Confidential manuscript submitted to Water Resource Research
2
In Situ Estimates of Freezing/Melting Point Depression in Agricultural Soils Using
Permittivity and Temperature Measurements
3
R. Pardo Lara1, A. A. Berg1, J. Warland2, Erica Tetlock3
4
1Department
5
2School
6
7
3National
1
of Geography, Environment and Geomatics, University of Guelph, Guelph, Canada.
of Environmental Science, University of Guelph, Guelph, Canada.
Hydrology Research Centre, Environment and Climate Change Canada, Saskatoon,
Saskatchewan, Canada.
8
9
10
11
12
13
14
15
16
17
Corresponding author: Renato Pardo Lara (rpardo@uoguelph.ca)
Key Points:
•
The freeze-thaw response of a widely used soil moisture probe was investigated and
permittivity soil freezing/thawing curves were identified.
•
A logistic growth model was fitted to the permittivity soil freezing/thawing curves
yielding freezing/melting point depression estimates.
•
In situ estimates of the freezing/melting point depression and frozen water saturation
provided for the Kenaston Soil Moisture Network.
1
Confidential manuscript submitted to Water Resource Research
18
Abstract
19
20
21
22
23
24
25
26
27
28
36
We present a method to characterize soil moisture freeze-thaw events and freezing/melting point
depression using permittivity and temperature measurements, readily available from in situ
sources. In cold regions soil freeze-thaw processes play a critical role in the surface energy and
water balance, with implications ranging from agricultural yields to natural disasters. Although
monitoring of the soil moisture phase state is of critical importance, there is an inability to
interpret soil moisture instrumentation in frozen conditions. To address this gap, we investigated
the freeze-thaw response of a widely used soil moisture probe, the HydraProbe (HP), in the
laboratory. Soil freezing curves (SFC) and soil thawing curves (STC) were identified using the
relationship between soil permittivity and temperature. The permittivity SFC/STC were fit using
a logistic growth model to estimate the freezing/melting point depression (𝑇𝑓⁄𝑚 ) and its spread
(𝑠). Laboratory results showed the fitting routine requires permittivity changes greater than 3.8 to
provide robust estimates and suggested a temperature bias is inherent in horizontally placed HPs.
We tested the method using field measurements collected over the last seven years from
Environment and Climate Change Canada and University of Guelph’s Kenaston Soil Moisture
Network in Saskatchewan, Canada. By dividing the time series into freeze-thaw events and then
into individual transitions the permittivity SFC/STC were identified. The freezing and melting
point depression for the network was estimated as 𝑇𝑓/𝑚 = −0.35 ± 0.2, with 𝑇𝑓 = −0.41 ±
0.22 °C and 𝑇𝑚 = −0.29 ± 0.16 °C respectively.
37
1 Introduction
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
Nearly all land area above 45° N undergoes a seasonal transition between frozen and
thawed conditions each year, with even more regions experiencing short-term diurnal freezethaw (F/T) events (Rowlandson et al., 2018). The spatial distribution and timing of soil freezethaw events are critical factors affecting terrestrial water, carbon, and energy balance with
consequential effects on hydrological, climatic, ecological, and biogeochemical processes (e.g.:
Wagner-Riddle et al. 2017). Hydrologically, this knowledge is critical to predict the fate of
snowmelt and thus the water balance of a watershed or field. In terms of groundwater, the
dominant effect of freeze-thaw events is the extent of hydraulic isolation associated with the
freezing front. The spatial and temporal occurrence of freeze-thaw events is seasonally variable
and may be modified under a future changing climate (Ireson et al. 2013). Soil freeze-thaw
monitoring is critical for predicting soil infiltration capacity and spring runoff, with implications
ranging from the duration of the agricultural growing season and prediction of inundation events
(Gray et al. 2001) to water futures. There is also a need to monitor these events at larger scales
such as those typically used in models (grid cells) and management (field scales). Currently,
however, there is no simple in-situ method to continuously measure these phenomena directly in
the field.
54
55
56
57
58
59
60
61
In situ, soil freeze-thaw state has typically been inferred from proxy measurements of air
and/or soil temperatures and classified based on a 0 °C threshold. (McColl et al. 2016; Roy et al.
2015; Podest, McDonald, and Kimball 2014; Rautiainen et al. 2014). However, over the
terrestrial temperature range, soil moisture is known to occur in both liquid and solid states at the
same time (Petit 1893; Bouyoucos and McCool 1916), a fact that is obscured by classification
between frozen and thawed states. Moreover, temperature observations alone are not ideal for
ground freeze-thaw classification. Soil moisture exhibits freezing point depression dependent on
its liquid water content, textural composition, solute concentration, and the pore pressure of the
29
30
31
32
33
34
35
2
Confidential manuscript submitted to Water Resource Research
62
63
64
soil (Petit 1893; Mousson 1858; Daanen, Misra, and Thompson 2011). Furthermore, the
equilibrium freezing point differs throughout the soil water, so the process of freezing or thawing
of soils generally takes place over a wide range of temperatures.
65
66
67
68
69
70
71
72
73
74
75
76
The phenomena of freezing point depression has been investigated in the laboratory by
way of the soil-freezing-curve (SFC; Koopmans & Miller, 1966), which shows how unfrozen
soil moisture in a saturated soil reduces with temperature below 0 °C. SFCs have been well
studied in laboratory settings using a variety of instrumentation ranging from tensiometers and
calorimeters to TDR and NMR (Koopmans and Miller 1966; Yoshikawa and Overduin 2005; Liu
and Yu 2013; Watanabe and Mizoguchi 2002; Wen et al. 2012; Tian et al. 2018; Qiang Cheng et
al. 2014). These studies are generally performed on a few, relatively small, disturbed soil
samples which are saturated and compacted. The data acquired using these methods is usually
limited in either its time or temperature resolution. More notably, these experiments are
performed at or near thermal equilibrium, by quasi-static or rapid cooling processes. More
recently, the hysteretic behavior between the freezing and thawing processes has led to the
definition of the soil-thawing-curve (STC; Zhou et al. 2019).
77
78
79
80
81
82
83
84
85
86
87
88
89
Recently, dielectric reflectometry devices have been investigated for use in soil freezing
conditions. Sun et al., (2012) presented a method for observing the soil freeze–thaw cycle using a
frequency domain permittivity sensor designed for use in access tubes and Cheng et al., (2014)
verified its feasibility in-situ, however this was based on bi-weekly measurements. Kelleners &
Norton (2012) attempted to determine depthwise water retention using the relationship between
freezing soil temperature and liquid soil water content measured with a coaxial impedance
dielectric reflectometry. Both Kelleners & Norton and Sun et al., adopted dielectric mixing
models to estimate the volumetric soil ice content. Williamson et al. (2018) classified the freezethaw state using relative thresholds based on frozen and thawed permittivity references.
However, these methods do not explicitly consider freezing point depression. Although
permittivity measurements can address the need for measurement of unfrozen water content in
situ, the accuracy of instrumentation for this purpose has been brought into question (Ireson et al.
2013).
90
91
92
93
94
95
96
97
98
99
100
101
102
The experiments described here present a unique relationship for the identification of
individual freeze-thaw events (transient or seasonal) in permittivity-temperature space using the
HydraProbe (HP). The identified relationship is supported by independent Heat Pulse Probes
(HPP) measurements in the laboratory. Since the primary driver for changes in soil permittivity
measurements is the moisture content, this relationship links the degree of phase transition to the
sub-freezing temperature yielding an event- and site-specific permittivity SFC or STC. We fit
this relationship using a logistic growth model for two parameters, interpreted as estimates of the
freezing point depression (Tf) and its temperature dispersion (𝑠). The HP is commonly used in
distributed soil moisture sensing networks deployed in several parts of the world as part of
agricultural, hydrologic, and climate studies. A substantial number of network sites are located in
cold regions that are prone to soil water freezing. Lastly, we demonstrate the method on in situ
data from one such network, the Kenaston Soil Moisture Network, located in the Brightwater
Creek basin, Saskatchewan, Canada (Tetlock et al. 2019).
103
2 Materials and Methods
104
105
The experiments described utilize the HP for volume measurements of the soil relative
permittivity and contact surface temperature measurements as well as HPPs for apparent heat
3
Confidential manuscript submitted to Water Resource Research
106
107
108
109
capacity measurements. The measurements were used to fit a proposed model of the relationship
between permittivity and temperature during freeze-thaw transitions (permittivity SFC or STC)
in the context of the HP. The model was also adapted and applied to seven years of field data
from ECCC’s Kenaston soil moisture monitoring network in Saskatchewan, Canada.
110
2.1 Instrumentation
111
2.1.1 HydraProbe (HP)
112
113
114
115
116
117
The HP is a commercially available soil moisture sensor that uses coaxial impedance
dielectric reflectometry resulting in high measurement accuracy that does not require calibration
for most soils (e.g: Rowlandson et al. 2013). This method fully characterizes the dielectric
spectrum using a radio frequency at 50 MHz. The sensing device has been found to be robust
under a wide variety of field conditions and it provides simultaneous in-situ measurement values
of soil permittivity, conductivity, and temperature (Seyfried et al. 2005).
118
119
120
121
122
123
124
125
126
127
128
129
The HP has four 0.3 cm diameter stainless steel tines that are 5.7 cm long, these tines
protrude from a metal base plate 4.2 cm in diameter. Three tines form a circle 3.0 cm in diameter
around a central tine. The base plate is part of the cylindrical head which houses the electronics
that produce the 50 MHz signal transmitted to the protruding tines and measure temperature. The
probe’s tines are used to measure the amplitude change of a reflected electromagnetic signal in
volts. The ratio of incident and reflected voltages is used to numerically solve Maxwell’s
equations, yielding the impedance and complex permittivity. The real component of the latter is
used to estimate soil water content by way of an empirical calibration equation. The support for
the soil permittivity ranges between approximately 50 to 110 cm3 and includes the soil between
and surrounding the tines. The base plate must be flush with the soil as the temperature is
measured using a thermistor in contact with the metal plate, yielding a support of approximately
7 cm2.
130
131
132
133
134
135
136
The primary driver for changes in soil permittivity measurements is the moisture content.
The bulk soil permittivity is an average of the permittivities of the soil constituents (water, ice,
soil, air) with different permittivities randomly distributed and oriented in a host (He et al.
2016). A study conducted by Seyfried et al. (2005) examined the relationship between
volumetric water content and the real dielectric constant of the soil measured by HydraProbes.
They conducted their experiment over a range of soil textures and investigated the use of a linear
calibration equation between volumetric water content (𝜃) and the square root of the real
dielectric (√𝜀); as shown in equation (1).
137
138
139
140
141
142
143
144
145
146
𝜃 = 𝐴√𝜀𝑟 + 𝐵
(1)
Rowlandson et al. (2013) found the lowest root mean square errors resulted from calibrating the
HydraProbes using individual equations for each field of their study area based on this linear
relationship.
2.1.2 Heat Pulse Probes (HPP)
In 2008, Ochsner and Baker monitored the soil heat flux under freezing and thawing
conditions, demonstrating a theoretical basis for the measurement of the volume-specific
apparent heat capacity (𝑐𝑎 ) using Heat Pulse Probes (HPP). HPP work by analyzing temperature
changes at one or more temperature sensing needles, responding to a heat pulse applied from a
4
Confidential manuscript submitted to Water Resource Research
147
148
149
150
151
parallel line-heat source probe (Bristow, Kluitenberg, and Horton 1994). Since the specific heat
capacity is not strictly associated with phase changes, the term apparent specific heat capacity is
employed to distinguish them from “true” specific heats (Williams 1964; D. M. Anderson 1973).
The apparent volumetric heat capacity is defined as
𝑐𝑎 = 𝑐 + 𝐿𝑓 𝜌𝑙
𝜕𝜃𝑙
(2)
𝜕𝑇
152
153
154
155
156
where 𝑐 is the volume-specific heat capacity (MJ m-3 °C-1), Lf is the latent heat of fusion for
water (J kg-1), l is the density of liquid water (kg m-3), l is the volumetric soil liquid water
content (m3 m-3), and T is temperature (°C). Thus, ca may be interpreted as the quantity of heat
required to raise the temperature of a unit volume of soil by 1 °C while a phase change between
liquid water and ice is occurring.
157
158
159
160
161
162
163
164
165
166
In unfrozen soil ca = c. In partially frozen soil, however, ca may vary by several orders of
magnitude across a 1 °C temperature range (Fuchs, Campbell, and Papendick 1978; Koopmans
and Miller 1966). When the temperature sensitivity of the thermal properties becomes very large,
the temperature increase induced by the heat pulse becomes very small. This occurs because an
increasing fraction of the total heat input is consumed in melting ice rather than in raising the
temperature of the soil. Just below the freezing point, where the temperature sensitivity of ca is
greatest, almost all of the heat pulse is consumed in melting ice and the temperature in the
measurement volume is nearly constant during the measurement. We exploit the fact HPP
measured ca provides a “flag” indicating the occurrence of a phase change, to characterize the
HP’s response to F/T transitions.
167
2.2 Laboratory experiments
168
169
170
171
172
173
174
175
176
177
178
Soil samples were collected in the from the University of Guelph’s Elora Research
Station (sandy loam; collected late Fall 2017) as well as private farms in Cambridge (loamy
sand; collected late Fall 2017) and Dunnville (clay loam; collected during a mid-winter thaw in
2018), all in Ontario. Ten undisturbed mesocosms were extracted from each site in PVC
cylinders measuring 12 cm in height and 10 cm in diameter. The holders were only filled to a
depth of 10 cm and the bottom was capped with plastic lid. Prior to collection, each PVC sample
holder was chamfered to facilitate sample extraction and machined to accommodate a
horizontally placed HP at a depth of 2.5 cm into the soil profile (4.5 cm below the top of the
holder). This was complemented by the orthogonal insertion of two heat pulse probes, placed
horizontally and diametrically opposed, covering the vertical span of the HP’s sensing volume,
see Figure 1.
179
180
181
182
183
184
185
186
187
Experiments were undertaken at the School of Environmental Science of the University
of Guelph in a NorLake2 mini-room walk-in controlled temperature chamber equipped with a
CP7L control panel. The collected samples were placed in insulated cardboard boxes and filled
with sand, as shown in Figure 1, an attempt to laterally insulate the mesocosms and mimic a 1-D
freezing front. HP output signals were logged with a CR800 datalogger and HPP output signals
were logged with a CR1000 datalogger (both from Campbell Scientific, Inc.). The temperature
and permittivity of each mesocosm were measured every minute using the HP while two HPP
alternately captured the apparent heat capacity at 24-minute intervals. Sensor output from
induced F/T events was recorded over different soil texture classes and soil moisture levels.
5
Confidential manuscript submitted to Water Resource Research
188
189
Table 1:
Characteristics of Soil Samples Used in this Study
Field Location
Dry bulk
density (g cm-3)
Dry soil
permittivity
Sand
(%)
Clay Silt
(%) (%)
Textural
class
Elora Research Farm
43°39′ N, 80°25′ W, 376 m
1.45
2.5±0.1
54
10
36
Sandy
Loam
Cambridge (private farm)
46°26′ N, 80°20′ W, 312 m
1.78
2.0±0.1
78.4
2.5
19.1
Loamy
sand
Dunnville (private farm)
42°52′ N, 79°44′ W, 192 m
1.40
2.4±0.2
33
28
39
Clay
loam
190
191
192
193
194
The soil samples were subjected to temperature transitions from +10 °C to -10 °C and
vice versa at ~24-hour intervals. Each mesocosm had different soil moisture content levels,
either from collection, addition of distilled water, or removal of water by oven drying. One
mesocosm of each soil type was oven dried at 105 °C for 48 hours to serve as a control.
195
196
197
198
199
Figure 1: Experimental set up of HydraProbe and Heat Pulse Probes from three different
perspectives and mesocosm arrangement in thermally insulated cardboard boxes filled with sand,
to scale.
2.3 Kenaston Soil Moisture Network transition data
200
201
202
203
204
205
206
207
208
As discussed earlier, a major gap in the understanding of hydrological processes in
seasonally frozen northern latitudes is the inability to effectively monitor processes in the field.
A number of large-scale soil moisture monitoring networks (e.g.: SCAN, CRN, AgriMET,
RISMA, Kentucky Mesonet, New York Mesonet, Snotel, Soil Moisture Analysis Network, and
ISMN), have shown the potential for freeze-thaw validation (Williamson, Rowlandson, et al.
2018). These networks are instrumented with probes that measure soil temperature and relative
permittivity, to estimate volumetric soil moisture content (Topp, Davis, and Annan 1980), at
standard World Meteorological Organization instrument depths (5, 20, and 50 cm below ground;
Dorigo et al. 2013)
209
210
211
212
213
The applicability of our methods was evaluated using field data obtained from one such
soil moisture monitoring network. Since 2007, soil moisture and precipitation have been
monitored in a hydrometeorological network within the Brightwater Creek basin, east of
Kenaston, SK, Canada (Tetlock et al. 2019). The network captures precipitation measurement
and soil moisture variation at two spatial scales (102 km2 region and 402 km2) with three
6
Confidential manuscript submitted to Water Resource Research
214
215
216
instrument depths for soil moisture and temperature. This agricultural region has been used for
remote sensing calibration and validation (e.g. Colliander et al. 2017; Lye et al. 2018) and
hydrological model validation (Garnaud et al. 2016).
217
218
219
220
221
222
223
224
225
226
227
Soil permittivity measurements collected from Environment and Climate Change
Canada’s 22 stations of the Kenaston Network starting from winter 2012/2013 were sectioned
into freeze-thaw events. An event includes both a freezing and a thawing transition, however in
the case that data collection starts/ends mid-event, that event is classified as either a thawing or a
freezing transition. These sites cover a textural composition range from 10.5% – 61.7% for sand,
31.2% – 72.4% for silt, and 1.2% – 41.1% for clay. It is noted that standard HPs have an
operating temperature range from -10 °C to +60 °C and extended range HPs have an operating
range between -30 °C and +60 °C. Over the years, some of the network’s near surface probes
have been replaced with extended temperature ones, so that both standard and extended range
probes are found in the network. To keep the data consistent, only measurements with
temperatures greater than -10 °C were analyzed.
228
229
230
231
232
233
234
235
236
Freeze-thaw events were identified based on the sign changes associated with
freezing/thawing temperatures in the Celsius scale. The cycles were then split into freezing and
thawing transitions based on the minimum/maximum soil permittivity at the minimum/maximum
temperature reached during the cycle. Freezing/thawing transitions were considered to start/end
when the measured temperature went below/above 0 °C and the preceding/following four
measurements (equivalent to 2 hours) were included for context. Transitions identified from the
same event were separated with a three measurement overlap between them. This subset of the
network’s data and the laboratory data are available at the polar data catalog (PDC;
https://dx.doi.org/10.20383/101.0200).
237
2.4 Logistic model of the SFC/STC
238
239
240
241
242
243
244
245
The relationship between unfrozen water content and soil temperature, known as the soil
freezing curve (SFC), is perhaps the most basic property of the physical processes involved in
soil freeze-thaw processes (Ireson et al. 2013). The SFC represents the phenomenon of freezing
point depression in soils and can be used for understanding the transportation of heat, water, and
solute in frozen soils (Koopmans and Miller 1966). The SFC is analogous to the soil moisture
characteristic for unfrozen conditions and has been recognized as a fundamental relationship in
cold region engineering which controls the hydraulic properties (D. Anderson and Morgenstern
1973; Ren, Vanapalli, and Han 2017).
246
247
248
249
250
251
252
253
254
255
During the thawing process of frozen soil, the relation between the unfrozen water
content and the temperature is usually different from the SFC. This relation is defined as the soil
thawing characteristic (STC; Zhou et al. 2019), and the difference between the STC and the SFC
is well-known as hysteresis. Zhou et al., defined this relation as the soil thawing characteristic
(STC). Thus, in general we expect 𝑆𝐹𝐶 = 𝜃(𝑇) and 𝑆𝑇𝐶 = 𝜃(𝑇), but 𝑆𝐹𝐶 ≠ 𝑆𝑇𝐶. This
hysteretic behavior can be attributed to several possible mechanisms, including supercooling
effects, electrolyte concentration changes induced by the freezing/thawing processes, differences
in ice–water interface curvatures during crystallization and melting, pore blocking effects,
contact angle effects, changes in pore structure, as well as particle displacement from freezing
expansion (Ren & Vanpalli, 2019).
7
Confidential manuscript submitted to Water Resource Research
256
257
258
259
260
261
262
263
264
265
266
As mentioned earlier, the primary driver for changes in soil permittivity measurements is
the moisture content. Thus, the HP’s measurements can be used to link the degree of phase
transition to the sub-freezing temperature yielding a permittivity SFC or STC. However, there
are some fundamental difference between these “permittivity SFC or STC” from undisturbed
samples or in situ stations and their well-studied SFC or STC counterparts. These measurements
are, generally, not from saturated samples and the higher temporal resolution comes at the
expense of accuracy, when compared to more complicated laboratory methods. Moreover, these
experiments are performed at or near thermal equilibrium, by quasi-static or rapid cooling
processes. The deviation between the results expected from dielectric models is attributed to the
HP’s measurement support, or measurement region (Western and Blöschl 1999), which
influences the shape of the permittivity SFC/STC.
267
268
269
270
271
272
273
274
275
276
277
278
279
In the remote sensing community, the widely accepted models of soil dielectric
permittivity are described by Zhang, Zhao, Jiang, & Zhao (2010) and Mironov & Savin (2016).
These models are both based on the Debye relaxation model, with temperature-dependency
considerations and different characterizations of the constituents of the model. Neither of these
models directly addresses the phenomena of freezing point depression. The Mironov & Savin
(2016) model conditionally assumes that the soil samples are in a frozen state in the temperature
range of -30 °C < T <-1 °C and the dielectric permittivity decreases exponentially with
temperature. Zhang et al., (2010) , on the other use a dielectric mixing model with fixed
permittivity values, in which the unfrozen water content decreases with temperature using a
power law relationship. Both of these yield a similar (exponential and power law respectively)
relationship between permittivity and temperature increase, which are truncated at a defined
temperature. However, these models are not congruent with the sigmoidal relationship seen in
Figures 2 and 3.
280
281
282
283
288
289
290
Land surface models commonly use a thermodynamical approach, with minor variations,
to describe the relationship between liquid water content and temperature (Koren et al., 1999;
Cox et al., 1999; Smirnova et al., 2000; Cherkauer and Lettenmeier, 2003). These models adopt a
power law description and include HydroGeosphere, ORCHIDEE, and, the Common Land
Model (CLM5; Brunner & Simmons, 2012; Ducharne, 2017; Lawrence et al., 2018). Again, this
does not yield a curve congruent with our sigmoidal results. Alternatively, the Canadian Land
Surface Scheme (CLASS), Soil Heat and Water (SHAW), Hydrus-1D, and the Noah-MP models
employ numerical solution schemes on discretized soil layers which solve for coupled water
flow and heat transport. Lastly, several empirical formulae have been presented, through the
analysis of experimental data. These formulae are summarized in Liu & Yu, (2013) and are,
again, based on power or exponential relationships.
291
292
293
294
295
296
297
298
299
300
For theoretical analysis of unfrozen water, there are three types of theories reported in
literature. Liquid film theory (Gilpin 1980), does not present any formulas for the unfrozen water
content. Similarity theories based on the similitude between saturated frozen soil and unsaturated
soil have been developed using the Young-Laplace equation and the Clapeyron equation
(Koopmans and Miller 1966; Black and Tice 1989; Liu and Yu 2013). However, there are
questions regarding the use of the Clapeyron equation in frozen soil and assumptions of the porewater and pore-ice pressures. Lastly, similarity theories using the Gibbs-Thomson equation have
also been proposed (Bai et al. 2018; Zhao et al. 2017; Zhou et al. 2019). Using these theories,
models of the Soil Moisture Curve (SMC) in unsaturated soil can be used to fit the SFC/STC in
the same form. This reformulation assumes the linear transformation of variables from water
284
285
286
287
8
Confidential manuscript submitted to Water Resource Research
301
302
303
304
305
content and head pressure to unfrozen water content and subfreezing temperature does not
change the form of the equation. Moreover, the effect of air is excluded, therefore strict
application of similarity theory requires the condition of saturated frozen soil. Recently,
however, Ren and Vanapalli (2019) raised several concerns regarding the (lack of) similarity
between the SFC and SMC.
306
307
308
309
310
311
312
313
314
Although, widely used SMC models are able to accommodate the sigmoidal relationship
seen in our data, they are dependent on at least three curve fitting parameters, some of which are
not interpretable (Hogarth et al. 1988; van Genuchten 1980; Fredlund and Xing 1994). It is noted
that these models are based on soil moisture content, but the raw data from our experiment is the
dielectric permittivity of the HydraProbe’s sensing volume. Moreover, the applicability of these
models to our data is debatable, since models accounting for the measurement support of the
HydraProbe suggest the sigmoidal shape seen between permittivity and temperature, is at least
partially caused by the separation of the probe’s temperature and permittivity measurement
regions.
315
316
317
318
319
320
321
For simplicity and to hone in on the freezing point depression and its variance as
measured by the HydraProbe, we employ a two parameter logistic model, which is fitted for
location and scale parameters. We fit the empirical relationship between the soil permittivity and
temperature using a logistic function, seen in equation (5), as it is a common model of restricted
population growth and it offers interpretable parameters. In the case of soil freezing/thawing, the
growing population is the ice/liquid water, which is limited by the total amount of H2O in the soil
volume and the minimum temperature, such that for freezing or thawing transitions,
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
𝑆𝐹𝐶 or 𝑆𝑇𝐶 = 𝜃(𝑇) = 𝜃𝑚𝑖𝑛 +
𝜃𝑚𝑎𝑥 −𝜃𝑚𝑖𝑛
1+𝑒
−(𝑇−𝑇𝑓⁄𝑚)⁄𝑠
(3)
Subbing in equation (1) yields
𝐴√𝜀(𝑇) + 𝐵 = (𝐴√𝜀𝑚𝑖𝑛 + 𝐵) +
(𝐴√𝜀𝑚𝑎𝑥 +𝐵)−(𝐴√𝜀𝑚𝑖𝑛 +𝐵)
1+𝑒
−(𝑇−𝑇𝑓⁄𝑚)⁄𝑠
(4)
which simplifies to
√𝜀(𝑇) = √𝜀𝑚𝑖𝑛 +
√𝜀𝑚𝑎𝑥 −√𝜀𝑚𝑖𝑛
1+𝑒
(5)
−(𝑇−𝑇𝑓⁄𝑚)⁄𝑠
where the minimum and maximum soil permittivities at the minimum and maximum
measured temperatures are 𝜀𝑚𝑖𝑛 and 𝜀𝑚𝑎𝑥 respectively. 𝑇𝑓/𝑚 is the temperature at the halfway
point of the transition, at which the change in permittivity reaches its maximum rate of change,
and 𝑠 is a scale factor inversely proportional to the growth rate. 𝑇𝑓⁄𝑚 and s can thus be
interpreted as the freezing/melting point depression and its spread in temperature space.
The model parameters are fitted using Levenberg-Marquardt non-linear least squares with
starting values of 𝑇𝑓/𝑚 = 0 °C and 𝑠 = 0.4 °C. The latter amount corresponds to the HP
instrumental accuracy uncertainty (Stevens Water Monitoring Systems 2015). The parameters
were further constrained. 𝑇𝑓/𝑚 was bounded between the transition’s maximum and minimum
temperature ( 𝑇𝑚𝑖𝑛 ≤ 𝑇𝑓/𝑚 ≤ 𝑇𝑚𝑎𝑥 ) and s was bounded between 0 and the temperature range
(0 ≤ 𝑠 ≤ 𝑇𝑚𝑎𝑥 − 𝑇𝑚𝑖𝑛 ). We note that 𝑠 is roughly half the standard deviation of the logistic
9
Confidential manuscript submitted to Water Resource Research
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
distribution associated with the fit (𝑠 = √3
𝜎 ≈ 0.55 𝜎). For the logistic distribution, the
𝜋
cumulative probability at values 𝑇𝑓/𝑚 ± 𝑠 is 0.269 and 0.731 respectively.
To summarize, the method described can provide estimates of the freezing/melting point
depression (𝑇𝑓/𝑚 ) and its temperature dispersion (𝑠) for the associated transition using a logistic
fit of empirical permittivity SFC/STC. The applicability of this model was tested using the
laboratory data and in situ data from the Kenaston Soil Moisture Network.
2.4.1 Logistic model adjustments for in situ data
One of the first challenges encountered in adapting the lab methods to field data lay in the
relative paucity of data. In the laboratory, measurements were recorded every minute; in the soil
moisture network, measurements are available every 30 minutes. To evaluate the effects of this
difference in temporal resolution, the laboratory data were down-sampled to 30-minute intervals.
The resulting fit parameters 𝑇𝑓/𝑚 and 𝑠 were compared yielding a cosine similarity score of 1.00
and 0.999 respectively on 154 observations (sand controls were excluded). The correlation
coefficients were 1.00 and 0.987 respectively. However, in the field data during the vernal thaw,
rapid soil temperature fluctuations and the melting snowpack can further reduce the number of
measurements collected for a transition. In effect this paucity leads to underfitting the data from
the most dynamic section of the transition (see section 3.2).
To ameliorate this underfitting, a weighting scheme was implemented based on the total
number of measurements (n) such that the data inside (m) and outside (n-m) a region of interest
have equal importance if m < n-m. The region was set between -1 °C and 1 °C, the most dynamic
section of the transition. Such that:
𝑛 − 𝑚 −1
) if 𝑚 < 𝑛 − 𝑚 and − 1 ℃ ≤ 𝑇 ≤ 1 ℃
𝑚
𝑤=
𝑚 −1
(1 +
) if 𝑚 < 𝑛 − 𝑚 and − 1 ℃ > 𝑇 > 1 ℃
𝑛−𝑚
{ 1
else
(1 +
360
361
362
363
This weighting scheme has the added benefit of making the fit statistics more representative of
the fit quality over the region of interest.
364
3 Results
365
366
367
368
369
370
371
372
373
3.1 Laboratory freeze/thaw transitions
A total of eleven freeze-thaw events were induced on six samples plus two controls at a
time, yielding a total of 176 transitions across three different soil types at various soil moisture
content levels. The two controls, comprised of a field sample oven-dried at 105 °C for 48 hours
and the dry sand used to insulate the soil samples, are suggestive of an instrumental minimum
soil permittivity of 2.3±0.2. Figure 2 shows the F/T cycle data collected from the Cambridge
loamy sand mesocosms, excluding the controls, as a function of soil temperature. Most notably,
the sigmoidal relationship between permittivity and temperature was seen in every sample for
both the freezing and thawing transitions.
10
Confidential manuscript submitted to Water Resource Research
374
a
b
375
376
377
378
379
Figure 2: Soil permittivity for freezing (blue) and thawing (red) transitions as well as apparent
heat capacity (black with star) measurements as a function of time (a) and soil temperature (b)
from a the Cambridge sandy loam samples, excluding the controls. The apparent heat capacity
greatly increases during phase transitions of the soil moisture.
380
381
382
383
384
385
386
387
388
389
The permittivity SFC/STC curves can be divided into three zones, i.e., boundary effect
zone (where no pore ice forms), transition zone (where sharp drop in the unfrozen water content
is experienced), and residual zone of unfrozen state (where variation in the unfrozen water
content is insignificant despite significant changes in temperature). The unfrozen water content
in the soil gradually decreases along the freezing curve. At a certain sub-freezing temperature,
most of the pore water turns into ice and beyond this temperature extremely low temperature
would be required to further reduce the unfrozen water. This specific unfrozen water content is
referred to as residual unfrozen water content. In addition, the permittivity SFC/STC curves
display the expected hysteretic behavior (Tian et al. 2014; Ren, Vanapalli, and Han 2017; Zhou
et al. 2019).
390
391
392
393
394
395
396
397
398
399
400
401
It is of interest that although large changes in soil permittivity are temporally correlated
with spikes in the apparent heat capacity, the measurements do not correlate in temperature
space. The soil permittivity continues increasing/decreasing at temperatures higher/lower than
those at which the apparent heat capacity measurements return to their constant values. These
results speak to the limitations imposed by the laboratory set-up. Fundamentally, the HP offers
different support (Bloschl and Sivapalan, 1995) between the volume measurement of the
permittivity and the average surface area measurement of the temperature from the thermistor
attached to the metal plate. Even though the samples were placed in insulated boxes filled with
dry sand in an attempt to simulate a 1-D freezing front in the soil, the sand’s thermal inertia was
lower than that of the samples. Consequently, the temperature of the sand surrounding the
HydraProbe responded more quickly to the air temperature changes driven by the environmental
chamber. Although the base plate was in contact with the soil sample, the cylindrical head and
11
Confidential manuscript submitted to Water Resource Research
402
403
the outermost part of the samples were surrounded by a medium with temperature biased towards
that imposed by the environmental chamber.
3.2 Kenaston Soil Moisture Network transition data
404
405
406
407
408
409
410
411
412
Soil moisture and precipitation have been monitored since 2007 in a hydrometeorological
network within the Brightwater Creek basin, East of Kenaston, SK, Canada (Tetlock et al. 2019).
Soil permittivity measurements collected from the topmost horizontal HP (5 cm depth) probes
for ECCC’s 22 stations for the Kenaston Soil Moisture Network were analyzed. In total, 3842
possible freeze or thaw transitions were identified using the criteria laid out in Sec. 2.4. As an
example, the freeze-thaw events isolated from Station 19 between October, 2013 and May 2014
can be seen on Figure 3.
a
b
413
414
415
416
417
Figure 3: Freeze-thaw event data isolated from the Kenaston Network station 19 between
October 1, 2013 and May 1, 2014. Soil permittivity for freezing (blue) and thawing (red)
transition measurements as a function of time (a) and soil temperature (b) from a sandy loam
sample. Various transient events are seen along with the main seasonal event.
418
419
420
Unlike our laboratory results, there is no visually discernible difference between the
freezing and thawing data acquired in-situ. However, the relationship between permittivity and
soil temperature continues to exhibit the sigmoidal form seen in our laboratory results.
12
Confidential manuscript submitted to Water Resource Research
421
422
423
424
425
426
427
428
429
430
431
432
433
434
4 Discussion
4.1 Model application to laboratory data
Ireson et al. (2013) questioned whether permittivity-based methods would be sufficiently
accurate to partition the total water content into frozen and unfrozen components. These
concerns were based on the expectation that the unfrozen water content should drop to close to
zero at temperatures of −4 °C. However, these anomalously high unfrozen water contents were
acquired using an “unrefined” TDR calibration. The authors also refer to work by Roth and
Boike (2001) which indicates a volume fraction of 0.05 for liquid water at -15 °C. Roth and
Boike justify these values as comparable to the accuracy of the TDR data and note the high clay
content of the soil used. We sidestep the soil moisture content accuracy issues by dealing directly
with the permittivity measurements. It is worthwhile to note that Ireson based his discussion on
daily TDR measurements; Roth and Baike based them on half-daily liquid water content
measurements. The data set used here provides much higher temporal resolution allowing for the
identification of more transient freeze-thaw events.
435
436
437
438
439
440
Figure 4: Soil permittivity for a freezing (blue) and thawing (red) transition as well as apparent
heat capacity (black with star) measurements as a function of soil temperature (a) and time (b)
from a Cambridge sandy loam sample. The apparent heat capacity greatly increases during phase
transitions of the soil moisture. The logistic models (black) were used to estimate the
freezing/melting point depression (𝑇𝑓/𝑚 ) and its temperature dispersion (𝑠 ≈ 0.5 𝜎).
441
442
443
Since a non-linear least squares method was employed, high R2 values are expected. The
low R2 seen on Figure 5 indicate that the model is not reliable when the permittivity range
(𝜀𝑟𝑎𝑛𝑔𝑒 = 𝜀𝑚𝑎𝑥 − 𝜀𝑚𝑖𝑛 ) associated with the phase change is small. Fitting an exponential model,
we estimate that the model will provide a suitable fit (high R2 values) for transitions with a
permittivity range greater than 3.8, with 95% probability. When this condition is met, the
444
445
13
Confidential manuscript submitted to Water Resource Research
446
447
freezing point depression appears to be robust with regard to soil texture and moisture content, as
seen on Figure 5.
448
449
450
451
Figure 5: Model R2, from the logistic fit as a function of the permittivity range. The thaw
transitions are shown in red, freeze transitions in blue, and controls (oven dried for 48 hours) in
black.
452
The freezing/melting point depression estimated from the model, 𝑇𝑓/𝑚 , as a function of
maximum permittivity (which is a proxy for soil moisture content) can be seen in Figure 6. 𝑇𝑓/𝑚 ,
interpreted as the freezing point depression, also appears to be robust with regard to soil texture
and soil moisture content. The model was used to estimate the temperature range of the freezing
point depression (𝑇 = 𝑇𝑓/𝑚 ± 𝑠). These temperatures are illustrated by the dashed lines on
Figure 4 and can be seen as the bars on Figure 6. By constraining the analysis to transitions with
a permittivity range greater than 3.8, the following averages, with standard deviation, were found
for freezing transitions: -2.0± 0.3 °C for all samples, -1.86 ± 0.05 °C for the Elora sandy loam, 1.86 ± 0.27 °C for the Cambridge loamy sand, and -2.1 ± 0.4 °C for the Dunnville clay loam; all
of which are within one standard deviation of each other. For thawing transitions, the averages
were: 2.05 ± 0.24 °C for all samples, 2.01 ± 0.04 °C for the Elora sandy loam, 2.2 ± 0.19 °C for
the Cambridge loamy sand, and 1.95 ± 0.24 °C for the Dunnville clay loam; again, all of which
are within one standard deviation of each other.
453
454
455
456
457
458
459
460
461
462
463
464
465
14
Confidential manuscript submitted to Water Resource Research
466
468
469
470
471
Figure 6: Estimated freezing/melting point depression, 𝑇𝑓/𝑚 , as a function of maximum soil
permittivity (a proxy for soil moisture content). The thawing transitions are shown in red,
freezing transitions in blue, and controls (oven dried for 48 hours) in black. The bars display the
temperature dispersion of the freezing point depression, as estimated by the scale parameter, s.
Bars not shown for transition with a permittivity range (𝜀𝑚𝑎𝑥 − 𝜀𝑚𝑖𝑛 ), lower than 3.8.
472
473
474
475
476
477
478
479
480
As mentioned earlier, these freezing/melting point depression estimates speak to the
limitations imposed by the laboratory set-up. The dry sand used to insulate the samples had
lower thermal inertia than the samples, responding more quickly to the temperature changes
driven by the environmental chamber. In effect, the thermistor and outermost part of the samples
were surrounded in a medium with temperature biased towards that being imposed by the
environmental chamber. This decoupling between the soil permittivity and biased temperature
measurements, shifted 𝑇𝑚 to temperatures greater than 0 °C during thawing transitions (an
unphysical range for terrestrial environments) and forced the freezing point depression
measurements, 𝑇𝑓 , during freezing transitions.
467
481
482
483
484
485
486
487
488
489
4.2 Model application to field data
The model, equation (5), and fitting techniques were applied along with the weighting
scheme to determine the freezing/melting point depression (𝑇𝑓/𝑚 ) and temperature dispersion (𝑠)
of the 3842 freeze or thaw transitions identified in the Kenaston Soil Moisture Network Data. In
terms of quality control, as concluded from the laboratory experiments, transitions with a
permittivity range of less than 3.8 units (𝜀𝑚𝑎𝑥 − 𝜀𝑚𝑖𝑛 < 3.8) were removed from further
analysis, leaving a total of 780 transitions suitable for analysis with our model. Of these, 29
transitions had R2 values of less than 0, indicating that a straight line through the average would
provide a better fit than that of the model, leaving 751 transitions for analysis. As an example,
15
Confidential manuscript submitted to Water Resource Research
490
491
the first freeze-thaw event from Station 19 for the fall of 2013 (starting October 28th and ending
October 31st, 2013) can be seen on Figure 7.
492
a
b
493
499
500
Figure 7: Sample data from Kenaston Network station 19 during the first freeze-thaw
event of 2013. Soil permittivity for freezing (blue) and thawing (red) transition measurements as
a function of time (a) and soil temperature (b) from a Cambridge sandy loam sample. The
logistic models fitted on the data were used to estimate the freezing/melting point depression,
𝑇𝑓/𝑚 , and associated temperature dispersion, 𝑠𝑓/𝑚 . These values correspond to cumulative
probabilities of 0.27, 0.50, and 0.73 from the associated logistic distribution. We interpret these
values as an estimate of the relative frozen soil moisture fraction at a given minimal temperature.
501
502
503
504
505
506
507
508
However, upon visual inspection a number of these were found to be misfits. The most
common cause for these misfits was unexpected behavior in the permittivity measurements
associated with the residual zone of unfrozen state. In particular, rainfall/snow melt events which
did not bring the temperature measurements above 0 °C bifurcated the residual zone of unfrozen
state measurements. In some transitions this zone showed a sloping linear trend. The next most
common cause for misfits was the occurrence of very transient transitions which confounded the
model due to the paucity of measurements and effects of thermal inertia, sometime leading to
event conflation.
509
510
511
512
513
514
515
Conflation of events is also possible due to our need for measurements before and after
the soil temperature crosses 0°C. Measurements have to be added to each freeze-thaw event to
“anchor” the thawed permittivity measurements before the start of the freezing transition and
after the end of the thawing transition. This, however, has proven to be a tricky compromise
between ensuring the permittivity measurement are representative of the thawed water content
and avoiding the conflation of multiple events, particularly for transient transitions. To minimize
the conflation of multiple events only the four preceding and succeeding measurements around
494
495
496
497
498
16
Confidential manuscript submitted to Water Resource Research
516
517
518
519
520
521
522
523
524
525
526
527
528
529
each cycle were added, equivalent to two hours. Although including more peripheral
measurements to each transition leads to the more conflation of events, this type of analysis can
be useful for assessing the infiltration of the melting snowpack. Less prevalent causes for misfits
involved transitions with missing data and probe failures. The misfits provided erroneous
estimates of 𝑇𝑓/𝑚 and/or 𝑠, which made them easy to identify as outliers using the standard
interquartile range criterion (IQR), as seen in Figure 8.
We employed the IQR, defined as the difference between the third and first quartiles
(𝐼𝑄𝑅 = 𝑄3 −𝑄1 ), to identify outliers in the data. For freezing transitions, 𝑄1 − 1.5 ⋅ 𝐼𝑄𝑅 =
−1.09 °C for 𝑇𝑓 and 𝑄3 + 1.5 ⋅ 𝐼𝑄𝑅 = 0.63 °C for 𝑠. On the other hand, for thawing transitions,
𝑄1 − 1.5 ⋅ 𝐼𝑄𝑅 = −0.89 °C for 𝑇𝑚 and 𝑄3 + 1.5 ⋅ 𝐼𝑄𝑅 = 0.71 °C for 𝑠. We chose the largest
absolute values (1.09 °C for 𝑇𝑓/𝑚 and 0.71 °C for 𝑠) to define outliers. Of the 751 transitions, 4
(0 Freezing transitions, 4 Thawing transitions) were outside the IQR for 𝑇𝑓/𝑚 , 58 (26 F, 32 T)
transitions were outside the IQR for 𝑠, and 18 (15 F, 3 T) were outside both the 𝑇𝑓/𝑚 and 𝑠 IQR,
for a total of 80 (41 F, 39 T) transitions eliminated from further analysis, leaving 671 transitions.
530
533
Figure 8: Boxplot showing all outliers for the freezing/melting point depression (𝑇𝑓 , 𝑇𝑚 ) and
their spread (𝑠𝑓 , 𝑠𝑚 ) for transitions between 2012 and 2019 with a permittivity range greater than
3.8.
534
535
536
537
538
539
540
541
542
543
Interestingly, the positive outliers for the freezing/melting point depression temperatures
were not misfits. Rather, these are biased measurements similar to those seen in the lab. This bias
is most visible in the thawing transitions, but some freezing transitions exhibit it as well. These
transitions have a short duration and a quick change in temperature in common. In the case of
thawing transitions, we hypothesize the plate attached to the thermistor reaches a temperature
above 0 °C before the front has penetrated the entire sensing volume. On the other hand, for
freezing, we hypothesize that as the front penetrates the soil profile the situation arises in which
the HydraProbe senses a change in the permittivity while the surface area of the plate attached to
the thermistor has not reached a temperature below 0 °C. Compared to the bias seen in the lab
(which underestimated freezing point depression and overestimate melting point depression due
531
532
17
Confidential manuscript submitted to Water Resource Research
544
545
546
547
to lack of thermal insulation) the bias seen in the field data appears to have an overestimation
effect for both the freezing and melting point depression temperatures. The bias in the field
seems subdued for events of longer duration, however we suspect the bias can only be addressed
by accounting for the measurement support of the instrumentation.
548
549
550
From the field data suitable for analysis, we calculated the freezing/melting point
depression for the Kenaston Soil Moisture Network. To exclude obviously biased temperature
measurements, as discussed above, only transitions with 𝑇𝑓/𝑚 values less than or equal to 0°C
were analyzed for a total 526 (268 F, 261 T) transitions. The mean freezing/melting point
depression, 𝑇𝑓/𝑚 , for the 526 transitions was -0.35 ± 0.20 °C, the freezing transition mean was
𝑇𝑓 = 0.41 ± 0.22 °C, and the thawing transitions mean was 𝑇𝑚 = −0.29 ± 0.16 °C. Based on
the instrumental uncertainty and 𝑇𝑓/𝑚 variance with these in situ measurements, we cannot
confirm the SFC/STC hysteresis or associate it with textural composition. The mean and
standard deviation for the freezing and melting point depression estimated for each station can be
seen in Figure 9, along with the network mean and standard deviation.
551
552
553
554
555
556
557
558
559
560
561
562
Figure 9: Mean freezing (blue) and melting (red) point depression estimates with standard
deviation error bars for the Kenaston Network stations analyzed. The mean for all transitions
with a permittivity range greater than 3.8 is shown by the black line (-0.35 °C) with the dashed
line showing the standard deviation (±0.20 °C).
563
5 Conclusions
564
565
566
567
568
In situ monitoring of the soil moisture phase state is of critical importance, however,
there is an inability to interpret soil moisture instrumentation in frozen conditions (Ireson et al.
2013). To address this gap, the instrumental response to freezing/thawing from a widely used soil
moisture probe, the HydraProbe (HP) was characterized using Heat Pulse Probes (HPP). Freezethaw cycles were induced on soil cores from three different agricultural sites (described in Table
18
Confidential manuscript submitted to Water Resource Research
577
1) in a laboratory setting (seen in Figure 1) over a range of soil moisture content levels. All
samples showed a sigmoidal relationship between the soil permittivity with respect to the soil
temperature measurements: examples can be seen in Figures 2 and 4. A temporal correlation was
evident between the order of magnitude increase in heat capacity, decrease in soil relative
permittivity, and the rate of change of the soil temperature. The relationship for freeze-thaw
events in permittivity-temperature space was identified as the SFC/STC and fit using a logistic
growth model (Equation 5). This allowed us to estimate the soil moisture freezing/melting point
depression (𝑇𝑓/𝑚 ), its temperature spread (𝑠), and assess the degree to which the soil is frozen for
a particular sample/location.
578
579
580
581
582
583
584
585
586
587
588
589
Laboratory results showed the model requires a change in permittivity greater than 3.8 to
provide robust estimates, as seen in Figure 5, and suggested a temperature bias can be induced in
the HydraProbe, as seen in Figure 6. This bias is believed to stem the low thermal inertia of the
insulating sand in combination with the HP’s measurement support. The HP provides a bulk soil
permittivity for a cylindrical soil volume and an average surface temperature of the soil in
contact with the probe’s metal plate. Thus, the difficulties in accurately measuring temperature
are associated with the time required to achieve uniform temperature within the bulk soil
specimen as well as the resolution and precision of the temperature sensor. Since this was not
achieved, the measured temperature was influenced by the temperature of the insulating sand
surrounding the sensor. Therefore, during this period, the reliable measurement of unfrozen
water content is difficult, since an equilibrium condition is not fully established. We suspect the
bias can be partially addressed by accounting for HP’s measurement region.
590
591
592
593
594
595
596
597
600
601
The method was adapted and applied to field measurements collected over the last seven
years from ECCC’s Kenaston soil moisture network in Saskatchewan, Canada (Tetlock et al.
2019). By thoughtfully dividing the permittivity-temperature time series into possible freezethaw cycles and then into individual transitions, see Figure 3, the permittivity SFC/STC were
identified in a majority of events meeting the required change in permittivity, see Figures 7 and
8. Again, the reliable measurement of unfrozen water content was difficult for events in which an
equilibrium condition was not fully established. Lastly, after culling these unreliable events, the
mean freezing/melting point depression for the network was estimated as 𝑇𝑓/𝑚 = −0.35 ±
0.20. Individually 𝑇𝑓 = −0.41 ± 0.22 °C and 𝑇𝑚 = −0.29 ± 0.16 °C respectively; station
means can be seen in Figure 9. Based on the instrumental uncertainty and 𝑇𝑓/𝑚 variance with
these in situ measurements, we cannot confirm the SFC/STC hysteresis or associate it with
textural composition.
602
603
604
605
606
607
608
609
610
611
612
Although soil permittivity probes are sensitive to soil moisture phase changes,
temperature or permittivity measurements alone do not provide enough information to
characterize soil moisture freeze-thaw events. Even though temperature is the primary factor
driving soil moisture phase changes, it is a proxy measurement that alone cannot provide a
precise description of the soil F/T state. On the other hand, while permittivity is a more direct
measurement of the soil F/T state, it is not uniquely dependent on the phase state of the soil. It is
imperative to consider the temperature dependence of changes in permittivity to begin to
disentangle the cause of these changes. The methodology developed does just that, opening up
the possibility of assessing how frozen the ground is using only in-situ measurements, allowing
us to cast aside the limitations associated with binary classification, while also providing
estimates of the freezing/melting point depression and its temperature dispersion. The model was
569
570
571
572
573
574
575
576
598
599
19
Confidential manuscript submitted to Water Resource Research
613
614
applicable to lab-based soil core measurements as well as field data, showing promise in
different spatio-temporal scales and soil types.
615
616
617
618
619
620
621
622
623
624
As noted by Painter et al. (2016), “while reduced dimensionality and simplified
representations of freeze/thaw dynamics in soils are appropriate for studies focusing on larger
scales, more detailed models have an important role to play in building confidence in the
approximations required for coarser scale models, as well as in exploring basic science questions
about permafrost dynamics in a changing climate.” Soil freeze-thaw experiments, such as this
one, can establish the link to physically based representations of the partitioning among liquid,
ice, and gas in freezing unsaturated soils. The method developed here can yield event- and sitespecific permittivity SFC or STC. For instance, this granularity opens up the possibility of
assessing the temporal transferability of SFC/STCs, which to our knowledge has not been
addressed.
625
626
627
628
629
630
631
632
633
It is anticipated that the method described will allow for the characterization of in situ
soil moisture freeze-thaw events for detection at various scales for remote sensing, land surface
analysis, and climate model validation. This unique relationship between the soil permittivity,
temperature, and moisture states possibly offers a pathway for improved near-surface
freeze/thaw detection in the near future as well as a tool to help predict the risk and severity of
potentially catastrophic events. Future work on the method includes refining the possible F/T
event identification and fitting algorithms to more cleanly isolate each transition and more
precisely identify the “final” post-thaw permittivity. The scalability of the model parameters
(𝑇𝑓/𝑚 , 𝑠) is under investigation in the spatial, temporal, and frequency dimensions as well.
634
Acknowledgments, Samples, and Data
635
636
637
638
639
640
641
This work was supported by the Global Water Futures Program funded by Canada First
Research Excellence Fund, the Canadian Space Agency, and the Natural Science and
Engineering Research Council (NSERC) of Canada’s FloodNET and Post-Graduate Scholarship
programs. Laboratory and field data supporting the conclusions will be found in the Polar Data
Catalogue (PDC) metadata and data repository upon publication. Special thanks to Jaison
Ambadan, Alex Mavrovic, Sandy McLaren, Sean Jordan, Daniel Newman, Natalie Dale, Olivia
Kaminski, Megan Cowan, and Beth Van Rys.
642
643
644
645
646
647
648
649
650
20
Confidential manuscript submitted to Water Resource Research
651
References
652
653
654
655
Anderson, D., and N. Morgenstern. 1973. “Physics, Chemistry and Mechanics of Frozen
Ground: A Review.” National Academy of Sciences,~North American
Contribution,~Yakutsk, USSR,~in: Proceedings of 2nd International Conference on
Permafrost, 257–88.
656
657
658
Anderson, Duwayne M. 1973. “Unfrozen Water and the Apparent Specific Heat.” In North
American Contribution to the Second International Conference on Permafrost, 289–95.
https://doi.org/10.3389/fncel.2014.00442.
659
660
661
Bai, Ruiqiang, Yuanming Lai, Mingyi Zhang, and Fan Yu. 2018. “Theory and Application of a
Novel Soil Freezing Characteristic Curve.” Applied Thermal Engineering 129: 1106–14.
https://doi.org/10.1016/j.applthermaleng.2017.10.121.
662
663
664
Black, Patrick B., and Allen R. Tice. 1989. “Comparison of Soil Freezing Curve and Soil Water
Curve Data for Windsor Sandy Loam.” Water Resources Research 25 (10): 2205–10.
https://doi.org/10.1029/WR025i010p02205.
665
666
Bloschl, G, and M Sivapalan. 1995. “Scale Issues In Hydrological Modelling: A Review.”
Hydrological Processes 9 (February 1994): 251–90.
667
668
Bouyoucos, George J., and M. M. McCool. 1916. “Further Studies on the Freezing Point
Lowering of Soils.” East Lansing, Michigan.
669
670
671
Bristow, Keith L., Gerard J. Kluitenberg, and Robert Horton. 1994. “Measurement of Soil
Thermal Properties with a Dual-Probe Heat-Pulse Technique.” Soil Science Society of
America Journal 58 (5): 1288. https://doi.org/10.2136/sssaj1994.03615995005800050002x.
672
673
674
Brunner, Philip, and Craig T. Simmons. 2012. “HydroGeoSphere: A Fully Integrated, Physically
Based Hydrological Model.” Ground Water 50 (2): 170–76. https://doi.org/10.1111/j.17456584.2011.00882.x.
675
676
677
678
Cheng, Q., Y. Sun, S. B. Jones, V. I. Vasilyev, V. V. Popov, G. Wang, and L. Zheng. 2014. “In
Situ Measured and Simulated Seasonal Freeze-Thaw Cycle: A 2-Year Comparative Study
between Layered and Homogeneous Field Soil Profiles.” Journal of Hydrology 519 (PB):
1466–73. https://doi.org/10.1016/j.jhydrol.2014.09.023.
679
680
681
682
Cheng, Qiang, Yurui Sun, Xuzhang Xue, and Jia Guo. 2014. “In Situ Determination of Soil
Freezing Characteristics for Estimation of Soil Moisture Characteristics Using a Dielectric
Tube Sensor.” Soil Science Society of America Journal 78 (1): 133–38.
https://doi.org/10.2136/sssaj2013.03.0120n.
683
684
685
686
Daanen, Ronald P, Debasmita Misra, and Anita M Thompson. 2011. “Frozen Soil Hydrology.”
In Encyclopedia of Snow, Ice and Glaciers, edited by Vijay P Singh, Pratap Singh, and
Umesh K Haritashya, 306–11. Dordrecht: Springer Netherlands.
https://doi.org/10.1007/978-90-481-2642-2_171.
687
688
Ducharne, A. 2017. “The Hydrol Module of ORCHIDEE : Scientific Documentation [ Rev 3977
] and on , Work in Progress !!,” 1–39.
689
690
Fredlund, D G, and A Xing. 1994. “Reproduced with Permission From.” Canadian Geotechnical
Journal 31 (3): 521–32.
21
Confidential manuscript submitted to Water Resource Research
691
692
693
Fuchs, M., G. S. Campbell, and R. I. Papendick. 1978. “An Analysis of Sensible and Latent Heat
Flow in a Partially Frozen Unsaturated Soil.” Soil Science Society of America Journal 42
(3): 379. https://doi.org/10.2136/sssaj1978.03615995004200030001x.
694
695
696
Garnaud, Camille, Stéphane Bélair, Aaron Berg, and Tracy Rowlandson. 2016. “Hyperresolution
Land Surface Modeling in the Context of SMAP Cal–Val.” Journal of Hydrometeorology
17 (1): 345–52. https://doi.org/10.1175/JHM-D-15-0070.1.
697
698
699
Genuchten, M. Th. van. 1980. “A Closed-Form Equation for Predicting the Hydraulic
Conductivity of Unsaturated Soils1.” Soil Science Society of America Journal 44 (5): 892.
https://doi.org/10.2136/sssaj1980.03615995004400050002x.
700
701
Gilpin, R R. 1980. “A Model for the Prediction of Ice Lensing and Frost Heave in Soils.” Water
Resources Research 16 (5): 918–30.
702
703
704
Gray, D. M., Brenda Toth, Litong Zhao, J. W. Pomeroy, and R. J. Granger. 2001. “Estimating
Areal Snowmelt Infiltration into Frozen Soils.” Hydrological Processes 15 (16): 3095–
3111. https://doi.org/10.1002/hyp.320.
705
706
707
708
709
He, Hailong, Miles Dyck, Ying Zhao, Bingcheng Si, Huijun Jin, Tingjun Zhang, Jialong Lv, and
Jinxing Wang. 2016. “Evaluation of Five Composite Dielectric Mixing Models for
Understanding Relationships between Effective Permittivity and Unfrozen Water Content.”
Cold Regions Science and Technology 130 (July): 33–42.
https://doi.org/10.1016/j.coldregions.2016.07.006.
710
711
712
Hogarth, W. L., J. Hopmans, J. Y. Parlange, and R. Haverkamp. 1988. “Application of a Simple
Soil-Water Hysteresis Model.” Journal of Hydrology 98 (1–2): 21–29.
https://doi.org/10.1016/0022-1694(88)90203-X.
713
714
715
716
Ireson, A. M., G. van der Kamp, G. Ferguson, U. Nachshon, and H. S. Wheater. 2013.
“Hydrogeological Processes in Seasonally Frozen Northern Latitudes: Understanding, Gaps
and Challenges.” Hydrogeology Journal 21 (1): 53–66. https://doi.org/10.1007/s10040-0120916-5.
717
718
719
Kelleners, T. J., and J. B. Norton. 2012. “Determining Water Retention in Seasonally Frozen
Soils Using Hydra Impedance Sensors.” Soil Science Society of America Journal 76 (1):
36–50. https://doi.org/10.2136/sssaj.
720
721
722
Koopmans, R W R, and R D Miller. 1966. “Soil Freezing and Soil Water Characteristic Curves.”
Soil Science Society of America Journal 30 (6): 680–85.
http://dx.doi.org/10.2136/sssaj1966.03615995003000060011x.
723
724
725
Lawrence, David, Rosie Fisher, Charles Koven, Keith Oleson, Sean Swenson, and Mariana
Vertenstein. 2018. “CLM5 Documentation,” 309.
http://www.cesm.ucar.edu/models/cesm2/land/CLM50_Tech_Note.pdf.
726
727
728
Liu, Zhen, and Xiong (Bill) Yu. 2013. “Physically Based Equation for Phase Composition Curve
of Frozen Soils.” Transportation Research Record: Journal of the Transportation Research
Board 2349 (1): 93–99. https://doi.org/10.3141/2349-11.
729
730
731
McColl, Kaighin A., Alexandre Roy, Chris Derksen, Alexandra G. Konings, Seyed Hamed
Alemohammed, and Dara Entekhabi. 2016. “Triple Collocation for Binary and Categorical
Variables: Application to Validating Landscape Freeze/Thaw Retrievals.” Remote Sensing
22
Confidential manuscript submitted to Water Resource Research
732
of Environment 176 (Complete): 31–42. https://doi.org/10.1016/j.rse.2016.01.010.
733
734
735
736
Mironov, V., and I. Savin. 2016. “Temperature-Dependent Spectroscopic Dielectric Model at
0.05-16 GHz for a Thawed and Frozen Alaskan Organic Soil.” Satellite Soil Moisture
Retrieval: Techniques and Applications 83–84: 169–86. https://doi.org/10.1016/B978-0-12803388-3.00009-7.
737
738
Mousson, A. 1858. “Einige Thatsachen Betreffend Das Schmelzen Und Gefrieren Des Wassers.”
Annalen Der Physik Und Chemie 10: 161–74.
739
740
741
Ochsner, Tyson E., and John M. Baker. 2008. “In Situ Monitoring of Soil Thermal Properties
and Heat Flux during Freezing and Thawing.” Soil Science Society of America Journal 72
(4): 1025. https://doi.org/10.2136/sssaj2007.0283.
742
743
744
745
Painter, Scott L., Ethan T. Coon, Adam L. Atchley, Markus Berndt, Rao Garimella, J. David
Moulton, Daniil Svyatskiy, and Cathy J. Wilson. 2016. “Integrated Surface/Subsurface
Permafrost Thermal Hydrology: Model Formulation and Proof-of-Concept Simulations.”
Water Resources Research 52 (8): 6062–77. https://doi.org/10.1002/2015WR018427.
746
747
748
Petit, A. 1893. “Untersuchungen Über Den Einfluß Des Frostes Auf Die Temperaturverhältnisse
Der Böden von Verschiedener Physikalischer Beschaffenheit.” Forschungen AgikulturPhysik XVI: 285–310.
749
750
751
Podest, E, K.C. McDonald, and J.S. Kimball. 2014. “Multi Sensor Microwave Sensitivity to
Freeze Thaw Dynamics across a Complex Boreal Landscape.” IEEE Transactions on
Geoscience and Remote Sensing (In-press) (11): 6818–28.
752
753
754
755
Rautiainen, Kimmo, Juha Lemmetyinen, Mike Schwank, Anna Kontu, Cécile B Ménard,
Christian Mätzler, Matthias Drusch, et al. 2014. “Detection of Soil Freezing from L-Band
Passive Microwave Observations.” Remote Sensing of Environment 147: 206–18.
https://doi.org/http://dx.doi.org/10.1016/j.rse.2014.03.007.
756
757
758
Ren, Junping, and Sai K Vanapalli. 2019. “Comparison of Soil-Freezing and Soil-Water
Characteristic Curves of Two Canadian Soils,” no. April.
https://doi.org/10.2136/vzj2018.10.0185.
759
760
761
Ren, Junping, Sai K Vanapalli, and Zhong Han. 2017. “Soil Freezing Process and Different
Expressions for the Soil-Freezing Characteristic Curve,” no. March 2018.
https://doi.org/10.3724/SP.J.1226.2017.00221.
762
763
764
Roth, Kurt, and Julia Boike. 2001. “Quantifying the Thermal Dynamics of a Permafrost Site near
Ny-Alesund, Svalbard.” Water Resources Research 37 (12): 2901–14.
https://doi.org/10.1029/2000WR000163.
765
766
767
768
Rowlandson, Tracy L., Aaron A. Berg, Paul R. Bullock, E. Ro Timi Ojo, Heather McNairn,
Grant Wiseman, and Michael H. Cosh. 2013. “Evaluation of Several Calibration Procedures
for a Portable Soil Moisture Sensor.” Journal of Hydrology 498: 335–44.
https://doi.org/10.1016/j.jhydrol.2013.05.021.
769
770
771
772
Rowlandson, Tracy L., Alexandre Roy, Aaron A Berg, Edward Kim, Renato Pardo Lara, Jarrett
Powers, Kristin Lewis, et al. n.d. “Capturing Agricultural Soil Freeze/Thaw State through
Remote Sensing and Ground Observations: A Soil Freeze/Thaw Validation Campaign.”
Remote Sensing of Environment.
23
Confidential manuscript submitted to Water Resource Research
773
774
775
776
Roy, A, A Royer, C Derksen, L Brucker, A Langlois, A Mialon, and Y H Kerr. 2015.
“Evaluation of Spaceborne L-Band Radiometer Measurements for Terrestrial Freeze/Thaw
Retrievals in Canada.” IEEE Journal of Selected Topics in Applied Earth Observations and
Remote Sensing 8 (9): 4442–59. https://doi.org/10.1109/JSTARS.2015.2476358.
777
778
779
Seyfried, M. S., L. E. Grant, E. Du, and K. Humes. 2005. “Dielectric Loss and Calibration of the
Hydra Probe Soil Water Sensor.” Vadose Zone Journal 4 (4): 1070.
https://doi.org/10.2136/vzj2004.0148.
780
Stevens Water Monitoring Systems, Inc. 2015. “The Hydra Probe ® Soil Sensor.”
781
782
783
784
Sun, Y., Q. Cheng, X. Xue, L. Fu, J. Chai, F. Meng, P. Schulze Lammers, and S. B. Jones. 2012.
“Determining In-Situ Soil Freeze-Thaw Cycle Dynamics Using an Access Tube-Based
Dielectric Sensor.” Geoderma 189–190: 321–27.
https://doi.org/10.1016/j.geoderma.2012.06.016.
785
786
787
788
Tetlock, Erica, Brenda Toth, Aaron Berg, Tracy Rowlandson, and Jaison Ambadan-Thomas.
2019. “An 11-Yr (2007-2017) Soil Moisture and Precipitation Dataset from the Kenaston
Network in the Brightwater Creek Basin, Saskatchewan, Canada.” Earth System Science
Data Discussions, no. June: 787–96. https://doi.org/10.5194/essd-2018-122.
789
790
791
Tian, Huihui, Changfu Wei, Yuanming Lai, and Pan Chen. 2018. “Quantification of Water
Content Durinfreeze–Thaw Cycles: A Nuclear Magnetic Resonance Based Method.”
Vadose Zone Journal 17 (1). https://doi.org/10.2136/vzj2016.12.0124.
792
793
794
795
Tian, Huihui, Changfu Wei, Houzhen Wei, and Jiazuo Zhou. 2014. “Freezing and Thawing
Characteristics of Frozen Soils: Bound Water Content and Hysteresis Phenomenon.” Cold
Regions Science and Technology 103: 74–81.
https://doi.org/10.1016/j.coldregions.2014.03.007.
796
797
798
Topp, G. C., James L. Davis, and A. P. Annan. 1980. “Electromagnetic Determination of Soil
Water Content: Measurements in Coaxial Transmission Lines.” Water Resources Research
16 (3): 574–82.
799
800
801
802
Wagner-riddle, Claudia, Katelyn A. Congreves, Diego Abalos, Aaron A. Berg, Shannon E.
Brown, Jaison Thomas Ambadan, Xiaopeng Gao, and Mario Tenuta. 2017. “Globally
Important Nitrous Oxide Emissions from Croplands Induced by Freeze-Thaw Cycles.”
Nature Geosci advance on (March). https://doi.org/10.1038/ngeo2907.
803
804
805
Watanabe, Kunio, and Masaru Mizoguchi. 2002. “Amount of Unfrozen Water in Frozen Porous
Media Saturated with Solution.” Cold Regions Science and Technology 34 (2): 103–10.
https://doi.org/10.1016/S0165-232X(01)00063-5.
806
807
808
809
Wen, Zhi, Wei Ma, Wenjie Feng, Yousheng Deng, Dayan Wang, Zhaosheng Fan, and Chenglin
Zhou. 2012. “Experimental Study on Unfrozen Water Content and Soil Matric Potential of
Qinghai-Tibetan Silty Clay.” Environmental Earth Sciences 66 (5): 1467–76.
https://doi.org/10.1007/s12665-011-1386-0.
810
811
Western, Andrew W., and Günter Blöschl. 1999. “On the Spatial Scaling of Soil Moisture.”
Journal of Hydrology 217 (3–4): 203–24. https://doi.org/10.1016/S0022-1694(98)00232-7.
812
813
Williams, Peter J. 1964. “Experimental Determination of Apparent Specific.” Geotechnique 14
(2): 133–42.
24
Confidential manuscript submitted to Water Resource Research
814
815
816
817
Yoshikawa, Kenji, and Pier Paul Overduin. 2005. “Comparing Unfrozen Water Content
Measurements of Frozen Soil Using Recently Developed Commercial Sensors.” Cold
Regions Science and Technology 42 (3): 250–56.
https://doi.org/10.1016/j.coldregions.2005.03.001.
818
819
820
821
Zhang, Lixin, Tianjie Zhao, Lingmei Jiang, and Shaojie Zhao. 2010. “Estimate of Phase
Transition Water Content in Freeze&#x2013;Thaw Process Using Microwave Radiometer.”
IEEE Transactions on Geoscience and Remote Sensing 48 (12): 4248–55.
https://doi.org/10.1109/TGRS.2010.2051158.
822
823
824
825
Zhao, Tianjie, Jiancheng Shi, Tongxi Hu, Lin Zhao, Defu Zou, Tianxing Wang, Dabin Ji, Rui Li,
and Pingkai Wang. 2017. “Estimation of High-Resolution near-Surface Freeze/Thaw State
by the Integration of Microwave and Thermal Infrared Remote Sensing Data on the Tibetan
Plateau.” Earth and Space Science, 1–13. https://doi.org/10.1002/2017EA000277.
826
827
828
829
Zhou, Yang, Jian Zhou, Xiang you Shi, and Guo qing Zhou. 2019. “Practical Models Describing
Hysteresis Behavior of Unfrozen Water in Frozen Soil Based on Similarity Analysis.” Cold
Regions Science and Technology 157 (February 2018): 215–23.
https://doi.org/10.1016/j.coldregions.2018.11.002.
830
25