Nonlinear Processes in Geophysics

Inferring flow energy, space and time scales: freely-drifting vs fixed point observations
Aurelien Luigi Serge Ponte, Lachlan Astfalck, Matthew Rayson, Andrew Zulberti, and Nicole Jones
Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2024-10,2024
Preprint under review for NPG (discussion: open, 0 comments)
We propose a novel method for the estimation of ocean flow properties in terms of its energy, spatial and temporal scales. The method relies on flow observations that are either collected at a fixed location or along the flow as they would if inferred from the trajectory of freely-drifting platforms. The accuracy of the method is quantified in different experimental configurations. We demonstrate freely drifting platforms can, even in isolation, enable to capture flow properties is a first.

Quantification of magnetosphere–ionosphere coupling timescales using mutual information: response of terrestrial radio emissions and ionospheric–magnetospheric currents
Alexandra Ruth Fogg, Caitríona M. Jackman, Sandra C. Chapman, James E. Waters, Aisling Bergin, Laurent Lamy, Karine Issautier, Baptiste Cecconi, and Xavier Bonnin
Nonlin. Processes Geophys., 31, 195–206, https://doi.org/10.5194/npg-31-195-2024, 2024
Auroral kilometric radiation (AKR) is a radio emission emitted by Earth. Due to the complex mixture of phenomena in the magnetosphere, it is tricky to estimate the time difference between the excitation of two systems. In this study, AKR is compared with indices describing Earth's system. Time differences between the excitation of AKR and the indices are estimated using mutual information. AKR feels an enhancement before the aurora but after more polar latitude features.

NORAD Tracking of the 2022 February Starlink Satellites and the Immediate Loss of 32 Satellites
Fernando L. Guarnieri, Bruce T. Tsurutani, Rajkumar Hajra, Ezequiel Echer, and Gurbax S. Lakhina
Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2024-9,2024
Preprint under review for NPG (discussion: open, 0 comments)
On February 03, 2022, SpaceX launched a new group of satellites for its Starlink constellation. This launch simultaneously released 49 satellites in orbits between 200 km and 250 km height. The launches occurred during a geomagnetic storm, followed by a second one. There was an immediate loss of 32 satellites. The satellite losses may have been caused by an unusually high level of atmospheric drag (unexplained by current theory/modeling) or a high level of satellite collisions.

Review article: Interdisciplinary perspectives on climate sciences – highlighting past and current scientific achievements
Vera Melinda Galfi, Tommaso Alberti, Lesley De Cruz, Christian L. E. Franzke, and Valerio Lembo
Nonlin. Processes Geophys., 31, 185–193, https://doi.org/10.5194/npg-31-185-2024, 2024
In the online seminar series "Perspectives on climate sciences: from historical developments to future frontiers" (2020–2021), well-known and established scientists from several fields – including mathematics, physics, climate science and ecology – presented their perspectives on the evolution of climate science and on relevant scientific concepts. In this paper, we first give an overview of the content of the seminar series, and then we introduce the written contributions to this special issue.

The sampling method for optimal precursors of El Niño–Southern Oscillation events
Bin Shi and Junjie Ma
Nonlin. Processes Geophys., 31, 165–174, https://doi.org/10.5194/npg-31-165-2024, 2024
Different from traditional deterministic optimization algorithms, we implement the sampling method to compute the conditional nonlinear optimal perturbations (CNOPs) in the realistic and predictive coupled ocean–atmosphere model, which reduces the first-order information to the zeroth-order one, avoiding the high-cost computation of the gradient. The numerical performance highlights the importance of stochastic optimization algorithms to compute CNOPs and capture initial optimal precursors.

Modelling of the terrain effect in magnetotelluric data from the Garhwal Himalaya region
Suman Saini, Deepak Kumar Tyagi, Sushil Kumar, and Rajeev Sehrawat
Nonlin. Processes Geophys., 31, 175–184, https://doi.org/10.5194/npg-31-175-2024, 2024
This work explores the effect of topography on magnetotelluric (MT) data along a synthetic model of the Roorkee–Gangotri profile (RGP). Two correction procedures were used to remove topography distortion from MT data. Flat-earth and terrain correction responses (TCRs) show that both procedures are capable of removing the topography effect. The similar topographic response and TCRs confirm that there is no need for topography correction along the RGP, as the slope angle is less than 1°.

Phytoplankton retention mechanisms in estuaries: a case study of the Elbe estuary
Laurin Steidle and Ross Vennell
Nonlin. Processes Geophys., 31, 151–164, https://doi.org/10.5194/npg-31-151-2024, 2024
Phytoplankton are key in estuaries, as they form the ecosystem's base. Despite being washed out by river flow and facing a large range of different salinities, they persist. Our Lagrangian simulation of the Elbe estuary shows that buoyancy helps them to be retained. Riverbanks and tidal flats offer refuges from strong currents. Our findings emphasize the need for careful ecosystem management in estuaries.

Variational techniques for a one-dimensional energy balance model
Gianmarco Del Sarto, Jochen Bröcker, Franco Flandoli, and Tobias Kuna
Nonlin. Processes Geophys., 31, 137–150, https://doi.org/10.5194/npg-31-137-2024, 2024
We consider a one-dimensional model for the Earth's temperature. We give sufficient conditions to admit three asymptotic solutions. We connect the value function (minimum value of an objective function depending on the greenhouse gas (GHG) concentration) to the global mean temperature. Then, we show that the global mean temperature is the derivative of the value function and that it is non-decreasing with respect to GHG concentration. 

Scaling and intermittent properties of oceanic and atmospheric pCO2 time series and their difference
Kévin Robache, François G. Schmitt, and Yongxiang Huang
Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2024-7,2024
Preprint under review for NPG (discussion: open, 0 comments)
In this work the multi-scale dynamics of 38 oceanic and atmospheric pCO2 time series, sea surface temperature and salinity from fixed buoys recorded with three-hour resolution are considered. The Fourier scaling exponents are estimated. The differences found for 3 ecosystems – coastal shelf, coral reefs, open ocean are discussed. Multifractal properties of pCO2 difference between ocean and atmosphere are found and characterized over the scale range from 3 hours to one year.

A comparison of two causal methods in the context of climate analyses
David Docquier, Giorgia Di Capua, Reik V. Donner, Carlos A. L. Pires, Amélie Simon, and Stéphane Vannitsem
Nonlin. Processes Geophys., 31, 115–136, https://doi.org/10.5194/npg-31-115-2024, 2024
Identifying causes of specific processes is crucial in order to better understand our climate system. Traditionally, correlation analyses have been used to identify cause–effect relationships in climate studies. However, correlation does not imply causation, which justifies the need to use causal methods. We compare two independent causal methods and show that these are superior to classical correlation analyses. We also find some interesting differences between the two methods.

Extraction of periodic signals in Global Navigation Satellite System (GNSS) vertical coordinate time series using the adaptive ensemble empirical modal decomposition method
Weiwei Li and Jing Guo
Nonlin. Processes Geophys., 31, 99–113, https://doi.org/10.5194/npg-31-99-2024, 2024
Improper handling of missing data and offsets will affect the accuracy of a signal of interest. The trend in GNSS belonging to GLOSS is key to getting the absolute sea level. However, this is affected by the periodic signals that are included. Although adaptive EEMD is capable of extracting periodic signals, missing data and offsets are ignored in previous work. Meanwhile, the time-varying periodic characteristics derived by adaptive EEMD are more conducive to analyzing the driving factors.

A two-fold deep-learning strategy to correct and downscale winds over mountains
Louis Le Toumelin, Isabelle Gouttevin, Clovis Galiez, and Nora Helbig
Nonlin. Processes Geophys., 31, 75–97, https://doi.org/10.5194/npg-31-75-2024, 2024
Forecasting wind fields over mountains is of high importance for several applications and particularly for understanding how wind erodes and disperses snow. Forecasters rely on operational wind forecasts over mountains, which are currently only available on kilometric scales. These forecasts can also be affected by errors of diverse origins. Here we introduce a new strategy based on artificial intelligence to correct large-scale wind forecasts in mountains and increase their spatial resolution.

Part 1: Multifractal analysis of wind turbine power and the associated biases
Jerry Jose, Auguste Gires, Yelva Roustan, Ernani Schnorenberger, Ioulia Tchiguirinskaia, and Daniel Schertzer
Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2024-5,2024
Preprint under review for NPG (discussion: final response, 2 comments)
Wind energy exhibits extreme variability in space and time. However, they also show scaling properties (properties that remain similar across different time and space of measurement), this can be quantified using appropriate statistical tools. In this line, the scaling properties of power from a wind farm are analyzed here. Since every turbine is manufactured by design for a rated power, this acts as an upper limit in the data. This bias is identified here using data and numerical simulations.

Part 2: Joint multifractal analysis of available wind power and rain intensity from an operational wind farm
Jerry Jose, Auguste Gires, Ernani Schnorenberger, Yelva Roustan, Daniel Schertzer, and Ioulia Tchiguirinskaia
Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2024-6,2024
Preprint under review for NPG (discussion: final response, 2 comments)
To understand the influence of rainfall on wind power production, turbine power and rainfall were simultaneously measured in an operational wind farm and subjected to analysis. The correlation between wind, wind power, air density and other fields was obtained across various temporal scales during rain and dry conditions. An increase in correlation was observed with an increase in rain; rain also influenced the correspondence between actual and expected values of power at various velocities.

A new approach to understanding fluid mixing in process-study models of stratified fluids
Samuel George Hartharn-Evans, Marek Stastna, and Magda Carr
Nonlin. Processes Geophys., 31, 61–74, https://doi.org/10.5194/npg-31-61-2024, 2024
Across much of the ocean, and the world's lakes, less dense water (either because it is warm or fresh) overlays denser water, forming stratification. The mixing of these layers affects the distribution of heat, nutrients, plankton, sediment, and buoyancy, so it is crucial to understand. We use small-scale numerical experiments to better understand these processes, and here we propose a new analysis tool for understanding mixing within those models, looking at where two variables intersect.

Leading the Lorenz-63 system toward the prescribed regime by model predictive control coupled with data assimilation
Fumitoshi Kawasaki and Shunji Kotsuki
Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2024-4,2024
Revised manuscript under review for NPG (discussion: final response, 4 comments)
Recently, scientists have been looking into ways to control the weather to lead to a desirable direction for mitigating weather-induced disasters caused by torrential rainfall and typhoons. This study proposed using model predictive control, known as an advanced control method, to control a chaotic system. Through numerical experiments using a low-dimensional chaotic system, we demonstrated that the system can be controlled successfully with shorter forecasts compared to previous studies.

A Comparison of Two Nonlinear Data Assimilation Methods
Vivian A. Montiforte, Hans E. Ngodock, and Innocent Souopgui
Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2024-3,2024
Preprint under review for NPG (discussion: open, 1 comment)
Advanced data assimilation methods are complex and computationally expensive. We compare two simpler methods, Diffusive Back and Forth Nudging and Concave-Convex Nonlinearity, that account for change over time with the potential of providing accurate results with a reduced computational cost. We evaluate the accuracy of the two methods by implementing them within simple chaotic models. We conclude that the length and frequency of observations impacts which method is better suited for a problem.

Multifractal structure and Gutenberg-Richter parameter associated with volcanic emissions of high energy in Colima, México (years 2013–2015)
Marisol Monterrubio-Velasco, Xavier Lana, and Raúl Arámbula-Mendoza
Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2024-2,2024
Preprint under review for NPG (discussion: open, 2 comments)
Understanding volcanic activity is crucial for uncovering the fundamental physical mechanisms governing this natural phenomenon. In this study, we show the application of multifractal and statistical analysis, to investigate changes associated with volcanic activity. We aim to identify significant variations within the physical processes related to changes in volcanic activity. These methodologies offer the potential to identify pertinent changes preceding a high-energy explosion.

Sensitivity of the polar boundary layer to transient phenomena
Amandine Kaiser, Nikki Vercauteren, and Sebastian Krumscheid
Nonlin. Processes Geophys., 31, 45–60, https://doi.org/10.5194/npg-31-45-2024, 2024
Current numerical weather prediction models encounter challenges in accurately representing regimes in the stably stratified atmospheric boundary layer (SBL) and the transitions between them. Stochastic modeling approaches are a promising framework to analyze when transient small-scale phenomena can trigger regime transitions. Therefore, we conducted a sensitivity analysis of the SBL to transient phenomena by augmenting a surface energy balance model with meaningful randomizations.

Aggregation of slightly buoyant microplastics in 3D vortex flows
Irina I. Rypina, Lawrence J. Pratt, and Michael Dotzel
Nonlin. Processes Geophys., 31, 25–44, https://doi.org/10.5194/npg-31-25-2024, 2024
This paper investigates the aggregation of small, spherical, slightly buoyant, rigid particles in a simple 3D vortex flow. Our goal was to gain insights into the behaviour of slightly buoyant marine microplastics in a flow that qualitatively resembles ocean eddies. Attractors are mapped out for the steady, axisymmetric; steady, asymmetric; and nonsteady, asymmetric vortices over a range of flow and particle parameters. Simple theoretical arguments are used to interpret the results.