Papers by Boualem Khouider
Research in the Mathematical Sciences, Feb 17, 2021
The representation of clouds and associated processes of rain and snow formation remain one of th... more The representation of clouds and associated processes of rain and snow formation remain one of the major uncertainties in climate and weather prediction models. In a companion paper (part I), we systematically derived a two-moment bulk cloud microphysics model for warm rain based on the kinetic coalescence equation (KCE) and the use of stochastic approximations to close the high order moment terms, independently of the collision kernel. Conservation of mass and consistency of droplet number concentration of the evolving cloud distribution combined with numerical simulations are used as design principles to reduce the parametrization problem to three key parameters. Here, we further derive physical limits or region of validity for these three parameters based on the physics of collision and coalescence processes: “the stochastic region of validity”. More importantly, in this second part, we validate the stochastically derived bulk cloud microphysics model against detailed simulations based on the KCE and in comparison with a similar model by Seifert and Beheng (J Atmos Sci 59–60:265–281, 2001; hereafter SB01) who instead prescribed the shapes of the droplet distributions of rain and clouds in order to close the high-order moments and have done so specifically for one given kernel only. A thorough parameter exploration of the stochastic validity region is conducted, and parameter values that faithfully reproduce the detailed KCE results are identified. The results show that for typical parameter values, dependent on the environmental conditions, the new parameterization outperforms that of SB01 when compared to the KCE benchmark simulations. These results can be explored in the future to design a Markov jump process to randomly select adequate parameters within the validity region conditional on the environmental conditions and the age of the cloud. Furthermore, sensitivity tests indicate that the stochastically derived model can be used with a time step as large as 30 s without significantly compromising accuracy, which makes it very attractive to use in medium to long range weather prediction models.
Climate Dynamics, Dec 21, 2015
Theoretical and Computational Fluid Dynamics, May 17, 2008
Journal of the Atmospheric Sciences, Mar 1, 2022
Climate Dynamics, Dec 17, 2022
arXiv (Cornell University), Sep 30, 2010
Proceedings of the National Academy of Sciences of the United States of America, Sep 30, 2003
Journal of the Atmospheric Sciences, Apr 1, 2006
HAL (Le Centre pour la Communication Scientifique Directe), Jun 1, 2021
arXiv (Cornell University), Dec 27, 2015
Mathematics of planet earth, 2019
A major part of this book discusses the use of stochastic models for atmospheric convection, name... more A major part of this book discusses the use of stochastic models for atmospheric convection, namely through the use of a stochastic model for CIN and a stochastic multicloud model which pertains to tracking the statistics of clouds of various types. These models rely on the theory of stochastic processes and Markov chains in particular. Here, we provide a brief introduction to this topic to help the reader better appreciate and comprehend the cloud models. The expert reader can skip this chapter. It is intended to readers with no or rather very little background in probability theory and stochastic processes. Nonetheless, we assume that the reader is familiar with the basic notions of probability distributions and random variables.
Mathematics of planet earth, 2019
Global climate and numerical weather prediction models (GCMs and NWPMs) simulate the atmospheric ... more Global climate and numerical weather prediction models (GCMs and NWPMs) simulate the atmospheric large-scale dynamical processes by solving the hydrostatic or non-hydrostatic primitive equations on a fixed grid with a horizontal mesh size of 25 km to 200 km. Atmospheric processes occurring at smaller scales that cannot be represented on those coarse resolutions are either neglected or represented via subgrid models known as parameterizations [246, 132]. As already demonstrated in the previous chapters convective clouds have a major impact on the atmospheric dynamics on synoptic and planetary scales that cannot be ignored. Convectively coupled waves and convective motions in general make the bulk of the atmospheric circulation in the tropical latitudes and account for the majority of precipitation which falls in this part of the globe. Among those, the Madden-Julian oscillation (MJO) [164, 163], in particular, constitutes the major source of atmospheric variability on the intra-seasonal and planetary scales and interacts with important global weather an climate patterns [300, 302].
Mathematics of planet earth, 2019
Mathematics of planet earth, 2019
As already discussed, the tropical atmosphere harbours a scale hierarchy of convective wave distu... more As already discussed, the tropical atmosphere harbours a scale hierarchy of convective wave disturbances that are often embedded in each other like Russian dolls, evolving on a wide spectrum of scales ranging from the individual cloud cell diameter to the size of planetary scale disturbances such as the Madden-Julian oscillation, see Figure 8.1a. A particularly interesting issue is to understand the way these multiscale convective systems interact with each other across temporal and spatial scales. There is enough evidence from both observations and numerical simulations that momentum transport plays a genuine role in these interactions [147, 194, 145, 287, 177, 138, 113]; the smaller embedded waves provide turbulent fluxes for the envelopes, while the larger scale envelope waves provide a background advecting wind for the smaller scale waves.
Mathematics of planet earth, 2019
The most popular state variables that are used to define a thermodynamic system are the pressure,... more The most popular state variables that are used to define a thermodynamic system are the pressure, the temperature, and the composition. For our purpose, the atmospheric composition is divided into two main constituents: dry air, comprising nitrogen, oxygen, carbon dioxide, etc., and water in its various states or phases including water vapour (referred to herein as moisture), liquid water in the form of suspended cloud or rain droplets, ice crystals, and snowflakes.
Mathematics of planet earth, 2019
The first evidence of equatorially trapped waves in observational records appeared in 1966 in the... more The first evidence of equatorially trapped waves in observational records appeared in 1966 in the work of Yanai and Maruyama [294], at the same time as the theoretical work of Matsuno [187]. Yanai and Maruyama [294] found signals of wave-like motion with strong cross equatorial wind in US Navy stratospheric wind data (which were apparently used to monitor nuclear activity during the cold war) when they were looking for evidence of eddy momentum transport as a plausible energy source for the quasi-biannual oscillation (QBO) in the equatorial stratosphere [188]. These waves correspond to the mixed Rossby-gravity waves from the Matsuno theory, which are also sometimes called Yanai-Maruyama or simply Yanai waves. Two years later Wallace and Kousky [271] (see also [83]) published their work on the discovery of Kelvin waves in the tropical stratosphere, which unlike those identified earlier by Yanai and Maruyama they are characterized by dominating zonal winds in phase with pressure perturbations. They were also motivated by the search for an energy source for the QBO in the form of wave eddy momentum.
Mathematics of planet earth, 2019
This chapter introduces the reader to basic simple ideas for convectively coupled wave models mos... more This chapter introduces the reader to basic simple ideas for convectively coupled wave models mostly in order to put the multicloud model, which will be discussed in Chapter 6, in the context of preceding theories. It explores some of the ideas that have been proposed in the literature and their main characteristics and pitfalls using simplistic models.
John Wiley & Sons, Inc. eBooks, Aug 2, 2013
Journal of Advances in Modeling Earth Systems, Jun 1, 2019
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Papers by Boualem Khouider