Evaluation of surface temperature and pressure derived from MERRA-2 and ERA5 reanalysis datasets and their applications in hourly GNSS precipitable water vapor retrieval over China

Temperature and pressure play key roles in Global Navigation Satellite System(GNSS) precipitable water vapor(PWV) retrieval. The National Aeronautics and Space Administration(NASA) and European Center for Medium-Range Weather Forecasts(ECMWF) have released their latest reanalysis product: the modern-era retrospective analysis for research and applications, version 2(MERRA-2) and the fifthgeneration ECMWF reanalysis(ERA5), respectively. Based on the reanalysis data, we evaluate and analyze the accuracy of the surface temperature and pressure products in China using the the measured temperature and pressure data from 609 ground meteorological stations in 2017 as reference values.Then the accuracy of the two datasets and their performances in estimating GNSS PWV are analyzed. The PWV derived from the pressure and temperature products of ERA5 and MERRA-2 has high accuracy. The annual average biases of pressure and temperature for ERA5 are-0.07 hPa and 0.45 K, with the root mean square error(RMSE) of 0.95 hPa and 2.04 K, respectively. The annual average biases of pressure and temperature for MERRA-2 are-0.01 hPa and 0.38 K, with the RMSE of 1.08 h Pa and 2.66 K, respectively.The accuracy of ERA5 is slightly higher than that of MERRA-2. The two reanalysis data show negative biases in most regions of China, with the highest to lowest accuracy in the following order: the south,north, northwest, and Tibet Plateau. Comparing the GNSS PWV calculated using MERRA-2(GNSS MERRA-2 PWV) and ERA5(GNSS ERA5 PWV) with the radiosonde-derived PWV from 48 co-located GNSS stations and the measured PWV of the co-location radiosonde stations, it is found that the accuracy of GNSS ERA5 PWV is better than that of GNSS MERRA-2 PWV. These results show the different applicability of surface temperature and pressure products from MERRA-2 and ERA5 data, indicating that both have important applications in meteorological research and GNSS water vapor monitoring in China.

Decadal trends in precipitable water vapor over the Indus River Basin using ERA5 reanalysis data

Precipitable Water Vapor(PWV)constitutes a pivotal parameter within the domains of atmospheric science,and remote sensing due to its profound influence on Earth’s climate dynamics and weather patterns.It exerts a significant impact on atmospheric stability absorption and emission of radiation,thus engendering alterations in the Earth’s radiative equilibrium.As such,precise quantification of PWV holds the potential to enhance weather prognostication and fortify preparedness against severe meteorological phenomena.This study aimed to elucidate the spatial and temporal changes in seasonal and annual PWV across the Indus River Basin and its sub-basins using ERA5 reanalysis datasets.The present study used ERA5 PWV(entire atmospheric column),air temperature at 2 m(t2m)and 500 hPa(T_500hPa),evapotranspiration,and total cloud cover data from 1960 to 2021.Theil Sen slope estimator and Mann-Kendall test were used for trend analysis.Correlation and multiple regression methods were used to understand the association of PWV with other factors.The findings have unveiled the highest increase in mean PWV during the monsoon(0.40 mm/decade),followed by premonsoon(0.37 mm/decade),post-monsoon(0.27 mm/decade),and winter(0.19 mm/decade)throughout the study period.Additionally,the mean PWV exhibited the most pronounced positive trend in the sub-basin Lower Indus(LI),followed by Panjnad(P),Kabul(K),and Upper Indus(UI)across all seasons,except winter.Annual PWV has also risen in the Indus basin and its sub-basins over the last six decades.PWV exhibits a consistent upward trend up to an elevation of 3500 m within the basin which is most pronounced during the monsoon season,followed by the pre-monsoon.The escalating PWV within the basin is reasonably ascribed to increasing air temperatures,augmented evapotranspiration,and heightened cloud cover.These findings hold potential utility for pertinent authorities engaged in water resource management and planning.

Rising trends of global precipitable water vapor and its correlation with flood frequency

Using 4 global reanalysis data sets, significant upward trends of precipitable water vapor(PWV) were found in the 3 time periods of 1958-2020, 1979-2020, and 2000-2020. During 1958-2020, the global PWV trends obtained using the ERA5 and JRA55 data sets are 0.19 ± 0.01 mm per decade(1.15 ± 0.31%)and 0.23 ± 0.01 mm per decade(1.45 ± 0.32%), respectively. The PWV trends obtained using the ERA5,JRA55, NCEP-NCAR, and NCEP-DOE data sets are 0.22 ± 0.01 mm per decade(1.18 ± 0.54%),0.21 ± 0.00 mm per decade(1.76 ± 0.56%), 0.27 ± 0.01 mm per decade(2.20 ± 0.70%) and 0.28 ± 0.01 mm per decade(2.19 ± 0.70%) for the period 1979-2020. During 2000-2020, the PWV trends obtained using ERA5, JRA55, NCEP-DOE, and NCEP-NCAR data sets are 0.40 ± 0.25 mm per decade(2.66 ± 1.51%),0.37 ± 0.24 mm per decade(2.19 ± 1.54%), 0.40 ± 0.26 mm per decade(1.96 ± 1.53%) and 0.36 ± 0.25 mm per decade(2.47 ± 1.72%), respectively. Rising PWV has a positive impact on changes in precipitation,increasing the probability of extreme precipitation and then changing the frequency of flood disasters.Therefore, exploring the relationship between PWV(derived from ERA5 and JRA55) change and flood disaster frequency from 1958 to 2020 revealed a significant positive correlation between them, with correlation coefficients of 0.68 and 0.79, respectively, which explains the effect of climate change on the increase in flood disaster frequency to a certain extent. The study can provide a reference for assessing the evolution of flood disasters and predicting their frequency trends.

Seasonal Difference of the Spatio-Temporal Variation of Precipitable Water Vapor in China

This study analyzes the spatial and temporal distribution characteristics of seasonal precipitable water vapor (PWV) in China between 1979 and 2008. To achieve this, the observed temperature dew point difference and atmospheric pressure at various altitudes of 102 radiosonde stations were utilized. The analysis involved calculating and examining the PWV variations across the different seasons in the study period. The results are illustrated as follows: 1) The annual mean and seasonal mean PWV over China is characterized by decreasing from southeast to northwest. The PWV has obvious seasonal features. It is the least in winter, which is mainly affected by latitude and altitude, and the most in summer, which is mainly affected by the monsoon. It is the medium in spring and autumn, with more in autumn than in spring. 2) The spatial distribution pattern of four seasonal PWV is approximately opposite to its variation coefficient distribution pattern, that is, the monsoon (non-monsoon) areas with more (less) PWV have a smaller (larger) variation amplitude. 3) The distribution pattern of four seasonal PWV shows a consistent distribution pattern in the whole region and the winter characteristics are the most significant. The abnormal variation of PWV shows consistent interdecadal oscillation, and it exhibits an obvious phase transition around 2002 when the PWV has an increasing shift in winter, spring, and summer, while it is more complicated in autumn.

The GNSS PWV retrieval using non-observation meteorological parameters based on ERA5 and its relation with precipitation

The pressure and temperature significantly influence precipitable water vapor(PWV) retrieval. Global Navigation Satellite System(GNSS) PWV retrieval is limited because the GNSS stations lack meteorological sensors. First, this article evaluated the accuracy of pressure and temperature in 68 radiosonde stations in China based on ERA5 Reanalysis data from 2015 to 2019 and compared them with GPT3model. Then, the accuracy of pressure and temperature calculated by ERA5 were estimated in 5 representative IGS stations in China. And the PWV calculated by these meteorological parameters from ERA5(ERA5-PWV) were analyzed. Finally, the relation between ERA5-PWV and precipitation was deeply explored using wavelet coherence analysis in IGS stations. These results indicate that the accuracy of pressure and temperature of ERA5 is better than the GPT3 model. In radiosonde stations, the mean BIAS and MAE of pressure and temperature in ERA5 are-0.41/1.15 hpa and-0.97/2.12 K. And the mean RMSEs are 1.35 hpa and 2.87 K, which improve 74.77% and 40.58% compared with GPT3 model. The errors of pressure and temperature of ERA5 are smaller than the GPT3 model in bjfs, hksl and wuh2, and the accuracy of ERA5-PWV is improved by 18.77% compared with the GPT3 model. In addition, there is a significant positive correlation between ERA5-PWV and precipitation. And precipitation is always associated with the sharp rise of ERA5-PWV, which provides important references for rainfall prediction.

Validation of the Relationship between Precipitable Water and Surface Vapor Pressure by Means of Reanalysis Data

By means of ERA-40, JRA-25, NCEP/NCAR and NCEP/DOE reanalysis data, empirical relations between precipitable water and surface vapor pressure in spatial and temporal scale were calculated. The reliabilities of precipitable water from reanalysis data were validated based on comparing different W-e empirical relations of various reanalysis data, in order to provide basis and reference for reasonable application. The results showed that W-e empirical relation of ERA-40 was closest to that of sounding data in China, and precipitable water from ERA-40 was the most credible. The worldwide comparison among W-e empirical relations of four reanalysis data showed that there was little difference in annual mean W-e empirical relations in the middle latitudes and great differences in low and high latitudes. Seasonal mean W-e empirical relations in the middle latitudes of the northern Hemisphere had little difference in spring, autumn and winter, but great difference in summer. Therefore, the reliabilities of precipitable water from reanalysis data in spring, autumn and winter in the middle latitudes of the northern hemisphere were higher than other areas and seasons. W-e empirical relations of NCEP/NCAR and NCEP/DOE had good stability in different years, while there was poor stability in ERA-40 and JRA-25.

Meteorological applications of precipitable water vapor measurements retrieved by the national GNSS network of China

In this study, the Global Navigation Satellite System （GNSS） network of China is discussed, which can be used to monitor atmospheric precipitable water vapor （PWV）. By the end of 2013, the network had 952 GNSS sites, including 260 belonging to the Crustal Movement Observation Network of China （CMONOC） and 692 belonging to the China Meteorological Administration GNSS network （CMAGN）. Additionally, GNSS observation collecting and data processing procedures are presented and PWV data quality control methods are investigated. PWV levels as determined by GNSS and radiosonde are compared. The results show that GNSS estimates are generally in good agreement with measurements of radio- sondes and water vapor radiometers （WVR）. The PWV retrieved by the national GNSS network is used in weather forecasting, assimilation of data into numerical weather prediction models, the validation of PWV estimates by radiosonde, and plum rain monitoring. The network is also used to monitor the total ionospheric electron content.

Moisture Analysis of a Squall Line Case Based on Precipitable Water Vapor Data from a Ground-Based GPS Network in the Yangtze River Delta

A squall line swept eastward across the area of the Yangtze River Delta and produced gusty winds and heavy rain from the afternoon to the evening of 24 August 2002. In this papers the roles of moisture in the genesis and development of the squall line were studied. Based on the precipitable water vapor （PWV） data from a ground-based GPS network over the Yangtze River Delta in China, plus data from a Pennsylvania State University/National Atmospheric Center （PSU/NCAR） mesoscale model （MM5） simulation, initialized by three-dimensional variational （3D-VAR） assimilation of the PWV data, some interesting features are revealed. During the 12 hours prior to the squall line arriving in the Shanghai area, a significant increase in PWV indicates a favorable moist environment for a squall line to develop. The vertical profile of the moisture illustrates that it mainly increased in the middle levels of the troposphere, and not at the surface. Temporal variation in PWV is a better precursor for squall line development than other surface meteorological parameters. The characteristics of the horizontal distribution of PWV not only indicated a favorable moist environment, but also evolved a cyclonic wind field for a squall line genesis and development. The ＂＋2 mm＂ contours of the three-hourly PWV variation can be used successfully to predict the location of the squall line two hours later.

Retrieval of the Change of Precipitable Water Vapor by GPS Technique

The feasibility of GPS precipitable water vapor （PWV） is discussed based on the comparison of Radiosonde and GPS PWV where the correlation coefficient is 0.94 and the RMS is 4.0 mm. PWV change in the Chinese mainland in 2004 is graphed with the gridding method of splines in tension, according to the GPS data of the crust monitor observation network in China, combined with relevant meteorology information. According to the distribution of the annual amount of rainfall in the country, it can be concluded that the total trend of the PWV is diminishing from the south-east coastland to the north-west inland. The PWV reaches its maximum during July and August, and the minimum is reached during January and February. According to the PWV, from high to low, all districts can be ranked as south-east coastland, the inland and the tableland.

Variational Assimilation of GPS Precipitable Water Vapor and Hourly Rainfall Observations for a Meso-βScale Heavy Precipitation Event During the 2002 Mei-Yu Season

Recent advances in Global Positioning System （GPS） remote sensing technology allow for a direct estimation of the precipitable water vapor （PWV） from delayed signals transmitted by GPS satellites, which can be assimilated into numerical models with four-dimensional variational （4DVAR） data assimilation. A mesoscale model and its 4DVAR system are used to access the impacts of assimilating GPS-PWV and hourly rainfall observations on the short-range prediction of a heavy rainfall event on 20 June 2002. The heavy precipitation was induced by a sequence of meso-β-scale convective systems （MCS） along the mei-yu front in China. The experiments with GPS-PWV assimilation cluster and also eliminated the erroneous rainfall successfully simulated the evolution of the observed MCS systems found in the experiment without 4DVAR assimilation. Experiments with hourly rainfall assimilation performed similarly both on the prediction of MCS initiation and the elimination of erroneous systems, however the MCS dissipated much sooner than it did in observations. It is found that the assimilation-induced moisture perturbation and mesoscale low-level jet are helpful for the MCS generation and development. It is also discovered that spurious gravity waves may post serious limitations for the current 4DVAR algorithm, which would degrade the assimilation efficiency, especially for rainfall data. Sensitivity experiments with different observations, assimilation windows and observation weightings suggest that assimilating GPS-PWV can be quite effective, even with the assimilation window as short as 1 h. On the other hand, assimilating rainfall observations requires extreme cautions on the selection of observation weightings and the control of spurious gravity waves.

Spatial variation of precipitable water vapor derived from GNSS CORS in Thailand

This research aims to study a distance variation of Precipitable Water Vapor(PWV) between Continuously Operating Reference Stations(CORS) in Thailand using a Precise Point Positioning(PPP) technique.Nowadays, Global Navigation Satellite System(GNSS) CORS is not only used to obtain precise positioning applications but also plays an important role in meteorological applications. With a recent establishment of GNSS CORS around Thai region, the PWV can be accurately derived from these GNSS CORS data using the scientific Position and Navigation Data Analyst(PANDA) GNSS processing software. One-year period of GNSS CORS data collected between January 1 and December 31, 2016 are used in this study. The GNSS CORS data used in this study are gathered from various agencies, i.e. Chulalongkorn University,Department of Lands and Department of Public Works and Town & Country Planning. However, a coverage distance from each GNSS CORS for PWV estimations is not precisely determined for Thai region.This information can help reduce expenses in an installation and maintenance of meteorology sensors at each GNSS CORS. Therefore, this paper focuses on determining the distance variation of PWV between GNSS CORS and the coverage distance from each CORS for PWV estimations. The result shows that the coverage distance from each CORS at 74 km or less can provide accurate PWV in Thai region.

Empirical model for mean temperature and assessment of precipitable water vapor derived from GPS

The estimation of Precipitable Water Vapor （PWV） derived from Global Positioning System （GPS） data at the IGS site WUHN is assessed by comparing with PWV obtained from radiosonde data （No.57494） in Wuhan. The applicability of Saastamoinen （SAAS）, Hopfield and Black models used for estimating Zenith Hydrostatic Delay （ZHD） and Zenith Wet Delay （ZWD） and different models is verified in the estimation of GPS-derived PWV for the applied area. The experimental results demonstrated that ： 1 ） the precision of PWV estimated from Black model used for calculating ZHD （ ZHDs ） is lower than that of SAAS （ ZHDsAAs ） model and Hopfield model （ZHDn） with the RMS of 4. 16 ram; 2） the RMS of PWV estimated from SAAS model used for calculating ZWD （SAAS） is 3.78 ram; 3 ） the well-known Bevis model gives similar accuracy compared with the site-specific models for Tm in terms of surface temperature （ Ts ） and surface pressure （Ps）, which can reach the accuracy inside 1 mm in the GPS-derived PWV estimates.

Change Features of GPS/MET Precipitable Water Vapor in Different Precipitation in Lianyungang

Based on the GPS/MET water vapor monitoring data and conventional meteorological data at Lianyungang station from April to July, 2015, the relationship between precipitable water vapor and real precipitation was studied. According to different precipitation, change trends of precipitable water vapor in convective precipitation and steady precipitation were analyzed. Results showed that necessary condition of precipitation generation was high precipitable water vapor value in the air. Precipitable water vapor change presented wave-shape and phased characters. In convection precipitation, precipitable water vapor changed frequently and had larger change amplitude, while its change was slow in steady precipi- tation. The appearing time of the maximum values of rainfall intensity and precipitable water vapor was not necessarily consistent, but it was known that severe rainfall usually began at the high-value stage of precipitable water vapor, and high-value stage of precipitable water vapor often corresponded to higher precipitation probability. In addition, precipitable water vapor showed different characteristics in the above two different precipitation, and these results could provide a reference for precipitation forecast.

Experiment on Driving Precipitable Water Vapor from Ground-Based GPS Network in Chengdu Plain

The estimates of total zenith delay are derived using Bernese GPS Software V4. 2 based on GPS data every 30 s from the first measurement experiment of a ground-based GPS network in Chengdu Plain of Southwest China during the period from July to September 2004. Then the estimates of 0.5 hourly precipitable water vapor （PWV） derived from global positioning system （GPS） are obtained using meteorological data from automatic weather stations （AWS）. The comparison of PWV derived from GPS and those from radiosonde observations is given for the Chengdu station, with RMS （root mean square） differences of 3.09m. The consistency of precipitable water vapor derived from GPS to those from radiosonde is good. It is concluded that Bevis＇ empirical formula for estimating the weighted atmospheric mean temperature can be applicable in Chengdu area because the relationship of GPS PWV with Bevis＇ formula and GPS PWV with radiosonde method shows a high correlation. The result of this GPS measurement experiment is helpful both for accumulating the study of precipitable water vapor derived from GPS in Chengdu areas located at the eastern side of the Tibetan Plateau and for studying spatial-temporal variations of regional atmospheric water vapor through many disciplines cooperatively.

Diurnal variation of precipitable water vapor over Central and South America

Annual and seasonal diurnal precipitable water vapor(PWV)variations over Central and South America are analyzed for the period 2007-2013.PWV values were obtained from Global Navigation Satellite Systems(GNSS)observations of sixty-nine GNSS tracking stations.Histograms by climate categories show that PWV values for temperate,polar and cold dry climate have a positive skewed distribution and for tropical climates(except for monsoon subtype)show a negative skewed distribution.The diurnal PWV and surface temperatures(T)anomaly datasets are analyzed by using principal components analysis(PCA).The first two modes represent more than 90%of the PWV variability.The first PCA mode of PWV variability shows a maximum amplitude value in the late afternoon few hours later than the respective values for surface temperature(T),therefore the temperature and the surface conditions(to yield evaporation)could be the main agents producing this variability;PWV variability in inland stations are mainly represented by this mode.The second mode of PWV variability shows a maximum amplitude at midnight,a possible explanation of this behavior is the effect of the sea/valley breeze.The coastal and valley stations are affected by this mode in most cases.Finally,the"undefined"stations,surrounded by several water bodies,are mainly affected by the second mode with negative eigenvectors.In the seasonal analysis,both the undefined and valley stations constitute the main cases that show a sea or valley breeze only during some seasons,while the rest of the year they present a behavior according to their temperature and the surface conditions.As a result,the PCA proves to be a useful numerical tool to represent the main sub-daily PWV variabilities.

Inversion Precipitable Water Vapor by GPS Observation of CMONOC

In this study, we have processed the GPS （Global Position System） and meteorological data from about 220 stations of CMONOC （Crustal Movement Observation Network of China in short） observed in 2014 by GAMIT software. The comparison result of ZTD （zenith total delay） calculated by GPS data and IGS （International GNSS （Global Navigation Satellite System） Service） ZTD product shows that the tropospheric delay based on calculation of CMONOC project data is accurate and reliable. Meanwhile, the PWV （precipitable water vapor） correlation coefficients between GPS observation and upper air sounding is close to 1, which proves that GPS observation data generated in CMONOC project applied to the weather forecast research is feasible. In addition, we make an isoline image for PWV distribution per hour on all stations covered the whole Chinese land area using interpolation algorithms. We observe obvious feature that the precipitable water in north and western area is less than south and east area all over this year. High latitudes area may be dry and low latitudes area is wet.

基于Galileo HAS服务的全球PWV反演验证分析

基于实时精密单点定位PPP的大气可降水量PWV反演技术近年来受到广泛研究,但目前该技术大多需利用网络通讯接收改正信息,这使其在通讯网络不能覆盖及因灾通讯受限地区的使用受到限制。2023年1月开通服务的Galileo系统高精度定位服务HAS(High Accuracy Service)为实现不依赖额外通讯手段的实时PWV反演提供了新手段。本文首先分析验证了Galileo系统HAS服务的卫星轨道和钟差改正信息精度,并将基于武汉大学IGS分析中心产品的PWV反演结果作为内部对比参考值、将基于ERA5数据及探空数据结果作为PWV结果对比的外部参考值,验证了基于HAS服务的PWV反演精度。结果表明HAS服务反演得到的PWV与两类参考值均具有较高的一致性。其中HAS服务计算得出的结果与IGS事后产品PWV解算结果的两序列差的RMS为2.91 mm,与探空数据的序列差的RMS为2.51 mm。初步验证了HAS可用于降雨的短时预报可行性。

GNSS/MET观测的台风“烟花”对上海地区PWV的影响

利用上海5个GNSS/MET站2021-07-21~08-08的观测数据,使用GAMIT软件反演大气可降水量(PWV),研究台风“烟花”期间上海地区PWV与降雨量之间的关系及PWV的空间分布特征。结果表明,GNSS PWV与探空PWV之间相关系数大于0.9。降水生成前,PWV经历了3次波动性上升过程,降水生成时间比台风登陆时间早约60 h;降水持续期间,PWV剧烈变化时会造成降水量急升或急降;降水结束后,PWV逐渐下降至40 mm以下。台风登陆前,PWV基本在75 mm以上,PWV大于80 mm的区域主要分布于上海南部和中部;台风登陆后,PWV在80 mm以上,高值区可达90 mm;台风远离后,PWV下降至85 mm以下。PWV高值区向西北方向的扩大、推移与台风路径基本吻合。

Isotopic composition of precipitation over Arid Northwestern China and its implications for the water vapor origin

In order to reveal the characteristics and climatic controls on the stable isotopic composition of precipitation over Arid Northwestern China, eight stations have been selected from Chinese Network of Isotopes in Precipitation(CHNIP).During the year 2005 and 2006, monthly precipitation samples have been collected and analyzed for the composition of δD and δ18O.The established local meteoric water line δD=7.42δ18O+1.38, based on the 95 obtained monthly composite samples, could be treated as isotopic input function across the region.The deviations of slope and intercept from the Global Meteoric Water Line indicated the specific regional meteorological conditions.The monthly δ18O values were characterized by a positive correlation with surface air temperature(δ18O(‰) =0.33 T(℃)-13.12).The amount effect visualized during summer period(δ18O(‰) =-0.04P(mm)-3.44) though not appeared at a whole yearly-scale.Spatial distributions of δ18O have properly portrayed the atmospheric circulation background in each month over Arid Northwestern China.The quan-titative simulation of δ18O, which involved a Rayleigh fractionation and a kinetic fractionation, demonstrated that the latter one was the dominating function of condensation of raindrops.Furthermore, the raindrop suffered a re-evaporation during falling processes, and the precipitation vapor might have been mixed with a quantity of local recycled water vapor.Multiple linear regression equations and a δ18O-T relation have been gained by using meteorological parameters and δ18O data to evaluate physical controls on the long-term data.The established δ18O-T relation, which has been based on the present-day precipitation, could be considered as a first step of quantitatively reconstructing the historical environmental climate.

基于水汽垂直指数分布特征的PWV快速层析方法

GNSS水汽层析技术可以反演对流层水汽三维时空变化情况,但该技术比较复杂、运算量大,需要消耗一定的时间.故本文提出了一种利用地基GNSS反演的大气可降水量(precipitable water vapor,PWV)结合水汽在垂直方向上的指数分布特性来计算大气水汽三维分布的快速层析方法.该方法利用香港地区2022年8月的GNSS数据开展试验,与传统GNSS水汽层析方法进行对比.试验结果表明:两种方法的层析解算结果与探空数据均具有良好的一致性.虽然快速层析方法的解算结果在底层区域缺少一些水汽变化的细节信息,精度略逊于传统层析方法,但是在中、高层时精度会有所提升,层析解算结果良好.而且本文提出的快速层析方法无需构建和解算复杂的层析方程组,可以在大量GNSS测站参与水汽层析时减少计算复杂度,提升运算能力,同时可以更快地得到任意高度层的水汽密度,是一种简便、高效的层析方法.