Application of Backward Nonlinear Local Lyapunov Exponent Method to Assessing the Relative Impacts of Initial Condition and Model Errors on Local Backward Predictability

2021 ◽  
Author(s):  
Xuan Li ◽  
Jie Feng ◽  
Ruiqiang Ding ◽  
Jianping Li
Keyword(s):  
Lyapunov Exponent ◽  
Initial Condition ◽  
Model Errors ◽  
Local Lyapunov Exponent

Uncertainty Quantification in Multi-Model Ensembles

2018 ◽  
Author(s):  
Benjamin Mark Sanderson
Keyword(s):  
Climate Change ◽  
Uncertainty Quantification ◽  
Climate Models ◽  
Climate Model ◽  
Initial Condition ◽  
Model Errors ◽  
Model Framework ◽  
Validation Data ◽  
Model Ensembles

Long-term planning for many sectors of society—including infrastructure, human health, agriculture, food security, water supply, insurance, conflict, and migration—requires an assessment of the range of possible futures which the planet might experience. Unlike short-term forecasts for which validation data exists for comparing forecast to observation, long-term forecasts have almost no validation data. As a result, researchers must rely on supporting evidence to make their projections. A review of methods for quantifying the uncertainty of climate predictions is given. The primary tool for quantifying these uncertainties are climate models, which attempt to model all the relevant processes that are important in climate change. However, neither the construction nor calibration of climate models is perfect, and therefore the uncertainties due to model errors must also be taken into account in the uncertainty quantification.Typically, prediction uncertainty is quantified by generating ensembles of solutions from climate models to span possible futures. For instance, initial condition uncertainty is quantified by generating an ensemble of initial states that are consistent with available observations and then integrating the climate model starting from each initial condition. A climate model is itself subject to uncertain choices in modeling certain physical processes. Some of these choices can be sampled using so-called perturbed physics ensembles, whereby uncertain parameters or structural switches are perturbed within a single climate model framework. For a variety of reasons, there is a strong reliance on so-called ensembles of opportunity, which are multi-model ensembles (MMEs) formed by collecting predictions from different climate modeling centers, each using a potentially different framework to represent relevant processes for climate change. The most extensive collection of these MMEs is associated with the Coupled Model Intercomparison Project (CMIP). However, the component models have biases, simplifications, and interdependencies that must be taken into account when making formal risk assessments. Techniques and concepts for integrating model projections in MMEs are reviewed, including differing paradigms of ensembles and how they relate to observations and reality. Aspects of these conceptual issues then inform the more practical matters of how to combine and weight model projections to best represent the uncertainties associated with projected climate change.

Ensemble quantification of short-term predictability of the ocean fine-scale dynamics: a western mediterranean test case at kilometric-scale resolution.

2020 ◽  
Author(s):  
Stéphanie Leroux ◽  
Jean-Michel Brankart ◽  
Aurélie Albert ◽  
Pierre Brasseur ◽  
Laurent Brodeau ◽  
...  
Keyword(s):  
Model Error ◽  
Western Mediterranean ◽  
Practical Approach ◽  
Initial Condition ◽  
Fine Scale ◽  
Model Errors ◽  
Model Accuracy ◽  
Vertical Grid ◽  
Different Levels ◽  
Ensemble Experiments

<p>“Predictability” in operational forecasting systems can be viewed as the ability to meet the forecast accuracy that is required for a given application. In the literature, the most usual approach is to assume that predictability is mainly limited by model instability (i.e. the chaotic behaviour of the system), which means assuming that initial and model errors are small. But, in operational systems, initial and model errors cannot usually be assumed small, because of the complexity of the system and because observations and model resources are limited. In this study, we propose  a practical approach to take into account such model and initial condition errors, in the aim to evaluate the predictability of the fine-scale dynamics in a CMEMS-like operational system, based on ensemble experiments with the ocean numerical model NEMO.</p><p>    To do so, we set up a regional model configuration MEDWEST60 with NEMO v3.6,  212 vertical levels and a kilometric-scale horizontal resolution (1/60º). Such a resolution allows to simulate the fine-scale dynamics up to an effective resolution of  ~10 km. The domain covers the Western Mediterranean sea from Gibraltar to Corsica-Sardinia. The configuration includes tides and is forced at the western and eastern boundaries with hourly outputs from a reference simulation on a larger domain, also including tides, and based on the exact same horizontal and vertical grid.</p><p>    The practical approach we follow consists first in performing a set of several  short (~1month) ensemble forecast experiments to study the growth of forecast errors for different levels of  model error and initial condition error. In practice, we need to implement a tunable source of model error in MEDWEST60, that might represent e.g. numerical errors, forcing errors, missing or uncertain physics via stochastic parameterization (in this presentation, we will focus on a first set of ensemble experiments where stochastic perturbations are added on the model vertical grid). It is then used to generate different levels of error on the initial conditions. </p><p>    In a second step, by inverting the dependence between forecast error on the one hand and initial and model error on the other hand, we aim to diagnose the level of initial and model accuracy needed for a given targeted accuracy of the forecasting system. </p><p>Practical questions addressed by such experiments relate to the relative importance of model accuracy vs initial condition accuracy for the  forecast of the finest scales in a CMEMS system. From this we can infer information about (a) predictability - for instance, the time along which a forecast remains meaningful for the fine scales. And information about (b) controllability by the observations, for instance, the minimal time to consider between two passes of a future satellite to be able to follow a given observed fine-scale structure - front, eddy, etc</p>

scholarly journals SUPREME LOCAL LYAPUNOV EXPONENTS AND CHAOTIC IMPULSIVE SYNCHRONIZATION

2013 ◽  
Vol 23 (10) ◽  
pp. 1350169 ◽  
Author(s):  
SHENGYAO CHEN ◽  
FENG XI ◽  
ZHONG LIU
Keyword(s):  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Finite Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
Local Instability ◽  
Impulsive Synchronization ◽  
Local Lyapunov Exponent ◽  
Expansion Behavior

Impulsively synchronized chaos with criterion from conditional Lyapunov exponent is often interrupted by desynchronized bursts. This is because the Lyapunov exponent cannot characterize local instability of synchronized attractor. To predict the possibility of the local instability, we introduce a concept of supreme local Lyapunov exponent (SLLE), which is defined as supremum of local Lyapunov exponents over the attractor. The SLLE is independent of the system trajectories and therefore, can characterize the extreme expansion behavior in all local regions with prescribed finite-time interval. It is shown that the impulsively synchronized chaos can be kept forever if the largest SLLE of error dynamical systems is negative and then the burst behavior will not appear. In addition, the impulsive synchronization with negative SLLE allows large synchronizable impulsive interval, which is significant for applications.

Nonlinear local Lyapunov exponent and atmospheric predictability research

2006 ◽  
Vol 49 (10) ◽  
pp. 1111-1120 ◽  
Author(s):  
Baohua Chen ◽  
Jianping Li ◽  
Ruiqiang Ding
Keyword(s):  
Lyapunov Exponent ◽  
Local Lyapunov Exponent ◽  
Atmospheric Predictability

scholarly journals The Study of the Chaotic Behavior in Retailer's Demand Model

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Junhai Ma ◽  
Yun Feng
Keyword(s):  
Lyapunov Exponent ◽  
Systems Theory ◽  
Bifurcation Diagram ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Deterministic Chaos ◽  
Model Parameters ◽  
Initial Condition ◽  
Maximal Lyapunov Exponent ◽  
Demand Model

Based on the work of domestic and foreign scholars and the application of chaotic systems theory, this paper presents an investigation simulation of retailer's demand and stock. In simulation of the interaction, the behavior of the system exhibits deterministic chaos with consideration of system constraints. By the method of space's reconstruction, the maximal Lyapunov exponent of retailer's demand model was calculated. The result shows the model is chaotic. By the results of bifurcation diagram of model parameters , and changing initial condition, the system can be led to chaos.

Local Lyapunov Exponent for the Bak–Sneppen Model

2003 ◽  
Vol 20 (12) ◽  
pp. 2118-2121 ◽  
Author(s):  
Ma Ke ◽  
Yang Chun-Bin ◽  
Cai Xu
Keyword(s):  
Lyapunov Exponent ◽  
Local Lyapunov Exponent
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