Convective Cells Research Articles

Wall-attached convection under strong inclined magnetic fields

We employ a linear stability analysis and direct numerical simulations to study the characteristics of wall modes in thermal convection in a rectangular box under strong and inclined magnetic fields. The walls of the convection cell are electrically insulated. The stability analysis assumes periodicity in the spanwise direction perpendicular to the plane of a homogeneous magnetic field. Our study shows that for a fixed vertical magnetic field, the imposition of horizontal magnetic fields results in an increase of the critical Rayleigh number along with a decrease in the wavelength of the wall modes. The wall modes become tilted along the direction of the resulting magnetic fields and therefore extend further into the bulk as the horizontal magnetic field is increased. Once the modes localized on the opposite walls interact, the critical Rayleigh number decreases again and eventually drops below the value for onset with a purely vertical field. We find that for sufficiently strong horizontal magnetic fields, the steady wall modes occupy the entire bulk and therefore convection is no longer restricted to the sidewalls. The aforementioned results are confirmed by direct numerical simulations of the nonlinear evolution of magnetoconvection. The direct numerical simulation results also reveal that at least for large values of horizontal magnetic field, the wall-mode structures and the resulting heat transfer are dependent on the initial conditions.

Convective Properties and Lightning Activity in Different Categories of Thunderstorms over the Beijing Area during Five Warm Seasons

Based on comprehensive observations, including total lightning, Doppler radar, precipitation, and other meteorological data, the variations in thunderstorm properties and lightning activity of different categories for thunderstorms over the Beijing area during five warm seasons were investigated. According to the morphology of radar echo, thunderstorms were classified into five categories, including single convective cells, multi-cells, linear mesoscale convective system (MCS), nonlinear MCS, and weak convective precipitation system (WCPS). The diurnal variability of lightning, thunderstorm occurrence, and precipitation showed late-afternoon maxima, with the peak time of lightning frequency occurring before that of precipitation. Despite WCPS having the lowest lightning frequency, the percentage of +CG/CG was the highest with large peak currents. The convective available potential energy (CAPE) of linear MCS, multi-cells, nonlinear MCS, single cells, and WCPS categories followed a pattern from largest to smallest. Meanwhile, warm cloud depth (WCD) exhibited a smaller value in the well-organized thunderstorm categories and a larger value in the WCPS. The topographic forcing mechanism and large wind gradient along mountain slopes facilitated convection occurrence and enhancement, further promoting lightning production. Meanwhile, the nocturnal convection mechanism significantly impacted the activity of nonlinear MCS and WCPS.

Thermo-magnetic convection and convective magneto-gravitational parametric resonance in a horizontal ferrofluid layer under time quasi-periodic vibrations: A balance harmonic analysis

Convective instability in a horizontal ferromagnetic liquid layer with rigid boundaries is investigated in the presence of both an uniform magnetic field and a vertical quasi-periodic forcing having two incommensurate frequencies ω1 and ω2. A linearized convective instability analysis predicting the onset of convection is performed and by means of a Galerkin projection truncated to the first order, the linear dynamic of the system is reduced to a damped quasi-periodic Mathieu oscillator. Using a balance harmonic analysis, it turns out that at sufficiently low vibration frequencies, we recover the critical instability parameters related to the unmodulated case where the convection is mainly due to the magnetic mechanism. This feature means that the buoyancy mechanism does not contribute into the convective cells formation and consequently heating from below or from above does not alter the onset of convection. However, at sufficiently high vibration frequencies, both the magnetic and buoyancy mechanisms are operative and here we are dealing with a magneto-gravitational parametric resonance convection. The transition between these convective modes is occurred via bicritical states giving rise to cusp points in the magnetic Rayleigh number besides discontinuities in its corresponding critical wave number. In addition, it is shown that a proper tuning of the irrational frequency ratio ω=ω2/ω1 provides a control of the convection onset as well as the nature of its mechanism. Moreover, special attention is devoted to highlight the effect of the Prandtl number on the dynamic of the system at different values of the frequency ratio ω.

A Fresh View of the Asian‐Australian Monsoon Complexity: The Intertropical Convective Cell (ITCC) Framework

AbstractThe monsoon holds great significance in Asian‐Australian civilization. Recent studies realized the link between the monsoon onset and the seasonal migration of the Intertropical Convergence Zone (ITCZ). However, no clear ITCZ band is observed in the Asian‐Australian sector due to the strong influence of topography. Instead, there exists a large‐scale (∼1,500 km) tropical convective cell––a perennial system that we hereafter coin as the “intertropical convective cell (ITCC).” Using ERA5 reanalysis and satellite‐based outgoing longwave radiation products, here we show by objective detection and tracking that the ITCC exhibits eight phases during its seasonal migration along the Asian‐Maritime land bridge. Particularly, its sudden northward jump in boreal spring coincides well with the earliest (abrupt) onset of the Asian rainy season, while its equatorward retreat heralds the overall (gradual) monsoon withdrawal. These findings demonstrate the close link of the ITCC behavior to the spring‐fall asymmetry of the monsoon. Dynamically, the off‐equatorial ITCC features a monsoon regime with a cross‐equatorial overturning circulation, differing markedly from its equatorial regime with two weak overturning cells on each side. Further budget analyses prove our hypothesis that the north‐south charging gradient of the moist static energy determines the ITCC's spring‐fall asymmetric propagation, illuminating the physical origin of the spring‐fall asymmetry in the monsoon. Our results demonstrate the usefulness of the ITCC framework in understanding the Asian‐Australian monsoon complexity in a fresh and holistic manner. The framework will facilitate monsoon diagnosis, modeling and subseasonal‐to‐seasonal forecasting in the Asian‐Australian sector.

An early warning approach for the rapid identification of extreme weather disasters based on phased array dual polarization radar cooperative network data.

In recent years, X-band phase array dual polarization weather radar technology has matured. The cooperative networking data from X-band phase array dual polarization weather radar have many advantages compared with traditional methods, namely, high spatial and temporal resolution (approximately 70 seconds in one scan, 30 m in radial distance resolution), wide coverages that can compensate for the observation blind spots, and data fusion technology that is used in the observation overlap area to ensure that the observed precipitation data have spatial continuity. Based on the above radar systems, this study proposes an improved hail and lightning weather disaster rapid identification and early warning algorithm. The improved thunderstorm identification, tracking, analysis, and nowcasting (TITAN) algorithm is used to quickly identify three-dimensional strong convective storm cells. Large sample observation experiment data are used to invert the localized hail index (HDR) to identify the hail position. The fuzzy logic method is used to comprehensively determine the probability of lightning occurrence. The comparative analysis experiment shows that, compared with the live observation data from the ground-based automatic station, the hail and lightning disaster weather warning algorithm developed by this study can increase warning times by approximately 7 minutes over the traditional algorithm, and its critical success index (CSI), false alarm ratio (FAR) and omission alarm ratio (OAR) scores are better than those of the traditional method. The average root mean square error (ARMSE) for identifying hail and lightning locations by this improved method is also significantly better than that of traditional methods. We show that our method can provide probabilistic predictions that improve hail and lightning identification, improve the precision of early warning and support operational utility at higher resolutions and with greater lead times that traditional methods struggle to achieve.

The Thunderstorms With the Greatest Lightning Densities on Earth

AbstractThe most intense thunderstorms on Earth were surveyed using the comprehensive meteorological instrumentation on the Tropical Rainfall Measuring Mission (TRMM) satellite. Expansive land‐based Mesoscale Convective Systems (MCSs) were consistently identified among the Earth's most intense thunderstorms, with their organization into many convective cells spanning a large areal extent permitting exceptional overall flash rates for these storms. In this study, we identify a new class of extreme thunderstorm. Lightning‐dense thunderstorms are relatively compact convective storms whose concentrated lightning activity hinders our ability to accurately measure their flash rates. The top storms have a flash rate of one flash spanning many seconds, as there is insufficient separation to distinguish one flash from another. While any particularly active convective cell could be capable of producing high lightning densities, we find that thunderstorms with the greatest lightning densities on Earth are found in maritime thunderstorms that have not been appreciated in prior work due to the inaccurate flash rate measurements. These storms that are mostly found throughout the Gulf of Mexico and east of South Africa (among other coastal and oceanic regions) have measured TRMM proxies for convective intensity that rival the top MCS thunderstorms, but their horizontal and vertical dimensions are small by comparison. Thus, the necessary microphysical elements for electrification processes are more highly concentrated, enabling the observed extreme lightning densities.

A Parameterization for Cloud Organization and Propagation by Evaporation‐Driven Cold Pool Edges

AbstractWhen the negatively buoyant air in the cloud downdrafts reaches the surface, it spreads out horizontally, producing cold pools. A cold pool can trigger new convective cells. However, when combined with the ambient vertical wind shear, it can also connect and upscale them into large mesoscale convective systems (MCS). Given the broad spectrum of scales of the atmospheric phenomenon involving the interaction between cold pools and the MCS, a parameterization was designed here. Then, it is coupled with a classical convection parameterization to be applied in an atmospheric model with an insufficient spatial resolution to explicitly resolve convection and the sub‐cloud layer. A new scalar quantity related to the deficit of moist static energy detrained by the downdrafts mass flux is proposed. This quantity is subject to grid‐scale advection, mixing, and a sink term representing dissipation processes. The model is then applied to simulate moist convection development over a large portion of tropical land in the Amazon Basin in a wet and dry‐to‐wet 10‐days period. Our results show that the cold pool edge parameterization improves the organization, longevity, propagation, and severity of simulated MCS over the Amazon and other different continental areas.

Formation of the Naxos nested domes and crustal differentiation by convection and diapirism

The Naxos dome, in the middle of the Aegean domain, exposes the former root of the Alpine orogenic belt and represents a key natural example to investigate the development of gravitational instabilities during orogenic evolution and their impact on crustal differentiation. The Naxos dome is cored by migmatites with structures depicting second order domes with a diameter of 1–2 km nested in the first order deca-kilometer scale dome that formed at the onset of orogenic collapse. Zircon grains from the migmatites record a succession of crystallization-dissolution cycles with a period of 1–2 Myr. These features have been attributed to the development of convective and diapiric gravitational instabilities, related to thermally induced and compositional buoyancy. In this paper, we test the pertinence of this model with a thermal-mechanical numerical experiment performed with a volume of fluid method (VOF) known to preserve material phase interfaces during large deformation of viscous layers. Partial melting of the crust is modeled by strain-rate and temperature dependent viscosity and temperature dependent density. Moreover, horizontal layers with density, viscosity and heat production variations mimic more felsic or more mafic lithologies in a crust of intermediate composition. With basal heating, gravitational instabilities initiate with local segregation of the buoyant versus heavier layers, followed by diapiric upwelling of buoyant pockets of aggregated less dense material. Convection starts after 5 Myr, approximately when half of the crust has a viscosity lower than 1019 Pa s. The size of the convection cells increases as the temperature rises in the crust and reaches ∼25 km in diameter after ca. 20 Myr, which defines the size of first order domes. Some of the heterogeneous material is entrained in the convection cells with a revolution period of 1 to 3 Myr. However, most of the denser material accumulates in the lower crust, while the buoyant material segregates at the top of the convection cells and forms diapirs that correspond to second order domes, of several kilometers in diameter and nested within the first order domes. This model, which reproduces the first order characteristic dimensions of the Naxos nested domes and the periodicity of their zircon geochronological record, demonstrates the efficiency of gravitational instabilities in the formation of migmatite domes and, more generally, in the multi-scale dynamics of crustal differentiation leading to a felsic upper crust, an intermediate middle crust and a mafic lower crust.

Use of ZDR columns for early detection of severe convection within the operational radar network of the United Kingdom

AbstractDifferential reflectivity () columns were observed using a Met Office three‐dimensional radar composite. An algorithm for automatic detection of columns was developed, based on dB and dBZ. Across three case days, detected columns were found to precede severe convection in tracked convective cells with a range of lead times from 0 to 20 min depending on the case day. Requiring maxima above 1.4 dB and 30 dBZ of and respectively was an appropriate second condition for all three cases although the skill in the early detection of severe convection varied across case days. Despite the high probability of detections, the high false alarm rate accompanied by low critical success index and data latency limit performance based on the three cases considered in this study. Nevertheless, the ability to detect columns in operational radar data with a useful lead time prior to severe convection in certain conditions is a promising development towards advancing nowcasting of severe convection in the United Kingdom.

IMPACT OF AN ANISOTROPIC POROUS MEDIA ON THERMOBIOCONVECTION INSTABILITY IN THE PRESENCE OF GYROTACTICMICROORGANISMS AND HEATING FROM BELOW

The onset of thermobioconvection in a horizontal fluid layer saturated by gyrotactic microorganisms into an anisotropic porous medium is examined. The modeling of the governing equations considers heating from below, Darcy flow, and Boussinesq approximations along with the presence of gyrotactic microorganisms. The system of ordinary differential equations is obtained using linear stability analysis and the normal mode technique. The single-term Galerkin method casts the analytical solutions while the higher-order Galerkin technique is employed to compute the numerical solutions. The influence of the mechanical and thermal anisotropy parameters along with all bioconvection parameters on the onset of thermobioconvection are analytically as well as numerically discussed. It is perceived that bioconvection Rayleigh-Darcy number <i>Rb</i>, the gyrotactic number<i> G</i>, and Péclet number <i>Q</i> are to fast-forward the onset of convective motion. On the other hand, thermal anisotropy produces a stable system and acts to postpone the bioconvection pattern formulation. Mechanical anisotropy is found to have a destabilizing impact on the stability of the suspension and helps in the development of bioconvection. The enhancement of mechanical and thermal anisotropy is found to increase the size of bioconvective cells whereas the augmentation of the concentration of gyrotactic specie reduces the convective cell size.

Linear and nonlinear investigations of the impact of chemical reaction on the thermohaline convection in a permeable layer saturated with Casson fluid

In this effort, the consequence of chemical reaction on the thermohaline convection in a permeable layer containing Casson fluid is inspected utilizing both linear and nonlinear stability procedures. To model the momentum equation, the Casson fluid version of Darcy's law is utilized. Applying the linear stability concept, the situation for the start of stationary and oscillatory pattern of convective motion is obtained, whereas the convective heat and mass transferences are determined using nonlinear stability theory. It is found that the oscillatory type of convective flow is probable only if the evaluation of the solutal Rayleigh–Darcy number is less than zero. The effect of the chemical reacting factor, the Casson factor, the Lewis number, and the solutal Rayleigh–Darcy number is to hurry the start of convection toward both stationary and oscillatory styles of convection and also surge the size of the convective cells. The convective heat and mass transfers enhance with increasing the Casson factor, the solutal and thermal Rayleigh–Darcy numbers while both decrease with enhancing the heat capacity quotient. The effect of chemical reacting factor is to increase the mass transmission in the system, while it has no effect on the heat transmission. It is also noted that the convective heat and mass transfers in the system enhance nearly 5.4% and 3.8%, respectively, with a 50% increase in the value of Casson factor.

A Deep Learning Nowcasting Model for Convective Cell Occurrence in Taiwan

A Deep Learning Nowcasting Model for Convective Cell Occurrence in Taiwan

U‐Net Segmentation for the Detection of Convective Cold Pools From Cloud and Rainfall Fields

AbstractConvective cold pools (CPs) mediate interactions between convective rain cells and help organize thunderstorm clusters, in particular mesoscale convective systems and extreme rainfall events. Unfortunately, the observational detection of CPs on a large scale has been hampered by the lack of relevant near‐surface data. Unlike numerical studies, where fields, such as virtual temperature or wind, are available at high resolution and frequently used to detect CPs, observational studies mainly identify CPs based on surface time series, for example, from weather stations or research vessels—thus limiting studies to a regional scope. To expand to a global scope, we here develop and evaluate a methodology for CP detection that relies exclusively on data with (a) global availability and (b) high spatiotemporal resolution. We trained convolutional neural networks to segment CPs in high‐resolution cloud‐resolving simulation output by deliberately restricting ourselves to only cloud top temperature and rainfall fields. Apart from simulations, such data are readily available from geostationary satellites that fulfill both (a) and (b). The networks employ a U‐Net architecture, popular with image segmentation, where spatial correlations at various scales must be learned. Despite the restriction imposed, the trained networks systematically identify CP pixels. Looking ahead, our methodology aims to reliably detect CPs over tropical land from space‐borne sensors on a global scale. As it also provides information on the spatial extent and the relative positioning of CPs over time, our method may unveil the role of CPs in convective organization.

Active longitudes and the structure of the large-scale magnetic field at solar minimum

We have studied deep minima of 11-year solar activity cycles 13–14, 14–15, 22–23, 23–24, 24–25, using the RGO and USAF/NOAA sunspot group catalogs. All of them have a large number of spotless days. Nonetheless, active longitudes as preferred zones, where sunspots occur, appear at this solar cycle phase. Analysis of synoptic maps and WSO daily magnetograms reflecting the structure of a weak large-scale field shows a non-axisymmetric component of the solar magnetic field. At solar minimum in the structure of the large-scale magnetic field, there are regions of the magnetic field of positive and negative polarity elongated along the meridian and crossing the equator. The most pronounced of them are located in the zone of active longitudes and are often connected with the polar magnetic fields.
 We discuss the possible nature of the meridional structures of the large-scale field during solar minimum. This might be due to giant convection cells with a banana cell structure.

Heat transport and flow structure in thermal convection with two liquid layers

We report an experimental investigation of the heat transport and flow field in a rectangular Rayleigh–Bénard convection (RBC) cell with two immiscible fluids: silicone oil and glycerol. The global heat transport of the system is divided into three ranges corresponding to the different flow structures formed in the glycerol layer. In range I, the glycerol layer is dominated by conduction, and no plume is formed over the interface. In range II, cellular rolls are formed in the glycerol layer and the horizontal motion of rolls causes an oscillation of temperature in the interface. In range III, the cellular pattern is time-independent, and the interface forms a group of wavelets with wave numbers consistent with the mode of the cellular pattern. In lower-thin glycerol, the Nusselt (Nu) grows from conduction to convection through an oscillating subcritical bifurcation at critical Rayleigh number $Ra_c$ . The value of $Ra_c$ in the present work is smaller than the theoretical prediction of both-rigid boundaries and greater than the prediction of one-rigid and one-free boundaries. In the upper-thick silicone oil layer, $Nu$ increases with increasing $Ra$ , but it is smaller than that of traditional RBC. For the silicone oil layer in two-layer RBC, the hot plumes emitting over the liquid–liquid interface showed different shape and different velocity from cold plumes emitting from the top rigid plate. This implies that the velocity boundary condition strongly influences the flow structure in turbulent convection.

Volumetric Lagrangian temperature and velocity measurements with thermochromic liquid crystals

We propose a Lagrangian method for simultaneous, volumetric temperature and velocity measurements. As tracer particles for both quantities, we employ encapsulated thermochromic liquid crystals (TLCs). We discuss the challenges arising from color imaging of small particles and present measurements in an equilateral hexagonal-shaped convection cell of height h = 60 mm and distance between the parallel side walls w = 104 mm, which corresponds to an aspect ratio Γ=1.73 . As fluid, we use a water-glycerol mixture to match the density of the TLC particles. We propose a densely-connected neural network, trained on calibration data, to predict the temperature for individual particles based on their particle image and position in the color camera images, which achieves uncertainties below 0.2 K over a temperature range of 3 K. We use Shake-the-Box to determine the 3D position and velocity of the particles and couple it with our temperature measurement approach. We validate our approach by adjusting a stable temperature stratification and comparing our measured temperatures with the theoretical results. Finally, we apply our approach to thermal convection at Rayleigh number Ra = 3.4×107 and Prandtl number Pr = 10.6. We can visualize detaching plumes in individual temperature and convective heat transfer snapshots. Furthermore, we demonstrate that our approach allows us to compute statistics of the convective heat transfer and briefly validate our results against the literature.

Активные долготы и структура крупномасштабного магнитного поля в минимуме солнечной активности

We have studied deep minima of 11-year solar activity cycles 13–14, 14–15, 22–23, 23–24, 24–25, using the RGO and USAF/NOAA sunspot group catalogs. All of them have a large number of spotless days. Nonetheless, active longitudes as preferred zones, where sunspots occur, appear at this solar cycle phase. Analysis of synoptic maps and WSO daily magnetograms reflecting the structure of a weak large-scale field shows a non-axisymmetric component of the solar magnetic field. At solar minimum in the structure of the large-scale magnetic field, there are regions of the magnetic field of positive and negative polarity elongated along the meridian and crossing the equator. The most pronounced of them are located in the zone of active longitudes and are often connected with the polar magnetic fields.
 We discuss the possible nature of the meridional structures of the large-scale field during solar minimum. This might be due to giant convection cells with a banana cell structure.

Radar‐based heavy precipitation events in Germany and associated circulation patterns

AbstractAs projected by multiple climate models, short‐duration heavy precipitation events (SDHPEs) are expected to intensify particularly quickly under the changing climate posing substantial risk to natural and human systems. Yet over the years, SDHPEs have received less scientific attention than long‐duration heavy precipitation events (LDHPEs), mainly due to the limitations of measurement systems. Our aim is to provide insight into spatial and temporal variability of SDHPEs detected by the radar network of the Deutscher Wetterdienst (DWD) in Germany from 2001 to 2020 as well as to explore their links to circulation patterns (CPs). The study is based on the Catalogue of Radar‐based heavy Rainfall Events (CatRaRE) generated using reprocessed gauge‐adjusted data of the DWD radar network as well as a new numerical method for classifying CPs over Central Europe called “Großwetterlagen for Reanalyses” (GWL‐REA). The results have demonstrated that SDHPEs, which are defined based on either locally valid precipitation values with a return period of 5 years (CatRaRE T5) or absolute precipitation values equal to DWD Warning Level 3 (CatRaRE W3), are common phenomena occurring most frequently in the afternoon hours of the summer season. They constitute up to 90% of all heavy precipitation events included in the catalogues covering relatively small areas—the median area of SDHPEs ranges from 22 km2 (CatRaRE T5) to 24 km2 (CatRaRE W3), while the median area of LDHPEs ranges from 175 km2 (CatRaRE W3) to 184 km2 (CatRaRE T5). As compared to LDHPEs, SDHPEs are generated by a wider spectrum of circulation conditions, including not only cyclonic but also anticyclonic CPs. In the warm season, the anticyclonic CPs, often accompanied by air mass advection from the south, can induce high thermal instability leading to the development of relatively small, isolated convective cells, which often cannot be captured by rain gauge stations.

The climatology and nature of warm-season convective cells in cold-frontal environments over Germany

Abstract. Cold fronts provide an environment particularly favourable for convective initiation in the mid-latitudes and can also be associated with convective hazards such as flooding, wind, hail and lightning. We build a climatology of cold-frontal convective cells between 2007–2016 for April–September in a cell-front distance framework by combining a radar-based cell detection and tracking dataset and automatic front detection methods applied to reanalysis data. We find that on average around twice as many cells develop on cold-frontal cell days compared to non-cold-frontal cell days. Using the 700 hPa level as a reference point, we show the maximum cell frequency is 350–400 km ahead of the 700 hPa front, which is marginally ahead of the typical surface front location. The 700 hPa front location marks the minimum cell frequency and a clear shift in regime between cells, with a weakened diurnal cycle on the warm side of the 700 hPa cold front and strongly diurnally driven cells on the cold side of the 700 hPa front. High cell frequency is found several hundreds of kilometres ahead of the surface front, and cells in this region are most likely to be associated with mesocyclones, intense convective cores and lightning. Namely, mesocyclones were detected in around 5.0 % of pre-surface-frontal cells compared to only 1.5 % of non-cold-frontal cells. The findings in this study are an important step towards a better understanding of cold-frontal convection climatology and links between cold fronts and convective hazards.

Natural convection effects in insulation layers of spherical cryogenic storage tanks

Natural convection effects in the insulation layers of spherical storage tanks are studied for different cryogenic fluids and tank sizes or curvatures. The non-vacuum-based insulation layers of these tanks are made of gas-filled porous materials such as perlite or glass bubbles. The large temperature difference that can exist between the inner cold wall and outer hot wall may create convective patterns with a multi-cellular flow within the insulation-filled annulus and lead to a higher boil-off rate and cryo-pumping effects. A main objective in the design of these systems is the elimination of the convective patterns by a proper choice of insulation properties. This work examines the impact of the insulation permeability or the Rayleigh number (Ra) on the type of convective flows for liquified natural gas (LNG) and liquid hydrogen (LH2) spherical storage tanks. Bifurcation diagrams of possible solutions are generated by numerical solutions of the governing equations at different Ra numbers. It is found that as Ra increases, new convective cells emerge near the south pole of the insulation layer due to unstable density stratification and lead to the distortion of isotherms, bringing the cold boundary towards the external hot boundary. When the temperature difference is large as in the case of LNG and LH2 tanks, there exist regions of multiple solutions in which multi-cell convective solutions may co-exist with a crescent-shaped weakly convective solution. In order to eliminate the possibility of multi-cell convection, inversion of the cold boundary, and reduce the boil-off rate, the Ra value of the insulation system should be below the limit point of the convective branch.