The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep terrain.Hybrid terrain-following(HTF)coordinates with smoo...The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep terrain.Hybrid terrain-following(HTF)coordinates with smooth slopes of vertical layers(slopeVL)generally overcome this difficulty.Therefore,the HTF coordinate becomes very desirable for atmospheric and oceanic numerical models.However,improper vertical layering in HTF coordinates may also increase the incidence of error.Except for the slopeVL of an HTF coordinate,this study further optimizes the HTF coordinate focusing on the thickness of vertical layers(thickVL).Four HTF coordinates(HTF1–HTF4)with similar slopeVL but different vertical transition methods of thickVL are designed,and the relationship between thickVL and numerical errors in each coordinate is compared in the classic idealized thermal convection[two-dimensional(2D)rising bubble]experiment over steep terrain.The errors of potential temperatureθand vertical velocity w are reduced most,by approximately 70%and 40%,respectively,in the HTF1 coordinate,with a monotonic increase in thickVL according to the increasing height;however,the errors ofθincreased in all the other HTF coordinates,with nonmonotonic thickVLs.Furthermore,analyses of the errors of vertical pressure gradient force(VPGF)show that due to the interpolation errors of thickVL,the inflection points in the vertical transition of thickVL induce the initial VPGF errors;therefore,the HTF1 coordinate with a monotonic increase in thickVL has the smallest errors among all the coordinates.More importantly,the temporal evolution of VPGF errors manifests top-type VPGF errors that propagate upward gradually during the time integration.Only the HTF1 and HTF4 coordinates with a monotonic increase in thickVL near the top of the terrain can suppress this propagation.This optimized HTF coordinate(i.e.,HTF1)can be a reference for designing a vertical thickVL in a numerical model.展开更多
为了探索都江堰—汶川G213线宽缓窄陡泥石流的降雨阈值,利用地震前后的遥感影像及地理信息系统(geographic information system,GIS)技术,提取研究区43条沟的地形因子;基于主成分分析法和SPSS软件分析各因子的相关性,建立综合地形因子...为了探索都江堰—汶川G213线宽缓窄陡泥石流的降雨阈值,利用地震前后的遥感影像及地理信息系统(geographic information system,GIS)技术,提取研究区43条沟的地形因子;基于主成分分析法和SPSS软件分析各因子的相关性,建立综合地形因子临界模型;通过引入降雨因素利用支持向量机分类模型得到不同沟道形态的降雨阈值模型。结果表明:综合地形因子以0.51为沟道形态分界线,大于0.51为窄陡型沟道,小于或等于0.51为宽缓型沟道,利用北川部分沟道进行模型验证,准确性达99%;基于综合地形因子所划分的沟道类型,通过研究区降雨数据进行数学分析得到综合地形因子和降雨因素之间的影响系数,利用随机向量机分类模型,对获得宽缓与窄陡沟道的降雨强度I和降雨历时D数据,建立I-D降雨阈值模型,I-D降雨阈值模型表明影响系数越大,地形因子就大,越利于泥石流的发生,激发泥石流所需的降雨阈值就越小,此类泥石流为窄陡型泥石流,反之亦然。研究成果可为不同区域、沟道类型、时间段的震后泥石流降雨阈值提供参考。展开更多
A new approach is proposed to use the covariant scalar equations of the a-coordinate （the covariant method）, in which the pressure gradient force （PGF） has only one term in each horizontal momentum equation, and t...A new approach is proposed to use the covariant scalar equations of the a-coordinate （the covariant method）, in which the pressure gradient force （PGF） has only one term in each horizontal momentum equation, and the PGF errors are much reduced in the computational space. In addition, the validity of reducing the PGF errors by this covariant method in the computational and physical space over steep terrain is investigated. First, the authors implement a set of idealized experiments of increasing terrain slope to compare the PGF errors of the covariant method and those of the classic method in the computational space. The results demonstrate that the PGF errors of the covariant method are consistently much-reduced, compared to those of the classic method. More importantly, the steeper the terrain, the greater the reduction in the ratio of the PGF errors via the covariant method. Next, the authors use geometric analysis to further investigate the PGF errors in the physical space, and the results illustrates that the PGF of the covariant method equals that of the classic method in the physical space; namely, the covariant method based on the non-orthogonal a-coordinate cannot reduce the PGF errors in the physical space. However, an orthogonal method can reduce the PGF errors in the physical space. Finally, a set of idealized experiments are carried out to validate the results obtained by the geometric analysis. These results indicate that the covariant method may improve the simulation of variables relevant to pressure, in addition to pressure itself, near steep terrain.展开更多
基金Supported by the National Natural Science Foundation of China(42230606)14th Five-Year Plan Basic Research Program of Institute of Atmospheric Physics,Chinese Academy of Sciences(E268081801)National Key Research and Development Program of China(2017YFA0603901)。
文摘The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep terrain.Hybrid terrain-following(HTF)coordinates with smooth slopes of vertical layers(slopeVL)generally overcome this difficulty.Therefore,the HTF coordinate becomes very desirable for atmospheric and oceanic numerical models.However,improper vertical layering in HTF coordinates may also increase the incidence of error.Except for the slopeVL of an HTF coordinate,this study further optimizes the HTF coordinate focusing on the thickness of vertical layers(thickVL).Four HTF coordinates(HTF1–HTF4)with similar slopeVL but different vertical transition methods of thickVL are designed,and the relationship between thickVL and numerical errors in each coordinate is compared in the classic idealized thermal convection[two-dimensional(2D)rising bubble]experiment over steep terrain.The errors of potential temperatureθand vertical velocity w are reduced most,by approximately 70%and 40%,respectively,in the HTF1 coordinate,with a monotonic increase in thickVL according to the increasing height;however,the errors ofθincreased in all the other HTF coordinates,with nonmonotonic thickVLs.Furthermore,analyses of the errors of vertical pressure gradient force(VPGF)show that due to the interpolation errors of thickVL,the inflection points in the vertical transition of thickVL induce the initial VPGF errors;therefore,the HTF1 coordinate with a monotonic increase in thickVL has the smallest errors among all the coordinates.More importantly,the temporal evolution of VPGF errors manifests top-type VPGF errors that propagate upward gradually during the time integration.Only the HTF1 and HTF4 coordinates with a monotonic increase in thickVL near the top of the terrain can suppress this propagation.This optimized HTF coordinate(i.e.,HTF1)can be a reference for designing a vertical thickVL in a numerical model.
文摘为了探索都江堰—汶川G213线宽缓窄陡泥石流的降雨阈值,利用地震前后的遥感影像及地理信息系统(geographic information system,GIS)技术,提取研究区43条沟的地形因子;基于主成分分析法和SPSS软件分析各因子的相关性,建立综合地形因子临界模型;通过引入降雨因素利用支持向量机分类模型得到不同沟道形态的降雨阈值模型。结果表明:综合地形因子以0.51为沟道形态分界线,大于0.51为窄陡型沟道,小于或等于0.51为宽缓型沟道,利用北川部分沟道进行模型验证,准确性达99%;基于综合地形因子所划分的沟道类型,通过研究区降雨数据进行数学分析得到综合地形因子和降雨因素之间的影响系数,利用随机向量机分类模型,对获得宽缓与窄陡沟道的降雨强度I和降雨历时D数据,建立I-D降雨阈值模型,I-D降雨阈值模型表明影响系数越大,地形因子就大,越利于泥石流的发生,激发泥石流所需的降雨阈值就越小,此类泥石流为窄陡型泥石流,反之亦然。研究成果可为不同区域、沟道类型、时间段的震后泥石流降雨阈值提供参考。
基金supported by the National Basic Research Program of China(973 Program)[grant number 2015CB954102]the National Natural Science Foundation of China[grant number41305095],[grant number 41175064]
文摘A new approach is proposed to use the covariant scalar equations of the a-coordinate （the covariant method）, in which the pressure gradient force （PGF） has only one term in each horizontal momentum equation, and the PGF errors are much reduced in the computational space. In addition, the validity of reducing the PGF errors by this covariant method in the computational and physical space over steep terrain is investigated. First, the authors implement a set of idealized experiments of increasing terrain slope to compare the PGF errors of the covariant method and those of the classic method in the computational space. The results demonstrate that the PGF errors of the covariant method are consistently much-reduced, compared to those of the classic method. More importantly, the steeper the terrain, the greater the reduction in the ratio of the PGF errors via the covariant method. Next, the authors use geometric analysis to further investigate the PGF errors in the physical space, and the results illustrates that the PGF of the covariant method equals that of the classic method in the physical space; namely, the covariant method based on the non-orthogonal a-coordinate cannot reduce the PGF errors in the physical space. However, an orthogonal method can reduce the PGF errors in the physical space. Finally, a set of idealized experiments are carried out to validate the results obtained by the geometric analysis. These results indicate that the covariant method may improve the simulation of variables relevant to pressure, in addition to pressure itself, near steep terrain.
