Retrogressive landslides are common geological phenomena in mountainous areas and on onshore and offshore slopes. The impact of retrogressive landslides is different from that of other landslide types due to the pheno...Retrogressive landslides are common geological phenomena in mountainous areas and on onshore and offshore slopes. The impact of retrogressive landslides is different from that of other landslide types due to the phenomenon of retrogression. The hazards caused by retrogressive landslides may be increased because retrogressive landslides usually affect housing, facilities, and infrastructure located far from the original slopes. Additionally, substantial geomorphic evidence shows that the abundant supply of loose sediment in the source area of a debris flow is usually provided by retrogressive landslides that are triggered by the undercutting of water. Moreover, according to historic case studies, some large landslides are the evolution result of retrogressive landslides. Hence the ability to understand and predict the evolution of retrogressive landslides is crucial for the purpose of hazard mitigation. This paper discusses the phenomenon of a retrogressive landslide by using a model experiment and suggests a reasonably simplified numerical approach for the prediction of rainfall-induced retrogressive landslides. The simplified numerical approach, which combines the finite element method for seepage analysis, the shear strength reduction finite element method, and the analysis criterion for the retrogression and accumulation effect, is presented and used to predict the characteristics of a retrogressive landslide. The results show that this numerical approach is capable of reasonably predicting the characteristics of retrogressive landslides under rainfall infiltration, particularly the magnitude of each landslide, the position of the slip surface, and the development processes of the retrogressive landslide. Therefore, this approach is expected to be a practical method for the mitigation of damage caused by rainfall-induced retrogressive landslides.展开更多
In this paper,two formulation theorems of time-difference fidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,with earlier major conserving time-discreti...In this paper,two formulation theorems of time-difference fidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,with earlier major conserving time-discretized schemes given as special cases.These two theorems can provide new mathematical basis for solving basic formulation problems of more types of conservative time- discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelity schemes by combining existing instantly conserving space-discretized schemes.Besides.the two theorems can also solve two large categories of problems about linear and nonlinear computational instability. The traditional global spectral-vertical finite-difference semi-implicit model for baroclinic primitive equations is currently used in many countries in the world for operational weather forecast and numerical simulations of general circulation.The present work,however,based on Theorem 2 formulated in this paper,develops and realizes a high-order total energy conserving semi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model of baroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved for long,whether in terms of theory or practice.The total energy conserving semi-implicit scheme formulated here is applicable to real data long-term numerical integration. The experiment of thirteen FGGE data 30-day numerical integration indicates that the new type of total energy conserving semi-implicit fidelity scheme can surely modify the systematic deviation of energy and mass conserving of the traditional scheme.It should be particularly noted that,under the experiment conditions of the present work,the systematic errors induced by the violation of physical laws of conservation in the time-discretized process regarding the traditional scheme designs(called type Z errors for short)can contribute up to one-third of the total systematic root-mean-square(RMS)error at the end of second week of the integration and exceed one half of the total amount four weeks afterwards.In contrast,by realizing a total energy conserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors, roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reduced at the end of second week of the integration,and averagely more than one-third reduced at integral time of four weeks afterwards.In addition,experiment results also reveal that,in a sense,the effects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging.展开更多
In fact,the popular semi-implicit time difference scheme of spectral model still includes some important linear terms using time explicit difference scheme,and the major terms are directly related to fast internal-and...In fact,the popular semi-implicit time difference scheme of spectral model still includes some important linear terms using time explicit difference scheme,and the major terms are directly related to fast internal-and external-gravity waves in the atmospheric forecasting equation. Additionally,due to using time difference on two terms at different time.the popular scheme artificially introduces unbalance between pressure gradient force and Coriolis force terms while numerically computing their small difference between large quantities.According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation,one improved semi-implicit time difference scheme is also designed in our study.By adopting a kind of revised time-explicit-difference scheme to these linear terms that still included in spectral model governing equations,the defect of spectral model which only partly using semi-implicit integrating scheme can be overcome effectively.Moreover,besides all spectral coefficients of prognostic equations,especially of Helmholtz divergence equation,can be worked out without any numerical iteration,the time-step (computation stability) can also be enlarged (enhanced) by properly introducing an adjustable coefficient.展开更多
Based on the atmospheric self_memorization principle, a complex memory function was introduced and the spectral form of atmospheric self_memorial equation was derived. Setting up and solving the equation constitute a ...Based on the atmospheric self_memorization principle, a complex memory function was introduced and the spectral form of atmospheric self_memorial equation was derived. Setting up and solving the equation constitute a new approach of the numerical weather prediction. Using the spectral model T42L9 as a dynamic kernel, a global self_memorial T42 model (SMT42) was established, with which twelve cases of 30_d integration experiments were carried out. Compared with the T42L9, the SMT42 is much better in 500 hPa forecast not only for daily circulation but also for monthly mean circulation. The anomaly correlation coefficient (ACC) of forecast for monthly mean circulation has been improved to 0.42, increased by 0.05, and the root_mean_square error (RMSE) has been reduced from 6.09 to 4.03 dagpm.展开更多
基金supported by the National Basic Research Program of China(Grant No.2014CB44701)the National Natural Science Foundation of China(NSFC)(Grants No.41272283,40902080,41130753)
文摘Retrogressive landslides are common geological phenomena in mountainous areas and on onshore and offshore slopes. The impact of retrogressive landslides is different from that of other landslide types due to the phenomenon of retrogression. The hazards caused by retrogressive landslides may be increased because retrogressive landslides usually affect housing, facilities, and infrastructure located far from the original slopes. Additionally, substantial geomorphic evidence shows that the abundant supply of loose sediment in the source area of a debris flow is usually provided by retrogressive landslides that are triggered by the undercutting of water. Moreover, according to historic case studies, some large landslides are the evolution result of retrogressive landslides. Hence the ability to understand and predict the evolution of retrogressive landslides is crucial for the purpose of hazard mitigation. This paper discusses the phenomenon of a retrogressive landslide by using a model experiment and suggests a reasonably simplified numerical approach for the prediction of rainfall-induced retrogressive landslides. The simplified numerical approach, which combines the finite element method for seepage analysis, the shear strength reduction finite element method, and the analysis criterion for the retrogression and accumulation effect, is presented and used to predict the characteristics of a retrogressive landslide. The results show that this numerical approach is capable of reasonably predicting the characteristics of retrogressive landslides under rainfall infiltration, particularly the magnitude of each landslide, the position of the slip surface, and the development processes of the retrogressive landslide. Therefore, this approach is expected to be a practical method for the mitigation of damage caused by rainfall-induced retrogressive landslides.
基金The work is supported by the National Natural Science Foundation of China(49675267).
文摘In this paper,two formulation theorems of time-difference fidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,with earlier major conserving time-discretized schemes given as special cases.These two theorems can provide new mathematical basis for solving basic formulation problems of more types of conservative time- discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelity schemes by combining existing instantly conserving space-discretized schemes.Besides.the two theorems can also solve two large categories of problems about linear and nonlinear computational instability. The traditional global spectral-vertical finite-difference semi-implicit model for baroclinic primitive equations is currently used in many countries in the world for operational weather forecast and numerical simulations of general circulation.The present work,however,based on Theorem 2 formulated in this paper,develops and realizes a high-order total energy conserving semi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model of baroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved for long,whether in terms of theory or practice.The total energy conserving semi-implicit scheme formulated here is applicable to real data long-term numerical integration. The experiment of thirteen FGGE data 30-day numerical integration indicates that the new type of total energy conserving semi-implicit fidelity scheme can surely modify the systematic deviation of energy and mass conserving of the traditional scheme.It should be particularly noted that,under the experiment conditions of the present work,the systematic errors induced by the violation of physical laws of conservation in the time-discretized process regarding the traditional scheme designs(called type Z errors for short)can contribute up to one-third of the total systematic root-mean-square(RMS)error at the end of second week of the integration and exceed one half of the total amount four weeks afterwards.In contrast,by realizing a total energy conserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors, roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reduced at the end of second week of the integration,and averagely more than one-third reduced at integral time of four weeks afterwards.In addition,experiment results also reveal that,in a sense,the effects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging.
基金The project is supported by the Beijing New Star Program of Science and Technology of China during 2001-2004 under Grant No.H013610330119.
文摘In fact,the popular semi-implicit time difference scheme of spectral model still includes some important linear terms using time explicit difference scheme,and the major terms are directly related to fast internal-and external-gravity waves in the atmospheric forecasting equation. Additionally,due to using time difference on two terms at different time.the popular scheme artificially introduces unbalance between pressure gradient force and Coriolis force terms while numerically computing their small difference between large quantities.According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation,one improved semi-implicit time difference scheme is also designed in our study.By adopting a kind of revised time-explicit-difference scheme to these linear terms that still included in spectral model governing equations,the defect of spectral model which only partly using semi-implicit integrating scheme can be overcome effectively.Moreover,besides all spectral coefficients of prognostic equations,especially of Helmholtz divergence equation,can be worked out without any numerical iteration,the time-step (computation stability) can also be enlarged (enhanced) by properly introducing an adjustable coefficient.
文摘Based on the atmospheric self_memorization principle, a complex memory function was introduced and the spectral form of atmospheric self_memorial equation was derived. Setting up and solving the equation constitute a new approach of the numerical weather prediction. Using the spectral model T42L9 as a dynamic kernel, a global self_memorial T42 model (SMT42) was established, with which twelve cases of 30_d integration experiments were carried out. Compared with the T42L9, the SMT42 is much better in 500 hPa forecast not only for daily circulation but also for monthly mean circulation. The anomaly correlation coefficient (ACC) of forecast for monthly mean circulation has been improved to 0.42, increased by 0.05, and the root_mean_square error (RMSE) has been reduced from 6.09 to 4.03 dagpm.
