The student Niccolò Tubini is developing a new interpretation of modeling freezing soils in his master's thesis. He aims to model coupled heat and water flow during freezing-thawing processes using a rigid soil scheme. The model considers unsaturated soil properties, freezing point depression due to capillary effects and solutes, and mass and energy conservation equations accounting for phase changes between water and ice. The apparent heat capacity is defined to account for heat effects during phase changes in the energy equation.
The carbon regeneration in the water column of
the Cariaco Basin (Venezuela) was investigated
using a regression model of total alkalinity (TA)
and the concentration of total inorganic carbon
(TCO2
). Primary productivity (PP) was determined
from the inorganic carbon fraction assimilated
by phytoplankton and the variation of the 22 and
23°C isotherm was used as an indicator of coastal
upwelling. The results indicate that CO2
levels were
lowest (1962 µmol/kg) at the surface and increased
to 2451 µmol/kg below the oxic-anoxic redox
interface. The vertical regeneration distribution of
carbon was dominated (82%) by organic carbon
originating from the soft tissue of photosynthetic
organisms, whereas 18% originated from the
dissolution of biogenic calcite. The regeneration
of organic carbon was highest in the surface layer
in agreement with the primary productivity values.
However, at the oxic-anoxic interface a second more
intense maximum was detected (70-80%), generated
by chemotrophic respiration of organic material
by microorganisms. The percentages in the anoxic
layers were lower than in the oxic zone because
aerobic decomposition occurs more rapidly than
anaerobic respiration of organic material because
more labile fractions of organic carbon have already
been mineralized in the upper layers.
The carbon regeneration in the water column of
the Cariaco Basin (Venezuela) was investigated
using a regression model of total alkalinity (TA)
and the concentration of total inorganic carbon
(TCO2
). Primary productivity (PP) was determined
from the inorganic carbon fraction assimilated
by phytoplankton and the variation of the 22 and
23°C isotherm was used as an indicator of coastal
upwelling. The results indicate that CO2
levels were
lowest (1962 µmol/kg) at the surface and increased
to 2451 µmol/kg below the oxic-anoxic redox
interface. The vertical regeneration distribution of
carbon was dominated (82%) by organic carbon
originating from the soft tissue of photosynthetic
organisms, whereas 18% originated from the
dissolution of biogenic calcite. The regeneration
of organic carbon was highest in the surface layer
in agreement with the primary productivity values.
However, at the oxic-anoxic interface a second more
intense maximum was detected (70-80%), generated
by chemotrophic respiration of organic material
by microorganisms. The percentages in the anoxic
layers were lower than in the oxic zone because
aerobic decomposition occurs more rapidly than
anaerobic respiration of organic material because
more labile fractions of organic carbon have already
been mineralized in the upper layers.
Extraction from the ocean chapters of IPCC Working Group II contribution to 5th Assessment Report by Svein Sundby, Institute of Marine Research, Norway
SICCME open session, 17 September 2014, ICES Annual Science Conference, A Coruña, Spain
"Environmental Impact of Hydraulic Fracturing Treatment Performed on the Łebień LE-2H Well in Poland" - An indepth study performed by the Polish Geological Institute on the environmental impacts of hydraulic fracturing at a well site in Poland carried out in August 2011. The study finds that soil, air and water are not negatively impacted by fracking when it's done according to regulation.
BC3 has in place a program called BC3 Visiting Programme under the attainment of its strategic objectives, Talent Attraction.
The aim of this programme is to promote research and dialogue between BC3 and other institutions by supporting and hosting local and international professors wishing to undertake research at BC3.
This is a presentation that Prof Maria Fernanda Sanchez Goñi (University of Bourdeauxl) gave withing the BC3 Seminars Programme.
Climate change impact on animal and human healthHinaMalik64
This presentation contains the shreds of evidence of climate change along with the impacts of changing climate on animal and human health. International agencies working on mitigation and adaptation steps.
The carbon regeneration in the water column of
the Cariaco Basin (Venezuela) was investigated
using a regression model of total alkalinity (TA)
and the concentration of total inorganic carbon
(TCO2). Primary productivity (PP) was determined
from the inorganic carbon fraction assimilated
by phytoplankton and the variation of the 22 and
23°C isotherm was used as an indicator of coastal
upwelling. The results indicate that CO2 levels were
lowest (1962 μmol/kg) at the surface and increased
to 2451 μmol/kg below the oxic-anoxic redox
interface. The vertical regeneration distribution of
carbon was dominated (82%) by organic carbon
originating from the soft tissue of photosynthetic
organisms, whereas 18% originated from the
dissolution of biogenic calcite. The regeneration
of organic carbon was highest in the surface layer
in agreement with the primary productivity values.
However, at the oxic-anoxic interface a second more
intense maximum was detected (70-80%), generated
by chemotrophic respiration of organic material
by microorganisms. The percentages in the anoxic
layers were lower than in the oxic zone because
aerobic decomposition occurs more rapidly than
anaerobic respiration of organic material because
more labile fractions of organic carbon have already
been mineralized in the upper layers.
Arctic Climate Feedbacks: Global ImplicationsOpen Knowledge
According to the WWF report "Arctic Climate Feedbacks: Global Implications", the consequences of a warming Arctic are far worse than previous projections.
Freezing-thawing processes study with numerical modelsRiccardo Rigon
This is the presentation given by Niccolò Tubini at the Carleton University last October 6th. Niccolò in his Master Thesis is working for a new implementation of the theory of freezing and thawing already covered by Matteo Dall'Amico in his Ph.D. Thesis and in Dall'Amico et al., 2001.
Extraction from the ocean chapters of IPCC Working Group II contribution to 5th Assessment Report by Svein Sundby, Institute of Marine Research, Norway
SICCME open session, 17 September 2014, ICES Annual Science Conference, A Coruña, Spain
"Environmental Impact of Hydraulic Fracturing Treatment Performed on the Łebień LE-2H Well in Poland" - An indepth study performed by the Polish Geological Institute on the environmental impacts of hydraulic fracturing at a well site in Poland carried out in August 2011. The study finds that soil, air and water are not negatively impacted by fracking when it's done according to regulation.
BC3 has in place a program called BC3 Visiting Programme under the attainment of its strategic objectives, Talent Attraction.
The aim of this programme is to promote research and dialogue between BC3 and other institutions by supporting and hosting local and international professors wishing to undertake research at BC3.
This is a presentation that Prof Maria Fernanda Sanchez Goñi (University of Bourdeauxl) gave withing the BC3 Seminars Programme.
Climate change impact on animal and human healthHinaMalik64
This presentation contains the shreds of evidence of climate change along with the impacts of changing climate on animal and human health. International agencies working on mitigation and adaptation steps.
The carbon regeneration in the water column of
the Cariaco Basin (Venezuela) was investigated
using a regression model of total alkalinity (TA)
and the concentration of total inorganic carbon
(TCO2). Primary productivity (PP) was determined
from the inorganic carbon fraction assimilated
by phytoplankton and the variation of the 22 and
23°C isotherm was used as an indicator of coastal
upwelling. The results indicate that CO2 levels were
lowest (1962 μmol/kg) at the surface and increased
to 2451 μmol/kg below the oxic-anoxic redox
interface. The vertical regeneration distribution of
carbon was dominated (82%) by organic carbon
originating from the soft tissue of photosynthetic
organisms, whereas 18% originated from the
dissolution of biogenic calcite. The regeneration
of organic carbon was highest in the surface layer
in agreement with the primary productivity values.
However, at the oxic-anoxic interface a second more
intense maximum was detected (70-80%), generated
by chemotrophic respiration of organic material
by microorganisms. The percentages in the anoxic
layers were lower than in the oxic zone because
aerobic decomposition occurs more rapidly than
anaerobic respiration of organic material because
more labile fractions of organic carbon have already
been mineralized in the upper layers.
Arctic Climate Feedbacks: Global ImplicationsOpen Knowledge
According to the WWF report "Arctic Climate Feedbacks: Global Implications", the consequences of a warming Arctic are far worse than previous projections.
Freezing-thawing processes study with numerical modelsRiccardo Rigon
This is the presentation given by Niccolò Tubini at the Carleton University last October 6th. Niccolò in his Master Thesis is working for a new implementation of the theory of freezing and thawing already covered by Matteo Dall'Amico in his Ph.D. Thesis and in Dall'Amico et al., 2001.
Decoding the Weather MachineDiscover how Earth’s intricate clima.docxrandyburney60861
Decoding the Weather Machine
Discover how Earth’s intricate climate system is changing.
copy this link in website the viedo around 1:53 mins
https://www.pbs.org/wgbh/nova/video/decoding-the-weather-machine
see the video and the all answers will be in viedeo
QUESTION 1
Concerns about climate change have emerged based on scientific research that identified over 26,000 independent lines of evidence that the planet is warming. Which of the following is NOT cited as evidence of climate change in the first few minutes of the video?
a. Length and intensity of heatwaves has increased.
b. Plants and trees are flowering earlier in the year.
c. Birds are migrating to higher latitudes.
d. Glaciers are melting.
e. All of the above are mentioned.
QUESTION 2
Earth’s climate has changed naturally in the past, as evidenced by the boulder placed in Central Park by a continental glacier. The scientific evidence says that today’s climate change is caused by:
a. Change in volcanic eruptions
b. Changes in solar output
c. Milankovitch cycles
d. Burning of fossil fuels
QUESTION 3
Joseph Fourier conducted experiments to understand Earth’s energy balance and infrared radiation in which year?
a. 1824
b. 1724
c. 1924
d. 2004
QUESTION 4
John Tyndall discovered that ________ is a “heat-trapping gas” in 1859.
a. oxygen
b. hydrogen
c. carbon dioxide
d. nitrogen
QUESTION 5
The work of Fourier and Tyndall set the scientific foundation for the understanding of:
a. the ozone cycle
b. the greenhouse effect
c. thermohaline circulation
d. albedo
QUESTION 6
In the 1950s, when Dave Keeling first began to measure levels of atmospheric carbon dioxide above Hawaii at Mauna Loa, the first few months of readings caused him to think that the equipment was malfunctioning.
Describe the results that caused this confusion. Write 2-3 sentences.
QUESTION 7
Was there an equipment malfunction? Explain the new discovery that this event revealed. Write 2-3 sentences.
QUESTION 8
How many years of data do ice core samples from Antarctica reveal?
a. 800,000
b. 8,000,000
c. 800
d. 8,000
QUESTION 9
Considering the composition of gases in the atmosphere, do the last 60 years of ice core data confirm the data from the Keeling curve?
Yes
No
QUESTION 10
Scientists who compare oxygen-16 and oxygen-18 levels incorporated into clamshells in order to determine past temperature patterns are examining:
a. the saffir-simpson scale
b. dendrochronology
c. isotopes
d. gyres
QUESTION 11
Describe the relationship between carbon dioxide levels and temperature, as indicated in the scientific record over millions of years:
QUESTION 12
Natural sources that add carbon dioxide to the atmosphere include all of the following, EXCEPT:
a. volcanoes
b. decay of forests
c. forest fires
d. photosynthesis
QUESTION 13
Air contains carbon atoms with different numbers of neutrons. Ralph Keeling and other scientists have tested carb.
Climate change discussion and various scientific viewpoints weave a matrix of knowledge in an incredibly complex global environment. Carbon dioxide sequestration is part of the matrix of environmental solutions that will accelerate our ability to develop and deploy green renewable energy.
ENHANCEMENT OF THERMAL EFFICIENCY OF NANOFLUID FLOWS IN A FLAT SOLAR COLLECTO...Barhm Mohamad
Flat plate solar collector (FPSC) is popular for their low cost, simplicity, and ease of installation and operation. In this work, FPSC thermal performance was analyzed. It's compared to diamond/H2O nanofluids. The volume percentage and kind of nanoparticles are analyzed numerically that validation with experimental data available in the literature. The hot climate of Iraq is employed to approximate the model. The numerical study is performed by using ANSYS/FLUENT software to simulate the case study of problem. Due to less solar intensity after midday, temperatures reduction. The greatest collector thermal efficiency is 68.90% with 1% ND/water nanofluid, a 12.2% increase over pure water. The efficiency of 1% nanofluid is better than other concentrations because of a change in physical properties and an increase in thermal conductivity. Since the intensity of radiation affects the outlet temperature from the solar collector and there is a direct link between them, this increases the efficiency of the solar collector, especially around 12:30 pm at the optimum efficiency.
This is a short introduction to understand just a little how hydrological models and some hydraulics works. Much relies on the oral presentation. Unfortunately this is is Italian
A short introduction to some hydrological extreme phenomenaRiccardo Rigon
For high School teachers. Kept at MUSE on October 20th 2017. It covers the typology of some phenomena giving a little of explanation of the diverse dynamics. Is a product of LIFE FRANCA EU project
This is the presentation given for the admission to his second year of Ph.D. studies by Michele Bottazzi. Besides sumamrizing the work done during the first year, Michele traces his pathways into the second year with an abrupt change of direction towards simulating and discussion transpiration from plants.
This is the presentation for his admission to the third year of his Ph.D.. It talks about the several direction his work had taken and look forward to the conclusion of some task in form of code release and published papers.
This contains a summary of the data available for torrente Meledrio. We are using it for the project SteepsStreams, and we want to estimate its water and sediment budgets.
This contains the talk given at the 2017 meeting of the SteepStream ERANET project. It is assumed to talk about the hydrological cycle of the Noce river in Val di Sole valley (Trentino, Italy). It is a preliminary view of what we are going to do in the project.
This contains some hints and discussions about how to implement Grids in a Object Oriented language. Specifically the discussion is made with Java in mind, but obviosly, not limited to it.
How to implement unstructured grids in Java (or BTW in another OO language). First start from understanding what grids are and how they are described in algebraic topology. Mathematics first, can be a good idea. No explicit implementation here, but concept and literature to study and start from..
This is the outstanding lecture given by Dani Or when receiving his Dalton Prize at 2017 Wien EGU General Assembly. It is a must-read for who deals with ET and good material also for teaching to students.
Projecting Climate Change Impacts on Water Resources in Regions of Complex To...Riccardo Rigon
The title describes it all. Jeremy Pal's student Brianna Pagàn and coworkers put an impressive set of tools to estimate the impacts of land use and climate change on water resources of south California.
This is the English translation, with some relevant corrections, of the talk I gave at University of Calabria, about the contemporary and post-contemporary flood forecasting.
Hydrological Extremes and Human societies Riccardo Rigon
This is the talk given by Giuliano di Baldassarre at the Summer School on Hydrological Modeling kept in Cagliari this here. The topic is very up-to-date and important. He presented an analysis of a few case studies and suggested some literature.
The Science of Water Transport and Floods from Theory to Relevant Application...Riccardo Rigon
This is the presentation given by Ricardo Mantilla at University of Iowa in 2017. It talks about the system implemented in Iowa for flood forecasting in real time
These are the slides presented at EGU 2017 General Meeting, the Pico session was entlited: Monitoring and modelling flow paths, supply and quality in a changing mountain cryosphere
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
1.4 modern child centered education - mahatma gandhi-2.pptx
Master thesis presentation by Niccolò Tubini
1. Department of Civil, Environmental and Mechanical Engineering
Master of Science in
Environmental and Land Engineering
THEORETICAL PROGRESS IN
FREEZING – THAWING PROCESSES STUDY
Supervisor Student
Prof. Riccardo Rigon Niccolò Tubini
Co-supervisors
Prof. Stephan Gruber
Dr. Francesco Serafin
2. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
This work is licensed under a Creative
Commons “Attribution-ShareAlike 4.0
International” license.
Niccolò Tubini Theoretical progress in freezing – thawing processes study
3. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
What is the purpose?
The aim of my Master’s thesis is to develop a new
interpretation of modeling freezing soils.
Niccolò Tubini Theoretical progress in freezing – thawing processes study 2 / 34
4. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Why studing the influence of coupled heat and water flow
in soils?
Freezing – thawing processes entail a huge
exchange of heat;
Niccolò Tubini Theoretical progress in freezing – thawing processes study 3 / 34
5. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Why studing the influence of coupled heat and water flow
in soils?
To simulate more realistic soil temperature
(Luo et al., 2003).
Niccolò Tubini Theoretical progress in freezing – thawing processes study 3 / 34
6. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Why studing the influence of coupled heat and water flow
in soils?
Studies have shown that proper frozen soil
schemes help improve climate model simulation
(Viterbo et al., 1999 and Smirnova et al., 2000).
Niccolò Tubini Theoretical progress in freezing – thawing processes study 3 / 34
7. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soils
Some definitions
Air gas
Liquid water
Soil particle
Va
Vw
Vs
Vc
Niccolò Tubini Theoretical progress in freezing – thawing processes study 4 / 34
8. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soils
Some definitions
Soil porosity
φ :=
Vs
Vc
Water content
θ :=
Vw
Vc
Niccolò Tubini Theoretical progress in freezing – thawing processes study 5 / 34
9. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soils
Some definitions
Assuming the rigid soil scheme
θs := φ
0 < θr ≤ θ ≤ θs < 1
Niccolò Tubini Theoretical progress in freezing – thawing processes study 6 / 34
10. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soils
Young – Laplace equation
r γaw
α pw = pa −
2γaw cos α
r
Niccolò Tubini Theoretical progress in freezing – thawing processes study 7 / 34
11. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soils
Young – Laplace equation
pa ← 0
Let us define suction as
ψ :=
pw
gρw
Niccolò Tubini Theoretical progress in freezing – thawing processes study 8 / 34
12. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soil hydraulic properties
Mualem’s assumption
Wetting and drying processes are assumed to be
selective processes.
Niccolò Tubini Theoretical progress in freezing – thawing processes study 9 / 34
13. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soil hydraulic properties
Water – retention – hydraulic – conductivity models
Dealing with unsaturated soils requires the
definition of the relationship between
θ–ψ and K–ψ
Niccolò Tubini Theoretical progress in freezing – thawing processes study 10 / 34
14. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soil hydraulic properties
Empirical curve-fitting models
Parameters of these models have been related to
the soil texture and other soil properties
Niccolò Tubini Theoretical progress in freezing – thawing processes study 11 / 34
15. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soil hydraulic properties
Empirical curve-fitting models
Parameters of these models have been related to
the soil texture and other soil properties
Despite their usfulness they do not emphasize the
physical significance of their empirical parameters
Niccolò Tubini Theoretical progress in freezing – thawing processes study 11 / 34
16. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soil hydraulic properties
Lognormal distribution model (Kosugi, 1996)
The idea is to derive the water retention curve from
the pore-size distribution:
f (r) :=
dθ
dr
Niccolò Tubini Theoretical progress in freezing – thawing processes study 12 / 34
17. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soil hydraulic properties
Lognormal distribution model (Kosugi, 1996)
r
0
50
100
150
f(r)
R
Water
f (r) =
θs − θr
√
2π σr
exp
−
ln
r
rm
2
2σ2
θ(R) = θr +
R
0
f (r)dr
Niccolò Tubini Theoretical progress in freezing – thawing processes study 13 / 34
18. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soil hydraulic properties
Lognormal distribution model (Kosugi, 1996)
Young-Laplace equation allows to transform the
pore-size distribution into the capillary pressure
distribution function
g(ψ) = f (r)
dr
dψ
Niccolò Tubini Theoretical progress in freezing – thawing processes study 14 / 34
19. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Unsaturated soil hydraulic properties
Lognormal distribution model (Kosugi, 1996)
θ(Ψ) = θr +
Ψ
−∞
g(ψ)dψ
Ψ = −
2γaw cos α
g ρw R
Niccolò Tubini Theoretical progress in freezing – thawing processes study 15 / 34
20. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Some definitions
Air gas
Ice
Liquid water
Particle soil
Va
Vi
Vw
Vs
Vc
Niccolò Tubini Theoretical progress in freezing – thawing processes study 16 / 34
21. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Some definitions
Liquid water content
θw :=
Vw
Vc
Ice content
θi :=
Vi
Vc
Niccolò Tubini Theoretical progress in freezing – thawing processes study 17 / 34
22. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Some definitions
Total water content
θ := θw + θi
0 < θr ≤ θ ≤ θs < 1
Niccolò Tubini Theoretical progress in freezing – thawing processes study 18 / 34
23. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Model assumptions
Model assumptions
rigid soil scheme
Niccolò Tubini Theoretical progress in freezing – thawing processes study 19 / 34
24. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Model assumptions
Model assumptions
rigid soil scheme
freezing = drying (Miller, 1965; Spaans and Baker, 1996)
Niccolò Tubini Theoretical progress in freezing – thawing processes study 19 / 34
25. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Model assumptions
Model assumptions
rigid soil scheme
freezing = drying (Miller, 1965; Spaans and Baker, 1996)
the phase change is assumed to occur at the
thermodynamic equilibrium
Niccolò Tubini Theoretical progress in freezing – thawing processes study 19 / 34
26. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Freezing point depression
Gibbs-Thomson equation (Acker et al., 2001)
Tm − T∗
=
2 γaw Tm cos α
ρw r
+
πw Tm
ρw
Capillary effect
Dissolved solutes
Niccolò Tubini Theoretical progress in freezing – thawing processes study 20 / 34
27. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Freezing point depression
Gibbs-Thomson equation (Acker et al., 2001)
The ice-water interface occurs at:
ˆr(T) := −
2 γaw Tm cos α
ρw (T − Tm)
for T < Tm∗
Niccolò Tubini Theoretical progress in freezing – thawing processes study 21 / 34
28. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Water and ice content
Let us define
r∗
:=
R if ˆr ≥ R or T ≥ Tm
ˆr otherwise
∂r∗
∂t
:=
∂R
∂t
if ˆr ≥ R or T ≥ Tm
∂ˆr
∂t
otherwise
Niccolò Tubini Theoretical progress in freezing – thawing processes study 22 / 34
29. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Water and ice content
r
0
50
100
150
f(r)
Rˆr = r∗
Water
Ice
θw = θr +
r∗
0
f (r)dr
θi =
R
r∗
f (r)dr
Niccolò Tubini Theoretical progress in freezing – thawing processes study 23 / 34
30. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Water and ice content
The phase change rate
θi =
R
r∗
f (r)dr
∂θi
∂t
=
∂R
∂t
f (R) −
∂r∗
∂t
f (r∗
)
Niccolò Tubini Theoretical progress in freezing – thawing processes study 24 / 34
31. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Water and ice content
The phase change rate
r
0
20
40
60
80
100
120
f(r)
R(t) R(t + δt)ˆr
Water
Ice at time t
Ice at time t + δt
Niccolò Tubini Theoretical progress in freezing – thawing processes study 25 / 34
32. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Water and ice content
The phase change rate
r
0
20
40
60
80
100
120
f(r)
Rˆr(t)ˆr(t + δt)
Water
Ice formed in δt
Ice at time t
Niccolò Tubini Theoretical progress in freezing – thawing processes study 26 / 34
33. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Water and ice content
The phase change rate
∂θi
∂t
=
∂Ψ
∂t
g(Ψ) −
∂ψ∗
∂t
g(ψ∗
)
Niccolò Tubini Theoretical progress in freezing – thawing processes study 27 / 34
34. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Mass conservation equation
θ
J ET
Jw
∂
∂t
(ρw θw + ρiθi) = −ρw · Jw
Niccolò Tubini Theoretical progress in freezing – thawing processes study 28 / 34
35. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Mass conservation equation
θ
J ET
Jw
∂
∂t
(ρw θw + ρiθi) = −ρw · Jw
Water flux:
Jw = −K(ψ∗
) (ψ∗
+ z)
Niccolò Tubini Theoretical progress in freezing – thawing processes study 28 / 34
36. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Mass conservation equation
Setting ρw = ρi
∂θ
∂t
=
∂Ψ
∂t
g(Ψ) = · [K(ψ∗
) (ψ∗
+ z)]
∂θi
∂t
=
∂Ψ
∂t
g(Ψ) −
∂ψ∗
∂t
g(ψ∗
)
∂θw
∂t
=
∂θ
∂t
−
∂θi
∂t
Niccolò Tubini Theoretical progress in freezing – thawing processes study 29 / 34
37. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Energy conservation equation
ε
J
HRn
ET
JwJg
∂ε
∂t
= − · (Jw + Jg)
Niccolò Tubini Theoretical progress in freezing – thawing processes study 30 / 34
38. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Energy conservation equation
ε
J
HRn
ET
JwJg
∂ε
∂t
= − · (Jw + Jg)
Advective flux:
Jw = Jw ρw [ + cw (T − Tm)]
Heat conduction:
Jg = −λ T
Niccolò Tubini Theoretical progress in freezing – thawing processes study 30 / 34
39. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Energy conservation equation
Setting ρw = ρi
CT
∂T
∂t
− ρi
∂Ψ
∂t
g(Ψ) −
∂ψ∗
∂t
g(ψ∗
)
−ρi(cw − ci)(T − Tm)
∂Ψ
∂t
g(Ψ) −
∂ψ∗
∂t
g(ψ∗
)
+ρicw Jw · T + ρigz · Jw − · Jg = 0
Niccolò Tubini Theoretical progress in freezing – thawing processes study 31 / 34
40. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Energy conservation equation: if ice occurs
ψ∗
:= ˆψ
∂ψ∗
∂t
:=
g Tm
∂T
∂t
Cph
∂T
∂t
− ρi[ + (cw − ci)(T − Tm)]
∂Ψ
∂t
g(Ψ)
+ ρicw Jw · T + ρigz · Jw − · Jg = 0
Niccolò Tubini Theoretical progress in freezing – thawing processes study 32 / 34
41. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
The apparent heat capacity
Cph := CT + ρi[ + (cw − ci)(T − Tm)]
g Tm
Niccolò Tubini Theoretical progress in freezing – thawing processes study 33 / 34
42. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
The apparent heat capacity
Cph := CT + ρi[ + (cw − ci)(T − Tm)]
g Tm
CT := ρscs(1 − θs) + ρiciθi + ρw cw θw
Niccolò Tubini Theoretical progress in freezing – thawing processes study 33 / 34
43. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
To take home
Freezing=drying and rigid soil scheme
assumptions are useful when freezing-induced
mechanical deformations are not considered;
Niccolò Tubini Theoretical progress in freezing – thawing processes study 34 / 34
44. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
To take home
Freezing/thawing processes do not occur at the
thermodynamic equilibrium (Kurylyk, 2013).
Niccolò Tubini Theoretical progress in freezing – thawing processes study 34 / 34
45. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
To take home
Kosugi retention model has the benefit to be
straightforward extended to freezing soils case
by making use of Gibbs – Thomson equation;
Niccolò Tubini Theoretical progress in freezing – thawing processes study 34 / 34
46. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
To take home
This formulation allows to take into account of
dissolved solutes;
Niccolò Tubini Theoretical progress in freezing – thawing processes study 35 / 34
47. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
To take home
It is possible to solve the mass and energy
equation in a decoupled way;
Niccolò Tubini Theoretical progress in freezing – thawing processes study 35 / 34
49. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
References
K. Kosugi, Lognormal distribution model for unsaturated
soil hydraulic properties, Water Resources Research, vol. 32,
no. 9, pp. 2697–2703, 1996.
J. T. Acker et al., Intercellular ice propagation:
experimental evidence for ice growth through membrane
pores, Biophysical journal, vol. 81, no. 3, pp. 1389–1397,
2001.
M. Dall’Amico et al., A robust and energy-conserving
model of freezing variably-saturated soil, The Cryosphere,
vol. 5, no. 2, p. 469, 2011.
M. Dall’Amico, Coupled water and heat transfer in
permafrost modeling, Ph.D. dissertation, University of
Trento, 2010.
Niccolò Tubini Theoretical progress in freezing – thawing processes study
50. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
References
E. J. Spaans and J. M. Baker, The soil freezing
characteristic: Its measurement and similarity to the soil
moisture characteristic, Soil Science Society of America
Journal, vol. 60, no. 1, pp. 13–19, 1996.
R. D. Miller, Phase equilibria and soil freezing, vol. 287, pp.
193–197, 1965.
B. L. Kurylyk and K. Watanabe, The mathematical
representation of freezing and thawing processes in
variably-saturated, non-deformable soils, Advances in Water
Resources, vol. 60, pp. 160–177, 2013.
Niccolò Tubini Theoretical progress in freezing – thawing processes study
51. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
References
L. Luo et al., Effects of frozen soil on soil temperature,
spring infiltration, and runoff: Results from the PILPS 2 (d)
experiment at Valdai, Russia, Journal of Hydrometeorology,
vol. 4, no. 2, pp. 334–351, 2003.
T. G. Smirnova, J. M. Brown, S. G. Benjamin, and D. Kim,
Parameterization of cold-season processes in the maps
land-surface scheme, Journal of Geophysical Research:
Atmospheres, vol. 105, no. D3, pp. 4077– 4086, 2000.
P. Viterbo, A. Beljaars, J.-F. Mahfouf, and J. Teixeira, The
representation of soil moisture freezing and its impact on
the stable boundary layer, Quarterly Journal of the Royal
Meteorological Society, vol. 125, no. 559, pp. 2401–2426,
1999.
Niccolò Tubini Theoretical progress in freezing – thawing processes study
52. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Freezing=drying assumptionDall’Amico,2010
pa
pw (R)
R
r
Air-water interface
pw (R) = pa −
2 γaw cos α
R
Niccolò Tubini Theoretical progress in freezing – thawing processes study
53. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Freezing=drying assumptionDall’Amico,2010
pa
pi
pw (r)
R
r
Air-ice interface
pi = pa −
2 γai cos α
R
Ice-water interface
pw (r) = pi −
2 γiw cos α
r
Niccolò Tubini Theoretical progress in freezing – thawing processes study
54. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Freezing=drying assumptionDall’Amico,2010
pa
pi ≡ pa
pw (r)
R
r
Air-water interface
pw (r) = pa −
2 γaw cos α
r
Niccolò Tubini Theoretical progress in freezing – thawing processes study
55. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
r
0
20
40
60
80
100
120f(r)
R = r∗
ˆr
Water
Niccolò Tubini Theoretical progress in freezing – thawing processes study
56. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
The phase change rate
Thanks to the Young-Laplace equation
ψ∗
:=
Ψ if ˆr ≥
2 γaw cos α
ρw g Ψ
or T ≥ Tm
ˆψ = ψ(ˆr) otherwise
Niccolò Tubini Theoretical progress in freezing – thawing processes study
57. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
The phase change rate
Thanks to the Young-Laplace equation
∂ψ∗
∂t
:=
∂Ψ
∂t
if ˆr ≥
2γaw cos α
ρw gΨ
or T ≥ Tm
∂ ˆψ
∂t
otherwise
Niccolò Tubini Theoretical progress in freezing – thawing processes study
58. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Comparison with Dall’Amico model (Dall’Amico et al., 2011)
By making use of Clausius – Clapeyron equation:
dT
dpw
=
T
ρw
Niccolò Tubini Theoretical progress in freezing – thawing processes study
59. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Comparison with Dall’Amico model (Dall’Amico et al., 2011)
By making use of Clausius – Clapeyron equation:
dT
dpw
=
T
ρw
T∗
= Tm +
g Tm
ψw0
ψ(T) = ψw0 +
g T∗
(T − T∗
)H(T∗
− T)
Niccolò Tubini Theoretical progress in freezing – thawing processes study
60. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Mass conservation equation: if there is no ice
ψ∗
:= Ψ
∂ψ∗
∂t
:=
∂Ψ
∂t
∂θ
∂t
=
∂Ψ
∂t
g(Ψ) = · [K(Ψ) (Ψ + z)]
∂θi
∂t
=
:0
∂Ψ
∂t
g(Ψ) −
∂ψ∗
∂t
g(ψ∗
)
∂θw
∂t
=
∂θ
∂t
Niccolò Tubini Theoretical progress in freezing – thawing processes study
61. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Mass conservation equation: if ice occurs
ψ∗
:= ˆψ
∂ψ∗
∂t
:=
g Tm
∂T
∂t
∂θ
∂t
=
∂ ˆψ
∂t
g(Ψ) = · [K( ˆψ) ( ˆψ + z)]
∂θi
∂t
=
∂Ψ
∂t
g(Ψ) −
∂ ˆψ
∂t
g( ˆψ)
∂θw
∂t
=
∂θ
∂t
−
∂θi
∂t
Niccolò Tubini Theoretical progress in freezing – thawing processes study
62. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Energy conservation equation: if there is no ice
ψ∗
:= Ψ
∂ψ∗
∂t
:=
∂Ψ
∂t
CT
∂T
∂t
− ρil
:0
∂Ψ
∂t
g(Ψ) −
∂ψ∗
∂t
g(ψ∗
)
− ρi(cw − ci)(T − Tm)
:0
∂Ψ
∂t
g(Ψ) −
∂ψ∗
∂t
g(ψ∗
)
+ ρicw Jw · T + ρigz · Jw − · Jg = 0
Niccolò Tubini Theoretical progress in freezing – thawing processes study
63. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Energy conservation equation: if there is no ice
CT
∂T
∂t
+ ρw cw Jw · T + ρw gz · Jw − · Jg = 0
Niccolò Tubini Theoretical progress in freezing – thawing processes study
64. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Energy conservation equation: if there is no ice
CT
∂T
∂t
+ ρw cw Jw · T + ρw gz · Jw − · Jg = 0
CT := ρscs(1 − θs) + ρiciθi + ρw cw θw
Niccolò Tubini Theoretical progress in freezing – thawing processes study
65. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Numerical scheme for unfrozen soils
The mass conservation equation ⇒ Nested Newton
method (Casulli and Zanolli, 2010).
The energy consevation equation ⇒ Implicit upwind
method
Niccolò Tubini Theoretical progress in freezing – thawing processes study
66. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Numerical scheme for frozen soils
The mass conservation equation becomes
∂θ
∂t
= · K( ˆψ) ( ˆψ + z)
Niccolò Tubini Theoretical progress in freezing – thawing processes study
67. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Numerical scheme for frozen soils
The mass conservation equation becomes
∂θ
∂t
= · K( ˆψ) ( ˆψ + z)
Nested Newton method (Casulli and Zanolli, 2010).
should be extended for equations of two variables
Niccolò Tubini Theoretical progress in freezing – thawing processes study
68. Introduction Water in soils Freezing soils Mass conservation Energy conservation Conclusions
Numerical scheme for frozen soils
The mass conservation equation becomes
∂θ
∂t
= · K( ˆψ) ( ˆψ + z)
Nested Newton method (Casulli and Zanolli, 2010).
should be extended for equations of two variables
The energy consevation equation ⇒ Implicit upwind
method
Niccolò Tubini Theoretical progress in freezing – thawing processes study