Atmospheric Tides Research Articles

Non‐Migrating Thermospheric Tides Shift and Deform the Solar Quiet Current Vortex Over Asia

AbstractVariations in the Solar quiet (Sq) current are typically attributed to the changes in atmospheric tides. In this study, we analyzed the ground‐based observations of the geomagnetic field to investigate the morphology of the Sq current over Asia (from 130° to 70°E). The analysis shows that the Sq current vortex deforms into a tilted ellipse over East Asia as it moves northwestward, which is more complex than previously thought. We also estimated the current generated by the polarized electric field (JEp) in the E‐region from the non‐migrating tidal winds of TIMED/TIDI (TIMED Doppler Interferometer on board the Thermosphere Ionosphere Mesosphere Energetics Dynamics satellite). The estimation is a qualitative approximation based on the fundamental polarization concept. We used the Observing Procedure Experiment (OPE) to reconstruct the Sq current and to evaluate its deformation and movement deviating from the geomagnetic equator. The results show that JEp can contribute to the shift and deformation of the Sq current. The observation and estimation indicate that the ionospheric current system modulated by winds blowing nonuniformly causes complex variations in the E‐region dynamo over Asia. This study additionally attempts to simulate the Sq vortex from the Thermosphere Ionosphere Electrodynamics General Circulation Model. Similarities and differences between the simulation and the observation are also discussed.

Martian Ionosphere‐Thermosphere Coupling in Longitude Structures: Statistical Results for the Main Ionization Peak Height

AbstractThe Martian ionosphere‐thermosphere (I‐T) coupling is variable due to complex variations of the driving factors such as atmospheric tides and crustal magnetic fields. In this study, variability of the I‐T coupling in longitude structures was investigated using a series of data segments of the MGS ionospheric measurements. Measurements in each data segment can cover different longitudes, and the solar forcing and local solar time just change a little. Ionospheric and thermospheric longitude variations are statistically correlated. Ionospheric peak electron density (NmM2) decreases while ionospheric main peak height (hmM2) increases with increasing neutral scale height (Hn) along longitudes. These correlated longitude variations are consistent with the photochemical coupling that Hn longitude disturbances induce ionospheric longitude structure through photochemical processes. Statistically, NmM2 is a better indicator than hmM2 for the Hn disturbances in the lower thermosphere. Hn longitude variation intensity is a crucial factor affecting the photochemical I‐T coupling in longitude structures; it is closely related to NmM2 longitude variation intensity and tends to decline with increasing altitudes. The I‐T coupling in longitude structures tends to decline near the terminator, which is in line with the declining longitude variation of Hn with increasing altitudes since hmM2 significantly increases near the terminator. Moreover, it tends to enhance at high solar activity level due to increased photoionization rate. The I‐T coupling in longitude structures also shows seasonal dependence, as seasonal variation of hmM2 can affect the Hn longitude variation intensity nearby the ionospheric main peak.

The Feasibility of Asynchronous Rotation via Thermal Tides for Diverse Atmospheric Compositions

The equilibrium rotation rate of a planet is determined by the sum of torques acting on its solid body. For planets with atmospheres, the dominant torques are usually the gravitational tide, which acts to slow the planet’s rotation rate, and the atmospheric thermal tide, which acts to spin up the planet. Previous work demonstrated that rocky planets with thick atmospheres may produce strong enough thermal tides to avoid tidal locking, but a study of how the strength of the thermal tide depends on atmospheric properties has not been done. In this work, we use a combination of simulations from a global climate model and analytic theory to explore how the thermal tide depends on the shortwave and longwave optical depth of the atmosphere, the surface pressure, and the absorbed stellar radiation. We find that for planets in the habitable zones of M stars only high-pressure but low-opacity atmospheres permit asynchronous rotation owing to the weakening of the thermal tide at high longwave and shortwave optical depths. We conclude that asynchronous rotation may be very unlikely around low-mass stars, which may limit the potential habitability of planets around M stars.

Analysis of climate change and climate variability impacts on coastal storms induced by extratropical cyclones: a case study of the August 2015 storm in central Chile

ABSTRACT The projected increase in coastal risk requires a reevaluation of coastal risk reduction strategies. A multi-model approach is proposed to examine the variability of coastal storms influenced by climate change and El Niño Southern Oscillation (ENSO). To this end, the historic coastal storm of August 8 2015, resulting from a local extratropical cyclone (ETC) off the central Chilean coast, was analyzed through the coupling of the WRF atmospheric model, Delft3D FM (D-FLOW and D-WAVE modules), and EOT20 astronomical tide model. The results show that the characteristics of local ETCs are susceptible to regional temperature gradients associated with climate change and ENSO. The coastal storm of August 8 2015, presented a decrease in wave height and counterclockwise rotation of wave direction along the Chilean coast under the climate change scenario. Meanwhile, the ENSO scenarios under cold conditions generated a ETC track’s displacement toward the north, causing both an increase in wave height along the coast of the Antofagasta and Atacama regions and a decrease in wave height in the Valparaíso, O’Higgins, and Maule regions. Findings from this study emphasize the importance of considering dynamic design for coastal structures rather than traditional methods to adapt to changing storm patterns.

Thermal tides in the middle atmosphere at mid-latitudes measured with a ground-based microwave radiometer

Abstract. In recent decades, theoretical studies and numerical models of thermal tides have gained attention. It has been recognized that tides have a significant influence on the dynamics of the middle and upper atmosphere; as they grow in amplitude and propagate upward, they transport energy and momentum from the lower to the upper atmosphere, contributing to the vertical coupling between atmospheric layers. The superposition of tides with other atmospheric waves leads to non-linear wave–wave interactions. However, direct measurements of thermal tides in the middle atmosphere are challenging and are often limited to satellite measurements in the tropics and at low latitudes. Due to orbit geometry, such observations provide only a reduced insight into the short-term variability in atmospheric tides. In this paper, we present tidal analysis from 5 years of continuous observations of middle-atmospheric temperatures. The measurements were performed with the ground-based temperature radiometer TEMPERA (TEMPErature RAdiometer), which was developed at the University of Bern in 2013 and was located in Bern (46.95° N, 7.45° E) and Payerne (46.82° N, 6.94° E). TEMPERA achieves a temporal resolution of 1–3 h and covers the altitude range between 25–50 km. Using an adaptive spectral filter with a vertical regularization (ASF2D) for the tidal analysis, we found maximum amplitudes for the diurnal tide of approximately 2.4 K, accompanied by seasonal variability. The maximum amplitude was reached on average at an altitude of 43 km, which also reflected some seasonal characteristics. We demonstrate that TEMPERA is suitable for providing continuous temperature soundings in the stratosphere and lower mesosphere with a sufficient cadence to infer tidal amplitudes and phases for the dominating tidal modes. Furthermore, our measurements exhibit a dominating diurnal tide and smaller amplitudes for the semidiurnal and terdiurnal tides in the stratosphere.

Unambiguous detection of mesospheric CO2 clouds on Mars using 2.7 μm absorption band from the ACS/TGO solar occultations

Mesospheric CO2 clouds are one of two types of carbon dioxide clouds known on Mars. We present observations of mesospheric CO2 clouds made by Atmospheric Chemistry Suite (ACS) onboard the ESA-Roscosmos ExoMars Trace Gas Orbiter (TGO). We analyzed 1663 solar occultation sessions of Thermal InfraRed (TIRVIM) and Middle InfraRed (MIR) channels of ACS covering more than two Martian years that contain spectra of 2.7 μm carbon dioxide ice absorption band. That allowed us to unambiguously discriminate carbon dioxide ice aerosols from mineral dust and water ice aerosols, not relying on the information of atmospheric thermal conditions. CO2 clouds were detected in eleven solar occultation observations at altitudes from 39 km to 90 km. In five cases, there were two or three layers of CO2 clouds that were vertically separated by 5–15 km gaps. Effective radius of CO2 aerosol particles is in the range of 0.1–2.2 μm. Spectra produced by the smallest particles indicate a need for a better resolved CO2 ice refractive index. Nadir optical depth of CO2 clouds is in the range 5 × 10−4–4 × 10−2 at both 2.7 μm and 0.8 μm. Asymmetrical diurnal distribution of detections observed by ACS is potentially due to local time variations of temperature induced by thermal tides. Two out of five cases of carbon dioxide cloud detections made by the TIRVIM instrument reveal the simultaneous presence of CO2 ice and H2O ice aerosols. Temperature profiles measured by the Near InfraRed (NIR) channel of ACS are used to calculate CO2 saturation ratio S at locations of carbon dioxide clouds. Supersaturation S > 1 is detected in only 6 out of 19 cases of CO2 cloud layers; extremely low values of S < 0.1 are found in 9 out of 19 cases.

The viscosity of Venus’ mantle inferred from its rotational state

Venus’ retrograde rotation is the slowest of all planetary objects in the solar system. It is commonly admitted that such a rotation state results from the balance between the torques created by solid and atmospheric tides (Dobrovolskis and Ingersol, 1980; Correia and Laskar, 2001; Correia and Laskar, 2003a; Revol et al. 2023). The internal viscous friction associated with gravitational tides drives the planet into synchronization (i.e. deceleration to a tidally locked rotation) while the bulge due to atmospheric thermal tides tends to accelerate the planet out of this synchronization (Correia and Laskar, 2001; Leconte et al., 2015). The purpose of this work is first to provide an estimate of the viscosity of Venus’ mantle explaining the current balance with atmospheric forcing. A second goal is to quantify the impact of the internal structure and its past evolution on the rotation history of Venus.Using atmospheric pressure simulations, we first provide an estimate of the atmospheric thermal torque value contrasting with previous estimates (Leconte et al., 2015). Computing the viscoelastic response of the interior to gravitational tides and to atmospheric loading (Dumoulin et al., 2017; Kervazo et al., 2021), we show that the current viscosity of Venus’ lower mantle must range between 2 × 1020 Pa s and 6 × 1021 Pa s to explain a rotation in equilibrium. We then investigate the possible past evolution of Venus’ rotation by considering simple viscosity and thermal evolution paths. We show that in absence of additional dissipation processes, viscous friction cannot slow down Venus’ rotation to its current state from an initial rotation period shorter than 1 day.

Effect of background wind and dissipation processes on the diurnal component of atmospheric solar tides

The radiation coming from the Sun heats the Earth’s atmosphere and generates atmospheric tides. In this paper, we model atmospheric tides in the presence of background wind and dissipation processes and investigate their effects. The equations for tidal oscillations of wind and temperature in the atmosphere encompass factors such as background wind, temperature profile, and background composition including ozone, carbon dioxide, hydro-magnetic interactions, Newtonian cooling, eddy, and molecular diffusion. These components interact to define the behavior of tidal phenomena comprehensively. Thermal forcing processes include the insolation absorption of H2O in the troposphere, O3 in the stratosphere, and a contribution from O2 absorption in the thermosphere. The method of solution for the equations is outlined for the solar diurnal tides during the March equinox by considering all these dissipation processes and the background wind. The obtained results are in good agreement with the Global Scale Wave Model (GSWM-00). It is found that the background wind plays significant role in affecting the horizontal wind oscillations below 100 km. At higher altitudes (100–200 km), the background wind, ion drag force, divergence of momentum, and heat fluxes due to molecular and eddy diffusion have a considerable role in affecting the zonal and meridional winds.

Effect of background wind and dissipation processes on the semidiurnal component of atmospheric solar tides

The equations governing the neutral wind velocities and temperature, which depict the oscillations of atmospheric tides, incorporate various elements of the atmosphere. These factors comprise background wind, temperature profiles, and the atmosphere’s composition, including ozone, oxygen, carbon dioxide, water, etc. The current work describes the method of solution of the atmospheric tidal model and investigates the effects of background wind and dissipation processes on the migrating semidiurnal tides during the March equinox. Thermal heating due to water vapour absorption in the troposphere, ozone in the stratosphere and oxygen absorption in the thermosphere is considered in this model. Furthermore, the model takes into account the various dissipation processes (i.e. ion drag and Hall coefficients, Newtonian cooling, divergence of momentum and heat fluxes due to molecular and eddy diffusion) and background wind. The semidiurnal tidal features obtained from the present model match well with the Global Scale Wave Model (GSWM-98). The bar charts are presented to quantify the effects of different parameters on horizontal winds for altitudes below 100 km and above 100 km, separately. It reveals that the background wind plays a vital role in deciding the semidiurnal tidal amplitudes of zonal and meridional winds. Momentum and heat flux coefficients also have a significant influence on semidiurnal tides. At higher altitudes (>100 km), the ion drag reduces the amplitude of semidiurnal tides considerably.

Vertical water renewal and dissolved oxygen depletion in a semi-enclosed Sea

The limited water renewal in semi-enclosed seas may contribute to the oxygen deficiency and thereby may exacerbate the ecological degradation. Previous research has focused more on horizontal water renewal, while the role of vertical water renewal remains poorly documented despite its significance to the bottom oxygen supply. This study explores the vertical water renewal process in the Bohai Sea, a semi-enclosed sea prone to oxygen deficiency, by developing a water age model, incorporated into a developed Delft3D hydrodynamic model. Findings unveiled the key role of thermal stratification, tides, and winds on vertical water renewal. Results revealed significant spatial heterogeneity and seasonal variations in water age in the Bohai Sea. During summer, stratified from the upper water column, the deep basin water age can reach up to 30 days. Thermal stratification was crucial in regulating vertical water renewal, acting as a constraint and impediment. Spring tides and neap tides can positively and negatively influence vertical water renewal by strengthening and weakening thermal stratification, respectively. Wind forces intensified the vertical water exchange by changing the flow field structure. Additionally, higher bottom water age coincides with the oxygen-poor areas and deep-water regions. Based on this, we employed the product of the oxygen consumption rate and the bottom water age (oxygen consumption duration) to approximate oxygen depletion. This method was applied to successfully estimate vertical oxygen depletion in the Bohai Sea. The findings will serve environmental management and oxygen-poor attribution analysis.

Diurnal and seasonal variations of orographic clouds in the Tharsis region with EMM/EXI observations and the Mars Planetary Climate Model

The diurnal and seasonal variations of orographic water ice clouds in the Tharsis region have been investigated with EXI observations for MY 36 and 37. In order to provide context, meteorological fields from the Mars PCM (Mars Planetary Climate Model led by Laboratoire de Météorologie Dynamique Paris, France) have been incorporated. These fields include water ice column, atmospheric temperature, meteorological winds, water vapor, and dust mixing ratio. The diurnal cycle has been studied for sunlit hours (6 am–6 pm) by sampling data into 5 local time bins. Both the EXI observations and the Mars PCM underscore the significant role plays by diurnal thermal tides in controlling the thickness and existence of water ice clouds in the Tharsis region. During Spring and Summer, water ice clouds form in the morning and late-afternoon hours and exhibit greater thickness compared to those that form during the afternoon, primarily due to the influence of thermal tides. During Fall and Winter, water ice clouds are typically observed in the Arsia Mons region, occasionally extending to the Pavonis Mons region. During the Fall and Winter seasons, the clouds that form are mostly thin and have a tendency to develop in the afternoon hours, while the morning hours typically remain cloud-free or exhibit extremely thin clouds. This phenomenon can be attributed to a combination of factors, including the existence of cold temperature zones at higher altitudes formed by the influence of strong trade winds and the impact of diurnal thermal tides. According to the Mars PCM, water ice clouds typically form at altitudes below 25 km during Spring and Summer, whereas during Fall and Winter, cloud formation occurs at altitudes above 25 km.

Comprehensive quantitative determination of aquifer confinement based on tidal response of well water level and its application in North China

Aquifer confinement represents a pivotal property that significantly influences the vulnerability and contamination risk of groundwater resources. Several methods have been proposed for determining aquifer confinement by analyzing the response of well water level to Earth tides and atmospheric tides. In this study, we evaluated the performance of the existing single methods and put forward an optimized comprehensive approach. We compared the determination results of the three single methods with those of a comprehensive method using water-level data from 39 earthquake precursor monitoring wells in North China. The results demonstrate that the comprehensive method effectively determined aquifer confinement, significantly reducing the uncertainty associated with the three single methods. The application of the comprehensive method in North China reveals that aquifer confinement may undergo temporal variations during long-term continuous observation, especially in areas where the confining properties of aquifers may vary due to human activities and earthquakes. In such areas, the comprehensive method facilitates accurate assessment of groundwater vulnerability, as well as the potential dispersion of underground pollutants.

High‐Order Harmonics of Thermal Tides Observed in the Atmosphere of Mars by the Pressure Sensor on the InSight Lander

AbstractThermal tides are atmospheric planetary‐scale waves with periods that are harmonics of the solar day. In the Martian atmosphere thermal tides are known to be especially significant compared to any other known planet. Based on the data set of pressure timeseries produced by the InSight lander, which is unprecedented in terms of accuracy and temporal coverage, we investigate thermal tides on Mars and we find harmonics even beyond the number 24, which exceeds significantly the number of harmonics previously reported by other works. We explore comparatively the characteristics and seasonal evolution of tidal harmonics and find that even and odd harmonics exhibit some clearly differentiated trends that evolve seasonally and respond to dust events. High‐order tidal harmonics with small amplitudes could transiently interfere constructively to produce meteorologically relevant patterns.

Did atmospheric thermal tides cause a daylength locking in the Precambrian? A review on recent results

After the initial suggestion by Zahnle and Walker (1987) that the torque accelerating the spin rate of the Earth and produced by the heating of the atmosphere by the Sun could counteract the braking luni-solar gravitational torque in the Precambrian, several authors have recently revisited this hypothesis. In these studies, it is argued that the geological evidence of the past spin state of the Earth plays in favor of this atmospheric tidal locking of the length of the day (LOD). In the present review of the recent literature, we show that the drawn conclusions critically depend on LOD estimates based on stromatolite growth band data of Panella at 1.88 and 2.0 Ga which are subject to large uncertainties. When only the most robust cyclostatigraphic estimates of the LOD are retained, the LOD locking hypothesis is not supported. Moreover, our consideration of the published General Circulation Model numerical simulations and of a new analytical model for the thermal atmospheric tides suggest that the atmospheric tidal resonance, which is the crucial ingredient for the LOD locking in the Precambrian, was never of sufficiently large amplitude to allow for this tidal LOD lock.

Tidal evolution of Earth-like planets in the habitable zone of low-mass stars

Earth-like planets in the habitable zone of low-mass stars undergo strong tidal effects that modify their spin states. These planets are expected to host dense atmospheres that can also play an important role in the spin evolution. On one hand, gravitational tides tend to synchronise the rotation with the orbital mean motion, but on the other hand, thermal atmospheric tides push the rotation away and may lead to asynchronous equilibria. Here, we investigate the complete tidal evolution of Earth-like planets by taking into account the effect of obliquity and eccentric orbits. We adopted an Andrade rheology for the gravitational tides and benchmarked the unknown parameters with the present rotation of Venus. We then applied our model to Earth-like planets, and we show that asynchronous rotation can be expected for planets orbiting stars with masses between 0.4 and 0.9 $M_ and semi-major axes between 0.2 and 0.7 au. Interestingly, we find that Earth-like planets in the habitable zone of stars with masses $ 0.8$ $M_ may end up with an equilibrium rotation of 24 hours. We additionally find that these planets can also develop high obliquities, which may help sustain temperate environments.

Quasi 6‐Day Planetary Wave Oscillations in Equatorial Plasma Irregularities

AbstractThe influence of atmospheric planetary waves on the occurrence of irregularities in the low latitude ionosphere is investigated using Whole Atmosphere Community Climate Model with thermosphere‐ionosphere eXtension (WACCM‐X) simulations and Global Observations of the Limb and Disk (GOLD) observations. GOLD observations of equatorial plasma bubbles (EPBs) exhibit a ∼6–8 day periodicity during January–February 2021. Analysis of WACCM‐X simulations, which are constrained to reproduce realistic weather variability in the lower atmosphere, reveals that this coincides with an amplification of the westward propagating wavenumber‐1 quasi‐six day wave (Q6DW) in the mesosphere and lower thermosphere (MLT). The WACCM‐X simulated Rayleigh‐Taylor (R‐T) instability growth rate, considered as a proxy of EPB occurrence, is found to exhibit a ∼6‐day periodicity that is coincident with the enhanced Q6DW in the MLT. Additional WACCM‐X simulations performed with fixed solar and geomagnetic activity demonstrate that the ∼6‐day periodicity in the R‐T instability growth rate is related to the forcing from the lower atmosphere. The simulations suggest that the Q6DW influences the day‐to‐day formation of EPBs through interaction with the migrating semidiurnal tide. This leads to periodic oscillations in the zonal winds, resulting in periodic variability in the strength of the prereversal enhancement, which influences the R‐T instability growth rate and EPBs. The results demonstrate that atmospheric planetary waves, and their interaction with atmospheric tides, can have a significant impact on the day‐to‐day variability of EPBs.

Atmospheric Tides in the Middle and Upper Atmosphere of Mars at Northern High Latitudes: A Comparison of MAVEN‐EUVM and MRO‐MCS Observations With Model Results

AbstractMuch of the variability in the Martian thermosphere can be attributed to vertically propagating atmospheric tides that are known to achieve significant amplitudes in this region. Concurrent observations from different altitudes have been used previously to discern the vertical propagation characteristics of tides but have primarily focused on low latitudes. The spectrum of tides and their vertical evolution are thereby less constrained at high latitudes. Few studies that have focused on high latitudes identified wavenumber‐3 structures which were interpreted to originate mainly from the non‐migrating tides SE1 and DE2. This paper presents the first analysis of MAVEN‐EUVM solar occultation observations to deduce atmospheric tides in the Martian thermosphere. These are compared to tides observed by MRO‐MCS in the middle atmosphere for six cases at high northern latitudes. To identify vertical propagation, wave signatures in the middle and upper atmosphere are compared and are found to be dominated by a mix of zonal wavenumbers‐2 and ‐3 in fixed local time. MCS observations show eastward propagating tides dominate, specifically highlighting SE1 near 76 km. Additionally, these observations indicate the presence of stationary planetary waves and terdiurnal tides. Mars Climate Database also indicates the presence of SE1, DE2, DE1, S0, TW1, and T0 tides. A change in the dominant wavenumber component with local time is seen, which is attributed to the presence of all three diurnal, semidiurnal and terdiurnal components at these latitudes. The significant decrease in the diurnal tide amplitude indicates the effect of zonal mean wind on vertical propagation.

Analyzing the Instabilities in the Venus Atmosphere Using Bred Vectors

AbstractBarotropic, baroclinic, and Rossby‐Kelvin instabilities exist in the Venus atmosphere, as revealed by previous studies using numerical models. This study aims to deepen our understanding of the instabilities in the Venus atmosphere using the breeding of growing modes (BGM) method for the first time. We conducted a 1‐year model simulation as the control run. First, we conducted identical twin experiments in which random perturbations were added to the control run at the initial time, and they grew freely. Perturbations in the upper layer (UL, 70–100 km altitudes) grow faster at the beginning but saturate earlier at a low value compared to those in the lower layer (LL, 40–70 km altitudes). Next, we implemented the BGM method and conducted multiple breeding cycle experiments with different rescaling amplitudes and intervals, the two parameters of the BGM method. The bred vectors (BVs) from these experiments identified instabilities in various regions. With large rescaling amplitudes, the structure and amplitude of the BVs in the LL closely resembled the deviations in the control run, indicating the growth of BVs due to barotropic, baroclinic, and Rossby‐Kelvin instabilities. Composite mean analysis shows larger BV amplitudes in the morning hemisphere at the 60–70 km altitudes in the mid‐latitudes, indicating enhanced baroclinic instability by the thermal tide. Finally, we estimated the intrinsic predictability related to baroclinic instability for Venus is &gt;1 month, which would be longer than that for the Earth of ∼2 weeks.

Thermal tides in neutrally stratified atmospheres: Revisiting the Earth’s Precambrian rotational equilibrium

Rotational dynamics of the Earth, over geological timescales, have profoundly affected local and global climatic evolution, probably contributing to the evolution of life. To better retrieve the Earth’s rotational history, and motivated by the published hypothesis of a stabilized length of day during the Precambrian, we examined the effect of thermal tides on the evolution of planetary rotational motion. The hypothesized scenario is contingent upon encountering a resonance in atmospheric Lamb waves, whereby an amplified thermotidal torque cancels out the opposing torque generated by the oceans and solid interior, driving the Earth into rotational equilibrium. With this scenario in mind, we constructed an ab initio model of thermal tides on rocky planets describing a neutrally stratified atmosphere. The model takes into account dissipative processes with Newtonian cooling and diffusive processes in the planetary boundary layer. We retrieved, from this model, a closed-form solution for the frequency-dependent tidal torque, which captures the main spectral features previously computed using 3D general circulation models. In particular, under longwave heating, diffusive processes near the surface and the delayed thermal response of the ground prove to be responsible for attenuating, and possibly annihilating, the accelerating effect of the thermotidal torque at the resonance. When applied to the Earth, our model prediction suggests the occurrence of the Lamb resonance in the Phanerozoic, but with an amplitude that is insufficient for the rotational equilibrium. Interestingly, though our study was motivated by the Earth’s history, the generic tidal solution can be straightforwardly and efficiently applied in exoplanetary settings.

Effect of atmospheric pressure changes on gas transmission through microperforated packages of respiring products

The objective of this work was to quantify the effect of atmospheric pressure changes on gas transmission through microperforations, in order to understand the role of fluctuations in the atmospheric pressure on the headspace composition of microperforated modified atmosphere packages. A 3D numerical model that considers the spatial-time and pressure dependence of the gas composition was adapted to simulate the gas exchange through microperforations at different fixed pressures and at variable pressure due to atmospheric pressure fluctuations (such as those caused by atmospheric tides or by the development of high and low-pressure systems) or to changes in altitude during land or air transport. The model results were successfully verified with experimental data recorded in an experimental system built to measure the CO2 exchange through microperforations affected by pressure changes due to weather conditions (the root mean squared error of the CO2 composition was 0.01%). The results reveal the importance of contemplating the convective flow generated by a change in pressure outside the package. In the simulated routes, the difference in CO2 concentration between considering the pressure-driven flow and neglecting it is one order of magnitude in a 10-h land transport through a medium mountain route, for a 1250 mL container with a single microperforation of 7420.6 μm2 area and initial CO2 concentrations on both sides of the hole of 0.05% and 20.95%. The air transport simulations showed that it is not enough to consider the difference in altitude between the cities of origin and destination, but rather all the pressure fluctuations along the route must be included in the model.