Mathematics of Climate and Weather Forecasting最新文献

On strongly nonlinear gravity waves in a vertically sheared atmosphere 关于垂直剪切大气中的强非线性重力波

Mathematics of Climate and Weather Forecasting Pub Date : 2020-01-01 DOI: 10.1515/mcwf-2020-0103

M. Schlutow, G. S. Voelker

引用次数: 1

Pattern formation in clouds via Turing instabilities 图灵不稳定性在云中的模式形成

Mathematics of Climate and Weather Forecasting Pub Date : 2020-01-01 DOI: 10.1515/mcwf-2020-0104

Juliane Rosemeier, P. Spichtinger

{"title":"Pattern formation in clouds via Turing instabilities","authors":"Juliane Rosemeier, P. Spichtinger","doi":"10.1515/mcwf-2020-0104","DOIUrl":"https://doi.org/10.1515/mcwf-2020-0104","url":null,"abstract":"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.","PeriodicalId":106200,"journal":{"name":"Mathematics of Climate and Weather Forecasting","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130590162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Shallow-cloud impact on climate and uncertainty: A simple stochastic model 浅云对气候和不确定性的影响:一个简单的随机模式

Mathematics of Climate and Weather Forecasting Pub Date : 2020-01-01 DOI: 10.1515/mcwf-2020-0002

E. A. Mueller, S. Stechmann

{"title":"Shallow-cloud impact on climate and uncertainty: A simple stochastic model","authors":"E. A. Mueller, S. Stechmann","doi":"10.1515/mcwf-2020-0002","DOIUrl":"https://doi.org/10.1515/mcwf-2020-0002","url":null,"abstract":"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, To and Ta, 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.","PeriodicalId":106200,"journal":{"name":"Mathematics of Climate and Weather Forecasting","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124220677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Expanding Grids for Efficient Cloud Dynamics Simulations Across Scales 扩展网格的有效云动力学模拟跨尺度

Mathematics of Climate and Weather Forecasting Pub Date : 2020-01-01 DOI: 10.1515/mcwf-2020-0101

David H. Marsico, S. Stechmann

引用次数: 4

Generalized modulation theory for strongly nonlinear gravity waves in a compressible atmosphere 可压缩大气中强非线性重力波的广义调制理论

Mathematics of Climate and Weather Forecasting Pub Date : 2019-11-28 DOI: 10.1515/mcwf-2020-0105

M. Schlutow, E. Wahlén

{"title":"Generalized modulation theory for strongly nonlinear gravity waves in a compressible atmosphere","authors":"M. Schlutow, E. Wahlén","doi":"10.1515/mcwf-2020-0105","DOIUrl":"https://doi.org/10.1515/mcwf-2020-0105","url":null,"abstract":"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.","PeriodicalId":106200,"journal":{"name":"Mathematics of Climate and Weather Forecasting","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134261160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Numerical Development and Evaluation of an Energy Conserving Conceptual Stochastic Climate Model 节能概念随机气候模型的数值开发与评价

Mathematics of Climate and Weather Forecasting Pub Date : 2019-02-01 DOI: 10.1515/mcwf-2019-0004

F. Gugole, C. Franzke

{"title":"Numerical Development and Evaluation of an Energy Conserving Conceptual Stochastic Climate Model","authors":"F. Gugole, C. Franzke","doi":"10.1515/mcwf-2019-0004","DOIUrl":"https://doi.org/10.1515/mcwf-2019-0004","url":null,"abstract":"Abstract In 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.","PeriodicalId":106200,"journal":{"name":"Mathematics of Climate and Weather Forecasting","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123970907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 11

Fractional Order on the Impact of Climate Change With Dominant Earth’s Fluctuations 分数阶对地球主导波动下气候变化影响的研究

Mathematics of Climate and Weather Forecasting Pub Date : 2019-02-01 DOI: 10.1515/mcwf-2019-0001

S. Eze, M. Oyesanya

引用次数: 8

Optimal Algorithms for Computing Average Temperatures 计算平均温度的最优算法

Mathematics of Climate and Weather Forecasting Pub Date : 2019-02-01 DOI: 10.1515/mcwf-2019-0003

S. Foucart, Matthew Hielsberg, G. Mullendore, G. Petrova, P. Wojtaszczyk

引用次数: 0

Stochastic Galerkin method for cloud simulation 云模拟的随机伽辽金方法

Mathematics of Climate and Weather Forecasting Pub Date : 2018-11-30 DOI: 10.1515/mcwf-2019-0005

A. Chertock, A. Kurganov, M. Lukáčová-Medvid’ová, P. Spichtinger, B. Wiebe

引用次数: 12

Intercomparison of Warm-Rain Bulk Microphysics Schemes using Asymptotics 暖雨体微物理方案的渐近比较

Mathematics of Climate and Weather Forecasting Pub Date : 2018-11-28 DOI: 10.1515/mcwf-2018-0005

Juliane Rosemeier, Manuel Baumgartner, P. Spichtinger

{"title":"Intercomparison of Warm-Rain Bulk Microphysics Schemes using Asymptotics","authors":"Juliane Rosemeier, Manuel Baumgartner, P. Spichtinger","doi":"10.1515/mcwf-2018-0005","DOIUrl":"https://doi.org/10.1515/mcwf-2018-0005","url":null,"abstract":"Abstract Clouds are important components of the atmosphere. As it is usually not possible to treat them as ensembles of huge numbers of particles, parameterizations on the basis of averaged quantities (mass and/or number concentration) must be derived. Since no first-principles derivations of such averaged schemes are available today, many alternative approximating schemes of cloud processes exist. Most of these come in the form of nonlinear differential equations. It is unclear whether these different cloud schemes behave similarly under controlled local conditions, and much less so when they are embedded dynamically in a full atmospheric flow model. We use mathematical methods from the theory of dynamical systems and asymptotic analysis to compare two operational cloud schemes and one research scheme qualitatively in a simplified context in which the moist dynamics is reduced to a system of ODEs. It turns out that these schemes behave qualitatively differently on shorter time scales, whereas at least their long time behavior is similar under certain conditions. These results show that the quality of computational forecasts of moist atmospheric flows will generally depend strongly on the formulation of the cloud schemes used.","PeriodicalId":106200,"journal":{"name":"Mathematics of Climate and Weather Forecasting","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132992695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7