Variations of precipitable water vapor in sandstorm season determined from GNSS data: the case of China’s Wuhai

Abstract

In recent years, the Global Navigation Satellite System (GNSS) has witnessed rapid development. However, during the sandstorm season, the precipitable water vapor (PWV_GNSS) determined from the GNSS data produces large fluctuations due to the influence of particulate matter, which can indirectly reflect the change in particulate matter concentration. To study the variations of PWV_GNSS during the sandstorm season, daily data of PWV_GNSS, particulate matter (PM10), and precipitation in Wuhai from 2017 to 2021 were used in this study. The principal components of PWV residual (PWV_RPC) were obtained by using the least-squares linear fitting, singular spectrum analysis, and least-squares spectral analysis on PWV_GNSS. The principal components of PM10 (PM10_PC) were obtained by using least squares linear fitting and singular spectrum analysis for PM10. This study performed a correlation analysis of PWV_RPC with PM10_PC and precipitation data. The results showed a strong correlation between PWV_RPC and PM10_PC, with a correlation coefficient greater than 0.6. However, it was found that the correlation between PWV_RPC and precipitation was not significant. This indicates that during the sandstorm season, PM10 affects PWV determined from GNSS data.

Graphical Abstract

Introduction

Precipitable water vapor (PWV) is the total amount of water vapor in a column extending from the surface of the Earth to the top of the atmosphere, which is a highly active component of the atmosphere and varies significantly with time and space (Gurbuz 2021; Zhang et al. 2022a). Excessive changes in water vapor can lead to extreme weather, so PWV can play an important role in many scientific research fields such as climate forecasting (Chang et al. 2015). As the Global Navigation Satellite System (GNSS) continues to advance, the utilization of GNSS for the estimation of PWV has reached a higher level of maturity. In recent years, China has made remarkable progress in the establishment of numerous Continuous Operational Reference System (CORS) stations and the deployment of the Crustal Movement Observation Network of China (CMONOC) through the utilization of GNSS technology. (Yu et al. 2019; Zhao et al. 2015). Compared to conventional methods of water vapor detection, the utilization of GNSS technology for PWV estimation offers distinct advantages, including continuous operation, all-weather capability, high accuracy, and enhanced resolution (Wang et al. 2016; Zhai and Eskridge 1996; Tao et al. 2021; Liu et al. 2000; Bevis et al. 1992; Yang 2022; Gurbuz and Bayik 2023). Studying the variations of precipitable water vapor (PWV_GNSS) determined from the GNSS data can indirectly reflect climate change and extreme weather events in the region. During the inversion process, PWV_GNSS is easily affected by extreme weather events such as haze and sandstorms, resulting in fluctuations in the calculation results (Guo et al. 2020).

As a common form of extreme weather, sandstorms pose a significant threat as a highly hazardous meteorological disaster and act as an important dust transport process that accelerates land desertification. Over the past 500 years, East Asia has experienced recurrent occurrences of sandstorms, with northwest China being particularly vulnerable to their devastating impact. These sandstorm disasters have inflicted significant harm on various aspects, including economic development, human well-being, public health, and the environment (Huo et al. 2019; Zhang et al. 2021). According to their diameters, sand particles are classified as a particulate matter (Watanabe et al. 2016), which refer to the general term for solid and liquid particulate matter that floats in the air. Respirable suspended particles, commonly known as PM10, are particles with a diameter of 10 µm or less. Furthermore, there are fine particles called PM2.5, which have a diameter of 2.5 µm or less (Lau and He 2017). Both PM10 and PM2.5 particles contain numerous harmful substances, posing substantial risks to human health and leading to various societal concerns. (Yao et al. 2015; Kiser et al. 2020; Paun et al. 2015; David and Gao 2016). Based on the long-term occurrence of sandstorms in Wuhai and in combination with the climate bulletins issued by the China Meteorological Administration and the government of Inner Mongolia Autonomous Region, this study concludes that the period from February to April is the sandstorm season in Wuhai. During the sandstorm season, the PWV_GNSS is influenced not only by precipitation but also by the presence of particulate matter (Guo et al. 2021a, 2021b; Wen et al. 2020). By studying the correlation between PWV_GNSS and particulate matter during sandstorms, this paper aims to identify the relationship between PWV_GNSS and particulate matter. By identifying the occurrence time and trajectory of sandstorms within the area, proactive alerts can be issued to mitigate the detrimental impact caused by these sandstorms.

Numerous studies have employed SSA in the analysis of data sets, including PWV and PM10 (Zhou et al. 2022). As a digital signal processing technique, SSA has gained significant prominence in the fields of climatology and measurement due to its wide range of applications. It is capable of effectively performing operations on time series data, including trend identification, period determination, data reconstruction, and data interpolation (Vautard et al. 1992; Wyatt et al. 2012; Chen et al. 2013; Zabalza et al. 2014; Guo et al. 2018; Shen et al. 2018).

To study the variations of PWV determined from GNSS data during the sandstorm season, daily average data of PWV_GNSS, precipitation, and particulate matter from January 1, 2017 to December 31, 2021 in Wuhai were selected for this study. The focus of this study is on PM10 due to its strong correlation with PM2.5, and also because the proportion of coarse particles in sandstorms during spring is significantly higher than that of fine particles (Alghamdi et al. 2015). The data processing procedure was as follows: firstly, this study aims to obtain principal components of PWV residual (PWV_RPC) and principal components of PM10 (PM10_PC) by using least-squares fitting, singular spectrum analysis, and least-squares spectrum analysis; Secondly, this study aims to obtain the correlation between PWV_RPC and PM10_PC and between PWV_RPC and precipitation.

Data and methods

Wuhai is located within the range of 106°40’E-107°09’E and 39°15’N-39°32’N, belonging to the northwest region of China (Fig. 1), close to the Loess Plateau and the border between China and Mongolia, where sandstorms frequently occur in spring. The Wuhai station (NMWH) established by CMONOC is shown in Fig. 1. On the one hand, the vast desert area in southern Mongolia is one of the key sources of sandstorms, from which most of the particulate matter of sandstorms in northern China originates (Han et al. 2021). On the other hand, the unique geographical location and climatic environment make it prone to sandstorms in spring every year.

Fig. 1

NMWH station and geographical location of Wuhai

Data

Precipitable water vapor

The PWV_GNSS data is provided by CMONOC, which belongs to GNSS data product service platform of China Earthquake Administration (http://www.cgps.ac.cn). The second sampling observation of GNSS reference stations in the CMONOC system primarily aims to monitor the total atmospheric water vapor content and stratified water vapor content, thereby offering a comprehensive water vapor product (Zhu et al. 2020).

The data processing software is GAMIT. The sampling rate of GNSS observation was 30 s, Rinex format, cut-off angle of 10°, GMF mapping functions. The zenith tropospheric delay (ZTD) correction is estimated hourly and the GAMIT default horizontal gradient are used (Liu et al. 2022).

After the parameters selection is completed, the hourly ZTD can calculated by GAMIT. The ZTD consists of zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD), and ZHD can be accurately calculated with the equation by Saastamoinen ( 1972):

$$ZHD = \frac{{\left( {2.2768 \pm 0.0024} \right)P_{S} }}{1 - 0.00266 \times \cos 2\theta + 0.00028 \times H}$$

(1)

where P_s is atmospheric pressure (unit: hPa). θ is the latitude of the GNSS station (unit: °). H is the height of the GNSS station (unit: km).

After obtaining ZHD, the ZWD can be calculated according to Eq. (2):

$$ZWD = ZTD - ZHD$$

(2)

The PWV can be calculated by the Eq. (3):

$$PWV = \Pi \times ZWD$$

(3)

where ∏ is the conversion, which can be calculated by equation (Bevis et al. 1994):

$$\Pi = \frac{{10^{6} }}{{\left( {k_{3} \times T_{m}^{ - 1} + k_{2}{\prime} } \right) \times R_{v} }}$$

(4)

where k₂’ and k₃ are the atmospheric refractivity constants ($k_{2}{\prime} = 22.1 \pm 2.2K/hPa,k_{3} = 3.375 \times 10^{5} \pm 0.012 \times 10^{5} K^{2} /hPa$), and Rv is the gas constant of water vapor (${\text{R}}_{v} = 461.495{\text{ J/(kg}} \cdot {\text{K)}}$). Tm is the weighted mean temperature (unit: K), which can be calculated using radiosonde profiles, or using numerical weather models (Bevis et al. 1994; Yao et al. 2012), most published studies to date estimate Tm by equation (Bevis et al. 1992):

$$T_{m} = 70.2 + 0.72 \times T_{s}$$

(5)

where Ts is the surface temperature, which can be obtained from ground-based weather stations co-located with GNSS stations.

In this study, PWV_GNSS data were provided by CMONOC for every two hours from January 1, 2017 to December 31, 2021 and were averaged over 12 PWV_GNSS data per day before being used.

Particulate Matter 10

The real-time data platform of the China National Environmental Monitoring Center (CNEMC) provides hourly PM10 and PM2.5 data (http://www.cnemc.cn/sssj). The process of calculating the correlation between PM10 and PM2.5 is as follows:

$$\begin{gathered} \rho (PM_{10} ,PM_{2.5} ) = \frac{{{\text{cov}} (PM_{10} ,PM_{2.5} )}}{{\sigma_{{PM_{10} }} \sigma_{{PM_{2.5} }} }} \hfill \\ \, = \frac{{E\left[ {\left( {PM_{10} - E(PM_{10} )} \right)\left( {PM_{2.5} - E(PM_{2.5} )} \right)} \right]}}{{\sigma_{{PM_{10} }} \sigma_{{PM_{2.5} }} }} \hfill \\ \, = \frac{{E(PM_{10} PM_{2.5} ) - E(PM_{10} )E(PM_{2.5} )}}{{\sqrt {E(PM_{10}^{2} ) - E^{2} (PM_{10} )} \sqrt {E(PM_{2.5}^{2} ) - E^{2} (PM_{2.5} )} }} \hfill \\ \end{gathered}$$

(6)

where ρ is the correlation coefficient, cov is the covariance, and σ is the standard deviation.

The correlation between PM10 and PM2.5 is 0.7982, so the PM10 data from January 1, 2017 to December 31, 2021 was selected for this study. The PM10 data were averaged over 24 data per day before being used.

Precipitation

ERA5 is the fifth generation of the European Centre Weather Forecasting (ECMWF) reanalysis dataset, which mainly used in global digital weather forecasting, air quality analysis, atmospheric composition monitoring, climate monitoring, etc. (Lavers et al. 2022). For this study, ERA5 was utilized to accquire hourly precipitation data from January 1, 2017 to December 31, 2021. Daily precipitation data were derived by summing up the 24-hourly precipitation values. Since ERA5 provides gridded data with a resolution of 0.25° × 0.25°, it should be interpolated to the Wuhai station based on longitude, latitude, and precipitation values.

Methods

The missing rate of PWV_GNSS data is 6.16% and the missing rate of PM10 data is 5.94%, so the missing of PWV_GNSS and PM10 data are interpolated by using SSA before being used. Firstly, SSA is performed on the PWV_GNSS and PM10 after removing their linear trends to obtain the main components of both, and the main period of both is determined using fast Fourier transform. Secondly, a fitted PWV (PWV_LSF) data is obtained through the application of least square spectral analysis to the PWV_GNSS. Then, the PWV residual (PWV_R) is obtained by subtracting PWV_LSF from PWV_GNSS, and the PWV_RPC is obtained through the application of SSA. Similarly, the PM10 residual (PM10_R) is obtained by subtracting PM10_PC from PM10. The correlation coefficients were obtained by correlating the PWV_RPC with the PM10_PC and precipitation.

Singular spectrum analysis

Interpolation

In this study, the SSA was used to pre-processing PWV_GNSS and PM10 data, and iterative interpolation was used for missing data (Guo et al. 2018; Jin et al. 2021). The specific steps of interpolation are as follows:

(1) The missing data in the original time series were filled with 0 and marked accordingly, followed by centralizing the completed data.

(2) The singular spectrum decomposition is performed on the new time series data to determine the first i-order reconstruction component (RC) as the main component of the original series, and the value at the missing position in the original series is replaced by the value in the first RC (noted as R1), and this process is repeated until the data residual RMS of the two interpolated data before and after is less than a certain value.

(3) Add the value in the second RC (noted as R2) to reconstruct the missing part of the data, i.e., the missing data is obtained by linear superposition of R1 and R2, and repeat the above step (2) until RC is linearly superimposed to the missing data.

Decomposition

In this study, SSA is performed on PWV_GNSS and PM10 to determine the trend and period data of both. The decomposition principle is as follows:

(1) Construct a time-delay matrix with the amount of data N and choose an appropriate window size M, in which M is generally greater than 1 and less than N/2. For time series where the period is already known, the window length M is generally taken as a common multiple of the period for better separation of the periodic part. Let $K = N - M + 1$, then the constructed time-delay matrix X can be expressed as:

$$X = \left[ {X_{1} ,X_{2} , \cdots ,X_{k} } \right] = \left( {x_{i,j = 1}^{L,k} } \right) = \left[ {\begin{array}{*{20}c} {x_{1} } & {x_{2} } & \cdots & {x_{N - M + 1} } \\ {x_{2} } & {x_{3} } & \cdots & {x_{N - M + 2} } \\ \vdots & \vdots & \ddots & \vdots \\ {x_{M} } & {x_{M + 1} } & \cdots & {x_{N} } \\ \end{array} } \right]$$

(7)

where $X_{i} = (x_{i} , \cdots ,x_{i + M - 1} )^{T} ,(1 \le i \le K)$. X is a time-delay matrix of order $M \times K$. Each row and column of it is a subsequence of the initial time series, and it is a Hankel matrix.

(2) Singular values decomposition (SVD), there was a matrix $S = XX^{T}$. $\lambda_{1} , \cdots ,\lambda_{M}$ the eigenvalues of S arranged in descending order of magnitude as $\lambda_{1} \ge \cdots \ge \lambda_{M} \ge 0$, and the corresponding eigenvectors are $U_{1} , \cdots ,U_{M}$, respectively. The matrices $X_{i}$ have rank 1; such matrices are sometimes called elementary matrices. The SVD of the time-delay matrix X can be expressed as:

$$X = X_{1} + X_{2} + \cdots + X_{d}$$

(8)

where $d = rank(X), \, X_{k} = \sqrt {\lambda_{k} } U_{k} V_{k}^{T} , \, V_{k} = X^{T} U_{k} /\sqrt {\lambda_{k} } (k = 1, \cdots ,d)$. $\sqrt {\lambda_{k} } (k = 1, \cdots ,d)$ is a singular value of $X_{k}$. The new matrix $X^{(r)} (r < d)$ can be constructed by selecting appropriate eigenvalues and corresponding eigenvectors. The collection will be called i-th eigentriple (abbreviated as ET) of the SVD.

(3) Diagonal averaging. The purpose of diagonal averaging is to reconvert the primitive matrix $X_{k}$ obtained from the decomposition in the previous step into a new time series of length N, called the RC, and the sum of all RCs is equal to the original series. Define the matrix $Z = X_{k} ,z_{1} ,z_{2} , \cdots ,z_{N}$, as the time series obtained by diagonal averaging of Z. Let $M^{*} = min(M,K),K^{*} = \max (M,K)$, if M < K, then $z_{ij}^{*} = z_{ij}$, otherwise $z_{ij}^{*} = z_{ji}$, the equation for diagonal averaging can be expressed as:

$$z_{i} = \left\{ {\begin{array}{*{20}c} {\frac{1}{i}\sum\limits_{m = 1}^{k} {z^{*}_{m,i = m + 1} ,1 \le i \le M^{*} } } \\ {\frac{1}{{M^{*} }}\sum\limits_{m = 1}^{{L^{*} }} {z^{*}_{m,i = m + 1} ,M^{*} \le i \le K^{*} } } \\ {\frac{1}{N - i + 1}\sum\limits_{{m = i - K^{*} + 1}}^{{N - K^{* + 1} }} {z^{*}_{m,i = m + 1} } ,K^{*} < i \le N} \\ \end{array} } \right.$$

(9)

Least squares spectrum analysis

The PWV_LSF data were obtained using least squares spectrum analysis, and their variation in rate, amplitude, and phase on the time scale was (Shi et al. 2022b):

$$y = a_{0} + a_{1} t + \sum\limits_{1}^{n} {A_{i} \sin (\omega_{i} (t - t_{0} ) + \varphi_{i} )}$$

(10)

where $A$ is the amplitude, $\omega$ is the periodic signal, $a_{0}$ is the deviation of the time series, $a_{1}$ is the linear trend, $\varphi_{i}$ is the initial phase.

Analysis

Analysis of precipitable water vapor data

PWVGNSS time series data analysis

To obtain the linear trend of PWV_GNSS (PWV_GNSSL) from 2017 to 2021, a least-squares linear fit is initially conducted:

$$PWV_{GNSSL} = 0.37Y + 10.42$$

(11)

where Y represents the year and PWV_GNSS shows an increasing trend during 2017–2021 with a growth rate of 0.37 mm/year. It can indicate that the climate in Wuhai area has gradually become wetter in recent years and the water vapor content in the air has increased (Zhu et al. 2022).

It is evident that PWV_GNSS exhibits a notable periodicity, reaching its peak in July and August each year, with a maximum value of 48.86 mm. Conversely, during the winter and spring seasons, the values typically remain below 10 mm (Fig. 2). The increase in temperature can enhance the atmosphere's ability to store water vapor. Under conditions where there is sufficient water vapor source, the higher the content of atmospheric water vapor, the larger the PWV_GNSS value (Shi et al. 2020). Wuhai experiences a characteristic temperate continental climate, characterized by distinct features such as hot and rainy conditions in summer and autumn, and relatively lower rainfall with drier weather in winter and spring. Consequently, the PWV_GNSS values in Wuhai tend to be higher during summer and autumn compared to winter and spring. Additionally, the occurrence of sandstorms is more frequent during the spring season.

Fig. 2

PWV_GNSS and PWV_GNSSL data for 2017 to 2021

PWVGNSS time series data analysis

The decomposition of the PWV_GNSS with the linear trend removed using SSA avoids the effect of the linear trend decomposition on each order. PWV_GNSS subtracts PWV_GNSSL to obtain a set of data without linear trend, and SSA analysis is performed on PWV_GNSS data without linear trend. Based on several practical experiences and periods, the window length M was chosen as 730 and the principal components of PWV_GNSS were obtained. The eigenvalues of different orders were arranged using the descending order method (Fig. 3).

Fig. 3

Order-eigenvalue and w-correlation of reconstruction. a Eigenvalues of different orders. b w-correlation for the first 30 orders of reconstruction

The eigenvalues obtained after the SSA decomposition of PWV_GNSS, the eigenvalues are decreasing in value as the order increases. When the order exceeds 4 times, the eigenvalues tend to level off (Fig. 3a). The larger the value of the eigenvalue, the greater the energy in the signal represented by its corresponding eigenvector, and the smaller the energy vice versa. The correlation between the orders after SSA decomposition is found using the w-correlation method (Hassani 2007), and the decomposition is poor when the order is greater than 4 (Fig. 3b). Therefore, the first four orders (RC1, RC2, RC3, RC4) reconstruct the PWV_GNSS time series. RC1 + RC2 form a new periodic term and RC3 + RC4 form a new periodic term.

From January 1, 2017 to December 31, 2021, the maximum value of PWV_GNSS is 48.86 mm. Although there is a clear trend of fluctuation in PWV_GNSS from sandstorm season each year, PWV_GNSS values are much larger in the non-sandstorm season than in the sandstorm season. After SSA decomposition of the PWV_GNSS time series with the linear trend removed, the variance contribution of the first 4th-order reconstructed components reached 69.61%, indicating that the first 4th-order reconstructed time series can characterize this PWV_GNSS time series. Analyzing RC1 + RC2 and RC3 + RC4 using the fast Fourier transform yields their respective periods (Fig. 4).

Fig. 4

Reconstruction component and Frequency-Power of PWV_GNSS. a Reconstruction of component RC1 + RC2. b Frequency-Power diagrams of (a). c Reconstruction of component RC3 + RC4. d Frequency-Power diagrams of (c)

The periodic term consisting of RC1 and RC2 with values ranging from $-$ 11.60 mm to 12.4283 mm. The peak of the new periodic term occurs during August each year and tends to decrease year by year, and the valley occurs in January each year (Fig. 4a). The first period is composed of RC1 and RC2, which are similar to two basic functions of the first period. The second period is composed of RC3 and RC4, which are similar to two basic functions of the second period. RC1 and RC2 have the same period, as do RC3 and RC4, therefore it is necessary to study RC1 + RC2 and RC3 + RC4. The main period of the period term consisting of RC1 + RC2 calculated by the fast Fourier transform, which has a principal period of 0.9355 year (Fig. 4b). The periodic term composed of RC3 and RC4 with values ranging from $-$ 4.46 mm to 4.99 mm, with peaks occurring in February and August each year and a decreasing trend year by year, and valleys occurring in May and November. The peak of the cycle consisting of RC3 + RC4 occurs approximately in the summer and winter of each year (Fig. 4c), a phenomenon due to the influence of PWV_GNSS by precipitation and particulate matter, respectively (Shi et al. 2022a, b; Wang et al. 2016). The main period of the period term consisting of RC3 + RC4 calculated by the fast Fourier transform, which has a principal period of 0.5102 year (Fig. 4d).

Least squares spectral analysis of PWVGNSS and determination of PWV residuals

In this study, the fitted data PWV_LSF was derived through least squares spectral analysis for PWV_GNSS data from January 1, 2017 to December 31, 2021. The fitting process involved incorporating two periods, namely 0.9355 years and 0.5102 years (Fig. 5a). The PWV_R is obtained by subtracting PWV_LSF from PWV_GNSS (Fig. 5b).

Fig. 5

PWV_LSF and PWV_R data. a 2017 to 2021 PWV_LSF time series data. b 2017 to 2021 PWV_R time series data

Determination of the principal components of the PWV residuals

SSA was applied to the PWV_R to extract its principal components, with a window length of 880 chosen based on practical usage experience and the period. The correlation between the decomposed components was evaluated using the w-correlation method (Fig. 6a).

Fig. 6

w-correlation of reconstruction and PWV_RPC data. a W-correlation of the first 30th order reconstruction components of PWV_R. b 2017 to 2021 PWV_R and PWV_RPC time series data

After decomposing the PWV_R by SSA, the first 6 orders are regarded as PWV_RPC. PWV_RPC has three annual peaks during 2017 to 2021 and each of these three peaks is caused by different drivers. The first peak occurs in April each year and is caused by particulate matter, such as PM10, brought in by weather such as sandstorms. The second peak occurs in August each year and has the longest duration and highest values compared to the other two peaks. The third peak occurs in December every year, which is because there is a lot of frost and snow in the winter in Wuhai (Fig. 6b).

Analysis of PM10 change pattern

PM10 time series data variation

Since the correlation coefficient between PM10 and PM2.5 is 0.7982, the study focused exclusively on PM10. From the data, it can be concluded that the average value of PM10 in the sandstorm season 2017 to 2021 is 142.01 μg/m³; the average value of 89.64 μg/m³ in the non-sandstorm season 2017 to 2021. The average values of PM10 for each year from 2017 to 2021 were 119.18 μg/m³, 137.29 μg/m³, 101.77 μg/m³, 87.69 μg/m³, and 100.96 μg/m³, respectively. The highest annual average PM10 value occurred in 2018, and the annual average PM10 value decreased after 2018. The highest single-day value of PM10 was 1187 μg/m³, which occurred in the spring of 2021 (Fig. 7). The slightly larger annual mean PM10 in 2021 than in 2020 is due to the transport of particulate matter from the Gobi Desert in southern Mongolia to China in the spring of 2021 due to the influence of the cold cyclone in Mongolia and the cold air behind it. And it caused most of northern China to experience the most extensive, intense, and longest-impacting dust and sand weather in China in the past decade (Zhang et al. 2022b).

Fig. 7

2017 to 2021 PWV_R and PM10 time series data

Determination of PM10 principal components

To obtain the linear trend of PM10 (PM10_L) from 2017 to 2021, a least-squares linear fit is initially conducted:

$$PM10_{L} = - 10.48Y + 135.54$$

(12)

where Y represents each year, and PM10 shows a decreasing trend during 2017 to 2021 at a rate of 10.48 μg·m⁻³/year. It shows that the air quality has been improved in recent years under the implementation of environmental protection policies in Wuhai area (Shi et al. 2007).

In order to avoid the impact of the linear trend on each order, it is necessary to subtract the linear trend from PM10 before performing the SSA. And the window length M was chosen to be 730 according to the usage experience and period. The correlation between the orders after SSA decomposition is found using the w-correlation method.

The first 4 orders were analyzed using the fast Fourier transform, and the periods of RC1 + RC2 and RC3 + RC4 were obtained as 0.9355 and 0.5102 year, respectively (Fig. 8). Thus, the linear trend fitted by Eq. (12) plus the first 4 orders after SSA decomposition form the PM10_PC (Fig. 9a). PM10 demonstrates approximately two peaks and one trough annually throughout the period from 2017 to 2021. The first peak consistently emerges in April, primarily attributable to heightened occurrences of sandstorm weather. The trough occurs in August each year, which is caused by the negative correlation between PM10 and precipitation (Yang et al. 2021). Rainfall plays a crucial role in cleansing the atmosphere by effectively washing away pollutants and particulate matter, leading to a notable reduction in concentrations of particulate matter. The second peak occurs in December each year, when PM10 values rise mainly due to haze weather. There is a gap between the second peak and the first peak of each year, as shown by the fact that the value of the second peak is smaller than the value of the first peak. This is because the increase in PM10 concentration caused by haze is weaker than the increase in PM10 concentration of sandstorms, but this difference will gradually decrease. This is due to the decreasing frequency and intensity of sandstorms during the sandstorm season as the quality of our environment continues to improve. The second peak in 2020 and the first peak in 2021 form a new peak (Fig. 9b). This is because the spring of 2021, when the Wuhai suffered from the largest and most intense as well as the longest duration sandstorm weather in the last decade (Zhang et al. 2022a, b), so it caused the two periods to merge into one.

Fig. 8

Reconstruction component and Frequency-Power of PM10. a Reconstruction of component RC1 + RC2. b Frequency-Power diagrams of (a). c Reconstruction of component RC3 + RC4. d Frequency-Power diagrams of (c)

Fig. 9

w-correlation of reconstruction and PM10_PC data. a w-correlation of the reconstructed components of the first 30 orders of PM10. b 2017 to 2021 PM10_PC time series data

Analysis of the variation pattern of precipitation data

Precipitation is also an important cause of PWV_GNSS variation, and PWV_GNSS shows a significant correlation with precipitation over short time periods (Shi et al. 2022a). From the data, it can be concluded that the average value of precipitation in the non-sandstorm season 2017–2021 is 123.61 mm; the average value of precipitation in the sandstorm season 2017 to 2021 is 18.58 mm. The number of days with daily precipitation exceeding 1 mm in each year of the sandstorm season from 2017 to 2021 were: 6 days, 7 days, 2 days, 1 day and 8 days, respectively. Precipitation in Wuhai is mainly concentrated in May to September, with the highest daily precipitation occurring in July or August each year, and less from October to April of the following year (Fig. 10).

Fig. 10

Precipitation time series data for 2017 to 2021

Correlation analysis of factors in the sandstorm season

In order to investigate the impact of PM10 and precipitation on PWV_GNSS during the sandstorm season, the correlation between PWV_RPC and PM10_PC, precipitation was calculated separately. Subsequently, the influence of PM10 and precipitation on PWV_GNSS was analyzed. From February to April is the sandstorm season in Wuhai, but there are some years when the season occurs late or ends early. Therefore, correlation analysis should be performed based on the actual time of the sandstorm season.

The correlation coefficients between PWV_RPC and PM10_PC are greater than 0.6 in the sandstorm season. The correlation coefficient between PWV_RPC and precipitation is less than 0.2 in the sandstorm season. It indicates that PM10 influences the variation of PWV_GNSS during the sandstorm season. Since there is less precipitation during the sandstorm season, the precipitation produces little change in PWV_GNSS. Due to the long time span of the non-sandstorm season, the factors influencing of PWV_GNSS are more complex than those of the sandstorm season (Table 1), so the correlation coefficients of PWV_RPC with PM10_PC and precipitation are not significant (Fig. 11).

Table 1 Correlation coefficients between PWV_RPC with PM10_PC and precipitation in the sandstorm and non-sandstorm seasons

Fig. 11

2017 to 2021 PWV_RPC and PM10_PC time series data

Results and discussion

The PWV obtained based on GNSS and PM10 were analyzed. The results showed that PWV_GNSS shows an increasing trend and two main periods of 0.9355 and 0.5102 year from 2017 to 2021. The PWV_GNSS is rising at a rate of 0.37 mm/year, which indicates that the climate in Wuhai has become progressively wetter in recent years. PM10 shows a decreasing trend from 2017 to 2021 with a rate of -10.48 μg·m⁻³/year, and there are two main periods of PM10 with 0.9355 and 0.5102 years respectively.

This study analyzed the relationship between the PWV_RPC with the PM10_PC and precipitation during the sandstorm season and non-sandstorm season. The results show that the correlation between PWV_RPC and PM10_PC during the sandstorm season is significant, with correlation coefficients greater than 0.6. Thus, PM10 is a factor in the influence of sandstorm season on the PWV determining from GNSS data.

Through their research, Wang and Guo have discovered that the changes of PWV determined from GNSS data influenced by particulate matter. Shi have discovered that a clear correspondence between PWV_GNSS and precipitation in the short term (Guo et al. 2021a, 2020; Wang et al. 2016; Shi et al. 2022a, b). This paper indicates that during the sandstorm season, the PWV_RPC (PWV_R represent the variations in PWV_GNSS influenced by other factors) has a significant correlation with PM10, while the correlation with precipitation is not significant. The lack of significant correlation with precipitation is primarily due to the paper focus on the period from February to April, during which there is less precipitation and frequent occurrences of sandstorm.

Compared to the expensive cost of building a meteorological station, the cost of establishing GNSS stations is relatively low. In the future, multiple GNSS stations can be set up along the sandstorm transport route in northwest China based on the clear correspondence between PWV_GNSS and particulate matter during the sandstorm season. GNSS technology can be utilized to detect the occurrence of sandstorms. This can further determine the actual path and arrival time of the sandstorm and issue warnings to mitigate the various hazards caused by sandstorms.