The moist C-vector and its applications
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摘要: C 矢量( C )是 Q 矢量( Q )在三维空间中的延伸,表征了三维非地转运动。然而, C 是基于地转风近似和绝热条件得到的,不包含大气运动的非绝热加热信息。大气中的降水及其影响天气系统往往与大气凝结潜热释放所产生的非绝热效应有关。从β平面下的p坐标系大气原始方程组出发,考虑大气非绝热效应,推导湿 C 矢量( C *),揭示 C *的物理意义。利用ERA5再分析资料和高原低涡数据集,通过 C *诊断青藏高原低涡(简称“高原涡”)个例形成、发展和移动过程,并与 C 的诊断结果进行对比以证实 C *的应用价值。结果表明,相较于 Q 和 C , C *包含更全面的非地转运动信息,在诊断中具有优势。 C *的水平分量(
$ {\boldsymbol{C}}_{{\text{hor}}}^* $ )表征了热成风非平衡和非绝热加热作用产生的次级环流,能更好地解释高原涡移动方向改变的原因; C *的垂直分量($C_p^*$ )恢复了被 Q 丢失的非地转运动信息,描述了地转非平衡产生的水平非地转运动,其负值中心表征高原涡中心的位置,且对高原涡发展具有一定的预示作用。此外,$ {\boldsymbol{C}}_{{\text{hor}}}^* $ 和$C_p^*$ 的相对大小还表明高原涡存在显著的斜压性。Abstract: The C -vector ( C ) is an extension of the Q -vector ( Q ) in the three-dimensional space, characterizing three-dimensional ageostrophic motion. However, C is derived from the geostrophic wind and adiabatic approximations, and the diabatic effect is excluded. Precipitation and its impact on weather systems in the atmosphere are frequently related to the diabatic effect produced by the release of latent heat. Based on the primitive equations in p-coordinate with the β-plane approximation and the diabatic effect, the moist C -vector ( C *) is proposed, and its physical interpretations are revealed. A Qingzang Plateau vortex case is diagnosed by C * using the fifth-generation European Center for Medium-Range Weather Forecasts atmospheric reanalysis data (ERA5) and the database of the Qingzang Plateau vortex. Results are compared with the diagnostic results of C to prove the application value of C *. It is found that compared with Q and C , C * contains more comprehensive information of the ageostrophic motion and thus has more advantages in diagnosis. The horizontal component of C * ($ {\boldsymbol{C}}_{{\text{hor}}}^* $ ) depicts the secondary circulation caused by thermal wind imbalance and diabatic effect, better explaining the reason for the direction change of the Qingzang Plateau vortex movement than that C . The vertical component of C * ($C_p^*$ ) restores the information of ageostrophic motion which is lost by Q , and depicts horizontal ageostrophic motion caused by geostrophic imbalance. The negative$C_p^*$ center represents the Qingzang Plateau vortex center, and has a certain predictive effect on the development of the Qingzang Plateau vortex. Besides, the relative sizes of$ {\boldsymbol{C}}_{{\text{hor}}}^* $ and$C_p^*$ indicate that the Qingzang Plateau vortex has a significant baroclinic property.-
Key words:
- Moist C-vector /
- C-vector /
- Ageostrophic motion /
- Diabatic effect /
- Qingzang Plateau vortex
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图 1 水平伸缩形变 (a) 和切变形变 (b) 破坏热成风平衡产生次级环流的机理示意 (底部虚线为等位温线,灰色粗箭头分别表示伸缩形变和切变形变;形变强迫改变位温梯度和水平拟涡度 (ζhor),破坏热成风平衡;Fb和
$\nabla $ pb分别为位温梯度改变产生的净浮力和对应的净浮力梯度;δu和Fc分别为热成风非平衡改变的水平拟涡度以及对应的科里奥利力;净浮力和科里奥利力产生了次级环流,可分别用Q*和$ {\boldsymbol{C}}_{{\text{hor1}}}^* $ 表示)Figure 1. Schematic diagram of the mechanism behind the horizontal telescoping deformation (a) and shearing deformation (b) destroying the thermal wind balance (the dashed lines at bottom are isotherms,and the gray thick arrows indicate the telescoping and shearing deformation;the deformation force changes the potential temperature gradient and the horizontal pseudovorticity (ζhor),and destroys the thermal wind balance;Fb and
$\nabla $ pb are the net buoyancy and related buoyancy gradient generated by the change of the potential temperature gradient;δu and Fc are the horizontal pseudovorticity and related Coriolis force changed by the thermal wind imbalance;the secondary circulation is generated by both the net buoyancy and Coriolis force,and can be represented by Q* and$ {\boldsymbol{C}}_{{\text{hor1}}}^* $ respectively)图 2 水平形变 (a) 和旋转 (b) 破坏地转平衡产生非地转运动的机理示意 (粗箭头分别表示形变和旋转,细箭头和虚线箭头分别为地转非平衡产生的水平运动 (δV) 及其对应的科里奥利力 (Fc))
Figure 2. Schematic diagram of the mechanism behind the horizontal deformation (a) and rotation (b) destroying the geostrophic balance (The thick arrows indicate the deformation and rotation respectively,and the thin and dashed arrows indicate the horizontal motion (δV) and related Coriolis force (Fc) respectively)
图 4 2016年6月28日12时至30日00时500 hPa高度上高原涡中心的 (a,图中数字前两位为日、后两位为时) 位置和移动路径 (黑色实线为青藏高原边界,灰阶为海拔高度) 以及 (b) 其位势高度 (实线) 和垂直相对涡度 (虚线) 的演变
Figure 4. (a) The track of the Qingzang plateau vortex center at 500 hPa from 12:00 UTC 28 June to 00:00 UTC 30 June 2016(the black line is the boundary of the Qingzang plateau and the altitude is shaded; the number is date (day) and tine (hour)),and (b) evolution of the geopotential height of the vortex center (solid line) and vertical relative vorticity (dashed line)
图 3 β效应破坏地转平衡的机理示意 (同心圆代表低压涡旋系统的等位势高度线,涡旋内位势梯度的大小一致;A和B为与涡旋中心处于同一经圈上的两个点,且二者与涡旋中心的纬距相等;A点的地转风涡度和地转风强度均小于B点;A和B点的
$C_{p2}^*$ 分别为负值和正值)Figure 3. Schematic diagram of the mechanism behind the
$ \beta $ -effect destroying geostrophic balance (The concentric circles represent the isohypses of the low-pressure vortex system,and the magnitude of the potential gradient within the vortex is consistent;A and B are two points on the same longitude circle as the center of the vortex,and the latitudinal distances between them and the center of the vortex are equal;both the geostrophic vorticity and the geostrophic wind intensity at point A are smaller than those at point B;$C_{p2}^*$ of A and B are negative and positive respectively)图 5 2016年6月28日06时至30日00时500 hPa高度上逐6 h的
$ {\boldsymbol{C}}_{{\text{hor}}}^* $ (箭矢,单位:10−10 s-3)、$C_p^*$ (色阶,单位:10−13 s-3) 和位势高度 (等值线,单位:gpm) 的分布 (红色三角代表高原涡中心位置,灰色实线为青藏高原边界)Figure 5. Distributions of
$ {\boldsymbol{C}}_{{\text{hor}}}^* $ (vectors,unit:10−10s-3),$C_p^*$ (shaded,unit:10−13 s-3) and geopotential height (contours,unit:gpm) every 6 h from 12:00 UTC 28 June to 00:00 UTC 30 June 2016 (the red triangle represents the location of the Qingzang Plateau vortex center,and the gray line is the boundary of the Qingzang Plateau) -
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