戈壁沙尘运动中风速与颗粒数及动能的标度律

doi:10.11755/j.issn.1006-7639-2025-02-0195

干旱气象 ›› 2025, Vol. 43 ›› Issue (2): 195-206.DOI: 10.11755/j.issn.1006-7639-2025-02-0195

戈壁沙尘运动中风速与颗粒数及动能的标度律

王振亭¹(), 孟小楠²^,³, 王雪松², 李庆⁴

1.干旱区生态安全与可持续发展重点实验室，中国科学院西北生态环境资源研究院，甘肃兰州 730000
2.北京师范大学地理科学学部，地表过程与资源生态国家重点实验室/防沙治沙教育部工程研究中心，北京 100875
3.北京市第八十中学睿德分校，北京 100176
4.河北省科学院地理科学研究所/河北省地理信息开发应用工程技术研究中心，河北石家庄 050011

收稿日期:2024-06-27 修回日期:2024-08-21 出版日期:2025-04-30 发布日期:2025-05-13
作者简介:王振亭（1975—），男，研究员，主要从事风沙物理与风沙地貌研究。E-mail： ztwang@lzb.ac.cn。
基金资助:
国家自然科学基金项目(42371005);国家自然科学基金项目(U21A2001)

Scaling laws in wind speed, particle number and kinetic energy in Gobi sand movement

WANG Zhenting¹(), MENG Xiaonan²^,³, WANG Xuesong², LI Qing⁴

1. Key Laboratory of Ecological Safety and Sustainable Development in Arid Lands， Northwest Institute of Eco-Environment and Resources， Chinese Academy of Sciences， Lanzhou 730000， China
2. State Key Laboratory of Earth Surface Processes and Resource Ecology/MOE Engineering Research Center of Desertification and Blown-Sand Control，Faculty of Geographical Science，Beijing Normal University， Beijing 100875， China
3. Beijing No. 80 Middle School Rui De Branch， Beijing 100176， China
4. Institute of Geographical Sciences/Hebei Engineering Research Center for Geographic Information Application， Hebei Academy Science， Shijiazhuang 050011， China

Received:2024-06-27 Revised:2024-08-21 Online:2025-04-30 Published:2025-05-13

摘要/Abstract

摘要：

中国西北极端干旱区戈壁广布，风大沙多，灾害频发。充分了解戈壁沙尘运动基本规律是灾害预警与科学防治的重要前提。鉴于目前难以精准预测瞬时输沙率，探讨风沙事件中气流与沙尘特征物理量的统计规律，进而开展统计预测，也许是在秒及以下时间尺度上建立风和沙之间定量关系的可行之路。本研究借鉴湍流统计理论的思路和方法，利用Hilbert-Huang变换分析4个戈壁沙尘运动野外观测数据集。结果表明，沙尘事件中的风速、跃移沙粒动能与个数、粉尘浓度等时间序列的Hilbert边际谱均符合幂次标度律，沙尘特征量和风速的标度指数范围分别为0.78~1.51和0.59~1.47。

关键词: 戈壁, 风沙, 粉尘, Hilbert边际谱, 标度律

Abstract:

In the extreme arid region of Northwest China, the Gobi desert is widely distributed, with strong winds and abundant sand, leading to frequent disasters. A deep understanding of the basic laws of the aeolian sand-dust movement over Gobi surfaces is an important prerequisite for disaster warning and scientific prevention. Given the current difficulty in accurately predicting the instantaneous aeolian sediment transport rate, exploring the statistical laws of airflow and sand-dust characteristic physical quantities in wind-sand events, and then conducting statistical forecasting, may be a feasible way to establish a quantitative relationship between wind and sand on time scales of seconds or less. This study borrows the ideas and methods from the statistical theory of turbulence, and analyzes four field observation datasets of Gobi sand-dust movement using the Hilbert-Huang transform. The results indicate that the Hilbert marginal spectra of the time series of wind speed, kinetic energy and number of saltation sand particle, and dust concentration in the aeolian events all follow the power scaling law. The scaling exponents of variables, characterizing aeolian sand and dust motions, and wind speed range from 0.78 to 1.51 and 0.59 to 1.47, respectively.

Key words: Gobi, aeolian sand, dust, Hilbert marginal spectra, scaling law

中图分类号:

K903
O359

王振亭, 孟小楠, 王雪松, 李庆. 戈壁沙尘运动中风速与颗粒数及动能的标度律[J]. 干旱气象, 2025, 43(2): 195-206.

WANG Zhenting, MENG Xiaonan, WANG Xuesong, LI Qing. Scaling laws in wind speed, particle number and kinetic energy in Gobi sand movement[J]. Journal of Arid Meteorology, 2025, 43(2): 195-206.

图/表 12

表1 戈壁沙尘运动数据集及观测条件

Tab.1 Datasets of aeolian sand and dust motions over Gobi and measurement conditions

数据来源	高度/m	物理量	传感器（厂家）	采样频率/Hz	采样精度
Wang et al.，2022	0.30、0.83、3.00	U、V、W	WindMaster Pro（Gill）	20	0.001 m·s^-1
Tan et al.，2020	0.05、0.12、0.38、0.80、1.38	KE、PC	H11-Lin（Sensit）	1	1×10^-7 J·s^-1、s^-1
Tan et al.，2020	0.70、2.00	U、φ、θ	Young-81000（RM Young）	20	0.01 m·s^-1、0.1°
Wang et al.，2023	0.05、0.12、0.38、0.80、1.41	KE、PC	H11-Lin（Sensit）	1	1×10^-7 J·s^-1、s^-1
Wang et al.，2023	1.20、2.80	U、V、W	WindMaster Pro（Gill）	1	0.001 m·s^-1
本研究团队	0.10、0.20、0.50、1.00、1.50、2.00	DA、DN	DustTrak-II（TSI）	0.2	0.001 mg·m^-3
本研究团队	0.50、1.00	U、V、W	Young-81000（RM Young）	20	0.01 m·s^-1

图1 4个野外观测地点分布注:基于国家测绘地理信息局标准地图服务网站标准地图[审图号为GS ( 2016 ) 2923号]制作，底图无修改。

Fig.1 The distribution of 4 field observation sites

图2 跃移沙粒动能（a）与个数（b）时间序列分解 [数据来自Tan等（2020）文献，测量高度0.05 m；物理量下标0为趋势项，1为脉动项，下同]

Fig.2 Decomposition of time series of kinetic energy （a） and count （b） of saltating sand grains (Data are sourced from the ref. (Tan et al., 2020), measured at 0.05 m height. Subscripts of variables 0 is for trend, 1 is for fluctuation, the same as follows)

图3 跃移沙粒动能分解后的脉动模态（a）一阶模态,（b）二阶模态,（c）三阶模态,（d）四阶模态 [数据来自Tan等（2020）文献，测量高度0.05 m]

Fig.3 Fluctuation modes of kinetic energy of saltating sand grains after decomposition (a) the first mode, (b) the second mode, (c) the third mode, (d) the fourth mode (Data are sourced from the ref. (Tan et al., 2020), measured at 0.05 m height)

图4 跃移沙粒动能（a）与个数（b）的时间序列分解 [数据来自Wang等（2023）文献，测量高度0.05 m]

Fig.4 Decomposition of time series of kinetic energy （a） and count （b） of saltating sand grains (Data are sourced from the ref. (Wang et al., 2023), measured at 0.05 m height)

图5 人工地表（a）与天然地表（b、c）粉尘浓度（测量高度0.10 m）时间序列分解

Fig.5 Decomposition of time series of dust concentration of artificial Gobi surface (a) and natural Gobi surface (b, c) measured at 0.10 m height

图6 水平风速（a）与垂向风速（b）（测量高度0.50 m）时间序列分解

Fig.6 Decomposition of time series of horizontal (a) and vertical (b) wind speeds measured at 0.50 m height

图7 跃移沙粒动能（a）与个数（b）的Hilbert边际谱（相应的时间序列见图2）

Fig.7 Hilbert marginal spectra of kinetic energy (a) and count (b) of saltating sand grains (The corresponding time series is shown in fig. 2)

图8 跃移沙粒动能（a）与个数（b）的Hilbert边际谱（相应的时间序列见图4）

Fig.8 Hilbert marginal spectra of kinetic energy (a) and count (b) of saltating sand grains (The corresponding time series is shown in fig. 4)

图9 人工地表（a）与天然地表（b）粉尘浓度的Hilbert边际谱（相应的时间序列见图5）

Fig.9 Hilbert marginal spectra of artificial (a) and natural (b) surface dust concentration (The corresponding time series is shown in fig. 5)

图10 水平（a）和垂向（b）风速的Hilbert边际谱（相应的时间序列见图6）

Fig.10 Hilbert marginal spectra of horizontal (a) and vertical (b) wind speed （The corresponding time series is shown in fig. 6)

表2 不同观测条件下的沙尘运动各特征物理量能谱的标度指数拟合结果

Tab.2 The fitting results of scaling exponents of energy spectrum of physical variables describing aeolian sand and dust motions under different measurement conditions

数据来源	高度/m	物理量	序列数	均值	标准差	95%置信区间	物理量	序列数	均值	标准差	95%置信区间
Wang et al.，2022	0.30	U	1 724	1.438	0.418	[1.418， 1.457]	W	1 724	1.336	0.491	[1.313， 1.360 ]
	0.83			1.445	0.345	[1.429， 1.461]			1.360	0.456	[1.339， 1.382 ]
	3.00			1.468	0.360	[1.451， 1.485]			1.404	0.508	[1.380， 1.428]
Tan et al.，2020	0.05	KE	37	1.141	0.175	[1.083， 1.200]	PC	34	1.393	0.295	[1.290， 1.496]
	0.12		37	1.110	0.193	[1.046， 1.174]		34	1.380	0.198	[1.311， 1.449]
	0.38		18	1.038	0.165	[0.956， 1.120]		24	1.224	0.212	[1.135， 1.314]
	0.80	PC	1	1.451
	0.70	U	1 006	1.192	0.055	[1.188， 1.195]	W	1 006	1.313	0.143	[1.305， 1.322]
	2.00	U	1 006	1.313	0.143	[1.305， 1.322]	W	1 006	1.134	0.184	[1.123， 1.146]
Wang et al.， 2023	0.05	KE	30	1.021	0.208	[0.943， 1.098]	PC	23	1.234	0.145	[1.172， 1.297]
	0.12		24	0.929	0.215	[0.839， 1.020]		28	1.176	0.186	[1.104，1.248]
	0.38		15	0.992	0.138	[0.916， 1.068]		14	1.055	0.185	[0.948，1.161]
	0.80		21	0.907	0.131	[0.847， 0.966]		15	1.121	0.137	[1.045，1.197]
	1.41		19	0.781	0.183	[0.692， 0.869]		21	1.204	0.216	[1.106，1.302]
	1.20	U	98	0.835	0.106	[0.813， 0.856]	W	98	0.590	0.089	[0.572，0.608]
	2.80	U	98	0.891	0.100	[0.871， 0.911]	W	98	0.629	0.104	[0.608，0.650]
本研究	0.10	DA	11	1.513	0.228	[1.360， 1.665]	DN	12	1.015	0.210	[0.882，1.149]
	0.20		7	1.400	0.192	[1.224， 1.577]		11	1.276	0.185	[1.152，1.401]
	0.50		11	1.276	0.185	[1.152， 1.401]		18	0.965	0.164	[0.883，1.046]
	1.00		23	0.922	0.199	[0.837， 1.008]		12	0.756	0.077	[0.708，0.805]
	1.50		10	1.022	0.216	[0.868， 1.176]
	2.00		15	0.901	0.108	[0.842， 0.961]		11	0.932	0.117	[0.854， 1.010]
	0.50	U	486	1.187	0.043	[1.183， 1.190]	W	486	0.899	0.067	[0.893， 0.905]
	1.00	U	486	1.214	0.042	[1.211， 1.218]	W	486	1.214	0.041	[1.210， 1.218]

表2 不同观测条件下的沙尘运动各特征物理量能谱的标度指数拟合结果

Tab.2 The fitting results of scaling exponents of energy spectrum of physical variables describing aeolian sand and dust motions under different measurement conditions

数据来源	高度/m	物理量	序列数	均值	标准差	95%置信区间	物理量	序列数	均值	标准差	95%置信区间
Wang et al.，2022	0.30	U	1 724	1.438	0.418	[1.418， 1.457]	W	1 724	1.336	0.491	[1.313， 1.360 ]
	0.83			1.445	0.345	[1.429， 1.461]			1.360	0.456	[1.339， 1.382 ]
	3.00			1.468	0.360	[1.451， 1.485]			1.404	0.508	[1.380， 1.428]
Tan et al.，2020	0.05	KE	37	1.141	0.175	[1.083， 1.200]	PC	34	1.393	0.295	[1.290， 1.496]
	0.12		37	1.110	0.193	[1.046， 1.174]		34	1.380	0.198	[1.311， 1.449]
	0.38		18	1.038	0.165	[0.956， 1.120]		24	1.224	0.212	[1.135， 1.314]
	0.80	PC	1	1.451
	0.70	U	1 006	1.192	0.055	[1.188， 1.195]	W	1 006	1.313	0.143	[1.305， 1.322]
	2.00	U	1 006	1.313	0.143	[1.305， 1.322]	W	1 006	1.134	0.184	[1.123， 1.146]
Wang et al.， 2023	0.05	KE	30	1.021	0.208	[0.943， 1.098]	PC	23	1.234	0.145	[1.172， 1.297]
	0.12		24	0.929	0.215	[0.839， 1.020]		28	1.176	0.186	[1.104，1.248]
	0.38		15	0.992	0.138	[0.916， 1.068]		14	1.055	0.185	[0.948，1.161]
	0.80		21	0.907	0.131	[0.847， 0.966]		15	1.121	0.137	[1.045，1.197]
	1.41		19	0.781	0.183	[0.692， 0.869]		21	1.204	0.216	[1.106，1.302]
	1.20	U	98	0.835	0.106	[0.813， 0.856]	W	98	0.590	0.089	[0.572，0.608]
	2.80	U	98	0.891	0.100	[0.871， 0.911]	W	98	0.629	0.104	[0.608，0.650]
本研究	0.10	DA	11	1.513	0.228	[1.360， 1.665]	DN	12	1.015	0.210	[0.882，1.149]
	0.20		7	1.400	0.192	[1.224， 1.577]		11	1.276	0.185	[1.152，1.401]
	0.50		11	1.276	0.185	[1.152， 1.401]		18	0.965	0.164	[0.883，1.046]
	1.00		23	0.922	0.199	[0.837， 1.008]		12	0.756	0.077	[0.708，0.805]
	1.50		10	1.022	0.216	[0.868， 1.176]
	2.00		15	0.901	0.108	[0.842， 0.961]		11	0.932	0.117	[0.854， 1.010]
	0.50	U	486	1.187	0.043	[1.183， 1.190]	W	486	0.899	0.067	[0.893， 0.905]
	1.00	U	486	1.214	0.042	[1.211， 1.218]	W	486	1.214	0.041	[1.210， 1.218]

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戈壁沙尘运动中风速与颗粒数及动能的标度律

Scaling laws in wind speed, particle number and kinetic energy in Gobi sand movement

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