﻿ Bevis公式在不同高度面的适用性以及基于近地大气温度的全球加权平均温度模型
 文章快速检索 高级检索
Bevis公式在不同高度面的适用性以及基于近地大气温度的全球加权平均温度模型

Applicability of Bevis formula at different height level and global weighted mean temperature model based on near-earth atmospheric temperature
YAO Yibin, SUN Zhangyu, XU Chaoqian
School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China
Foundation support: The National Natural Science Foundation of China (No. 41574028)
First author: YAO Yibin(1976—), male, PhD, professor, majors in GNSS near-earth space environmentE-mail:ybyao@sgg.whu.edu.cn
Abstract: Weighted mean temperature is a critical parameter in GNSS technology to retrieve precipitable water vapor (PWV). It is convenient to obtain high-accuracy Tm estimation near surface utilizing Bevis formula and surface temperature. However, some researches pointed out that the Bevis formula has large uncertainties in high-altitude regions. This paper researches the applicability of Bevis formula at different height levels and finds that the Bevis formula has relatively high precision when the altitude is low, while with altitude increasing, the precision decreases gradually. To solve the problem, this paper studies the relationship between Tm and atmospheric temperature of the near-earth space range (the height range between 0~10 km) and finds that they have high correlation on a global scale. Accordingly, this paper builds a global weighted mean temperature model based on near-earth atmospheric temperature. Validation results of the model show that this model can provide high-accuracy Tm estimation at any height level in the near-earth space range.
Key words: weighted mean temperature     Bevis formula     near-earth atmospheric temperature     global model

Tm可以通过对测站上空的温度和湿度廓线沿天顶方向进行数值积分得到，这些资料通常可以从无线电探空数据、数值天气预报(numerical weather prediction, NWP)产品或者大气再分析资料中获得[3]。因为无线电探空站分布稀疏，其空间分辨率不足以满足GNSS测站的需求，从而大多数GNSS测站都无法获得配套的无线电探空资料，因此NWP产品或者再分析资料成为GNSS测站获取高精度Tm的主要数据源[8]。然而，由于NWP产品的时间分辨率不够高且更新存在延迟的问题，其不能够用作实时/近实时水汽监测[8-9]。为了实现实时/近实时GNSS水汽遥感，必须通过更简便的方法获取Tm，一种常用的获取Tm的简便方法是利用Tm与地表温度(surface temperature, Ts)的线性关系。文献[7]发现TmTs之间存在很强的线性关系，并建立了两者之间的线性回归公式。该方法只需要得到测站地表处的温度即可通过一个简单的线性公式估计出高精度的Tm。然而也有不少学者认为，TmTs之间的关系并不是定值，而是随着季节和地区发生变化的，并由此建立了区域性的线性回归公式[10-14]

1 原理和试验数据介绍

(1)

(2)
(3)

(4)

(5)

ECMWF以格网形式提供了从1979年至今的丰富气象数据，格网最高分辨率可以达到0.125°，时间分辨率可以达到6 h[20-21]。ECMWF再分析资料包括地表的气象数据以及整个大气分层的气象数据，其中的气压分层数据总共可以提供37层从1000 hPa到1 hPa的气象数据。从不同的气压层开始利用式(4)一直积分到顶层即可得到不同气压层的Tm。本文分别将气压从1000 hPa到250 hPa的气压层(高程范围大致为0~10 km)作为底层开始往顶层积分，得到了这些气压层对应高度面的Tm。本文利用全球范围格网分辨率为2.5°的ECMWF气压分层数据来获得Tm廓线和近地大气温度廓线。

 图 1 678个探空站的分布 Fig. 1 Distribution of the 678 radiosonde stations

2 Bevis公式在不同高度面的适用性

Bevis公式在海拔较低的区域利用地表温度计算Tm时拥有较高的精度，然而在高海拔地区，Bevis公式的适用性需要进一步的验证。本文分别利用ECMWF的一个格网点(60°N 60°E)和一个探空站(24.43°N 54.65°E)3年(2013—2015年)的温度和湿度廓线，利用式(4)进行积分得到Tm廓线并将其作为参考值，然后再根据式(5)，利用Bevis公式和分层温度得到Tm廓线，将两条廓线作差即可得到不同高度层的Tm残差。图 2给出了利用两种数据源检验Bevis公式的残差廓线结果，其中图 2(a)是利用ECMWF的再分析资料检验的结果，图 2(b)是利用探空站数据检验的结果。

 图 2 利用多源数据的分层温度检验Bevis公式的残差廓线 Fig. 2 The residual profiles of Bevis formula tested with stratified temperature of multi sources data

(6)
(7)
(8)

 图 3 利用多源数据在全球范围内探究Bevis公式在不同高度层的残差统计结果 Fig. 3 The residual statistics of Bevis formula at different levels using multi sources data on a global scale

3 基于近地大气温度的全球Tm模型 3.1 近地大气温度与Tm的相关性分析

 图 4 由多源数据计算得到的近地大气温度与Tm相关系数全球分布 Fig. 4 The global distribution of correlation coefficients between near-earth atmospheric temperature and Tm obtained from multi sources data

3.2 模型构建及模型系数求解

(9)

(10)

 图 5 选取用来建模的探空站和ECMWF格网点全球分布 Fig. 5 The global distribution of radiosonde stations and ECMWF grid points selected for building model

(11)

 图 6 模型系数的平均值、年周期幅值和半年周期幅值全球分布状况 Fig. 6 The global distribution of mean values, annual and semi-annual amplitudes of model coefficients

3.3 模型有效性检验

3.3.1 内符合精度检验

 图 7 内符合精度检验结果Bias和RMS全球分布图 Fig. 7 The global distribution of bias and RMS results in internal accuracy test

3.3.2 利用ECMWF和无线电探空分层数据的外符合精度检验

 图 8 利用多源数据的分高度层外符合精度检验结果 Fig. 8 The height-dependent external accuracy test results using multi sources data

3.3.3 利用高海拔地区无线电探空地表数据的外符合精度检验

 经纬度 海拔/m BTm的Bias/K TTm的Bias/K BTm的RMS/K TTm的RMS/K 15.9°S 47.9°W 1061 0.96 -0.32 2.76 2.63 35.7°N 51.3°E 1204 -4.23 -1.39 5.93 5.21 35.5°N 106.7°E 1348 -1.81 1.61 3.95 3.93 38.1°N 46.3°E 1367 -4.88 -2.10 6.02 4.49 37.1°N 79.9°E 1375 -4.54 -0.62 5.86 4.59 2.8°N 5.4°E 1377 -3.99 -0.44 6.26 5.03 32.9°N 59.2°E 1491 -5.78 -3.82 6.82 5.45 37.1°N 82.7°E 1409 -3.64 0.57 5.85 5.58 16.4°N 120.6°E 1500 1.60 0.25 2.76 1.81 41.8°N 97.0°E 1770 -4.09 1.49 5.63 4.79 36.7°N 101.8°E 2296 -3.31 1.36 4.91 4.33 4.7°N 74.2°W 2547 -1.04 -1.02 2.19 2.06 36.4°N 94.9°E 2809 -6.50 -1.62 7.49 4.44 35.0°N 102.9°E 2910 -3.86 0.87 5.12 3.75 36.3°N 98.1°E 3190 -6.89 -1.81 7.62 3.72 31.1°N 97.2°E 3307 -5.61 -1.91 6.62 4.47 31.6°N 97.2°E 3394 -5.14 -1.31 6.15 4.09 29.7°N 100.0°E 3650 -6.27 -2.89 7.31 5.02 33.0°N 97.0°E 3716 -5.51 -0.76 6.59 4.08 31.5°N 92.1°E 4508 -5.41 -0.25 7.08 5.06

4 结论

Bevis公式是GNSS气象学中一个很重要的公式，因为该公式可以利用地表温度和一个简单的线性关系估计出高精度的加权平均温度。然而，不少研究指出，Bevis公式在高海拔地区存在较大误差，本文利用ECMWF再分析资料和无线电探空资料3年(2013—2015年)的气压分层数据，对Bevis公式在不同高度面上的适用性进行探究，并提出了解决Bevis公式在高海拔地区适用性较低问题的可能办法，取得了如下成果：①Bevis公式在海拔较低时适用性较好，Tm估计精度较高，而随着海拔升高，适用性逐渐降低，因为Bevis公式在高海拔地区估计出的Tm可能会偏高，这个偏差值会在到达8 km时趋于稳定，最高偏差会达到11~12 K，这会在最后的PWV反演中引入约1.5~1.8 mm的误差；②提出了近地大气温度的概念，通过研究近地大气温度与加权平均温度的相关性发现，两者在全球范围内都具有很高的相关性，特别是在低纬度地区，相关系数会达到0.97以上；③利用球谐函数建立了基于近地大气温度的全球加权平均温度新模型TTm，并对该模型进行了检验。检验结果表明，该模型在近地空间范围内(0~10 km高程范围)近20个不同的高度层上都可以取得较高的精度，由此可推断，该模型在对应高程范围内的任意高度面上都可以得到高精度的Tm估计值，其在任意高度层的Bias数值都较小，基本都处于-1 K~1 K的区间中，对应约0.15 mm的PWV误差，其RMS始终维持在4 K左右，对应的PWV误差约为0.6 mm，不存在随着高程增加精度逐渐降低的现象。因此也可以推断，该模型在任何地表海拔高度面上都可以利用地表温度提供高精度的加权平均温度估计值。

﻿

 [1] ROCKEEN C, VAN HOVE T, WARE R. Near real-time GPS sensing of atmospheric water vapor[J]. Geophysical Research Letters, 1997, 24(24): 3221–3224. DOI:10.1029/97GL03312 [2] ALLAN R P. The role of water vapour in earth's energy flows[J]. Surveys in Geophysics, 2012, 33(3-4): 557–564. DOI:10.1007/s10712-011-9157-8 [3] BEVIS M, BUSINGER S, CHISWELL S, et al. GPS meteorology: mapping zenith wet delays onto precipitable water[J]. Journal of Applied Meteorology, 1994, 33(3): 379–386. DOI:10.1175/1520-0450(1994)033<0379:GMMZWD>2.0.CO;2 [4] SAASTAMOINEN J. Atmospheric correction for the troposphere and stratosphere in radio ranging satellites[M]. Washington, D.C.: American Geophysical Union, 1972: 247-251. [5] HOPFIELD H S. Tropospheric effect on electromagnetically measured range: prediction from surface weather data[J]. Radio Science, 1971, 6(3): 357–367. DOI:10.1029/RS006i003p00357 [6] ASKNE J, NORDIUS H. Estimation of tropospheric delay for microwaves from surface weather data[J]. Radio Science, 1987, 22(3): 379–386. DOI:10.1029/RS022i003p00379 [7] BEVIS M, BUSINGER S, HERRING T A, et al. GPS meteorology: remote sensing of atmospheric water vapor using the global positioning system[J]. Journal of Geophysical Research: Atmospheres, 1992, 97(D14): 15787–15801. DOI:10.1029/92JD01517 [8] WANG Xiaoming, ZHANG Kefei, WU Suqin, et al. Water vapor-weighted mean temperature and its impact on the determination of precipitable water vapor and its linear trend[J]. Journal of Geophysical Research: Atmospheres, 2016, 121(2): 833–852. DOI:10.1002/2015JD024181 [9] DING Maohua. A neural network model for predicting weighted mean temperature[J]. Journal of Geodesy, 2018, 92(10): 1187–1198. DOI:10.1007/s00190-018-1114-6 [10] ROSS R J, ROSENFELD S. Estimating mean weighted temperature of the atmosphere for global positioning system applications[J]. Journal of Geophysical Research: Atmospheres, 1997, 102(D18): 21719–21730. DOI:10.1029/97JD01808 [11] DUAN Jingping, BEVIS M, FANG Peng, et al. GPS meteorology: direct estimation of the absolute value of precipitable water[J]. Journal of Applied Meteorology, 1996, 35(6): 830–838. DOI:10.1175/1520-0450(1996)035<0830:GMDEOT>2.0.CO;2 [12] WANG Junhong, ZHANG Liangying, DAI Aiguo. Global estimates of water-vapor-weighted mean temperature of the atmosphere for GPS applications[J]. Journal of Geophysical Research: Atmospheres, 2005, 110(D21): D21101. DOI:10.1029/2005JD006215 [13] YAO Yibin, ZHANG Bao, XU Chaoqian, et al. Analysis of the global Tm-Ts correlation and establishment of the latitude-related linear model[J]. Chinese Science Bulletin, 2014, 59(19): 2340–2347. DOI:10.1007/s11434-014-0275-9 [14] YAO Y, ZHANG B, XU C, et al. Improved one/multi-parameter models that consider seasonal and geographic variations for estimating weighted mean temperature in ground-based GPS meteorology[J]. Journal of Geodesy, 2014, 88(3): 273–282. DOI:10.1007/s00190-013-0684-6 [15] YAO Yibin, ZHU Shuang, YUE Shunqiang. A globally applicable, season-specific model for estimating the weighted mean temperature of the atmosphere[J]. Journal of Geodesy, 2012, 86(12): 1125–1135. DOI:10.1007/s00190-012-0568-1 [16] ZHANG Hongxing, YUAN Yunbin, LI Wei, et al. GPS PPP-derived precipitable water vapor retrieval based on Tm/Ps from multiple sources of meteorological data sets in China[J]. Journal of Geophysical Research: Atmospheres, 2017, 122(8): 4165–4183. DOI:10.1002/2016JD026000 [17] 于胜杰, 柳林涛. 水汽加权平均温度回归公式的验证与分析[J]. 武汉大学学报(信息科学版), 2009, 34(6): 741–744. YU Shengjie, LIU Lintao. Validation and analysis of the water-vapor-weighted mean temperature from Tm-Ts relationship[J]. Geomatics and Information Science of Wuhan University, 2009, 34(6): 741–744. [18] DAVIS J L, HERRING T A, SHAPIRO I I, et al. Geodesy by radio interferometry: effects of atmospheric modeling errors on estimates of baseline length[J]. Radio Science, 1985, 20(6): 1593–1607. DOI:10.1029/RS020i006p01593 [19] BEVIS M, BUSINGER S, CHISWELL S. Earth-based GPS meteorology: an overview, american geophysical union 1995 fall meeting[J]. EOS, 1995(76): 46. [20] SIMMONS A, UPPALA S, DEE D. ERA-interim: new ECMWF reanalysis products from 1989 onwards[J]. ECMWF Newsletter, 2006(110): 25–36. [21] DEE D P, UPPALA S M, SIMMONS A J, et al. The ERA-interim reanalysis: configuration and performance of the data assimilation system[J]. Quarterly Journal of the Royal Meteorological Society, 2011, 137(656): 553–597. DOI:10.1002/qj.v137.656 [22] BÖHM J, MÖLLER G, SCHINDELEGGER M, et al. Development of an improved empirical model for slant delays in the troposphere (GPT2w)[J]. GPS Solutions, 2015, 19(3): 433–441. DOI:10.1007/s10291-014-0403-7 [23] LAGLER K, SCHINDELEGGER M, BÖHM J, et al. GPT2: empirical slant delay model for radio space geodetic techniques[J]. Geophysical Research Letters, 2013, 40(6): 1069–1073. DOI:10.1002/grl.50288 [24] YAO Yibin, ZHANG Bao, YUE Shunqiang, et al. Global empirical model for mapping zenith wet delays onto precipitable water[J]. Journal of Geodesy, 2013, 87(5): 439–448. DOI:10.1007/s00190-013-0617-4 [25] ACKERMAN S, KNOX J A. Meteorology: understanding the atmosphere[M]. Pacific Grove, CA: Thomson Learning, 2006.
http://dx.doi.org/10.11947/j.AGCS.2019.20180160

0

#### 文章信息

YAO Yibin, SUN Zhangyu, XU Chaoqian
Bevis公式在不同高度面的适用性以及基于近地大气温度的全球加权平均温度模型
Applicability of Bevis formula at different height level and global weighted mean temperature model based on near-earth atmospheric temperature

Acta Geodaetica et Cartographica Sinica, 2019, 48(3): 276-285
http://dx.doi.org/10.11947/j.AGCS.2019.20180160