scholarly journals Statistical approximation of high-dimensional climate models

2020 ◽  
Vol 214 (1) ◽  
pp. 67-80 ◽  
Author(s):  
Alena Miftakhova ◽  
Kenneth L. Judd ◽  
Thomas S. Lontzek ◽  
Karl Schmedders
Keyword(s):  
Climate Models ◽  
High Dimensional ◽  
Statistical Approximation

scholarly journals An efficient training scheme for supermodels

2017 ◽  
Vol 8 (2) ◽  
pp. 429-438 ◽  
Author(s):  
Francine J. Schevenhoven ◽  
Frank M. Selten
Keyword(s):  
Climate Models ◽  
State Of The Art ◽  
Atmospheric Model ◽  
High Dimensional ◽  
Model Errors ◽  
Global Atmospheric Model ◽  
Training Scheme ◽  
Skill Scores ◽  
Weather And Climate ◽  
The Individual

Abstract. Weather and climate models have improved steadily over time as witnessed by objective skill scores, although significant model errors remain. Given these imperfect models, predictions might be improved by combining them dynamically into a so-called supermodel. In this paper a new training scheme to construct such a supermodel is explored using a technique called cross pollination in time (CPT). In the CPT approach the models exchange states during the prediction. The number of possible predictions grows quickly with time, and a strategy to retain only a small number of predictions, called pruning, needs to be developed. The method is explored using low-order dynamical systems and applied to a global atmospheric model. The results indicate that the CPT training is efficient and leads to a supermodel with improved forecast quality as compared to the individual models. Due to its computational efficiency, the technique is suited for application to state-of-the art high-dimensional weather and climate models.

Analysing Conceptual Climate Models with Monte Carlo Basin Bifurcation Analysis

2020 ◽  
Author(s):  
Maximilian Gelbrecht ◽  
Jürgen Kurths ◽  
Frank Hellmann
Keyword(s):  
Monte Carlo ◽  
Complex Systems ◽  
Bifurcation Analysis ◽  
Climate Models ◽  
Climate Model ◽  
Initial Conditions ◽  
Balance Model ◽  
High Dimensional ◽  
Asymptotic State ◽  
Wide Range

<p>Many high-dimensional complex systems such as climate models exhibit an enormously complex landscape of possible asymptotic state. On most occasions these are challenging to analyse with traditional bifurcation analysis methods. Often, one is also more broadly interested in classes of asymptotic states. Here, we present a novel numerical approach prepared for analysing such high-dimensional multistable complex systems: Monte Carlo Basin Bifurcation Analysis (MCBB).<span>  </span>Based on random sampling and clustering methods, we identify the type of dynamic regimes with the largest basins of attraction and track how the volume of these basins change with the system parameters. In order to due this suitable, easy to compute, statistics of trajectories with randomly generated initial conditions and parameters are clustered by an algorithm such as DBSCAN. Due to the modular and flexible nature of the method, it has a wide range of possible applications. While initially oscillator networks were one of the main applications of this methods, here we present an analysis of a simple conceptual climate model setup up by coupling an energy balance model to the Lorenz96 system. The method is available to use as a package for the Julia language.<span> </span></p>

scholarly journals Ensemble Averaging and the Curse of Dimensionality

2018 ◽  
Vol 31 (4) ◽  
pp. 1587-1596 ◽  
Author(s):  
Bo Christiansen
Keyword(s):  
Climate Models ◽  
High Dimensional ◽  
Ensemble Averaging ◽  
Random Vectors ◽  
Multimodel Ensemble ◽  
General Consequence ◽  
Median Error ◽  
Ensemble Mean ◽  
The Mean ◽  
The Individual

When comparing climate models to observations, it is often observed that the mean over many models has smaller errors than most or all of the individual models. This paper will show that a general consequence of the nonintuitive geometric properties of high-dimensional spaces is that the ensemble mean often outperforms the individual ensemble members. This also explains why the ensemble mean often has an error that is 30% smaller than the median error of the individual ensemble members. The only assumption that needs to be made is that the observations and the models are independently drawn from the same distribution. An important and relevant property of high-dimensional spaces is that independent random vectors are almost always orthogonal. Furthermore, while the lengths of random vectors are large and almost equal, the ensemble mean is special, as it is located near the otherwise vacant center. The theory is first explained by an analysis of Gaussian- and uniformly distributed vectors in high-dimensional spaces. A subset of 17 models from the CMIP5 multimodel ensemble is then used to demonstrate the validity and robustness of the theory in realistic settings.

scholarly journals An efficient training scheme that improves the forecast skill of a supermodel

2017 ◽  
Author(s):  
Francine Schevenhoven ◽  
Frank Selten
Keyword(s):  
Climate Models ◽  
State Of The Art ◽  
Atmospheric Model ◽  
High Dimensional ◽  
Model Errors ◽  
Global Atmospheric Model ◽  
Training Scheme ◽  
Skill Scores ◽  
Weather And Climate ◽  
The Individual

Abstract. Weather and climate models have improved steadily over time as witnessed by objective skill scores, although significant model errors remain. Given these imperfect models, predictions might be improved by combining them dynamically into a so-called supermodel. In this paper a new training scheme to construct such a supermodel is explored using a technique called Cross Pollination in Time (CPT). In the CPT approach the models exchange states during the prediction. The number of possible predictions grows quickly with time and a strategy to retain only a small number of predictions, called pruning, needs to be developed. The method is explored using low-order dynamical systems and applied to a global atmospheric model. The results indicate that the CPT training is efficient and leads to a supermodel with improved forecast quality as compared to the individual models. Due to its computational efficiency, the technique is suited for application to state-of-the art high-dimensional weather and climate models.

Supplementary material to "Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models"

2018 ◽  
Author(s):  
Lesley De Cruz ◽  
Sebastian Schubert ◽  
Jonathan Demaeyer ◽  
Valerio Lucarini ◽  
Stéphane Vannitsem
Keyword(s):  
Climate Models ◽  
High Dimensional ◽  
Supplementary Material ◽  
Lyapunov Instability

Neural Partial Differential Equations for Simple Climate Models 

2021 ◽  
Author(s):  
Maximilian Gelbrecht ◽  
Niklas Boers ◽  
Jürgen Kurths
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Climate Models ◽  
Training Data ◽  
Training Dataset ◽  
High Dimensional ◽  
Partial Differential ◽  
Artificial Neural

<p>When predicting complex systems such as parts of the Earth system, one typically relies on differential equations which can often be incomplete, missing unknown influences or higher order effects. By augmenting the equations with artificial neural networks we can compensate these deficiencies. The resulting hybrid models are also known as universal differential equations. We show that this can be used to predict the dynamics of high-dimensional chaotic partial differential equations, such as the ones describing atmospheric dynamics, even when only short and incomplete training data are available. In a first step towards a hybrid atmospheric model, simplified, conceptual atmospheric models are used in synthetic examples where parts of the governing equations are replaced with artificial neural networks. The forecast horizon for these high dimensional systems is typically much larger than the training dataset, showcasing the large potential of the approach.<span> </span></p>

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