Secular Timescales Research Articles

Correct Criterion of Crustal Failure Driven by Intense Magnetic Stress in Neutron Stars

Magnetar outbursts are powered by an intense magnetic field. The phenomenon has recently drawn significant attention because of a connection to some fast radio bursts that has been reported. Understanding magnetar outbursts may provide the key to mysterious transient events. The elastic deformation of the solid crust due to magnetic field evolution accumulates over a secular timescale. Eventually, the crust fractures or responds plastically beyond a particular threshold. Determination of the critical limit is required to obtain the shear strain tensor in response to magnetic stress. In some studies, the tensor was substituted with an approximate expression determined algebraically from the magnetic stress. This study evaluated the validity of the approximation by comparing it with the strain tensor obtained through appropriate calculations. The differential equations for the elastic deformation driven by the magnetic field were solved. The results indicated that the approximation did not represent the correct strain tensor value, in both magnitude and spatial profile. Previous evolutionary calculations based on spurious criteria are likely to overestimate the magnitude of the strain tensor, and crustal failure occurs on a shorter timescale. Therefore, revisiting evolutionary calculations using the correct approach is necessary. This study is essential for developing the dynamics of crustal fractures and the magnetic field evolution in a magnetar.

Analytical Models for Secular Descents in Hierarchical Triple Systems

Three-body systems are prevalent in nature, from planetary to stellar to supermassive black hole scales. In a hierarchical triple system, oscillations of the inner orbit’s eccentricity and inclination can be induced on secular timescales. Over many cycles, the octupole-level terms in the secular equations of motion can drive the system to extremely high eccentricities via the eccentric Kozai–Lidov (EKL) mechanism. The overall decrease in the inner orbit’s pericenter distance has potentially dramatic effects for realistic systems, such as tidal disruption events. We present an analytical approximation in the test-particle limit to describe individual stepwise increases in eccentricity of the inner orbit. A second approximation, also in the test-particle limit, is obtained by integrating the equations of motion and calibrating to numerical simulations to estimate the overall octupole-level time evolution of the eccentricity. The latter approach is then extended beyond the test particle to the general case. The three novel analytical approximations are compared to numerical solutions to show that the models accurately describe the form and timescale of the secular descent from large distances to a close-encounter distance (e.g., the Roche limit). By circumventing the need for numerical simulations to obtain the long-term behavior, these approximations can be used to readily estimate properties of close encounters and descent timescales for populations of systems. We demonstrate this by calculating rates of EKL-driven migration for Hot Jupiters in stellar binaries.

Secular dynamics and the lifetimes of lunar artificial satellites under natural force-driven orbital evolution

In this paper, we study the long-term (time scale of several years) orbital evolution of lunar satellites under the sole action of natural forces. In particular, we focus on secular resonances, caused either by the influence of the multipole moments of the lunar potential and/or by the Earth’s and Sun’s third-body effect on the satellite’s long-term orbital evolution. Our study is based on a simplified secular model obtained in ‘closed form’, i.e., without expansions in the satellite’s orbital eccentricity. Contrary to the case of artificial Earth satellites, in which many secular resonances compete in dynamical impact, we give numerical evidence that for lunar satellites only the 2g−resonance (ω̇=0) affects significantly the orbits at secular timescales. We interpret this as a consequence of the strong effect of lunar mascons. We show that the lifetime of lunar satellites is, in particular, nearly exclusively dictated by the 2g resonance. By deriving a simple analytic model, we propose a theoretical framework which allows for both qualitative and quantitative interpretation of the structures seen in numerically obtained lifetime maps. This involves explaining the main mechanisms driving eccentricity growth in the orbits of lunar satellites. In fact, we argue that the re-entry process for lunar satellites is not necessarily a chaotic process (as is the case for Earth satellites), but rather due to a sequence of bifurcations leading to a dramatic variation in the structure of the separatrices in the 2g resonance’s phase portrait, as we move from the lowest to the highest limit in inclination (at each altitude) where the 2g resonance is manifested.

Resonant and Ultra-short-period Planet Systems Are at Opposite Ends of the Exoplanet Age Distribution

Exoplanet systems are thought to evolve on secular timescales over billions of years. This evolution is impossible to directly observe on human timescales in most individual systems. While the availability of accurate and precise age inferences for individual exoplanet host stars with ages τ in the interval 1 Gyr ≲ τ ≲ 10 Gyr would constrain this evolution, accurate and precise age inferences are difficult to obtain for isolated field dwarfs like the host stars of most exoplanets. The Galactic velocity dispersion of a thin-disk stellar population monotonically grows with time, and the relationship between age and velocity dispersion in a given Galactic location can be calibrated by a stellar population for which accurate and precise age inferences are possible. Using a sample of subgiants with precise age inferences, we calibrate the age–velocity dispersion relation in the Kepler field. Applying this relation to the Kepler field’s planet populations, we find that Kepler-discovered systems plausibly in second-order mean-motion resonances have 1 Gyr ≲ τ ≲ 2 Gyr. The same is true for systems plausibly in first-order mean-motion resonances, but only for systems likely affected by tidal dissipation inside their innermost planets. These observations suggest that many planetary systems diffuse away from initially resonant configurations on secular timescales. Our calibrated relation also indicates that ultra-short-period (USP) planet systems have typical ages in the interval 5 Gyr ≲ τ ≲ 6 Gyr. We propose that USP planets tidally migrated from initial periods in the range 1 day ≲ P ≲ 2 days to their observed locations at P < 1 day over billions of years and trillions of cycles of secular eccentricity excitation and inside-planet damping.

Metal-poor Stars in the MW Disk: Resonant Cooling of Vertical Oscillations of Halo Stars in Barred Galaxies

Using numerical simulations of a barred disk galaxy embedded in nonspinning and spinning dark matter (DM) halos, we present a novel mechanism of “cooling” the vertical oscillations of DM particles, which acquire disk kinematics. The underlying mechanism consists of resonant interactions between halo particles and the stellar bar, facilitated by a chaotic phase space of the system. The cooling mechanism acts both on dynamical and secular timescales, from ∼0.5 Gyr to a few Gyr. The stellar bar acts to absorb the kinetic energy of the vertical motions. Using a Milky Way (MW)–type stellar halo, we estimate the population of metal-poor disk stars trapped by the MW disk and analyze its kinematics. We find that the population of metal-poor MW disk stars with ∣z∣ ≲ 3 kpc detected by the Gaia DR3 and other surveys can have their origin in the stellar halo. The cooled population also migrates radially outwards by exchanging energy and angular momentum with the spinning bar, and prograde-moving stars have a different distribution from retrograde ones. Next, we calculated the ratio of the prograde-to-retrograde orbits of the cooled population and found that this ratio varies radially, with the fast-spinning stellar halo resulting in the shallower radial increase of this ratio outside of the corotation. The nonspinning stellar halo shows a monotonic increase of this ratio with radius outside the corotation. Together with the analyzed radial migration of these halo stars, the cooling phenomenon of halo metal-poor stars can explain their current disk population and has corollaries for the chemical evolution of disk galaxies in general.

Scaling of the geomagnetic secular variation timescale

SUMMARY The ratio of the magnetic power spectrum and the secular variation spectrum measured at the Earth’s surface provides a timescale $\tau _{\rm sv}(l)$ as a function of spherical harmonic degree l. $\tau _{\rm sv}$ is often assumed to be representative of timescales related to the dynamo inside the outer core and its scaling with l is debated. To assess the validity of this surmise and to study the time variation of the geomagnetic field $\dot{\boldsymbol {B}}$ inside the outer core, we introduce a magnetic timescale spectrum $\tau (l,r)$ that is valid for all radius r above the inner core and reduces to the usual $\tau _{\rm sv}$ at and above the core–mantle boundary (CMB). We study $\tau$ in a numerical geodynamo model. At the CMB, we find that $\tau \sim l^{-1}$ is valid at both the large and small scales, in agreement with previous numerical studies on $\tau _{\rm sv}$. Just below the CMB, the scaling undergoes a sharp transition at small l. Consequently, in the interior of the outer core, $\tau$ exhibits different scaling at the large and small scales, specifically, the scaling of $\tau$ becomes shallower than $l^{-1}$ at small l. We find that this transition at the large scales stems from the fact that the horizontal components of the magnetic field evolve faster than the radial component in the interior. In contrast, the magnetic field at the CMB must match onto a potential field, hence the dynamics of the radial and horizontal magnetic fields are tied together. The upshot is $\tau _{\rm sv}$ becomes unreliable in estimating timescales inside the outer core. Another question concerning $\tau$ is whether an argument based on the frozen-flux hypothesis can be used to explain its scaling. To investigate this, we analyse the induction equation in the spectral space. We find that away from both boundaries, the magnetic diffusion term is negligible in the power spectrum of $\dot{\boldsymbol {B}}$. However, $\dot{\boldsymbol {B}}$ is controlled by the radial derivative in the induction term, thus invalidating the frozen-flux argument. Near the CMB, magnetic diffusion starts to affect $\dot{\boldsymbol {B}}$ rendering the frozen-flux hypothesis inapplicable. We also examine the effects of different velocity boundary conditions and find that the above results apply for both no-slip and stress-free conditions at the CMB.

Rendez-vous with massive interstellar objects, as triggers of destabilization

ABSTRACT We study how close passages of interstellar objects of planetary and substellar masses may affect the immediate and long-term dynamics of the Solar system. We consider two nominal approach orbits, namely the orbits of actual interstellar objects 1I/’Oumuamua and 2I/Borisov, assuming them to be typical or representative for interstellar swarms of matter. Thus, the nominal orbits of the interloper in our models cross the inner part of the Solar system. Series of massive numerical experiments are performed, in which the interloper’s mass is varied with a small step over a broad range. We find that, even if a Jovian-mass interloper does not experience close encounters with the Solar system planets (and this holds for our nominal orbits), our planetary system can be destabilized on time-scales as short as several million years. In what concerns substellar-mass interlopers (free-floating brown dwarfs), an immediate (on a time-scale of ∼10–100 yr) consequence of such a massive interstellar object (MISO) flyby is a sharp increase in the orbital eccentricities and inclinations of the outer planets. On an intermediate time-scale (∼103 to 105 yr after the MISO flyby), Uranus or Neptune can be ejected from the system, as a result of their mutual close encounters and encounters with Saturn. On a secular time-scale (∼106 to 107 yr after the MISO flyby), the perturbation wave formed by secular planetary interactions propagates from the outer Solar system to its inner zone.

Mapping landscape evolution in 3D: Climate change, natural hazard and human settlements across the 1618 Piuro landslide in the Italian Central Alps

AbstractNatural and anthropogenic mountain landscapes coevolve responding on different temporal scales to climate changes and geodynamics by a series of increments that cause the dynamic association of morphological stabilization surfaces, stratigraphic units and landforms. Understanding the incremental history of palimpsest landscapes helps to recognize and forecast the effects of climate change on the sensitive mountain environments, contributes to archaeological and historical reconstruction and supports management strategies for natural risks prevention and mitigation. The Italian Bregaglia Valley provides an excellent site to unravel the recent/historical increments of evolution of landforms and human settlement, permitting to map the paleo‐digital terrain models (DTMs) corresponding to the relevant landscape turning points. After the last de‐glaciation, two large‐scale landslides reshaped the valley floor, both predisposed by deep‐seated gravitational slope deformations and one surely triggered by intense rainfalls. The most recent and impacting event buried in 1618 the rich border town of Piuro, the ancient one occurred in the same area at least 1.5 ka before. Combining stratigraphic, geomorphological, topographic, archaeological and historical data, we drew the paleo‐DTMs of the pre‐ and post‐1618 settings of Piuro, sketching the landscape evolution. Since two millennia, human settlements took advantage of the decadal to secular most stable surfaces, represented by the inactive lobes of debris‐flow fans, the highest trunk river terraces and the top of humps formed by the ancient landslide body in the valley centre. Stratigraphic relationships, archaeological findings and age determinations show that both landslides diverted the trunk river and covered the existing fan lobes. On a secular timescale, fan progradation and trunk river terracing buried and reworked both the landslide bodies. The paleo‐DTMs show their original areal extent and permit to compute their volume and to sketch the setting of the buried Piuro settlements, drawing the changes of the Mera trunk river course and the chronology of activity of the lateral debris‐flow fan lobes.

Spatiotemporal Intertropical Convergence Zone dynamics during the last 3 millennia in northeastern Brazil and related impacts in modern human history

Abstract. Changes in tropical precipitation over the past millennia have usually been associated with latitudinal displacements of the Intertropical Convergence Zone (ITCZ). Recent studies provide new evidence that contraction and expansion of the tropical rain belt may also have contributed to ITCZ variability on centennial timescales. Over tropical South America few records point to a similar interpretation, which prevents a clear diagnosis of ITCZ changes in the region. In order to improve our understanding of equatorial rain belt variability, our study presents a reconstruction of precipitation for the last 3200 years from the northeastern Brazil (NEB) region, an area solely influenced by ITCZ precipitation. We analyze oxygen isotopes in speleothems that serve as a faithful proxy for the past location of the southern margin of the ITCZ. Our results, in comparison with other ITCZ proxies, indicate that the range of seasonal migration, contraction, and expansion of the ITCZ was not symmetrical around the Equator on secular and multidecadal timescales. A new NEB ITCZ pattern emerges based on the comparison between two distinct proxies that characterize the ITCZ behavior during the last 2500 years, with an ITCZ zonal pattern between NEB and the eastern Amazon. In NEB, the period related to the Medieval Climate Anomaly (MCA – 950 to 1250 CE) was characterized by an abrupt transition from wet to dry conditions. These drier conditions persisted until the onset of the period corresponding to the Little Ice Age (LIA) in 1560 CE, representing the longest dry period over the last 3200 years in NEB. The ITCZ was apparently forced by teleconnections between Atlantic and Pacific that controlled the position, intensity, and extent of the Walker cell over South America, changing the zonal ITCZ characteristics, while sea surface temperature changes in both the Pacific and Atlantic stretched or weakened the ITCZ-related rainfall meridionally over NEB. Wetter conditions started around 1500 CE in NEB. During the last 500 years, our speleothems document the occurrence of some of the strongest drought events over the last centuries, which drastically affected population and environment of NEB during the Portuguese colonial period. The historical droughts were able to affect the karst system and led to significant impacts over the entire NEB region.

The eccentric Koza–Lidov mechanism as the cause of exocomet transits of KIC 8462852

ABSTRACT KIC 8462852 is a star in the Kepler field that exhibits almost unique behaviour. The deep, irregular, and aperiodic dips in its light curve have been interpreted as the breakup of a large exocomet on a highly eccentric orbit whose post-disruption material obscures the star. It is hypothesized that a nearby M-dwarf, recently confirmed to be bound to the system, could be exciting planetesimals in a source belt to high eccentricities if its orbit is highly misaligned with the belt: an effect known as the ‘Eccentric Kozai–Lidov Mechanism’. To quantify how often this effect is expected to occur, this paper presents a Monte Carlo model of wide binary stars with embedded, misaligned planetesimal belts. These belts collisionally erode over time until they are excited to high eccentricities on secular time-scales by a companion star if its orbit is sufficiently misaligned. The large planetesimals then produce an observable dimming signature in the light curve for a set period of time which may or may not overlap with similar events. The model finds that, for dimming events that persist for 100 yr, the most likely companion stars are located at 102−104 au, the most likely belts are at 102−103 au and the system age is most likely to be 102−103 Myr. However, the probability of observing one or more stars exhibiting this phenomenon in the Kepler field is 1.3 × 10−3, such that it is unlikely this mechanism is driving the observations of KIC 8462852.

Sahel Droughts Induced by Large Volcanic Eruptions Over the Last Millennium in PMIP4/Past1000 Simulations

AbstractThis work provides evidence of the influence of large volcanic eruptions on Sahel rainfall relying on PMIP4/past1000 multi‐model simulations, covering the last millennium. A classification of volcanic eruptions in the last millennium according to the meridional symmetry of the associated radiative forcing reveals different mechanisms of the West African Monsoon response at inter‐annual timescale. In all cases, these simulated changes result in Sahel drying up to 2 years after an eruption. Besides, we add evidence of a role of varying volcanic activity across the past millennium in the Sahel precipitation variability at multi‐decadal to secular timescales.

Large Ensemble Particle Filter for Spatial Climate Reconstructions Using a Linear Inverse Model

AbstractProxy records that document the last 2000 years of climate provide evidence for the wide range of the natural climate variability from inter‐annual to secular timescales not captured by the short window of recent direct observations. Assessing climate models ability to reproduce such natural variations is crucial to understand climate sensitivity and impacts of future climate change. Paleoclimate data assimilation (PDA) offers a powerful way to extend the short instrumental period by optimally combining the physics described by General Circulation Climate Models (GCMs) with information from available proxy records while taking into account their uncertainties. Here we present a new PDA approach based on a sequential importance resampling (SIR) Particle filter (PF) that uses Linear Inverse Modeling (LIM) as an emulator of several CMIP‐class GCMs. We examine in a perfect‐model framework the skill of the various LIMs to forecast the dynamics of the surface temperatures and provide spatial field reconstructions over the last millennium in a SIR PF. Our results show that the LIMs allow for skillful ensemble forecasts at 1‐year lead‐time based on GCMs dynamical knowledge with best prediction in the tropics and the North Atlantic. The PDA further provides a set of physically consistent spatial fields allowing robust uncertainty quantification related to climate models biases and proxy spatial sampling. Our results indicate that the LIM yields dynamical memory improving climate variability reconstructions and support the use of the LIM as a GCM‐emulator in real reconstruction to propagate large ensembles of particles at low cost in SIR PF.

A novel Lagrangian formulation to construct relativistic rotating stars: towards its application to their evolution calculations

ABSTRACT We present a new formulation to construct numerically equilibrium configurations of rotating stars in general relativity. Having in mind the application to their quasi-static evolutions on a secular time-scale, we adopt a Lagrangian formulation of our own devising, in which we solve force-balance equations to seek for the positions of fluid elements corresponding to the grid points, instead of the ordinary Eulerian formulation. Unlike previous works in the literature, we do not employ the first integral of the Euler equation, which is not obtained analytically in general. We assign a mass, specific angular momentum and entropy to each fluid element in contrast to the previous Eulerian methods, in which the spatial distribution of the angular velocity or angular momentum is specified. These distributions are determined after the positions of all fluid elements (or grid points) are derived in our formulation. We solve the large system of algebraic non-linear equations that are obtained by discretizing the time-independent Euler and Einstein equations in the finite-element method by using our new multidimensional root-finding scheme, named the W4 method. To demonstrate the capability of our new formulation, we construct some rotational configurations, both barotropic and baroclinic. As toy models, we also solve three evolutionary sequences that mimic the cooling, mass-loss, and mass-accretion.

The Regional Diagnosis of Onset and Demise of the Rainy Season over Tropical and Subtropical Australia

Abstract In this paper, we introduce a novel strategy to robustly diagnose the onset and demise of the rainy season using daily observed rainfall over seven specific regions across Australia, as demarcated by the Natural Resource Management (NRM) agency of Australia. The methodology lies in developing an ensemble spread of the diagnosed onset and demise from randomly perturbing the observed daily time series of rainfall at synoptic scales to obtain a measure of the uncertainty of the diagnosis. Our results indicate that the spread of the ensemble in the diagnosis of the onset and demise dates of the rainy season is higher in the subtropical region than the tropical region. Secular change of earlier onset, later demise, longer length, and wetter season are also identified in many of these regions. The influence of the PDO at decadal scale, ENSO and Indian Ocean dipole at interannual scale, and MJO at intraseasonal scale also reveals significant influence on the evolution of the rainy season over these regions in Australia. Most important, the covariability of the onset date with the length of the season and seasonal rainfall anomaly of the season is highlighted as a valuable relationship that can be exploited for real-time monitoring and providing an outlook of the forthcoming rainy season, which could serve some of the NRM regions. Significance Statement We document the rainfall variability during the rainy season over tropical, subtropical, and semiarid regions of Australia and relate them to modes of climate variability spanning from intraseasonal to secular time scales. The study highlights the varied influence of the modes of climate variability on various aspects of the evolution of the rainy season, such as its onset and demise dates and the seasonal rainfall anomaly over these Australian regions. The study uses 114 years of data and shows that the variations in the length of the rainy season and its seasonal rainfall anomaly are strongly dictated by variations of rainy-season onset date. This provides a quick seasonal outlook of the forthcoming rainy season by just monitoring the onset-date evolution in these regions.

Medium Earth Orbit Secular Resonances and Navigation Satellites

AbstractInclination-only dependent lunisolar resonances shape the dynamics of MEO (Medium Earth Orbit) objects over secular time scales (i.e. several decades). Their main effect is to increase an object’s eccentricity, possibly up to a value where the orbit’s perigee meets the Earth’s atmosphere and friction will determine the object’s re-entry. Thus, understanding this mechanism allows the design of low-cost end-of-life disposal strategies which exploit the resonant dynamics. In this proceeding, we will summarize our results in developing an analytic theory for lunisolar resonances and the characterization of diffusion properties along them. On this topic, the techniques proposed are of interest in most problems of secular resonances encountered in Celestial Mechanics.

Anatomy of a Slow Merger: Dissecting Secularly Driven Inspirals of LIGO/Virgo Gravitational Wave Sources

The dozens of compact object mergers detected by LIGO/Virgo raise a key theoretical question: how do initially wide binaries shrink sufficiently quickly that they are able to merge via gravitational wave (GW) radiation within a Hubble time? One promising class of answers involves secular driving of binary eccentricity by some external tidal perturbation. This perturbation can arise due to the presence of a tertiary point mass, in which case the system exhibits Lidov-Kozai (LK) dynamics, or it can stem from the tidal field of the stellar cluster in which the binary orbits. While these secular tide-driven mechanisms have been studied exhaustively in the case of no GW emission, when GWs are included the dynamical behavior is still incompletely understood. In this paper we consider compact object binaries driven to merger via high-eccentricity excitation by (doubly averaged, test-particle quadrupole level) cluster tides—which includes LK-driven mergers as a special case—and include the effects of both general relativistic precession and GW emission. We provide for the first time an analytical understanding of the different evolutionary stages of the binary’s semimajor axis, secular oscillation timescale, and phase-space structure all the way to merger. Our results will inform future population synthesis calculations of compact object binary mergers from hierarchical triples and stellar clusters.

Amplification of regional tides in response to sea level

The study investigates the temporal change in tides under the background of rapid sea level rise, for a highly vulnerable coastal region. It highlights the existence of non-astronomic tidal variability at seasonal and secular time-scales in the Ganga-Brahmaputra-Meghna (GBM) delta, along with increasing low and high tidal levels. The observed variability in semi-diurnal tides was found to be coherent to the mean sea level changes. M2 tide can be a proxy for sea level changes as they show a direct relationship. Steric changes were introduced in the barotropic ADCIRC (ADvanced CIRCulation) model and the results proved that change in water depth modulates the energetics of the tidal wave thereby causing amplification. A regionally varying tidal response was noticed, such that the regions associated with the GBM delta showed maximum amplification. The factors that can cause tidal amplification are region-dependent and coastal geomorphology plays an important role in it. Tidal prediction based on changing sea level was able to capture the observed seasonal modulation of tides and increasing trend in low and high tidal levels. Incorporating the effect of changing tides can improve the accuracy of tidal predictions and will help advance studies regarding regional sea level change, coastal flooding and tide-surge interaction.

Accumulation of Elastic Strain toward Crustal Fracture in Magnetized Neutron Stars

This study investigates elastic deformation driven by the Hall drift in a magnetized neutron-star crust. Although the dynamic equilibrium initially holds without elastic displacement, the magnetic-field evolution changes the Lorentz force over a secular timescale, which inevitably causes the elastic deformation to settle in a new force balance. Accordingly, elastic energy is accumulated, and the crust is eventually fractured beyond a particular threshold. We assume that the magnetic field is axially symmetric, and we explicitly calculate the breakup time, maximum elastic energy stored in the crust, and spatial shear–stress distribution. For the barotropic equilibrium of a poloidal dipole field expelled from the interior core without a toroidal field, the breakup time corresponds to a few years for the magnetars with a magnetic-field strength of ∼1015 G; however, it exceeds 1 Myr for normal radio pulsars. The elastic energy stored in the crust before the fracture ranges from 1041 to 1045 erg, depending on the spatial-energy distribution. Generally, a large amount of energy is deposited in a deep crust. The energy released at a fracture is typically ∼1041 erg when the rearrangement of elastic displacements occurs only in the fragile shallow crust. The amount of energy is comparable to the outburst energy on the magnetars.

Secular Trends in Global Tides Derived From Satellite Radar Altimetry

AbstractPrevious studies have demonstrated that tides are subject to considerable changes on secular time scales. However, these studies rely on sea level observations from tide gauges that are predominantly located in coastal and shelf regions and therefore, the large‐scale patterns remain uncertain. Now, for the first time, satellite radar altimetry (TOPEX/Poseidon &amp; Jason series) has been used to study worldwide linear trends in tidal harmonic constants of four major tides (M2, S2, O1, and K1). This study demonstrates both the potential and challenges of using satellite data for the quantification of such long‐term changes. Two alternative methods were implemented. In the first method, tidal harmonic constants were estimated for consecutive 4‐year periods, from which the linear change was then estimated. In the second method, the estimation of linear trends in the tidal constants of the four tides was integrated in the harmonic analysis. First, both methods were assessed by application to tide gauge data that were sub‐sampled to the sampling scheme of the satellites. Thereafter the methods were applied to the real satellite data. Results show both statistically significant decreases and increases in amplitude up to 1 mm/year and significant phase changes up to ∼0.1 deg/year. The level of agreement between altimeter‐derived trends and estimates from tide gauge data differs per region and per tide.

Annual integral solar proton fluences for 1984–2019

Aims. Long-term fluxes or integral fluences of solar energetic particles (SEPs), and their variability within and beyond the 11-year solar cycle, make an important contribution to space physics. However, large uncertainties exist in the evaluation of average SEP fluxes or fluences over the last few decades, as they have been assessed by different methods and from different datasets. Here we revisit the derivation of annual integral SEP fluences from available data based on in situ measurements since 1984. Methods. We reconstructed a full time series of integral SEP fluxes above 10, 30, 60, 100, and 200 MeV for the period from 1984 to 2019 using observations performed by the GOES satellites. Intercalibration of the fluxes was performed via a linear relation between overlapping pairs of observations in order to obtain a uniform dataset. Galactic cosmic ray (GCR) background subtraction and identification of SEP event periods were carefully performed, allowing for a precise calculation of annual SEP fluences. Results. Annual integral fluences of SEPs with energies above 10, 30, 60, 100, and 200 MeV were calculated for the period from 1984 to 2019 (solar cycles 22–24), along with their uncertainties. It is shown that solar cycle 24 was significantly (by a factor of 5–8) weaker in the SEP fluence than the preceding cycles 22 and 23. The cumulative occurrence probability of years with the fluence above a given value is found to be perfectly described by the Weibull distribution. This can be used as a projection for the occurrence of solar extreme eruptive events on the secular timescales.