Physically Consistent Atmospheric Variational Objective Analysis Model and Its Applications over the Tibetan Plateau. Part I: Method and Evaluation
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摘要: 本文系统地介绍了基于约束变分客观分析法构建的物理协调大气变分客观分析模型，并将模型首次应用于青藏高原那曲试验区。该模型可融合不同时空分辨率的多来源数据，通过利用地面降水和地面、大气顶部的热通量等大气上下边界的观测资料来约束调整探空观测变量，从而尽可能保证气柱内的质量、热量、水汽和动量收支平衡。对模型及其产生的第三次青藏高原大气科学试验那曲试验区2014年8月期间的大气分析数据集进行评估分析，结果表明模型生成的常规状态量很好地保留了观测特征，模型生成的重要大尺度衍生量（如，垂直速度、散度、温度/水汽平流、视热源、视水汽汇等）可以较好地反映试验期内大气柱的动力、热力和水汽结构特征，有利于对大气降水过程的分析研究。分析发现，350～400 hPa高度层是该时期那曲试验区的动力、热量和水汽的重要变化中心。从各种观测资料对模型生成的分析场的影响来看，探空观测对高空风场的影响最大，但这种影响的幅度在1 m/s以内；降水和上下边界通量观测主要影响大尺度衍生量，如垂直速度，其中降水主要影响降水时期的上升运动，通量观测主要影响弱/无降水时期的下沉运动。总体而言，物理协调大气变分客观分析模型具备较好的稳定性和合理性。
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关键词:
- 物理协调大气变分客观分析模型 /
- 约束变分分析 /
- 青藏高原那曲试验区 /
- 多来源观测 /
- 评估
Abstract: A physically consistent atmospheric objective analysis model, based on the constrained variational analysis method, was applied to the Tibetan Plateau for large-scale atmospheric structure analysis. This objective analysis model can deal with multisource measurements with different spatial and temporal resolutions, and satisfy the conservation of column-integrated mass, heat, moisture, and momentum using surface precipitation and flux data at the surface and top of the atmosphere to constrain the sounding measurements. An experiment during August 2014 around Naqu in the Tibetan Plateau shows that those state variables generated by the model can retain observational characteristics. The analyzed large-scale derivatives, such as vertical velocity, divergence, temperature and water vapor advection, apparent heat source, and apparent moisture sink, obtained by the objective analysis model, can reasonably demonstrate dynamic, thermal, and moisture structures during the analysis period, which is conducive to precipitation process studies. It also shows that the layer of 350–400 hPa is an important change center of dynamics, heat, and water vapor in the analysis region during August 2014. Different sources of measurements have different impacts on the final analysis fields in this model. The sounding measurement significantly impacts the upper-level wind, but the amplitude of this impact is small, within 1 m/s. Precipitation and flux measurements mainly affect the large-scale derivatives, such as vertical velocity, in which precipitation mainly affects the upward movement during precipitation periods, and flux data mainly affect the downward movement during light rain/no-rain periods. Generally, the physically consistent atmospheric variational objective analysis model has high stability and strong validity. -
图 1 基于传统客观分析方法的物理概念模型（左）和基于约束变分客观分析方法的物理概念模型（右）
Figure 1. Physical conceptions based on a traditional objective analysis method with only mass constraint (left) and the constrained variational analysis (CVA) method (right)
图 2 2014年8月青藏高原那曲试验区的资料分布。“+”表示0.25°×0.25°的ERA5背景场格点；“••”表示121个地面气象自动站，其中只有78个黄色站可提供除了降水以外的温、压、湿、风等其他常规地面要素的有效观测；“o”表示探空站；“×”表示1°×1°的CERES格点；“◊”为边界层观测站点；“*”为人为选定的分析点（F0～F12），构成气柱边界和中心
Figure 2. Data network of the Tibetan Plateau-Naqu analysis region during August 2014. Symbols “+” represent the ERA5 background grid points with a spatial resolution of 0.25°×0.25°; “••” represent the 121 surface meteorological automatic stations in which the yellow ones denote only 78 stations that could give the measurements of other state variables besides precipitation; “o” represent the sounding stations; “×” represent the CERES (Clouds and the Earth’ s Radiant Energy System) grid points with a spatial resolution of 1°×1°; “◊” represent the boundary-layer stations; and “*” represent the artificial analysis points (F0–F12) which form the air column boundary and the center of the Tibetan Plateau-Naqu analysis region during August 2014
图 3 2014年8月物理协调大气变分客观分析模型在变分客观分析前（左）和变分客观分析后（右）的气柱（a、b）质量剩余（单位：g m−2 s−1）、（c、d）水汽剩余（单位：mm d−1）和（e、f）热量剩余（单位：kW m−2）
Figure 3. Residuals of (a, b) mass (units: g m−2 s−1), (c, d) moisture (mm d−1), and (e, f) heat (kW m−2) before (left) and after (right) the CVA procedure in the physically consistent atmospheric variational objective analysis model during August 2014
图 4 2014年8月青藏高原那曲试验区区域平均的（a）物理协调大气变分客观分析模型输出数据（实线）和ERA5再分析资料（虚线）的地面气压（单位：hPa）的时间变化，以及（b）试验区气象自动站观测和（c）ERA5再分析资料的地面气压频率分布
Figure 4. (a) Time series of the domain-averaged surface pressure (units: hPa) derived from the physically consistent atmospheric variational objective analysis model (solid line) and the ERA5 reanalysis data (dashed line), and frequency of the surface pressure from (b) automatic stations and (c) ERA5 reanalysis data in the Tibetan Plateau-Naqu analysis region during August 2014
图 5 2014年8月青藏高原那曲试验区高空纬向风（左，单位：m/s）、经向风（右，单位：m/s）：（a、b）那曲探空站数据，观测时间分辨率为12 h，白色矩形条表示缺测；（c、d）物理协调大气变分客观分析模型输出数据，时间分辨率为1 h；（e、f）ERA5再分析资料，时间分辨率为1 h
Figure 5. Upper-level zonal wind (left column, units: m/s) and meridional wind (right column, units: m/s) in the Tibetan Plateau-Naqu analysis region during August 2014: (a, b) Naqu sounding station with 12-h temporal resolution, the white blanks represent missing data; (c, d) the physically consistent atmospheric variational objective analysis model with 1-h temporal resolution; (e, f) ERA5 reanalysis data with 1-h temporal resolution
图 6 2014年8月13～22日青藏高原那曲试验区高空（a、b）垂直速度（单位：hPa/h）和（c、d）散度（单位：10−5 s−1）。左边为物理协调大气变分客观分析模型输出结果，右边为ERA5结果，黑色实线表示地面降水率（单位：mm/d）
Figure 6. Domain-averaged (a, b) vertical velocity (units: hPa/h) and (c, d) divergence (units: 10−5 s−1) derived from the physically consistent atmospheric variational objective analysis model (left column) and the ERA5 reanalysis (right column) the Tibetan Plateau-Naqu analysis region from 13 August to 22 August 2014. The black line represents the surface rainfall rate (units: mm/d)
图 7 2014年8月青藏高原那曲试验区区域平均地面降水率（单位：mm/d）的时间序列
Figure 7. Time series of the domain-averaged surface rainfall rate (units: mm/d) in the Tibetan Plateau-Naqu analysis region during August 2014
图 8 2014年8月青藏高原那曲试验区不同降水强度的垂直速度廓线（单位：m/s，正值表示上升运动）。黑色实线表示8月的平均结果，虚线表示强降水时期（＞5 mm/d）的平均结果，点线表示弱降水时期（1～5 mm/d）的平均结果，点虚线表示无雨时期（＜1 mm/d）的平均结果
Figure 8. Profiles of vertical velocity (units: m/s, positive values mean upward motion) for monthly average (solid line), strong rainfall (＞5 mm/d, dashed line), weak rainfall (1–5 mm/d, dotted line), and no rainfall (＜1 mm/d, dash-dotted line) in the Tibetan Plateau-Naqu analysis region during August 2014
图 9 2014年8月青藏高原那曲试验区不同降水强度的平流廓线：（a）水平热量（单位：K/h）；（b）垂直热量（单位：K/h）；（c）水平水汽（单位：g kg−1 h−1）；（d）垂直水汽（单位：g kg−1 h−1）。黑色实线表示8月平均的结果，虚线表示强降水时期（＞5 mm/d）的结果，点线表示弱降水时期（1～5 mm/d）的结果，点虚线表示无雨时期（＜1 mm/d）的结果
Figure 9. Advection profiles of (a) horizontal heat (units: K/h), (b) vertical heat (units: K/h), (c) horizontal moisture (units: g kg−1 h−1), and (d) vertical moisture (units: g kg−1 h−1) for monthly average (solid line), strong rainfall (＞5 mm/d, dashed line), weak rainfall (1–5 mm/d, dotted line), and no rainfall (＜1 mm/d, dash-dotted line) in the Tibetan Plateau-Naqu analysis region during August 2014
图 10 2014年8月青藏高原那曲试验区不同降水强度的（a）视热源Q1（单位：K/h）和（b）视水汽汇Q2（单位：K/h）的廓线。黑色实线表示8月平均的结果，虚线表示强降水时期（＞5 mm/d）的结果，点线表示弱降水时期（1～5 mm/d）的结果，点虚线表示无雨时期（＜1 mm/d）的结果
Figure 10. Profiles of (a) apparent heat source Q1 (units: K/h) and (b) apparent moisture sink Q2 (units: K/h) for monthly average (solid line), strong rainfall (＞5 mm/d, dashed line), weak rainfall (1–5 mm/d, dotted line), and no rainfall (＜1 mm/d, dash-dotted line) in the Tibetan Plateau-Naqu analysis region during August 2014
图 11 物理协调大气变分客观分析模型仅输入ERA-Interim再分析资料时青藏高原那曲试验区资料点分布。“*”表示由人为补充站构成的分析点，“o”表示探空站，“+”表示背景场格点
Figure 11. Data network of the physically consistent atmospheric variational objective analysis model, with only inputs from the ERA-Interim reanalysis data. “*” represents artificial analysis points, “o” represents fictitious sounding stations, and “+” represents background grid points
图 12 E0试验（蓝色点线）和E1试验（绿色虚线）所得的2014年8月青藏高原那曲试验区平均的（a）纬向风（u, 单位：m/s）、（b）经向风（v, 单位：m/s）、（c）温度（T, 单位：°C）、（d）水汽混合比（q, 单位：g/kg）
Figure 12. Profiles of the (a) zonal wind (u, units: m/s), (b) meridional wind (v, units: m/s), (c) temperature (T, units: °C), and (d) water vapor mixing ratio (q, units: g/kg) averaged in the Tibetan Plateau-Naqu analysis region during August 2014, produced by two sensitivity tests E0 (dotted blue line) and E1 (dashed green line)
图 13 （a）E0试验和（b）E1试验分析所得的2014年8月青藏高原那曲试验区平均的垂直速度（彩色阴影，单位：hPa/h）、地面观测降水演变（黑色实线）
Figure 13. Domain-averaged vertical velocity (color shadings, units: hPa/h) and surface rainfall rate (black line) in the Tibetan Plateau-Naqu analysis region during August 2014, produced by two sensitivity tests (a) E0 and (b) E1
图 14 2014年8月青藏高原那曲试验区平均的降水率（单位：mm/d）。绿色点线：ERA-Interim再分析资料；蓝色虚线：CMORPH融合降水资料；黑色实线：地面自动站观测资料
Figure 14. Time series of the domain-averaged surface rainfall rate (units: mm/d) from ERA-Interim reanalysis (green dotted line), CMORPH fusion precipitation data (blue dashed line), and surface automatic stations (black solid line) in the Tibetan Plateau-Naqu analysis region during August 2014
图 15 2014年8月青藏高原那曲试验区平均的E2试验、E3试验分析结果与E1试验所获得分析结果的差异：（a）纬向风（单位：m/s）；（b）经向风（单位：m/s）；（c）温度（单位：°C）；（d）水汽混合比（单位：g/kg）
Figure 15. Differences of the (a) zonal wind (units: m/s), (b) meridional wind (units: m/s), (c) temperature (units: °C), and (d) water vapor mixing ratio (units: g/kg) between test E2 and test E1, between test E3 and test E1 averaged in the Tibetan Plateau-Naqu analysis region during August 2014
图 16 2014年8月青藏高原那曲试验区平均的（a）E2试验输入L波段探空和自动站观测降水资料以及（b）E3试验输入L波段探空和CMORPH融合降水资料后的高空垂直速度（彩色阴影，单位：hPa/h）、地面降水强度演变（黑色实线）。（c）2014年8月14～17日、20～22日青藏高原那曲试验区模型输入不同降水资料后平均的垂直速度廓线
Figure 16. Domain-averaged vertical velocity (color shadings, units: hPa/h) and surface rainfall rate (black line) in the Tibetan Plateau-Naqu analysis region during August 2014, produced by two sensitivity tests (a) E2 and (b) E3. (c) Profiles of the vertical velocity (units: hPa/h) from E2 and E3 averaged in the Tibetan Plateau-Naqu analysis region from 14 to 17 August 2014 and from 20 to 22August 2014
图 17 2014年8月青藏高原那曲试验区平均的（a）地面潜热通量、（b）地面感热通量、（c）地面净向上辐射通量、（d）大气顶净向下辐射通量。图a、b中，实线表示边界层综合观测结果（8月30日后存在缺测）；图c、d中，实线表示CERES卫星观测订正后的结果。虚线表示ERA-Interim再分析结果
Figure 17. Time series of the domain-averaged (a) surface latent heat flux, (b) surface sensible heat flux, (c) surface net upward radiative flux, (d) top-of-atmosphere (TOA) net downward radiative flux in the Tibetan Plateau-Naqu analysis region during August 2014. In Figs. a and b, the solid lines mean observation from the boundary-layer station; in Figs. c and d, the solid lines mean CERES (Clouds and the Earth’ s Radiant Energy System)-produced results. The dashed lines mean ERA-Interim reanalysis
图 18 2014年8月青藏高原那曲试验区平均的E0试验、E2试验、E4试验分析所得的（a）纬向风（单位：m/s）、（b）经向风（单位：m/s）、（c）温度（单位：°C）、（d）水汽混合比（单位：g/kg）
Figure 18. Profiles of the (a) zonal wind (units: m/s), (b) meridional wind (units: m/s), (c) temperature (units: °C), and (d) water vapor mixing ratio (units: g/kg) averaged in the Tibetan Plateau-Naqu analysis region during August 2014, produced by three sensitivity tests E0, E2, and E4
表 1 2014年8月青藏高原那曲试验区物理协调大气变分客观分析模型的输入资料
Table 1. Information of the input data for the physically consistent atmospheric variational objective analysis model during August 2014 in the Tibetan Plateau-Naqu analysis region
资料种类 资料来源 变量 时间
分辨率空间
分辨率背景场 ERA5 气压层纬向风 1 h 0.25°×
0.25°气压层经向风 气压层温度 气压层湿度 高空观测 L波段探空 高空纬向风 12 h 站点 高空经向风 高空气压 高空温度 高空湿度 地面观测 地面自动气象站 10 m纬向风 1 h 站点 10 m经向风 地面气压 2 m温度 2 m湿度 地面降水 边界层观测 TIPEX-III 地面潜热通量 0.5 h 站点 地面感热通量 卫星资料 CERES 地面向上短波辐射 1 h 1°×1° 地面向下短波辐射 地面向上长波辐射 地面向下长波辐射 大气顶向下短波辐射 大气顶向下长波辐射 大气云液态水含量 
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表 2 物理协调大气变分客观分析模型输出的变量产品
Table 2. Variables derived by the physically consistent atmospheric variational objective analysis model
单层变量 单层变量 序号 变量名 单位 序号 变量名 单位 1 降水率 mm/h 14 大气顶向上长波辐射 W/m2 2 地面潜热通量 W/m2 15 大气云液态水含量 cm 3 地面感热通量 W/m2 16 气柱整层水汽变化 mm/h 4 气柱平均地面气压 hPa 17 气柱整层水汽平流 mm/h 5 中心点地面气压 hPa 18 地面蒸发率 mm/h 6 地面温度 °C 19 气柱整层热量变化 W/m2 7 地面相对湿度 % 20 气柱整层热量平流 W/m2 8 地面全风速 m/s 21 气柱净辐射 W/m2 9 地面纬向风 m/s 22 气柱潜热 W/m2 10 地面经向风 m/s 23 地面垂直速度 hPa/h 11 地面净向下短波辐射 W/m2 24 2 m水汽混合比 g/kg 12 地面净向上长波辐射 W/m2 25 2 m干静力能 K 13 大气顶向下短波辐射 W/m2 26 大气可降水量 cm 多层变量 多层变量 序号 变量名 单位 序号 变量名 单位 1 温度 K 10 垂直水汽平流 g kg−1 h−1 2 水汽混合比 g/kg 11 热能 K 3 纬向风 m/s 12 水平热能平流 K/h 4 经向风 m/s 13 垂直热能平流 K/h 5 垂直速度 hPa/h 14 热能变化率 K/h 6 水平辐合辐散 1/s 15 温度变化率 K/h 7 水平温度平流 K/h 16 水汽变化率 g kg−1 h−1 8 垂直温度平流 K/h 17 视热源 K/h 9 水平水汽平流 g kg−1 h−1 18 视水汽汇 K/h
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表 3 输入物理协调大气变分客观分析模型的不同来源资料的敏感性试验
Table 3. Sensitivity tests to examine the effect of different sources of the input data on the physically consistent atmospheric variational objective analysis model
变量 来源资料 试验E0 试验E1 试验E2 试验E3 试验E4 垂直多层次的气压、温度、湿度、风（背景场） ERA-Interim ERA-Interim ERA-Interim ERA-Interim ERA-Interim 垂直多层次的气压、温度、湿度、风（探空场） ERA-Interim L波段探空 L波段探空 L波段探空 L波段探空 降水量 ERA-Interim ERA-Interim 自动站 CMORPH 自动站 地面气压、温度、湿度、风 ERA-Interim ERA-Interim ERA-Interim ERA-Interim 自动站 地面感热、潜热通量 ERA-Interim ERA-Interim ERA-Interim ERA-Interim 边界层观测站 地面和大气顶和大气顶净辐射 ERA-Interim ERA-Interim ERA-Interim ERA-Interim CERES 云液态水含量 ERA-Interim ERA-Interim ERA-Interim ERA-Interim CERES
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