TCThe CryosphereTCThe Cryosphere1994-0424Copernicus GmbHGöttingen, Germany10.5194/tc-9-1983-2015Numerical simulation of formation and preservation of Ningwu ice cave, Shanxi, ChinaYangS.ShiY.shiyl@ucas.ac.cnState Key Laboratory of Continental Tectonics and Dynamics, Institute of Geology, Chinese Academy of Geological Sciences, Beijing, 100037, ChinaKey Laboratory of Computational Geodynamics, Chinese Academy of Sciences, Beijing, 10049, ChinaUniversity of Chinese Academy of Sciences, Beijing, 100049, ChinaY. Shi (shiyl@ucas.ac.cn)22October2015951983199325January201514April20153September20154October2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://tc.copernicus.org/articles/9/1983/2015/tc-9-1983-2015.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/9/1983/2015/tc-9-1983-2015.pdf
Ice caves exist in locations where annual average air temperature is higher than 0 ∘C. An example is Ningwu
ice cave, Shanxi Province, the largest ice cave in China. In order to
quantitatively investigate the mechanism of formation and preservation of
the ice cave, we use the finite-element method to simulate the heat transfer
process at this ice cave. There are two major control factors. First, there
is the seasonal asymmetric heat transfer. Heat is transferred into the ice
cave from outside very inefficiently by conduction in spring, summer and
fall. In winter, thermal convection occurs that transfers heat very
efficiently out of the ice cave, thus cooling it down. Secondly, ice–water
phase change provides a heat barrier for heat transfer into the cave in
summer. The calculation also helps to evaluate effects of global warming,
tourists, colored lights, climatic conditions, etc. for sustainable
development of the ice cave as a tourism resource. In some other ice caves in
China, managers have installed airtight doors at these ice caves' entrances
with the intention of “protecting” these caves, but this in fact prevents cooling in winter and
these cave ices will entirely melt within tens of years.
Introduction
An ice cave is a type of natural cave that contains significant amounts of
perennial ice. An ice cave is a rare phenomenon. Among the best known are
Eisriesenwelt ice cave, Austria (May et al., 2011; Obleitner and
Spötl, 2011; Schöner et al., 2011); Dobšináice cave,
Slovakia (Bella, 2006; Lalkovič, 1995); Scărisoara ice cave,
Romania (Holmlund et al., 2005; Perşoiu et al., 2011); and Monlesi ice cave, Switzerland
(Luetscher et al., 2007, 2008). Eisriesenwelt ice cave is the largest in the world. Dobšiná ice cave
is also huge, with an ice volume of over 110 000 m3 (Bella, 2006).
In China, more than 10 ice caves have been found, including Ningwu,
Wudalianchi, Taibaishan, Cuihuashan, Baiyizhai and Shennongjia ice caves.
Studies of ice caves began as early as 1861 (Peters, 1861). In recent
decades, in the context of interest in global climate change, six
international conferences on ice caves have been held, with the
reconstruction of regional ancient climate change as an important topic for
discussion (Laursen, 2010). Several articles have reported seasonal air
temperature oscillations of several degrees Celcius from ventilated cave systems
(Roberts et al., 1998; Lacelle et al., 2004; Johnson et al., 2006).
Therefore, to evaluate the impact of changing climatic conditions on cave
environments, a better explanation of subsurface heat and mass transfers is
necessary (Luetscher et al., 2008). Moreover, ice caves are
tourism resources. A better explanation of subsurface heat and mass
transfers could help to manage ice caves more scientifically.
Location (a), cross section (b), entrance (c)
and inside (d) of Ningwu ice cave. In (b): (a) the main cavern, (b) block
ice, (c) layered ice, (d) limestone, (e) the entrance, and (f) a fracture.
In the past, empirical calibrations have been performed to determine the spatial
and temporal distribution of cave air temperature as a function of the
external atmospheric conditions (de Freitas and Littlejohn, 1987;
de Freitas et al., 1982). In temperate karst environments, explanation of
the survival of subsurface ice accumulations represents probably the most
severe test for models of the magnitude and direction of heat and mass
transfers induced by cave air circulation (Luetscher et al.,
2008). In mathematics and engineering, the finite-element method (FEM) and
the finite-difference method (FDM) are popular for finding approximate
solutions for partial differential equations. We have not found any study in
which these numerical techniques are applied to ice caves.
In China, ice cave studies started only recently, after 1998, when Ningwu
ice cave was found. Although Ningwu ice cave has been widely reported during
the past decade (Gao et al., 2005; Meng et al., 2006),
little was known about the processes controlling the formation and
preservation of perennial subsurface ice deposits under changing climate
conditions (Chen, 2003). We attempt to apply FEM to simulate the energy
fluxes of Ningwu ice cave and then quantitatively interpret the formation
and preservation mechanism of the ice deposit in Ningwu ice cave. Some
suggestions are given to manage Ningwu ice cave.
Study site
Ningwu ice cave (38∘57′ N, 112∘10′ E; 2121 m a.s.l. (above sea
level); Fig. 1a) is the largest ice cave ever found in China. Located on
the northern slopes of Guancen Mountain, Ningwu County, Shanxi Province, it
is known to local people as “the ten-thousand-years ice cave”. The
surrounding rock consists of Ordovician Majiagou limestone, dolomitic
limestone, argillaceous dolomite and thin brecciated limestone which is
locally densely fractured (Shao et al., 2007). A geophysical
exploration (using magnetotelluric measurement) was carried out by Shao et al. (2007) in order to investigate the shape of the ice
cave, and they obtained the vertical cross section of the ice cave. The cave space is
about 85 m depth. The widest part is in the middle, with a width of 20 m.
The ice cave is a major tourist attraction. From May to October, about
1000 visitors enter the cave per day. The ice cave has only one entrance (Fig. 1c),
and has wooden spiral stairs leading to a bowling-pin-shaped room. Ice
covers the host rock almost completely. Ice stalactites and ice stalagmites
(Fig. 1d) can be seen in all parts of the cave.
The outside of the ice cave has a temperate climate. The external mean air
temperature from June to September is about 14.6 ∘C, and the mean
annual air temperature is 2.3 ∘C (Meng et al., 2006). The
daily temperature from 1957 to 2008 is obtained from Wuzhai meteorological
station (about 320 m lower than Ningwu ice cave), which is the nearest
station to the ice cave. We averaged observational air temperature at Wuzhai
station to obtain the annual temperature and then derived the mean annual
temperature at Wuzhai station. We calculated the difference between the
average annual air temperature at Ningwu ice cave and that at Wuzhai
station. After reducing the annual temperature at Wuzhai station by the
difference, we then obtain the annual temperature variation outside the ice
cave (Fig. 2).
Qualitative analysis
There are different hypotheses about the preservation mechanism of ice
deposit in Ningwu ice cave. Chen (2003) proposed that the existence of a
“cold source” led to the negative geothermal anomaly which preserves the
ice deposit. Meng et al. (2006) ascribed the ice deposit to multiple factors,
including geographical location, the “icehouse effect”, the “chimney effect”,
and the “thermal effect” produced by the ice deposit and the “millennial
volcano”. However, they did not provide any further details about these factors. Gao et
al. (2005) analyzed two aspects: terrain and climate. Because this region
has a long, cold winter and a short, cool summer, they considered that far
more cold air than warm air entered the region and thus the ice cave stayed
cold over the year.
Subsurface temperature usually increases with depth at a geothermal gradient
of about 1.0–3.0 ∘C (100 m)-1 (Hu et al., 2001).
The notion that there is a permanent “cold source” underground is
unfounded. Even if a cold region had somehow formed, it would be heated up
by the geothermal flux from underneath in geological time. Reversal of
geotherms can occur in the presence of the advective heat transfer due to crustal movement or groundwater flow (Shi and Wang, 1987). A
reversal of geotherms can also occur from transient changes in surface
temperature and be induced by steep topography (Gruber et al.,
2004). However, the outside of Ningwu ice cave has a temperate climate. It is
hard to preserve an ice cave in a temperate climate without a sustainable
cooling mechanism. In the presence of a geothermal gradient, the host rock
continuously transfers heat to the ice cave, so there must be a sustainable
mechanism to remove the heat from underneath and ensure the maintenance of
the ice cave.
Yearly variation in external air temperature of Ningwu ice cave.
The temperature outside the ice cave undergoes annual cyclic variations: in
spring, summer and fall, it is higher than the internal temperature, but in
winter it is lower. As Ningwu ice cave is bowling-pin-shaped with only an
opening in the upper part, cold air in spring, summer, and fall is heavy and
sinks into the cave and thus will not produce natural thermal convection.
Conduction is the main form of heat transfer from the outside down to the
ice cave, and from the host rock due to the terrestrial heat flows. Thermal conductivities are not high for either
rock or air, and the conductive heat transfer efficiency is very
low, so the heat transferred to the ice cave in the three seasons is quite
limited. In winter, the temperature is low inside the ice cave but even
lower outside. The air in the ice cave is lighter and air outside the cave
entrance is heavier. It could thus become gravitationally unstable, and
thermal convection could occur. The external cold air flows into the cave to
cool it down, and it removes the heat transferred into the cave from the host
rock, as well as the heat transferred into the cave through the entrance in
spring, summer and fall. Since convective heat transfer is much more
efficient than conduction, the heat transferred out of the cave in the
winter months is enough to balance the heat that transferred into the cave year-round.
Ice melting into water absorbs a lot of latent heat. The melting heat of ice
is 334 kJ kg-1 and the specific heat of limestone is about
0.84 kJ kg-1 K-1. During summer, much of the heat transferred to cave is
consumed to melt the ice to 0 ∘C water. Therefore, ice–water phase
change can reduce the rate of temperature rise. Similarly, when the ambient
temperature decreases, ice–water phase change can reduce the rate of
temperature decrease. Therefore, ice–water phase change in the ice cave can
“buffer” the temperature change. A small amount of ice melting near the
cave entrance effectively prevents the heat from being transferred into the
deep cave. When the surface water flows into the ice cave from the entrance,
the ice cave temperature will not significantly increase.
The calculated energy balance of some cave ices (e.g., Eisriesenwelt ice cave)
is largely determined by the input of long-wave radiation originating at the
host rock surface (Obleitner and Spötl, 2011). Ice covers the host
rock in Ningwu cave almost completely. Therefore, we suggest that long-wave
radiation originating at the host rock surface is not a predominant factor
in the processes of the formation and preservation of ice deposit in Ningwu ice cave.
In summary, the air and the host rock transfer heat to the ice cave, making
the cave temperature rise in spring, summer and fall. In winter, the heat
convection of air makes the heat flow out of the cave, lowering the cave
temperature. However, the ice–water phase transition effect occurs all year
round. The annual heat budget of income and output is balanced, so the cave
will be in a cyclic state with very small temperature fluctuations, and the
average temperature is always lower than 0 ∘C; thus ice bodies in
the ice cave can be preserved.
Snow crystals (or hoar frost) are single crystals of ice that grow from water
vapor. If humidity enters a cave and then forms an ice deposit, snow crystals
could be discovered (Kenneth, 2005). However, it is difficult to find snow
crystals in Ningwu ice cave. No clear traces of water or snow entering the
cave through its entrance could be found. However, karstified
carbonate rock is heterogeneous and highly fractured, and with a permeability
developed such that water movement occurs below the surface (Fairchild
and Baker, 2012). In summary, we infer that most of the ice in the cave is
formed by freezing of infiltration water.
Water and ice are in a dynamic equilibrium state. Water infiltrates into
Ningwu ice cave throughout the year and forms ice. Ice at the bottom of
Ningwu ice cave is thawed under geothermal flow, and the produced water
infiltrates into areas beneath Ningwu ice cave. Ice stalactites and ice
stalagmites (Fig. 1d) can be seen in all parts of Ningwu ice cave. This can
verify the former process, but no directly observational evidence supports
the latter process.
Ra, the Rayleigh number, is a dimensionless number associated with
buoyancy-driven flow. When Ra is below a critical value for that fluid, heat
transfer is primarily in the form of conduction; when it exceeds the
critical value, heat transfer is primarily in the form of convection. Nu, the
Nusselt number, is a dimensionless number, defined as the ratio of
convection heat transfer to pure conduction heat transfer under the same
conditions. The process of ice build-up in Ningwu ice cave is a self-regulating
process. If too much ice accumulates in Ningwu ice cave, then the cavity
will become small. Thus, Ra and Nu will be reduced, meaning the freezing
efficiency becomes low. Some of the cave ice will be thawed, and the cavity will become
large, and thus Ra and Nu will be increased; this means that the freezing efficiency will become high, and therefore ice will be accumulated in Ningwu ice cave.
Principle of simulationBasic ideas of simulation
Two heat transmission mechanisms must be taken into account to explain the
preservation of ice mass in ice cave, namely thermal conduction and
convection. The phase change must also be considered. The heat conduction
equation can be used to describe the heat-conducting process, while for the
convection process, due to the complicated geometrical shape structure
inside the ice cave and complex varying boundary conditions, the convection
pattern of air and its thermal consequences are hard to determine exactly.
In view of this, a widely used, simplified method is applied in this study:
evaluation of Nu and solving the conductive equation by introducing an equivalent
thermal conductivity of the convecting air. In the case of an upright
circular tube, the relation between the temperature difference of the top
and the bottom and Nu can be determined by adopting the experimental relation
of natural thermal convection. The enthalpy method can be adopted to
calculate the phase change.
In every time step of our modeling process, it is judged whether air convection
occurs based on the temperature difference between the top and the bottom of
the cave. If there is no convection, the simple conduction problem will be solved,
while if convection occurs, an effective conductivity is used in the
thermal equation.
Equation and physical parameters
The heat conduction equation is
cρ∂T∂t=k∇2T,
where c is the specific heat, ρ is density, T is temperature (unknown
number), t is time and k is thermal conductivity. For the convective heat
transfer process, an equivalent thermal conductivity is used in Eq. (1) based
on Nu.
The enthalpy method is used to calculate the phase change process. A
physical quantity enthalpy, H, is introduced in Eq. (2), where Tr is
an arbitrary lower-temperature limit. For phase change, enthalpy H can be
determined by Eqs. (3)–(5) (Lewis, 1996); in particular, (Ts, Tl) is the phase change range. Water–ice phase change occurs at
0 ∘C. But in the numerical model, it is necessary to give a phase change range.
H(T)=∫TrTρc(T)dT,H(T)=∫TrTρcs(T)dTT≤Ts,H(T)=∫TrTsρcs(T)dT+∫TsTρdLdT+ρcf(T)dTTs<T<Tl,H(T)=∫TrTsρcs(T)dT+ρL+∫TsTlρcf(T)dT+∫TlTρcl(T)dTT≥Tl,
where cs is the specific heat in solid phase, cl is the specific heat
in liquid phase, cf is the specific heat in solid–liquid mixing state
and L is the latent heat. There are many ways to calculate heat capacity
(Lewis and Roberts, 1987). The simple and accurate backward
differentiation formula (Lewis and Roberts, 1987; Morgan et al.,
1978) is adopted here, as expressed in Eq. (6), where (n) and (n- 1) stand
for the time step. Equation (6) can be substituted into the heat equation along
with the relevant material parameters for calculation.
(cρ)(n)=dHdT(n)=H(n)-H(n-1)T(n)-T(n-1)
Relevant materials include limestone, ice, ice–limestone mixture, air and
water. Parameters of these materials are listed in Table 1. The physical
parameter of ice–limestone mixture is taken as the arithmetic mean of those
of ice and limestone. We assume that the ice body exists when temperature is
below -0.1 ∘C, and that an ice–water mixture exists between -0.1 and
0.1 ∘C, and this becomes water when the temperature exceeds 0.1 ∘C.
The ratio of ice and water in the mixture is linear to the
temperature within the phase change range, and so are the physical
parameters. The latent heat L of the ice–water phase change is 334 kJ kg-1.
When the convection occurs, heat transfer is Nu times greater than the
conductive heat transfer under the same conditions. In other words, an
equivalent thermal conductivity can be introduced, which is Nu times greater
than the air thermal conductivity (Schmeling and Marquart, 2014).
Nu is related to the temperature difference of air at the top and the bottom
of the cave, to physical properties (e.g., viscosity and conductivity of
air), and also to the geometry of the cave. Ningwu ice cave can be approximated by an
upright circular tube. For such a tube, Nu can be calculated based on fluid
thermodynamics studies. When Eq. (7) is satisfied (Sparrow and
Gregg, 1956; Yang and Tao, 2006), which is the case for Ningwu ice cave, the
natural convection heat transfer experimental relation (Sparrow and
Gregg, 1956; Incropera et al., 2011) is expressed as Eq. (8).
d/h≥35/Gr1/4Num=C(Gr⋅Pr)mn
In Eqs. (7) and (8), d and h are respectively the diameter and height of a circular tube; Num is the Nusselt number, where subscript “m” represents
the arithmetic mean temperature of the boundary layer; Gr is the Grashof
number, which approximates the ratio of the buoyancy to viscous force acting
on a fluid; Pr is the Prandtl number; and C and n are constants, the values of which
are shown in Table 2.
Gr number and constant for different flow types (Yang and Tao, 2006).
The Prandtl number, a dimensionless number, is defined as the ratio of
momentum diffusively to thermal diffusively. Pr is dependent only on the fluid
material. For air, Pr is 0.7. The Grashof number is
Gr=gβΔTl3/υ2,
where g is the acceleration of gravity, β is the coefficient of cubical
expansion, ΔT is a temperature difference, l is a characteristic
length and υ is the coefficient of kinematic viscosity. The values
are g= 9.8 m s-2, β= 3.67 × 10-3 k-1,
l= 80 m, υ= 13.30 × 10-6 m2 s-1 and
are substituted into Eq. (9) to obtain
Gr=1.041×1014ΔT.
According to Eq. (10), when the temperature difference is only
10-3∘C, Gr can reach 1.041 × 1011.
According to Table 2, we infer that natural convection will occur and the
flow state of air is a turbulent flow when the temperature is higher inside
than outside the ice cave. Equation (11), relating Nu to the temperature
difference, can be obtained when relevant parameters are substituted into Eq. (8).
Nu=11 000(0.0740ΔT)1/3
Even if Eq. (7) is not satisfied, corresponding experimental relations
can also be found in the literature (Cebeci, 1974; Minkowycz and Sparrow,
1974; Yang and Tao, 2006).
Models and boundary conditions
The rectangular Eulerian computational domain corresponds to a physical
domain of 300 × 190 m on the basis of the ice cave cross section
(Fig. 1b). There are 32 825 nodes and 64 986 elements involved in drawing
the FEM grid. The grids for the ice body and the interior air are denser.
The mean value of the geothermal gradient of the Lvliang highland area, where
Ningwu ice cave is located, is 2.02 ∘C (100 m)-1 (Li,
1996). The mean value of the geothermal gradient of the low-lying Linxian
and Liulin areas in Shanxi Province is 2.20 ∘C (100 m)-1
(Hu et al., 2001). We take the normal geothermal gradient value
of 2.0 ∘C (100 m)-1 in the model. The temperature boundary
conditions are assigned to both sides of the model, with the annual average
temperature at the surface and increase with depth following the geothermal
gradient. The heat flow boundary condition is assigned for the bottom
boundary. The terrestrial heat flow value is the product of the geothermal
gradient times the thermal conductivity of the limestone host rock.
According to Fig. 2, we prescribe the variation temperature to the top boundary.
The initial thermal structure is calculated assuming the surface temperature
remained constant at the annual average (Fig. 3).
During the simulation, models with phase transition included and phase
transition neglected are both calculated for comparison. When phase change
is considered, latent heat and the material property variation are considered.
Simulated result and analysisEvolution of an ice-deposit-forming model
Because of the periodic change of the ambient air temperature, the
temperature in the ice cave will show a periodic variation corresponding to
conduction and convective heat transfer. Figure 4a shows the evolution of
the temperature at the bottom of the ice cave. It can be interpreted as the
process of formation of the cave ice. If a cave was formed but not connected
with the outside, it may have a temperature distribution similar to that in Fig. 3.
If the cave became connected to the outside, i.e., it collapsed at its top
and produced an entrance to the cave, an ice cave would then form within a
decade due to the winter convective cooling and would stabilize in a century.
Figure 4b shows the details of the first two decades and that the
calculated results with phase change considered (black line) do not differ
significantly from those without considering phase change (red line) in the
cooling process. Starting from normal ground temperature, the internal
temperature of the ice cave drops rapidly in the first decade, then drops
more gradually and finally tends to become stable.
Figure 4b shows the details of temperature evolving in the ice cave during
its initial 16 years of formation. It is seen that the cave ice can be
maintained below 0 ∘C all year round after winter cooling for about
5 years. The cave temperature increases in spring, summer and fall and
decreases in winter, presenting annually periodic variation. The air
temperature of Ningwu ice cave decreases rapidly in winter, but the
temperature increases slowly in spring, summer and fall because the heat
conduction in these seasons is much less efficient than convective
heat transfer in winter. With phase change considered (black line), the
increased rate of temperature in summer is smaller than that without phase
change (red line), because latent heat is required to melt ice near the
cave entrance, thus delaying the conduction of heat to the bottom of the
cave. In winter, the convective cooling is so effective that the difference
is minimized.
Initial reference temperature distribution around Ningwu ice cave.
(a) Formation process of Ningwu ice cave, (b) initial
formation process and (c) quasi-stable state.
Figure 4c shows the cave temperature annual fluctuations for the case where the process
has lasted two centuries, long enough to have evolved to a stable cyclic
state. The amplitude of the temperature variation is about 1.0 ∘C
(from -3.9 to -2.9 ∘C). Ningwu ice cave has been opened to
tourists, so the cave temperature has been disturbed. According to our
measurement on 5 June 2012, the lowest internal temperature of the ice cave
was -1.5 ∘C. Through the record in the literature, the actual measured
internal temperature of the ice cave ranges between -1.0
(Meng et al., 2006), -4.0 and -6.0 ∘C (Gao et al., 2005). The difference in measured results may be
caused by different measuring methods and different measuring time and
positions. Similar to what is shown in Fig. 4b, the cave temperature presents annual
periodic variation, and the overall increasing rate of cave temperature is
lower than its decreasing rate, because the heat transfer efficiency of
conduction is much lower than that of heat convection. The variation in cave
temperature for the model with phase change considered (black line) is basically
the same as that without phase change considered (red line). The reason is
that, although we considered phase change during calculation, the temperature
of the ice body in the cave is always kept below 0 ∘C when it
reaches a stable cyclic state and no phase change actually occurs.
Figure 5a and b show the spatial temperature distribution around the ice
cave in winter and summer, respectively, during the stable stage. Both panels
show that a small portion of rock at the top of the ice cave presents a
negative geothermal gradient and that most of the host rock presents a normal
positive geothermal gradient. Beneath the bottom of the cave, however,
geothermal gradients are much higher than normal. The ice body temperature
is always kept below 0 ∘C, although the external temperature is
completely different. In Fig. 5a, the temperature of the shallow ground is
lower than 0 ∘C, corresponding to a frozen zone in winter. In
Fig. 5b, the temperature of shallow parts of ground is higher than 0 ∘C,
indicating that the frozen part is melted and there is no permafrost. These
features agree with actual conditions.
Temperature distribution around Ningwu ice cave in winter (a)
and summer (b).
Internal temperature evolution diagram when ice is melting.
Evolution of an ice-deposit-melting model
The ice body in the ice cave will melt if there is no air convection heat
transfer in winter. With the temperature shown in Fig. 5a taken as an initial
temperature, the evolution of temperature distribution will be calculated
with or without the phase change effect considered. The results are shown in
Fig. 6 as a black line and a red line, respectively. They are the same when
temperature does not reach the phase change temperature. The ice body takes
much longer to thaw when the latent heat of melting is taken into
consideration than when it is not. A complete thaw of the ice body takes
23 years when the latent heat of phase change is not considered, compared with
37 years when it is considered.
Sensitivity to model parameters
The external air temperature, Nu and the number of tourists could
directly affect the energy transfer in Ningwu ice cave. Therefore,
sensitivity experiments need to be performed for these factors. With respect
to the external air temperature, we consider two aspects: (1) the mean annual
temperature and (2) the amplitude of annual temperature. For the case where
the mean annual temperature increases (decreases) by 1.0 ∘C, the
computation results are shown as Fig. 7a and g (Fig. 7b and h). For the case
where the amplitude of external temperature increases (decreases) by
5.0 ∘C, the computation results are shown as Fig. 7c and i (Fig. 7d
and j). For an increase (decrease) in Nu by 10 %, the computation
results are shown as Fig. 7e and k (Fig. 7f and l). About 1000 visitors enter
the cave per day from May to October. The heat potentially released by a
single person is 840 J. We assume that each visitor spends 1 h in Ningwu ice
cave. Additionally, there are two hundred 15 W light bulbs. Figure 7m shows
the computation results for when we consider the number of tourists and light
bulbs.
Similar to what is seen in Fig. 4b, Fig. 7a–f show the details of first two decades
and indicate that the ice deposit would be formed in Ningwu ice cave within the
first two decades in these different experiments. Figure 7g–l correspond
to Fig. 7a–f. As shown in Fig. 4c, Fig. 7g–l depict
the cave temperature annual fluctuations for when the process has lasted two
centuries, long enough to have evolved to a stable cyclic state. Compared with
Fig. 4c, Fig. 7m shows that the current density of tourists and
number of light bulbs in Ningwu ice cave could not cause the ice deposit to melt. Figure 7n shows the ice cave temperature annual fluctuations when the
mean annual temperature increases by 3.5 ∘C. We can see the temperature
ceiling is -0.1 ∘C. We consider this to be the minimum climatic
condition required to form Ningwu ice cave.
Discussion
The age of the cave and that of the ice body are different. The formation of the
cave cavity could be old and have taken place in a warmer climate. The
formation of the ice body in the cave is a much later process that took
place when the bowling-pin-shaped cave was formed and the climate became
cold enough. In the present climate, our numerical modeling suggests that
the year-round ice body can be formed within a decade.
In spring, summer and fall, air and host rock transmit heat to the ice cave
by thermal conduction, increasing the temperature in the ice cave only
slightly, since the conduction efficiency is low. In winter, heat is
transmitted out of the ice cave by natural thermal convection of air,
efficiently decreasing the temperature in the ice cave. Phase change
accompanies the thermal processes. Considering these mechanisms, the results
show that (1), starting from a normal ground temperature, a year-round ice
body will be formed in the cave in less than a decade, about 5 years in our
model (Fig. 4b), and the ice cave temperature will decrease continuously
for more than a century, and also that (2) the ice cave will finally reach a stable cyclic
state and its temperature will fluctuate within a certain range, less than
1.0 ∘C (from -3.9 to -2.9 ∘C) for Ningwu ice
cave. At this stage, the annual total heat transferred to the cave by
thermal conduction and the heat removed from the cave by convection are balanced.
(a–f) Initial formation process of Ningwu ice cave in different
sensitivity experiments. (g–l) Corresponding quasi-stable state. (m) Sensitivity experiment featuring density of tourists and light bulbs. (n) Quasi-stable state when the mean annual
temperature increases by 3.5 ∘C.
It would be interesting to further investigate the possibility of imitating
nature and constructing a new kind of air conditioning system. At locations
with similar climate conditions, people could construct a basement more than
10 m deep, using natural air convection to freeze ice in the basement in
winter and circulate air to the basement for air conditioning in summer.
Installing an airtight door at a cave entrance, as one park has done in China
to “protect” the ice cave at night during the tourist season and for the
entire winter, when the cave is closed to tourists, actually blocks air
convection in winter. As a result, cold air cannot bring out heat from the
cave, and accumulation of heat flow from the surface and the deep crust will
finally lead to melting of the ice body in the cave. Our computation shows
that it takes less than 40 years to completely melt the whole ice body in
the cave. This implies that Ningwu ice cave is probably not currently
undergoing thawing of the relict ice. This also suggests that scientific
management is important for sustainable usage of natural tourism resources.
Otherwise, well-meaning acts such as installing a door to completely
seal the entrance for protection will actually destroy the natural wonder in
a few decades.
Conclusions
This paper has focused on quantitative analysis of the formation and
preservation mechanism of an ice body in Ningwu ice cave, a static ice cave.
The finite-element modeling leads to the following conclusion: the
controlling factor for forming and sustaining the ice body in the cave is
effective cooling of the cave in winter by natural air convection. Heat
conduction in spring, summer and fall is very ineffective at warming up the
cave. Ice–water phase change further prevents melting of ice in summer. The
formation of the cave may take a long geological time, but the formation of
the perennial ice body in the cave only takes decades or years under the
current temperature and geothermal gradient in the Ningwu area by winter air
convection. Once the ice body has formed, the cave temperature will maintain a stable cyclic
state. At this time, the amplitude of annual temperature variation in the
Ningwu ice cave is within 1.0 ∘C. Environmental warming even up to
1.0 ∘C in the Ningwu area will increase the cave temperature but not
melt the perennial ice body. The present heat from electric lighting and
visitors will not melt the ice body either. However, if the air convective
heat transfer is stopped in the winter, as has happened in some other Chinese ice
caves, the ice body in the cave could be completely melted within about
40 years. This analysis is important for sustainable management of the ice cave
as a tourism resource. The mechanism of ice cave formation may be adopted
for construction of energy-saving buildings: ice can be produced in winter
in a basement and used for air conditioning in summer.
Acknowledgements
We thank Yong'en Cai and Bojing Zhu for helpful discussions. Constructive
comments and suggestions from Stuart A. Harris and an anonymous reviewer
significantly improved the quality of this paper. This research is supported
by the National Natural Science Foundation of China (NSFC), project 41174067, and
the CAS/CAFEA international partnership program for creative research teams
(no. KZZD-EW-TZ-19).
Edited by: S. Gruber
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