Remote sensing of atmospheric water vapor from synthetic aperture radar interferometry: case studies in Shanghai, China

Abstract. The estimation of atmospheric water vapor with high resolution is important for operational weather forecasting, climate monitoring, atmospheric research, and numerous other applications. The 40  m×40  m and 30  m×30  m differential precipitable water vapor (ΔPWV) maps are generated with C- and L-band synthetic aperture radar interferometry (InSAR) images over Shanghai, China, respectively. The ΔPWV maps are accessed via comparisons with the spatiotemporally synchronized PWV measurements from the European Centre for Medium-Range Weather Forecasts Interim reanalysis at the finest resolution and global positioning system observations, respectively. Results reveal that the ΔPWV maps can be estimated from both C- and L-band InSAR images with an accuracy of better than 2.0 mm, which, therefore, demonstrates the ability of InSAR observations at both C- and L-band to detect the water vapor distribution with high spatial resolution.


Introduction
Atmospheric water vapor is one of the most important and most abundant greenhouse gases in the Earth's atmosphere, keeping the temperature of the Earth surface above the freezing level, as well as playing an important role in many atmospheric processes over a wide range of temporal and spatial scales. The phase variability of water vapor in time and space affects the distribution of clouds and rainfall, the structure of atmospheric storm systems, the vertical stability of the atmosphere, the evolution of the weather, and the energy balance of the global climate system. 1,2 The concept of precipitable water vapor (PWV), which is also referred to as total column or integrated water vapor, is the total water vapor contained in an air column from the Earth's surface to the top of the atmosphere, and it is a good indicator of the water vapor variability in the lower troposphere and related processes. 3 Therefore, more accurate precipitation and severe weather forecasts, together with a better understanding of climate change could be achieved via improved monitoring of atmospheric water vapor.
Radiosonde is one of the most common techniques to monitor global atmospheric water vapor. However, the radiosonde observations are available only twice a day at most sites, and they are limited due to the high operational costs, as well as the poor coverage over oceans and in the Southern Hemisphere. 4 Since the early 1990s, estimation of PWV using ground-based global positioning system (GPS) observations has been well investigated. 2,[5][6][7][8][9][10][11] GPS has become increasingly an operational tool to monitor the PWV due to its advantages including continuous measurements in all weather conditions, high accuracy, long-term stability, and low cost. Unfortunately, high spatial resolution of the water vapor distribution is still difficult to obtain in areas of sparse GPS sites.
Space-borne based monitoring is an effective way to estimate water vapor distribution with high resolution. A number of launched space-borne sensors can be used to extract the PWV measurements, such as the moderate resolution imaging spectroradiometer, 12 the medium resolution imaging spectrometer, 13 the atmospheric infrared sounder, 14 the infrared atmospheric sounding interferometer, 15 the microwave radiometers, 16 the Tropical Rainfall Measuring Mission's Microwave Imager, 17 the global precipitation measurement microwave imager, 17 etc. However, these sensors can provide the PWV measurements only with a resolution of several kilometers, which may remain insufficient for the small scale weather forecasts. The synthetic aperture radar interferometry (InSAR) technique is a potential way to measure the PWV distribution with a resolution up to several meters. 18 Considering the SAR signal delay caused by atmospheric water vapor is one of the major sources of noise for the InSAR technique, 19 accurate surface deformation can be obtained after mitigating InSAR atmospheric distortions effectively. [20][21][22][23][24] In this study, we aim to estimate and evaluate the PWV distributions with C-and L-band InSAR observations when the surface deformation can be neglected during the time between the SAR image pairs acquisition. Cheng et al. 25 made a reliable comparison of atmospheric delay between GPS zenith tropospheric delay and SAR atmospheric phase screen in both differential and pseudoabsolute modes. Mateus et al. [26][27][28] emphasized that the PWV spatial distribution with a sampling period of a few days can be obtained by processing time series of InSAR images from different tracks of the same satellite and/or different space-borne missions. Efforts to construct accurate atmospheric water vapor distributions were also made by integrating persistent scatterer InSAR and global navigation satellite systems observations. 29,30 Recently, a few papers have also been published to measure the three-dimensional (3-D) state of the atmospheric water vapor by bridging InSAR and GPS tomography. [31][32][33] However, most published works were exhibited using the C-band Environmental Satellite (ENVISAT) advanced SAR (ASAR) image pairs only, whereas the abilities of InSAR images at other bands in estimating the PWV measurements may need to be further inspected. In this study, both the C-and L-band InSAR observations are used to estimate the atmospheric water vapor maps over Shanghai, China. Moreover, the derived water vapor distributions are accessed via comparison with the spatiotemporally synchronized European Centre for Medium-Range Weather Forecasts (ECMWF) Interim reanalysis (ERA-Interim) data and GPS observations. The rest of this paper is structured as follows. Section 2 introduces the principles of PWV estimation with GPS and InSAR observations. Section 3 describes the datasets used in this study and the InSAR data processing method. In Sec. 4, case studies of C-and L-band InSAR water vapor estimation in Shanghai, China, and their assessments are presented. Finally, some conclusions are addressed in Sec. 5.

GPS PWV Estimation
When traveling from the GPS satellites to the ground-based GPS receivers, the radio (microwave) signals are delayed by the ionosphere and neutral atmosphere. The ionospheric delay is frequency-dependent and can be removed by 99% with the data from dual-frequency GPS receivers. 34 The total tropospheric delay can then be expressed as 2,5 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 6 ; 1 2 9 ΔL ¼ ZHD · m h ðεÞ þ ZWD · m w ðεÞ; (1) where ZHD is the zenith hydrostatic delay, ZWD is the zenith wet delay, ε is the satellite elevation angle, m h ðεÞ is the hydrostatic mapping function, and m w ðεÞ is the wet mapping function.
The total tropospheric delay in the vertical direction (i.e., ZTD) is the sum of ZHD and ZWD, 35 and the former can be estimated by 36 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 6 ; 7 1 1 ZHD ¼ ð2.2779 AE 0.0024ÞP s ∕½1 − 0.00266 cosð2ϕÞ − 0.00028h; (2) where P s is the pressure (millibars) at the Earth's surface, ϕ is the latitude, and h is the height above the ellipsoid (kilometres). Considering ZTD can be estimated from GPS observations [e.g., with the GPS analysis at Massachusetts Institute of Technology (GAMIT) software], ZWD can then be extracted by subtracting ZHD from ZTD. Moreover, PWV can be estimated from ZWD via a dimensionless parameter Π E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 6 ; 6 2 1 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 1 1 6 ; 5 8 6 where T m is the water-vapor-weighted mean temperature T m , R v is the specific gas constant for water vapor, and K 3 and K 0 2 are the physical constants and given by Bevis et al. 2

Atmospheric Delay Feature in InSAR Interferograms
The atmospheric delay in SAR observations consists of bending and propagation delay, whereas the former can be neglected for zenith angles <87 deg. 37 Therefore, the total zenith atmospheric delay can be expressed as 38 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 5 ; 1 1 6 ; 4 6 2 where Δd ion is the zenith ionospheric delay and Δd liq is the zenith liquid delay caused by liquid water in the air. Liquid water delay is neglected due to its amplitude being <1 mm under usual atmospheric circumstances, 38 whereas the ionosphere delay is regarded as minimal in low latitude regions. For repeat-pass InSAR, the interferometric phase is the phase difference between the master and slave images, and the phase delay in InSAR observations can be expressed as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 1 1 6 ; 3 5 8 where λ is the wave length, θ is the incidence angle, and ΔZHD and ΔZWD are the difference of ZHD and ZWD between the master and slave images, respectively. Considering the minimal spatial variation and temporal stability of ZHD (1-mm accuracy of prediction), 38 the hydrostatic part is neglected in this study. When the interferometric pairs used for atmospheric studies are acquired with a short-time interval, the deformation contribution during intervals between the SAR images overpass time can be considered as negligible, and the coherent interferometric phase can then be assumed due to the atmospheric propagation delay only and not related to surface deformation. 26 As such, the coherent interferometric phase can finally be converted to the PWV distribution variation by Eqs. (3) and (4).

Region of Interest and Datasets
In this study, four ENVISAT ASAR and three Advanced Land Observing Satellite (ALOS) Phased Array type L-band SAR (PALSAR) images are used to generate the InSAR interferograms (Ifms), respectively. As described in Table 1, the ASAR images were acquired in ascending orbit on June 30, 2008, August 4, 2008, September 8, 2008, and November 17, 2008, respectively, and the PALSAR images were acquired on August 27, 2008, October 12, 2008, and November 27, 2008, respectively. As a result, three C-band and two L-band Ifms are generated. It is also shown in Table 1 that the timespans between the master and slave images of the generated Ifms are all <70 days. Considering the maximum subsidence rate of Shanghai in 2008 was ∼15 mm∕year, 39 the amount of deformation corresponding to a 70-day interval is, therefore, <2.9 mm when assuming that the deformation is temporally linear. Therefore, the deformation contribution to the interferometric phases can be considered as negligible in this study, since it can cause a phase shift of about only 0.05 cycles. 20 Figure 1 shows the location of the region of interest (ROI) and the coverages of the ASAR and PALSAR images, respectively. In this study, a total of 11 GPS stations are located inside the ROI. The GPS data are used to estimate the PWV measurements, and further assess the accuracy of InSAR derived PWV distributions. In order to obtain accurate GPS baseline solutions and ZWD measurements, we process the GPS data in double-difference phase baseline mode with the GAMIT 10.60 software and extract the ZWD series for 30-min intervals.
ERA-Interim is a third generation of comprehensive global reanalysis, which uses a much improved atmospheric model and assimilation system from those used in ERA-40. 40 ERA-Interim represents a major undertaking by ECMWF with several of the inaccuracies exhibited by ERA-40 being eliminated or significantly reduced. In this study, total column water vapor from ERA-Interim at the finest resolution (i.e., 0.125 deg × 0.125 deg) every 6 h  (i.e., 00, 06, 12, and 18 h) is adopted to compare with the InSAR derived PWV distributions. It should be noted that the spline interpolation is used for PWV time-series from ERA-Interim data to get the PWV measurements at SAR overpass time.

InSAR Data Processing
In this paper, the SAR images are processed with GAMMA Remote Sensing software by the two-pass differential InSAR approach. Precise DORIS orbit data provided by the European Space Agency ( The coherence values of the C-and L-band Ifms are shown in Fig. 2. A mean coherence of 0.90, 0.86, and 0.91 is observed in C-band Ifm1, Ifm2, and Ifm3, respectively. The slightly low coherence in Ifm2 [ Fig. 2(b)] may lie in the longer perpendicular baseline of Ifm2 compared with Ifm1 and Ifm3 (Table 1). In addition, a mean coherence of 0.96 is also detected in L-band Ifm4 and Ifm5. It should be mentioned that despite the perpendicular baseline of Ifm4 being longer than that of Ifm1, the coherence in the former is higher than the latter. The significant coherence gain in L-band Ifms may result from the longer wavelength of ALOS PALSAR and therefore the better penetration than ENVISAT ASAR. Moreover, the coherence in each Ifm is in general higher over the city of Shanghai and part of Pudong, Jiading, Minghang, Fengxian, and Songjiang districts than Changxing, Hengsha, and Chongming islands.
The Ifms are then smoothed by adaptive filtering and unwrapped by the branch-cut method with the coherence threshold set to be 0.5. The baselines are refined next using the unwrapped phase and the independent DEM, which can help to generate more reasonable values for areas with low coherence. Moreover, a two-dimensional quadratic model phase function from the differential Ifm is also estimated to mitigate possible orbital errors. At last, the unwrapped Ifms are mapped into the line of sight (LOS) direction in the Universal Transverse Mercator coordinate system. Figure 3 shows the unwrapped interferometric phases of the C-and L-band Ifms. It is clear that there are no apparent systematic phase trends in Fig. 3. Considering the "bridges" construction may introduce extra errors during the phase unwrapping processes, as well as prevent objective assessment of InSAR derived PWV distributions, we have not constructed the "bridges" between the center area and the islands. As a result, the unwrapped interferometric phases over the areas of Changxing Island, Hengsha Island, Chongming Island, and Qidong City are masked.

Comparison of PWV Maps Between InSAR and ERA-Interim Data
As analyzed in Sec. 2, the unwrapped interferometric phases in the radar LOS direction can be regarded as the slant total wet delay without considering the hydrostatic delay component. The LOS wet delay maps are then converted into the zenith direction with the simplest mapping function 1∕ cos θ, where θ is the incidence angle of each SAR image pixel. The converted ZWD is further used to extract the differential PWV (ΔPWV; master minus slave) distributions via the dimensionless quality in Eq. (3). Given that the ERA-Interim data at the finest resolution are still far sparser than InSAR Ifms, the ΔPWV measurements from InSAR images are compared with ERA-Interim data at the locations of ERA-Interim grids only (i.e., on 0.125 deg × 0.125 deg grid). Figure 4 shows the comparison of ΔPWV distributions from C-band InSAR Ifms and spatiotemporally synchronized ERA-Interim data, together with the spatial distributions and histograms of ΔPWV differences. As we can see in Fig. 4(a) the negative ΔPWV measurements  Fig. 4(b)] is 1.9 mm. As a result, an overall STD of 1.9 mm for the ΔPWV differences (InSAR minus ERA-Interim) between Figs. 4(a) and 4(b) is detected in Fig. 4(c). Moreover, it can be detected from the histogram of Ifm1 [ Fig. 4(d)] that the ΔPWV differences generally range from −2 to 2 mm with an overall root mean square (RMS) of about 1.9 mm. The C-band InSAR derived ΔPWV distribution in Ifm2 [ Fig. 4(e)] is surrounded by positive signals except that mild negative signals are found in the middle-north of the study area. In contrast, the ΔPWV map estimated from ERA-Interim data [ Fig. 4(f)] exhibits obvious gradient from northwest to southeast. The ΔPWV variation in Ifm2 and spatiotemporally synchronized ERA-Interim data in terms of STD are about 1.3 and 1.2 mm, respectively, as well as the overall STD of their ΔPWV differences is about 1.3 mm. In Fig. 4(h), inspiring results are also shown since their ΔPWV differences occur more frequently from −1 to 1 mm with an RMS of about 1.3 mm. The ΔPWV variation in Ifm3 [ Fig. 4(i)] and spatiotemporally synchronized ERA-Interim data [ Fig. 4(j)] in terms of STD are about 1.0 and 1.3 mm, respectively, together with the overall STD of their ΔPWV differences is about 1.6 mm [ Fig. 4(k)]. Furthermore, the frequency histogram of ΔPWV differences of Ifm3 [ Fig. 4(l)] again demonstrates that the C-band InSAR derived ΔPWV can be estimated with an accuracy of <2.0 mm when compared with spatiotemporally synchronized ERA-Interim data.

C-band ENVISAT ASAR
The probable cause for the ΔPWV differences between InSAR and spatiotemporally synchronized ERA-Interim data may result from uncertainties existing in the latter, as well as the errors introduced by interpolating the ERA-Interim PWV time series. Moreover, the uncertainties in InSAR data processing (e.g., phase errors induced by the SRTM height uncertainties, baseline errors, etc.) and temporal variations of ZHD between the acquire time of the master and slave images may also contribute to the discrepancies of ΔPWV differences.  Fig. 5(g)]. Furthermore, it can be observed from Fig. 5(g) that their ΔPWV differences are all within AE1.5 mm. Therefore, the L-band PALSAR InSAR images with proper perpendicular baseline length can also help to estimate the moisture distributions effectively.

Validation of InSAR Derived ΔPWV Measurements with GPS Observations
GPS is able to estimate the PWV measurements with high temporal resolution and high precision, which makes it an ideal tool to validate the ΔPWV distributions from InSAR images. In addition, the water vapor sensed by GPS observations is typically estimated by sampling throughout a conical section of the atmosphere above the GPS receiver. In this study, the GPS satellites cut-off elevation angle was set to 15 deg during the GPS data processing with the GAMIT 10.60 software. Therefore, the InSAR estimates are obtained by averaging all pixels located at a distance <5.23 km from the GPS station during the comparisons of ΔPWV from InSAR and GPS data. 19 Figure 6 shows each ΔPWV measurement from C-band ASAR Ifms and spatiotemporally synchronized GPS observations, as well as the histograms of their ΔPWV differences. As can be seen in Fig. 6(a) the ΔPWV measurements from ASAR unwrapped phases and GPS data show similar variation at all available GPS sites, except that the ΔPWV differences are larger than 2 mm at SHBS, SHJS, and SHNH. As a result, an overall STD of 1.9 mm is obtained from the ΔPWV differences between Ifm1 and spatiotemporally synchronized GPS data. In addition, the histogram of Ifm1 in Fig. 6(b) shows that their ΔPWV differences are within AE3 mm, with a mean of −0.8 mm at all GPS sites.

C-band ENVISAT ASAR
In Fig. 6(c), 9 of 11 GPS sites are available for ΔPWV comparison from Ifm2 and spatiotemporally synchronized GPS data. The maximum ΔPWV difference of 2.9 mm is found at SHFX, and the minimum ΔPWV difference of 0.5 mm is found at DSJG. In addition, an STD of 2.0 mm and an overall mean of 0.7 mm are observed from their ΔPWV differences [ Fig. 6(d)]. As for the comparison in Ifm3 [Figs. 6(e)-6(f)], all ΔPWV measurements at 11 GPS sites are estimated, and the ΔPWV differences between Ifm3 and spatiotemporally synchronized GPS data are < AE 1 mm at 7 of 11 GPS sites. As a result, an STD of 1.3 mm is achieved during their ΔPWV differences comparison, which shows better agreement than the comparisons of Ifm1 and Ifm2. Moreover, the histogram of their ΔPWV differences [ Fig. 6(f)] is close to normal distribution, with an overall mean of ΔPWV differences close to zero.   Figure 7 shows the ΔPWV measurements from L-band PALSAR Ifms and spatiotemporally synchronized GPS observations, as well as the histograms of their ΔPWV differences. As we can see in Fig. 7(a), 6 of 7 GPS sites are available for the ΔPWV comparison in Ifm4. The ΔPWV differences between Ifm4 and spatiotemporally synchronized GPS data are within the range of −0.2 to 0.9 mm for all the sites except for SHBS, which shows an RMS of 1.5 mm and an STD of 1.3 mm. Moreover, the histogram in Fig. 7(b) also illustrates that their ΔPWV differences occur more frequently around zero with an overall mean of about −0.3 mm.
In Figs. 7(c) and 7(d), all seven GPS sites are available for the comparison in Ifm5, and the ΔPWV differences between Ifm5 and spatiotemporally synchronized GPS data range from −1.7 to 1.9 mm for all the sites. Comparison of their ΔPWV measurements in Ifm5 gives an overall mean of 0.5 mm and an RMS of 1.3 mm, which is a very good validation of this study.

Conclusions
In this study, interferometric phases from C-and L-band InSAR images are incorporated to derive the atmospheric water vapor information with the high spatial resolution of 40 m × 40 m and 30 m × 30 m, respectively. We conduct analysis to extract the PWV measurements on three ASAR and two PALSAR image pairs over the city of Shanghai, China. Moreover, the estimated ΔPWV distributions are accessed via comparisons with those results from spatiotemporally synchronized ERA-Interim grids and GPS observations. Comparisons of ΔPWV distributions from C-band ASAR Ifms and spatiotemporally synchronized ERA-Interim data show an overall STD of 1.9, 1.3, and 1.6 mm for Ifm1, Ifm2, and Ifm3, respectively, while those comparisons from L-band PALSAR Ifms and spatiotemporally synchronized ERA-Interim data give an overall STD of 2.3 and 0.7 mm for Ifm4 and Ifm5, respectively. The large discrepancies of ΔPWV measurements from Ifm4 and spatiotemporally synchronized ERA-Interim data may result from the long perpendicular baseline of Ifm4. In addition, the comparisons of ΔPWV maps from C-band ASAR Ifms and spatiotemporally synchronized GPS data give an STD of 1.9, 2.0, and 1.3 mm in Ifm1, Ifm2, and Ifm3, respectively. The STD of ΔPWV differences from L-band PALSAR Ifms and spatiotemporally synchronized GPS data is 1.3 and 1.2 mm in Ifm4 and Ifm5, respectively. As such, it could be, therefore, concluded from this study that InSAR images can detect the ΔPWV measurements with an RMS of better than 2.0 mm.
In addition, the water vapor information in plain areas is necessary for numerical forecasting procedures [e.g., those based on the 3-D variational data assimilation (3-DVAR) and four-dimensional variational data assimilation (4-DVAR) analysis], and PWV spatial distributions in high-altitude regions are also important for meteorologists to forecast precipitation and severe weather conditions. However, extractions of water vapor information from InSAR images in these areas are not conducted in this study, which would be an important issue in the future.