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WATER, HEAT AND SOLUTE
PROCESSES IN SEASONALLY
FROZEN SOILS—EXPERIMENTAL
AND MODELING STUDY
MOUSONG WU
April 2015
TRITA-LWR LIC 2015:01
ISSN 1650-8629
ISRN KTH/LWR/LIC 2015:01-SE
ISBN 978-91-7595-602-2
Mousong Wu
TRITA LWR Lic Thesis 2015:01
© Mousong Wu 2015
Lic thesis
Land and Water Resources Engineering
Department of Sustainable Development, Environmental Science and Engineering
Royal Institute of Technology (KTH)
SE-100 44 STOCKHOLM, Sweden
Reference to this publication should be written as: Wu, M. (2015) “Water, heat and
solute processes in seasonally frozen soils-Experimental and modeling study” TRITA
LWR LIC 2015:01.
ii
Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
A BSTRACT
Soil freezing and thawing is of importance in transport of water, heat and
solute, which has coupled effects. Solute type and solute content in frozen soil
could influence the osmotic potential of frozen soil and decrease freezing
point, resulting in differences in soil freezing characteristic curves under
various solute conditions. Prediction model provides an approach for
estimating soil freezing characteristic curves under various water and solute
conditions based on soil freezing characteristic curve obtained at certain water
and solute conditions. Water, heat and solute transport in seasonally frozen soil
is a coupled process strongly linked to evaporation and energy balance of soil
surface. High solute content and shallow GWTD provide good conditions for
water and solute accumulation in surface layer, which would result in more
evaporation during thawing. Also, high solute content in upper layer would
cause more liquid water to exist in upper layer, which may enhance evaporation
during freezing period. Obvious increase in cumulative evaporation amount
was detected for frost tube experiments, 51.0, 96.6, to 114.0 mm when initial
solute content increased from 0.2%, 0.4%, to 0.6%, and initial GWTD of 1.5
m. Similar trends were observed for other GWTD and solute treatments. Water
and heat transport simulated by the CoupModel combined with GLUE
calibration showed good performances, when constrained by certain criteria.
Uncertainties were investigated using ensemble of modeling results. Simulated
energy partitioning showed intensive oscillations in daily courses during soil
freezing/thawing periods and strongly influenced the stability of energy system
on surface of soil. The study demonstrated the complexity in water, heat and
solute transport in seasonally frozen soil, and the necessity of combining
experimental data with numerical model for better understanding the processes
as well in decision making for irrigation district water resources management.
Keywords: frozen soil; water-heat-solute transport; coupled effects; water
and energy balance; uncertainties
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Mousong Wu
TRITA LWR Lic Thesis 2015:01
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Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
S UMMARY
Nedfrysning och upptining av mark spelar en viktig roll för transport av vatten,
värme samt vattenlösliga ämnen (här hänvisar vi till salter). Fenomenen ärkopplade
till till varandra då exempelvisstyp av salter och concentration i frysna jordar påverkar
den osmotiska potentialen och därmed fryspunkten, vilket skapar skillnader i
återkopplingar till vatten- och värmeflöden Emipiriska modeller kan användas för att
uppskatta fryspunken under olika vatten- och saltförhållanden. Dynamiken hos
vatten, värme och lösta ämnen i säsongsvis fryysen mark regleras av kopplade
processer relaterad till avdunstning och energibalansen av markytan. Högt innehåll av
salter och ytligt grundvatten ger goda förutsättningar för vatten och salter att
ackumuleras i toppskiktet, vilket resulteras i mer avdustning Dessutom kan höga
halter av salter i översta lagret orsaka större mängder av vatten där, vilket i sig ökar
avdustningeh under frysningsperioden. Uppenbar ökning i kumulativ avdunstning
har upptäckts för frost tub experiment, 51,0, 96,6, till 114,0 mm när inledande
saltinnehåll ökade från 0.2%, 0.4%, till 0.6%, och inledande GWTD av 1.5m.
Liknande trender observerades för andra GWTD och salt behandlingar. Transport av
vatten och värme simulerades av CoupModel combinerad med GLUE-ualibrering
gav goda resultat, fer vissa avgränsade kriterier är som. Osäkerheter har undersökts
med hjälp grupper modelleringsresultatet. Simulerad energy partitioning intensiva
oscillationer i dagskurser under markfrysning-eller markupptiningsperioder och starkt
påverkade stabiliteten i energisystem på jordytan. Studien visade komplexiteten i
transport av vatten, värme och salter i säsongsvis fryysen mark , och nödvändigheten
av att kombinera experimentella data meden numerisk modell för bättre förståelse av
processerna och för mer tillförlitliga beslutsfattanden.
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Mousong Wu
TRITA LWR Lic Thesis 2015:01
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Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
摘要
土壤冻融过程对于水热及溶质的运移具有十分重要的影响，并对于寒旱区水文过程的研究有
着深远意义。在冻土中，溶质的种类及溶质含量会对土壤溶质势产生影响，并导致冰点的降
低，进而影响土壤冻结曲线的变化。本研究通过建立含盐冻土冻结曲线的预报模型，有效地
利用一定水盐试验条件下的冻结曲线对未知条件下的冻结曲线进行预测，进而为数值模型实
时根据土壤水盐条件获得准确的液态含水量与温度的关系时提供了可行的方法。冻融土壤中
的水热盐运移过程与地表的水热平衡有着密切联系，进而影响冻融土壤蒸发过程。试验研究
表明，高溶质含量及浅埋深地下水条件为地表的蒸发提供了便利条件，因为高溶质含量土壤
冰点降低，同一负温条件下的液态含水量增大，为蒸发提供了可利用水分；而浅埋深地下水
对冻融期水盐的表聚提供的方便，进而有助于融化期地表水分的大量蒸发及下层土层水分的
大量向上补给。例如，当地下水初始埋深设置在 1.5 m 时，对于初始含盐量分别为 0.2%，0.4%
和 0.6% g/g 的冻融试验组，冻融期累积蒸发量分别为 51.0，96.6 和 114.0 mm。同样的增加趋
势在其它初始地下水埋深设置试验组里也被验证，且初始地下水埋深越浅，累积蒸发量也越
大。CoupModel 与 GLUE 相结合的方法能够有效地根据实测数据对模型进行率定并经过筛
选后得出较好的模拟结果集合。通过对筛选的模拟输出集合的不确定性分析，对模型模拟过
程的不确定性有了很好的了解。模拟的地表能量分配过程显示，地表能量的日变化过程较为
剧烈，并且对地表能量平衡系统的稳定性产生了显著影响。研究通过试验与模拟相结合的方
法，展示了季节性冻融土壤中水热盐耦合运移过程的复杂性，同时也表明利用试验取样与数
值模型相结合的方法研究冻融土壤中水热盐运移过程的必要性，并为高效的水资源管理决策
的制定提供了有效的手段。
关键词：冻土；水热盐运移；耦合关系；水热平衡；不确定性
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Mousong Wu
TRITA LWR Lic Thesis 2015:01
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Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
A CKNOWLEDGMENTS
This research was funded by the China Scholarship Council (CSC) and
Department of Sustainable Development, Environmental Science and
Engineering in KTH. I would like to thank my main supervisor Per-Erik
Jansson (KTH), as well as supervisors Jiesheng Huang (Wuhan University,
China), Klas Hansson (Trafikverket, Sweden), and David Gustafsson (KTH),
for their invaluable support, guidance, discussions, and comments on my work.
Especially, I would like to thank Prof. Per-Erik Jansson, for his patience in
discussing with me and profession in giving me very useful suggestions for
each step of my work. As a supervisor, Per-Erik is more like a friend, and this
kind of relationship made me feel relaxed when I communicated with him
about my research, which helped me find my shortcomings and correct them
quickly to put my work forward.
I also value the discussions and happy experiences with many colleagues in
KTH, Liwen, Alireza, Christine, Liangchao, Junzhi, Hadi, Yuanying and Minyu.
The discussions with them also helped me a lot in improving my
understanding in my research, and also in learning from their research
experiences. I would also like to say ‘thank you’ to my roommates, Wen and
Anqi, for their kindness in helping me to be accustomed to life and study in
Sweden and sharing their experiences with me. Besides, other professors in
KTH also let me learn a lot about their professions in research, especially Prof.
Bo Olofsson, and Prof. Gunno. Even though they did not supervise me in my
research topic, the conversations with them during break time let me broaden
my knowledge in related research areas, and I also admire their passions for
work and life.
I also thank my partners in China, Prof. Jingwei Wu, and Mr. Xiao Tan. Our
collaborations in solving soil salinization in Hetao Irrigation District made my
work much easier and more efficient, and the discussions on the specific topics
always gave me deep insight into my research. Besides, the administrative staff
in KTH helped me a lot in my registration, as well as my adaptation to my
work in KTH. They are Vladimir, Magnus, Aira, and Britt. Thank them for
their patience in dealing with my problems and giving a lot of useful
suggestions for my work here. Finally, I would like to thank my family and
friends for their companion as well as support in my choice of studying in
KTH, which gave me motivation each time when I felt hopeless.
Mousong Wu
Stockholm
2015
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Mousong Wu
TRITA LWR Lic Thesis 2015:01
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Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
L IST
OF PAPERS
This thesis is based on the following papers, which are referred to in the text
by their Roman numerals.
Papers included in the thesis:
I.
Wu, M., Tan, X., Huang, J., Wu, J., Jansson, P.-E., 2015. Solute and water
effects on soil freezing characteristics based on laboratory experiments.
Cold Regions Science and Technology, 115(2015): 22-29.
II.
Wu, M., Huang, J., Wu, J., Tan, X., Jansson, P.-E., 2015. Experimental
study on evaporation from seasonally frozen soils under various water,
solute and groundwater conditions in Inner Mongolia, China, 2015.
Journal of Hydrology (under revision).
III.
Wu, M., Jansson, P.-E., Tan, X., Wu, J., Huang, J., 2015. Simulations of
water and heat dynamics in a seasonally frozen soil using field data to
improve understanding, 2015. European Journal of Soil Science (under
review).
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TRITA LWR Lic Thesis 2015:01
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Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
TABLE
OF CONTENT
Abstract ...................................................................................................................................................... iii
Summary ...................................................................................................................................................... v
摘要 ............................................................................................................................................................ vii
Acknowledgments ......................................................................................................................................ix
List of papers..............................................................................................................................................xi
Table of content ...................................................................................................................................... xiii
1.
Introduction...................................................................................................................................... 1
1.1
2.
Material and methods ...................................................................................................................... 3
2.1
Study area description (Paper I, II, III) .................................................................................. 3
2.2
Soil freezing experiments setup (Paper I) ............................................................................... 4
2.3
2.4
3.
2.2.1
Freezing test ....................................................................................................................... 4
2.2.2
SFCC prediction model ...................................................................................................... 4
Field experiments on water, heat and solute transport in seasonally frozen soil (Paper II) 5
2.3.1
Experimental design ........................................................................................................... 5
2.3.2
Estimation of evaporation from frost tubes ....................................................................... 6
Modeling of water and energy balance for seasonally frozen soil (Paper III) ...................... 6
Results............................................................................................................................................... 7
3.1
SFCC with various solute types and solute content levels (Paper I)...................................... 7
3.2
Water, heat, and solute transport in frozen soil (Paper II) ..................................................... 8
3.3
4.
5.
6.
Objectives .................................................................................................................................. 2
3.2.1
Precipitation, frost depth, and air temperature .................................................................... 8
3.2.2
Water, heat and solute dynamics in field and frost tubes ..................................................... 8
Simulation of water and heat dynamics (Paper III) ............................................................... 9
Discussion ...................................................................................................................................... 11
4.1
Water and solute effects on SFCC (Paper I) ........................................................................... 11
4.2
Evaporation in frozen soil with various conditions (Paper II) ............................................. 13
4.3
Seasonal course for simulated energy balance in frozen soil (Paper III) ............................ 14
Conclusions .................................................................................................................................... 16
References ...................................................................................................................................... 16
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Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
1. I NTRODUCTION
Soil freezing and thawing is a complicated process, coupling water, heat and
solute transport. Water movement in frozen soils plays a significant role in
agricultural and engineering activities in cold regions, e.g., in predicting frost
heave (Konrad and Morgenstern, 1980), in investigating water and solutes
transport and redistributions in cold periods (Baker and Spaans, 1997), as well
as in waste disposal using artificial ground freezing (McCauley et al., 2002).
The study of frozen soil could descend from 1930s, when Taber (1930) and
Beskow (1947) observed the movement of water toward frozen layer. Then
this phenomenon was explained by Everett (1961) from the perspective of
capillary force theory. Besides, a series of experimental studies have been
conducted to investigate the movement of water in freezing soil column
(Dirksen and Miller, 1966; Hoekstra and Miller, 1967; Nakano et al., 1982;
Nakano and Tice, 1987; Perfect and Williams, 1980; Konrad and Morgenstern,
1981). Results of these studies indicated that, water potential and temperature
gradients could drive water to move from unfrozen layer to frozen layer. Solute
in soil moved mainly with water by convection, thus the transport of solute in
frozen soil was also influenced by water and heat transport. Besides, Cary et al.
(1979) pointed out that the accumulation of solute in frozen front could also
influence the transport of water and heat by decreasing osmotic potential of
soil. Solute movement in frozen soil could be governed by soil type, soil water
content, solute concentration and solute type, as well as thermal conditions
during soil freezing (Baker and Osterkamp, 1989). Low et al. (1968) and Banin
and Anderson (1974) provided some thermodynamic relationships between
soil freezing point and solute concentration. Baker and Osterkamp (1989)
observed significant redistribution of solute in freezing soil column and also
solute rejection in freezing front.
Experiments on hydraulic properties of frozen soil have been conducted by
many. However, due to the complexity of frozen soil with existence of ice and
phase transition, the determination of hydraulic and thermal properties has
become a major challenge in quantifying water, heat and solute transport in
frozen soil (Flerchinger et al., 2006). Soil freezing characteristic curve was
determined by many and compared with soil water retention curve in unfrozen
condition by using Clausius-Clapeyron equation (Koopmans and Miller, 1966;
Spaans and Baker, 1996; Bittelli et al., 2003). Also, the hydraulic conductivity of
frozen soil was measured at low temperature ranges (Burt and Williams, 1976;
McCauley et al., 2002). Watanabe and Flury (2008) used capillary bundle to
construct the relationship between hydraulic conductivity and soil temperature
in frozen condition. Lebeau and Konrad (2012) also combined capillary and
thin film flow model to determine hydraulic conductivity in air-free frozen soil.
The introduction of computers during the 1970s made it possible to simulate
soil freezing/thawing processes. Harlan (1973) first introduced a coupled
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Mousong Wu
TRITA LWR Lic Thesis 2015:01
model for water and heat transport in frozen soil, and then Guymon and
Luthin (1974) developed it. But the influences of solute were not considered.
Cary and Mayland (1972) and Fuchs et al. (1978) added the osmotic effects in
their models when simulating soil freezing/thawing processes. More recently,
numerical models were set up by many for specific purposes, such as the
SHAW model (Flerchinger and Saxton, 1989; Flerchinger et al., 1996), the
SOIL model (Halldin, 1979), the CoupModel (Jansson and Karlberg, 2004),
and HYDRUS-1D model soil freezing tutorial (Hansson et al., 2004). All these
models made it possible to consider complicated water, heat and solute (for
some models) transport in frozen soil.
In China, as the third largest country with frozen soil, the seasonally frozen soil
occupies 53.5% of the land, mainly in regions with latitude larger than 30o.
Most of the regions with seasonally frozen soil are places with arid and
semi-arid climate and have problems in water resources. In Hetao Irrigation
District, located in Inner Mongolia, China, the agricultural field is frozen for
more than half time of the year. Due to the upward movement of saline
groundwater during freezing periods, large amount of solute accumulate to the
surface layer, resulting in soil salinization in this region. This has become
another cause for soil salinization except for the high evaporation
accompanying low precipitation. The major solution for this solute
accumulation during soil freezing and thawing periods in that region is to
increase the amount of irrigation water to leach solute from soil as well as
from groundwater in autumn, before soil freezing. The autumn irrigation in
this region has two aims: one is to leaching solute; the other is to store water in
soil for sowing in next spring. However, unreasonable irrigation practices in
this region actually do not reach the expectation for controlling soil salinization,
sometimes make it worse. For example, too much irrigation water would cause
more water loss for evaporation during thawing periods and thus cause solute
accumulation in upper layer. Besides, poor drainage system in this region
makes it difficult to drain solute rapidly from field before freezing, and will
cause significant increase in groundwater level. Higher groundwater level
would supply better source during soil freezing, and cause water solute
accumulation in upper frozen layer. Thus, reasonable irrigation and drainage
system is of importance in this region for controlling soil salinization as well as
for development of water-saving agriculture.
1.1
Objectives
In this thesis, the goal is to investigate the coupled effects of water, heat and
solute in seasonally frozen soil, based on experimental work (Paper I, II) and
numerical model tool (Paper III), as described in Fig. 1.
In Paper I, the influences of solute type and solute content on soil freezing
were investigated based on laboratory experiments, and a prediction model for
soil freezing characteristic in saline frozen soil was setup.
In Paper II, field study of dynamics in water, heat and solute transport was
2
Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
conducted in Inner Mongolia, and the effects of solute and groundwater on
soil evaporation during freezing/thawing periods were addressed.
In Paper III, modeling work for water and energy balance was conducted
accompanying uncertainty analysis, to discuss the influences of seasonal
courses on water and heat dynamics by the merging of data and using various
criteria to investigate how the performance of the model can be understood.
Fig. 1 Scheme for work in study of water, heat and solute transport in frozen soil.
2. M ATERIAL
2.1
AND METHODS
Study area description (Paper I, II, III)
The study site is located at Yichang Experimental Station, Hetao Irrigation
District, Inner Mongolia, China (40°12′ N, 108°08′ E), which is a typical Yellow
River irrigated district. It is also a typical salinization affected district in
Northern China Plain, due to high evaporation (yearly around 2000 mm) and
low precipitation (yearly around 200 mm). Every year after crop harvest,
irrigation is conducted in late autumn, to leach salt from root zone and to store
water in frozen soil for plants utility in next spring. The agricultural field covers
an area of 20 ha, and is cultivated with sunflowers from May to early October
every year, equipped with drainage ditches and irrigation canals.
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Mousong Wu
TRITA LWR Lic Thesis 2015:01
2.2 Soil freezing experiments setup (Paper I)
2.2.1Freezing test
Soil sample for this study was dug from the depths of 0- to 40-cm in
experimental site, and classified as silt loam. Soil was air-dried and diluted by
using deionized water to salt mass content below 0.1%, then sieved by 2-mm
sieve. Soil sample was then put into plastic bags and stored in an incubator
with temperature of 5 oC for experiments.
The adapted TDR combining PT100 temperature sensors were used in the
laboratory experiments, to detect soil freezing characteristic curves (SFCCs)
under five types of solute (NaCl, KCl, CaCl2, MgSO4, and MgCl2) combining
five solute content levels (with 0.1%, 0.3%, 0.5%, 0.7%, and 1.0% g solute
contained in per g of dry soil), when initial water content was set to be 30%
cm3/cm3. CK was also set for testing SFCC with the soil sample without
adding solute. Besides, four initial water content levels were set, i.e. 15%, 20%,
25%, and 30% in volumetric water content, with one repetition for each, to
investigate water content effects on soil freezing characteristic curves.
Freezing tests were conducted in a freezing cell, which could control
temperature with accuracy of 0.1 oC. Unfrozen water content and temperature
were collected with data-loggers in 4-hr intervals, and temperature of freezing
cell was stepped from 0 to -25 oC during freezing test. To detect the phase
transition around freezing point carefully, temperature interval was set as 1 oC
from 0 to -5 oC, and then set as 2 oC between -5 to -25 oC. Due to the limited
precision of probes and the fast phase transition between 0 and -1 oC, this test
procedure might not capture the SFCC nature well between this temperature
zone. Thus the obtained data mainly had temperature ranging from -1 to -25
o
C.
2.2.2 SFCC prediction model
A seven-step prediction model was set up for predicting SFCC using
experimental data: (i) use the known relationship to calculate freezing points of
soil with initial water content of
and
,
and
, respectively; (ii)
calculate the freezing point depression due to initial water content decreasing
from
to
due to salt,
,
; (iii) calculate freezing point depression
; (iv) calculate the total freezing point depression,
; (v) calculate liquid water content under temperature
; (vi) calculate modified factor for slope of SFCC,
calculate the parameters of SFCC for soil with initial water content of
4
,
; (vii)
and
Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
salt concentration of
,
,
.
2.3 Field experiments on water, heat and solute transport in seasonally
frozen soil (Paper II)
2.3.1Experimental design
The experiments were conducted in the Yonglian Experimental Station
between 1, December, 2012 and 30, April, 2013. Fig. 2 depicts the experiments
conducted at the experimental site, and the site covered an area of 20 ha, with
agricultural field (western part) and micro experimental zones (eastern part).
Experiments in frost tubes were conducted in micro experimental zones, and
treatments with three GWTD levels (W1−W3, at 2.0 m, 1.5 m, 1.0 m,
respectively) combining three solute content levels (S1−S3, at 0.2%, 0.4%,
0.6%, respectively, in g/g dry soil) were designed in frost tubes (5 cm in
diameter and 3 m in depth), each with six duplicates for sampling at different
timings (every 25 days). The six sampling timings also divided the whole
freezing/thawing processes into 5 periods (P1-P5).
The soil below the pre-set water table was saturated with non-saline water, soil
water and solute content above water table were controlled by adding
pre-dissolved NaCl solution to the air-dry soil, and then packed into the tubes
with 5 cm depth for each time to obtain initial water content of 0.30 cm3/cm3
and bulk density of 1.50 g/cm3, representing the typical field capacity and bulk
density in this region. After being filled with soil, the sides of frost tubes were
covered with insulation cotton of 1.5 cm in thickness. Sampling in three frost
tube experiments was conducted with interval of twenty-five days at six
timings by splitting the tubes and digging the soil out with shovel.
Fig. 2 Design of field experiments on water, heat and solute transport in frozen
soil under various water and solute conditions (Paper II).
5
Mousong Wu
TRITA LWR Lic Thesis 2015:01
2.3.2
Estimation of evaporation from frost tubes
The water balance method was used to estimate the evaporation from the
frozen soils. The water mass in the whole tube (Mi) was determined by the
water content of each soil layer at each sampling date by adding the water
content of each layer (θij):
n
M i = ∑ Af θij h j
j =1
(1)
where i is the sampling time (i=1, 2,…, 6); j is the soil layer (j=1, 2,…, n); n is
the total number of soil layers (in this experiment, n=15); hj is the thickness of
layer j (cm); Mi is the total water content in sampling time i (g); θij is the
volumetric water content of layer j in sampling time i (cm3/cm3); and Af is the
frost tube sectional area (cm).
Therefore, the evaporated water mass during stage i (Emass,i) could be calculated
as:
Emass ,i =
M i +1 − M i
Ti Af
(i=1, 2, …, 5)
(2)
where Ti is the number of days during stage i (d).
2.4 Modeling of water and energy balance for seasonally frozen soil
(Paper III)
The study was carried out from 10/1/2012 to 4/30/2013. Study period
included autumn irrigation (AI) practice, and freezing/thawing (FT) processes.
AI practice occurred during 11/8/2012 through 11/10/2012, with irrigation
rate of 86 mm/d (totally 258 mm), groundwater table depth was measured
every day from 11/7/2012 to 11/15/2012, then every five days during FT
periods.
Model parameters with reasonable ranges related to soil water and heat
processes were selected for calibration using generalized likelihood uncertainty
estimation (GLUE) method by Beven and Binley (1992). Soil temperature and
total water content from 10/1/2012 to 4/30/2013 at depths of 5, 15, 25, and
35 cm were used to describe the performance of the model. Three
performance indices R2, the determination coefficient, RMSE, the root mean
square error of the model, and ME, the mean error of the model, were chosen
to describe the performance of simulation efficiency in representing observed
data, in a similar approach as others (Conrad and Fohrer, 2009; Dean et al.,
2009; Juston et al., 2010; Wu et al., 2011).
To choose around 100 behavioral models from 20,000 simulations, R2>0.90,
0.35 were chosen. And RMSE<1/3 of obtained prior width of RMSE for soil
temperature and total water content, was selected. For ME, posterior values
with a central range close to zero based on 1/4 of width for prior range was
used to constrain soil temperature and total water content. Finally, a total of
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Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
20,000 simulations were made considering 19 parameters, among which 73
behavioral models were selected constrained by the criteria.
3. R ESULTS
3.1
SFCC with various solute types and solute content levels (Paper I)
SFCCs of different solute types and solute content levels are depicted in Fig. 3.
Liquid water content decreased rapidly when soil temperature was 0 to 5 oC
below zero, decreasing from 0.30 cm3/cm3 to about 0.05 cm3/cm3 with rates
of 0.010 to 0.026 cm3/cm3/oC, and when negative temperature was larger than
10 oC, the rates of change in liquid water content decreased, with 0.002 to
0.010 cm3/cm3/oC, finally kept values at 0.05 to 0.10 cm3/cm3 at -25 oC.
Besides, the decreasing rates of liquid water content also changed with solute
types, and freezing process in soil samples with solutes of NaCl and MgCl2
seemed to be easier, with average rates of 0.017 and 0.020 cm3/cm3/oC,
respectively, during 0 to -5 oC temperature zone. While the latter period (<-5
o
C) of freezing seemed to be less different for various solute types.
The value of parameter a increased linearly with solute content from around
0.2 at 0.1% to around 0.3 at 1.0% (g/g) solute content. As for NaCl and CaCl2,
the values increased to as large as 0.4086 and 0.2963 respectively when solute
content rose to 1.0%. The values for MgSO4 and MgCl2 increased slowly from
0.1650 to 0.2162 and 0.1851 to 0.2220 as solute content increased from 0.1%
to 1.0%. The change in value of a in the fitting curve resulted in the upward
and downward translation of the curve in the
plot. Thus it could
reflect the effects of solute on soil freezing. As to parameter b, its
mathematical meaning is the controlling of rotation of the curve in the
plot. While plotted in log-log coordinate, b represented the slope of the
plot, and the value of b indicated the changing rate of liquid
water with temperature. The values of b changed irregularly with solute
content and the values of different solute types changed differently. For NaCl,
KCl, and CaCl2, the values of b increased with solute content as a whole,
though a decrease was detected in low solute content level. While for MgSO4
and MgCl2, the values of b changed little, even decreased.
7
Mousong Wu
TRITA LWR Lic Thesis 2015:01
Fig. 3 SFCC under various solute types and solute content levels (Paper I). CK here is
the curve for treatment without solute addition.
3.2 Water, heat, and solute transport in frozen soil (Paper II)
3.2.1 Precipitation, frost depth, and air temperature
During the 150-day experiment the air temperature shows regularly diurnal
patterns with a daily range of around 10 oC and mean daily lowest temperature
was around -15 oC. Falling snow was only observed for five times, and the
maximum snow depth was 20 mm. No rain fell due to the low temperatures
during the soil freezing/thawing process. The depth of frost increased
gradually during soil freezing period, and the maximum frost depth of 100 cm
was observed. Thawing process was detected to occur from two sides of
frozen layer. Both thawing fronts met at a soil depth of approximated 50 cm.
The thawing process occurred faster than the freezing process with rapid
increase of air temperature during thawing period.
3.2.2
Water, heat and solute dynamics in field and frost tubes
Fig. 4 shows mean water, solute and temperature profiles of 5 plots in field, as
well as their changes in different periods. Water and solute profiles in field
indicated that accumulation of water and solute to upper layers occurred in P1
to P3, especially for 0 to 40 cm depth. While for temperature, the gradients for
whole soil profile were as high as 4.7 to 14.5 oC/m. And the position of zero
degree isotherm plane also indicated that rapid freezing occurred in P1 and P2,
and the maximum depth for freezing front penetration was around 100 cm.
During soil thawing periods (P4 and P5), solute still tended to accumulate to
upper layer of soil, while water content seemed to lose rapidly, indicating that
there might be more intensive evaporation in these periods as soil began
thawing with high positive temperature. The redistribution of water and solute
was obvious during the whole experimental periods.
For frost tubes, the profiles for water, solute and temperature for treatment
W2S1 (with initial GWTD of 1.5 m and initial solute content of 0.2% g/g) are
8
Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
depicted in Fig. 5. For this treatment, initial solute content and GWTD was
similar to that in field, but with lower initial water content (0.30 cm3/cm3).
Similar changes in water and solute accumulation in upper layers were detected
in this treatment, during P1 to P3. However, due to no connections to deeper
groundwater, water and solute in frost tubes tended to redistribute in whole
soil profile. In soil thawing periods (P4 and P5), water loss and solute
accumulation was not that intense as in field, but the whole profile showed
changes in these periods.
Fig. 4 Water, heat and solute profiles for field plots experiments (Paper II).
Fig. 5 Water, heat and solute profiles for frost tubes with treatment W2S1 (Paper II).
3.3 Simulation of water and heat dynamics (Paper III)
Simulated soil temperature generally reflected the actual changes of soil
temperature during study period, with R2 0.92 and 0.96 for 5 and 35 cm depths
(Fig. 6). However, simulated soil temperature had an obvious constant period
(about one week) when temperature changed from positive to negative during
freezing, and negative to positive during thawing. This meant that continuous
phase transition from water to ice or ice to water occurred when soil began
freezing or thawing. And during these periods, available energy was mostly
used for phase transition, soil temperature would keep steady at zero during
these periods. Besides, the actual soil water was dissolved with some salts or
other solvents, which resulted in a freezing point depression in soil water,
causing the freezing point of soil water to be lower than zero (Koopmans and
Miller, 1966; Banin and Anderson, 1974; Fuchs et al., 1978; Watanabe and
Mizoguchi, 2002). Actually, another constant soil temperature ‘plateau’ was
presented in the measured soil temperature, but it occurred earlier and was
shorter than the simulated one. This indicated that, in this soil with high solute
concentrations the freezing point depression was more pronounced than what
9
Mousong Wu
TRITA LWR Lic Thesis 2015:01
was simulated by the model.
Simulated total water content also showed good performance, in comparison
with measured one (Fig. 7), with R2 of 0.45 and 0.55 for 5 and 35 cm depths.
But in the surface layer, the total water content was underestimated during soil
freezing/thawing (FT). This might be due to the fact that the surface layer had
more extensive water and heat exchange with atmosphere. Also, during FT, the
cover of surface with some ice layer due to the remaining of irrigation water in
the ponds would also influence the energy and water exchange, and the cyclic
FT during day and night would result in the exchange of water between surface
layer and ice layer. Besides, the trade-off effect existed when choosing a model
with good performance for both water and temperature because the non-linear
responses in model to driving data. Further work should be conducted by
using multiply measurements to constrain the model performance, and deeper
investigation into the water and heat processes in frozen soil, especially under
saline conditions was needed.
Fig. 6 Simulated soil temperature at 5 and 35 cm depths with calibrated parameters
(Paper III).
10
Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
Fig. 7 Simulated total water content at 5 and 35 cm depths with calibrated parameters
(Paper III).
4. D ISCUSSION
4.1
Water and solute effects on SFCC (Paper I)
To determine the effects of solute type and solute content as well as their
interactions on soil freezing characteristics, the ANOVA test was conducted as
shown in Table 1. The results showed that not only initial water content, but
also solute type and solute content had significant influences on a, for the
change in values of b would result in the translation of SFCC upward when its
value increased. Therefore, it could indicate the influences of solute type and
solute content effectively. Solute type (P=0.0033) had more significant effects
on SFCC than solute content (P=0.0444) and the interactions (P=0.0156) of
solute type and solute content, as could be seen from the statistical results of
ANOVA. As to b, the influences of solute type and solute content were both
significant at 0.01 probability level. The differences in influences of solute type
on SFCC were mainly a result of the major ions in soil. Svensson and Hansen
(2010) studied Ca and Na forms of Wyoming bentonite with time-resolved
synchrotron X-ray diffraction, and completely different textures of ice
diffraction rings were observed, with a more dispersed texture for
Na-montmorillonite and a more coarse texture for Ca-montmorillonite. And
11
Mousong Wu
TRITA LWR Lic Thesis 2015:01
Kozlowski and Nartowska (2012) also observed higher unfrozen water content
in Na forms of soil than in Ca forms of soil at temperature above -2 oC.
The predicted parameters for SFCC of different solute types and solute
content levels based on the SFCC of non-saline soil indicated that the
predicting results did not correlate well with the measured ones, a and b values
tended to be overestimated when values were small and underestimated when
values were large. This was because solute content in this study was low and
the freezing point caused by solute was very small, thus leading to
unreasonable results in step (v), for the description of SFCC using a power
function may lead to overestimation of liquid water content when negative
temperature was very closed to zero because of infinite large value
corresponded to zero. Thus, when
differences in
and
is very small (mainly due to small
or low salt content differences), the value of
in step (v) would result in a very large value, even exceeds saturation. This
would cause an error in determining modified factor
and then parameters
for SFCC.
Herein, a trial and error method was used to obtain SFCC of saturated saline
soil first. The parameters of SFCC for saturated saline soil was preset first,
then were used to predict SFCC parameters which had been obtained by
experiment. Then the predicted parameters and experimental results were
compared, and the preset parameters were adjusted to make the parameters for
saturated saline soil to achieve a relative error to measured data controlled to
be less than 0.001. The final parameters were then accepted as SFCC
parameters of saturated saline soils with different solute types and solute
content levels. These adjusted parameters were then used to predict SFCC of
water and solute conditions based on the modified SFCC prediction model.
Finally, the SFCC of a specific soil could be predicted based on the SFCC
under a certain water and solute condition.
The modified prediction model was tested using the SFCC of a saturated
non-saline soil to predict the SFCCs of different solute types and solute
content levels. The predicted parameters had good correlation with measured
values, with R2 of 0.934 and 0.980. This indicated that the modified prediction
model could serve as a useful approach to predicting SFCC based on
experimental data obtained from certain water and solute conditions.
12
Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
Table 1 Univariate tests of significance of the factors of solute type and solute content
and their interactions for the SFCC fitting parameters (Paper I).
Parameter
Sum of squares
df
Mean square
F
P
Significance
a
Model
0.0436
24
0.0018
3.08
0.0034
**
ST†
0.0123
4
0.0031
5.24
0.0033
**
SC‡
0.0067
4
0.0017
2.86
0.0444
*
ST×SC
0.0245
16
0.0015
2.60
0.0156
*
Error
0.0147
25
0.0006
/
/
/
b
Model
0.1824
24
0.0076
4.36
0.0003
***
ST
0.0376
4
0.0094
5.39
0.0029
**
SC
0.0352
4
0.0088
5.05
0.0040
**
ST×SC
0.1096
16
0.0068
3.93
0.0011
**
Error
0.0436
25
0.0017
/
/
/
*** Significant at the 0.001 probability level; ** significant at the 0.01 probability level; *
significant at the 0.05 probability level; NS not significant at the 0.05 probability level.
†ST represents solute type.
‡SC represents solute content.
4.2 Evaporation in frozen soil with various conditions (Paper II)
Measurements taken with different experimental treatments showed that
cumulative evaporation generally decreased with deep groundwater table depth
(GWTD) and increased with high solute content (Fig. 8).
For frost tubes, when the solute content was the same, the cumulative
evaporation amount decreased as the GWTD increased. This was because a
shallower GWTD may produce better conditions for supplying upper soil
layers when the soil is freezing, as more water would accumulate in the upper
soil layers under various temperature and other potential gradients, which
would later be available for evaporation during thawing.
However, the interactions between surface evaporation and groundwater water
flow were not direct in frozen soil. During freezing and thawing periods, the
profile between the groundwater table and the soil surface was mostly frozen,
and the soil permeability could be very low. For this reason, less water was
transported directly from groundwater to surface. The water accumulated in
the upper layer was stored as ice during the freezing process, and then thawed
to supply water to the surface layer for evaporation.
As shown in Fig. 8(b), changes of cumulative evaporation amount with initial
solute content of soil profile indicated that solute also had strong influence on
soil evaporation. Soil with higher initial solute content would result in higher
cumulative evaporation amount. It was very obvious for frost tube experiments
13
Mousong Wu
TRITA LWR Lic Thesis 2015:01
that when initial solute content increased from 0.2%, 0.4%, to 0.6%,
cumulative evaporation amount increased from 51.0, 96.6, to 114.0 mm with
initial GWTD of 1.5 m. This was mainly because higher solute content in soil
would result in lower freezing point of soil. Thus, more liquid water would
exist at negative temperatures in soil, which would not reduce hydraulic
conductivity of frozen soil that rapidly. Thus this allowed for a more efficient
redistribution of water flow from the deeper horizons to the upper layers,
which may increase the amount of water available for evaporation from the
soil surface.
Liquid water in frozen soil indicated the mobile water for mass exchange to
atmosphere or lower unfrozen layer. Thus, high liquid water content in upper
layer meant more available water for evaporation. Evaporation rate in different
treatments increased with increasing liquid water content. From the calculation
of liquid water based on Fuchs et al. (1978) it could be known that solute and
temperature effects were also taken into consideration for liquid water content
in frozen soil. Solute in unfrozen soil influenced evaporation due to decreasing
water potential of soil, making it more difficult for evaporation from saline soil,
which needed more energy to move water from soil to atmosphere (Black et al.,
1969; Shimojima et al., 1996). While temperature decided the freezing/thawing
status of soil. Thus the liquid water in frozen soil was controlled by soil solute
content and temperature, and eventually influenced evaporation from frozen
soils.
Fig. 8 Cumulative evaporation amount changes with initial groundwater table depth and
initial solute content for various treatments (Paper II).
4.3 Seasonal course for simulated energy balance in frozen soil (Paper
III)
Simulated changes in heat fluxes, as well as air temperature during soil freezing,
and the diurnal changes in energy partitioning showed large oscillations (Fig. 9).
When soil began freezing, air temperature gradually decreased to below zero,
and more intensive changes in energy partitioning were observed. At the
beginning of this period, e.g. 11/23/2012, two peaks were observed for energy
components. However, after that, energy balance components reached the first
peak around 10:30. Then, energy balance components kept stable from 12:00
14
Water, heat and solute processes in seasonally frozen soils—Experimental and modeling study
to 15:00 before the second peak occurred. This was also due to high cloud
fraction (cloud fraction of 1.0) during these three hours. During this stage, soil
began freezing, but not enough energy from net radiation, thus upward heat
flux was overestimated for compensation of energy for freezing latent heat
consumption. Changes in energy balance components in this typical day in
Period II indicated that, at the beginning of soil freezing, as the air temperature
fluctuated around zero, energy partitioning tended to be more complex
between different components and the cloud fraction in the day still seemed to
be a major factor in energy partitioning as well.
However, as air temperature was stable below zero for the whole day, e.g.,
11/25/2012, energy balance system seemed to be also more stable. And the
sensible heat flux seemed to be compensated by the latent heat flux at night
time (e.g., before 7:00 and after 18:00) when net radiation was small. And the
negative values for latent heat flux after 18:00 indicated that condensation of
vapor in air occurred due to low air temperature.
Changes in longwave radiation at different dates showed great disturbances by
cloud fraction during the day, which eventually influenced the partitioning of
energy on soil surface. However, due to lack in measured heat flux for
calibration, the correlation between atmospheric conditions and energy
partitioning on surface needed to be investigated in the future with more
detailed eddy covariance flux data. Besides, the calibrated albedo of surface soil
showed higher ranges with mean values of 57% for the wintertime, in
comparison with the normal ranges for soil, 20% to 35%. However, the values
for calibrated albedo indicated the possible existence snow on surface, for the
albedo of snow ranged from 35% to 90%. In this study, the snow cover was
not included for sparse snow-falling during the wintertime, but ice cover was
observed due to freezing of ponding water after irrigation, which existed on
surface for three months. Ice could have larger albedo value than bare soil due
to its special properties in reflecting energy, and it could also block energy
exchange between atmosphere and soil surface. However, only snow layer
energy balance was considered in the CoupModel, and energy balance for ice
layer was not taken into consideration. Thus, more work about energy balance
in ice layer during soil FT was needed for understanding water and heat
transport in atmosphere-surface canopy-soil system in wintertime.
15
Mousong Wu
TRITA LWR Lic Thesis 2015:01
Fig. 9 Simulated energy partitioning changes in specific dates during soil freezing and
thawing periods (Paper III).
5. C ONCLUSIONS
To investigate the coupled effects of water, heat and solute in frozen soil,
experimental and modeling studies were conducted. For the laboratory soil
freezing experiment (Paper I), the influences of initial water content solute
contents and solute types on soil freezing characteristic curves were shown to
be significant. An empirical model for soil freezing characteristic curve in saline
frozen soil was set up to describe soil freezing characteristic curves under
various conditions. Field experiments (Paper II) on dynamics of water, heat
and solute transport showed the coupled effects of water, heat and solute in
frozen soil, and evaporation from frozen soil was influenced by liquid water
content in upper layer, which was also affected by the solute conditions. In
frozen soil, the solute content and groundwater table depth had coupled
effects on water, heat and solute transport, as well as soil evaporation.
Modeling of water and heat balance in frozen soil (Paper III) demonstrated
that uncertainties exist in modeling water and heat processes in frozen soil.
Water and heat balance in surface was influenced by many factors, and the daily
course of soil freezing and thawing was obvious. Besides, the meteorological
conditions and surface cover had significant effects on the partitioning into the
components of the energy balance at the soil surface. The CoupModel
combined with ensemble based uncertainty methods was shown to be a useful
tool for understanding of water and heat processes in seasonally frozen soil,
and the role of measurements to reduce the uncertainty in water and heat
balance modeling.
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