Extreme weather and climate-related events occur in a particular place, by definition, infrequently. It is therefore challenging to detect systematic changes in their occurrence given the relative shortness of observational records. However, there is a clear interest from outside the climate science community in the extent to which recent damaging extreme events can be linked to human-induced climate change or natural climate variability. Event attribution studies seek to determine to what extent anthropogenic climate change has altered the probability or magnitude of particular events. They have shown clear evidence for human influence having increased the probability of many extremely warm seasonal temperatures and reduced the probability of extremely cold seasonal temperatures in many parts of the world. The evidence for human influence on the probability of extreme precipitation events, droughts, and storms is more mixed. Although the science of event attribution has developed rapidly in recent years, geographical coverage of events remains patchy and based on the interests and capabilities of individual research groups. The development of operational event attribution would allow a more timely and methodical production of attribution assessments than currently obtained on an ad hoc basis. For event attribution assessments to be most useful, remaining scientific uncertainties need to be robustly assessed and the results clearly communicated. This requires the continuing development of methodologies to assess the reliability of event attribution results and further work to understand the potential utility of event attribution for stakeholder groups and decision makers.

Attribution of Extreme Weather Events in the Context of Climate Change

Although the concept of entropy is originated from thermodynamics, its concepts and relevant principles, especially the principles of maximum entropy and minimum cross-entropy, have been extensively applied in finance. In this paper, we review the concepts and principles of entropy, as well as their applications in the field of finance, especially in portfolio selection and asset pricing. Furthermore, we review the effects of the applications of entropy and compare them with other traditional and new methods.

Applications of Entropy in Finance: A Review

[1] The complex system of the Earth's magnetosphere corresponds to an open spatially extended nonequilibrium (input-output) dynamical system. The nonextensive Tsallis entropy has been recently introduced as an appropriate information measure to investigate dynamical complexity in the magnetosphere. The method has been employed for analyzing Dst time series and gave promising results, detecting the complexity dissimilarity among different physiological and pathological magnetospheric states (i.e., prestorm activity and intense magnetic storms, respectively). This paper explores the applicability and effectiveness of a variety of computable entropy measures (e.g., block entropy, Kolmogorov entropy, T complexity, and approximate entropy) to the investigation of dynamical complexity in the magnetosphere. We show that as the magnetic storm approaches there is clear evidence of significant lower complexity in the magnetosphere. The observed higher degree of organization of the system agrees with that inferred previously, from an independent linear fractal spectral analysis based on wavelet transforms. This convergence between nonlinear and linear analyses provides a more reliable detection of the transition from the quiet time to the storm time magnetosphere, thus showing evidence that the occurrence of an intense magnetic storm is imminent. More precisely, we claim that our results suggest an important principle: significant complexity decrease and accession of persistency in Dst time series can be confirmed as the magnetic storm approaches, which can be used as diagnostic tools for the magnetospheric injury (global instability). Overall, approximate entropy and Tsallis entropy yield superior results for detecting dynamical complexity changes in the magnetosphere in comparison to the other entropy measures presented herein. Ultimately, the analysis tools developed in the course of this study for the treatment of Dst index can provide convenience for space weather applications.

Investigating dynamical complexity in the magnetosphere using various entropy measures

This paper reviews the major progress on development of the science and prediction of heavy rainfall over China since the beginning of the reform and opening-up of new China (roughly between 1980 and 2019). The progress of research on the physical mechanisms of heavy rainfall over China is summarized from three perspectives: 1) the relevant synoptic weather systems, 2) heavy rainfall in major sub-regions of China, and 3) heavy rainfall induced by typhoons. The development and application of forecasting techniques for heavy rainfall are summarized in terms of numerical weather prediction techniques and objective forecasting methods. Greatly aided by the rapid progress in meteorological observing technology and substantial improvement in electronic computing, studies of heavy rainfall in China have advanced to investigating the evolution of heavy-rain-producing storms and observational analysis of the cloud microphysical features. A deeper and more systematic understanding of the synoptic systems of importance to the production of heavy rainfall has also been developed. Operational forecast of heavy rainfall in China has changed from subjective weather event forecasts to a combination of both subjective and objective quantitative precipitation forecasts, and is now advancing toward probabilistic quantitative precipitation forecasts with the provision of forecast uncertainty information.

Science and Prediction of Heavy Rainfall over China: Research Progress since the Reform and Opening-Up of New China

The pre-summer heavy rainfall over southern China during 3–8 June 2008 is simulated using a two-dimensional cloud-resolving model. The model is integrated with imposed zonally uniform vertical velocity, zonal wind, horizontal temperature and vapour advection from National Centers for Environmental Prediction (NCEP)/Global Data Assimilation System (GDAS) data. The effects of vertical wind shear and cloud radiative processes on the response of rainfall to largescale forcing are analysed through the comparison of two sensitivity experiments with the control experiment. One sensitivity experiment excludes the large-scale vertical wind shear and the other excludes the cloud radiative effects. During the decay phase of convection, the increase in model domain-mean surface rain-rate resulting from the exclusion of vertical wind shear is associated with the slowdown in the decrease of perturbation kinetic energy due to the exclusion of barotropic conversion from mean kinetic energy to perturbation kinetic energy. The increase in domain-mean rain-rate from the exclusion of cloud radiative effects is related to the enhancement of condensation and associated latent heat as a result of strengthened radiative cooling. The increase in the domain-mean surface rain-rate is mainly associated with the increase of convective rainfall, which is in turn related to the local atmospheric change from moistening to drying. During the onset and mature phases of convection, the domain-mean surface rain-rates are generally insensitive to vertical wind shear and cloud radiative effects whereas convective and stratiform rain-rates are sensitive to vertical wind shear and cloud radiative effects. The decrease in convective rain-rate and the increase in stratiform rain-rate are primarilyassociated with the enhanced transport of hydrometeor concentration from convective regions to raining stratiform regions. Copyright c � 2011 Royal

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Effects of vertical wind shear and cloud radiative processes on responses of rainfall to the large‐scale forcing during pre‐summer heavy rainfall over southern China

The concept of entropy and its relevant principles, mainly the principle of maximum entropy production (MEP), the effect of negative entropy flow (NEF) on the organization of atmospheric systems and the principle of the Second Law of thermodynamics, as well as their applications to atmospheric sciences, are reviewed. Some formulations of sub-grid processes such as diffusion parameterization schemes in computational geophysical fluid dynamics that can be improved based on full-irreversibility are also discussed, although they have not yet been systematically subjected to scrutiny from the perspective of the entropy budgets. A comparative investigation shows that the principle of MEP applies to the entropy production of macroscopic fluxes and determines the most probable state, that is, a system may choose a development meta-stable trajectory with a smaller production since entropy production behavior involves many specific dynamical and thermodynamic processes in the atmosphere and the extremal principles only provide a general insight into the overall configuration of the atmosphere. In contrast to the principle of MEP, the analysis of NEF is able to provide a new insight into the mechanism responsible for the evolution of a weather system as well as a new approach to predicting its track and intensity trend.

https://www.mdpi.com/1099-4300/13/1/211/pdf

Understanding Atmospheric Behaviour in Terms of Entropy: A Review of Applications of the Second Law of Thermodynamics to Meteorology

Torrential rainfall processes associated with a landfall of severe tropical storm Bilis (2006): a two-dimensional cloud-resolving modeling study.

A mixed rain-snow storm associated with a strong burst of cold air and development of an extratropical cyclone occurred over North China from 3 to 5 November 2012. This early snowfall event was characterized by a dramatic drop in temperature, strong winds, high precipitation intensity, broad spatial extent, and coexistence of multi-phase precipitating hydrometeors. This study investigates the multi-scale interactions between the large-scale circulation background and the synoptic-scale weather systems associated with the storm. The results are as follows. (1) The Arctic Oscillation (AO) had been in its negative phase long before the event, leading to southward advection of cold air into North China in advance of the storm. (2) The large-scale atmospheric circulation experienced a decreased number of long waves upstream of North China prior to the storm, resulting in reduced wave velocity and an almost stagnant low pressure system (extratropical cyclone) over North China. (3) An Ω-shaped blocking high over East Asia and the western Pacific obstructed the eastward movement of an upstream trough, allowing the corresponding surface cyclone to stabilize and persist over Beijing and its neighboring areas. This blocking high was a major factor in making this event a historically most severe precipitation event in autumn in Beijing for the past 60 years. (4) Baroclinic instability at lower levels gave rise to rapid development of the cyclone under the classical “second type” development mechanism for extratropical cyclones. (5) Moisture originated from the Yellow Sea entered the slowly-moving cyclone in a steady stream, creating fairly favorable water vapor supply for the heavy rainfall-snowfall, especially during the later stage of the cyclone development. (6) Moisture transport and frontal lifting triggered low-level instability and updrafts. Intensification of the front enhanced the vertical wind shear, causing conditional symmetric instability (CSI) to expand upward within the unstable lower troposphere, and to eventually gear into the CSI region of the upper troposphere, which facilitated the upward development of low-level updrafts.

A case study of the November 2012 mixed rain-snow storm over North China

The rare snowfall event in 2012 over North China due to the development of an unusual cyclone was analyzed. The results show that the cyclonic vorticity occurs first at the middle troposphere, and then extends to both the upper and lower troposphere. The trigger mechanism for the cyclone genesis is the baroclinic forcing with the upper unusual vorticity advection promoting its rapid development. The efficient deployment of the highand lowlevel jets forms a favorable environment for its development and also transports a great number of vapor and the instability energy into the area of blizzard, resulting in the occurrence of the rare event. (Citation: Liu, Y., D. Wang, Z. Liang, and C. Liu, 2016: The structure and development of an extratropical cyclone over northeastern Asia. SOLA, 12, 253−258, doi:10.2151/sola.2016-050)

The Structure and Development of an Extratropical Cyclone over Northeastern Asia

Effects of vertical wind shear, radiation, and ice clouds on cloud microphysical budget associated with torrential rainfall during landfall of severe tropical storm Bilis (2006) are investigated by using a series of analysis of two-day grid-scale sensitivity experiment data When upper-tropospheric upward motions and lower-tropospheric downward motions occur on 15 July 2006, the removal of vertical wind shear and ice clouds increases rainfall contributions from the rainfall type (CM) associated with positive net condensation and hydrometeor loss/convergence, whereas the exclusion of cloud radiative effects and cloud-radiation interaction reduces rainfall contribution from CM The elimination of vertical wind shear and cloud-radiation interaction increases rainfall contribution from the rainfall type (Cm) associated with positive net condensation and hydrometeor gain/divergence, but the removal of cloud radiative effects and ice clouds decreases rainfall contribution from Cm The enhancements in rainfall contribution from the rainfall type (cM) associated with negative net condensation and hydrometeor loss/convergence are caused by the exclusion of cloud radiative effects, cloud-radiation interaction and ice clouds, whereas the reduction in rainfall contribution from cM results from the removal of vertical wind shear When upward motions appear throughout the troposphere on 16 July, the exclusion of all these effects increases rainfall contribution from CM, but generally decreases rainfall contributions from Cm and cM

Ying Liu

Papers

Understanding Atmospheric Behaviour in Terms of Entropy: A Review of Applications of the Second Law of Thermodynamics to Meteorology

Torrential rainfall processes associated with a landfall of severe tropical storm Bilis (2006): a two-dimensional cloud-resolving modeling study.

A case study of the November 2012 mixed rain-snow storm over North China

The Structure and Development of an Extratropical Cyclone over Northeastern Asia

Cloud microphysical budget associated with torrential rainfall during the landfall of severe tropical storm Bilis (2006)