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Global Convergence of Over-parameterized Deep Equilibrium Models [article]

Zenan Ling, Xingyu Xie, Qiuhao Wang, Zongpeng Zhang, Zhouchen Lin
2022 arXiv   pre-print
A deep equilibrium model (DEQ) is implicitly defined through an equilibrium point of an infinite-depth weight-tied model with an input-injection.  ...  The training dynamics of over-parameterized DEQs are investigated in this study.  ...  (2) We show that the unique equilibrium point of an over-parameterized DEQ always exists throughout the training process, even without using any normalization or re-parameterization method. (3) To the  ... 
arXiv:2205.13814v1 fatcat:yvqtrkdplbg4pcrq6yrvi4yaby

The interaction between moist convection and the atmospheric circulation in the tropics

Lorenzo Tomassini
2020 Bulletin of The American Meteorological Society - (BAMS)  
However, the implementation of these new insights in numerical models lags behind.  ...  Two main schools of thought are highlighted: (i) one which emphasizes the lower-level control of convection through moisture convergence and variations in convective inhibition, and (ii) one which sees  ...  Very valuable and constructive comments and suggestions by Brian Mapes, Larissa Back, Richard Seager, an anonymous reviewer, and a number of other colleagues helped to significantly improve the manuscript  ... 
doi:10.1175/bams-d-19-0180.1 fatcat:ni2x7os3tnfqdh7o2vkd7gzuom

Boundary layer control on convective available potential energy: Implications for cumulus parameterization

Leo J. Donner
2003 Journal of Geophysical Research  
Cumulus parameterizations based on quasi-equilibrium may be limited in their ability to model diurnal cycles as a result.  ...  The coupling under conditions of deep convection implies a constraint on the intensity of deep convection which can be used as a closure for cumulus parameterization.  ...  Discussions with Dave Randall (Colorado State University), Guang Zhang (Scripps Institution of Oceanography), Jun-Ichi Yano (CNRM Meteo France), and Olivier Pauluis (Princeton University) on quasi-equilibrium  ... 
doi:10.1029/2003jd003773 fatcat:ubbhn75lwzb5vfx3wtvngche4q

The NCAR Climate System Model Global Ocean Component*

Peter R. Gent, Frank O. Bryan, Gokhan Danabasoglu, Scott C. Doney, William R. Holland, William G. Large, James C. McWilliams
1998 Journal of Climate  
This paper describes the global ocean component of the NCAR Climate System Model. New parameterizations of the effects of mesoscale eddies and of the upper-ocean boundary layer are included.  ...  Updated forcing fields are used to drive the ocean-alone solution, which is integrated long enough so that it is in equilibrium.  ...  Gokhan Danabasoglu and Jan Morzel were supported by the NOAA Office of Global Programs under Grant NA56GP0246.  ... 
doi:10.1175/1520-0442(1998)011<1287:tncsmg>2.0.co;2 fatcat:6iogeu4us5er5mrnu6cscwduzu

On the Theory of Implicit Deep Learning: Global Convergence with Implicit Layers [article]

Kenji Kawaguchi
2021 arXiv   pre-print
A deep equilibrium model uses implicit layers, which are implicitly defined through an equilibrium point of an infinite sequence of computation.  ...  Despite non-convexity, convergence to global optimum at a linear rate is guaranteed without any assumption on the width of the models, allowing the width to be smaller than the output dimension and the  ...  and over-parameterization.  ... 
arXiv:2102.07346v2 fatcat:qw44ewh7wjd6va4iu4psxgxu4q

Skill of Medium-Range Forecasts over the Indian Monsoon Region Using Different Parameterizations of Deep Convection

Someshwar Das, A. K. Mitra, G. R. Iyengar, J. Singh
2002 Weather and forecasting  
using three different parameterizations of deep convection namely, a Kuo-Anthes-type cumulus parameterization scheme referred to as "KUO" scheme, the relaxed Arakawa-Schubert (RAS) scheme, and the simplified  ...  The operational global spectral model of the National Center for Medium Range Weather Forecasting (NCMRWF) at T80 resolution and 18 vertical levels has been used to study the skill of medium-range forecasts  ...  The original model of NCMRWF was adopted from NCEP. The authors are grateful to Drs. Srinivas Moorthi and H.-L. Pan of NCEP for providing the RAS and SAS schemes.  ... 
doi:10.1175/1520-0434(2002)017<1194:somrfo>2.0.co;2 fatcat:a6ul3jr53bh2pi2yjhcvxmu47u

Understanding and representing atmospheric convection across scales: recommendations from the meeting held at Dartington Hall, Devon, UK, 28-30 January 2013

Christopher E. Holloway, Jon C. Petch, Robert J. Beare, Peter Bechtold, George C. Craig, Stephen H. Derbyshire, Leo J. Donner, Paul R. Field, Suzanne L. Gray, John H. Marsham, Douglas J. Parker, Robert S. Plant (+4 others)
2014 Atmospheric Science Letters  
The main recommendation was to facilitate the development of physically based convective parameterizations that are scale-aware, non-local, non-equilibrium, and stochastic.  ...  Specific recommendations included increased convective-scale observations, high-resolution virtual laboratories, and a system of parameterization test beds with a range of complexities.  ...  the Tropopause Folding, Stratospheric Intrusions and Deep Convection (TROSIAD) project, Grant NE/H008225/1.  ... 
doi:10.1002/asl2.508 fatcat:hpc3epgxp5eorbfb2koseomliy

An offline implicit solver for simulating prebomb radiocarbon

Ann Bardin, François Primeau, Keith Lindsay
2014 Ocean Modelling  
We present an implicit solver for computing prebomb D 14 C that requires the equivalent of only a few tens of model years to reach equilibrium.  ...  It takes several thousand years for the deep-ocean concentration of natural radiocarbon to come to equilibrium with surface fluxes, making it computationally too expensive to routinely simulate it with  ...  Acknowledgments This work was supported by grant from the Department of Energy Biological and Environmental Sciences Division. F.  ... 
doi:10.1016/j.ocemod.2013.09.008 fatcat:4wbn7zvqivefjjyqtp2shperh4

An improved parameterization of tidal mixing for ocean models

A. Schmittner, G. D. Egbert
2013 Geoscientific Model Development Discussions  
Two modifications to an existing scheme of tidal mixing are implemented in the coarse resolution ocean component of a global climate model.  ...  Estimates based on satellite altimetry lead to larger diffusivities in the deep ocean and hence a stronger deep overturning circulation in our climate model that is in better agreement with observation  ...  "Deep global" is the deep overturning cell calculated as the (negative) minimum of the global stream function below 1.5 km depth.  ... 
doi:10.5194/gmdd-6-4475-2013 fatcat:xxinhrcdbbaw3gcq7rc76q5m2y

An improved parameterization of tidal mixing for ocean models

A. Schmittner, G. D. Egbert
2014 Geoscientific Model Development  
</strong> Two modifications to an existing scheme of tidal mixing are implemented in the coarse resolution ocean component of a global climate model.  ...  Estimates based on satellite altimetry lead to larger diffusivities in the deep ocean and hence a stronger deep overturning circulation in our climate model that is in better agreement with observation  ...  "Deep global" is the deep overturning cell calculated as the (negative) minimum of the global stream function below 1.5 km depth.  ... 
doi:10.5194/gmd-7-211-2014 fatcat:agcuk7dynrglnfh2nx3vj4dxbi

On using the seasonal cycle to interpret extratropical temperature changes since 1950

Karen A. McKinnon, Peter Huybers
2014 Geophysical Research Letters  
Representation of the equilibrium near-surface air temperature change, ΔT i,j , due to land-ocean heat fluxes parameterized in the EBM, is particularly simple for a fixed SST model simulation.  ...  Unlike the seasonal cycle analysis, meridional heat flux convergence anomalies are not included or parameterized.  ...  The calculation of seasonal feedbacks in CCSM4 was undertaken in collaboration with Cecilia Bitz during a visit by K.A.M. to the University of Washington.  ... 
doi:10.1002/2014gl060404 fatcat:hs7grg5yy5gb7ciyxiegww4hhe

Imprint of the convective parameterization and sea-surface temperature on large-scale convective self-aggregation

Tobias Becker, Bjorn Stevens, Cathy Hohenegger
2017 Journal of Advances in Modeling Earth Systems  
Radiative-convective equilibrium simulations with the general circulation model ECHAM6 are used to explore to what extent the dependence of large-scale convective self-aggregation on sea-surface temperature  ...  is set to zero or when the convective parameterization is removed from the model.  ...  Journal of Advances in Modeling Earth Systems 10.1002/2016MS000865  ... 
doi:10.1002/2016ms000865 fatcat:zaxdm6t5srfcxhivemabhmb4ni

Equilibrium Vs. Activation Control of Large-Scale Variations of Tropical Deep Convection [chapter]

Brian E. Mapes
1997 The Physics and Parameterization of Moist Atmospheric Convection  
This essay highlights the distinction between processes which supply moisture or available energy over the depth of the convecting layer (equilibrium control), versus inhibition and initiation processes  ...  The hypothesis that activation control may prevail on all scales short of globally-averaged climate is difficult to refute.  ...  NOAA TOGA-COARE grant, jointly funded by the Office of Global Programs of the U.S.  ... 
doi:10.1007/978-94-015-8828-7_13 fatcat:ynex7pbs7jfwznmitznx4yyjde

REAL-TIME, ADAPTIVE LEARNING VIA PARAMETERIZED EXPECTATIONS

Michele Berardi, John Duffy
2013 Macroeconomic Dynamics  
We argue that this method of real-time parameterized expectations learning provides a plausible alternative to real-time adaptive learning dynamics under linearized versions of the same nonlinear system  ...  Rather than linearizing nonlinear Euler equations where expectations play a role around a steady state, we instead approximate the nonlinear expected values using the method of parameterized expectations  ...  for mean convergence times and variances over the 100 runs of the 9 model parameterizations.  ... 
doi:10.1017/s1365100513000370 fatcat:mh7nckgnq5e6dfacnpwqvpa374

Phenomenology of convection-parameterization closure

J.-I. Yano, M. Bister, Z. Fuchs, L. Gerard, V. Phillips, S. Barkidija, J.-M. Piriou
2012 Atmospheric Chemistry and Physics Discussions  
The present manuscript is an outcome of discussions over e-mail organized under a framework of COST Action ES0905.  ...  Quaas The publication of this article is financed by CNRS-INSU.  ...  We pose this question as a way of introducing the closure problem of convection parameterization both from global and regional perspectives.  ... 
doi:10.5194/acpd-12-25743-2012 fatcat:x3qc7icslba7hkrdnoc7fimxbq
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