Macroweather predictions and climate projections

2019 ◽  
Author(s):  
Shaun Lovejoy
Keyword(s):  
Blow Up ◽  
Initial Conditions ◽  
Point Of View ◽  
Climate Projections ◽  
Small Perturbations ◽  
Weather Patterns ◽  
Physical Mechanisms ◽  
Mathematical Expressions ◽  
Butterfly Effect

“Does the Flapping of a Butterfly’s Wings in Brazil Set off a Tornado in Texas?” This was the provocative title of an address given by Edward Lorenz, the origin for the (nearly) household expression “butterfly effect.” It was December 1972 and it had been nearly ten years since he had discovered it,1 yet its significance was only then being recognized. Lorenz explained: “In more technical language, is the behavior of the atmosphere unstable to small perturbations?” His answer: “Although we cannot claim to have proven that the atmosphere is unstable, the evidence that it is so is overwhelming.” Imagine two planets identical in every way except that on one there is a butterfly that flaps its wings. The butterfly effect means that their future evolutions are “sensitively dependent” on the initial conditions, so that a mere flap of a wing could perturb the atmosphere sufficiently so that, eventually, the weather patterns on the two planets would evolve quite differently. On the planet with the Brazilian butterfly, the number of tornadoes would likely be the same. But on a given day, one might occur in Texas rather than Oklahoma. This sensitive dependence on small perturbations thus limits our ability to predict the weather. For Earth, Lorenz estimated this predictability limit to be about two weeks. From Chapters 4 and 5 and the discussion that follows, we now understand it as the slightly shorter weather– macroweather transition scale. In Chapter 1, we learned that the ratio of the nonlinear to linear terms in the (deterministic) equations governing the atmosphere is typically about a thou­sand billion. The nonlinear terms are the mathematical expressions of physical mechanisms that can blow up microscopic perturbations into large effects. Therefore, we expect instability. Chapter 4, we examined instability from the point of view of the higher level statistical laws— the fact that, at weather scales, the fluctuation exponents H for all atmospheric fields are positive (in space, up to the size of the planet; in time, up to the weather– macroweather transition scale at five to ten days).

Nonnormal Amplification of the Thermohaline Circulation

2005 ◽  
Vol 35 (9) ◽  
pp. 1593-1605 ◽  
Author(s):  
Laure Zanna ◽  
Eli Tziperman
Keyword(s):  
Thermohaline Circulation ◽  
Initial Temperature ◽  
Initial Conditions ◽  
Small Perturbations ◽  
Stable Regime ◽  
Physical Mechanisms ◽  
Freshwater Forcing ◽  
Centennial Time Scale ◽  
Amplification Mechanism ◽  
Maximum Amplification

Abstract A simple zonally averaged coupled ocean–atmosphere model, with a relatively high resolution in the meridional direction, is used to examine physical mechanisms leading to transient amplification of thermohaline circulation (THC) anomalies. It is found that in a stable regime, in which small perturbations eventually decay, there are optimal initial conditions leading to a dramatic amplification of initial temperature and salinity anomalies in addition to the THC amplification. The maximum amplification occurs after about 40 years, and the eventual decay is on a centennial time scale. The initial temperature and salinity anomalies are considerably amplified by factors of a few hundreds and 20, respectively. The initial conditions leading to this amplification are characterized by mutually canceling initial temperature and salinity anomalies contributions to the THC anomaly, such that the initial THC anomaly vanishes. The mechanism of amplification is analyzed and found to be the result of an interaction between a few damped (oscillatory and nonoscillatory) modes with decay time scales lying in a range of 20–800 years. The amplification mechanism is also found to be distinct from the advective feedback leading to THC instabilities for large freshwater forcing.

Sophie Laws, with Caroline Harper and Rachel Marcus. Research for Development: A Practical Guide. New Delhi: Vistaar Publications. 2003. xiii+475 pages. Paperback. Indian Rupees 450.00.

2003 ◽  
Vol 42 (2) ◽  
pp. 170-172
Author(s):  
Mir Annice Mahmood
Keyword(s):  
Policy Research ◽  
Point Of View ◽  
Basic Question ◽  
New Delhi ◽  
Economic Point ◽  
Scarce Resources ◽  
Is Research ◽  
The Subject ◽  
Development Workers

To implement any successful policy, research about the subject-matter is essential. Lack of knowledge would result in failure and, from an economic point of view, it would lead to a waste of scarce resources. The book under review is essentially a manual which highlights the use of research for development. The book is divided into two parts. Part One informs the reader about concepts and some theory, and Part Two deals with the issue of undertaking research for development. Both parts have 11 chapters each. Chapter 1 asks the basic question: Is research important in development work? The answer is that it is. Research has many dimensions: from the basic asking of questions to the more sophisticated broad-based analysis of policy issues. The chapter, in short, stresses the usefulness of research which development workers ignore at their own peril.

scholarly journals On Kaufmann's theory of the impact of the pianoforte hammer

1920 ◽  
Vol 97 (682) ◽  
pp. 99-110 ◽  
Keyword(s):  
Initial Conditions ◽  
Practical Importance ◽  
Prima Facie ◽  
Point Of View ◽  
Infinite Length ◽  
Modes Of Vibration ◽  
Rigorous Treatment ◽  
The Subject ◽  
Set Up ◽  
The Impact

The theory of the vibrations of the pianoforte string put forward by Kaufmann in a well-known paper has figured prominently in recent discussions on the acoustics of this instrument. It proceeds on lines radically different from those adopted by Helmholtz in his classical treatment of the subject. While recognising that the elasticity of the pianoforte hammer is not a negligible factor, Kaufmann set out to simplify the mathematical analysis by ignoring its effect altogether, and treating the hammer as a particle possessing only inertia without spring. The motion of the string following the impact of the hammer is found from the initial conditions and from the functional solutions of the equation of wave-propagation on the string. On this basis he gave a rigorous treatment of two cases: (1) a particle impinging on a stretched string of infinite length, and (2) a particle impinging on the centre of a finite string, neither of which cases is of much interest from an acoustical point of view. The case of practical importance treated by him is that in which a particle impinges on the string near one end. For this case, he gave only an approximate theory from which the duration of contact, the motion of the point struck, and the form of the vibration-curves for various points of the string could be found. There can be no doubt of the importance of Kaufmann’s work, and it naturally becomes necessary to extend and revise his theory in various directions. In several respects, the theory awaits fuller development, especially as regards the harmonic analysis of the modes of vibration set up by impact, and the detailed discussion of the influence of the elasticity of the hammer and of varying velocities of impact. Apart from these points, the question arises whether the approximate method used by Kaufmann is sufficiently accurate for practical purposes, and whether it may be regarded as applicable when, as in the pianoforte, the point struck is distant one-eighth or one-ninth of the length of the string from one end. Kaufmann’s treatment is practically based on the assumption that the part of the string between the end and the point struck remains straight as long as the hammer and string remain in contact. Primâ facie , it is clear that this assumption would introduce error when the part of the string under reference is an appreciable fraction of the whole. For the effect of the impact would obviously be to excite the vibrations of this portion of the string, which continue so long as the hammer is in contact, and would also influence the mode of vibration of the string as a whole when the hammer loses contact. A mathematical theory which is not subject to this error, and which is applicable for any position of the striking point, thus seems called for.

scholarly journals On some kinds of dense orbits in general nonautonomous dynamical systems

2020 ◽  
Vol 7 (1) ◽  
pp. 163-175
Author(s):  
Mehdi Pourbarat
Keyword(s):  
Dynamical Systems ◽  
Initial Conditions ◽  
Point Of View ◽  
Topological Conjugacy ◽  
Topological Transitivity ◽  
Nonautonomous Systems ◽  
Nonautonomous Dynamical Systems ◽  
Sensitive Dependence ◽  
Dense Orbits

AbstractWe study the theory of universality for the nonautonomous dynamical systems from topological point of view related to hypercyclicity. The conditions are provided in a way that Birkhoff transitivity theorem can be extended. In the context of generalized linear nonautonomous systems, we show that either one of the topological transitivity or hypercyclicity give sensitive dependence on initial conditions. Meanwhile, some examples are presented for topological transitivity, hypercyclicity and topological conjugacy.

Artificial Planning Experience by Means of a Heuristic Cell-Space Model: Simulating International Migration in the Urban Process

1995 ◽  
Vol 27 (10) ◽  
pp. 1647-1665 ◽  
Author(s):  
J Portugali ◽  
I Benenson
Keyword(s):  
Urban Policy ◽  
Initial Conditions ◽  
Point Of View ◽  
Town Planning ◽  
Space Model ◽  
Self Organized ◽  
A Cell ◽  
Policy And Planning ◽  
The City ◽  
Theory And Model

We suggest considering the city as a complex, open, and thus self-organized system, and describing it by means of a cell-space model. A central property of self-organizing systems is that they are not controllable—not by individuals, nor by economic, political, and planning institutions. The city, in this respect, is complex and untamable. Inability to recognize and accept this property is one of the reasons for the difficulties and problems of modernist town planning. The theory and model we present are built to describe the urban process as a historical one in which, given identical initial conditions, each simulation run is unique and never fully repeats itself. From the point of view of urban policy and planning, our heuristic model can guide decisionmakers by answering the following question: ‘given the initial conditions of an inflow of new immigrants (that is, from the ex-USSR), what possible urban scenarios can result, and what are their global structural properties?’.

scholarly journals Thin-film-induced morphological instabilities over calcite surfaces

2015 ◽  
Vol 471 (2176) ◽  
pp. 20150031 ◽  
Author(s):  
R. Vesipa ◽  
C. Camporeale ◽  
L. Ridolfi
Keyword(s):  
Morphological Evolution ◽  
Water Film ◽  
Environmental Parameters ◽  
Climatic Conditions ◽  
Point Of View ◽  
Theoretical Point ◽  
Carbon Dioxide Transport ◽  
Physical Mechanisms ◽  
Water Films ◽  
Dissolved Ions

Precipitation of calcium carbonate from water films generates fascinating calcite morphologies that have attracted scientific interest over past centuries. Nowadays, speleothems are no longer known only for their beauty but they are also recognized to be precious records of past climatic conditions, and research aims to unveil and understand the mechanisms responsible for their morphological evolution. In this paper, we focus on crenulations, a widely observed ripple-like instability of the the calcite–water interface that develops orthogonally to the film flow. We expand a previous work providing new insights about the chemical and physical mechanisms that drive the formation of crenulations. In particular, we demonstrate the marginal role played by carbon dioxide transport in generating crenulation patterns, which are indeed induced by the hydrodynamic response of the free surface of the water film. Furthermore, we investigate the role of different environmental parameters, such as temperature, concentration of dissolved ions and wall slope. We also assess the convective/absolute nature of the crenulation instability. Finally, the possibility of using crenulation wavelength as a proxy of past flows is briefly discussed from a theoretical point of view.

Cyclotron auto resonance maser and free electron laser devices: a unified point of view

2017 ◽  
Vol 83 (1) ◽  
Author(s):  
E. Di Palma ◽  
E. Sabia ◽  
G. Dattoli ◽  
S. Licciardi ◽  
I. Spassovsky
Keyword(s):  
Free Electron ◽  
Free Electron Laser ◽  
Point Of View ◽  
Physical Mechanisms ◽  
Two Systems ◽  
Practical Tool ◽  
Laser Devices

We take advantage of previous research in the field of cyclotron auto resonance maser (CARM) and undulator-based free electron laser (U-FEL) sources to establish a common formalism for the relevant description of the underlying physical mechanisms. This strategy is aimed at stressing the deep analogies between the two devices and at providing a practical tool for their study based on the use of well-tested scaling formulae developed independently for the two systems.

BASIN CONFIGURATION OF A SIX-DIMENSIONAL MODEL OF AN ELECTRIC POWER SYSTEM

2002 ◽  
Vol 12 (06) ◽  
pp. 1333-1356 ◽  
Author(s):  
YOSHISUKE UEDA ◽  
HIROYUKI AMANO ◽  
RALPH H. ABRAHAM ◽  
H. BRUCE STEWART
Keyword(s):  
Power Systems ◽  
Power System ◽  
Initial Conditions ◽  
Electrical Power ◽  
Practical Importance ◽  
Intervention Strategy ◽  
Basins Of Attraction ◽  
Electric Power System ◽  
Point Of View ◽  
Electrical Power System

As part of an ongoing project on the stability of massively complex electrical power systems, we discuss the global geometric structure of contacts among the basins of attraction of a six-dimensional dynamical system. This system represents a simple model of an electrical power system involving three machines and an infinite bus. Apart from the possible occurrence of attractors representing pathological states, the contacts between the basins have a practical importance, from the point of view of the operation of a real electrical power system. With the aid of a global map of basins, one could hope to design an intervention strategy to boot the power system back into its normal state. Our method involves taking two-dimensional sections of the six-dimensional state space, and then determining the basins directly by numerical simulation from a dense grid of initial conditions. The relations among all the basins are given for a specific numerical example, that is, choosing particular values for the parameters in our model.

GRAVITATIONAL BAG EFFECTS ON KALUZA KLEIN AND STRING EXCITATIONS

1989 ◽  
Vol 04 (19) ◽  
pp. 5119-5131 ◽  
Author(s):  
E. I. GUENDELMAN
Keyword(s):  
Extra Dimensions ◽  
Blow Up ◽  
Point Of View ◽  
Spherically Symmetric ◽  
Massive String ◽  
Free Objects ◽  
Higher Dimensional ◽  
Central Regions ◽  
The Masses ◽  
Kaluza Klein

Gravitational Bags are spherically symmetric solutions of higher-dimensional Kaluza Klein (K – K) theories, where the compact dimensions become very large near the center of the geometry, although they are small elsewhere. The K – K excitations therefore become very light when located near the center of this geometry and this appears to affect drastically the naive tower of the masses spectrum of K – K theories. In the context of string theories, string excitations can be enclosed by Gravitational Bags, making them not only lighter, but also localized, as observed by somebody, that does not probe the central regions. Strings, however, can still have divergent sizes, as quantum mechanics seems to demand, since the extra dimensions blow up at the center of the geometry. From a projected 4-D point of view, very massive string bits may lie inside their Schwarzschild radii, as pointed out by Casher, Gravitational Bags however are horizon free objects, so no conflict with macroscopic causality arises if the string excitations are enclosed by Gravitational Bags.

scholarly journals Photovoltaic Energy All-Day and Intra-Day Forecasting Using Node by Node Developed Polynomial Networks Forming PDE Models Based on the L-Transformation

Energies ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 7581
Author(s):  
Ladislav Zjavka
Keyword(s):  
Spatial Data ◽  
Initial Conditions ◽  
Weather Prediction ◽  
Cloud Amount ◽  
Differential Polynomial ◽  
Order Partial Differential Equation ◽  
Computing Technique ◽  
Weather Patterns ◽  
Model Complex ◽  
Short Time

Forecasting Photovoltaic (PV) energy production, based on the last weather and power data only, can obtain acceptable prediction accuracy in short-time horizons. Numerical Weather Prediction (NWP) systems usually produce free forecasts of the local cloud amount each 6 h. These are considerably delayed by several hours and do not provide sufficient quality. A Differential Polynomial Neural Network (D-PNN) is a recent unconventional soft-computing technique that can model complex weather patterns. D-PNN expands the n-variable kth order Partial Differential Equation (PDE) into selected two-variable node PDEs of the first or second order. Their derivatives are easy to convert into the Laplace transforms and substitute using Operator Calculus (OC). D-PNN proves two-input nodes to insert their PDE components into its gradually expanded sum model. Its PDE representation allows for the variability and uncertainty of specific patterns in the surface layer. The proposed all-day single-model and intra-day several-step PV prediction schemes are compared and interpreted with differential and stochastic machine learning. The statistical models are evolved for the specific data time delay to predict the PV output in complete day sequences or specific hours. Spatial data from a larger territory and the initially recognized daily periods enable models to compute accurate predictions each day and compensate for unexpected pattern variations and different initial conditions. The optimal data samples, determined by the particular time shifts between the model inputs and output, are trained to predict the Clear Sky Index in the defined horizon.

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