journal: Mathematics of Climate and Weather Forecasting

Ceased

Open Access Published from September 1, 2015 to January 1, 2020

Mathematics of Climate and Weather Forecasting

ISSN: 2353-6438

About this journal

THE JOURNAL IS CLOSED FOR SUBMISSIONS

MCWF was an open access journal that published articles that use mathematical methods in climate change science and weather forecasting. The scope included numerical methods, stochastic processes, PDE analysis, time series analysis, data filtering and assimilation, applied to any topic of atmosphere and ocean sciences.

The journal was published in Open Access model and is archived in Portico.

All authors retain copyright, unless – due to their local circumstances – their work is not copyrighted. The copyrights are governed by the Creative-Commons license.

The journal was edited by: Prof. Boualem Khouider, University of Victoria, Canada

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Volume 6 Issue 1

January 2020

Open Access February 1, 2020

Regularity “in Large” for the 3D Salmon’s Planetary Geostrophic Model of Ocean Dynamics

Chongsheng Cao, Edriss S. Titi

Page range: 1-15

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Abstract

It is well known, by now, that the three-dimensional non-viscous planetary geostrophic model, with vertical hydrostatic balance and horizontal Rayleigh friction/damping, coupled to the heat diffusion and transport, is mathematically ill-posed. This is because the no-normal flow physical boundary condition implicitly produces an additional boundary condition for the temperature at the lateral boundary. This additional boundary condition is different, because of the Coriolis forcing term, than the no-heat-flux physical boundary condition. Consequently, the second order parabolic heat equation is over-determined with two different boundary conditions. In a previous work we proposed one remedy to this problem by introducing a fourth-order artificial hyper-diffusion to the heat transport equation and proved global regularity for the proposed model. A shortcoming of this higher-oder diffusion is the loss of the maximum/minimum principle for the heat equation. Another remedy for this problem was suggested by R. Salmon by introducing an additional Rayleigh-like friction/damping term for the vertical component of the velocity in the hydrostatic balance equation. In this paper we prove the global, for all time and all initial data, well-posedness of strong solutions to the three-dimensional Salmon’s planetary geostrophic model of ocean dynamics. That is, we show global existence, uniqueness and continuous dependence of the strong solutions on initial data for this model. Unlike the 3D viscous PG model, we are still unable to show the uniqueness of the weak solution. Notably, we also demonstrate in what sense the additional damping term, suggested by Salmon, annihilate the ill-posedness in the original system; consequently, it can be viewed as “regularizing” term that can possibly be used to regularize other related systems.

Open Access March 20, 2020

Shallow-cloud impact on climate and uncertainty: A simple stochastic model

Eli A. Mueller, Samuel N. Stechmann

Page range: 16-37

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Abstract

Shallow clouds are a major source of uncertainty in climate predictions. Several different sources of the uncertainty are possible—e.g., from different models of shallow cloud behavior, which could produce differing predictions and ensemble spread within an ensemble of models, or from inherent, natural variability of shallow clouds. Here, the latter (inherent variability) is investigated, using a simple model of radiative statistical equilibrium, with oceanic and atmospheric boundary layer temperatures, T o and T a , and with moisture q and basic cloud processes. Stochastic variability is used to generate a statistical equilibrium with climate variability. The results show that the intrinsic variability of the climate is enhanced due to the presence of shallow clouds. In particular, the on-and-off switching of cloud formation and decay is a source of additional climate variability and uncertainty, beyond the variability of a cloud-free climate. Furthermore, a sharp transition in the mean climate occurs as environmental parameters are changed, and the sharp transition in the mean is also accompanied by a substantial enhancement of climate sensitivity and uncertainty. Two viewpoints of this behavior are described, based on bifurcations and phase transitions/statistical physics. The sharp regime transitions are associated with changes in several parameters, including cloud albedo and longwave absorptivity/carbon dioxide concentration, and the climate state transitions between a partially cloudy state and a state of full cloud cover like closed-cell stratocumulus clouds. Ideas of statistical physics can provide a conceptual perspective to link the climate state transitions, increased climate uncertainty, and other related behavior.

Open Access July 30, 2020

Expanding Grids for Efficient Cloud Dynamics Simulations Across Scales

David H. Marsico, Samuel N. Stechmann

Page range: 38-49

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Abstract

With large eddy simulations (LES) and/or cloud-resolving models (CRMs), it is now possible to simultaneously simulate shallow and deep convection. However, using traditional methods, the computational expense is typically very large, due to the small grid spacings needed to resolve shallow clouds. Here, the main purpose is to present a method that is computationally less expensive by a factor of roughly 10 to 50. Unlike traditional grid stretching of only the vertical z grid spacing, the present method involves expansion of the grid spacing in all coordinate directions (x,y,z) and time t. A ˝ne grid spacing of O(10)-O(100) m can be used near the surface to resolve boundary layer turbulence, and the grid spacing expands to be O(1000) m at higher altitudes, which reduces computational cost while still resolving deep convection. Example simulations are conducted with a simpli˝ed LES/CRM in 2D to verify the theoretical cost savings.

Open Access December 31, 2020

Estimation of seasonal boundaries using temperature data: a case of northwest part of Bangladesh

Syed Mustafizur Rahman, Syed Mahbubur Rahman, Md. Shuzon Ali, Md. Abdullah Al Mamun, Md. Nezam Uddin

Page range: 50-62

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Abstract

Seasons are the divisions of the year into months or days according to the changes in weather, ecology and the intensity of sunlight in a given region. The temperature cycle plays a major role in defining the meteorological seasons of the year. This study aims at investigating seasonal boundaries applying harmonic analysis in daily temperature for the duration of 30 years, recorded at six stations from 1988 to 2017, in northwest part of Bangladesh. Year by year harmonic analyses of daily temperature data in each station have been carried out to observe temporal and spatial variations in seasonal lengths. Periodic nature of daily temperature has been investigated employing spectral analysis, and it has been found that the estimated periodicities have higher power densities of the frequencies at 0.0027 and 0.0053 cycles/day. Some other minor periodic natures have also been observed in the analyses. Using the frequencies between 0.0027 to 0.0278 cycles/day, the observed periodicities in spectral analysis, harmonic analyses of minimum and maximum temperatures have found four seasonal boundaries every year in each of the stations. The estimated seasonal boundaries for the region fall between 19-25 February, 19-23 May, 18-20 August and 17-22 November. Since seasonal variability results in imbalance in water, moisture and heat, it has the potential to significantly affect agricultural production. Hence, the seasons and seasonal lengths presented in this research may help the concerned authorities take measures to reduce the risks for crop productivity to face the challenges arise from changing climate. Moreover, the results obtained are likely to contribute in introducing local climate calendar.

Open Access January 27, 2021

On strongly nonlinear gravity waves in a vertically sheared atmosphere

Part I: Spectral stability of the refracted wave

Mark Schlutow, Georg S. Voelker

Page range: 63-74

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Abstract

We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

Open Access January 27, 2021

Pattern formation in clouds via Turing instabilities

Juliane Rosemeier, Peter Spichtinger

Page range: 75-96

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Abstract

Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare. From many scientific disciplines the occurrence of patterns in non-equilibrium systems due to Turing instabilities is known, i.e. unstable modes grow and form spatial structures. In this study we investigate a generic cloud model for the possibility of Turing instabilities. For this purpose, the model is extended by diffusion terms. We can show that for some cloud models, i.e special cases of the generic model, no Turing instabilities are possible. However, we also present a general class of cloud models, where Turing instabilities can occur. A key requisite is the occurrence of (weakly) nonlinear terms for accretion. Using numerical simulations for a special case of the general class of cloud models, we show spatial patterns of clouds in one and two spatial dimensions. From the numerical simulations we can see that the competition between collision terms and sedimentation is an important issue for the existence of pattern formation.

Open Access December 31, 2020

Generalized modulation theory for strongly nonlinear gravity waves in a compressible atmosphere

Mark Schlutow, Erik Wahlén

Page range: 97-112

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Abstract

This study investigates strongly nonlinear gravity waves in the compressible atmosphere from the Earth’s surface to the deep atmosphere. These waves are effectively described by Grimshaw’s dissipative modulation equations which provide the basis for finding stationary solutions such as mountain lee waves and testing their stability in an analytic fashion. Assuming energetically consistent boundary and far-field conditions, that is no energy flux through the surface, free-slip boundary, and finite total energy, general wave solutions are derived and illustrated in terms of realistic background fields. These assumptions also imply that the wave-Reynolds number must become less than unity above a certain height. The modulational stability of admissible, both non-hydrostatic and hydrostatic, waves is examined. It turns out that, when accounting for the self-induced mean flow, the wave-Froude number has a resonance condition. If it becomes 1/1/21/\sqrt 2, then the wave destabilizes due to perturbations from the essential spectrum of the linearized modulation equations. However, if the horizontal wavelength is large enough, waves overturn before they can reach the modulational stability condition.

Mathematical Citation Quotient	0.41

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Editorial

Journal Editor
Boualem Khouider, University of Victoria, Canada

Editorial Advisory Board
Henk A. Dijkstra, Utrecht University, The Netherlands
Michael Ghil, University of California, Los Angeles, USA and Ecole Normale Supérieure, Paris, France
Christian Jakob, Monash University, Australia
Hans G. Kaper, Georgetown University and Argonne National Laboratory, USA
George Kiladis, NOAA - National Oceanic and Atmospheric Administration, USA
Rupert Klein, Freie Universitaet Berlin, Germany
Andrew J. Majda, New York University, USA
Mitchell Moncrieff, NCAR - National Center for Atmospheric Research, USA
Leslie Smith, University of Wisconsin - Madison, USA
Roger Temam, Indiana University, Bloomington, USA
Edriss Titi, Texas A&M, USA, and Weizmann Institute of Science, Israel
Joseph Tribbia, NCAR - National Center for Atmospheric Research, USA
Chidong Zhang, University of Miami, USA
Francis Zwiers, Pacific Institute for Climate Consortium, University of Victoria, Canada

Publisher
DE GRUYTER Poland
Bogumiła Zuga 32A Str.
01-811 Warsaw, Poland
T: +48 22 701 50 15

Editorial Contact
Agnieszka.Bednarczyk-Drag@degruyter.com

(Deutsch)

Type: Journal
Language: English
Publisher: De Gruyter Open Access
First published: September 1, 2015
Last published: January 1, 2020
Publication Frequency: 1 Issue per Year
Audience: researchers in the field of weather forecasting