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We present statistical analysis of a compilation of observational constraints on the Precambrian length of day and find that the day length stalled at about 19 h for about 1 billion years during the mid-Proterozoic. We suggest that the accelerative torque of atmospheric thermal tides from solar energy balanced the decelerative torque of lunar oceanic tides, temporarily stabilizing Earth’s rotation. This stalling coincides with a period of relatively limited biological evolution known as the boring billion.Analysis of changes in the Earth’s rotation in the Precambrian suggests that day length stabilized at 19 h for 1 billion years due to tidal resonance, which may have been linked to a relatively quiescent period of tectonic activity and biological evolution.

1. Treeless grasslands with climates that can support tree growth are common in upland regions around the world. In South Africa, the upland grasslands are adjacent to lowland savannas in many areas, with an abrupt boundary between them that could be termed a savanna‐grassland ‘treeline’. Both systems are dominated by C4 grasses and burn regularly, yet fire‐tolerant savanna trees do not survive in the grasslands. The upland grasslands experience lower temperatures throughout the year and frost in winter, compared with the warmer savannas. 2. We tested whether frost in the dormant season or slow growth in the growing season in conjunction with frequent fires may explain the tree‐less state of grasslands. We measured Acacia seedling growth for a year in a transplant experiment at ten sites across an altitudinal gradient (42–1704 m) from savannas to grasslands. The effect of frost on seedlings was scored during the following winter. 3. Across all species, height (t = −6.04, d.f. = 471, P < 0.001), biomass (t = −4.56, d.f. = 228, P < 0.001) and height increase (t = −3.40, d.f. = 471, P < 0.001) were significantly higher at savanna sites. As the plants were irrigated and initially supplied with nutrients, the main factor affecting growth was likely to be growing season temperature. 4. Saplings that experience slow growing conditions will take longer to reach a height above the flame zone and will therefore have a lower probability of reaching adult tree height and surviving fires. Day length may be the most important cue for the end of the growing season in savanna trees, as growth decreased with shortening day length in February–March while temperatures were still high and plants were not water limited. 5. Synthesis. Savanna trees grew more slowly in cooler upland grassland sites compared with lower elevation warm savanna sites and, under frequent fire regimes, would be prevented from reaching maturity. This may be true globally for similar grasslands where tree growth can occur and could partly explain the lack of trees in grasslands.

1. Understanding the processes responsible for macro-scale spatial and temporal phenological patterns is a critical step in developing predictive phenological models. While phenological responses may involve the integration of multiple environmental cues, the spring phenology of many plant and animal species appears to be especially sensitive to temperature. 2. As a result of the success of citizen science schemes in mobilizing amateur naturalists, for some parts of the world, there now exist extensive data sets of phenological timings, spanning many species, locations and years. In macroecology, two types of models — time windows and growing degree-days — are widely used to predict phenology on the basis of temperature. 3. Here, we compare the performance of the two methods in predicting spatiotemporal variation in the timing of Quercus robur first leafing. The methods agree on the time at which leafing becomes sensitive to temperature and provide weak support for a delay in initiation of thermal sensitivity with increasing latitude due to a day-length requirement. Both methods explain c. 50% of the variation in first dates and identify plasticity, rather than local adaptation, as the major cause of spatial covariation between temperature and phenology. For a 1°C rise in spring temperatures we predict that a plastic response of first leafing will give rise to an advance of about seven days. 4. Synthesis: Time-window and growing degree-day methods provide remarkably congruent insights into the processes underpinning geographic variation in Quercus robur first leafing dates. We find that a spatially invariant plastic response to temperature dominates spatiotemporal phenological variation, which means that it may be reasonable to substitute space for time to project how this species will respond to climate change. This study demonstrates the contribution that top-down macroecological approaches can make to our understanding of the processes that give rise to intraspecific phenological variation.

The properties of low-frequency global seismic noise, represented by continuous records for 24 years, 1997–2020, are investigated at 229 broadband stations located around the world. The property of waveforms, known as the Donoho–Johnston threshold, which separates the absolute values of the orthogonal wavelet coefficients into \"small\" and \"large\" is analyzed. The ratio of the number of \"large\" coefficients to their total number is determined by the dimensionless DJ index, which takes values from 0 to 1. The DJ index is considered as a measure of the nonstationarity of noise: the larger is the DJ index, the more is nonstationary the waveform. For each station, daily DJ index values are calculated. An auxiliary network of 50 reference points is introduced, the positions of which are determined by clustering the positions of seismic stations. For each reference point, a time series is constructed with a time step of 1 day, which is calculated as the median of daily DJ index values from the 5 nearest operable stations. For all pairs of reference points, the coherence between the DJ index values is estimated in a sliding time window of 365 days with an offset of 3 days, and the maximum values of the coherence function and the frequency at which the maximum coherence is reached are determined. The average values of the maximum coherences show strong growth after 2003, and the maximum distances between the reference points, for which the maximum coherence exceeded the threshold of 0.9, undergo an explosive increase in values after 2012. By extrapolating and averaging the DJ index values at the reference points, the region of concentration of maximum DJ index values was determined at the North-East Siberia. The bursts in the mean value of the maximum coherences between the day length and the DJ index values at the control points precede the release of seismic energy with a delay of about 530 days.

In the report he submitted to the Académie des Sciences, Poisson imagined a set of concentric spheres at the origin of Earth’s magnetic field. It may come as a surprise to many that Poisson as well as Gauss both considered the magnetic field to be constant. We propose in this study to test this surprising assertion for the first time, evoked by Poisson in 1826. First, we present a development of Maxwell’s equations in the framework of a static electric field and a static magnetic field in order to draw the necessary consequences for the Poisson hypothesis. In a second step, we see if the observations can be in agreement with Poisson. To do so, we choose to compare (1) the polar motion drift and the secular variation of Earth’s magnetic field, (2) the seasonal pseudo-cycles of day length together with those of the sea level recorded by different tide gauges around the globe and those of Earth’s magnetic field recorded in different magnetic observatories. We then propose a mechanism, in the spirit of Poisson, to explain the presence of the 11-year cycle in the magnetic field. We test this mechanism with observations, and finally, we study closely the evolution of the g1,0 coefficient of the International Geomagnetic Reference Field (IGRF) over time.

Changes in Earth rotation are strongly related to fluctuations in the angular momentum of the atmosphere, and therefore contain integral information about the atmospheric state. Here we investigate the extent to which observed Earth rotation parameters can be used to evaluate and potentially constrain atmospheric models. This is done by comparing the atmospheric excitation function, computed geophysically from reanalysis data and climate model simulations constrained only by boundary forcings, to the excitation functions inferred from geodetic monitoring data. Model differences are assessed for subseasonal variations, the annual and semiannual cycles, interannual variations, and decadal‐scale variations. Observed length‐of‐day anomalies on the subseasonal timescale are simulated well by the simulations that are constrained by meteorological data only, whereas the annual cycle in length‐of‐day is simulated well by all models. Interannual length‐of‐day variations are captured fairly well as long as a model has realistic, time‐varying SST boundary conditions and QBO forcing. Observations of polar motion are most clearly relatable to atmospheric dynamics on subseasonal to annual timescales, though angular momentum budget closure is difficult to achieve even for data‐constrained atmospheric simulations. Closure of the angular momentum budget on decadal timescales is difficult and strongly dependent on estimates of angular momentum fluctuations due to core‐mantle interactions in the solid Earth. Key Points Earth rotation parameters contain global information about atmospheric dynamics Length‐of‐day observations can constrain modeled winds in tropical regions Polar motion observations can constrain modeled mass movements in midlatitudes

Barystatic sea level stores excess water mass from the atmosphere and land to maintain global mass conservations within the Earth system. Besides the secular contribution to global sea‐level rise, changes in barystatic sea level also play an important role in mass‐induced length‐of‐day (LOD) variations over a few years or shorter periods. Compared to barystatic sea level changes deduced from the geophysical models, Gravity Recovery and Climate Experiment and GRACE follow‐on (GRACE/GFO) measurements provide actual observed ocean mass changes. Here, we investigate short‐term both seasonal (annual and semiannual) and non‐seasonal LOD variations caused by mass redistribution using GRACE/GFO mass estimates and effective angular momentum (EAM) products, particularly quantitatively assessing the excitation from the barystatic sea level. Note that correcting the problem of global mass non‐conservation is necessary for GRACE/GFO mass estimates in both spherical harmonic and mascon solutions to calculate the LOD excitation accurately. LOD mass term contributions derived from GRACE/GFO mass estimates considering global mass conservation show high consistency with satellite laser ranging results and are much closer to geodetic LOD observations than EAM products at seasonal and non‐seasonal time scales. The barystatic sea level exhibits the most significant amplitude in mass‐induced LOD variations, compensating for most land hydrological excitation, but shows no clear correlation with the atmosphere. Due to slight fluctuations in cryospheric effects and the substantial compensatory action of the barystatic sea level, differences in the land hydrological excitation do not lead to significant deviations in the total LOD mass term between EAM products and GRACE/GFO mass estimates. Plain Language Summary At periods of a few years and shorter, mass redistribution occurs among various Earth's surface fluids, including the atmosphere, ocean, land hydrology and cryosphere. These mass changes can result in short‐term length‐of‐day (LOD) variations. Barystatic sea level plays a crucial role in maintaining global mass conservation and influencing LOD variations related to mass changes, as it continuously receives or supplements water mass changes from other Earth subsystems. These effects not only contribute to global sea‐level rise but are also critical in the short‐term mass exchanges. In addition to using geophysical fluid models to calculate barystatic sea level caused by mass changes in other Earth's surface fluids, we also utilize Gravity Recovery and Climate Experiment (GRACE) and GRACE follow‐on (GFO) measurements to evaluate the barystatic sea level excitation to seasonal and non‐seasonal LOD variations on the short‐term time scales. Our results reveal that barystatic sea level is a significant factor in short‐term mass‐induced LOD variations, largely offsetting the impacts of mass changes from the land (land hydrology and cryosphere). Under global mass conservation, barystatic sea level excites LOD variations by adjusting the global water cycle. These findings help us further understand short‐term LOD variations caused by global mass migration and redistribution. Key Points LOD mass terms from Earth's surface fluids are analyzed using EAM products, GRACE/GFO spherical harmonic and mascon solutions GRACE/GFO mass estimates, after correcting global mass non‐conservation, show high consistency with SLR results for the LOD excitation Under global mass conservation, barystatic sea level largely offsets the excitation of the land mass term to LOD variations

Differences in formulation of the equations of celestial mechanics may result in differences in interpretation. This paper focuses on the Liouville-Euler system of differential equations as first discussed by Laplace. In the “modern” textbook presentation of the equations, variations in polar motion and in length of day are decoupled. Their source terms are assumed to result from redistribution of masses and torques linked to Earth elasticity, large earthquakes, or external forcing by the fluid envelopes. In the “classical” presentation, polar motion is governed by the inclination of Earth’s rotation pole and the derivative of its declination (close to length of day, lod). The duration and modulation of oscillatory components such as the Chandler wobble is accounted for by variations in polar inclination. The “classical” approach also implies that there should be a strong link between the rotations and the torques exerted by the planets of the solar system. Indeed there is, such as the remarkable agreement between the sum of forces exerted by the four Jovian planets and components of Earth’s polar motion. Singular Spectral Analysis of lod (using more than 50 years of data) finds nine components, all with physical sense: first comes a “trend”, then oscillations with periods of ∼80 yrs (Gleissberg cycle), 18.6 yrs, 11 yrs (Schwabe), 1 year and 0.5 yr (Earth revolution and first harmonic), 27.54 days, 13.66 days, 13.63 days and 9.13 days (Moon synodic period and harmonics). Components with luni-solar periods account for 95% of the total variance of the lod. We believe there is value in following Laplace’s approach: it leads to the suggestion that all the oscillatory components with extraterrestrial periods (whose origin could be found in the planetary and solar torques), should be present in the series of sunspots and indeed, they are.

A wide variety of organisms use the regular seasonal changes in photoperiod as a cue to align their life cycles with favorable conditions. Yet the phenological consequences of photoperiodism for organisms exposed to new climates are often overlooked. We present a conceptual approach and phenology model that maps voltinism (generations per year) and the degree of phenological mismatch that can arise when organisms with a short-day diapause response are introduced to new regions or are otherwise exposed to new climates. Our degree-day-based model combines continent-wide spatialized daily climate data, calculated date-specific and latitude-specific day lengths, and experimentally determined developmental responses to both photoperiod and temperature. Using the case of the knotweed psyllid Aphalara itadori, a new biological control agent being introduced from Japan to North America and Europe to control an invasive weed, we show how incorporating a short-day diapause response will result in geographic patterns of attempted voltinism that are strikingly different from the potential number of generations based on degreedays alone. The difference between the attempted and potential generations represents a quantitative measure of phenological mismatch between diapause timing and the end of the growing season. We conclude that insects moved from lower to higher latitudes (or to cooler climates) will tend to diapause too late, potentially resulting in high mortality from inclement weather, and those moved from higher to lower latitude (to warmer climates) may be prone to diapausing too early, therefore not fully exploiting the growing season and/or suffering from insufficient reserves for the longer duration in diapause. Mapped output reveals a central region with good phenology match that shifts north or south depending on the geographic source of the insect and its corresponding critical photoperiod for diapause. These results have direct relevance for efforts to establish populations of classical biocontrol agents. More generally, our approach and model could be applied to a wide variety of photoperiod- and temperature-sensitive organisms that are exposed to changes in climate, including resident and invasive agricultural pests and species of conservation concern.