Permutation Entropy of Weakly Noise-Affected Signals

We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations.

A derivative-free optimisation method for global ocean biogeochemical models

The performance of global ocean biogeochemical models, and the Earth System Models in which they are embedded, can be improved by systematic calibration of the parameter values against observations. However, such tuning is seldom undertaken as these models are computationally very expensive. Here we investigate the performance of DFO-LS, a local, derivative-free optimisation algorithm which has been designed for computationally expensive models with irregular model-data misfit landscapes typical of biogeochemical models. We use DFO-LS to calibrate six parameters of a relatively complex global ocean biogeochemical model (MOPS) against synthetic dissolved oxygen, inorganic phosphate and inorganic nitrate observations from a reference run of the same model with a known parameter configuration. The performance of DFO-LS is compared with that of CMA-ES, another derivative-free algorithm that was applied in a previous study to the same model in one of the first successful attempts at calibrating a global model of this complexity. We find that DFO-LS successfully recovers 5 of the 6 parameters in approximately 40 evaluations of the misfit function (each one requiring a 3000 year run of MOPS to equilibrium), while CMA-ES needs over 1200 evaluations. Moreover, DFO-LS reached a baseline misfit, defined by observational noise, in just 11–14 evaluations, whereas CMA-ES required approximately 340 evaluations. We also find that the performance of DFO-LS is not significantly affected by observational sparsity, however fewer parameters were successfully optimised in the presence of observational uncertainty. The results presented here suggest that DFO-LS is sufficiently inexpensive and robust to apply to the calibration of complex, global ocean biogeochemical models.

Using local dynamics to explain analog forecasting of chaotic systems

Analogs are nearest neighbors of the state of a system. By using analogs and their successors in time, one is able to produce empirical forecasts. Several analog forecasting methods have been used in atmospheric applications and tested on well-known dynamical systems. Such methods are often used without reference to theoretical connections with dynamical systems. Yet, analog forecasting can be related to the dynamical equations of the system of interest. This study investigates the properties of different analog forecasting strategies by taking local approximations of the system’s dynamics. We find that analog forecasting performances are highly linked to the local Jacobian matrix of the flow map, and that analog forecasting combined with linear regression allows to capture projections of this Jacobian matrix. Additionally, the proposed methodology allows to efficiently estimate analog forecasting errors, an important component in many applications. Carrying out this analysis also allows to compare different analog forecasting operators, helping to choose which operator is best suited depending on the situation. These results are derived analytically and tested numerically on two simple chaotic dynamical systems. The impact of observational noise and of the number of analogs is evaluated theoretically and numerically.

A Cycle Slip Repair Method Against Ionospheric Effects and Observational Noises for BDS Triple-Frequency Undifferenced Phases

The cycle slip detection (CSD) and cycle slip repair (CSR) are easily affected by ionospheric delay and observational noise. Aiming at mitigating the above disadvantage, a new BeiDou navigation satellite system (BDS) triple-frequency CSR method (BTCSR) is proposed for the undifferenced phase. BTCSR learns from the classic triple-frequency CSR (CTCSR), with combinations of phases and pseudoranges in correcting ionospheric delay and optimizing observational noise. Different from CTCSR, though, BTCSR has made the following improvements: (1) An optimal model of calculating cycle slip combination is established, which further takes into account the minimization of the effect of residual ionospheric error after the correction. The calculation of cycle slip combination is obtained with the root mean squared errors (0.0646, 0.1261, 0.1069) of cycles, resulting in CSR success rate of 99.9927%, and the wavelengths (4.8842,3.5738,8.1403) of m. (2) A discriminant function is added to guarantee the CSR correctness. This function utilizes epoch-difference value of the ionosphere-free and geometry-free phase to select the correct cycle slip value, which eliminates the interference of large pseudorange errors in determining the final cycle slip. Consequently, the performances of BTCSR and CTCSR have been compared. For the real BDS pseudorange observation with additional 1.5 m errors, which can cover situations of 99.96% pseudorange noise, results of CTCSR show failure, but results of BTCSR keep correct. Moreover, BTCSR has made the following improvements relative to the geometry-free cycle slip detection method (GFCSD) and Melboune–Wubbena cycle slip combination detection method (MWCSD): (1) During a moderate magnetic storm of level 6, CSR testing, with the BDS monitoring station in a low latitude region, showed that some failures occur in GFCSD because of severe ionospheric variation, but BTCSR could correctly identify and fix cycle slips. (2) For the BDS observation data with an additional 1.5 m error on the actual pseudoranges, MWCSD exhibited failures, but the repair results of BTCSR were correct and reliable. (3) For the special slips of (0,59,62) cycles, and equal slips of (1,1,1) cycles on (B1,B2,B3), that are hard to detect by GFCSD and MWCSD, respectively, BTCSR could repair these correctly. Finally, BTCSR obtains reliable repair results under large pseudorange errors and severe ionospheric variations, and the cut-off elevation larger than 10 degrees is the suggested background.

Earth-like planetary magnetotails as non-linear oscillators

A non-linear oscillator model of a simple system analogous to Earth-like magnetotail plasmoid formation and release dynamics is presented. In this context, Earth-like refers to any magnetosphere with an upstream bow-shock and an elongated downstream tail that undergoes tail plasmoid formation and release. It includes, for the first time in such a model, separate drivers for the Dungey and Vasyliunas Cycles and the capacity to include stochastic and deterministic driving in varying relative and absolute terms. The effects of measurement noise on the model output can also be simulated. This makes the model suitable to investigate the magnetotail dynamics of Mercury, Earth, Jupiter, Saturn and hypothetical exoplanets with similar magnetospheric configurations. The capacity to predict, in general terms, the behavior of a wide range of stellar-wind – magnetosphere interactions has become even more important in the light of the discovery of thousands of exoplanets in recent years. This model represents the first step towards being able to make such predictions for a wide variety of cases without resorting to detailed modelling of individual cases. It is demonstrated that the model can exhibit limit cycle (periodic) and chaotic (long-term unpredictable) behavior. The effects of a sufficiently strong dynamical noise component (stochastic driving) are shown to be inherently different from the effects of an equivalent level of simulated observational noise (simulated Gaussian instrument error). The possibilities of chaotic behavior and of dynamical noise dominating the underlying determinism imply that often only short-term forecasting of magnetotail plasmoid formation is possible.

Identifying reionization-epoch galaxies with extreme levels of Lyman continuum leakage in James Webb Space Telescope surveys

ABSTRACT The James Webb Space Telescope (JWST) NIRSpec instrument will allow rest-frame ultraviolet/optical spectroscopy of galaxies in the epoch of reionization (EoR). Some galaxies may exhibit significant leakage of hydrogen-ionizing photons into the intergalactic medium, resulting in faint nebular emission lines. We present a machine learning framework for identifying cases of very high hydrogen-ionizing photon escape from galaxies based on the data quality expected from potential NIRSpec observations of EoR galaxies in lensed fields. We train our algorithm on mock samples of JWST/NIRSpec data for galaxies at redshifts z = 6–10. To make the samples more realistic, we combine synthetic galaxy spectra based on cosmological galaxy simulations with observational noise relevant for z ≳ 6 objects of a brightness similar to EoR galaxy candidates uncovered in Frontier Fields observations of galaxy cluster Abell-2744 and MACS-J0416. We find that ionizing escape fractions (fesc) of galaxies brighter than mAB,1500 ≈ 27 mag may be retrieved with mean absolute error Δfesc ≈ 0.09(0.12) for 24 h (1.5 h) JWST/NIRSpec exposures at resolution R = 100. For 24 h exposure time, even fainter galaxies (mAB,1500 < 28.5 mag) can be processed with Δfesc ≈ 0.14. This framework simultaneously estimates the redshift of these galaxies with a relative error less than 0.03 for both 24 (mAB,1500 < 28.5 mag) and 1.5 h (mAB,1500 < 27 mag) exposure times. We also consider scenarios where just a minor fraction of galaxies attain high fesc and present the conditions required for detecting a subpopulation of high-fesc galaxies within the data set.

Representation of Vertical Atmospheric Structures by Radio Occultation Observations in the Upper Troposphere and Lower Stratosphere: Comparison to High-Resolution Radiosonde Profiles

Global positioning system (GPS) radio occultation (RO) is capable of retrieving vertical profiles of atmospheric parameters with high resolution (<100 m), which can be achieved in spherically symmetric atmosphere. Horizontal inhomogeneity of real atmosphere results in representativeness errors of retrieved profiles. In most cases these errors increase with a decrease of vertical scales of atmospheric structures and may not allow one to fully utilize the physical resolution of RO. Also, GPS RO–retrieved profiles are affected by observational noise of different types, which, in turn, affect the representation of small-scale atmospheric structures. This study investigates the effective resolution and optimal smoothing of GPS RO–retrieved temperature profiles using high-pass filtering and cross correlation with collocated high-resolution radiosondes. The effective resolution is a trade-off between representation of real atmospheric structures and suppression of observational noise, which varies for different latitudes (15°S–75°N) and altitudes (10–27 km). Our results indicate that at low latitudes the effective vertical resolution is about 0.2 km near the tropical tropopause layer and about 0.5 km in the lower stratosphere. The best resolution of 0.1 km is at the cold-point tropical tropopause. The effective resolutions at the midlatitudes are slightly worse than at low latitudes, varying from ~0.2 to 0.6 km. At high latitudes, the effective resolutions change notably with altitude from ~0.2 km at 10–15 km to ~1.4 km at 22–27 km. Our results suggest that the atmospheric inhomogeneity plays an important role in the representation of the vertical atmospheric structures by RO measurements.

Seismic performance

Context. Asteroseismology is a unique tool that can be used to study the interior of stars and hence deliver unique information for the studiy of stellar physics, stellar evolution, and Galactic archaeology. Aims. We aim to develop a simple model of the information content of asteroseismology and to characterize the ability and precision with which fundamental properties of stars can be estimated for different space missions. Methods. We defined and calibrated metrics of the seismic performance. The metrics, expressed by a seismic index ℰ defined by simple scaling relations, are calculated for an ensemble of stars. We studied the relations between the properties of mission observations, fundamental stellar properties, and the performance index. We also defined thresholds for asteroseismic detection and measurement of different stellar properties. Results. We find two regimes of asteroseismic performance: the first where the signal strength is dominated by stellar properties and not by observational noise; and the second where observational properties dominate. Typically, for evolved stars, stellar properties provide the dominant terms in estimating the information content, while main sequence stars fall in the regime where the observational properties, especially stellar magnitude, dominate. We estimate scaling relations to predict ℰ with an intrinsic scatter of around 21%. Incidentally, the metrics allow us to distinguish stars burning either hydrogen or helium. Conclusions. Our predictions will help identify the nature of the cohort of existing and future asteroseismic observations. In addition, the predicted performance for PLATO will help define optimal observing strategies for defined scientific goals.

Влияние шума наблюдений на эффект ложной связи между осцилляторами при оценивании по временным рядам

The practice of identifying structure of couplings between elements of complex systems from experimental recordings of their oscillations (time series) using the Wiener – Granger causality method has revealed a number of problems that prevent one from obtaining reliable results. In particular, the presence of observational noise can lead to the “effect of spurious coupling”, i.e. to inference of mutual coupling between two elements that are actually coupled in a unidirectional way. A quantitative analysis of this phenomenon is carried out and recommendations allowing one to reduce its probability are presented. It is shown that the effect typically takes place only for large noise levels comparable to the level of observed oscillations. However, we have also singled out less typical situations where the effect occurs at much weaker noise.