soils, except for URG, PRG and CDM. The volumetric fraction of soil minerals
other than quartz is defined as
fother=1-fq-θsat-fSOM,withfq=Q×1-θsat.
Thermal properties of 14 grassland soils in southern France:
λsat, fq and Q retrievals using the λ
model (Eqs. 7–9 and 10) for degree of saturation values higher than 0.4,
together with the minimized RMSD between the simulated and observed
λ values and the number of used λ
observations (n). The soils are sorted from the largest to the smallest
ratio of msand to mSOM. Full station names are given in
Supplement 1 (Table S1.1).
Station
λsat
RMSD
n
fq
Q
msandmSOM
(W m-1 K-1)
(W m-1 K-1)
(m3 m-3)
(kg kg-1)
SBR
2.80
0.255
6
0.62
0.96
37.2
LGC
2.07
0.311
20
0.44
0.77
26.6
CBR
1.92
0.156
20
0.44
0.88
18.4
LZC
1.71
0.107
20
0.29
0.51
17.3
SVN
1.78
0.163
20
0.34
0.61
15.4
MNT
1.96
0.058
20
0.42
0.76
13.8
BRN
1.71
0.131
20
0.25
0.40
13.5
SFL
1.57
0.134
20
0.22
0.37
12.5
MTM
1.52
0.095
20
0.21
0.35
7.0
URG
1.37
0.066
20
0.05
0.10
6.2
LHS
1.57
0.136
20
0.26
0.45
5.3
CDM
1.82
0.086
20
0.26
0.44
5.0
PRG
1.65
0.086
20
0.18
0.32
3.7
PRD
1.26
0.176
20
0.14
0.28
3.7
Retrieved λ values (dark dots) vs. the observed degree of
saturation of the soil at a depth of 0.10 m for (from top to bottom) Sabres
(SBR), Montaut (MNT), Mouthoumet (MTM) and Prades-le-Lez (PRD), together with
simulated λ values from dry to wet conditions (dark lines).
Reverse modeling
The λsat values are retrieved through reverse modeling using
the λ model described above (Eqs. 7–11). This model is used to
produce simulations of λ at the same soil moisture conditions as
those encountered for the
λ values derived from observations in Sect. 2.4. For a
given station, a set of 401 simulations is produced for λsat
ranging from 0 to 4 W m-1 K-1, with a resolution of
0.01 W m-1 K-1. The λsat retrieval corresponds
to the λ simulation presenting the lowest root mean square
difference (RMSD) value with respect to the
λ observations. Only λ observations for
Sd values higher than 0.4 are used because in dry conditions:
(1) conduction is not the only mechanism for heat exchange in soils, as the
convective water vapor flux may become significant (Schelde et al., 1998;
Parlange et al., 1998); (2) the Ke functions found in the literature
display more variability; and (3) the λsat retrievals are
more sensitive to uncertainties in λ observations. The threshold
value of Sd=0.4 results from a compromise between the need of
limiting the influence of convection, of the shape of the Ke
function on the retrieved values of λsat, and of using as
many observations as possible in the retrieval process. Moreover, the data
filtering technique to limit the impact of soil heterogeneities, described in
Supplement 2, is used to select valid λ observations.
Finally, the fq value is derived from the retrieved
λsat solving Eq. (10).
Scores
Pedotransfer functions for quartz and λsat are evaluated
using the following scores:
the Pearson correlation coefficient (r) and the squared
correlation coefficient (r2) are used to assess the fraction of
explained variance
the RMSD
the mean absolute error (MAE), i.e., the mean of absolute differences
the mean bias, i.e., the mean of differences.
In order to test the predictive and generalization power of the pedotransfer
regression equations, a simple bootstrapping resampling technique is used. It
consists of calculating a new estimate of fq for each soil using
the pedotransfer function obtained without using this specific soil.
Gathering these new fq estimates, one can calculate new scores
with respect to the retrieved fq values. Also, this method
provides a range of possible values of the coefficients of the pedotransfer
function and permits assessing the influence of a given fq
retrieval on the final result.
Results
λsat and fq retrievals
Retrievals of λsat and fq could be obtained
for 14 soils. Figure 3 shows retrieved and modeled λ values against
the observed degree of saturation of the soil, at a depth of 0.10 m for
contrasting retrieved values of λsat, from high to low
values (2.80, 1.96, 1.52 and 1.26 W m-1 K-1) at the SBR, MNT,
MTM and PRD stations, respectively.
All the obtained λsat and fq retrievals are
listed in Table 2, together with the λ RMSD values and the number of
selected λ observations. For three soils (CRD, MZN and VLV), the
reverse modeling technique described in Sect. 2.6 could not be applied as not
enough λ observations could be obtained for Sd values
higher than 0.4. For four soils (NBN, PZN, BRZ and MJN), all the λ
retrievals were filtered out as the obtained values were influenced by
heterogeneities in soil density (see Supplement 2). For the other 14 soils,
λsat and fq retrievals were obtained using a
subset of 20 λ retrievals per soil, at most, corresponding to the
soil temperature data presenting the lowest vertical gradient close to the
soil surface (Supplement 2).
Pedotransfer functions for quartz
The fq retrievals can be used to assess the possibility of
estimating fq using other soil characteristics, which can be
easily measured. Another issue is whether volumetric or gravimetric fraction
of quartz should be used. Figure 4 presents the fraction of variance
(r2) of Q and fq explained by various indicators. A key
result is that fq is systematically better correlated with soil
characteristics than Q. More than 60 % of the variance of
fq can be explained using indicators based on the sand fraction
(either fsand or msand). The use of other soil mineral
fractions does not give good correlations, even when they are associated to
the sand fraction as shown by Fig. 4. For example, the fgravel and
fgravel+fsand indicators present low r2 values of
0.04 and 0.24, respectively.
Fraction of variance (r2) of gravimetric and volumetric
fraction of quartz (Q and fq, red and blue bars, respectively)
explained by various predictors.
The fq values cannot be derived directly from the indicators as
illustrated by Fig. 5: assuming fq=fsand tends to
markedly underestimate λsat. Therefore, more elaborate
pedotransfer equations are needed. They can be derived from the best
indicators, using them as predictors of fq. The modeled
fq is written as
fqMOD=a0+a1×PandfqMOD≤1-θsat-fSOM,
where P represents the predictor of fq.
λsatMOD values derived from volumetric
quartz fractions fq assumed equal to fsand, using
observed θsat values, vs.
λsat retrievals.
The a0 and a1 coefficients are given in Table 3 for four
pedotransfer functions based on the best predictors of fq. The
pedotransfer functions are illustrated in Fig. 6. The scores are displayed in
Table 4. The bootstrapping indicates that the SBR sandy soil has the largest
individual impact on the obtained regression coefficients. This is why the
scores without SBR are also presented in Table 4.
Coefficients of four pedotransfer functions of fq
(Eq. 12) for 14 soils of this study (all with
msand/mSOM < 40), together with indicators of the
coefficient uncertainty, derived by bootstrapping and by perturbing the
volumetric heat capacity of soil minerals (Chmin). The best
predictor is in bold.
Predictor of fq
Coefficients for 14 soils
Confidence interval
Impact of a change of
from bootstrapping
±0.08 × 106 J m-3 K-1
in Chmin
a0
a1
a0
a1
a0
a1
msand/mSOM
0.12
0.0134
[0.10, 0.14]
[0.012, 0.014]
[0.11, 0.13]
[0.013, 0.013]
msand*
0.08
0.944
[0.00, 0.11]
[0.85, 1.40]
[0.07, 0.09]
[0.919, 0.966]
msand
0.15
0.572
[0.08, 0.17]
[0.54, 0.94]
[0.14, 0.17]
[0.55, 0.56]
1-θsat-fsand
0.73
-1.020
[0.71, 0.89]
[-1.38, -0.99]
[0.70, 0.73]
[-1.00, -0.99]
* Only msand values smaller than 0.6 kg kg-1
are used in the regression.
Scores of four pedotransfer functions of fq for 14 soils
of this study, together with the scores obtained by bootstrapping, without
the sandy SBR soil. The MAE score of these pedotransfer functions for three
Chinese soils of Lu et al. (2007) for which
msand/mSOM < 40 is given (within brackets and in
italics). The best predictor and the best scores are in bold.
Predictor of fq
Regression scores
Bootstrap scores
Scores without SBR
(and MAE for three Lu soils)
r2
RMSD
MAE
r2
RMSD
MAE
r2
RMSD
MAE
(m3 m-3)
(m3 m-3)
(m3 m-3)
(m3 m-3)
(m3 m-3)
(m3 m-3)
msand/mSOM
0.77
0.067
0.053
0.72
0.074
0.059
0.62
0.070
0.057
(0.135)
msand*
0.74
0.072
0.052
0.67
0.126
0.100
0.56
0.075
0.056
(0.071)
msand
0.67
0.081
0.060
0.56
0.121
0.084
0.56
0.075
0.056
(0.086)
1-θsat-fsand
0.65
0.084
0.064
0.56
0.102
0.079
0.45
0.084
0.061
(0.158)
* Only msand values smaller than 0.6 kg kg-1
are used in the regression.
Ability of the Eqs. (10)–(13) empirical model to estimate
λsat values for 14 soils and impact of changes in gravel and
SOM volumetric content: fgravel=0 m3 m-3 and
fSOM=0.013 m3 m-3 (the smallest fSOM value,
observed for CBR). r2 values smaller than 0.60, RMSD values higher than
0.20 W m-1 K-1 and mean bias values higher (smaller) than
+0.10 (-0.10) are in bold.
Model configuration
Predictor of fq
r2
RMSD
Mean bias
(W m-1 K-1)
(W m-1 K-1)
Model using θsat observations
msand/mSOM
0.86
0.14
+0.01
msand*
0.83
0.15
-0.01
msand
0.81
0.16
-0.03
1-θsat-fsand
0.82
0.16
-0.03
Full model using θsatMOD (Eq. 13)
msand/mSOM
0.85
0.14
+0.03
msand*
0.85
0.14
-0.03
msand
0.84
0.15
-0.03
1-θsat-fsand
0.82
0.16
-0.02
Same with
msand/mSOM
0.57
0.35
+0.20
fSOM=0.013 m3 m-3
msand*
0.83
0.15
+0.00
msand
0.81
0.16
-0.02
1-θsat-fsand
0.83
0.15
-0.02
Same with
msand/mSOM
0.87
0.19
-0.12
fgravel=0 m3 m-3
msand*
0.70
0.23
+0.11
msand
0.79
0.17
+0.04
1-θsat-fsand
0.81
0.17
+0.05
Same with
msand/mSOM
0.63
0.31
+0.16
fSOM=0.013 m3 m-3
msand*
0.52
0.36
+0.24
and fgravel=0 m3 m-3
msand
0.59
0.29
+0.16
1-θsat-fsand
0.70
0.25
+0.16
* Only msand values smaller than 0.6 kg kg-1
are used in the regression.
Pedotransfer functions for quartz: fq retrievals (dark
dots) vs. the four predictors of fq given in Table 3. The
modeled fq values are represented by the dashed
lines.
For the msand predictor, an r2 value of 0.56 is obtained
without SBR against a value of 0.67 when all the 14 soils are considered. An
alternative to this msand pedotransfer function consists of
considering only msand values smaller than 0.6 kg kg-1 in
the regression, thus excluding the SBR soil. The corresponding predictor is
called msand*. In this configuration, the sensitivity of
fq to msand is much increased (with a1=0.944,
against a1=0.572 with SBR). For SBR, fq is overestimated
by the msand* equation, but this is corrected by the
fqMOD limitation of Eq. (12), and in the end a better r2 score
is obtained when the 14 soils are considered (r2=0.74).
Values of r2 larger than 0.7 are obtained for two predictors of
fq: msand/mSOM and msand*. A value
of r2=0.65 is obtained for 1-θsat-fsand
(the fraction of soil solids other than sand). The
msand/mSOM predictor presents the best r2 and RMSD
scores in all the configurations (regression, bootstrap and regression
without SBR). Another characteristic of the msand/mSOM
pedotransfer function is that the confidence interval for the a0 and
a1 coefficients derived from bootstrapping is narrower than for the
other pedotransfer functions (Table 3), indicating a more robust relationship
of fq with msand/mSOM than with other
predictors.
An alternative way to evaluate the quartz pedotransfer functions is to
compare the simulated λsat with the retrieved values
presented in Table 2. Modeled values of λsat(λsatMOD) can be derived from fqMOD using
Eq. (10) together with θsat observations. The
λsatMODr2, RMSD and mean bias scores are given
in Table 5. Again, the best scores are obtained using the
msand/mSOM predictor of fq, with r2, RMSD
and mean bias values of 0.86, 0.14 W m-1 K-1 and
+0.01 W m-1 K-1, respectively (Fig. 7).
λsatMOD values derived from the
msand/mSOM pedotransfer function for the volumetric quartz
fractions, using observed θsat values, vs.
λsat retrievals.
Finally, we investigated the possibility of estimating θsat
from the soil characteristics listed in Table 1 and of deriving a statistical
model for θsat (θsatMOD). We found the
following statistical relationship between θsatMOD,
mclay, msilt and mSOM:
θsatMOD=0.456-0.0735mclaymsilt+2.238mSOM
(r2=0.48, F test p value = 0.0027, RMSD =
0.036 m3 m-3).
Volumetric fractions of soil components need to be consistent with
θsatMOD and can be calculated using the modeled bulk density
values derived from θsatMOD using Eq. (1).
Equations (10) to (13) constitute an empirical end-to-end model of
λsat. Table 5 shows that using θsatMOD
(Eq. 13) instead of the θsat observations has little impact on
the λsatMOD scores.
Impact of gravels and SOM on λsat
Gravels and SOM are often neglected in soil thermal conductivity models used
in LSMs. The Eqs. (10)–(13) empirical model obtained in Sect. 3.2 permits
the assessment of the impact of fgravel and fSOM on
λsat. Table 5 shows the impact on
λsatMOD scores of imposing a null value of
fgravel and a small value of fSOM to all the soils. The
combination of these assumptions is evaluated, also.
Imposing fSOM=0.013 m3 m-3 (the smallest
fSOM value, observed for CBR) has a limited impact on the scores,
except for the msand/mSOM pedotransfer function. In this
case, λsat is overestimated by +0.20 W m-1 K-1
and r2 drops to 0.57.
Neglecting gravels (fgravel=0 m3 m-3) also has a
limited impact but triggers the underestimation (overestimation) of
λsat for the msand/mSOM (msand*)
pedotransfer function by -0.12 W m-1 K-1
(+0.11 W m-1 K-1).
On the other hand, it appears that combining these assumptions has a marked
impact on all the pedotransfer functions. Neglecting gravels and imposing
fSOM=0.013 m3 m-3 has a major impact on
λsat: the modeled λsat is
overestimated by all the pedotransfer functions (with a mean bias ranging
from +0.16 to +0.24 W m-1 K-1) and r2 is markedly
smaller, especially for the msand and msand*
pedotransfer functions. These results are illustrated in Fig. 8 in the case
of the msand* pedotransfer function. Figure 8 also shows that
using the θsat observations instead of θsatMOD
(Eq. 13) has little impact on λsatMOD (Sect. 3.2)
but tends to enhance the impact of neglecting gravels. A similar result is
found with the msand pedotransfer function (not shown).
λsatMOD values derived from the
msand* pedotransfer function for the volumetric quartz fractions,
using θsatMOD (Eq. 13) or the observed
θsat (dark dots and open diamonds, respectively),
vs. λsat retrievals: (top) full model, (middle) fSOM=0.013 m3 m-3, and (bottom) fSOM=0.013 m3 m-3
and fgravel=0 m3 m-3. Scores are
given for the θsatMOD configuration.
Discussion
Can uncertainties in heat capacity estimates impact retrievals ?
In this study, the de Vries (1963) mixing model is applied to estimate soil
volumetric heat capacity (Eq. 6), and a fixed value of
2.0 × 106 J m-3 K-1 is used for soil minerals.
Soil-specific values for Chmin may be more appropriate than
using a constant standard value. For example, Tarara and Ham (1997) used a
value of 1.92×106 J m-3 K-1. However, we did not
measure this quantity and we were not able to find such values in the
literature.
We investigated the sensitivity of our results to these uncertainties,
considering the following minimum and maximum Chmin values:
Chmin=1.92×106 J m-3 K-1 and
Chmin=2.08×106 J m-3 K-1. The impact
of changes in Chmin on the retrieved values of
λsat and fq is presented in Supplement 3
(Fig. S3.1). On average, a change of + (-) 0.08×106 J m-3 K-1 in Chmin triggers a change in
λsat and fq of +1.7 % (-1.8 %) and
+4.8 % (-7.0 %), respectively.
The impact of changes in Chmin on the regression coefficients
of the pedotransfer functions is presented in Table 3 (last column). The
impact is very small, except for the a1 coefficient of the
msand* pedotransfer function. However, even in this case, the
impact of Chmin on the a1 coefficient is much lower than
the confidence interval given by the bootstrapping, indicating that the
relatively small number of soils we considered (as in other studies, e.g., Lu
et al., 2007) is a larger source of uncertainty.
Moreover, uncertainties in the fclay, fsilt,
fgravel or fSOM fractions may be caused by (1) the
natural heterogeneity of soil properties, (2) the living root biomass or
(3) stones that may not be accounted for in the gravel fraction.
In particular, during the installation of the probes, it was observed that
stones are present at some stations. Stones are not evenly distributed in
the soil, and it is not possible to investigate whether the soil area where
the temperature probes were inserted contains stones as it must be left
undisturbed.
The grasslands considered in this study are not intensively managed. They
consist of set-aside fields cut once or twice a year. Calvet et al. (1999)
gave an estimate of 0.160 kg m-2 for the root dry matter content of
such soils for a site in southwestern France, with most roots contained in
the 0.25 m top soil layer. This represents a gravimetric fraction of organic
matter smaller than 0.0005 kg kg-1, i.e., less than 4 % of the
lowest mSOM values observed in this study (0.013 kg kg-1) or
less than 5 % of fSOM values. We checked that increasing
fSOM values by 5 % has negligible impact on heat capacity and
on the λ retrievals.
Can the new λsat model be applied to other soil
types?
The λsat values we obtained are consistent with values
reported by other authors. In this study, λsat values ranging
between 1.26 and 2.80 W m-1 K-1 are found (Table 2). Tarnawski
et al. (2011) gave λsat values ranging between 2.5 and
3.5 W m-1 K-1 for standard sands. Lu et al. (2007) gave
λsat values ranging between 1.33 and
2.2 W m-1 K-1.
A key component of the λsat model is the pedotransfer
function for quartz (Eq. 12). The fq pedotransfer functions we
propose are based on available soil characteristics. The current global soil
digital maps provide information about SOM, gravels and bulk density
(Nachtergaele et al., 2012). Therefore, using Eqs. (1) and (6)–(12) on a
large scale is possible, and porosity can be derived from Eq. (1). On the
other hand, the suggested fq pedotransfer functions are obtained
for temperate grassland soils containing a rather large amount of organic
matter and are valid for msand/mSOM ratio values lower than
40 (Table 2). These equations should be evaluated for other regions. In
particular, hematite has to be considered together with quartz for tropical
soils (Churchman and Lowe, 2012). Moreover, the pedotransfer function we get
for θsat (Eq. 13) and we use to conduct the sensitivity study
of Sect. 3.3 is valid for the specific sites we considered. Equation (13)
cannot be used to predict porosity in other regions.
In order to assess the applicability of the pedotransfer function for quartz
obtained in this study, we used the independent data from Lu et al. (2007)
and Tarnawski et al. (2009) for 10 Chinese soils (see Supplement 4 and
Table S4.1). These soils consist of reassembled sieved soil samples and
contain no gravel, while our data concern undisturbed soils. Moreover, most
of these soils contain very little organic matter and the
msand/mSOM ratio can be much larger that the
msand/mSOM values measured at our grassland sites. For the
14 French soils used to determine pedotransfer functions for quartz, the
msand/mSOM ratio ranges from 3.7 to 37.2 (Table 2). Only
three soils of Lu et al. (2007) present such low values of
msand/mSOM. The other seven soils of Lu et al. (2007)
present msand/mSOM values ranging from 48 to 1328 (see
Table S4.1).
Pedotransfer functions of fq (Eq. 12) for seven soils of
Lu et al. (2007) with msand/mSOM > 40. The best
predictor and the best scores are in bold. The regression p values are
within brackets and in italics.
Predictor of fq
Regression scores
Coefficients
for seven Lu soils with
msand/mSOM > 40
r2
RMSD
MAE
a0
a1
(p value)
(m3 m-3)
(m3 m-3)
msand/mSOM
0.40
0.089
0.075
0.20
0.000148
(0.13)
msand*
0.82
0.073
0.054
0.07
0.425
(0.005)
msand
0.82
0.048
0.042
0.04
0.386
(
0.005
)
1-θsat-fsand
0.81
0.050
0.043
0.44
-0.814
(0.006)
* Only msand values smaller than 0.6 kg kg-1
are used in the regression.
We used λsat experimental values derived from Table 3 in
Tarnawski et al. (2009) to calculate Q and fq for the 10 Lu et
al. (2007) soils. These data are presented in Supplement 4. Figure S4.1 shows
the statistical relationship between these quantities and msand.
Very good correlations of Q and fq with msand are
observed, with r2 values of 0.72 and 0.83, respectively. This is
consistent with our finding that fq is systematically better
correlated with soil characteristics than Q (Sect. 3.2).
The pedotransfer functions derived from French soils tend to overestimate
fq for the Lu et al. (2007) soils, especially for the seven soils
presenting msand/mSOM values larger than 40. Note that Lu
et al. (2007) obtained a similar result for coarse-textured soils with their
model, which assumed Q = msand. For the three other soils,
presenting msand/mSOM values smaller than 40,
fq MAE values are given in Table 4. The best MAE score
(0.071 m3 m-3) is obtained for the msand* predictor of
fq.
These results are illustrated by Fig. 9 for the msand predictor of
fq. Figure 9 also shows the fq and
λsat estimates obtained using specific coefficients
in Eq. (12), based on the seven Lu et al. (2007) soils presenting
msand/mSOM values larger than 40. These coefficients are
given together with the scores in Table 6. Table 6 also presents these values
for other predictors of fq. It appears that msand gives
the best scores. The contrasting coefficient values between Tables 6 and 3
(Chinese and French soils, respectively) illustrate the variability of the
coefficients of pedotransfer functions from one soil category to another, and
the msand/mSOM ratio seems to be a good indicator of the
validity of a given pedotransfer function.
Estimated λsat and volumetric fraction of quartz
fq (top and bottom, respectively) vs. values derived from the
λsat observations of Lu et al. (2007) given by Tarnawski et
al. (2009) for 10 Chinese soils, using the gravimetric fraction of sand
msand as a predictor of fq. Dark dots correspond to the
estimations obtained using the msand pedotransfer function for
southern France, and the three soils for which
msand/mSOM < 40 are indicated by green diamonds. Red
triangles correspond to the estimations obtained using the msand
pedotransfer function for the seven soils for which
msand/mSOM > 40 (see Table 6).
On the other hand, the msand/mSOM ratio is not a good
predictor of fq for the Lu et al. (2007) soils presenting
msand/mSOM values larger than 40, and r2 presents a
small value of 0.40 (Table 6). This can be explained by the very large range
of msand/mSOM values for these soils (see Table S4.1).
Using ln(msand/mSOM) instead of
msand/mSOM is a way to obtain a predictor linearly
correlated with fq. This is shown by Fig. S4.2 for the 10 Lu et
al. (2007) soils: the correlation is increased to a large extent (r2=0.60).
Can msand-based fq pedotransfer functions
be used across soil types?
Given the results presented in Tables 3, 4 and 6, it can be concluded that
msand is the best predictor of fq across mineral soil
types. The msand/mSOM predictor is relevant for the mineral
soils containing the largest amount of organic matter.
Although the msand/mSOM predictor gives the best r2
scores for the 14 grassland soils considered in this study, it seems more
difficult to apply this predictor to other soils, as shown by the high MAE
score (MAE = 0.135 m3 m-3) for the corresponding Lu et
al. (2007) soils in Table 4. Moreover, the scores are very sensitive to
errors in the estimation of mSOM as shown by Table 5. Although the
msand* predictor gives slightly better scores than msand
(Table 4), the a1 coefficient in more sensitive to errors in
Chmin (Table 3), and the bootstrapping reveals large
uncertainties in a0 and a1 values.
The results presented in this study suggest that the
msand/mSOM ratio can be used to differentiate between
temperate grassland soils containing a rather large amount of organic matter
(3.7 < msand/mSOM < 40) and soils containing less
organic matter (msand/mSOM > 40). The msand
predictor can be used in both cases to estimate the volumetric fraction of
quartz, with the following a0 and a1 coefficient values in
Eq. (12): 0.15 and 0.572 for msand/mSOM ranging between 3.7
and 40 (Table 3) and 0.04 and 0.386 for msand/mSOM > 40
(Table 6).
Prospects for using soil temperature profiles
Using standard soil moisture and soil temperature observations is a way to
investigate soil thermal properties over a large variety of soils, as the
access to such data is facilitated by online databases (Dorigo et al., 2011).
A limitation of the data set we used, however, is that soil temperature
observations (Ti) are recorded with a resolution of ΔTi=0.1 ∘C only (see Sect. 2.1). This low resolution affects the
accuracy of the soil thermal diffusivity estimates. In order to limit the
impact of this effect, a data filtering technique is used (see Supplement 5)
and Dh is retrieved with a precision of 18 %.
It can be noticed that if Ti data were recorded with a resolution of
0.03 ∘C (which corresponds to the typical uncertainty of PT100
probes), Dh could be retrieved with a precision of about 5 % in
the conditions of Eq. (S5.3). Therefore, one may recommend revising the
current practise of most observation networks consisting in recording soil
temperature with a resolution of 0.1 ∘C only. More precision in the
λ estimates would permit investigating other processes of heat
transfer in the soil such as those related to water transport (Rutten, 2015).