NONLINEAR PROCESSES IN GEOPHYSICS (NPG) 是一本国际性、跨学科/跨学科的非营利性期刊，致力于打破地球和空间科学标准方法经常面临的僵局。因此，它寻求颠覆性和创新的概念和方法，以及这些概念和方法的原始应用，以解决地球科学系统以及相互作用的社会和生物系统中普遍存在的复杂性。这样的系统是非线性的，响应与扰动非常不成比例，并显示出跨尺度的相关极端可变性。

Nonlinear Processes in Geophysics (NPG) is an international, interdisciplinary, non-profit journal dedicated to overcoming the limitations often faced by standard methods in Earth and space sciences. It seeks to explore disruptive and innovative concepts and methods, as well as their original applications in addressing the pervasive complexities present in Earth science systems and their interactions with social and biological systems. Such systems are typically nonlinear, exhibiting disproportionately large responses to disturbances and showing extreme variability across scales.

《Nonlinear Processes in Geophysics》（NPG）是一本国际性、跨学科的非营利性期刊，旨在突破地球与空间科学标准方法所面临的局限。期刊致力于探索颠覆性和创新的概念与方法，以及这些概念和方法在解决地球科学系统及其与社会和生物系统相互作用中普遍存在的复杂性方面的原始应用。这些系统通常是非线性的，对扰动的响应往往不成比例，并且表现出跨尺度的极端可变性。

Nonlinear Processes in Geophysics

Abstract. A derivation of discrete dynamical equations for the dry atmosphere in the absence of dissipative processes based on the least action (i.e. Hamilton's) principle is presented. This approach can be considered the finite-element method applied to the calculation and minimization of the action. The algorithm possesses the following characteristic features: For a given set of grid points and a given forward operator (i.e. the mode of interpolation), through the minimization of action, the algorithm ensures maximal closeness (in a broad sense) of the evolution of the discrete system to the motion of the continuous atmosphere (a dynamically optimal algorithm). The grid points can be irregularly spaced, allowing for variable spatial resolution. The spatial resolution can be adjusted locally while executing calculations. By using a set of tetrahedra as finite elements the algorithm ensures a better representation of the topography (piecewise linear rather than staircase). The algorithm automatically calculates the evolution of passive tracers by following the trajectories of the fluid particles, which ensures that all tracer properties required a priori are satisfied. For testing purposes, the algorithm is realized in 2D, and a numerical example representing a convection event is presented.

Alexander G. Voronovich

Nonlinear processes in geophysics

Dynamically optimal models of atmospheric motion

大气运动动态最优模型

Abstract. A novel method for the inference of spatiotemporal decomposition of oceanic surface flow variability is presented and its performance assessed in a synthetic idealized configuration with horizontally divergentless flow. Inference methodology is designed for observations of surface velocity. The ability of networks of surface drifters and moorings to infer the spatiotemporal scales of surface ocean flow variability is quantified. The sensitivity of inference performance for both types of platforms to the number of observations, geometrical configurations, and flow regimes is presented. As drifters simultaneously sample spatial and temporal variability, they are shown to be able to capture both spatial and temporal flow properties even when deployed in isolation. Moorings are particularly adept for the characterization of the flow's temporal variability and may also capture spatial scales provided they are deployed as arrays. In particular, we show that our method correctly identifies whether drifters are preferentially sampling spatial vs. temporal variability. Pending further developments, this method opens novel avenues for the analysis of existing datasets as well as the design of future experimental campaigns targeting the characterization of small-scale (e.g., &lt;100 km) ocean variability.

Aurelien Luigi Serge Ponte

Lachlan C. Astfalck

Matthew D. Rayson

Andrew P. Zulberti

Nicole L. Jones

Inferring flow energy, space scales, and timescales: freely drifting vs. fixed-point observations

推断流动能量、空间尺度和时间尺度：自由漂移与固定点观测

Abstract. In the increasing global transition towards renewable and carbon-neutral energy, understanding the uncertainties associated with wind power production is extremely important. In addition to the widely acknowledged uncertainties from turbulence and wind intermittency, further complexity arises from the influence of rainfall, which only a limited number of studies have addressed so far. To understand this, multiple 3D sonic anemometers, mini meteorological stations, and optical disdrometers were employed on a meteorological mast on the Pays d'Othe wind farm (110 km south-east of Paris, France) in the framework of the Rainfall Wind Turbine or Turbulence (RW-Turb) project (https://hmco.enpc.fr/portfolio-archive/rw-turb/, last access: 26 November 2024). With these simultaneously measured data, wind power and its associated atmospheric fields were studied under various rainy conditions. Variations of the wind velocity, power available on the wind farm, power produced by wind turbines, and air density are examined here, under rainy and dry conditions, using the scale-invariant framework of universal multifractals (UM). Since rated power acts like an upper threshold in statistical analysis of turbine power (discussed in Part 1), theoretically available power was used as a proxy. From an event-based analysis, differences in UM parameters were observed between rainy and dry conditions for the fields. This is explored further using joint multifractal analysis, which revealed an increase in the correlation exponent between various fields with the rain rate. Here we also examine the possibility of variation in power production by rainy conditions (convective or stratiform) as well as by regimes of wind velocity. While examining time steps according to wind velocity, turbine power curves showed different regions of departure from the state curve according to the rain rate.

Jerry Jose

Auguste Gires

Ernani Schnorenberger

Yelva Roustan

Daniel Schertzer

Ioulia Tchiguirinskaia

Multifractal analysis of wind turbine power and rainfall from an operational wind farm – Part 2: Joint analysis of available wind power and rain intensity

风力发电机功率和降雨的多重分形分析——第2部分：可用风力发电和降雨强度的联合分析

Abstract. The inherent variability in atmospheric fields, which extends over a wide range of temporal and spatial scales, is also transferred to energy fields extracted from them. In the specific case of wind power generation, this can be seen in the theoretical power available for extraction and the empirical power produced by turbines. To model and analyse them, it is important to quantify their variability, intermittency, and correlations with other interacting fields across scales. To understand the uncertainties involved in power production, power outputs from four 2 MW turbines are analysed (from an operational wind farm at Pay d'Othe, 110 km south-east of Paris, France) using the scale-invariant framework of universal multifractals (UM). Their scaling properties were compared with power available at the same location from simultaneously measured wind velocity. While statistically analysing the turbine output, the rated power acts like an upper threshold that results in biased estimators. This is identified and quantified here using the theoretical framework of UM and validated using numerical simulations. Understanding the effect of instrumental thresholds in statistical analysis is important in retrieving actual fields and modelling them, more so in wind power production, where the uncertainties due to turbulence are already a leading challenge. This is expanded in Part 2, where the influence of rainfall on power production is studied across scales using UM and joint multifractals.

Multifractal analysis of wind turbine power and rainfall from an operational wind farm – Part 1: Wind turbine power and the associated biases

风电机组功率和降雨的多重分形分析——第1部分：风电机组功率及其相关偏差

Abstract. The design and implementation of boundary conditions for the robust generation and simulation of periodic finite-amplitude internal waves is examined in a quasi two-layer continuous stratification using a spectral-element-method-based incompressible flow solver. The commonly used Eulerian approach develops spurious, and potentially catastrophic small-scale numerical features near the wave-generating boundary in a non-linear stratification when the parameter A/(δc) is sufficiently larger than unity; A and δ are measures of the maximum wave-induced vertical velocity and pycnocline thickness, respectively, and c is the linear wave propagation speed. To this end, an Euler–Lagrange approach is developed and implemented to generate robust high-amplitude periodic deep-water internal waves. Central to this approach is to take into account the wave-induced (isopycnal) displacement of the pycnocline in both the vertical and (effectively) upstream directions. With amplitudes not restricted by the limits of linear theory, the Euler–Lagrange-generated waves maintain their structural integrity as they propagate away from the source. The advantages of the high-accuracy numerical method, whose minimal numerical dissipation cannot damp the above near-source spurious numerical features of the purely Eulerian case, can still be preserved and leveraged further along the wave propagation path through the robust reproduction of the non-linear adjustments of the waveform. The near- and far-source robustness of the optimized Euler–Lagrange approach is demonstrated for finite-amplitude waves in a sharp quasi two-layer continuous stratification representative of seasonally stratified lakes. The findings of this study provide an enabling framework for two-dimensional simulations of internal swash zones driven by well-developed non-linear internal waves and, ultimately, the accompanying turbulence-resolving three-dimensional simulations.

Pierre Lloret

Peter J. Diamessis

Marek Stastna

Greg N. Thomsen

A robust numerical method for the generation and propagation of periodic finite-amplitude internal waves in natural waters using high-accuracy simulations

一种利用高精度模拟生成和传播天然水域中周期性有限振幅内波的鲁棒数值方法

Abstract. The spectral signatures of vegetation are indicative of ecosystem states and health. Spectral indices used to monitor vegetation are characterized by long-term trends, seasonal fluctuations, and responses to weather anomalies. This study investigates the potential of neural networks in learning and predicting vegetation response, including extreme behavior from meteorological data. While machine learning methods, particularly neural networks, have significantly advanced in modeling nonlinear dynamics, it has become standard practice to approach the problem using recurrent architectures capable of capturing nonlinear effects and accommodating both long- and short-term memory. We compare four recurrent-based learning models, which differ in their training and architecture for predicting spectral indices at different forest sites in Europe: (1) recurrent neural networks (RNNs), (2) long short-term memory networks (LSTMs), (3) gated recurrent unit networks (GRUs), and (4) echo state networks (ESNs). While our results show minimal quantitative differences in their performances, ESNs exhibit slightly superior results across various metrics. Overall, we show that recurrent network architectures prove generally suitable for vegetation state prediction yet exhibit limitations under extreme conditions. This study highlights the potential of recurrent network architectures for vegetation state prediction, emphasizing the need for further research to address limitations in modeling extreme conditions within ecosystem dynamics.

Francesco Martinuzzi

Miguel D. Mahecha

Gustau Camps-Valls

David Montero

Tristan Williams

Karin Mora

Learning extreme vegetation response to climate drivers with recurrent neural networks

利用循环神经网络学习极端植被对气候驱动因素的响应

Abbreviation	Nonlin. Processes Geophys.
Journal Impact	1.87
Quartiles(Global)	PHYSICS, FLUIDS & PLASMAS(Q3)

ISSN	1023-5809, 1607-7946
h-index	67

Publication Information	Publisher: Copernicus Publications，Publishing cycle: Bimonthly，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 1994，Proportion of original research papers: 95.45%，Self Citation Rate:5.90%， Gold OA Rate: 100.00%
Journal Fees	$Details
Average review cycle	网友分享经验：较慢,6-12周
Average recruitment ratio	网友分享经验：容易

Nonlinear Processes in Geophysics

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Dynamically optimal models of atmospheric motion

Inferring flow energy, space scales, and timescales: freely drifting vs. fixed-point observations

Multifractal analysis of wind turbine power and rainfall from an operational wind farm – Part 2: Joint analysis of available wind power and rain intensity

Multifractal analysis of wind turbine power and rainfall from an operational wind farm – Part 1: Wind turbine power and the associated biases

A robust numerical method for the generation and propagation of periodic finite-amplitude internal waves in natural waters using high-accuracy simulations

Multifractal analysis of wind turbine power and rainfall from an operational wind farm – Part 2: Joint analysis of available wind power and rain intensity

Multifractal analysis of wind turbine power and rainfall from an operational wind farm – Part 1: Wind turbine power and the associated biases

Dynamically optimal models of atmospheric motion

Inferring flow energy, space scales, and timescales: freely drifting vs. fixed-point observations

Learning extreme vegetation response to climate drivers with recurrent neural networks