Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm based on the 3500th-order Taylor expansion and the 4180-digit multiple precision data,we have done a reliable simulation of chaotic solution of Lorenz equation in a rather long interval 0 t 10000 LTU(Lorenz time unit).Such a kind of mathematically reliable chaotic simulation has never been reported.It provides us a numerical benchmark for mathematically reliable long-term prediction of chaos.Besides,it also proposes a safe method for mathematically reliable simulations of chaos in a finite but long enough interval.In addition,our very fine simulations suggest that such a kind of mathematically reliable long-term prediction of chaotic solution might have no physical meanings,because the inherent physical micro-level uncertainty due to thermal fluctuation might quickly transfer into macroscopic uncertainty so that trajectories for a long enough time would be essentially uncertain in physics.
In this paper,a multistep finite difference scheme has been proposed,whose coefficients are determined taking into consideration compatibility and generalized quadratic conservation,as well as incorporating historical observation data.The schemes have three advantages:high-order accuracy in time,generalized square conservation,and smart use of historical observations.Numerical tests based on the one-dimensional linear advection equations suggest that reasonable consideration of accuracy,square conservation,and inclusion of historical observations is critical for good performance of a finite difference scheme.
This study shows a new way to implement terrain-following s-coordinate in a numerical model,which does not lead to the well-known"pressure gradient force(PGF)"problem.First,the causes of the PGF problemare analyzedwith existing methods that are categorized into two different types based on the causes.Then,the new method that bypasses the PGF problem all together is proposed.By comparing these threemethods and analyzing the expression of the scalar gradient in a curvilinear coordinate system,this study finds out that only when using the covariant scalar equations of s-coordinate will the PGF computational form have one term in each momentum component equation,thereby avoiding the PGF problem completely.A convenient way of implementing the covariant scalar equations of s-coordinate in a numerical atmospheric model is illustrated,which is to set corresponding parameters in the scalar equations of the Cartesian coordinate.Finally,two idealized experimentsmanifest that the PGF calculated with the new method is more accurate than using the classic one.This method can be used for oceanic models as well,and needs to be tested in both the atmospheric and oceanic models.
This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions.With some criteria,the domain is dynamically decomposed into three parts:kinetic regions where fluids are far from equilibrium,hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition.The Boltzmann-BGK equation is solved in kinetic regions,while Euler equations in hydrodynamic regions and both equations in buffer regions.By a well defined monitor function,our moving mesh method smoothly concentrate the mesh grids to the regions containing rapid variation of the solutions.In each moving mesh step,the solutions are conservatively updated to the new mesh and the cut-off function is rebuilt first to consist with the region decomposition after the mesh motion.In such a framework,the evolution of the hybrid model and the moving mesh procedure can be implemented independently,therefore keep the advantages of both approaches.Numerical examples are presented to demonstrate the efficiency of the method.
The snow/sea-ice albedo was measured over coastal landfast sea ice in Prydz Bay, East Antarctica(off Zhongshan Station)during the austral spring and summer of 2010 and 2011. The variation of the observed albedo was a combination of a gradual seasonal transition from spring to summer and abrupt changes resulting from synoptic events, including snowfall, blowing snow, and overcast skies. The measured albedo ranged from 0.94 over thick fresh snow to 0.36 over melting sea ice. It was found that snow thickness was the most important factor influencing the albedo variation, while synoptic events and overcast skies could increase the albedo by about 0.18 and 0.06, respectively. The in-situ measured albedo and related physical parameters(e.g., snow thickness, ice thickness, surface temperature, and air temperature) were then used to evaluate four different snow/ice albedo parameterizations used in a variety of climate models. The parameterized albedos showed substantial discrepancies compared to the observed albedo, particularly during the summer melt period, even though more complex parameterizations yielded more realistic variations than simple ones. A modified parameterization was developed,which further considered synoptic events, cloud cover, and the local landfast sea-ice surface characteristics. The resulting parameterized albedo showed very good agreement with the observed albedo.
The clustering of severe and sustained droughts in Southwest China(SWC)during the last decade has resulted in tremendous losses,including crop failure,a lack of drinking water,ecosystem destruction,health problems,and even deaths.Various attempts have been made to explore the variability and causes of drought in SWC.Here,the authors summarize and integrate this accumulated but fragmented knowledge.On the whole,general agreement has been reached on the evolution of drought in SWC,which has become more frequent and intense during the past 50 years and is projected to continue throughout the 21st century.However,it is unclear and even disputable as to what and how sea surface temperatures and circulation oscillation patterns affect the drought condition.Meanwhile,the presence of strong nonlinearity places considerable challenges in both understanding and predicting drought in SWC.Therefore,much remains to be learned concerning the mechanisms responsible for drought disasters in SWC and accurate forecast practice.In addition to pursuing research on factors and processes involved in drought formation,above all,there is an urgent need to develop appropriate strategies and plans for mitigating the threats of drought.
Mesoscale convective system (MCS) cloud clusters,defined using an objective recognition analysis based on hourly geostationary infrared satellite data over East Asia during the warm seasons of 1996-2008 (except 2004),were investigated in this study.The geographical pattern of MCS distribution over East Asia shows several high-frequency centers at low latitudes,including the Indo-China peninsula,the Bay of Bengal,the Andaman Sea,the Brahmaputra river delta,the south China coastal region,and the Philippine Islands.There are several middle-frequency centers in the middle latitudes,e.g.,the central-east of the Tibet Plateau,the Plateau of west Sichuan,Mount Wuyi,and the Sayan Mountains in Russia;whereas in Lake Baikal,the Tarim Basin,the Taklimakan Desert,the Sea of Japan,and the Sea of Okhotsk,rare MCS distributions are observed.MCSs are most intensely active in summer,with the highest monthly frequency in July,which is partly associated with the breaking out and prevailing of the summer monsoon in East Asia.An obvious diurnal cycle feature is also found in MCS activities,which shows that MCSs are triggered in the afternoon,mature in the evening,and dissipate at night.MCS patterns over East Asia can be characterized as small,short-lived,or elongated,which move slowly and usually lead to heavy rains or floods.
An improved parallel multiple-precision Taylor(PMT) scheme is developed to obtain clean numerical simulation(CNS) solutions of chaotic ordinary differential equations(ODEs). The new version program is about 500 times faster than the reported solvers developed in the MATHEMATICA, and also 2–3 times faster than the older version(PMT-1.0) of the scheme. This solver has the ability to yield longer solutions of Lorenz equations [up to5000 TU(time unit)]. The PMT-1.1 scheme is applied to a selection of chaotic systems including the Chen, Rossler,coupled Lorenz and Lu¨ systems. The Tc-M and Tc-K diagrams for these chaotic systems are presented and used to analyze the computation parameters for long-term solutions. The reliable computation times of these chaotic equations are obtained for single- and double-precision computation.
