Hasselmann’s stochastic climate model viewed from a statistical mechanics perspective

2001 ◽  
pp. 285-295
Author(s):  
Peter Müller
Keyword(s):  
Statistical Mechanics ◽  
Climate Model ◽  
Stochastic Climate Model

scholarly journals Numerical Development and Evaluation of an Energy Conserving Conceptual Stochastic Climate Model

2019 ◽  
Vol 5 (1) ◽  
pp. 45-64 ◽  
Author(s):  
Federica Gugole ◽  
Christian L. E. Franzke
Keyword(s):  
Energy Conservation ◽  
Total Energy ◽  
Prediction Models ◽  
Climate Model ◽  
Empirical Orthogonal Functions ◽  
Correlated Noise ◽  
Spatial Covariance ◽  
Conservation Of Energy ◽  
Stochastic Climate Model ◽  
Energy Conserving

AbstractIn this study we aim to present the successful development of an energy conserving conceptual stochastic climate model based on the inviscid 2-layer Quasi-Geostrophic (QG) equations. The stochastic terms have been systematically derived and introduced in such away that the total energy is conserved. In this proof of concept studywe give particular emphasis to the numerical aspects of energy conservation in a highdimensional complex stochastic system andwe analyzewhat kind of assumptions regarding the noise should be considered in order to obtain physical meaningful results. Our results show that the stochastic model conserves energy to an accuracy of about 0.5% of the total energy; this level of accuracy is not affected by the introduction of the noise, but is mainly due to the level of accuracy of the deterministic discretization of the QG model. Furthermore, our results demonstrate that spatially correlated noise is necessary for the conservation of energy and the preservation of important statistical properties, while using spatially uncorrelated noise violates energy conservation and gives unphysical results. A dynamically consistent spatial covariance structure is determined through Empirical Orthogonal Functions (EOFs). We find that only a small number of EOFs is needed to get good results with respect to energy conservation, autocorrelation functions, PDFs and eddy length scale when comparing a deterministic control simulation on a 512 × 512 grid to a stochastic simulation on a 128 × 128 grid. Our stochastic approach has the potential to seamlessly be implemented in comprehensive weather and climate prediction models.

scholarly journals ESD Ideas: The stochastic climate model shows that underestimated Holocene trends and variability represent two sides of the same coin

2018 ◽  
Vol 9 (4) ◽  
pp. 1279-1281 ◽  
Author(s):  
Gerrit Lohmann
Keyword(s):  
Climate Model ◽  
Sea Surface ◽  
System Sensitivity ◽  
Statistical Fluctuations ◽  
Fluctuation Dissipation ◽  
Temperature Trends ◽  
Fluctuation Dissipation Theorem ◽  
Stochastic Climate Model ◽  
Two Sides

Abstract. Holocene sea surface temperature trends and variability are underestimated in models compared to paleoclimate data. The idea is presented that the local trends and variability are related, which is elaborated in a conceptual framework of the stochastic climate model. The relation is a consequence of the fluctuation–dissipation theorem, connecting the linear response of a system to its statistical fluctuations. Consequently, the spectrum can be used to estimate the timescale-dependent climate response. The non-normality in the propagation operator introduces enhanced long-term variability related to nonequilibrium and/or Earth system sensitivity. The simple model can guide us to analyze comprehensive models' behavior.

scholarly journals Investigating climate tipping points under various emission reduction and carbon capture scenarios with a stochastic climate model

2021 ◽  
Vol 477 (2256) ◽  
Author(s):  
Alexander Mendez ◽  
Mohammad Farazmand
Keyword(s):  
Upper Bound ◽  
Emission Reduction ◽  
Carbon Capture ◽  
Climate Model ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Tipping Point ◽  
Balance Model ◽  
Critical Threshold ◽  
Stochastic Climate Model

We study the mitigation of climate tipping point transitions using an energy balance model. The evolution of the global mean surface temperature is coupled with the CO 2 concentration through the green-house effect. We model the CO 2 concentration with a stochastic delay differential equation (SDDE), accounting for various carbon emission and capture scenarios. The resulting coupled system of SDDEs exhibits a tipping point phenomena: if CO 2 concentration exceeds a critical threshold (around 478   ppm ), the temperature experiences an abrupt increase of about six degrees Celsius. We show that the CO 2 concentration exhibits a transient growth which may cause a climate tipping point, even if the concentration decays asymptotically. We derive a rigorous upper bound for the CO 2 evolution which quantifies its transient and asymptotic growths, and provides sufficient conditions for evading the climate tipping point. Combining this upper bound with Monte Carlo simulations of the stochastic climate model, we investigate the emission reduction and carbon capture scenarios that would avert the tipping point.

Atlantic Atmosphere–Ocean Interaction: A Stochastic Climate Model–Based Diagnosis

2005 ◽  
Vol 18 (7) ◽  
pp. 1086-1095 ◽  
Author(s):  
Timothy J. Mosedale ◽  
David B. Stephenson ◽  
Matthew Collins
Keyword(s):  
Simple Model ◽  
General Circulation Model ◽  
General Circulation ◽  
Climate Model ◽  
Surface Air Temperature ◽  
Circulation Model ◽  
Daily Data ◽  
Stochastic Climate Model ◽  
Fully Coupled ◽  
Northeastern Atlantic

Abstract A simple linear stochastic climate model of extratropical wintertime ocean–atmosphere coupling is used to diagnose the daily interactions between the ocean and the atmosphere in a fully coupled general circulation model. Monte Carlo simulations with the simple model show that the influence of the ocean on the atmosphere can be difficult to estimate, being biased low even with multiple decades of daily data. Despite this, fitting the simple model to the surface air temperature and sea surface temperature data from the complex general circulation model reveals an ocean-to-atmosphere influence in the northeastern Atlantic. Furthermore, the simple model is used to demonstrate that the ocean in this region greatly enhances the autocorrelation in overlying lower-tropospheric temperatures at lags from a few days to many months.

scholarly journals Coupled Variability and Predictability in a Stochastic Climate Model of the Tropical Atlantic

2008 ◽  
Vol 21 (23) ◽  
pp. 6247-6259 ◽  
Author(s):  
Faming Wang ◽  
Ping Chang
Keyword(s):  
Climate Model ◽  
Dominant Role ◽  
Error Variance ◽  
Ocean Dynamics ◽  
Tropical Atlantic ◽  
Coupled Models ◽  
Stochastic Forcing ◽  
Predictive Skill ◽  
Stochastic Climate Model ◽  
Coupled Variability

Abstract The coupled variability and predictability of the tropical Atlantic ocean–atmosphere system were analyzed within the framework of a linear stochastic climate model. Despite the existence of a meridional dipole as the leading mode, tropical Atlantic variability (TAV) is dominated by equatorial features and the subtropical variability is largely uncorrelated between the northern and southern Atlantic. This suggests that atmospheric stochastic forcing plays a dominant role in defining the spatial patterns of TAV, whereas the active air–sea feedbacks mainly enhance variability at interannual and decadal time scales, causing the spectra distinctive from the red spectrum. Under the stochastic forcing, the useful predictive skill for sea surface temperature measured by normalized error variance is limited to 2 months on average, which is 1 month longer than the predictive skill of damped persistence, indicating that the contribution of ocean dynamics and air–sea feedbacks is moderate in the tropical Atlantic. To achieve maximum predictability, processes such as ocean dynamics, thermodynamical and dynamical air–sea feedbacks, and the delicate mode–mode interactions should be correctly resolved in the coupled models. Therefore, predicting TAV poses more challenge than predicting El Niño in the tropical Pacific.

scholarly journals ESD Ideas: The stochastic climate model shows that underestimated Holocene trends and variability represent two sides of the same coin

2018 ◽  
Author(s):  
Gerrit Lohmann
Keyword(s):  
Climate Model ◽  
Sea Surface ◽  
System Sensitivity ◽  
Statistical Fluctuations ◽  
Fluctuation Dissipation ◽  
Temperature Trends ◽  
Fluctuation Dissipation Theorem ◽  
Stochastic Climate Model ◽  
Two Sides

Abstract. Holocene sea surface temperature trends and variability are underestimated in models as compared to paleoclimate data. The idea is presented that the trends and variability are related which is elaborated in a conceptual framework of the stochastic climate model. The relation is a consequence of the fluctuation-dissipation theorem, connecting the linear response of a system to its statistical fluctuations. Consequently, the spectrum can be used to estimate the timescale-dependent climate sensitivity. The non-normality in the propagation operator introduces enhanced long-term variability related to non-equilibrium and/or Earth system sensitivity.

Sign in / Sign up

Export Citation Format

Share Document