In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The eff...In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.展开更多
We consider acoustic scattering of time-harmonic waves at objects composed of several homogeneous parts.Some of those may be impenetrable,giving rise to Dirichlet boundary conditions on their surfaces.We start from th...We consider acoustic scattering of time-harmonic waves at objects composed of several homogeneous parts.Some of those may be impenetrable,giving rise to Dirichlet boundary conditions on their surfaces.We start from the recent secondkind boundary integral approach of[X.Claeys,and R.Hiptmair,and E.Spindler.A second-kind Galerkin boundary element method for scattering at composite objects.BIT Numerical Mathematics,55(1):33-57,2015]for pure transmission problems and extend it to settings with essential boundary conditions.Based on so-called global multipotentials,we derive variational second-kind boundary integral equations posed in L^(2)(S),where S denotes the union of material interfaces.To suppress spurious resonances,we introduce a combined-field version(CFIE)of our new method.Thorough numerical tests highlight the low andmesh-independent condition numbers of Galerkin matrices obtained with discontinuous piecewise polynomial boundary element spaces.They also confirm competitive accuracy of the numerical solution in comparison with the widely used first-kind single-trace approach.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.42225501 and 42105059)the National Key Scientific and Tech-nological Infrastructure project“Earth System Numerical Simula-tion Facility”(EarthLab).
文摘In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.
基金The authors would like to thank L.Kielhorn for his great support during the development of the code for the first-and second-kind formulation in BETL2[25]The work of E.Spindler was partially supported by SNF under grant 20021137873/1X.Claeys received support from the ANR Research Grant ANR-15-CE23-0017-01.
文摘We consider acoustic scattering of time-harmonic waves at objects composed of several homogeneous parts.Some of those may be impenetrable,giving rise to Dirichlet boundary conditions on their surfaces.We start from the recent secondkind boundary integral approach of[X.Claeys,and R.Hiptmair,and E.Spindler.A second-kind Galerkin boundary element method for scattering at composite objects.BIT Numerical Mathematics,55(1):33-57,2015]for pure transmission problems and extend it to settings with essential boundary conditions.Based on so-called global multipotentials,we derive variational second-kind boundary integral equations posed in L^(2)(S),where S denotes the union of material interfaces.To suppress spurious resonances,we introduce a combined-field version(CFIE)of our new method.Thorough numerical tests highlight the low andmesh-independent condition numbers of Galerkin matrices obtained with discontinuous piecewise polynomial boundary element spaces.They also confirm competitive accuracy of the numerical solution in comparison with the widely used first-kind single-trace approach.
