Capturing the signature of heavy rainfall events using the 2-d-/ 4-d 1 water vapour information derived from GNSS measurement 2 in Hong Kong

Apart from the well-known applications like positioning, navigation and timing (PNT), 11 Global Navigation Satellite System (GNSS) has manifested its ability in many other areas that are 12 vital to society largely. With the dense setting of the regional continuously operating reference 13 station (CORS) networks, monitoring the variations in atmospheric water vapour using a GNSS 14 technique has become the focus in the field of GNSS meteorology. Most previous studies mainly 15 concentrate on the analysis of relationship between the two-dimensional (2-d) Precipitable Water 16 Vapour (PWV) and rainfall while the four-dimensional (4-d) variations of atmospheric water 17 vapour derived from the GNSS tomographic technique during rainfall events are rarely discussed. 18 This becomes the focus of this work, which investigates the emerging field of GNSS technology 19 for monitoring changes in atmospheric water vapour during rainfall, especially in the vertical 20 direction. This paper includes an analysis of both 2-d, and 4-d, precipitable water vapour profiles. 21 A period with heavy rainfall events in this study was selected to capture the signature of 22 atmospheric water vapour variation using the ground-based GNSS tomographic technique. GNSS 23 observations from the CORS network of Hong Kong were used. Analysed results of the 2-d 24 PWV/4-d water vapour profiles change during the arrival, occurrence, and depression of heavy 25 rainfall show that: (i) the PWV time series shows an increasing trend before the arrival of heavy 26 rainfall and decreases to its average value after the depression of rainfall; (ii) rainfall leads to an 27 anomalous variation in relative humidity and temperature while their trends are totally opposite 28 and show daily periodicity for periods without rain (this is highly correlated with the changes in 29 solar radiation); (iii) atmospheric water vapour presents unstable conditions with intense vertical 30 Ann. Geophys. Discuss., https://doi.org/10.5194/angeo-2018-76 Manuscript under review for journal Ann. Geophys. Discussion started: 23 July 2018 c © Author(s) 2018. CC BY 4.0 License.


Introduction
Precipitable water vapour (PWV), which refers to the total content of integrated water vapour density along the zenith direction, is a significant component reflecting the short-term atmospheric water vapour variations used in severe weather detection (Shoji, 2009(Shoji, , 2013;;Bai, 2004) as well as in long-term climate studies (Gradinarsky et al., 2002, Vey et al., 2010;Ning et al., 2012;Liu et al., 2013;Bock et al., 2014).However, it is difficult to obtain a satisfactory spatio-temporal resolution of atmospheric water vapour due to the limitation of both the number of radiosondes and the observation times (Brenot et al., 2013;Zhang et al., 2015).For the past 20 years, the ability to estimate water vapour content with an accuracy of 1 to 2 mm has been proved using the Global Navigation Satellite System (GNSS) technique, which generally formed a new field of study in GNSS Meteorology (Bevis et al., 1992).Therefore, the variation of atmospheric water vapour with high accuracy, as well as the high spatio-temporal resolution can be obtained using the hyper-dense GNSS networks (with receivers only a few kilometres apart).
GNSS PWV can be used to provide information about water vapour distribution, which is related to form of precipitation and not only to severe weather events.(Zhang et al., 2015;Yao et al., 2017;Zhao et al., 2018aZhao et al., , 2018b)).GNSS PWV is operationally used for their assimilation into numerical weather prediction models (NWM) than just for operational meteorology (JMA, 2013;Bennitt and Jupp, 2012;Guerova et al., 2016;Barindelli et al., 2018).In those areas, the zenith total delays (ZTD) or PWV estimated from ground-based GNSS measurements are generally assimilated into numerical weather prediction (NWP) models (De Haan 2013;Saito et al., 2017).In addition, ZTD or PWV can be used for early warnings than that it is used, which has been investigated in areas of Greater Lisbon in Portugal as well as Zhejiang Province in China (Brenot et al., 2013;Benevides et al., 2015;Yao et al., 2018;Zhao et al., 2018aZhao et al., , 2018b)).These applications have verified the ability of GNSS as used in meteorology, but those cases are mainly focussed on two-dimensional (2-d) PWV which cannot reflect the specific vertical variations in atmospheric water vapour.
Although GNSS tropospheric tomography has been proposed (Flores et al., 2000), and can be used to obtain four-dimensional (4-d) water vapour variations, the development of this technique has mainly focussed on the improvement of theoretical and model aspects while its application is rarely discussed.For example, the reliability of GNSS tomography was validated using radiosonde data by Troller et al. (2006) and Shangguan et al. (2013).The joint reconstruction of atmospheric water vapour was also investigated by combing multi-GNSS observations as well as multi-source data derived from the GNSS Radio occultation technique, Interferometric Synthetic Aperture Radar (InSAR), radiosonde, etc. (Bender and Raabe, 2007;Bender et al., 2011;Wang et al., 2014;Alshawaf, 2013;Heublein et al., 2015;Benevides et al., 2015;Zhao et al., 2018c).For the improvement of tomographic models and resolution thereof, Perler et al. (2011) proposed a new parameterised tomographic method, which is capable of obtaining better tomographic results.Some methods concerned with the resolution of tomographic models have been proposed such as the extended sequential successive filtering method.(Braun et al, 2003(Braun et al, , 2004;;Wang et al., 2014;Zhao et al., 2017aZhao et al., , 2018d;;Chen and Liu, 2014).In addition, maximal use of GNSS signals penetrating from the side faces of tomography areas has obtained a significant improvement and is realised by introducing the water vapour scale factor (Yao and Zhao, 2016;Yao et al., 2016;Zhao et al., 2017b).
Currently, GNSS tomography technique is maturing in terms of theoretical and model aspects through almost 20 years of development, but its application in GNSS meteorology remains to be further investigated, therefore, we focus on capturing the signature of heavy rainfall events using the 2-d/4-d water vapour information derived from GNSS measurements in Hong Kong.The 2-d PWV time series is first analysed for correlation with heavy rainfall.Thereafter, the signatures of 4-d water vapour variations derived from GNSS tomography are investigated during heavy rainfall events while the tomographic modelling is resolved using the optimal weighting determination method.

Retrieval of GNSS PWV
Satellite signals are delayed and bent when crossing the troposphere, which can be divided into two parts: hydrostatic delay and non-hydrostatic delay.The first part in a zenith direction, also called zenith hydrostatic delay (ZHD), can be precisely calculated by the Saastamoinen model (Saastamoinen, 1972) with the observed surface pressure.The second part can be estimated in the zenith direction using GNSS data, which is also called zenith wet delay (ZWD), from which the PWV can be calculated.Therefore, GNSS meteorology is formed, as first proposed by Bevis et al. (1992).The calculation used in obtaining PWV is expressed as follows: the zenith total delay is first estimated by processing the GNSS observations using the GNSS processing software such as Bernese (Dach et al., 2015), GAMIT (Herring et al., 2010), etc.In the GNSS data processing, the ZHD is usually taken from an a priori model and later precisely computed from i.e. real meteorological observation.The ZWD is then obtained by extracting the ZHD from ZTD and thus the PWV can be calculated based on the following equations (Saastamoinen, 1972;Askne and Nordius, 1987;Bevis et al., 1992): Where  refers to the conversion factor.' 2 k , 3 k , and v R are constants with values of 22.1 K/hPa, 3.739 × 10 5 K 2 /hPa and 461.495J/kg/K, respectively.Tm represents the weighted mean temperature, which is related to surface parameters such as temperature and pressure.Therefore, Tm is usually calculated based on the empirical model using the data from radiosonde or numerical weather model due to the observed layered meteorological parameters which are rarely obtained (Bevis et al., 1994;Yao et al., 2012).In the fourth formula in Eq. ( 1), P , H and  represent the surface pressure (hPa), geodetic height (km) and station latitude (rad), respectively.In our study, the value of Tm is calculated based on the established regional Tm model using the radiosonde data and observed temperature (Section 3.2).

Establishment of tomographic model
Generally, the slant wet delay (SWD) or slant integrated water vapour (SIWV) is considered as the input information for GNSS troposphere tomography (Flores et al., 2000;Hirahara, 2000;Skone and Hoyle, 2005;Rohm and Bosy, 2009;Chen and Liu., 2014) and the following equation gives an expression used to obtain SIWV (Flores et al., 2000): Where w m represents the gradient mapping function, and global mapping function (GMF) is used in our experiment (Böhm et al., 2006).ele and azi refer to the elevation angle and azimuth angle, respectively.w NS G and w WE G are the horizontal tropospheric gradient parameters of ZWD in the south-north and west-east directions, respectively, which are caused by the atmospheric inhomogeneous.Additionally, a post-fit residual for SIWV is existed, which contains some information about tropospheric water vapor distribution during the severe weather events and cannot captured by ZTD or gradients (Kacmarík et al., 2017).
If a sufficient number of SIWVs derived from some stations in a regional CORS network can be obtained, the GNSS tomographic technique can be used to reconstruct the three-dimensional (3-d) distribution of atmospheric water vapour field.Therefore, a four-dimensional (4-d) water vapour information is a time series of such a 3-d tomographic result, which can be used to reflect the regional atmospheric water vapour variations in both the spatial and temporal domains.As described by Flores et al. (2000), the linear observation equation between SIWV and water vapour density can be expressed as follows: SIWV ( ) Where , ij and k represent the location of the area of interest in the longitudinal, latitudinal, and zenith directions, respectively.x refer to the distance travelled by satellite signals and the water vapour density remains to be estimated, respectively in the discretized voxels ( ,, i j k ).Therefore, the matrix form of the tomographic observation equation can be described as follows: Where y represents the column vector of SIWV derived from GNSS measurements.A and x are the coefficient matrix of distance penetrated by satellite rays and the column vector of water vapour density, respectively.
Although Rohm (2013) developed a GNSS tomography solution using no constraints, most studies still used some constraints to overcome the influence caused by the ill-posed problem in the inversion of the tomographic normal equation (Flores et al., 2000;Bi et al., 2006;Bender et al., 2011;Rohm andBosy, 2011 Chen andLiu, 2014).In our study, both horizontal and vertical constraints are considered.The water vapour density in a certain voxel is regarded as the weighted mean value of its horizontal neighbouring voxels (Rius et al., 1997) and the negative exponential function is introduced to describe the relationship between the nearby voxels in the zenith direction while the coefficients of functional model are established using radiosonde data (Yao and Zhao, 2016).Consequently, the tomographic modelling can be expressed after imposing the constraints as: Where H and V are the coefficient matrices of horizontal and vertical equations, respectively.
To obtain a reasonable tomographic result from the above equation, an optimal tropospheric solution method is used, which can adaptively tune the weightings of different types of equations (Zhao et al., 2018d).
3 Data description and establishment of a regional Tm model

Data description
To validate the ability of GNSS technique in capturing the signature of atmospheric water vapour variation during heavy rainfall events, two periods of GNSS observations (19 to 27, July 2015 and 1 to 8, August 2015) from 13 GNSS stations in the CORS network of Hong Kong are selected in the experiment.Those two periods are selected because they correspond to a heavy rainfall event and a no-rainfall event, respectively according to hourly rainfall data from 45 rain gauges evenly distributed across this area (Figure 1).There is a radiosonde station located in this area where the radiosonde balloon is launched twice daily at UTC 00:00 and 12:00, respectively.The 20-years of radiosonde data from 1998 to 2017 are used to establish the regional Tm model in this study.In addition, the surface temperature and relative humidity are also selected to analyse their changes during those two periods.To explain the variations of surface temperature and relative humidity, the solar radiation data are also used in this study, which is derived from the CRU-NCEP Ver. 7 dataset (Wu et al., 2015).This dataset is a combination product of the CRU TS3.2 climate dataset and the NCEP reanalysis data.The temporal-spatial resolution of the solar radiation dataset are four times daily (UTC 00:00, 06:00, 12:00 and 18:00) and 0.5°×0.5°,respectively.
GNSS observations are processed using Precise Point Positioning (PPP) data processing software developed by our research group.The post-processing mode is used and the orbit and satellite clock errors are corrected using the final products downloaded from ftp://ftp.gfz-potsdam.de/.The GMF is selected (Böhm et al., 2006) while the cut-off elevation angle is 7° in our experiment.The sampling rate of GPS observation is 30s and the and the ZTD parameter is estimated every 5 minutes.The gradient parameters in south-north and east-west directions are also estimated at intervals of 2 h.The detailed description of processing strategy has been presented in Zhao et al. (2018d).The root-mean-square error (RMSE) of the estimated ZTD parameter has been proved with the values of 7.2 mm and 8.1 mm when the ZTD estimated from the GAMIT (v10.5) and Bernese (v5.2) software based on the double-difference model are regarded as references, respectively (Zhao et al., 2018a).Due to the accurately ZHD parameter can be estimated using the empirical model, therefore, the final error in the estimated PWV values is approximately 1-1.5mm (Zhao et al., 2018e).The corresponding meteorological parameters, such as the surface pressure and temperature, are also obtained at the selected GNSS stations.Therefore, the precise ZHD can be calculated by the empirical model using the observed surface pressure.The conversion factor, as described in Eq. ( 1), is also obtained, in which Tm is calculated based on the established Tm model which will be introduced in the following section.Finally, the PWV time series, as well as the SIWVs for the 13 selected GNSS stations, can be obtained.Five of the 45 rain gauges (R21, TMS, PEN, SSP, and KSC) are selected to analyse the variations in atmospheric water vapour during different weather conditions (Figure 1).
Figure 1.Geographic distribution of selected GNSS and radiosonde stations as well as the rain gauges used in the experiment

Establishment of the regional Tm model
Due to the layered information about vertical profile of some meteorological parameters as water vapour pressure or air temperature is generally unavailable for the location of GNSS stations, therefore, the Tm values of those stations are calculated based on the empirical model in this experiment.It has been proved that Tm is highly correlated with the variations of temperature, pressure, and the seasons (Bevis et al., 1992;Yao et al., 2012;Yao et al., 2014Yao et al., , 2015;;Liu et al., 2018).Therefore, a regional Tm model which includes as parameters: temperature, surface pressure, and seasonal variation, is established and expressed as follows:  6) were obtained by the least square regression method using 20-year radiosonde data for 45004 while the values of a to f are 129.1225, 0.5370, -0.0023, 0.358, 0.813, -0.178, and 0.255, respectively.
The performance of the established Tm model is analysed and compared with the empirical formula proposed by Bevis et al. (1994).Statistical result of 20-years of radiosonde data reveals that when compared to the Tm values calculated using the observed radiosonde data, the standard deviation and bias for the established Tm model and the empirical formula proposed by Bevis et al. (1994) are 2.04/0.0009K and 3.41/2.53K, respectively, which indicates that the established regional Tm model shows a good result in research area.To further analyse the impact of Tm model error on the calculated PWV, a comparison experiment is carried out for radiosonde station 45004 with a variation in Tm of 1 K, 3 K, 5 K, 7 K, and 9 K, respectively and compared with the actual PWV values over the period of 1998 to 2017.Statistical analysis shows that the PWV errors induced by the change in Tm of 1 K, 3 K, 5 K, 7 K, and 9 K are 0.15 mm, 0.45 mm, 0.75 mm, 1.04 mm, and 1.34 mm, respectively under the condition of PWV > 0 mm, while the values are 0.18 mm, 0.54 mm, 0.91 mm, 1.27 mm, and 1.63 mm, respectively when PWV > 40 mm.Therefore, the PWV errors caused by the established Tm model in this study are less than 0.4 mm and 0.5 mm when PWV > 0 mm and PWV > 40 mm, respectively.Such result is deemed acceptable for the analysis of PWV variations with rainfall events (Akilan et al., 2015) and corresponds to the previous result obtained from Guerova et al. (2016).

Signature of 2-d/4-d variations in atmospheric water vapour during rainfall
According to the recordings derived from the Hong Kong Observatory, the convectional rain happened during the period of 19 to 27, July 2015.It is continuous rains in Hong Kong and the hourly rainfall have been accumulated for 45 rain gauges with the largest rainfall more than 300 mm for the entire experimental period in HKSC station.The weather conditions are cloudy and sunny without rainfall happened for the period of 1 to 8, August 2015.Therefore, those two periods are selected in this paper to investigate the variation characteristics of atmospheric water vapor.

Cases of 2-d PWV time series change
To capture the signature of PWV time series change in different weather conditions, the comparison between the 5-minute GNSS-derived PWV and hourly rainfall are performed for the periods of 19 to 27, July 2015 and 1 to 8, August 2015, respectively.Four GNSS stations (HKKS, HKSC, HKPC, and HKSL) and the surrounding rainfall gauges (HSC, SSP, PEN, and R21) are selected for this experiment.Additionally, other meteorological parameters (temperature, relative humidity and solar radiation) are also analysed during this experimental period.
Figure 2 shows the variations of 5-minute PWV time series data with hourly rainfall as well as the cumulative rainfall at those four stations for the period of 19 to 27, July 2015.It can be seen from the first column of Figure 2 that the PWV time series show an increasing trend before the arrival of rainfall and reaches a relatively large value during rainfall, PWV then returns to its average value after rainfall.Such phenomenon found above can be used to forecast the nowcasting rainfall (Yao et al., 2017;Zhao et al., 2018a).The second column of Figure 2 reveal that the cumulative rainfall first increased at about UTC 11:00, 20 July, 2015 with different levels reached and the event terminated at UTC 12:00, 23 July, 2015.The largest cumulative rainfall reached more than 300 mm at HKSC station while the minimum recorded rainfall was about 100 mm at HKSL station across the four selected gauge stations.The PWV time series is also analysed at those four stations for the period from 1 to 8, August, 2015 in which no rainfall was recorded (Figure 3).
Figure 3 shows the 5-minute PWV time series changes from which it can be found that PWV does not show any continuous increasing trend when there is no rainfall, but the range of PWV variation is relatively large (from about 35 mm to greater than 55 mm).Comparing the PWV time series in Figures 3 and 4, it also can be observed that the PWV values during rainfall are much larger than that of no rainfall time at the situation occurred in the selected time periods.
In addition, 5-minute surface temperature and relative humidity data are also analysed during those two periods.The first and second columns of Figure 4 show the changes in temperature and relative humidity for the period 19 to 27, July, 2015.It also can be seen that the temperature and relative humidity do not show any trend during heavy rainfall but show a tendency to run counter to one another on 19, 26, and 27, July.one explanation is that heavy rainfall breaks the trend in temperature and relative humidity for the period from 20 to 25, July, 2015.The third column of Figure 4 shows the changes in solar radiation for this period, from which it can be observed that the solar radiation undergoes a day periodic change.To verify this explanation, the variations of temperature and relative humidity, as well as those in solar radiation, are also presented at those four stations for period of 1 to 8 August without rainfall (Figure 5): temperature and solar radiation show a similar trend while relative humidity presents the opposite trend.Additionally, it can be observed from the first and third columns of Figures 5 that the maximum values of solar radiation and temperature occurred at UTC 4:00 (local time 12:00) while the minimum value of relative humidity also occurred at that time.The phenomenon found in Figure 5 further confirmed the explanation presented above.In addition, the values of solar radiation are more fluctuated at the four stations during rainfall when compared to that without rain (Figures 4 and 5): a possible reason for this is that the part of solar radiation is decreased by cloud cover during heavy rain.

Cases of water vapour profile variation during heavy rainfall
The variations in 4-d atmospheric water vapour are also analysed during heavy rainfall.In this section, the tomographic technique is introduced and the research area is discretised.There are 7 and 8 grids in longitudinal and latitudinal directions, respectively and 29 layers in zenith direction.
Therefore, there are total 7 × 8 × 29 voxels.The horizontal steps are 0.05° and 0.06° in longitudinal and latitudinal directions, respectively while the inhomogeneous vertical step is selected based on the water vapour distribution at different altitudes (Yao and Zhao, 2017) with resolutions of 0.2 km × 10, 0.3 km × 8, 0.4 km × 6, 0.6 km × 4, and 0.8 km × 1, respectively.A comparison of water vapour density profiles derived from tomographic result and radiosonde data at the location of radiosonde station 45004 is first presented (Figure 6) to validate the performance of the GNSS tomographic technique.It can be seen from the Figure 6 that the profiles derived from tomographic results were consistent with the observed radiosonde data at most altitudes, which manifests the ability of the GNSS tomographic technique to reflect variations in water vapour content during rainfall.Due to this paper is mainly focus on the analysis of 4-d water vapour variation during the heavy rainfall events and the quality evaluations of vertical profiles from GNSS tomography reconstruction have been carried out by our research group for this research area in the previous studies (Yao andZhao, 2016, 2017;Zhao et al., 2017a;Zhao et al., 2018d), therefore, more detailed comparison information is not presented.
Two heavy rainfall periods are selected in this experiment: the first at UTC 18 to 22, 21 July 2015 and three rain gauges are used to analyse the variations in water vapour profiles.The hourly rainfall for those three rain gauges is presented in Table 1 while the water vapour profile variations over time for SPP, PEN and TKL are shown in Figure 7. From this figure it can be observed that atmospheric water vapour profile undergoes vertical movement about 1-2 hours before the arrival of heavy rain, which is reflected by the fluctuating water vapour density at different altitudes.It can be observed from SPP rain gauge ((a1)-(h1)) that the water vapour content in the lower atmosphere increases from an altitude of about 1.8-2.5 km to 3.5 km while the water vapour content decreases from 4-5 km to 3.5 km.It can also be observed from PEN and TKL rain gauges ((a2)-( h2) and ((a3)-( h3))) that an upward and downward movement happened in the atmospheric water vapour profile in the lower and upper atmosphere, respectively: this results in a large increase in atmosphere water vapour at altitudes of about 2.3 km and 1.6 km, respectively (especially at PEN).The upward and downward motions of atmospheric water vapor in the lower and upper atmosphere are expected to the occurrence of the strong convective weather.The above phenomenon of vertical water vapor motion corresponds to the convectional rain reported.In addition, it was found that the variations of water vapour profiles in zenith direction at station TKL are weaker than that from stations PEN and SPP.A possible explanation is that the rainfall was 30.5 mm and 20.5 mm for PEN and SPP at UTC 20, 21 July 2015 while the value is only 1 mm at station TKL at UTC 21, 21 July 2015 (Table 1).The above phenomenon indicates that the heavy rainfall could be induced by vertical motion of water vapour.The variations in water vapour profiles during rainfall reveal that the significant vertical motion of water vapour occurred before the onset of rainfall while the water vapour profiles were relatively stable during rainfall events.
In addition, the time series of water vapour density profiles, at a temporal resolution of 1 minute, for the three rain gauges are also presented in Figure 8. From which it can be seen that the vertical water vapour density profile undergoes a significant vertical motion about 1-2 hours before the arrival of rain (black dotted rectangles, Figure 8) while the profiles are relatively stable during rain.
By analysing the Figure 7, it also can be found that the vertical variations of water vapour density profiles at SPP and PEN stations 1 hour before rainfall are more active than that at TKL station: this can be explained by considering that the continued heavy rainfall happened at SPP and PEN stations while the TKL had little rainfall (Table 1), therefore, the continuing water vapour transportation in the zenith direction existed in the lower atmosphere at stations SPP and PEN.     2. Figures 9 and 10 both reflect that the change in water vapour profiles at PEN and TMS stations are similar to that of above conditions.The water vapour content at PEN and TMS is increased at altitudes of 2.5 km and 3.2 km, respectively, some 1-2 hours before onset of rainfall and returns to its average value at the moment that the rainfall is about to begin.One possible explanation for this is that: before onset of rainfall, the atmospheric water vapour was conditionally unstable with intense vertical movement as proved by Brenot et al., (2006).The ascending motion of water vapour in the lower atmosphere and the descending motion of water vapour in the upper atmosphere significantly increases the water vapour content at a certain height where hydrometeors are formed.
The hydrometeors consist of liquid water and icy hydrometeors, formation of which is random in time and space.Due to the delays to satellite signals induced by liquid water and icy species generally being much smaller than the water vapour species-induced delays, therefore, these delays cannot be reflected evidently in the case of GNSS observations.These newly-generated hydrometeors particles form raindrops with a continual accretion thereof.When the atmosphere is unable to support the weight of the formed raindrop, the drop falls as rain.The formation of hydrometeors particles and raindrops require some time, hence the intense vertical movement of atmospheric water vapour before onset of rainfall.The time taken to generate hydrometeors and raindrops provides the possibility of now-casting rainfall based on the GNSS technique.
Table 2. Hourly Rainfall for the selected four rain gauges over the period UTC 1 to 5, 23 July is presented with a spatio-temporal resolution of 20 minutes and 20 layers to an altitude of 5 km, respectively (Figure 11).According to the hourly rainfall recordings at 45 rain gauges in this area, most parts of the experimental area suffered heavy rainfall at UTC 20:00, 21 July 2015 that lasted for several hours.It can be found from Figure 11 that the significant vertical motion of water vapour observed over the period from UTC 18:00 to 19:40, and returns to its relatively stable condition at UTC 20:00 but with a lower water vapour content in most layers.The main reason for this may be water vapour transfer to the liquid water particles and icy hydrometeors, which have little impact on the delay of satellite signals and cannot be reflected evidently by the GNSS technique.For the period of heavy rainfall that occurred after UTC 20:00, the atmospheric water vapour profiles were relatively stable with slight vertical variation in water vapour content.In addition, it can be concluded that the place at which hydrometeors were generated in the lower atmosphere is possibly where rainfall occurred.Therefore, where heavy rainfall occurred is possibly predictable before the onset of rainfall according to the 4-d atmospheric water vapour variations at different altitudes derived from GNSS tomography.It also can be found that there is the horizontal motion of atmospheric water vapor as well in different layers, especially at the bottom layers.This is because the happening of rainfall requires the enough water vapor supplement, the horizontal motion of water vapor at the bottom layers implies the continuous water vapor transportation.PWV time series data derived from GNSS observations are first compared with hourly rainfall measurements, which reveals the continuous increasing trend in PWV before the onset of rainfall and returns to its average value after rainfall.In addition, it is also found that the variations of surface temperature and relative humidity have day-periodicity and are mainly caused by the variations in solar radiation during no rain periods, but their changes are disturbed by rainfall during rainfall periods.
A 4-d water vapour reconstruction technique is performed using GNSS data to analyse the vertical water vapour movement during rainfall period.It is found that significant vertical motion occurred about 1-2 hours before the arrival of rainfall and this was reflected by the ascending and descending motions of water vapour in the lower and upper atmosphere, respectively.
Hydrometeors are then formed at a certain altitude where sufficient water vapour was concentrated.
The formation of hydrometeors and raindrops requires some time, which makes it possible for the forecasting of now-casting rainfall.At the moment of onset of rainfall, the water vapour profiles return to their average values at different altitudes and show a relative stable condition but with a decreasing trend in the water vapour content in the lower atmosphere.In addition, the place where the rainfall is most possible happened may be forecasted by locating out the location of the point of decreasing water vapour content in the lower atmosphere.These results revealed that rainfall had a direct relationship with atmospheric water vapour content as well as the vertical variations of water vapour density profiles, which further manifested the significant potential of the GNSS technique for monitoring and forecasting during the lifecycle of rainfall event.

P
represent the initial value of Tm, surface temperature and surface pressure, respectively; doy refers to the day of year; a and b are coefficients of c to f refer to the coefficients of the seasonal correction function.In our study, the coefficients in Eq. (

Figure 2 .
Figure 2. Variations of 5-minutely PWV time series with hourly rainfall and the cumulative rainfall for HKKS, HKSC, HKPC and HKSL stations over the period of 19 to 27, July 2015, the first column represents the variations of PWV and rainfall and the second column refers to the cumulative rainfall

Figure 6 .
Figure 6.Distribution of water vapor density (WVD) profiles at UTC 00:00 and 12:00, respectively derived from the GNSS tomographic result (green curve) and the radiosonde data of the observed height (red hot) for the location of radiosonde station (45004) over the period of 20 to 23, July 2015

Figure 8 .
Figure 8.Time series of water vapor density (WVD) profiles derived from GNSS tomographic result with the temporal resolution of 1 minute for the locations of three rain gauges over the period of UTC 18:00 to 23:00, 21 July 2015, where the rainfall happened at UTC 20:00 21 July for (a) SPP and (b) PEN rain gauges while the rainfall occurred at UTC 21:00 21 July for (c) TKL rain gauge.The WVD profiles with drastic vertical motion are marked by the black dotted rectangles for three rain gauges while the locations of black solid lines are the starting time of rainfall

Figure 9 .
Figure 9. Distribution of water vapor density (WVD) profiles from GNSS tomographic result with the temporal resolution of 20 minutes for the location of PEN rain gauge over the period of UTC 00:20 to 03:20, 23 July 2015

Figure 11 .
Figure 11.Three-dimensional distribution of atmospheric water vapor density derived from GNSS tomographic result with the temporal resolution of 20 minutes over the period of UTC 18:00 to 20:20, 21 July 2015 with 20 layers from the ground to 5km

Table 1
Hourly Rainfall information of the selected four rain gauges over period of UTC 19 to 23, 358