Ensemble prediction is widely used to represent the uncertainty of single deterministic Numerical Weather Prediction(NWP) caused by errors in initial conditions(ICs). The traditional Singular Vector(SV) initial pertur...Ensemble prediction is widely used to represent the uncertainty of single deterministic Numerical Weather Prediction(NWP) caused by errors in initial conditions(ICs). The traditional Singular Vector(SV) initial perturbation method tends only to capture synoptic scale initial uncertainty rather than mesoscale uncertainty in global ensemble prediction. To address this issue, a multiscale SV initial perturbation method based on the China Meteorological Administration Global Ensemble Prediction System(CMA-GEPS) is proposed to quantify multiscale initial uncertainty. The multiscale SV initial perturbation approach entails calculating multiscale SVs at different resolutions with multiple linearized physical processes to capture fast-growing perturbations from mesoscale to synoptic scale in target areas and combining these SVs by using a Gaussian sampling method with amplitude coefficients to generate initial perturbations. Following that, the energy norm,energy spectrum, and structure of multiscale SVs and their impact on GEPS are analyzed based on a batch experiment in different seasons. The results show that the multiscale SV initial perturbations can possess more energy and capture more mesoscale uncertainties than the traditional single-SV method. Meanwhile, multiscale SV initial perturbations can reflect the strongest dynamical instability in target areas. Their performances in global ensemble prediction when compared to single-scale SVs are shown to(i) improve the relationship between the ensemble spread and the root-mean-square error and(ii) provide a better probability forecast skill for atmospheric circulation during the late forecast period and for short-to medium-range precipitation. This study provides scientific evidence and application foundations for the design and development of a multiscale SV initial perturbation method for the GEPS.展开更多
We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous...We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small.The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.展开更多
The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysi...The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.展开更多
Many studies have explored the importance and influence of planetary boundary layer processes on tropical cyclones (TCs). However, few studies have focused on the influence of land surface processes on the activity of...Many studies have explored the importance and influence of planetary boundary layer processes on tropical cyclones (TCs). However, few studies have focused on the influence of land surface processes on the activity of TCs. To test the effect of initial perturbations of land surface processes on TCs, a land surface process perturbation module is built in a global ensemble prediction system. Ensemble experiments for the TCs that occurred from 12 UTC 22 August to 18 UTC 24 November, 2006 show that consideration of the uncertainties within the land surface process could increase the predictability of the global ensemble prediction system. Detailed analysis on TC Xangsane (2006) indicates that the perturbation of land surface processes may increase the variation of sensible heat flux and latent heat flux. Meanwhile, the effect from land surface perturbation can be transferred to the upper atmosphere, which leads to better TC forecasts.展开更多
Given the chaotic nature of the atmosphere and inevitable initial condition errors,constructing effective initial perturbations(IPs)is crucial for the performance of a convection-allowing ensemble prediction system(CA...Given the chaotic nature of the atmosphere and inevitable initial condition errors,constructing effective initial perturbations(IPs)is crucial for the performance of a convection-allowing ensemble prediction system(CAEPS).The IP growth in the CAEPS is scale-and magnitude-dependent,necessitating the investigation of the impacts of IP scales and magnitudes on CAEPS.Five comparative experiments were conducted by using the China Meteorological Administration Mesoscale Numerical Weather Prediction System(CMA-MESO)3-km model for 13 heavy rainfall events over eastern China:smaller-scale IPs with doubled magnitudes,larger-,meso-,and smaller-scale IPs;and a chaos seeding experiment as a baseline.First,the constructed IPs outperform unphysical chaos seeding in perturbation growth and ensemble performance.Second,the daily variation of smaller-scale perturbations is more sensitive to convective activity because smaller-scale perturbations during forecasts reach saturation faster than meso-and larger-scale perturbations.Additionally,rapid downscaling cascade that saturates the smallest-scale perturbation within 6 h for larger-and meso-scale IPs is stronger in the lower troposphere and near-surface.After 9-12 h,the disturbance development of large-scale IPs is the largest in each layer on various scales.Moreover,thermodynamic perturbations,concentrated in the lower troposphere and near-surface with meso-and smaller-scale components being dominant,are smaller and more responsive to convective activity than kinematic perturbations,which are concentrated on the middle-upper troposphere and predominantly consist of larger-and meso-scale components.Furthermore,the increasing magnitude of smaller-scale IPs enables only their smaller-scale perturbations in the first 9 h to exceed those of larger-and meso-scale IPs.Third,for forecast of upper-air and surface variables,larger-scale IPs warrant a more reliable and skillful CAEPS.Finally,for precipitation,larger-scale IPs perform best for light rain at all forecast times,whereas meso-scale IPs are optimal for moderate and heavy rains at 6-h forecast time.Increasing magnitude of smaller-scale IPs improves the probability forecast skills for heavy rains during the first 3-6 h.展开更多
Pangu-Weather(PGW),trained with deep learning–based methods(DL-based model),shows significant potential for global medium-range weather forecasting.However,the interpretability and trustworthiness of global medium-ra...Pangu-Weather(PGW),trained with deep learning–based methods(DL-based model),shows significant potential for global medium-range weather forecasting.However,the interpretability and trustworthiness of global medium-range DLbased models raise many concerns.This study uses the singular vector(SV)initial condition(IC)perturbations of the China Meteorological Administration's Global Ensemble Prediction System(CMA-GEPS)as inputs of PGW for global ensemble prediction(PGW-GEPS)to investigate the ensemble forecast sensitivity of DL-based models to the IC errors.Meanwhile,the CMA-GEPS forecasts serve as benchmarks for comparison and verification.The spatial structures and prediction performance of PGW-GEPS are discussed and compared to CMA-GEPS based on seasonal ensemble experiments.The results show that the ensemble mean and dispersion of PGW-GEPS are similar to those of CMA-GEPS in the medium range but with smoother forecasts.Meanwhile,PGW-GEPS is sensitive to the SV IC perturbations.Specifically,PGWGEPS can generate realistic ensemble spread beyond the sub-synoptic scale(wavenumbers≤64)with SV IC perturbations.However,PGW's kinetic energy is significantly reduced at the sub-synoptic scale,leading to error growth behavior inconsistent with CMA-GEPS at that scale.Thus,this behavior indicates that the effective resolution of PGW-GEPS is beyond the sub-synoptic scale and is limited to predicting mesoscale atmospheric motions.In terms of the global mediumrange ensemble prediction performance,the probability prediction skill of PGW-GEPS is comparable to CMA-GEPS in the extratropic when they use the same IC perturbations.That means that PGW has a general ability to provide skillful global medium-range forecasts with different ICs from numerical weather prediction.展开更多
Initial perturbation scheme is one of the important problems for ensemble prediction. In this paper, ensemble initial perturbation scheme for Global/Regional Assimilation and PrEdiction System （GRAPES） global ensemb...Initial perturbation scheme is one of the important problems for ensemble prediction. In this paper, ensemble initial perturbation scheme for Global/Regional Assimilation and PrEdiction System （GRAPES） global ensemble prediction is developed in terms of the ensemble transform Kalman filter （ETKF） method. A new GRAPES global ensemble prediction system （GEPS） is also constructed. The spherical simplex 14-member ensemble prediction experiments, using the simulated observation network and error characteristics of simulated observations and innovation-based inflation, are carried out for about two months. The structure characters and perturbation amplitudes of the ETKF initial perturbations and the perturbation growth characters are analyzed, and their qualities and abilities for the ensemble initial perturbations are given. The preliminary experimental results indicate that the ETKF-based GRAPES ensemble initial perturbations could identify main normal structures of analysis error variance and reflect the perturbation amplitudes. The initial perturbations and the spread are reasonable. The initial perturbation variance, which is approximately equal to the forecast error variance, is found to respond to changes in the observational spatial variations with simulated observational network density. The perturbations generated through the simplex method are also shown to exhibit a very high degree of consistency between initial analysis and short-range forecast perturbations. The appropriate growth and spread of ensemble perturbations can be maintained up to 96-h lead time. The statistical results for 52-day ensemble forecasts show that the forecast scores of ensemble average for the Northern Hemisphere are higher than that of the control forecast. Provided that using more ensemble members, a real-time observational network and a more appropriate inflation factor, better effects of the ETKF-based initial scheme should be shown.展开更多
Due to uncertainties in initial conditions and parameters, the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern. Our objective is to determine the types and pat...Due to uncertainties in initial conditions and parameters, the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern. Our objective is to determine the types and patterns of initial and parameter perturbations that yield the greatest instability and uncertainty in simulated grassland ecosystems using theoretical models. We used a nonlinear optimization approach, i.e., a conditional nonlinear optimal perturbation related to initial and parameter perturbations （CNOP） approach, in our work. Numerical results indicated that the CNOP showed a special and nonlinear optimal pattern when the initial state variables and multiple parameters were considered simultaneously. A visibly different complex optimal pattern characterizing the CNOPs was obtained by choosing different combinations of initial state variables and multiple parameters in different physical processes. We propose that the grassland modeled ecosystem caused by the CNOP-type perturbation is unstable and exhibits two aspects： abrupt change and the time needed for the abrupt change from a grassland equilibrium state to a desert equilibrium state when the initial state variables and multiple parameters are considered simultaneously. We compared these findings with results affected by the CNOPs obtained by considering only uncertainties in initial state variables and in a single parameter. The numerical results imply that the nonlinear optimal pattern of initial perturbations and parameter perturbations, especially for more parameters or when special parameters are involved, plays a key role in determining stabilities and uncertainties associated with a simulated or predicted grassland ecosystem.展开更多
The effects of initial perturbations on the Rayleigh–Taylor instability (RTI), Kelvin–Helmholtz instability (KHI), and the coupled Rayleigh–Taylor–Kelvin–Helmholtz instability (RTKHI) systems are investigated usi...The effects of initial perturbations on the Rayleigh–Taylor instability (RTI), Kelvin–Helmholtz instability (KHI), and the coupled Rayleigh–Taylor–Kelvin–Helmholtz instability (RTKHI) systems are investigated using a multiple-relaxation-time discrete Boltzmann model. Six different perturbation interfaces are designed to study the effects of the initial perturbations on the instability systems. It is found that the initial perturbation has a significant influence on the evolution of RTI. The sharper the interface, the faster the growth of bubble or spike. While the influence of initial interface shape on KHI evolution can be ignored. Based on the mean heat flux strength D3,1, the effects of initial interfaces on the coupled RTKHI are examined in detail. The research is focused on two aspects: (i) the main mechanism in the early stage of the RTKHI, (ii) the transition point from KHI-like to RTI-like for the case where the KHI dominates at earlier time and the RTI dominates at later time. It is found that the early main mechanism is related to the shape of the initial interface, which is represented by both the bilateral contact angle θ_(1) and the middle contact angle θ_(2). The increase of θ_(1) and the decrease of θ_(2) have opposite effects on the critical velocity. When θ_(2) remains roughly unchanged at 90 degrees, if θ_(1) is greater than 90 degrees (such as the parabolic interface), the critical shear velocity increases with the increase of θ_(1), and the ellipse perturbation is its limiting case;If θ_(1) is less than 90 degrees (such as the inverted parabolic and the inverted ellipse disturbances), the critical shear velocities are basically the same, which is less than that of the sinusoidal and sawtooth disturbances. The influence of inverted parabolic and inverted ellipse perturbations on the transition point of the RTKHI system is greater than that of other interfaces: (i) For the same amplitude, the smaller the contact angle θ_(1), the later the transition point appears;(ii) For the same interface morphology, the disturbance amplitude increases, resulting in a shorter duration of the linear growth stage, so the transition point is greatly advanced.展开更多
We investigate the time-asymptotically nonlinear stability of rarefaction waves to the Cauchy problem of a one-dimensional compressible Navier-Stokes type system for a viscous,compressible,radiative and reactive gas,w...We investigate the time-asymptotically nonlinear stability of rarefaction waves to the Cauchy problem of a one-dimensional compressible Navier-Stokes type system for a viscous,compressible,radiative and reactive gas,where the constitutive relations for the pressure p,the speci c internal energy e,the speci c volume v,the absolute temperature θ,and the specific entropy s are given by p=Rθv+aθ^(4)/3,e=C_(v)θ+avθ^(4),and s=C_(v)lnθ+4avθ^(3)/3+Rln v with R>0,C_(v)>0 and a>0 being the perfect gas constant,the speci c heat and the radiation constant,respectively.For such a specific gas motion,a somewhat surprising fact is that,generally speaking,the pressure p(v,s)is not a convex function of the specific volume v and the specific entropy s.Even so,we show in this paper that the rarefaction waves are time-asymptotically stable for large initial perturbation provided that the radiation constant a and the strength of the rarefaction waves are sufficiently small.The key point in our analysis is to deduce the positive lower and upper bounds on the specific volume and the absolute temperature,which are uniform with respect to the space and the time variables,but are independent of the radiation constant a.展开更多
An initial conditions （ICs） perturbation method was developed with the aim to improve an operational regional ensemble prediction system （REPS）. Three issues were identified and investigated： （1） the impacts of...An initial conditions （ICs） perturbation method was developed with the aim to improve an operational regional ensemble prediction system （REPS）. Three issues were identified and investigated： （1） the impacts of perturbation scale on the ensemble spread and forecast skill of the REPS; （2） the scale characteristic of the IC perturbations of the REPS; and （3） whether the REPS＇s skill could be improved by adding large-scale information to the IC perturbations. Numerical experiments were conducted to reveal the impact of perturbation scale on the ensemble spread and forecast skill. The scales of IC perturbations from the REPS and an operational global ensemble prediction system （GEPS） were analyzed. A ＂multi-scale blending＂ （MSB） IC perturbation scheme was developed, and the main findings can be summarized as follows： The growth rates of the ensemble spread of the REPS are sensitive to the scale of the IC perturbations; the ensemble forecast skills can benefit from large-scale perturbations; the global ensemble IC perturbations exhibit more power at larger scales, while the regional ensemble IC perturbations contain more power at smaller scales; the MSB method can generate IC perturbations by combining the small-scale component from the REPS and the large-scale component from the GEPS; the energy norm growth of the MSB-generated perturbations can be appropriate at all forecast lead times; and the MSB-based REPS shows higher skill than the original system, as determined by ensemble forecast verification.展开更多
How to construct appropriate perturbations for convection-permitting ensemble prediction systems(CPEPSs)is a critical issue awaiting urgent solutions.As two common perturbations,initial perturbations(IPs)and lateral b...How to construct appropriate perturbations for convection-permitting ensemble prediction systems(CPEPSs)is a critical issue awaiting urgent solutions.As two common perturbations,initial perturbations(IPs)and lateral boundary perturbations(BPs)interact with each other,affecting the model error growth,especially in mesoscale models.Using the China Meteorological Administration(CMA)-CPEPS,this study tries to elucidate how BPs interact with matched and mismatched IPs under varied large-scale weather conditions/forcings.Seven groups of experiments were conducted for strong-forcing and weak-forcing weather regimes over southern China:three with single IPs,one with single BPs,and three with combined perturbations.It is found that the perturbation magnitudes were dominated by meso-α-scale components,and IPs under weak forcing exhibited more pronounced effects than under strong forcing;whereas BPs exerted more pronounced effects under strong forcing than weak forcing regimes.Furthermore,it lasts longer for high-level variables when the perturbation energy from BPs is higher than that from IPs,compared to low-level variables.Moreover,for precipitation and dynamic variables,IPs and BPs can mutually reinforce.The source of these perturbations,and their specific vertical levels,do not alter the extent of their interactions.Nevertheless,the weather regime and the scales of the perturbations influence the strength of their mutual reinforcement.In particular,the weak-forcing regimes exhibit a more pronounced reinforcing effect,and meso-α-scale perturbations are more conducive to fostering interactions compared to meso-β-scale ones.Ultimately,it is the perturbation magnitude inherent in the initial perturbation itself that determines the interactions between IPs and BPs.展开更多
The AREMv2.3 mesoscale numerical model is used to explore storm processes in South China during the pre-rainy season in 2006 by imposing perturbations on the initial fields of physical variables （temperature, humidit...The AREMv2.3 mesoscale numerical model is used to explore storm processes in South China during the pre-rainy season in 2006 by imposing perturbations on the initial fields of physical variables （temperature, humidity, and wind fields）. Sensitivity experiments are performed to examine the impacts of initial uncertainties on precipitation, on the error growth, and on the predictability of mesoscale precipitation in South China. The primary conclusion is that inherent initial condition uncertainties can significantly limit the predictability of storm. The 24-h accumulated precipitation is most sensitive to temperature perturbations. Larger-amplitude initial uncertainties generally lead to larger perturbation energies than those with smaller amplitude, but these kinds of differences decrease with time monotonically so the mechanism for the growth of perturbation energy is nonlinear. The power spectra of precipitation differences indicate that predictability increases with accumulated time. This also indicates the difficulties faced for short-term, small-scale precipitation forecasting.展开更多
In this paper we consider the initial-boundary value problem for a second order hyperbolic equation with initial jump. The bounds on the derivatives of the exact solution are given. Then a difference scheme is constru...In this paper we consider the initial-boundary value problem for a second order hyperbolic equation with initial jump. The bounds on the derivatives of the exact solution are given. Then a difference scheme is constructed on a non-uniform grid. Finally, uniform convergence of the difference solution is proved in the sense of the discrete energy norm.展开更多
In this study, the approach of conditional nonlinear optimal perturbation related to initial perturbation （CNOP-I） was employed to investigate the maximum variations in plant amount for three main woody plants （a t...In this study, the approach of conditional nonlinear optimal perturbation related to initial perturbation （CNOP-I） was employed to investigate the maximum variations in plant amount for three main woody plants （a temperate broadleaved evergreen, a temperate broadleaved summergreen, and a boreal needleleaved evergreen） in China. The investigation was conducted within a certain range of land use intensity using a state-of-the-art Lund-Potsdam-Jena dynamic global vegetation model （LPJ DGVM）. CNOP-I represents a class of deforestation and can be considered a type of land use with respect to the initial perturbation. When deforestation denoted by the CNOP-I has the same intensity for all three plants, the variation in plant amount of the boreal needleleaved evergreen in northern China is greater than the variation in plant amount of both the temperate broadleaved evergreen and temperate broadleaved summergreen in southern China. As deforestation intensity increases, the plant amount variation in the three woody plant functional types carbon changes, in a nonlinear fashion. The impact of land use on plant functional types is minor because the interaction between climate condition and land use is not considered in the LPJ model. Finally, the different impacts of deforestation on net primary production of the three plant functional types were analyzed by modeling gross primary production and autotrophic respiration. Our results suggest that the CNOP-I approach is a useful tool for exploring the nonlinear and different responses of terrestrial ecosystems to land use.展开更多
Limitations are existed in current ensemble forecasting initial perturbation methods for describing the interactions among various spheres of the Earth system. In this study, a new method is proposed, namely, the coup...Limitations are existed in current ensemble forecasting initial perturbation methods for describing the interactions among various spheres of the Earth system. In this study, a new method is proposed, namely, the coupled conditional nonlinear optimal perturbation(C-CNOP) method, which incorporates multisphere interactions much appropriately. The El Nino-Southern Oscillation(ENSO) is a typical ocean-atmosphere “coupling”(or “interaction”) phenomenon. The C-CNOP method is applied to ensemble forecasting of ENSO. It is demonstrated that the C-CNOP method can generate coupled initial perturbations(CPs) that appropriately consider initial ocean-atmosphere coupling uncertainty for ENSO ensemble forecasts. Results reveal that the CPs effectively improve the ability of ENSO ensemble-mean forecasts in both temporal variability of Nio3.4 sea surface temperature anomalies(SSTAs) and spatial variability of ENSO mature-phase SSTAs. Notably, despite the weakest ocean-atmosphere coupling strength in the tropical Pacific occurring during the boreal spring and summer, CPs still capture the uncertainties of this weak coupling when ENSO predictions are initialized at these seasons. This performance of CPs significantly suppresses the rapid increase of ENSO prediction errors due to the high ocean-atmosphere coupling instability during these seasons, and thus effectively extends the lead time of skillful ENSO forecasting. Hence, the C-CNOP method is a suitable initial perturbation approach for ENSO ensemble forecast that can describe initial ocean-atmosphere coupling uncertainty. It is expected that the CCNOP method plays a significant role in predictions of other high-impact climate phenomena, and even future Earth system predictions.展开更多
Mesoscale ensemble is an encouraging technology for improving the accuracy of heavy rainfall predictions. Occurrences of heavy rainfall are closely related to convective instability and topography. In mid-latitudes, p...Mesoscale ensemble is an encouraging technology for improving the accuracy of heavy rainfall predictions. Occurrences of heavy rainfall are closely related to convective instability and topography. In mid-latitudes, perturbed initial fields for medium-range weather forecasts are often configured to focus on the baroclinic instability rather than the convective instability. Thus, alternative approaches to generate initial perturba- tions need to be developed to accommodate the uncertainty of the convective instability. In this paper, an initial condition perturbation approach to mesoscale heavy rainfall ensemble prediction, named as Different Physics Mode Method （DPMM）, is presented in detail. Based on the PSU/NCAR mesoscale model MM5, an ensemble prediction experiment on a typical heavy rainfall event in South China is carried out by using the DPMM, and the structure of the initial condition perturbation is analyzed. Further, the DPMM ensem- ble prediction is compared with a multi-physics ensemble prediction, and the results show that the initial perturbation fields from the DPMM have a reasonable mesoscale circulation structure and could reflect the prediction uncertainty in the sensitive regions of convective instability. An evaluation of the DPMM ini- tial condition perturbation indicates that the DPMM method produces better ensemble members than the multi-physics perturbation method, and can significantly improve the precipitation forecast than the control non-ensemble run.展开更多
The three-dimensional premixed H2-O2 detonation propagation in rectangular ducts is simulated using an in-house parallel detonation code based on the second-order space-time conservation element and solution element（...The three-dimensional premixed H2-O2 detonation propagation in rectangular ducts is simulated using an in-house parallel detonation code based on the second-order space-time conservation element and solution element（CE/SE） scheme.The simulation reproduces three typical cellular structures by setting appropriate cross-sectional size and initial perturbation in square tubes.As the cross-sectional size decreases,critical cellular structures transforming the rectangular or diagonal mode into the spinning mode are obtained and discussed in the perspective of phase variation as well as decreasing of triple point lines.Furthermore,multiple cellular structures are observed through examples with typical aspect ratios.Utilizing the visualization of detailed three-dimensional structures,their formation mechanism is further analyzed.展开更多
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered.Using the iteration method and the comparison theorem, the existence and its asymptotic ...In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered.Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of solution for the problem are studied.展开更多
基金supported by the Joint Funds of the Chinese National Natural Science Foundation (NSFC)(Grant No.U2242213)the National Key Research and Development (R&D)Program of the Ministry of Science and Technology of China(Grant No. 2021YFC3000902)the National Science Foundation for Young Scholars (Grant No. 42205166)。
文摘Ensemble prediction is widely used to represent the uncertainty of single deterministic Numerical Weather Prediction(NWP) caused by errors in initial conditions(ICs). The traditional Singular Vector(SV) initial perturbation method tends only to capture synoptic scale initial uncertainty rather than mesoscale uncertainty in global ensemble prediction. To address this issue, a multiscale SV initial perturbation method based on the China Meteorological Administration Global Ensemble Prediction System(CMA-GEPS) is proposed to quantify multiscale initial uncertainty. The multiscale SV initial perturbation approach entails calculating multiscale SVs at different resolutions with multiple linearized physical processes to capture fast-growing perturbations from mesoscale to synoptic scale in target areas and combining these SVs by using a Gaussian sampling method with amplitude coefficients to generate initial perturbations. Following that, the energy norm,energy spectrum, and structure of multiscale SVs and their impact on GEPS are analyzed based on a batch experiment in different seasons. The results show that the multiscale SV initial perturbations can possess more energy and capture more mesoscale uncertainties than the traditional single-SV method. Meanwhile, multiscale SV initial perturbations can reflect the strongest dynamical instability in target areas. Their performances in global ensemble prediction when compared to single-scale SVs are shown to(i) improve the relationship between the ensemble spread and the root-mean-square error and(ii) provide a better probability forecast skill for atmospheric circulation during the late forecast period and for short-to medium-range precipitation. This study provides scientific evidence and application foundations for the design and development of a multiscale SV initial perturbation method for the GEPS.
文摘We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small.The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.
基金supported by the"Strategic Priority Research Program-Climate Change:Carbon Budget and Relevant Issues"of the Chinese Academy of Sciences (Grant No.XDA01020304)
文摘The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.
基金National Natural Science Foundation of China (4073094841075079)+2 种基金NMC-TIGGE Program(GYHY200706001GYHY200906007)Special Public Welfare Research Fund for Meteorological Profession of CMA (GYHY201006015)
文摘Many studies have explored the importance and influence of planetary boundary layer processes on tropical cyclones (TCs). However, few studies have focused on the influence of land surface processes on the activity of TCs. To test the effect of initial perturbations of land surface processes on TCs, a land surface process perturbation module is built in a global ensemble prediction system. Ensemble experiments for the TCs that occurred from 12 UTC 22 August to 18 UTC 24 November, 2006 show that consideration of the uncertainties within the land surface process could increase the predictability of the global ensemble prediction system. Detailed analysis on TC Xangsane (2006) indicates that the perturbation of land surface processes may increase the variation of sensible heat flux and latent heat flux. Meanwhile, the effect from land surface perturbation can be transferred to the upper atmosphere, which leads to better TC forecasts.
基金Supported by the National Natural Science Foundation of China(U2242213)National Science Foundation for Young Scholars of China(42205166).
文摘Given the chaotic nature of the atmosphere and inevitable initial condition errors,constructing effective initial perturbations(IPs)is crucial for the performance of a convection-allowing ensemble prediction system(CAEPS).The IP growth in the CAEPS is scale-and magnitude-dependent,necessitating the investigation of the impacts of IP scales and magnitudes on CAEPS.Five comparative experiments were conducted by using the China Meteorological Administration Mesoscale Numerical Weather Prediction System(CMA-MESO)3-km model for 13 heavy rainfall events over eastern China:smaller-scale IPs with doubled magnitudes,larger-,meso-,and smaller-scale IPs;and a chaos seeding experiment as a baseline.First,the constructed IPs outperform unphysical chaos seeding in perturbation growth and ensemble performance.Second,the daily variation of smaller-scale perturbations is more sensitive to convective activity because smaller-scale perturbations during forecasts reach saturation faster than meso-and larger-scale perturbations.Additionally,rapid downscaling cascade that saturates the smallest-scale perturbation within 6 h for larger-and meso-scale IPs is stronger in the lower troposphere and near-surface.After 9-12 h,the disturbance development of large-scale IPs is the largest in each layer on various scales.Moreover,thermodynamic perturbations,concentrated in the lower troposphere and near-surface with meso-and smaller-scale components being dominant,are smaller and more responsive to convective activity than kinematic perturbations,which are concentrated on the middle-upper troposphere and predominantly consist of larger-and meso-scale components.Furthermore,the increasing magnitude of smaller-scale IPs enables only their smaller-scale perturbations in the first 9 h to exceed those of larger-and meso-scale IPs.Third,for forecast of upper-air and surface variables,larger-scale IPs warrant a more reliable and skillful CAEPS.Finally,for precipitation,larger-scale IPs perform best for light rain at all forecast times,whereas meso-scale IPs are optimal for moderate and heavy rains at 6-h forecast time.Increasing magnitude of smaller-scale IPs improves the probability forecast skills for heavy rains during the first 3-6 h.
基金supported by the joint funds of the Chinese National Natural Science Foundation(NSFC)(Grant No.U2242213)the funds of the NSFC(Grant No.42341209)+2 种基金the National Key Research and Development(R&D)Program of the Ministry of Science and Technology of China(Grant No.2021YFC3000902)the National Science Foundation for Young Scholars(Grant No.42205166)the Joint Research Project for Meteorological Capacity Improvement(Grant No.22NLTSQ008)。
文摘Pangu-Weather(PGW),trained with deep learning–based methods(DL-based model),shows significant potential for global medium-range weather forecasting.However,the interpretability and trustworthiness of global medium-range DLbased models raise many concerns.This study uses the singular vector(SV)initial condition(IC)perturbations of the China Meteorological Administration's Global Ensemble Prediction System(CMA-GEPS)as inputs of PGW for global ensemble prediction(PGW-GEPS)to investigate the ensemble forecast sensitivity of DL-based models to the IC errors.Meanwhile,the CMA-GEPS forecasts serve as benchmarks for comparison and verification.The spatial structures and prediction performance of PGW-GEPS are discussed and compared to CMA-GEPS based on seasonal ensemble experiments.The results show that the ensemble mean and dispersion of PGW-GEPS are similar to those of CMA-GEPS in the medium range but with smoother forecasts.Meanwhile,PGW-GEPS is sensitive to the SV IC perturbations.Specifically,PGWGEPS can generate realistic ensemble spread beyond the sub-synoptic scale(wavenumbers≤64)with SV IC perturbations.However,PGW's kinetic energy is significantly reduced at the sub-synoptic scale,leading to error growth behavior inconsistent with CMA-GEPS at that scale.Thus,this behavior indicates that the effective resolution of PGW-GEPS is beyond the sub-synoptic scale and is limited to predicting mesoscale atmospheric motions.In terms of the global mediumrange ensemble prediction performance,the probability prediction skill of PGW-GEPS is comparable to CMA-GEPS in the extratropic when they use the same IC perturbations.That means that PGW has a general ability to provide skillful global medium-range forecasts with different ICs from numerical weather prediction.
基金Supported by the National Natural Science Foundation of China under Grant Nos.40675064,40518001, and 40675062CMA NWP Innovational Research Project-"Key Technology of Global Operational Data Assimilation System"
文摘Initial perturbation scheme is one of the important problems for ensemble prediction. In this paper, ensemble initial perturbation scheme for Global/Regional Assimilation and PrEdiction System （GRAPES） global ensemble prediction is developed in terms of the ensemble transform Kalman filter （ETKF） method. A new GRAPES global ensemble prediction system （GEPS） is also constructed. The spherical simplex 14-member ensemble prediction experiments, using the simulated observation network and error characteristics of simulated observations and innovation-based inflation, are carried out for about two months. The structure characters and perturbation amplitudes of the ETKF initial perturbations and the perturbation growth characters are analyzed, and their qualities and abilities for the ensemble initial perturbations are given. The preliminary experimental results indicate that the ETKF-based GRAPES ensemble initial perturbations could identify main normal structures of analysis error variance and reflect the perturbation amplitudes. The initial perturbations and the spread are reasonable. The initial perturbation variance, which is approximately equal to the forecast error variance, is found to respond to changes in the observational spatial variations with simulated observational network density. The perturbations generated through the simplex method are also shown to exhibit a very high degree of consistency between initial analysis and short-range forecast perturbations. The appropriate growth and spread of ensemble perturbations can be maintained up to 96-h lead time. The statistical results for 52-day ensemble forecasts show that the forecast scores of ensemble average for the Northern Hemisphere are higher than that of the control forecast. Provided that using more ensemble members, a real-time observational network and a more appropriate inflation factor, better effects of the ETKF-based initial scheme should be shown.
基金provided by grants from National Natural Science Foundation of China (Grant Nos. 40905050and 40830955)the Chinese Academy of Sciences (CASGrant No. KZCX3-SW-230)
文摘Due to uncertainties in initial conditions and parameters, the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern. Our objective is to determine the types and patterns of initial and parameter perturbations that yield the greatest instability and uncertainty in simulated grassland ecosystems using theoretical models. We used a nonlinear optimization approach, i.e., a conditional nonlinear optimal perturbation related to initial and parameter perturbations （CNOP） approach, in our work. Numerical results indicated that the CNOP showed a special and nonlinear optimal pattern when the initial state variables and multiple parameters were considered simultaneously. A visibly different complex optimal pattern characterizing the CNOPs was obtained by choosing different combinations of initial state variables and multiple parameters in different physical processes. We propose that the grassland modeled ecosystem caused by the CNOP-type perturbation is unstable and exhibits two aspects： abrupt change and the time needed for the abrupt change from a grassland equilibrium state to a desert equilibrium state when the initial state variables and multiple parameters are considered simultaneously. We compared these findings with results affected by the CNOPs obtained by considering only uncertainties in initial state variables and in a single parameter. The numerical results imply that the nonlinear optimal pattern of initial perturbations and parameter perturbations, especially for more parameters or when special parameters are involved, plays a key role in determining stabilities and uncertainties associated with a simulated or predicted grassland ecosystem.
基金This work was supported by the Natural Science Foundation of Shandong Province(Grant Nos.ZR2020MA061 and ZR2019PA021)Shandong Province Higher Educational Youth Innovation Science and Technology Program(Grant No.2019KJJ009)+5 种基金the National Natural Science Foundation of China(Grant Nos.12172061,11875001,and 12102397)CAEP Foundation(Grant No.CX2019033)the opening project of State Key Laboratory of Explosion Science and Technology(Beijing Institute of Technology)(Grant No.KFJJ21-16M)the China Postdoctoral Science Foundation(Grant No.2019M662521)Science Foundation of Hebei Province(Grant No.A2021409001)“Three,Three and Three Talent Project”of Hebei Province(Grant No.A202105005).
文摘The effects of initial perturbations on the Rayleigh–Taylor instability (RTI), Kelvin–Helmholtz instability (KHI), and the coupled Rayleigh–Taylor–Kelvin–Helmholtz instability (RTKHI) systems are investigated using a multiple-relaxation-time discrete Boltzmann model. Six different perturbation interfaces are designed to study the effects of the initial perturbations on the instability systems. It is found that the initial perturbation has a significant influence on the evolution of RTI. The sharper the interface, the faster the growth of bubble or spike. While the influence of initial interface shape on KHI evolution can be ignored. Based on the mean heat flux strength D3,1, the effects of initial interfaces on the coupled RTKHI are examined in detail. The research is focused on two aspects: (i) the main mechanism in the early stage of the RTKHI, (ii) the transition point from KHI-like to RTI-like for the case where the KHI dominates at earlier time and the RTI dominates at later time. It is found that the early main mechanism is related to the shape of the initial interface, which is represented by both the bilateral contact angle θ_(1) and the middle contact angle θ_(2). The increase of θ_(1) and the decrease of θ_(2) have opposite effects on the critical velocity. When θ_(2) remains roughly unchanged at 90 degrees, if θ_(1) is greater than 90 degrees (such as the parabolic interface), the critical shear velocity increases with the increase of θ_(1), and the ellipse perturbation is its limiting case;If θ_(1) is less than 90 degrees (such as the inverted parabolic and the inverted ellipse disturbances), the critical shear velocities are basically the same, which is less than that of the sinusoidal and sawtooth disturbances. The influence of inverted parabolic and inverted ellipse perturbations on the transition point of the RTKHI system is greater than that of other interfaces: (i) For the same amplitude, the smaller the contact angle θ_(1), the later the transition point appears;(ii) For the same interface morphology, the disturbance amplitude increases, resulting in a shorter duration of the linear growth stage, so the transition point is greatly advanced.
基金supported by the Fundamental Research Funds for the Central Universities and National Natural Science Foundation of China(Grant Nos.11731008 and 11671309)supported by the Fundamental Research Funds for the Central Universities(Grant No.YJ201962)supported by National Postdoctoral Program for Innovative Talents of China(Grant No.BX20180054).
文摘We investigate the time-asymptotically nonlinear stability of rarefaction waves to the Cauchy problem of a one-dimensional compressible Navier-Stokes type system for a viscous,compressible,radiative and reactive gas,where the constitutive relations for the pressure p,the speci c internal energy e,the speci c volume v,the absolute temperature θ,and the specific entropy s are given by p=Rθv+aθ^(4)/3,e=C_(v)θ+avθ^(4),and s=C_(v)lnθ+4avθ^(3)/3+Rln v with R>0,C_(v)>0 and a>0 being the perfect gas constant,the speci c heat and the radiation constant,respectively.For such a specific gas motion,a somewhat surprising fact is that,generally speaking,the pressure p(v,s)is not a convex function of the specific volume v and the specific entropy s.Even so,we show in this paper that the rarefaction waves are time-asymptotically stable for large initial perturbation provided that the radiation constant a and the strength of the rarefaction waves are sufficiently small.The key point in our analysis is to deduce the positive lower and upper bounds on the specific volume and the absolute temperature,which are uniform with respect to the space and the time variables,but are independent of the radiation constant a.
基金supported by the National Natural Science Foundation of China (Grant No. 91437113)the Special Fund for Meteorological Scientific Research in the Public Interest (Grant Nos. GYHY201506007 and GYHY201006015)+1 种基金the National 973 Program of China (Grant Nos. 2012CB417204 and 2012CB955200)the Scientific Research & Innovation Projects for Academic Degree Students of Ordinary Universities of Jiangsu (Grant No. KYLX 0827)
文摘An initial conditions （ICs） perturbation method was developed with the aim to improve an operational regional ensemble prediction system （REPS）. Three issues were identified and investigated： （1） the impacts of perturbation scale on the ensemble spread and forecast skill of the REPS; （2） the scale characteristic of the IC perturbations of the REPS; and （3） whether the REPS＇s skill could be improved by adding large-scale information to the IC perturbations. Numerical experiments were conducted to reveal the impact of perturbation scale on the ensemble spread and forecast skill. The scales of IC perturbations from the REPS and an operational global ensemble prediction system （GEPS） were analyzed. A ＂multi-scale blending＂ （MSB） IC perturbation scheme was developed, and the main findings can be summarized as follows： The growth rates of the ensemble spread of the REPS are sensitive to the scale of the IC perturbations; the ensemble forecast skills can benefit from large-scale perturbations; the global ensemble IC perturbations exhibit more power at larger scales, while the regional ensemble IC perturbations contain more power at smaller scales; the MSB method can generate IC perturbations by combining the small-scale component from the REPS and the large-scale component from the GEPS; the energy norm growth of the MSB-generated perturbations can be appropriate at all forecast lead times; and the MSB-based REPS shows higher skill than the original system, as determined by ensemble forecast verification.
基金Supported by the National Natural Science Foundation of China(U2242213 and 42105154).
文摘How to construct appropriate perturbations for convection-permitting ensemble prediction systems(CPEPSs)is a critical issue awaiting urgent solutions.As two common perturbations,initial perturbations(IPs)and lateral boundary perturbations(BPs)interact with each other,affecting the model error growth,especially in mesoscale models.Using the China Meteorological Administration(CMA)-CPEPS,this study tries to elucidate how BPs interact with matched and mismatched IPs under varied large-scale weather conditions/forcings.Seven groups of experiments were conducted for strong-forcing and weak-forcing weather regimes over southern China:three with single IPs,one with single BPs,and three with combined perturbations.It is found that the perturbation magnitudes were dominated by meso-α-scale components,and IPs under weak forcing exhibited more pronounced effects than under strong forcing;whereas BPs exerted more pronounced effects under strong forcing than weak forcing regimes.Furthermore,it lasts longer for high-level variables when the perturbation energy from BPs is higher than that from IPs,compared to low-level variables.Moreover,for precipitation and dynamic variables,IPs and BPs can mutually reinforce.The source of these perturbations,and their specific vertical levels,do not alter the extent of their interactions.Nevertheless,the weather regime and the scales of the perturbations influence the strength of their mutual reinforcement.In particular,the weak-forcing regimes exhibit a more pronounced reinforcing effect,and meso-α-scale perturbations are more conducive to fostering interactions compared to meso-β-scale ones.Ultimately,it is the perturbation magnitude inherent in the initial perturbation itself that determines the interactions between IPs and BPs.
基金supported by the R&D Special Fund for Public Welfare Industry (me-teorology) (GYHY200806010)
文摘The AREMv2.3 mesoscale numerical model is used to explore storm processes in South China during the pre-rainy season in 2006 by imposing perturbations on the initial fields of physical variables （temperature, humidity, and wind fields）. Sensitivity experiments are performed to examine the impacts of initial uncertainties on precipitation, on the error growth, and on the predictability of mesoscale precipitation in South China. The primary conclusion is that inherent initial condition uncertainties can significantly limit the predictability of storm. The 24-h accumulated precipitation is most sensitive to temperature perturbations. Larger-amplitude initial uncertainties generally lead to larger perturbation energies than those with smaller amplitude, but these kinds of differences decrease with time monotonically so the mechanism for the growth of perturbation energy is nonlinear. The power spectra of precipitation differences indicate that predictability increases with accumulated time. This also indicates the difficulties faced for short-term, small-scale precipitation forecasting.
文摘In this paper we consider the initial-boundary value problem for a second order hyperbolic equation with initial jump. The bounds on the derivatives of the exact solution are given. Then a difference scheme is constructed on a non-uniform grid. Finally, uniform convergence of the difference solution is proved in the sense of the discrete energy norm.
基金Funding was provided from the State Key Development Program for Basic Research，National Natural Science Foundation of China，the KZCX3-SW-230 of the Chinese Academy of Sciences
文摘In this study, the approach of conditional nonlinear optimal perturbation related to initial perturbation （CNOP-I） was employed to investigate the maximum variations in plant amount for three main woody plants （a temperate broadleaved evergreen, a temperate broadleaved summergreen, and a boreal needleleaved evergreen） in China. The investigation was conducted within a certain range of land use intensity using a state-of-the-art Lund-Potsdam-Jena dynamic global vegetation model （LPJ DGVM）. CNOP-I represents a class of deforestation and can be considered a type of land use with respect to the initial perturbation. When deforestation denoted by the CNOP-I has the same intensity for all three plants, the variation in plant amount of the boreal needleleaved evergreen in northern China is greater than the variation in plant amount of both the temperate broadleaved evergreen and temperate broadleaved summergreen in southern China. As deforestation intensity increases, the plant amount variation in the three woody plant functional types carbon changes, in a nonlinear fashion. The impact of land use on plant functional types is minor because the interaction between climate condition and land use is not considered in the LPJ model. Finally, the different impacts of deforestation on net primary production of the three plant functional types were analyzed by modeling gross primary production and autotrophic respiration. Our results suggest that the CNOP-I approach is a useful tool for exploring the nonlinear and different responses of terrestrial ecosystems to land use.
基金supported by the National Natural Science Foundation of China(Grant Nos.42330111 and41930971)。
文摘Limitations are existed in current ensemble forecasting initial perturbation methods for describing the interactions among various spheres of the Earth system. In this study, a new method is proposed, namely, the coupled conditional nonlinear optimal perturbation(C-CNOP) method, which incorporates multisphere interactions much appropriately. The El Nino-Southern Oscillation(ENSO) is a typical ocean-atmosphere “coupling”(or “interaction”) phenomenon. The C-CNOP method is applied to ensemble forecasting of ENSO. It is demonstrated that the C-CNOP method can generate coupled initial perturbations(CPs) that appropriately consider initial ocean-atmosphere coupling uncertainty for ENSO ensemble forecasts. Results reveal that the CPs effectively improve the ability of ENSO ensemble-mean forecasts in both temporal variability of Nio3.4 sea surface temperature anomalies(SSTAs) and spatial variability of ENSO mature-phase SSTAs. Notably, despite the weakest ocean-atmosphere coupling strength in the tropical Pacific occurring during the boreal spring and summer, CPs still capture the uncertainties of this weak coupling when ENSO predictions are initialized at these seasons. This performance of CPs significantly suppresses the rapid increase of ENSO prediction errors due to the high ocean-atmosphere coupling instability during these seasons, and thus effectively extends the lead time of skillful ENSO forecasting. Hence, the C-CNOP method is a suitable initial perturbation approach for ENSO ensemble forecast that can describe initial ocean-atmosphere coupling uncertainty. It is expected that the CCNOP method plays a significant role in predictions of other high-impact climate phenomena, and even future Earth system predictions.
基金Supported by the National Natural Science Foundation of China under Grant No.40675061,the project from Ministry of ScienceTechnology of China under Grant Nos.2004DIB3Jl19 and GYHY200706001the key project from Meteorological Bureau of Sichuan Province.
文摘Mesoscale ensemble is an encouraging technology for improving the accuracy of heavy rainfall predictions. Occurrences of heavy rainfall are closely related to convective instability and topography. In mid-latitudes, perturbed initial fields for medium-range weather forecasts are often configured to focus on the baroclinic instability rather than the convective instability. Thus, alternative approaches to generate initial perturba- tions need to be developed to accommodate the uncertainty of the convective instability. In this paper, an initial condition perturbation approach to mesoscale heavy rainfall ensemble prediction, named as Different Physics Mode Method （DPMM）, is presented in detail. Based on the PSU/NCAR mesoscale model MM5, an ensemble prediction experiment on a typical heavy rainfall event in South China is carried out by using the DPMM, and the structure of the initial condition perturbation is analyzed. Further, the DPMM ensem- ble prediction is compared with a multi-physics ensemble prediction, and the results show that the initial perturbation fields from the DPMM have a reasonable mesoscale circulation structure and could reflect the prediction uncertainty in the sensitive regions of convective instability. An evaluation of the DPMM ini- tial condition perturbation indicates that the DPMM method produces better ensemble members than the multi-physics perturbation method, and can significantly improve the precipitation forecast than the control non-ensemble run.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10732010 and 10972010)
文摘The three-dimensional premixed H2-O2 detonation propagation in rectangular ducts is simulated using an in-house parallel detonation code based on the second-order space-time conservation element and solution element（CE/SE） scheme.The simulation reproduces three typical cellular structures by setting appropriate cross-sectional size and initial perturbation in square tubes.As the cross-sectional size decreases,critical cellular structures transforming the rectangular or diagonal mode into the spinning mode are obtained and discussed in the perspective of phase variation as well as decreasing of triple point lines.Furthermore,multiple cellular structures are observed through examples with typical aspect ratios.Utilizing the visualization of detailed three-dimensional structures,their formation mechanism is further analyzed.
基金Supported by Important Study Project of the National Natural Science Foundation of China( 90 2 1 1 0 0 4 ) and by the"Hundred Talents Project" of Chinese Academy of Sciences
文摘In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered.Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of solution for the problem are studied.
