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Modeling the Impact of Greenland Ice Sheet Melting on
Global Sea Level Elevation and Climate Change Feedback
Mechanisms
Siqi Li1,a,*
1College of Letters and Science, University of California, Santa Barbara, CA, USA
a. li68@ucsb.edu
*corresponding author
Abstract: The rapid acceleration of global warming is leading to an increased rate of glacier
melt at the Earth's poles, which exacerbates the threats posed by the climate crisis and
contributes to rising ocean levels. The Greenland Ice Sheet, recognized as the second-largest
ice sheet globally, has housed its extensive glaciers and ice caps for at least 18 million years
[1]. The melting and potential collapse of this ice sheet could significantly affect Worldwide
climate and sea height. This research aims to develop a coupled model to assess rising sea
levels caused by the thawing of the Greenland Ice Sheet, incorporating factors such as global
warming, glacier volume, hydrothermal expansion, isostatic rebound, ice dynamics, changes
in the gravitational field, and the absorption and release of methane gas. Additionally, the
paper investigates the hazards connected to melting glaciers exacerbating global warming.
This research provides a crucial foundation for forecasting the long-term impacts of the
Greenland Ice Sheet's melting on global climate change.
Keywords: Greenland Ice Sheet, Thermal Expansion, Climate Change, Isostatie Rebound, Ice
Dynamics, Gravity Field, Methane.
1. Introduction
In the autumn of 2024, osmanthus flowers did not bloom as usual, and the summer of this year broke
high-temperature records again. According to a statement by Samantha Burgess, Deputy Director of
ESA's Copelnix Climate Change Service, the world experienced the warmest June and August on
record [2].Scorching heat waves swept across many regions, not only killing people in some areas
due to severe heat sickness but also triggering a series of catastrophic effects, especially the
occurrence of large-scale forest fires. The influence of extreme heat, arid vegetation, and flammable
environmental conditions make wildfires more difficult to control, taking a huge toll on local
ecosystems and residents' lives and property. However, even the coldest regions on Earth are not
immune, and rising temperatures are quietly changing these previously frozen regions, putting them
at unprecedented risk of melting. This phenomenon highlights the increasing risks posed by climate
change, emphasizing the immediate need for intervention. Nowadays, "global warming" is no longer
an unfamiliar term for individuals, and with global temperatures rising, the potential crisis is slowly
expanding from the poles of the Earth. High temperatures accelerate the melting of ice in the Arctic
and Antarctic, and this melting process further heats the planet. According to Shepherd, the Greenland
Proceedings of the 4th International Conference on Computing Innovation and Applied Physics
DOI: 10.54254/2753-8818/86/2025.20193
© 2025 The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0
(https://creativecommons.org/licenses/by/4.0/).
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ice sheet has played a substantial role in the increase of global sea levels. Between 1992 and 2018,
Greenland lost 3,902±342 billion tons of ice, raising sea levels by an average of 10.8±0.9 mm. This
illustrates the strong feedback loop between glacier melting and global warming [3].
Additionally, melting snow and ice further drive global warming, as about 90% of solar radiation
hitting snow and ice is typically reflected into space. The Earth absorbs more solar energy with a less
reflective surface, releasing additional heat into the atmosphere and accelerating warming [4]. This
feedback cycle worsens the climate crisis, especially in the polar regions. For instance, Greenland's
significant annual ice loss remains a crucial driver of rising global sea levels. Rignot et al. observed
that Antarctic ice sheet loss has accelerated by 14.5±2 Gt/year² to 36.3±2 Gt/year², nearly three times
faster than the loss from mountain glaciers and ice caps (12±6 Gt/year). If this trend continues, ice
sheets will significantly contribute to rising sea levels in the 21st century. Eight years later,
Oppenheimer noted, "The combined impact of glacier and ice sheet melt is now the primary
contributor to global mean sea level rise, with very high confidence" [5][6].
The melting of glaciers not only exacerbates global warming but also gradually contributes to the
rise in sea levels. An increase in sea level would profoundly impact coastal areas and their inhabitants.
Evidence suggests that the global rise in sea levels since 1970 is largely attributable to climate change
induced by human actions [7]. Globally, the Greenland Ice Sheet is recognized as the second-largest
ice sheet. As the surface ice sheet melts, there is a post-glacial rebound, which is when the massive
weight of the ice plate is removed, and the land is raised, resulting in isostatic subsidence[8].
Meanwhile, the Earth's gravitational field also changes with the redistribution of ice and the mass of
melted water [8]. However, changes in the gravity field also mean that the Earth's axis is shifted,
which in turn causes changes in the Earth's rotation, leading to a series of related effects. According
to the National Ocean Service, Typically, regions of the planet with stronger gravitational forces
experience higher mean sea levels, while areas where gravitational forces are weaker have lower
mean sea levels [9]. When considering the ice loss from the Greenland ice sheet, the ice sheet's
dynamic is also an important factor. The ice sheet flows under the action of its own weight, and its
flow speed is determined by the balance between gravity, the basement resistance relative to the ice
sheet, and the internal deformation of the ice sheet [10]. During a field trip to the West Greenland Ice
Sheet in 2016, researchers observed that CH₄ concentrations in the air released by glacial runoff were
significantly higher, reaching up to 15 times the atmospheric background levels at subglacial
discharge points [11]. Methane, recognized as a potent greenhouse gas, has a substantial impact on
global warming. However, in January 2024, researchers at the University of Copenhagen made a
surprising discovery. They found that Greenland is not a significant source of methane but a net
methane sink. The ice-free part of Greenland consumes more than 65,000 tons of methane per year,
while the wet areas only release 9,000 tons of methane per year [12]. However, the volume of the wet
areas may increase with the melting of the ice, potentially leading to a release and increase of methane
gas that could exacerbate global warming. With global warming enhanced, the temperature increases,
resulting in the thermal expansion of seawater, thus increasing the volume of seawater [13].
In light of these factors are linked to each other to form a feedback mechanism, they are closely
related ice sheets melt and rising sea levels. The aim of this study was to quantify the contribution of
glacier melting to global sea level elevation and temperature change by analyzing global warming,
Ice sheet melting, hydrothermal expansion, Isostatie Rebound, Ice sheet dynamics, gravitational field
changes, and methane gas release. The ice sheet model in Matlab is used to combine various models
to form a coupled model to simulate temperature change, glacier melting rate, and sea level rise rate.
It also discusses the possible ice sheet decline rate and its impact under future global warming
scenarios [14].
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2. Methodology
We initially employed the mass balance method to estimate the potential rise in ocean levels resulting
from Greenland's ice mass depletion. This approach assesses the impact of melting ice sheet volume
on sea levels. The increase in sea level due to the ice volume can be determined by dividing the total
volume of melted water by the total area of the oceans.
Hice Vwater
Aocean 1
where Hiceis the height of rising ocean level by melted water, Vwater is the meltwater volume, and
Aocen is the surface area of the world’s oceans.
For Vwater that is equal to the volume of ice in Greenland multiply the density of ice and divided
by density of water. Since ice melting is related to temperature change, considering the effect of
global warming on Greenland ice sheet, therefore the volume of ice melt can be denoted as V(t) which
can be modeled over time as a function of rising global temperatures.
VtV0fTtt2
V0 is the initial volume of ice, T(t) is the temperature at time t, f(T(t)) is the function representing
the melting rate at temperature T(t) and Δt is the time interval.
Temperature change is the primary factor driving ice melt, as well as influencing water thermal
expansion. As the surface area of the ice sheet decreases, the reduction in snow and ice albedo
accelerates global warming. Additionally, Greenland releases and absorbs methane, a potent
greenhouse gas, each year. Therefore, the annual impact of methane on temperature change is also a
crucial factor to consider.
TtTt1TglobaltTicetTmethanet 3
T(t-1) is the temperature at the previous point in time, ΔTglobal (t) represents the global temperature
increase due to climate changeby human activities over time, ΔTice (t) is the temperature feedback
effect from the melting ice, which would further exacerbating climate warming, and ΔTmethane (t)
accounts for the temperature change attributed to methane release from the melting ice sheet, which
exacerbates global warming.
According to the zero dimensional climate model [16], the temperature change influenced by
human factors per year can be obtained as follows:
Tglobalt 1
CS1α
4ABT0aln CO2
CO2PI
AGT0G′T0TT0
BG′T0
S is the solar insolation which is around 1368 W/m2,α is planetary reflectivity which is around 0.3,
therefore S1α
4 is absorbed solar radiation.G(t) denotes outgoing thermal radiation, and B represents
the climate feedback parameter. Human-caused greenhouse effect is written asa ln CO2
CO2PI
, where a is
CO2 forcing coefficient and CO2PIis preindustrial CO2 concentration.
In a similar manner, Tice(t) can be expressed as:
Ticet1
C1
STicet14LficeutAbasetht
t
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CdT
dt SσT4Qicet
ℎ
C is heat capacty of the Earth system, S is solar radiation input, σT4 represents The energy
radiated by the Earth into space (Stefan-Boltzmann law), Qice(t) represents additional heat input due
to melting ice sheet, Lf is the latent heat of melting of ice about 334,000 J/kg, u(t) is ice velocity at
time t, the speedat which ice moves outward and is usually affected by temperature and ice thickness,
Abase(t) is the area of the bottom of the ice sheet refers to the area of the base of the ice sheet in contact
with the surface and the area can change as ice melts or accumulates, and the thickness of the ice
sheet in time is written as h(t).
The direct relationship between methane emissions and temperature change can be express it as:
TmethanetCH4 lnCCH4t1CCH4t
CCH4t06
αCH4 is radiative forcing sensitivity constant for methane, used to convert changes in methane
concentration into changes in temperature , CCH4 (t) is methane concentration at time t, usually
expressed in parts per million (ppm).
According to Jesper and Christian hourly flux rate calculation formula [11]:
2
427315
2731536001067
FCO2/CH4 represents the flux rate in g CH4/CO2 m-2h-1, C is the dry mole fraction concentration
(µmol mol-1), u
is the wind speed(m s-1), A is the cross-section area(m2), Mv is the molar volume
(m3 mol-1),Ta is the air temperature(℃) and M is the molar mass of CH4 or CO2(g mol-1)
Therefore the aunnally flux rate model would be:
2
4
27315
2731587601068
CCH4t2
4
hereisperyear 9
Moreover, researchers at the University of Copenhagen claims that the ice-free part of Greenland
consumes more than 65,000 tons of methane per year, while the wet areas only release 9,000 tons of
methane per year [12]. Therefore we assume Fwet is methane released from wetland areas and α
wetFwet is methane released converted to temperature increments and αwet is a coefficient that
represents the positive effect of methane released from a wetland area on temperature. Similarly we
can also write methane consume as αconsumeFconsume. Since the amount of methane been released
and consumed might change, thus we can write Fwet and Fconsume into:
Fwettαwet24
Fconsumetαconsume24
TmethanetαCH4 lnCCH4t1αwet2
4
αconsume2
4
CCH4t0
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Fwet, baseis the amount of methane released from wet areas under baseline conditions (in tons).
Fconsume, base is the amount of methane consumed by the ice sheet under baseline conditions (in
tons).αwet and αconsume here is a coefficient reflecting the effect of wetland release and ice sheet
depletion on the total flux
Thus, the full temperature model can be expressed as:
TtTt11
CS1α
4ABT0aln CO2
CO2PI1
C1
SσTicet14LfρiceutAbasetht
t
αCH4 ln CCH4t1αwet2
4
αconsume2
4
CCH4t0
Since water thermal expansion includes initial sea water and greenland ice sheet meltwater, it is
crucial to account for the combined volume change when estimating sea level elevation.
VexpansiontVtotalt1VicemelttTt 12
Vinitial is the initial volume of seawater which is the volume before ice melts, Vtotal(t-1)
represents the total volume of seawater at the previous time step t-1, Vicemelt(t) is the volume of
meltwater from the Greenland ice sheet at the current time t, β is the coefficient of thermal expansion
of water and ΔT(t) represents the temperature increase at time t, which influences the expansion and
is equal to T(t) subtract Tbaseline.
Vicemelt(t) is strongly influenced by temperature change, at the same time, the surface area of
ocean would also change as increasingin sea level.
13
Aice(t) is the surface area of the Greenland ice sheet at time t, dice(t) is the thinkness o the ice
sheet at time t,ΔTice(t) is the temperature change affecting the ice sheet at time t, and Tmelt is the
temperature threshold above which ice starts melting.
02 14
Aocean(t) is the increase in surface area due to sea level rise at time t, Aocean(o) is the initial
surface area of the ocean which is approximately to 3.61 ×108, REarth is the radius of Earth which
is approximately 6,371 kmand Htotal represents the total ocean level rise at time t, which is the result
of both thermal expansion and ice melt.
Thus the height of thermal expansion-driven rise in ocean levels at time t would looks like:
1
0215
Apart from the volume of ice in the Greenland ice sheet itself, as well as thermal expansion, affects
sea level, as does Isostatic Rebound.
2
16
Hrebound(t) represents the height rebound of the land surface at time t due to teh melting of ice
sheet, α2is a proportionality constant that can account for local geological variations, effectively
converting teh mass change into a height change, Δm(t) is the change in mass of ice sheet over time
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which is equal to the substration of Vmelt(t) and density of ice. ρ is the average density of the
crust(kg/m3). This varies depending on geological conditions but normally around 2700 kg/m3 for
continental crust, g is the acceleration depends on gravity, approximately 9.81 m/s2, and et
τ is the
exponential decay term accounts for the time-dependent nature of the rebound. τ is a time constant
that reflects how fast the rebound occurs after the removal of the ice load.
Ice sheet dynamics is another essential factor, and it is closely related to Isostatic rebound.
According to Glen’s Flow Law: 17
AtA0eQ
RT2731518
u
is the velocity of ice flow, A is the flow rate factor that depends on temperature and other
conditions,τ is the effective stress acting on the ice and n is typically around 3 for ice. A0 is the initial
area at t equal to 0, Q represent the heat energy involved in the preocess and ice usually is 60 kJ/mol,
R is the universal gas constant, typically R euqal to 8.314J/(molK)and T is temperature. Since mt
is equivalent to Vmelt(t) times ρice. Furthermore, Vmelt(t) can be written as u
tAbase tℎt.
Thus Hrebound after consider ice sheet dynamics can be written as:
2
A0eQ
RT27315
19
As Greenland ice sheet melt, the gravitational field would also change. The change of sea level
height due to gravity field change can be written as :
HgravitytGMicet
R213
2cos220
G represents gravitational constant(6.674×10-11 m3kg-1s-2), Mice t is Change in the mass of the
Greenland ice sheet at timeR is mean radius of the Earth which is approximately 6.371×106m, and θ
is latitude of the observation point.
Therefore the total sea level height change would be:
21
2.1. Contribution of Greenland Ice Sheet Melt to Sea Level Rise
The study found that with global warming, the melting rate of the Greenland ice sheet has accelerated
significantly, becoming one of the main drivers of global ocean level rise. The rate of ice sheet melting
is directly related to the rise in global temperature, and the simulation results show that the melting
of the Greenland ice sheet will lead to global rise in ocean levels of several centimeters to tens of
centimeters in the coming decades, depending on the magnitude of the temperature rise. Under the
high-temperature scenario, the rate of ice sheet loss will accelerate significantly, and the contribution
to the rise of the global ocean level will be more significant.
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2.2. The Relationship Between Thermal Expansion of Seawater and Sea Level Rise
In addition to melting ice sheets, the thermal expansion of ocean water is a crucial contributor to sea
level elevation. As global temperatures rise, the oceans absorb more heat, causing the volume of
seawater to expand, further exacerbating sea level rise. The study shows that the thermal expansion
effect contributes to a considerable proportion of elevated sea levels globally, especially in tropical
and subtropical seas, so the thermal expansion effect is more pronounced. The simulation results
show that even without additional ice sheet melting, the thermal expansion effect of seawater alone
would cause significant rise in sea levels.
2.3. The Impact of Isostatic Rebound and Changes in the Gravitational Field
With the melting of the Greenland ice sheet, the isostatic rebound effect has gradually emerged. After
the ice sheet lost its massive mass, the Earth's crust gradually rose, leading to a slower rate of sea
level rise in and around Greenland than the global average. At the same time, melting ice sheets also
trigger changes in the Earth's gravity field, further affecting the global distribution of sea levels. The
study found that some areas farther away from Greenland could experience faster ocean level rise due
to the redistribution of the gravitational field. In contrast, the rise of sea level near Greenland would
be relatively slower. In addition, the impact of melting ice sheets on Earth's rotation could also have
potential follow-on effects, further altering global climate and ocean dynamics.
2.4. The Impact of Integrated Feedback Mechanisms
In conclusion, the study explores the multiple impacts of the loss of ice sheets from Greenland on the
rise of the global sea level by establishing a coupled model. Studies have shown that with the
intensification of global warming, the melting rate of ice sheets has increased significantly, becoming
one of the critical factors driving ocean level elevation. In addition, the thermal expansion effect of
seawater also plays a significant role in rising sea levels, especially in higher-temperature waters. At
the same time, the melting of the ice sheet also triggered the isostatic rebound of the crust and the
change of the gravity field, resulting in the sea level rise in different regions showing obvious
imbalance. These results reveal the complex feedback mechanism between ice sheet melting and
global climate change. They provide an essential scientific basis for predicting future sea level
changes and their impacts on coastal regions worldwide. Through the analysis of this study, we can
better understand the interaction between climate change, ice sheet melting, and ocean level rise,
which can help promote more effective climate response measures and disaster prevention planning
of coastal cities worldwide.
3. Conclusion
This paper systematically analyses the role of the melting of the Greenland ice sheet in rising global
sea levels through coupled models. Global warming has been found to lead to the accelerated melting
of the Greenland Ice Sheet, which has become one of the main drivers of sea level rise. Model
simulations show that sea levels will rise significantly in the coming decades as temperatures rise.
The study also analyzed the impacts of hydrothermal expansion, equilibrium rebound, and changes
in gravity field on sea level and found that the combined effects of these factors lead to an uneven
rise in sea level, which provides a scientific reference for disaster prevention planning in coastal areas.
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