scholarly journals Predictability in Deterministic Dynamical Systems with Application to Weather Forecasting and Climate Modelling

10.5772/66752 ◽  
2017 ◽  
Author(s):  
Sergei Soldatenko ◽  
Rafael Yusupov
Keyword(s):  
Dynamical Systems ◽  
Weather Forecasting ◽  
Climate Modelling ◽  
Deterministic Dynamical Systems

Stochastically perturbed limit cycles

1978 ◽  
Vol 15 (02) ◽  
pp. 311-320
Author(s):  
Charles J. Holland
Keyword(s):  
Dynamical Systems ◽  
Invariant Measure ◽  
Probability Measure ◽  
Limit Cycles ◽  
Noise Intensity ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
Additive White Noise ◽  
Small Intensity ◽  
Deterministic Dynamical Systems

In this paper we examine the effects of perturbing certain deterministic dynamical systems possessing a stable limit cycle by an additive white noise term with small intensity. We place assumptions on the system guaranteeing that when noise is present the corresponding random process generates an ergodic probability measure. We then determine the behavior of the invariant measure when the noise intensity is small.

scholarly journals Climate Modelling in Low Precision: Effects of Both Deterministic & Stochastic Rounding.

2021 ◽  
pp. 1-43
Author(s):  
E. Adam Paxton ◽  
Matthew Chantry ◽  
Milan Klöwer ◽  
Leo Saffin ◽  
Tim Palmer
Keyword(s):  
Climate Models ◽  
Climate Model ◽  
Weather Forecasting ◽  
Stress Test ◽  
Grid Point ◽  
Atmospheric Model ◽  
Extreme Weather Events ◽  
Climate Modelling ◽  
Double Precision ◽  
Rounding Error

AbstractMotivated by recent advances in operational weather forecasting, we study the efficacy of low-precision arithmetic for climate simulations. We develop a framework to measure rounding error in a climate model which provides a stress-test for a low-precision version of the model, and we apply our method to a variety of models including the Lorenz system; a shallow water approximation for ow over a ridge; and a coarse resolution spectral global atmospheric model with simplified parameterisations (SPEEDY). Although double precision (52 significant bits) is standard across operational climate models, in our experiments we find that single precision (23 sbits) is more than enough and that as low as half precision (10 sbits) is often sufficient. For example, SPEEDY can be run with 12 sbits across the code with negligible rounding error, and with 10 sbits if minor errors are accepted, amounting to less than 0.1 mm/6hr for average grid-point precipitation, for example. Our test is based on the Wasserstein metric and this provides stringent non-parametric bounds on rounding error accounting for annual means as well as extreme weather events. In addition, by testing models using both round-to-nearest (RN) and stochastic rounding (SR) we find that SR can mitigate rounding error across a range of applications, and thus our results also provide some evidence that SR could be relevant to next-generation climate models. Further research is needed to test if our results can be generalised to higher resolutions and alternative numerical schemes. However, the results open a promising avenue towards the use of low-precision hardware for improved climate modelling.

Random dynamical systems with jumps

2004 ◽  
Vol 41 (03) ◽  
pp. 890-910 ◽  
Author(s):  
Katarzyna Horbacz
Keyword(s):  
Dynamical Systems ◽  
Iterated Function System ◽  
Infinite Family ◽  
Learning Systems ◽  
Random Dynamical Systems ◽  
Infinite Dimensional ◽  
Markov Operators ◽  
Iterated Function ◽  
Random Evolutions ◽  
Deterministic Dynamical Systems

We consider random dynamical systems with randomly chosen jumps on infinite-dimensional spaces. The choice of deterministic dynamical systems and jumps depends on a position. The system generalizes dynamical systems corresponding to learning systems, Poisson driven stochastic differential equations, iterated function system with infinite family of transformations and random evolutions. We will show that distributions which describe the dynamics of this system converge to an invariant distribution. We use recent results concerning asymptotic stability of Markov operators on infinite-dimensional spaces obtained by T. Szarek.

NOISE-INDUCED CHAOS: A CONSEQUENCE OF LONG DETERMINISTIC TRANSIENTS

2008 ◽  
Vol 18 (02) ◽  
pp. 509-520 ◽  
Author(s):  
TAMÁS TÉL ◽  
YING-CHENG LAI ◽  
MÁRTON GRUIZ
Keyword(s):  
Dynamical Systems ◽  
Dynamical Model ◽  
Invariant Sets ◽  
Transient Chaos ◽  
Weak Noise ◽  
Fractal Properties ◽  
Deterministic Dynamical Systems ◽  
Chaotic Transients ◽  
Noise Phenomenon

We argue that transient chaos in deterministic dynamical systems is a major source of noise-induced chaos. The line of arguments is based on the fractal properties of the dynamical invariant sets responsible for transient chaos, which were not taken into account in previous works. We point out that noise-induced chaos is a weak noise phenomenon since intermediate noise strengths destroy fractality. The existence of a deterministic nonattracting chaotic set, and of chaotic transients, underlying noise-induced chaos is illustrated by examples, among others by a population dynamical model.

Airborne Atmospheric Measurements with the mini Max Planck CloudKite

2020 ◽  
Author(s):  
Marcel Schröder ◽  
Freja Nordsiek ◽  
Oliver Schlenczek ◽  
Antonio Ibanez Landeta ◽  
Eberhard Bodenschatz ◽  
...  
Keyword(s):  
Weather Forecasting ◽  
Volcanic Eruptions ◽  
Radiation Budget ◽  
Trade Wind ◽  
Climate Modelling ◽  
Max Planck ◽  
Atmospheric Measurements ◽  
Spatial And Temporal Scales ◽  
Microphysical Properties ◽  
Wide Range

<p>Clouds play a key role in the energy balance of the Earth's atmosphere and its radiation budget. The lack of detailed understanding of clouds is one of the reasons for the uncertainties in weather forecasting and climate modelling. The dynamics of clouds extend over a wide range of spatial and temporal scales from micrometers to km and milliseconds to hours. Besides Plinian volcanic eruptions, clouds show the highest turbulence level on earth. The multiscale properties of the turbulent flow in combination with moisture and temperature transport, phase transitions, and inertial particle dynamics present a challenge for modelling and parameterization.<span>  </span>Here we use a specially developed airborne platform, the Mini-Max-Planck-CloudKite (Mini-MPCK), to measure meteorological and cloud microphysical properties with high spatial and temporal resolution. The mini-MPCK is a 75 qm helium-filled balloon kite carrying a tether-mounted instrument for measuring atmospheric state parameters, and the density and size distribution of cloud particles. We will report on measurements from the trade wind region obtained during the EUREC4A campaign in Jan-Feb 2020.</p>

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