伴随敏感性方法、第一奇异向量方法以及条件非线性最优扰动方法在台风目标观测敏感区识别中的比较研究

周菲凡; 叶一苇; 段晚锁; 张贺

doi:10.3878/j.issn.1006-9895.2202.22008

伴随敏感性方法、第一奇异向量方法以及条件非线性最优扰动方法在台风目标观测敏感区识别中的比较研究

doi: 10.3878/j.issn.1006-9895.2202.22008

周菲凡^{1, 2,},
叶一苇^{1, 2},
段晚锁^{2, 3},
张贺^{4, 5}

1.
中国科学院大气物理研究所云降水物理与强风暴重点实验室, 北京 100029
2.
中国科学院大学, 北京 100049
3.
中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室, 北京 100029
4.
中国科学院大气物理研究所国际气候与环境科学中心, 北京 100029
5.
南京信息工程大学气象灾害预报预警与评估协同创新中心, 南京 210044

基金项目: 国家重点研发计划项目2018YFC1506402、2017YFC1501601，国家自然科学基金项目42175079

详细信息

作者简介:
周菲凡，女，1982年出生，研究员，主要从事台风、暴雨的可预报性研究。E-mail: zhouff04@163.com

中图分类号: P411
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出版历程
- 收稿日期: 2022-01-06
- 录用日期: 2022-03-03
- 网络出版日期: 2022-03-03
- 刊出日期: 2022-05-19

Comparisons of Adjoint Sensitivity, Leading Singular Vector, and Conditional Nonlinear Optimal Perturbations in the Identification of Sensitive Areas for Tropical-Cyclone-Targeted Observations

Feifan ZHOU^{1, 2
,},
Yiwei YE^{1, 2},
Wansuo DUAN^{2, 3},
He ZHANG^{4, 5}

1.
Key Laboratory of Cloud–Precipitation Physics and Severe Storms, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
2.
University of Chinese Academy of Sciences, Beijing 100049
3.
State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
4.
International Center for Climate and Environment Sciences (ICCES), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
5.
Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science & Technology, Nanjing 210044

Funds: National Key Research and Development Program of China (Grants 2018YFC1506402, 2017YFC1501601), National Natural Science Foundation of China (Grant 42175079)

摘要

摘要: 本文通过深入分析伴随敏感性（ADS）方法、第一奇异向量（LSV）方法、以及条件非线性最优扰动（CNOP）方法在目标观测敏感区识别方面的原理，提出了非线性程度的概念和计算方法，考察了转向型和直线型台风的非线性程度，分析了上述三种方法在不同非线性程度下识别的敏感区的异同，同时对比了转向型和直线型台风的敏感区的差异，并通过敏感性试验探讨了在不同非线性程度下以及在转向型与直线型台风中，预报对敏感区内初值的敏感性程度，进而探讨台风目标观测在不同情况下的有效性。结果表明，转向型台风的非线性程度差别比较大，或者特别强，或者特别弱；而直线型台风非线性程度居中，不同台风个例之间的非线性程度差别较小。对于非线性较弱的台风，三种方法识别的敏感区较为相似，而对于非线性较强的台风，LSV方法与ADS方法识别的敏感区较为相似，但是与CNOP方法识别的敏感区具有较大的差别。对于转向型台风，敏感区主要位于行进路径的右前方，而对于直线型台风，敏感区主要位于初始台风位置的后方。敏感性试验表明，不论台风非线性强弱，转向还是直行，CNOP敏感区内的随机扰动发展最大，而LSV敏感区内叠加的随机扰动发展次之，ADS敏感区内叠加的扰动发展最小；此外，非线性弱的台风，扰动的发展大于非线性强的台风的扰动的发展，表明非线性弱的台风预报受初值影响更大，目标观测的效果可能会更明显。
- 伴随敏感性 /
- 第一奇异向量 /
- 条件非线性最优扰动 /
- 非线性程度 /
- 敏感区 /
- 台风
Abstract: By analyzing how adjoint sensitivity (ADS), leading singular vector (LSV), and conditional nonlinear optimal perturbation (CNOP) methods are used to identify sensitive areas for target observation, the authors developed the concept of nonlinear degree. Moreover, the authors investigated the nonlinear degrees of straight and recurved types of typhoons. Subsequently, the sensitive areas identified using the three methods indicated earlier under different nonlinear degrees, together with the sensitive areas for straight and recurved types of typhoons, were analyzed. Finally, the sensitivity of the forecast to the initial values in the sensitive areas under different nonlinear degrees and for straight and recurved types of typhoons was explored. The results showed that the nonlinear degrees of recurved typhoons were quite different, either particularly strong or particularly weak, whereas negligible differences were observed among the nonlinear degrees of straight typhoons. For typhoons with weak nonlinearity, the sensitive areas identified using the three methods were similar, whereas for typhoons with strong nonlinearity, the sensitive areas identified by the LSV and ADS methods were similar, but they were quite different from those identified by the CNOP method. For recurved typhoons, the sensitive area was mainly located at the right front of its travel path, whereas for straight typhoons, the sensitive area was mainly located behind its travel path. The sensitivity test showed that the development of random perturbation in CNOP sensitive areas was the largest, regardless of whether the typhoon was strong nonlinear or not. In addition, the development of perturbation for weak nonlinear typhoons was greater than that for strong nonlinear typhoons. These results imply that the prediction for weak nonlinear typhoons is more sensitive to the initial uncertainty; thus, targeted observations for this kind of typhoon may be more effective.
- Adjoint sensitivity /
- Leading singular vector /
- CNOP (conditional nonlinear optimal perturbation) /
- Nonlinearity /
- Sensitivity area /
- Typhoon

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图 1 目标函数J₁对初始分析场x₀的梯度的求解过程示意图

Figure 1. Schematic diagram of the solving process for the gradient of the cost function (J₁), with respect to the initial analysis (x₀). M indicates the nonlinear model, and G is the measurement of the forecasts (x_t), L^* is the adjoint model of L, which is the tangent model of M

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图 2 （a–c）2004Meari、（d–f）2011Meari、（g–i）2010Megi_2台风，$\sigma $=0.7层ADS方法（上）、LSV方法（中）、CNOP方法（下）识别的风场（箭头）、温度场（彩色阴影）敏感区以及各台风研究时段起始时刻的500 hPa位势高度场（等值线，等值线间隔20 gpm）。上行图中，箭头表示矢量风梯度，只绘制了值≥4 m s⁻¹的区域；彩色阴影表示温度梯度，只绘制了绝对值≥3 J kg⁻¹ K⁻¹的区域。中、下行图中，箭头表示风场，只绘制了值≥0.3 m s⁻¹的区域；彩色阴影表示温度场，只绘制了绝对值≥0.2 K的区域。长方形区域为验证区域，圆圈和加号表示研究时段初始时刻台风中心所处的位置

Figure 2. The sensitive areas of wind (arrows) and temperature (color shadings) identified by ADS (adjoint sensitivity, top panels) method, LSV (leading singular vector, middle panels) method, CNOP (conditional nonlinear optimal perturbation, bottom panels) method at the level of $\sigma $=0.7 for (a–c) typhoon 2004Meari; (d–f) typhoon 2011Meari; (g–i) typhoon 2010Megi_2. In top panels, arrows represent the gradients with respect to wind whose values are larger than 4 m s⁻¹ are plotted, color shadings represent the gradient with respect to temperature whose absolute values are larger than 3 J kg⁻¹ K⁻¹ are plotted. In middle and bottom panels, arrows represent wind whose value is larger than 0.3 m s⁻¹ are plotted, color shadings represent temperature whose absolute value is larger than 0.2 K are plotted. The rectangles indicate the targeted area, and the circle and cross symbols indicate the initial position of the typhoon

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图 3 同图2，但为（a–c）2011Muifa、（d–f）2004Mindulle和（g–i）2005Matsa的敏感区及各台风研究时段起始时刻的500 hPa位势高度场

Figure 3. As in Fig. 2, but for the sensitive areas of (a–c) 2011 Muifa, (d–f) 2004 Mindulle, and (g–i) 2005 Matsa and 500-hPa geopotential height at the beginning of the study period for each typhoon

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图 4 （a）2004Meari、（b）2010Megi_1、（c）2010Chandu、（d）2011Meari、（e）2011Muifa台风在研究时段的行进路径（蓝色线段）以及研究时段前、后各24 h的行进路径（红色线段）以及CNOP方法识别的$\sigma $=0.7层的风场和温度场的敏感区

Figure 4. Tracks of (a) 2004 Meari, (b) 2010 Megi_1, (c) 2010 Chandu, (d) 2011 Meari, and (e) 2011 Muifa during the study period (blue lines), 24 h before and after the study period (red lines), and the sensitive areas of wind (vectors, units: m/s) and temperature (shadings, units: K) identified by the CNOP method

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图 5 同图4，但为（a）2005Matsa、（b）2010Lionrock、（c）2010Megi_2、（d）2004Rananim、（e）2004Mindulle行进路径及风场、温度场的敏感区

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图 6 CNOP、LSV、ADS识别的敏感区内随机扰动能量随预报时间的变化：（a）2011Meari；（b）2011Muifa

Figure 6. Energy development of the random perturbations added in the CNOP-, LSV-, and ADS-identified sensitive areas with lead time: (a) 2011 Meari; (b) 2011 Muifa

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图 7 （a–c）2011Meari、（d–f）2011Muifa，在（a、d）ADS、（b、e）LSV、（c、f）CNOP方法识别的敏感区内叠加随机初始扰动导致的海平面气压变化（彩色阴影，单位：Pa）以及研究时段终止时刻分析资料的500 hPa位势高度场（等值线，单位：gpm，等值线间隔20 gpm）。长方形区域为验证区域，圆圈和加号符号表示研究时段终止时刻未叠加扰动预报的台风中心所处的位置，黑色三角形符号表示叠加随机初始扰动后预报终止时刻台风中心所处的位置

Figure 7. Variations of the sea level pressures (shadings, units: Pa) caused by the random initial perturbations added in the sensitive areas identified by the (a, d) ADS, (b, e) LSV, and (c, f) CNOP methods, and 500-hPa geopotential height (contours, units: gpm, contours interval: 20 gpm) at the end of the study time period from the analytical data for (a–c) typhoon 2011 Meari and (d–f) typhoon 2011 Muifa. The rectangles indicate the targeted area, the circle and cross symbols indicate the final position of the typhoon from control forecasts (without perturbations), and the solid triangle indicates the final position of the typhoon from the forecasts with perturbations

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图 8 （a）不同非线性程度下CNOP、LSV、ADS方法识别的敏感区内的随机扰动的能量随预报时间的变化，-N表示非线性较强的台风，-L表示非线性较弱的台风；（b）转向型与直线型台风中CNOP、LSV、ADS方法识别的敏感区内随机扰动能量的平均发展情况，-turn表示转向型，-straight表示直线型

Figure 8. (a) The average energy development of the random perturbations respectively added in CNOP-, LSV-, and ADS-identified sensitive areas with lead time for strong nonlinear typhoons (-N) and weak nonlinear typhoons (-L). (b) The average energy development of the random initial perturbations respectively added in CNOP-, LSV-, and ADS-identified sensitive areas for straight typhoons (-straight) and recurved typhoons (-turn)

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表 1 台风类型、名称及其对应的研究时段、强度、偏折角度和非线性程度

Table 1. The types, names of the typhoons and the studied period for each typhoon with the corresponding strength, recurved degree, and the nonlinear degree

类别	台风名称	研究时段（协调世界时）	强度（最小海平面气压）	偏折角度	非线性程度
转向型	2004Meari	2004年9月26日00时至27日00时	台风—强台风（950 hPa）	114°	1.29
	2010Megi_1	2010年10月19日00时至20日00时	强台风（940 hPa）	90°	2.14
	2010Chandu	2010年7月20日12时至21日12时	热带风暴—强热带风暴—台风（975 hPa）	61°	9.71
	2011Meari	2011年6月26日00时至27日00时	强热带风暴（980 hPa）—热带风暴—热带低压	93°	1.19
	2011Muifa	2011年8月2日00时至3日00时	强台风（940 hPa）	73°	50
直线型	2005Matsa	2005年8月5日00时至6日00时	强台风（950 hPa）—台风		4.57
	2010Lionrock	2010年8月28日18时至29日18时	热带风暴（995 hPa）		4.67
	2010Megi_2	2010年10月20日00时至21日00时	强台风（940 hPa）		2.10
	2004Rananim	2004年8月11日12时至12日12时	台风—强台风（950 hPa）		8.47
	2004Mindulle	2004年6月28日00时至29日00时	台风—强台风（950 hPa）		6.99
注：非线性程度数值越大，非线性越强。

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