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Jozef Skakala

Publications and source records attributed to Jozef Skakala.

At least 19 recordsLinked to original sources

Deep learning model emulators for marine biogeochemistry forecasting from days to decades

Deep-learning emulators have emerged as a promising approach for reducing the computational cost of Earth System Models while potentially improving forecasting skill. Here, we demonstrate the successful emulation of a high-complexity marine biogeochemistry model within a simplified one-dimensional water-column framework. We explore two emulator architectures: Long Short-Term Memory (LSTM) neural networks that emulate a selected subset of variables at daily resolution, and physics-informed one-dimensional Convolutional Neural Networks (1D CNNs) that emulate the full pelagic system throughout the water column also at daily resolution. Using ocean physics simulator inputs, both emulators remain largely stable over multi-decadal timescales and accurately reproduce the parent model in both decadal climate projections and short-range (10-day) forecasting applications. The former includes the ability to predict the timing of phytoplankton Spring blooms several years in advance. When trained on reanalysis data, the emulators substantially outperform the parent model's forecast skill score for several key ecosystem variables, including phytoplankton and zooplankton. If similar performance can be achieved in three-dimensional regional applications, these emulators could provide substantially higher-quality predictions at a fraction of the computational cost. We further apply novel explainability techniques to identify key drivers of emulator behaviour and gain insights into emergent ecosystem dynamics. Performance is evaluated using a range of metrics, including the reproduction of daily variability and extreme events. These approaches have considerable potential for future applications in operational forecasting, climate-scale simulations, and marine autonomous systems.

q-bio.QM

Assimilation of machine learning-predicted nitrate to improve the quality of phytoplankton forecasting in the shelf sea environment

We demonstrate that assimilating Neural Network (NN)-predicted surface nitrate leads to a major improvement in phytoplankton short-range (1-5 day) dynamical model forecasts for the North-West European Shelf (NWES) seas. We show that assimilation of only ocean color chlorophyll-$a$ in the current Met Office NWES operational system can lead to excess surface nitrate concentrations in the post-Spring bloom period and these are a major reason behind some known, fast-growing biases in NWES phytoplankton forecasts during late Spring and Summer. Assimilating observations of nitrate would potentially help address this, but NWES nitrate data are typically not available in sufficient abundance to be effectively assimilated. We have therefore used a recently developed and validated neural network (NN) model predicting surface nitrate concentrations from a range of observable variables and assimilated the NN-predicted nitrate within a research and development version of the Met Office's NWES operational forecasting system. As a result of nitrate assimilation the phytoplankton 5-day forecast skill improves by up to 30%. We show that although much of this improvement can be achieved by using a weekly nitrate climatology predicted by the NN model, there is a clear advantage in using flow-dependent nitrate data. We discuss the impacts of this improvement on a range of additional eutrophication indicators, such as dissolved inorganic phosphorus and sea bottom oxygen. We argue that it should be feasible to upgrade this approach to a fully hybrid machine learning - data assimilation within the near-real time NWES operational forecasting system.

q-bio.QM

Estimating carbon pools in the European Shelf sea environment: replacing reanalysis by model-informed machine learning?

Shelf seas are important for the economy and the carbon cycle, but shelf sea observations for carbon pools are often sparse, or highly uncertain. An alternative can be provided by carbon reanalyses (whether assimilating proxy variables, such as chlorophyll-$a$, or directly carbon), but these are often expensive to run. We propose to use a computationally cheap ensemble of neural networks (i.e. deep ensemble) to learn the relationship between the directly observable (atmospheric, riverine and ocean) variables and marine carbon pools from a coupled physics-biogeochemistry model. The deep ensemble was trained on a North-West European Shelf (NWES) physical-biogeochemistry model free run simulation. After training, the deep ensemble was run using inputs from the NWES reanalysis instead of the free run, demonstrating that it can efficiently predict several NWES carbon pools (e.g., detritus, zooplankton, heterotrophic bacteria) in much better agreement with the reanalysis than the free run, while also providing uncertainty information. We further show that the deep ensemble performs similarly well when it is driven directly by the observations assimilated into the reanalysis, with the limitation that carbon pools can then be predicted only at the observed locations and times. We focus on explainability of the results and demonstrate potential use of the deep ensembles for future climate what-if scenarios. We suggest that model-informed machine learning presents a viable alternative to expensive reanalyses and could complement observations, wherever they are missing and/or highly uncertain.

q-bio.QM

Low complexity model to study scale dependence of phytoplankton dynamics in the tropical Pacific

We demonstrate that a simple model based on reaction-diffusion-advection (RDA) equation forced by realistic surface velocities and nutrients is skilled in reproducing the distributions of the surface phytoplankton chlorophyll in the tropical Pacific. We use the low-complexity RDA model to investigate the scale-relationships in the impact of different drivers (turbulent diffusion, mean and eddy advection, primary productivity) on the phytoplankton chlorophyll concentrations. We find that in the 1/4° (~25km) model, advection has a substantial impact on the rate of primary productivity, whilst the turbulent diffusion term has a fairly negligible impact. Turbulent diffusion has an impact on the phytoplankton variability, with the impact being scale-propagated and amplified by the larger scale surface currents. We investigate the impact of a surface nutrient decline and some changes to mesoscale eddy kinetic energy (climate change projections) on the surface phytoplankton concentrations. The RDA model suggests that unless mesoscale eddies radically change, phytoplankton chlorophyll scales sub-linearly with the nutrients, and it is relatively stable with respect to the nutrient concentrations. Furthermore we explore how a white multiplicative Gaussian noise introduced into the RDA model on its resolution scale propagates across spatial scales through the non-linear model dynamics under different sets of phytoplankton drivers. The unifying message of this work is that the low complexity (e.g. RDA) models can be successfully used to realistically model some specific aspects of marine ecosystem dynamics and by using those models one can explore many questions that would be beyond computational affordability of the higher-complexity ecosystem models.

q-bio.PE

Black hole thermodynamics as seen through a microscopic model of a relativistic Bose gas

Equations of gravity when projected on spacetime horizons resemble Navier-Stokes equation of a fluid with a specific equation of state [1-3]. We show that this equation of state describes massless ideal relativistic gas. We use these results, and build an explicit and simple molecular model of the fluid living on the Schwarzschild and Reissner-Nordström black hole horizons. For the spin zero Bose gas, our model makes two predictions: (i) The horizon area/entropy is quantized as given by Bekenstein's quantization rule, (ii) The model explains the correct type of proportionality between horizon area and entropy. However, for the physically relevant range of parameters, the proportionality constant is never equal to 1/4.

gr-qc

No minimally coupled scalar black hole hair in Lanczos-Lovelock gravity

We extend here the result of Bekenstein [1,2] proving the non-existence of minimally coupled scalar black hole hair in general relativity to the Lanczos-Lovelock gravity in arbitrary dimension with non-negative coupling constants. The only physical requirement on the multiplet of minimally coupled scalar fields is that it fulfills the weak energy condition. We also assume, similarly to Bekenstein, spherical symmetry and asymptotic flatness.

gr-qc

Black hole hair in Lovelock gravity

We present a method to analyse black hole hair in the spherical symmetric sector of the Lovelock theory in arbitrary dimensions that is an alternative to solving the equations of motion in their complete form. We explicitly show that the method matches with the known black hole solutions for the vacuum and electro-vacuum spacetimes in Lovelock gravity theories. We further apply the method to the case of minimally coupled non-self-interacting massless scalar field and prove that there is no (non-self-interacting) massless scalar hair for the spherically symmetric Lovelock black holes.

gr-qc

Horizon spectroscopy in and beyond general relativity

In this work we generalize the results for the entropy spectra typically derived for black holes in general relativity to a generic horizon within the spherically symmetric (asymptotically flat and non-flat) space-times of more general theories of gravity. We use all the standard --- Bekenstein's universal lower bound on the entropy transition, the highly damped quasi-normal modes and reduced phase-space quantization --- approaches to derive the spectra. In particular, the three approaches show that the Bekenstein-like spectra for the horizon entropy is a robust result. Our results confirm the suggestion made relatively recently by an independent fourth argument by Kothawala et al [1].

gr-qc

The effect of magnetic fields on the r-modes of slowly rotating relativistic neutron stars

We study here the r-modes in the Cowling approximation of a slowly rotating and magnetized neutron star with a poloidal magnetic field, where we neglect any deformations of the spherical symmetry of the star. We were able to quantify the influence of the magnetic field in both the oscillation frequency $σ_r$ of the r-modes and the growth time $t_{gw}$ of the gravitational radiation emission. We conclude that magnetic fields of the order $10^{15}$ G at the center of the star are necessary to produce any changes. Our results for $σ_r$ show a decrease of up to $\sim$ $5\%$ in the frequency with increasing magnetic field, with a $B^2$ dependence for rotation rates $Ω/Ω_K \gtrsim 0.07$ and $B^4$ for $Ω/Ω_K \lesssim 0.07$. (These results should be trusted only within slow rotation approximation and we kept $Ω/Ω_{K}< 0.3$.) For $t_{gw}$, we find that it is approximately $30\%$ smaller than previous Newtonian results for non-magnetized stars, which would mean a faster growth of the emission of gravitational radiation. The effect of the magnetic field in $t_{gw}$ causes a non-monotonic effect, that first slightly increases $t_{gw}$ and then decreases it further by another $\sim$ $5\%$. (The value of magnetic field for which $t_{gw}$ starts to decrease depends on the rotational frequency, but it is generally around $10^{15}$G.) Future work should be dedicated to the study of the effect of viscosity in the presence of magnetic fields, in order to establish the magnetic correction to the instability window.

gr-qc

Quantization of horizon entropy and the thermodynamics of spacetime

This is a review of my work published in the papers [1-4]. It offers a more detailed discussion of the results than what was given in the published papers and it links my results to some conclusions recently made by other people. It also offers some new arguments for the conclusions previously made. The fundamental idea of this work is that the semi-classical quantization of the black hole entropy, as suggested by Bekenstein [5], holds (at least) generically for the spacetime horizons. We support this conclusion by two separate arguments: 1. we generalize Bekenstein's lower bound on the horizon area transition to much larger class of horizons than only the black hole horizon, 2. we obtain the same entropy spectra via the asymptotic quasi-normal frequencies of some particular spherically symmetric multi-horizon spacetimes, (in the way proposed by Maggiore [6]). The main result of this paper supports the conclusions made by other people in [7,8], but uses different arguments.

gr-qc

Slowly rotating neutron stars with small differential rotation: equilibrium models and oscillations in the Cowling approximation

Newly born neutron stars can present differential rotation, even if later it should be suppressed by viscosity or a sufficiently strong magnetic field. And in this early stage of its life, a neutron star is expected to have a strong emission of gravitational waves, which could be influenced by the differential rotation. We present here a new formalism for modelling differentially rotating neutron stars: working on the slow rotation approximation and assuming a small degree of differential rotation, we show that it is possible to separate variables in the Einstein field equations. The dragging of inertial frames is determined by solving three decoupled ODEs. After we establish our equilibrium model, we explore the influence of the differential rotation on the f and r-modes of oscillation of the neutron star in the Cowling approximation, and we also analyze an effect of the differential rotation on the emission of gravitational radiation from the f-modes. We see that the gravitational radiation from the f-modes is slightly suppressed by introducing differential rotation to the equilibrium stars.

gr-qc

No asymptotically highly damped quasi-normal modes without horizons?

We explore the question of what happens with the asymptotically highly damped quasi-normal modes ($\ell$ fixed, $|ω_{I}|\to\infty$) when the underlying spacetime has no event horizons. We consider the characteristic oscillations of a scalar field in a large class of asymptotically flat spherically symmetric static spacetimes without (absolute) horizons, such that the class accommodates the cases that are known to be of some sort of physical interest. The question of the asymptotic quasi-normal modes in such spacetimes is relevant to elucidate the connection between the behavior of the asymptotic quasi-normal modes and the quantum properties of event horizons, as put forward in some recent important conjectures. We prove for a large class of asymptotically flat spacetimes without horizons that the scalar field asymptotically highly damped modes do not exist. This provides in our view additional evidence that there is indeed a close link between the asymptotically highly damped modes and the existence of spacetime horizons (and their properties).

gr-qc

Quasinormal modes for the scattering on a naked Reissner-Nordstrom singularity

What should be the quasinormal modes associated with a spacetime that contains a naked singularity instead of a black hole? In the present work we address this problem by studying the scattering of scalar fields on a curved background described by a Reissner-Nordström spacetime with $|q| > m$. We show that there is a qualitative difference between cases with $1 < q^2/m^2 \lesssim 9/8$ and cases with $q^2/m^2 \gtrsim 9/8$. We discuss the necessary conditions for the well-posedness of the problem, and present results for the low damped modes in the low $l$ and large $l$ limit. We also consider the asymptotically highly damped quasinormal modes. We present strong evidence that such modes are absent in the case of a naked Reissner-Nordström singularity, corroborating recent conjectures relating them to classical and quantum properties of horizons.

gr-qc

Quasi-normal modes, area spectra and multi-horizon spacetimes

We suggest an interpretation for the highly damped QNM frequencies of the spherically symmetric multi-horizon spacetimes (Reissner-Nordstrom, Schwarzschild-deSitter, Reissner-Nordstrom-deSitter) following Maggiore's proposal about the link between the asymptotic QNM frequencies and the black hole thermodynamics. We show that the behavior of the asymptotic frequencies is easy to understand if one assumes that all of the horizons have the same equispaced area spectra. The QNM analysis is then consistent with the choice of the area spectra to be the one originally proposed for the black hole's horizon by Bekenstein: A=8πn (in Planck units). The interpretation of the highly damped QNM frequencies in the multi-horizon case is based on the similar grounds as in the single horizon (Schwarzschild) case, but it has some new features that are discussed in the paper.

gr-qc

Non-extremal Reissner-Nordstrom black hole: Do asymptotic quasi-normal modes carry information about the quantum properties of the black hole?

We analyze the largely accepted formulas for the asymptotic quasi-normal frequencies of the non-extremal Reissner-Nordström black hole, (for the electromagnetic-gravitational/scalar perturbations). We focus on the question of whether the gap in the spacing in the imaginary part of the QNM frequencies has a well defined limit as n goes to infinity and if so, what is the value of the limit. The existence and the value of this limit has a crucial importance from the point of view of the currently popular Maggiore's conjecture, which represents a way of connecting the asymptotic behavior of the quasi-normal frequencies to the black hole thermodynamics. With the help of previous results and insights we will prove that the gap in the imaginary part of the frequencies does not converge to any limit, unless one puts specific constraints on the ratio of the two surface gravities related to the two spacetime horizons. Specifically the constraints are that the ratio of the surface gravities must be rational and such that it is given by two relatively prime integers N, M, whose product is an even number. If the constraints are fulfilled the limit of the sequence is still not guaranteed to exist, but if it exists its value is given as the lowest common multiplier of the two surface gravities. At the end of the paper we discuss the possible implications of our results.

gr-qc

New ideas about multiplication of tensorial distributions

There is a need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. Significant progress has been made through the concept of Colombeau algebras, and the construction of full Colombeau algebras on differential manifolds for arbitrary tensors. Despite the fact that this goal was achieved, it does not incorporate clearly enough the concept of covariant derivative and hence is of a limited use. We take a different approach: we consider any type of preference for smooth distributions (on a smooth manifold) as nonintuitive, which means all our approach must be based fully on the Colombeau equivalence relation as the fundamental feature of the theory. After taking this approach we very naturally obtain a canonical and geometric theory defining tensorial operations with tensorial distributions, including covariant derivative. This also happens because we no longer need any explicit canonical geometric construction of Colombeau algebras. The big advantage of our approach lies also in the fact that it brings a physical insight into the mathematical concepts used and naturally leads to formulation of physics on (what we call) piecewise smooth manifolds, rather than on smooth manifold. This brings to the language of physics much higher symmetry (in the same way as turning from Poincare invariance to diffeomorphism invariance), and is compatible with our intuition, that "pointwise" properties in some metaphorical sense "do not matter".

gr-qc

Aspects of General Relativity: Pseudo-Finsler extensions, Quasi-normal frequencies and Multiplication of tensorial distributions

This thesis is based on three different projects, all of them are directly linked to the classical general theory of relativity, but they might have consequences for quantum gravity as well. The first chapter deals with pseudo-Finsler geometric extensions of the classical theory, these being ways of naturally representing high-energy Lorentz symmetry violations. The second chapter deals with the problem of highly damped quasi-normal modes related to different types of black hole spacetimes. Besides the astrophysical meaning of the quasi-normal modes, there are conjectures about the link between the highly damped modes and black hole thermodynamics. The third chapter is related to the topic of multiplication of tensorial distributions.

gr-qc

The causal structure of spacetime is a parameterized Randers geometry

There is a by now well-established isomorphism between stationary 4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries - these Randers geometries being a particular case of the more general class of 3-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes - the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (time-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.

gr-qc