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The Coupled Model Intercomparison Project (phase 6) (CMIP6) global circulation models (GCMs) predict equilibrium climate sensitivity (ECS) values ranging between 1.8 and 5.7 $^\circ$C. To narrow this range, we group 38 GCMs into low, medium and high ECS subgroups and test their accuracy and precision in hindcasting the mean global surface warming observed from 1980-1990 to 2011-2021 in the ERA5 T2m, HadCRUT5, GISTEMP v4, and NOAAGlobTemp v5 global surface temperature records. We also compare the GCM hindcasts to the satellite-based UAH MSU v6 lower troposphere global temperature record. We use 143 GCM ensemble averaged simulations under four slightly different forcing conditions, 688 GCM member simulations, and Monte Carlo modeling of the internal variability of the GCMs under three different model accuracy requirements. We found that the medium and high ECS GCMs run too hot up to over 95% and 97% of cases, respectively. The low ECS GCM group agrees best with the warming values obtained from the surface temperature records, ranging between 0.52 and 0.58 $^\circ$C. However, when comparing the observed and GCM hindcasted warming on land and ocean regions, the surface-based temperature records appear to exhibit a significant warming bias. If the satellite based UAH MSU lt record is accurate, actual surface warming from 1980 to 2021 may have been around 0.40 $^\circ$C (or less), i.e. up to about 30% less than what is reported by the surface based temperature records. The latter situation implies that even the low ECS models would have produced excessive warming from 1980 to 2021. These results suggest that the actual ECS may be relatively low, i.e. lower than 3 $^\circ$C or even less than 2 $^\circ$C. Therefore, the projected global climate warming over the next few decades could be moderate and probably not particularly alarming., 26 pages, 13 figures. Climate Dynamics (2022)

The general circulation of the atmosphere determines the long-term variability of weather processes. This circulation is driven by the temperature differences between the poles and the equator, causing air to move along the Earth's surface. However, this requires enhanced pressure at the poles, which is not observed. To sustain the circulation, an additional non-hydrostatic pressure gradient is required. In my research, I propose the emergence of an additional non-hydrostatic pressure gradient resulting from the centrifugal force generated by the Earth's rotation. This centrifugal force creates a non-hydrostatic vertical pressure gradient, which is essential for the closed circulation of unequally heated air in the meridional direction. The circulation is composed of three distinct streams flowing in opposite directions, with the polar and tropical tropopause acting as boundaries. The temperature in the atmosphere decreases from the surface to the polar tropopause and remains constant above it., 17 pages, 12 figures

The influence of the thermal expansion of the Earth's atmosphere on the stability of vertical stratification of fluid density and temperature is studied. We show that such an influence leads to the instability of incompressible flows. Modified by the thermal expansion coefficient, a new expression for the Brunt-V{\"a}is{\"a}l{\"a} frequency is derived, and a critical value of the thermal expansion coefficient for which the instability occurs is revealed., Comment: 6 pages, 3 figures; Revised version to appear in Physics Letters A (2023)

The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the possible steady states under different forcing is the bifurcation diagram, that reveals the regions of multi-stability, the position of tipping points, and the range of stability of each steady state. However, its construction is highly time consuming in climate models with a dynamical deep ocean, interactive ice sheets or carbon cycle, where the relaxation time becomes larger than thousand years. Using a coupled setup of MITgcm, we test two techniques with complementary advantages. The first is based on the introduction of random fluctuations in the forcing and permits to explore a wide part of phase space. The second reconstructs the stable branches and is more precise in finding the position of tipping points., Comment: 9 pages, 5 figures, Supplemental Material, accepted for publication in Phys. Rev. E

The Thorndike et al., (\emph{J. Geophys. Res.} {\bf 80} 4501, 1975) theory of the ice thickness distribution, $g(h)$, treats the dynamic and thermodynamic aggregate properties of the ice pack in a novel and physically self-consistent manner. Therefore, it has provided the conceptual basis of the treatment of sea-ice thickness categories in climate models. The approach, however, is not mathematically closed due to the treatment of mechanical deformation using the redistribution function $\psi$, the authors noting ``The present theory suffers from a burdensome and arbitrary redistribution function $\psi .$'' Toppaladoddi and Wettlaufer (\emph{Phys. Rev. Lett.} {\bf 115} 148501, 2015) showed how $\psi$ can be written in terms of $g(h)$, thereby solving the mathematical closure problem and writing the theory in terms of a Fokker-Planck equation, which they solved analytically to quantitatively reproduce the observed winter $g(h)$. Here, we extend this approach to include open water by formulating a new boundary condition for their Fokker-Planck equation, which is then coupled to the observationally consistent sea-ice growth model of Semtner (\emph{J. Phys. Oceanogr.} {\bf 6}(3), 379, 1976) to study the seasonal evolution of $g(h)$. We find that as the ice thins, $g(h)$ transitions from a single- to a double-peaked distribution, which is in agreement with observations. To understand the cause of this transition, we construct a simpler description of the system using the equivalent Langevin equation formulation and solve the resulting stochastic ordinary differential equation numerically. Finally, we solve the Fokker-Planck equation for $g(h)$ under different climatological conditions to study the evolution of the open-water fraction., Comment: 8 pages, 10 figures

Seismically generated sound waves that propagate through the ocean are used to infer temperature anomalies and their vertical structure in the deep East Indian Ocean. These T waves are generated by earthquakes off Sumatra and received by hydrophone stations off Diego Garcia and Cape Leeuwin. Between repeating earthquakes, a T wave's travel time changes in response to temperature anomalies along the wave's path. What part of the water column the travel time is sensitive to depends on the frequency of the wave, so measuring travel time changes at a few low frequencies constrains the vertical structure of the inferred temperature anomalies. These measurements reveal anomalies due to equatorial waves, mesoscale eddies, and decadal warming trends. By providing direct constraints on basin-scale averages with dense sampling in time, these data complement previous point measurements that alias local and transient temperature anomalies.

Earth System Models (ESMs) are essential tools for understanding the impact of human actions on Earth's climate. One key application of these models is studying extreme weather events, such as heat waves or dry spells, which have significant socioeconomic and environmental consequences. However, the computational demands of running a sufficient number of simulations to analyze the risks are often prohibitive. In this paper we demonstrate that diffusion models -- a class of generative deep learning models -- can effectively emulate the spatio-temporal trends of ESMs under previously unseen climate scenarios, while only requiring a small fraction of the computational resources. We present a diffusion model that is conditioned on monthly averages of temperature or precipitation on a $96 \times 96$ global grid, and produces daily values that are both realistic and consistent with those averages. Our results show that the output from our diffusion model closely matches the spatio-temporal behavior of the ESM it emulates in terms of the frequency of phenomena such as heat waves, dry spells, or rainfall intensity., Presented at Tackling Climate Change with Machine Learning, ICLR 2023

Employing a linear shallow water equation (LSWE) model in the spherical coordinates, this paper investigates the tsunami waves generated by the atmospheric pressure shock waves due to the explosion of the submarine volcano Hunga Tonga-Hunga Ha'apai on January 15, 2022. Using the selected 59 atmospheric pressure records in the Pacific Ocean, an empirical atmospheric pressure model is first constructed. Applying the atmospheric pressure model and realistic bathymetric data in the LSWE model, tsunami generation and propagation are simulated in the Pacific Ocean. The numerical results show clearly the co-existence of the leading locked waves, propagating with the speed of the atmospheric pressure waves (~1,100 km/hr), and the trailing free waves, propagating with long gravity ocean wave celerity (~ 750 km/hr). During the event, tsunamis were reported by 41 DART buoys in the Pacific Ocean, which require corrections because of the occurrence of atmospheric pressure waves. The numerically simulated tsunami arrival time and the amplitudes of the wave crest and trough of the leading locked waves compare reasonably well with the corrected DART measurements. The comparisons for the trailing waves are less satisfactory, since free waves could also have been generated by other tsunami generation mechanisms, which have not been considered in the present model, and by the scattering of locked waves over changing bathymetry. In this regard, the numerical results show clearly that the deep Tonga trench (~ 10 km) amplifies the trailing waves in the Southeast part of the Pacific Ocean via the Proudman resonance condition.

Principal Geodesic Analysis (PGA) is applied to a climate time series. First, we transform each multidimensional sequence into the path signature. Since the signature lives in a curved space, usual principal component analysis (PCA) is not applicable. Instead, we treat the signature space as a geodesic manifold. By replacing the notion of straight lines with that of geodesics, the domain of PCA can be extended to the curved space. Then, the first principal component is derived as the geodesic that minimizes the unexplained variance in the data. As an application, we computed the leading modes for one-year NINO SST time series, which are divided into segments that represent annual variations of monthly averages. It is interesting that some months in a year reveal characteristic undulations that could indicate the early signs of upcoming El Nin\~{o} events., Comment: The theoretical structure, in particular the existence of the Riemannian metric, was flawed and will be resubmitted after reconsideration

Observations are increasingly used to detect critical slowing down (CSD) to measure stability changes in key Earth system components. However, most datasets have non-stationary missing-data distributions, biases and uncertainties. Here we show that, together with the pre-processing steps used to deal with them, these can bias the CSD analysis. We present an uncertainty quantification method to address such issues. We show how to propagate uncertainties provided with the datasets to the CSD analysis and develop conservative, surrogate-based significance tests on the CSD indicators. We apply our method to three observational sea-surface temperature and salinity datasets and to fingerprints of the Atlantic Meridional Overturning Circulation derived from them. We find that the properties of these datasets and especially the specific gap filling procedures can in some cases indeed cause false indication of CSD. However, CSD indicators in the North Atlantic are still present and significant when accounting for dataset uncertainties and non-stationary observational coverage.

New particle formation (NPF) in the tropical free troposphere (FT) is a globally important source of cloud condensation nuclei, affecting cloud properties and climate. Oxidized organic molecules (OOMs) produced from biogenic volatile organic compounds are believed to contribute to aerosol formation in the tropical FT, but without direct chemical observations. We performed in-situ molecular-level OOMs measurements at the Bolivian station Chacaltaya at 5240 meters above sea level, on the western edge of Amazonia. For the first time, we demonstrate the presence of OOMs, mainly with 4-5 carbon atoms, simultaneously in both gas and particulate phases in tropical FT air from Amazonia. These observations, combined with air mass history analyses, indicate that the observed OOMs are linked to isoprene emitted from the rainforests hundreds of kilometers away. Based on particle-phase measurements, we find that these compounds can contribute to the growth of newly formed particles, and are potentially crucial for new particle formation in the tropical free troposphere on a continental scale. Our study will thus improve the understanding of aerosol formation process in the tropics.

Solar activities may disturb the geomagnetic field and impact the power grid via geomagnetically induced currents. We study active and reactive powers as well as the power factor of Iran's power grid transformers (230 kV and 400 kV) and their correlations with geomagnetic disturbances indices (SYM-H < -30 nT and sizable horizontal geomagnetic field fluctuation) from 19 March 2018 to 20 March 2020. Out of 128,627 cases with a transformer power factor of less than 0.7, we observe that 12,112 samples correlated with SYM-H. Our investigation shows that about 4 percent of two years, the SYM-H has values less than -30 nT. Analysis of high-performance transformers (a power factor greater than 0.7 at 95 percent of working time) shows at least a 55 percent correlation of power factor less than 0.7 and SYM-H less than -30 nT. We observe that the transformers' power factor of Rafsanjan-Kerman and Sarcheshmeh-Kerman (wye connection on 230 kV side) substations decreased to less than 0.7 and correlated with SYM-H. We show that the reactive power of the Sefidrood-Guilan and Shahid Beheshti-Guilan transformers (wye configurations) increased considerably on 9 January 2020 and positively correlated with SYM-H may produce large GICs at this part of the grid. We observe that the increase in reactive power at the Shahid Beheshti-Guilan substation correlated with the sizable changes in the horizontal field recorded by the Jaipur station. However, more details (temperature and current of transformers) need records to estimate the impact of geomagnetic induction current on the power grid.

Clouds, especially low clouds, are crucial for regulating Earth’s energy balance and mediating the response of the climate system to changes in greenhouse gas concentrations. Despite their importance for climate, they remain relatively poorly understood and are inaccurately represented in climate models. A principal reason is that the high computational expense of simulating them with large-eddy simulations (LES) has inhibited broad and systematic numerical experimentation and the generation of large datasets for training parametrization schemes for climate models. Here we demonstrate LES of low clouds on Tensor Processing Units (TPUs), application-specific integrated circuits that were originally developed for machine learning applications. We show that TPUs in conjunction with tailored software implementations can be used to simulate computationally challenging stratocumulus clouds in conditions observed during the Dynamics and Chemistry of Marine Stratocumulus (DYCOMS) field study. The TPU-based LES code successfully reproduces clouds during DYCOMS and opens up the large computational resources available on TPUs to cloud simulations. The code enables unprecedented weak and strong scaling of LES, making it possible, for example, to simulate stratocumulus with $10\times$ speedup over real-time evolution in domains with a $34.7 \mathrm{km} \times 53.8 \mathrm{km}$ horizontal cross section. The results open up new avenues for computational experiments and for substantially enlarging the sample of LES available to train parameterizations of low clouds.

Authors: Thomas Pähtz, Katharina Tholen, Sandesh Kamath, Eric Parteli, Klaus KroyTitle: Anomalous scaling of aeolian sand transport reveals coupling to bed rheologyPredicting transport rates of windblown sand is a central problem in aeolian research, with implications for climate, environmental, and planetary sciences. Though studied since the 1930s, the underlying many-body dynamics is still incompletely understood, as underscored by the recent empirical discovery of an unexpected third-root scaling in the particle-fluid density ratio [1]. Here, by means of grain-scale simulations and analytical modeling, we elucidate how a complex coupling between grain-bed collisions and granular creep within the sand bed yields a dilatancy-enhanced bed erodibility. Our minimal saltation model robustly predicts both the observed scaling and a new undersaturated steady transport state that we confirm by simulations for rarefied atmospheres [2].[1] Pähtz, Durán, Scaling laws for planetary sediment transport from DEM-RANS numerical simulations, https://arxiv.org/abs/2203.00562[2] Tholen, Pähtz, Kamath, Parteli, Kroy, Anomalous scaling of aeolian sand transport reveals coupling to bed rheology , Physical Review Letters, accepted.

Climate change is predicted to lead to major changes in terrestrial ecosystems. However, significant differences in climate model projections for given scenarios of greenhouse gas emissions, continue to hinder detailed assessment. Here we show, using a traditional Koppen-Geiger bioclimate classification system, that the latest CMIP6 Earth System Models actually agree very well on the fraction of the global land-surface that will undergo a significant change per degree of global warming. Data from historical and ssp585 model runs are used to create bioclimate maps at various degrees of global warming, and to investigate the performance of the ensemble mean when classifying climate data into discrete categories. Using a streamlined scheme with 13 classifications, global bioclimate classification maps at 2K and 4K of global warming above a 1901-1931 reference period are presented. These projections show large shifts in bioclimate distribution, with an almost exclusive change from colder, wetter bioclimates to hotter, dryer ones. Historical model run performance is assessed and examined by comparison with the bioclimatic classifications derived from the observed climate over the same time period. The fraction of the land experiencing a change in its bioclimatic class as a function of global warming is estimated by combining the results from the individual models. Despite the discrete nature of the bioclimatic classification scheme, we find only a weakly-saturating dependence of this fraction on global warming which implies about 12 pct of land experiencing a significant change in climate, per 1K increase in global mean temperature between the global warming levels of 1 and 3K. Therefore, we estimate that stabilising the climate at 1.5K rather than 2K of global warming, would save over 7 million square kilometres of land from a major bioclimatic change., 22 pages, some large figures

The eddy-driven jet stream and storm tracks in the mid-latitude atmosphere are known to shift in latitude on various timescales, but the physical processes that cause these shifts are still unclear. In this study, we introduce a minimal dynamical system derived from the classical Phillips two-level model with the goal of elucidating the essential mechanisms responsible for the interaction between eddies and mean flow. Specifically, we aim to understand the link between the structure of the eddies and the shift of the latitudinal maximum of the zonal flow. By varying the horizontal shape of the eddies, we find three distinct dynamical regimes whose occurrence depends on the intensity of the external baroclinic forcing: a purely zonal flow, a barotropic eddy regime with net poleward momentum flux, and a baroclinic eddy regime with both net poleward momentum and temperature flux. For weak baroclinic forcing, the classical zonal flow solution with latitudinal maximum at the centre of the beta-channel is found. For strong forcing, if eddies are southwest-northeast tilted and zonally elongated, the system is in the baroclinic eddy regime, resulting in a poleward shift of the jet. The intermediate barotropic eddy regime also features a poleward shifted jet, yet with eddies structurally distinct from the baroclinic regime. Changing the parameters yields transitions between the regimes that can be either continuous or discontinuous in terms of the properties of the atmosphere. The findings of this study also provide insights into the properties of the storm track change between the jet entrance and jet exit regions of the North Atlantic., Comment: 15 pages, 4 figures

Earth's water, intrinsic oxidation state, and metal core density are fundamental chemical features of our planet. Studies of exoplanets provide a useful context for elucidating the source of these chemical traits. Planet formation and evolution models demonstrate that rocky exoplanets commonly formed with hydrogen-rich envelopes that were lost over time. These findings suggest that Earth may also have formed from bodies with H$_2$-rich primary atmospheres. Here we use a self-consistent thermodynamic model to show that Earth's water, core density, and overall oxidation state can all be sourced to equilibrium between H$_2$-rich primary atmospheres and underlying magma oceans in its progenitor planetary embryos. Water is produced from dry starting materials resembling enstatite chondrites as oxygen from magma oceans reacts with hydrogen. Hydrogen derived from the atmosphere enters the magma ocean and eventually the metal core at equilibrium, causing metal density deficits matching that of Earth. Oxidation of the silicate rocks from solar-like to Earth-like oxygen fugacities also ensues as Si, along with H and O, alloys with Fe in the cores. Reaction with hydrogen atmospheres and metal-silicate equilibrium thus provides a simple explanation for fundamental features of Earth's geochemistry that is consistent with rocky planet formation across the galaxy., Comment: 3 main figures, 5 auxiliary figures

Two drifting wave buoys were deployed in the central Arctic Ocean, north of the Laptev Sea, where there are historically no wave observations available. An experimental wave buoy was deployed alongside a commercial buoy. The inter-buoy comparison showed that the experimental buoy measured wave heights and periods accurately; so the buoy data were used to study the predictability of a wave-ice model in this region. The first event we focused was when both buoys observed a sudden decrease in significant wave heights $H_{m0}$. The sudden decrease was caused by the change of wind directions from along the ice edge to off-ice wind. This event was compared with the ARC MFC wave-ice model product, which underestimated the $H_{m0}$. The inaccurate model representation of an ice tongue located upwind of the buoys was found to constrain the available fetch for wave growth. The second case was when the buoys entered ice cover as new ice formed; an on-ice wave event was observed and the buoy downwind measured 1.25 m $H_{m0}$. In this instance, the ARC MFC wave-ice model product largely underestimated the downwind buoy $H_{m0}$. To investigate this event, model sea ice conditions were examined by comparing the ARC MFC sea ice forcing with the neXtSIM sea ice model product. Our analysis revealed that the thin ice thickness distribution for ice types like young and grey ice, typically less than 30 cm, were not resolved. The ARC MFC model's wave dissipation rate has a sea ice thickness dependence, and therefore, it overestimates wave dissipation in thin ice cover; sea ice forcing that can resolve the thin thickness distribution is needed to improve the predictability. This study provides an observational insight into better predictions of waves in marginal ice zones when new ice forms.

Methane is a powerful greenhouse gas, and a primary target for mitigating climate change in the short-term future due to its relatively short atmospheric lifetime and greater ability to trap heat in Earth's atmosphere compared to carbon dioxide. Top-down observations of atmospheric methane are possible via drone and aircraft surveys as well as satellites such as the TROPOspheric Monitoring Instrument (TROPOMI). Recent work has begun to apply the divergence method to produce regional methane emission rate estimates. Here we show that spatially incomplete observations of methane can produce negatively biased time-averaged regional emission rate estimates via the divergence method, but that this effect can be counteracted by adopting a procedure in which daily advective fluxes of methane are time-averaged before the divergence method is applied. Using such a procedure with TROPOMI methane observations, we calculate yearly Permian emission rates of 3.1, 2.4 and 2.7 million tonnes per year for the years 2019 through 2021. We also show that highly-resolved plumes of methane can have negatively biased estimated emission rates by the divergence method due to the presence of turbulent diffusion in the plume, but this is unlikely to affect regional methane emission budgets constructed from TROPOMI observations of methane. The results from this work are expected to provide useful guidance for future implementations of the divergence method for emission rate estimation from satellite data - be it for methane or other gaseous species in the atmosphere., Comment: 17 pages, 10 figures, submitted to Environmental Research Letters

Improving and homogenizing time and space reference systems on Earth and, more specifically, realizing the Terrestrial Reference Frame (TRF) with an accuracy of 1 mm and a long-term stability of 0.1 mm/year are relevant for many scientific and societal endeavors. The knowledge of the TRF is fundamental for Earth and navigation sciences. For instance, quantifying sea level change strongly depends on an accurate determination of the geocenter motion but also of the positions of continental and island reference stations, such as those located at tide gauges, as well as the ground stations of tracking networks. Also, numerous applications in geophysics require absolute millimeter precision from the reference frame, as for example monitoring tectonic motion or crustal deformation, contributing to a better understanding of natural hazards. The TRF accuracy to be achieved represents the consensus of various authorities, including the International Association of Geodesy (IAG), which has enunciated geodesy requirements for Earth sciences. Moreover, the United Nations Resolution 69/266 states that the full societal benefits in developing satellite missions for positioning and Remote Sensing of the Earth are realized only if they are referenced to a common global geodetic reference frame at the national, regional and global levels. Today we are still far from these ambitious accuracy and stability goals for the realization of the TRF. However, a combination and co-location of all four space geodetic techniques on one satellite platform can significantly contribute to achieving these goals. This is the purpose of the GENESIS mission, a component of the FutureNAV program of the European Space Agency. The GENESIS platform will be a dynamic space geodetic observatory carrying all the geodetic instruments referenced to one another through carefully calibrated space ties. The co-location of the techniques in space will solve the inconsistencies and biases between the different geodetic techniques in order to reach the TRF accuracy and stability goals endorsed by the various international authorities and the scientific community. The purpose of this paper is to review the state-of-the-art and explain the benefits of the GENESIS mission in Earth sciences, navigation sciences and metrology. This paper has been written and supported by a large community of scientists from many countries and working in several different fields of science, ranging from geophysics and geodesy to time and frequency metrology, navigation and positioning. As it is explained throughout this paper, there is a very high scientific consensus that the GENESIS mission would deliver exemplary science and societal benefits across a multidisciplinary range of Navigation and Earth sciences applications, constituting a global infrastructure that is internationally agreed to be strongly desirable., Earth, Planets and Space, 75 (1), ISSN:1343-8832, ISSN:1880-5981

The Marginal Ice Zone is a highly dynamic region where the atmosphere, ocean, waves and sea ice meet. Waves play a fundamental role in this coupled system, but progress in our understanding of wave-ice interactions is currently hindered by the lack of observations of sea ice properties in-situ. In this study we aim to estimate the ice thickness and effective elastic modulus of sea ice passively using observations of waves in ice. Specifically, we use three low-cost geophones deployed in triangular formation with sides of about 200 m on fast ice. The focus here is on three major wave events recorded, each consisting of initial high frequency vibrations with a frequency at around 10 Hz, followed by low frequency dispersive waves within a frequency range of 0.08-0.28 Hz. Based on the phase speed of the initial high frequency vibrations, we estimate the purely elastic effective modulus to be 4-4.5 GPa. By comparing the arrival times of the dispersive low frequency wave events to the dispersion relationship of waves in a thin elastic ice sheet we obtain estimates of the effective elastic modulus in the range of 0.4-0.7 GPa. This is close to the measured effective elastic modulus through cantilever experiments of 0.5 GPa but considerably smaller than the default value of 5.5 GPa currently in use in contemporary wave models. We could not, however, obtain explicit estimates of the ice thickness and effective modulus individually as their impacts on the shape of the dispersion relationship are similar in this frequency range. Distinction is only possible for dispersive wave events larger than about 1 Hz, such as for vibrations generated by (thermal) cracking, which are frequently observed in our dataset. With our results, we show that low-cost geophones can be used to estimate sea ice properties in fast ice and substantiate that this to be possible on very large ice floes as well.

The spatiotemporal variation in tropical air-sea interaction is investigated by applying a simple model that considers the fundamental dynamics in tropical oceans. The model decomposes sea surface temperature anomaly (SSTA) variation into a series of spatial modes that oscillates with their natural frequencies. The results suggest that the first mode associates with the dipole-like SSTA variation between the western and the eastern coast, such as EP El Ni\~no, the Atlantic Ni\~no, and IOD; whereas the second mode associates with the tripole-like SSTA pattern among the central and eastern, western coast, such as CP El Ni\~no and minor SSTA variations in the tropical Atlantic and Indian Ocean. Each mode oscillates with its natural frequency that depends on the strength of air-sea coupling and the basin size. The model provides a systematic framework for the comprehensive understanding of the complex air-sea interaction in tropical oceans.

Klaus Hasselmann's revolutionary intuition was to take advantage of the stochasticity associated with fast weather processes to probe the slow dynamics of the climate system. This has led to fundamentally new ways to study the response of climate models to perturbations, and to perform detection and attribution for climate change signals. Hasselmann's program has been extremely influential in climate science and beyond. We first summarise the main aspects of such a program using modern concepts and tools of statistical physics and applied mathematics. We then provide an overview of some promising scientific perspectives that might better clarify the science behind the climate crisis and that stem from Hasselmann's ideas. We show how to perform rigorous model reduction by constructing parametrizations in systems that do not necessarily feature a time-scale separation between unresolved and resolved processes. We propose a general framework for explaining the relationship between climate variability and climate change, and for performing climate change projections. This leads us seamlessly to explain some key general aspects of climatic tipping points. Finally, we show that response theory provides a solid framework supporting optimal fingerprinting methods for detection and attribution., Comment: 16 pages, 5 figures

We investigate the statistics and dynamics of extreme heat waves over different areas of Europe. We find heatwaves over France and Scandinavia to be associated with recurrent wavenumber three teleconnection patterns in surface temperature and mid-tropospheric geopotential height. For heatwaves with return times of 4 years these teleconnection patterns and their dynamics are robustly represented in a hierarchy of models of different complexity and in reanalysis data. For longer return times, reanalysis records are too short to give statistically significant results, while models confirm the relevance of these large scale patterns for the most extreme heatwaves. A timeseries analysis shows that heatwave indices defined at synoptic scale are fairly well described by Gaussian stochastic processes, and that these Gaussian processes reproduce well return time plots even for very rare events. These results suggest that extreme heatwaves over different areas of Europe show recurrent typical behaviours in terms of long-range spatial correlations and subseasonal-scale temporal correlations. These properties are consistently represented among models of different complexity and observations, thus suggesting their relevance for a better understanding of the drivers and causes of the occurrence of extreme midlatitude heatwaves and their predictability., Comment: 24 pages, 11 figures

The general circulation of the atmosphere determines the long-term variability of weather processes. This circulation is driven by the temperature differences between the poles and the equator, causing air to move along the Earth's surface. However, this requires enhanced pressure at the poles, which is not observed. To sustain the circulation, an additional non-hydrostatic pressure gradient is required. Here I propose the emergence of an additional non-hydrostatic pressure gradient resulting from the centrifugal force generated by the Earth's rotation. This centrifugal force creates a non-hydrostatic vertical pressure gradient, which is essential for the closed circulation of unequally heated air in the meridional direction. The circulation is composed of three distinct streams flowing in opposite directions, with the polar and tropical tropopause acting as boundaries. The temperature in the atmosphere decreases from the surface to the polar tropopause and remains constant above it., Comment: 8 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2306.11057

One of the most challenging and consequential problems in climate modeling is to provide probabilistic projections of sea level rise. A large part of the uncertainty of sea level projections is due to uncertainty in ice sheet dynamics. At the moment, accurate quantification of the uncertainty is hindered by the cost of ice sheet computational models. In this work, we develop a hybrid approach to approximate existing ice sheet computational models at a fraction of their cost. Our approach consists of replacing the finite element model for the momentum equations for the ice velocity, the most expensive part of an ice sheet model, with a Deep Operator Network, while retaining a classic finite element discretization for the evolution of the ice thickness. We show that the resulting hybrid model is very accurate and it is an order of magnitude faster than the traditional finite element model. Further, a distinctive feature of the proposed model compared to other neural network approaches, is that it can handle high-dimensional parameter spaces (parameter fields) such as the basal friction at the bed of the glacier, and can therefore be used for generating samples for uncertainty quantification. We study the impact of hyper-parameters, number of unknowns and correlation length of the parameter distribution on the training and accuracy of the Deep Operator Network on a synthetic ice sheet model. We then target the evolution of the Humboldt glacier in Greenland and show that our hybrid model can provide accurate statistics of the glacier mass loss and can be effectively used to accelerate the quantification of uncertainty.

The radiation environment over the African continent, at aviation altitudes, remains mostly uncharacterized and unregulated. In this paper we present initial measurements made by a newly developed active dosimeter on-board long-haul flights between South Africa and Germany. Based on these initial tests, we believe that this low-cost and open-source dosimeter is suitable for continued operation over the Africa continent and can provide valuable long-term measurements to test dosimteric models and inform aviation policy, Comment: Accepted to appear in Journal of Space Weather and Space Climate

Previous studies on the impact and influence of solar activity on terrestrial weather has yielded contradictory results in literature. Present study presents, on a global scale, the correlation between surface air temperature and two solar activity indices (Sunspot number, 'Rz', and solar radio flux at 10.7, 'F10.7' ) at different time scales during solar cycle 23. Global air temperature has higher correlation values of $\pm 0.8$ with F10.7 compared to Rz ($\pm 0.3$). Our results showed hemispheric delineation of the correlation between air temperature and solar activity with negative correlation in the southern hemisphere and positive correlation in the northern hemisphere. At the onset of the solar cycle, this hemispheric delineation pattern was prevalent, however, an inverse hemispheric delineation was observed at the recession of the solar cycle., Comment: To appear in Sun and Geosphere

Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations (DNS) by solving the equations that govern the statistics themselves. DSS suffers, however, from the curse of dimensionality as the statistics (such as correlations) generally have higher dimension than the underlying dynamical variables. Here we investigate two approaches to reduce the dimensionality of DSS, illustrating each method with numerical experiments with the Lorenz-96 dynamical system. The forms of DSS chosen here involve approximate closures at second and third order in the equal time cumulants. We demonstrate significant reduction in computational effort that can be achieved without sacrificing the accuracy of DSS. The methods developed here can be applied to turbulent fluid and magnetohydrodynamical systems., Comment: 16 pages, 13 figures and 6 tables

Most gravitational currents occur on sloping topographies, often in the presence of particles that can settle during the current propagation. Yet, an exhaustive exploration of associated parameters in experimental studies is still lacking. Here, we present an extensive experimental investigation of the slumping regime of turbidity (particle-laden) currents in two lock-release (dam-break) systems with inclined bottoms. We identify 3 regimes controlled by the ratio between settling and current inertia. (i) For negligible settling, the turbidity current morphodynamics correspond to those of saline homogeneous gravity currents, in terms of velocity, slumping (constant-velocity) regime duration and current morphology. (ii) For intermediate settling, the slumping regime duration decreases to become fully controlled by a particle settling characteristic time. (iii) When settling overcomes the current initial inertia, the slumping (constant-velocity) regime is not detected any more. In the first two regimes, the current velocity increases with the bottom slope, of about $35~\%$ between $0^\circ$ and $15^\circ$. Finally, our experiments show that the current propagates during the slumping regime with the same shape in the frame of the moving front. Strikingly, the current head is found to be independent of all experimental parameters covered in the present study. We also quantify water entrainment coefficients $E$ and compare them with previous literature, hence finding that $E$ increases linearly with the current Reynolds number., Comment: 23 pages, 10 figures, submitted to Journal of Fluid Mechanics

The partitioning of precipitation (P) water input on land between green (evapotranspiration, ET) and blue (runoff, R) water fluxes distributes the annually renewable freshwater resource among sectors and ecosystems. We decipher the worldwide pattern and key determinants of this water flux partitioning (WFP) and investigate its predictability based on a machine learning (ML) model trained and tested on data for 3,614 hydrological catchments around the world. The results show considerably higher WFP to the green (ET/P) than the blue (R/P) flux in most of the world. Land-use changes toward expanded agriculture and forestry will increase this WFP asymmetry, jeopardizing blue-water availability and making it more vulnerable to future P changes for other sectors and ecosystems. The predictive ML-model of WFP developed in this study can be used with climate model projections of P to assess future blue and green water security for various regions, sectors, and ecosystems around the world.

High-energy gamma radiation in the Earth's atmosphere is associated with the bremsstrahlung of Relativistic Runaway Electron Avalanches (RREA) developing in thunderstorm electric fields. In this paper, RREA development is studied in the system of two strong electric-field regions within thunderstorms, which accelerate runaway electrons toward each other. Such a system is called the simple reactor. It is discovered that the propagation of gamma rays and runaway electrons from one region to another leads to positive feedback. This feedback called the reactor feedback can make RREA self-sustaining, thus effectively multiplying high-energy particles inside thunderstorms containing the simple reactor. The spectrum and characteristic time scale of the simple reactor gamma radiation are in agreement with Terrestrial Gamma-ray Flashes (TGFs) data. The applicability of the simple reactor model to TGF is discussed, and the distinguishing observable properties of the simple reactor radiation during TGF and Thunderstorm Ground Enhancement are considered., Comment: 13 pages, 6 figures

The rotation of the earth breaks time-reversal and reflection symmetries in an opposite sense north and south of the equator, leading to a topological origin for certain atmospheric and oceanic equatorial waves. Away from the equator the rotating shallow water and stably stratified primitive equations exhibit Poincare inertio-gravity waves that have nontrivial topology as evidenced by their strict superinertial timescale and a phase singularity in frequency-wavevector space. This non-trivial topology then predicts, via the principle of bulk-interface correspondence, the existence of two equatorial waves along the equatorial interface, the Kelvin and Yanai waves. To directly test the nontrivial topology of Poincare-gravity waves in observations, we examine ERA5 reanalysis data and study cross-correlations between the wind velocity and geopotential height of the mid-latitude stratosphere at the 50 hPa height. We find the predicted vortex and anti-vortex in the relative phase of the geopotential height and velocity at the high frequencies of the waves. By contrast, lower-frequency planetary waves are found to have trivial topology also as expected from theory. These results demonstrate a new way to understand stratospheric waves, and provide a new qualitative tool for the investigation of waves in other components of the climate system., Comment: 25 pages, 6 figures. Small corrections and clarifications to make the paper more broadly accessible

Present-day Mars is cold and dry, but mineralogical and morphological evidence shows that liquid-water existed on the surface of ancient Mars. In order to explain this evidence and assess ancient Mars's habitability, one must understand the size and composition of the ancient atmosphere. Here we place constraints on the ancient Martian atmosphere by modeling the coupled, self-consistent evolution of atmospheric CO2, N2, and Ar on Mars from 3.8 billion years ago (Ga) to the present. Our model traces the evolution of these species' abundances and isotopic composition caused by atmospheric escape, volcanic outgassing, and crustal interaction. Using a Markov-Chain Monte Carlo method to explore a plausible range of parameters, we find hundreds of thousands of model solutions that recreate the modern Martian atmosphere. These solutions indicate that Mars's atmosphere contained 0.3-1.5 bar CO2 and 0.1-0.5 bar N2 at 3.8 Ga. The global volume of deposited carbonates critically determines the ancient atmospheric composition. For example, a ~1 bar CO2 ancient atmosphere with 0.2-0.4 bar N2 requires ~0.9 bar CO2 deposited in carbonates primarily in open-water systems. With the joint analysis of C, N, and Ar isotopes, we refine the constraints on the relative strengths of outgassing and sputtering, leading to an indication of a reduced early mantle from which the outgassing is sourced. Our results indicate that a CO2-N2 atmosphere with a potential H2 component on ancient Mars is consistent with Mars's geochemical evolution and may explain the evidence for its past warm and wet climate., Comment: 27 pages, 11 figures, 2 tables, Accepted to The Planetary Science Journal

It is well known that rapid changes in tropical cyclone motion occur during interaction with extratropical waves. While the translation speed has received much attention in the published literature, acceleration has not. Using a large data sample of Atlantic tropical cyclones, we formally examine the composite synoptic-scale patterns associated with tangential and curvature components of their acceleration. During periods of rapid tangential acceleration, the composite tropical cyclone moves poleward between an upstream trough and downstream ridge of a developing extratropical wavepacket. The two systems subsequently merge in a manner that is consistent with extratropical transition. During rapid curvature acceleration, a prominent downstream ridge promotes recurvature of the tropical cyclone. In contrast, during rapid tangential or curvature deceleration, a ridge is located directly poleward of the tropical cyclone. Locally, this arrangement takes the form of a cyclone-anticyclone vortex pair somewhat akin to a dipole block. On average, the tangential acceleration peaks 18 hours prior to extratropical transition while the curvature acceleration peaks at recurvature. These findings confirm that rapid acceleration of tropical cyclones is mediated by interaction with extratropical baroclinic waves. Furthermore, The tails of the distribution of acceleration and translation speed show a robust reduction over the past 5 decades. We speculate that these trends may reflect the poleward shift and weakening of extratropical Rossby waves.

In contrast to the wet gets wetter and dry gets drier paradigm, here, using observations and climate model simulations, we show that the mean rainfall over the semi-arid northwest parts of India and Pakistan has increased by 10 to 50 percent during 1901 to 2015 and is expected to increase by 50 to 200 percent under moderate greenhouse gas (GHG) scenarios, e.g, SSP2 4.5. The GHG forcing primarily drives the westward expansion of the Indian summer monsoon (ISM) rainfall and is a result of a westward expansion of the inter-tropical convergence zone (ITCZ), facilitated by a westward expansion of the Indian Ocean warm pool. While an adaptation strategy to increased hydrological disasters is a must, harvesting the increased rainfall would lead to a significant increase in food productivity, bringing transformative changes in the socio-economic condition of people in the region.

The twin Sentinel-3 satellites have multi-band radiometers which observe at methane-sensitive shortwave infrared bands with daily global coverage and 500 m ground pixel resolution. We investigate the methane observation capability of Sentinel-3 and how its coverage-resolution combination fits between Sentinel-5p and Sentinel-2. We show that methane plume enhancements can be retrieved from the shortwave infrared bands of Sentinel-3. We report a lowest emission detection by Sentinel-3 of 9 t/h under favorable detection conditions of low wind speeds and high surface albedo. We demonstrate Sentinel-3-based identification and monitoring of methane leaks using two case studies. Near Moscow, Sentinel-3 shows that two major short-term leaks separated by 30 km occurred simultaneously at a gas pipeline and appear as a single methane plume in Sentinel-5p data. For a major Sentinel-5p leak detection near the Hassi Messaoud oil/gas field in Algeria, Sentinel-3 identifies the leaking facility emitting continuously for 6 days, and Sentinel-2 pinpoints the source of the leak at an oil/gas well. Sentinel-2 and Sentinel-3 also show the 6-day leak was followed by a four-month period of burning of the leaking gas, suggesting a gas well blowout to be the cause of the leak. We find similar source rate quantifications from plume detections by Sentinel-3 and Sentinel-2 for these leaks, demonstrating utility of Sentinel-3 for emission quantification. These case studies show that zooming in with Sentinel-3 and Sentinel-2 in synergy allows precise identification and quantification as well as monitoring of the sources corresponding to methane anomalies observed in global scans of Sentinel-5p.

The recent work by (Rieger et al 2021) is concerned with the problem of extracting features from spatio-temporal geophysical signals. The authors introduce the complex rotated MCA (xMCA) to deal with lagged effects and non-orthogonality of the feature representation. This method essentially (1) transforms the signals to a complex plane with the Hilbert transform; (2) applies an oblique (Varimax and Promax) rotation to remove the orthogonality constraint; and (3) performs the eigendecomposition in this complex space (Horel et al, 1984). We argue that this method is essentially a particular case of the method called rotated complex kernel principal component analysis (ROCK-PCA) introduced in (Bueso et al., 2019, 2020), where we proposed the same approach: first transform the data to the complex plane with the Hilbert transform and then apply the varimax rotation, with the only difference that the eigendecomposition is performed in the dual (kernel) Hilbert space. The latter allows us to generalize the xMCA solution by extracting nonlinear (curvilinear) features when nonlinear kernel functions are used. Hence, the solution of xMCA boils down to ROCK-PCA when the inner product is computed in the input data space instead of in the high-dimensional (possibly infinite) kernel Hilbert space to which data has been mapped. In this short correspondence we show theoretical proof that xMCA is a special case of ROCK-PCA and provide quantitative evidence that more expressive and informative features can be extracted when working with kernels; results of the decomposition of global sea surface temperature (SST) fields are shown to illustrate the capabilities of ROCK-PCA to cope with nonlinear processes, unlike xMCA., 10 pages

The Earth's climate has experienced numerous critical transitions during its history, which have often been accompanied by massive and rapid changes in the biosphere. Such transitions are evidenced in various proxy records covering different timescales. The goal is then to identify, date, and rank past critical transitions in terms of importance, thus possibly yielding a more thorough perspective on climatic history. To illustrate such an angle, which inspired the punctuated equilibrium angle on the theory of evolution, we have analyzed 2 key high-resolution datasets: the CENOGRID marine compilation (past 66 Myr), and North Atlantic U1308 record (past 3.3 Myr). By combining recurrence analysis of the individual time series with a multivariate representation of the system based on the theory of the quasi-potential, we identify the key abrupt transitions associated with major regime changes that differentiate various clusters of climate variability. This allows interpreting the time-evolution of the system as a trajectory taking place in a dynamical landscape, whose multiscale features are associated with a hierarchy of tipping points., 27 pages, 5 figures plus supplementary material

Using the theory of wave turbulence for rapidly rotating incompressible fluids derived by Galtier (2003), we find the locality conditions that the solutions of the kinetic equation must satisfy. We show that the exact anisotropic Kolmogorov-Zakharov (KZ) spectrum satisfies these conditions, which justifies the existence of this constant (positive) energy flux solution. Although a direct cascade is predicted in the transverse ($\perp$) and parallel ($\parallel$) directions to the rotation axis, we show numerically that in the latter case some triadic interactions can have a negative contribution to the energy flux, while in the former case all interactions contribute to a positive flux. Neglecting the parallel energy flux, we estimate the Kolmogorov constant at $C_K \simeq 0.749$. These results provide theoretical support for recent numerical and experimental studies., 10 pages, 4 figures

The goal of this note is to provide a theoretical explanation for the saturation of the drag coefficient in strong wind conditions. The hydrodynamic model under consideration takes into account the important effects of airborne droplets of water in a thin layer above the water surface that effectively behave as a different fluid between the water and the air. Above this layer the model is coupled with a log-wind profile for the strong winds blowing above the sea. The main underlying mechanism governing the behavior of the drag coefficient is the Kelvin Helmholtz instability for capillary waves on the water surface and the continuity of shear stress along the intermediate interface.

A physically plausible lower bound on the spatially varying geostrophic mesoscale eddy energy dissipation time-scale within the ocean, related to the geographical energy transfer rate out of the geostrophic mesoscales, is provided by means of a simple and computational inexpensive inverse calculation. Data diagnosed from a high resolution global configuration ocean simulation is supplied to a parameterized model of the geostrophic mesoscale eddy energy, from which the dissipation time-scale results as a solution to an optimization calculation. We find that the dissipation time-scale is shortest in the Southern Ocean, in the Western Boundary Currents, and on the western boundaries, consistent with the expectation that these regions are notable sites of baroclinic activity with processes leading to energy transfer out of the geostrophic mesoscales. Although our solution should be interpreted as a lower bound given the assumptions going into the calculation, it serves as an important physically consistent base line reference for further investigations into ocean energetics, as well as for an intended inference calculation that is more complete but also much more complex., Comment: 27 pages, 8 figures, pre-print version (with minor updates to figures to reduce file size) submitted to J. Adv. Model. Earth Syst

Mesoscale wave processes are a transport mechanism for the energy exchange between the troposphere and stratosphere, since the tropopause blocks such an exchange. It is believed that internal gravity waves (IGW) are the main wave process in the atmosphere. However, the explanation of the process of IGW occurrence cannot be considered sufficiently substantiated, because the reasons for the appearance of the selected air parcel, which is affected by the initial disturbance, are not yet clear. The data of the performed experiments on the detection of wave processes shows the presence of noticeable oscillatory movements not only during the passage of fronts or other disturbances, but also in good weather. As an alternative to IGW, I consider a possible process of generating volumetric acoustic oscillations due to the formation of an acoustic resonator in the atmosphere. The probability of formation of such oscillations is high, because they do not require the presence of sharp changes in the parameters of the atmosphere to appear., 13 pages, 10 figures

Volcanic jet flows in explosive eruptions emit radio frequency signatures, indicative of their fluid dynamic and electrostatic conditions. The emissions originate from sparks supported by an electric field built up by the ejected charged volcanic particles. When shock-defined, low-pressure regions confine the sparks, the signatures may be limited to high-frequency content corresponding to the early components of the avalanche-streamer-leader hierarchy. Here, we image sparks and a standing shock together in a transient supersonic jet of micro-diamonds entrained in argon. Fluid dynamic and kinetic simulations of the experiment demonstrate that the observed sparks originate upstream of the standing shock. The sparks are initiated in the rarefaction region, and cut off at the shock, which would limit their radio frequency emissions to a tell-tale high-frequency regime. We show that sparks transmit an impression of the explosive flow, and open the way for novel instrumentation to diagnose currently inaccessible explosive phenomena., Comment: 9 pages, 6 figures

The Juno mission observed that both poles of Jupiter have polar cyclones that are surrounded by a ring of circumpolar cyclones. The North Pole holds eight circumpolar cyclones and the South Pole possesses five, with both circumpolar rings positioned along latitude ~84{\deg} N/S. Here we explain the location, stability, and number of the Jovian circumpolar cyclones by establishing the primary forces that act on them, which develop because of vorticity gradients in the background of a cyclone. In the meridional direction, the background vorticity varies owning to the planetary sphericity and the presence of the polar cyclone. In the zonal direction, the vorticity varies by the presence of adjacent cyclones in the ring. Our analysis successfully predicts the latitude and number of circumpolar cyclones for both poles, according to the size and spin of the respective polar cyclone. Moreover, the analysis successfully predicts that Jupiter can hold circumpolar cyclones while Saturn currently cannot. The match between the theory and observations implies that vortices in the polar regions of the giant planets are largely governed by barotropic dynamics, and that the movement of other vortices at high-latitudes is also driven by interaction with the background vorticity., Comment: 13 Pages, 8 figures

Ocean swell plays an important role in the transport of energy across the ocean, yet its evolution is still not well understood. In the late 1960s, the nonlinear Schr{\"o}dinger (NLS) equation was derived as a model for the propagation of ocean swell over large distances. More recently, a number of dissipative generalizations of the NLS equation based on a simple dissipation assumption have been proposed. These models have been shown to accurately model wave evolution in the laboratory setting, but their validity in modeling ocean swell has not previously been examined. We study the efficacy of the NLS equation and four of its generalizations in modeling the evolution of swell in the ocean. The dissipative generalizations perform significantly better than conservative models and are overall reasonable models for swell amplitudes, indicating dissipation is an important physical effect in ocean swell evolution. The nonlinear models did not out-perform their linearizations, indicating linear models may be sufficient in modeling ocean swell evolution.

Vertical transport in the ocean plays a critical role in the exchange of freshwater, heat, nutrients, and other biogeochemical tracers. While there are situations where vertical fluxes are important, studying the vertical transport and displacement of material requires analysis over a finite interval of time. One such example is the subduction of fluid from the mixed layer into the pycnocline, which is known to occur near density fronts. Divergence has been used to estimate vertical velocities indicating that surface measurements, where observational data is most widely available, can be used to locate these vertical transport conduits. We evaluate the correlation between surface signatures derived from Eulerian (horizontal divergence, density gradient, and vertical velocity) and Lagrangian (dilation rate and finite time Lyapunov exponent) metrics and vertical displacement conduits. Two submesoscale resolving models of density fronts and a data-assimilative model of the western Mediterranean were analyzed. The Lagrangian surface signatures locate significantly more of the strongest displacement features and the difference in the expected displacements relative to Eulerian ones increases with the length of the time interval considered. Ensemble analysis of forecasts from the Mediterranean model demonstrates that the Lagrangian surface signatures can be used to identify regions of strongest downward vertical displacement even without knowledge of the true ocean state., 30 pages, 8 figures. Submitted to Ocean Modelling

There are a lot of oscillatory motions of various kinds in the atmosphere, for example, internal gravity waves (IGW), which have a period less than the time of flight of the radiosonde. Oscillatory motions lead to adiabatic cooling during the shift of air mass upwards from equilibrium or heat when shifting down. The magnitude and sign of the shift from the equilibrium state of a specific volume of air at the time of measurements by radiosonde are unknown. Therefore the displacement of measured (essentially instantaneous) temperature is unknown relative to the equilibrium temperature. These errors in some cases can reach values of 10 degrees or more. The algorithm for correcting of these effects is proposed. The algorithm of correction calculates the shift of the vertical displacement of the radiosonde from the polynomial curve. The correction for temperature is calculated as a product of the dry adiabatic lapse rate and the shift of the radiosonde altitude. The result is subtracted from the measured temperature. The observed height is corrected in dependence of the shift value., 4 pages, 3 figures

The polar cyclone at Jupiter's south pole and the five cyclones surrounding it oscillate in position and interact. These cyclones, observed since 2016 by NASA's Juno mission, present a unique opportunity to study vortex dynamics and interactions on long time scales. The cyclones' position data, acquired by Juno's JIRAM instrument, is analyzed, showing dominant oscillations with ~12 month periods and amplitudes of ~400 km. Here, the mechanism driving these oscillations is revealed by considering vorticity-gradient forces generated by mutual interactions between the cyclones and the latitudinal variation in planetary vorticity. Data-driven estimation of these forces exhibits a high correlation with the measured acceleration of the cyclones. To further test this mechanism, a model is constructed, simulating how cyclones subject to these forces exhibit similar oscillatory motion., 9 pages, 5 figures, 11 supplementary pages, 9 supplementary figures

The 4D-Var method for filtering partially observed nonlinear chaotic dynamical systems consists of finding the maximum a-posteriori (MAP) estimator of the initial condition of the system given observations over a time window, and propagating it forward to the current time via the model dynamics. This method forms the basis of most currently operational weather forecasting systems. In practice the optimization becomes infeasible if the time window is too long due to the non-convexity of the cost function, the effect of model errors, and the limited precision of the ODE solvers. Hence the window has to be kept sufficiently short, and the observations in the previous windows can be taken into account via a Gaussian background (prior) distribution. The choice of the background covariance matrix is an important question that has received much attention in the literature. In this paper, we define the background covariances in a principled manner, based on observations in the previous $b$ assimilation windows, for a parameter $b\ge 1$. The method is at most $b$ times more computationally expensive than using fixed background covariances, requires little tuning, and greatly improves the accuracy of 4D-Var. As a concrete example, we focus on the shallow-water equations. The proposed method is compared against state-of-the-art approaches in data assimilation and is shown to perform favourably on simulated data. We also illustrate our approach on data from the recent tsunami of 2011 in Fukushima, Japan., Comment: 15 pages, 5 figures