4D Modeling of Precipitable Water Vapor to Assess Flood Forecasting by Using GPS Signals

doi:10.21203/rs.3.rs-1502945/v1

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4D Modeling of Precipitable Water Vapor to Assess Flood Forecasting by Using GPS Signals

https://doi.org/10.21203/rs.3.rs-1502945/v1

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published 27 Sep, 2023

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Every year the government and people suffer from the cost of damages caused by natural disasters such as hurricanes and floods. Thanks to Global Positioning System (GPS) permanent station data, today it is possible to determine the amount of Water Vapor (WV) very accurately and reliably. GPS signals pass through different layers of the atmosphere, such as the ionosphere and troposphere, and therefore they are delayed. A significant part of the delay is due to the troposphere, which is one of the serious sources of error in GPS. In this research, by using 5 GPS permanent stations located in the Arasbaran region, in northwest of Iran, the Precipitable Water Vapor (PWV) is evaluated in order to show the capacity of this method in forecasting the October 2012 flood over the region. The results showed that the amount of PWV in the atmosphere had increased by 2 mm a few hours before the flood, which could be used as a forecast indicator. The Tikhonov regularization for tropospheric tomography covering the GPS stations region was also performed for latitude and altitude components for 3 consecutive days: the day before the flood, the flood day, and the day after the flood. A high amount of PWV was observed in the troposphere on the day before the flood, and especially on the flood day. During the study period, the results from tomography and the radiosonde were in good agreement, with a significance correlation of around 0.95. Also, the values of PWV obtained from GPS and MODIS-NIR do not have an absolute error more than 4.4 mm over the 8 days from 8 October 2012 to 15 October 2012.

Flood

GPS

PWV

Tomography

4D Modeling

GPS signals pass through various layers of the atmosphere, including the ionosphere and troposphere. There is a considerable delay in GPS signals due to the bulk of the troposphere layer. The tropospheric delay is a systematic error that can be divided into dry (hydrostatic) and wet delays. The dry delay entirely depends on the dry gases present in the troposphere. The error caused by the dry component is about 2.3 meters in the zenith direction (Seeber, 2003). To remove the effect of this error in precise positioning, the dry delay can be well modeled by using local temperature and atmospheric pressure measurements near the GPS antenna. The wet component depends on the distribution and amount of WV, and its effect is about a few centimeters in dry areas and up to 35 centimeters in wet areas (Mascitelli et al. 2019).

WV is one of the critical parameters in the analysis of atmospheric events. The source of atmospheric WV is mainly evaporation from the earth's surface. The atmospheric temperature due to the saturation vapor pressure falls with increasing altitude and thus, WV distribution is not uniform around the earth. WV varies strongly with time and place and particularly we can see a great decrease when moving towards the poles (Yue and Ye, 2019). Unlike the dry component, the wet component cannot be easily modeled with surface measurements, such as temperature and pressure.

Many empirical models such as Hopfiled, Saastamonien, Ifadis, and Berman have been developed to express tropospheric delays, which are useful for low accurate positioning (Reuveni, 2019). Generally, the meteorological parameters such as atmospheric pressure, temperature, and humidity are required as inputs to these models. The amount of refraction along the slant propagation path of the GPS signal from the satellite to the ground receiver is difficult to quantify. Therefore, several mapping functions have been developed to calculate signal delays along the Zenith direction for all GPS satellites (Wang et al. 2019).

At present, the amount of WV can be estimated by several methods such as radiosonde, radiometer, and satellite imagery (Yang et al. 2019). Zenith wet delay (ZWD) estimated by GPS signals is compatible with radiosonde observations (Reuveni, 2019). The PWV obtained from 8 GPS stations in Australia shows a correlation greater than 0.88 compared to that of radiosondes (Choy et al. 2019). The estimates of Integrated Water Vapor) IWV (from GPS at high latitudes are also compatible with radiometers (2-channel and 3-channel) and radiosonde) Fiondaet al. 2019). Before the 2013 Colorado flood, the GPS-estimated PWV indicated an increase from 22 mm to 32 mm) Huelsinget al. 2017). During severe floods, GPS-PWV and meteorological data show a decrease of 3.52 mm, as well as during the winter monsoon in which abnormal peaks of PWV are observed) Supartaet al. 2012). It is shown in Yao et al. (2017) that GPS-PWV variations are highly compatible with hourly precipitation from 1 September 2014 to 31 August 2015, and give a correct forecast rate of 80%. Based on the relationship between Global Navigation Satellite System (GNSS) derived PWV and actual rainfalls, a short-term rainfall forecasting method by 6 hours in advance could be established.

The GPS-PWV tomography combined with radiosonde, synoptic data and non-hydrostatic model (NHM) can be used to predict the atmospheric instability before floods occur) Chen, 2017). There is a good consistency between tropospheric GNSS tomography, radiosonde data, and ERA5 reanalysis products on water vapor density profiles) Dong and Jin, 2018). Tikhonov regularization, based on a smoothing matrix, can solve the problem of limited data tomography. Tikhonov tomography derived from GPS and radiosonde has a resolution better than GPS alone, and has the potential to be used in disaster management of situations caused by weather conditions (Biet al. 2006).

In this research, we attempt to study the PWV behavior through flood forming so that it can be used for flood forecasting. The tomography over GPS stations has been also performed and evaluated using Tikhonov regularization for latitude and altitude for three consecutive days: the day before the flood, the flood day, and the day after the flood. Radiosonde data and MODIS-PWV observations were used for October 2012 for verification of GPS results.

2.1 Tropospheric effect on GPS signals

Due to the variability of the tropospheric refractive index, GPS signals are significantly affected when passing through the tropospheric layer. Tropospheric delay obtained along the zenith line, called Zenith Tropospheric Delay (ZTD), is a combination of Zenith Hydrostatic Delay (ZHD) and Zenith Wet Delay (ZWD) (Akilan et al. 2019):

$$ZTD=ZHD+ZWD$$

(1)

The ZTD is typically estimated at 2.50m, where about 90% of this value is caused by the ZHD and approximately 10% by the ZWD (Feng et al. 2019). As GPS satellites decrease in elevation angle toward the horizon, slant tropospheric delay, including the slant hydrostatic delay or the slant wet delay, increases significantly. The speed of the signals change when the slant signals pass through the different atmospheric layers, such as the ionosphere and troposphere. The tropospheric layer is a non-dispersive environment for GPS signals, therefore, the tropospheric delays, unlike the ionospheric delays, cannot be eliminated using the combination of two different GPS frequencies (ionospheric-free linear combination).

Since measuring the refraction along the signal propagation path is not possible, different tropospheric models have been developed to estimate the tropospheric delays, although they are not suitable for precise positioning (Tanget et al. 2019). To achieve precise positioning, the distribution of WV is required to model the tropospheric wet component.

2.2 Tropospheric wet delay estimation using GPS

Because the tropospheric empirical and theoretical models are not suitable for high accuracy applications in positioning, an alternative method based on tropospheric wet delay estimation using GPS has been developed to improve GPS positioning accuracy. If the coordinates of the ground GPS sites are known and all other error sources are successfully eliminated or sufficiently reduced, we can compute the descriptive parameters of the WV profiles around each GPS station (Alinia et al. 2019). By assuming that the slant tropospheric delays are symmetric with respect to the azimuth, they can be mapped to the zenith line by using mapping functions. The dry component can also be modelled and removed by measuring the surface parameters, such as temperature and pressure, and finally, we can estimate the zenith wet delay (Bi et al. 2006).

The GPS-derived PWV over each station is estimated by multiplying the zenith wet delay (ZWD) with a conversion factor П (~ 0.15), which is a function of water vapor‐weighted mean temperature Tm at the station (Bi et al. 2006; Fionda et al. 2019; Huelsing et al. 2017).

PWV = ∏(Tm) × ZWD

(2)

$$\prod =\frac{{10}^{6}}{\rho {R}_{v}[{k}_{3}/{T}_{m})+{k\text{'}}_{2}]}$$

(3)

Where is the density of liquid water, is gas constant, , is physical constants.

$${T}_{m}= \frac{{\int }_{}^{}({p}_{v}/T){d}_{z}}{{\int }_{}^{}({p}_{v}/{T}^{2}){d}_{z}}$$

(4)

Here is partial pressure of WV, z is the distance in zenith direction and is surface temperature. It should be noted that any modeling and calculation errors affect ZHD, ZWD, and PWV values.

Water vapor tomography has been developed as a powerful tool to model the spatial and temporal distribution of atmospheric water vapor. But the tomography is considered as an inverse problem which is often ill-posed. Tikhonov regularization is a stable method for approximating the solutions of ill-posed inverse problems which is widely used for many applications (Xu et al. 2016). To solve the normal equation's system, in Tikhonov regularization, unlike the truncated singular value decomposition (SVD) method, the small singular values of the spectral form of the coefficient matrix are not eliminated. The small singular values are involved to solve the discrete ill-posed inverse problem with a different weight relative to the large singular values, and therefore it helps to improve the initial solution stability (Chen, 2017).

GPS water vapor tomography refers to the 3D reconstruction of tropospheric water vapor using a large number of GPS signals. The modeling area is usually discretized into serval voxels. Figure 1 shows a schematic representation of GPS signals in a 3D tomography model in which the pathway of GPS signals travel through some voxels toward GPS antenna. Unfortunately, some voxels are not crossed by any GPS signals and result in an ill-posed problem that cannot be solved directly with the general least-squares technique. To overcome this problem, the Tikhonov regularization is used.

IWV in the slant path between the receiver and GPS satellite is called Slant Water Vapor (SWV) which is a function of water vapor density, mapping functions, gradient mapping functions, and non-homogeneous variation of water vapor (Dong and Jin, 2018). A linear system of tomographic linear equations between Slant PWV and water vapor density can be established as follows (Bi et al. 2006):

$$\left(\frac{{S}_{PWV}}{0}\right)=\left(\frac{A}{W}\right)x$$

(5)

Where, is Slant PWV, A is the design matrix for rays in voxels, W is the smoothing constraint and x is PWV. To solve this form of the ill-posed inverse problem, the Tikhonov function is defined as follows (Fermi et al. 2019):

$${F}_{Tikh}\left(x;\gamma \right)={\Vert Ax-b\Vert }_{2}^{2}+\gamma {\Vert x\Vert }_{2}^{2}$$

(6)

where b is observations and is regularization parameter. The Tikhonov method, similar to the least-squares (LS) method, assumes that the observation errors are random, the probability of error distribution is normal, as well as the mathematical expectation of the errors is zero. Therefore, this method looks for a solution with the minimum norm of residuals by using the L2-norm of Hilbert space which gives an optimal solution (Xu et al. 2016). Therefore, the Tikhonov method benefits the advantage of stabilization. Selecting the$\text{I}³$ parameter is one of the most challenging issues so that several methods have been developed for this purpose. In this study, the L-curve approach has been chosen because of rapid convergence, no need for knowledge about observation errors, stability, and high accuracy (Wang et al. 2018).

The precepetation that occurred in the north of Iran on October 14, 2012 caused heavy rainfall in the three provinces of Mazandaran, Golestan, and East-Azarbaijan. The Arasbaran region in the East-Azarbaijan province, as one of the affected areas, has a Mediterranean climate, but the Caspian and Caucasian climates had a major impact on this event (Ramezani et al. 2019). Because of the high altitude of the Arasbaran region, the area has a variety of climates that naturally affect the vegetation of the area. Kaleybar city in the Arasbaran region was affected by the 2012 flood, causing serious damage to many buildings and cars. Fortunately, one of the Iranian permanent GPS stations was located in Kaleybar (named KLBR) and was used to help us in the tropospheric WV study. In this research, the tropospheric delay and the PWV have been evaluated using five existing stations in the Azerbaijan region during Day of Year (DOY) 286 to 291 in 2012. The Arasbaran flood occurred on DOY 289. The distribution of the five GPS stations is shown in Fig. 2, where KLBR and SKOH stations are located at a higher elevation than other stations.

Among the five GPS stations, AHAR, KLBR, and SKOH are equipped with meteorological sensors that can record air pressure, humidity, and temperature. Based on the meteorological data, KLBR station had the highest air pressure as well as the maximum humidity during the flooding days of DOY 287 to 291. The temperature range also decreases during the duration DOY 287 to 291 (Fig. 3).

GPS data of the five stations was processed using Bernese software (Dach et al. 2015) with a protocol of double-difference equations at a sampling rate of 30 seconds, and an elevation cut off angle of 5˚. The global mapping function (GMF) model was used to estimate ZHD (Rohm et al. 2014). The ZTD estimate for GPS stations varies from 1.80 to 2.20m (Fig. 4-a). The maximum amount of ZTD is observed at station AHAR and the minimum amount at station TABZ. The GPS-PWV estimates were evaluated in 5 phases for all five GPS stations with a focus on station KLBR (Fig. 4-b): during the first phase, a jump of 2 mm in a few hours before the flood, during the second phase, an increase of 3 mm, during the third phase, a jump of 3.5 mm, during the fourth phase (end of precipitation), a decrease of 3 mm, and during the fifth phase (the day after), a decrease of 4 mm was observed. The PWV jumps are marked with red squares (first, second, and third) and the PWV falls (fourth and fifth) with blue squares (Fig. 4-b). Stations that are not in flood areas have fewer variations than others.

ERA5 is a climate reanalysis dataset including hourly estimates of a large number of climatic, terrestrial, oceanic, and atmospheric variables from 2010 to 2017 with a horizontal resolution of 31 km grid spacing) Dong and Jin, 2018). In reduced spatial and temporal resolutions, the ERA5 has information about uncertainty for all variables in which temporal resolution reaches one hour (Jiang et al. 2020).

Based on the ERA5 model, the PWV value can be calculated based on specific humidity and air pressure at a horizontal resolution of 0.25°⋅0.25° and a vertical resolution of 37 pressure levels (Zhang et al. 2019). By integrating GPS-derived PWV and ERA5-PWV (Wang and Lio, 2019), tomography and regularization were performed using Tikhonov to achieve 4 Dimension (4D) PWV. The PWV increases 7–8 mm at altitude 3 km on the day before the flood, reaches 5-8mm at altitude 3–4 km on the flood day, and decreases 4–5 mm at altitude 3–4 km on the day after the flood. Also, the PWV reaches 10 mm at an altitude of 1–2 km, and is less than 4 mm at an altitude of more than 5 km on the day before the flood (Fig. 5).

On the day of the flood, an increase of PWV is observed from altitude 2 km to 4 km over KLBR and AHAR stations, and on the day after the flood, a significant decrease of PWV is estimated from altitude 2 km to 4 km. PWV changes in higher than altitude 3 km can be observed in which PWV increase is abnormal. By simultaneously examining the PWV time series (Fig. 4) and PWV tomography (Fig. 5), we can see an increase of PWV in intervals of less than 3 hours in phase 2 before the flood and a reduction of PWV in intervals of less than 3 hours in phase 4 and 5 after the flood. The increase in PWV at intervals of less than 3 hours can cause flooding in the region. It can be a feature of climate, topography, or other influential factors that require future flood studies to estimate the increase in PWV. Examining several floods and the rate of increase of PWV in the study area can be developed as an indicator for a flood forecast.

Fig. PWV tomography on a) DOY 288, b) DOY 289 and c) DOY 290

Tomographic validation is essential to verify the correctness of the proposed method and confirm the results. For this purpose, in this research, two sensors: Radiosonde data at TABRIZ station and Moderate Resolution Imaging Spectroradiometer (MODIS) satellite have been used. Radiosonde data at TABRIZ station (TABZ) have been applied for the validation of the tomography results (Fig. 6). The obtained results from the tomography and the radiosonde on the day before the flood (DOY 288), the day of the flood (DOY 289), and the day after the flood (DOY 290) are in good agreement (Fig. 6). The correlation between radiosonde and tomography with a difference of -1.5 to 1.5 mm and a significant correlation of 0.95 is also shown in Fig. 6-d. The difference on the flood day was more than 1mm at an altitude of ~ 1.5 km, but it was lower at other altitudes (Fig. 6-c).

MODIS is capable of recording phenomena information in 36 bands ranging from 4.4 to 4.14 microns with variable resolution (2 bands 250 m, five bands 500 m, and 29 bands 1 km). In this study, MOD05-L2 data with a resolution of 1˚×1˚ was used for the final validation of PWV for an 8-day duration (from 8 October 2012 to 15 October 2012). Details of the MODIS-Near-Infrared (NIR) Water Vapor algorithm are discussed in Gui et al. (2017). Figure 7 shows the PWV values obtained from the GPS and MODIS-NIR in the study area over the 8 days. The differences between GPS-PWV and MODIS-PWV for the 5 GPS stations are given in Table 1.

Table 1

Differences of GPS-PWV and MODIS-PWV for the 5 GPS stations
GPS station	GPS-PWV (mm)	MODIS-PWV (mm)	Difference (mm)
TABZ	14.62	13.87	0.75
SKOH	13.81	13.10	0.71
KHJE	22.56	20.79	1.77
AHAR	20.37	22.77	-2.4
KLBR	23.55	28.72	-5.17

According to the obtained results, stations KLBR, AHAR, TABZ, and SKOH have a difference of less than 3 mm, and KHJE station has a difference of about 5 mm. The absolute error between GPS-PWV and MODIS-NIR-PWV is not more than 4.4 mm. In addition, MODIS-NIR-PWV data is known to have larger uncertainty than typical GPS data even for strictly co-located observations. This is probably another factor contributing to the large difference (up to 5 mm) between the GPS and MODIS data. GPS spatial resolution is low due to various constraints, while MODIS offers a much better spatial resolution. In contrast, MODIS like radiosonde has a lower temporal resolution than GPS with a sampling rate of 30 seconds. This is a prominent advantage of GPS in meteorological studies.

High ZTD/PWV does not create floods. It is high precipitation together with other factors that can generate floods. High PWV does not necessarily mean there will be precipitation. On the other hand, there is no precipitation without high PWV. Unlike other studies, in this study, an increase in PWV was observed at several stations before the flood (Supartaet al. 2012). Many studies have tried to link high PWV to precipitation, indicating many times a high correlation between PWV and precipitation, which have been used in attempts of predicting flood generating precipitation events. The most convincing ones stem from regions in the tropics where events are extremely severe. There the analysis of extremely high PWV, or the change in it, could be linked to the onset of heavy rain events (Huelsinget al. 2017; Yao et al. 2017; Chen, 2017; Dong and Jin, 2018; Biet al. 2006).

What will increase the potential of GPS for meteorology is the determination of the real time PWV. This can be used in artificial intelligence algorithms to estimate flash floods and heavy rainfall (Carreau al. 2021; Dtissibe al. 2020). These high-accuracy algorithms can help detect flood signals with PWV GPS.

In this study, the behavior of the PWV during the formation of a flood is studied using 5 GPS permanent stations in the northwest of Iran. The results show that PWV in the atmosphere increased by 2 mm in a few hours before the flood, which can be a precursor. Increased PWV is estimated at higher altitudes on the day before the flood as well as the flood day. The tomography results at TABZ GPS station were validated and verified with radiosonde observations with a correlation of 0.95, which is significant. An absolute error of 3.4 mm was observed between GPS-PWV and MODIS-PWV, which indicates a high consistency between them. The results obtained from GPS-PWV variations are very similar to previous research and can play an important role in short-term flood predictions (Yao et al. 2017).

Data deficiency in terms of accuracy and time, especially under complex weather conditions impedes progress in weather forecasting. Various methods for water vapor estimation are proposed, but several factors such as accuracy, cost, temporal and spatial resolution as well as operational restrictions must be considered in their selection. Radiosonde can measure WV with high vertical resolution, but its horizontal and temporal resolution is limited and inadequate. One of the weaknesses of weather forecasting methods is referred to as “rapid changes in weather conditions”, which prevents these methods from providing accurate and reliable information. On the other hand, continuous GPS networks with high temporal and spatial resolution have a good capacity to be used as an early warning system for floods, despite rapid changes. Apart from geodetic objectives, today permanent GPS networks are used as meteorological sensors to measure PWV, with high accuracy and more economically than other existing methods.

Funding: The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Competing Interests: The authors have no relevant financial or non-financial interests to disclose.

Authors contributions: The authors contributed to the study conception and design, formal analysis and investigation, writing - original draft preparation, writing-review and editing. All authors read and approved the final manuscript.

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4D Modeling of Precipitable Water Vapor to Assess Flood Forecasting by Using GPS Signals

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Abstract

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Introduction

2.1 Tropospheric effect on GPS signals

2.2 Tropospheric wet delay estimation using GPS

Tikhonov Regularization In Tropospheric Tomography

Result And Discussion

Conclusion

Declarations

References

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