Error Evaluation of L-Band InSAR Precipitable Water Vapor Measurements by Comparison with GNSS Observations in Japan

Abstract

Interferometric synthetic aperture radar (InSAR) enables us to obtain precipitable water vapor (PWV) maps with high spatial resolution through the phase difference caused by refraction in the atmosphere. Although previous studies have evaluated the error level of InSAR PWV observations, they validated it only with C-band InSAR PWV observations. Since ionospheric disturbance seriously contaminates the InSAR phase in the case of the lower-frequency SAR system, it is necessary for a PWV error level evaluation correcting the ionospheric effect appropriately if we use lower-frequency SAR systems, such as the Advanced Land Observing Satellite-2 (ALOS-2). In this paper, we evaluated the error level of the L-band InSAR PWV observation obtained from ALOS-2 data covering four areas in Japan. We compared the InSAR observations with global navigation satellite system (GNSS) atmospheric observations and estimated the L-band InSAR PWV error value by utilizing the error propagation theory. As a result, the L-band InSAR PWV absolute error reached 2.83 mm, which was comparable to traditional PWV observations. Moreover, we investigated the impacts of the seasonality, the interferometric coherence, and the height dependence on the PWV observation accuracy in InSAR.

1. Introduction

Water vapor in the atmosphere plays an important role in weather and climatic processes [1,2]. Tropospheric water vapor has highly fluctuating characteristics in both time and space, leading to a relatively poor understanding of it compared with other atmospheric variables, such as wind and temperature fields. In short timescale cases ranging from minutes to hours, previous studies have reported an increase in the amount of water vapor just before severe precipitation [3,4,5]. Therefore, monitoring the amount and the spatial distribution of atmospheric water vapor in detail is crucial to improving precipitation prediction and understanding the terrestrial water cycle [6,7].

Interferometric synthetic aperture radar (InSAR) has been used to measure precipitable water vapor (PWV) maps with high spatial resolution (a few tens of meters) (e.g., [8,9,10,11,12]). When microwaves emitted from a satellite travel through the neutral atmosphere, the phase velocity of the microwave is changed, and the travel path is bended due to having a different refractive index to the vacuum. This effect is called the neutral atmospheric propagation delay effect. In particular, in the case of InSAR, water vapor plays a dominant role in the neutral atmospheric propagation delay effect due to its high variability in both time and space. The dry atmospheric InSAR delay is large, but the heterogeneity of it over the scene depends on the scene size. In the case of the standard strip map observation mode, the effect of the dry atmosphere is smaller than that of the wet atmosphere [13].

The satellite InSAR technique was originally used to measure the surface displacement occurring between two SAR acquisition times by using the microwave phase difference. In view of the surface deformation observation, atmospheric water vapor is one of the most problematic error sources in InSAR observations. Therefore, even if there is no surface displacement between two observations, InSAR phase information mainly reflects the effect of atmospheric water vapor. In sum, if the atmospheric delay signal and other contributions, such as the surface displacement and the ionospheric noise, can be adequately separated from the InSAR data, it is possible to obtain the water vapor distribution at a high spatial resolution in orders of tens to hundreds of meters, regardless of the weather conditions [14].

The distribution of water vapor in the atmosphere is not uniform but is greatly affected by weather conditions. There are two types of water vapor observation techniques currently used for operational weather predictions: one is ground-based observations, such as the radiosonde and the global navigation satellite system (GNSS), and the other is satellite observations using GNSS radio occultation techniques [15] and infrared/passive microwave sensors. However, ground-based observations such as the GNSS have the limitation that the spatial resolution depends on the station’s density, resulting in, for example, tens of kilometers in the best operational case scenario of GNSS [16]. Water vapor is observed at a low spatial density as the geometric distance between neighboring observation points is usually at least several tens of kilometers or more. On the other hand, the satellite infrared observation cannot be used for water vapor in cloudy conditions.

It is expected that the accuracy of precipitation prediction can be improved by incorporating InSAR data into weather forecast models in addition to traditional observation data, as InSAR has the advantage of its unprecedented high spatial resolution, even under cloudy conditions, which may complement the weakness of traditional water vapor observation techniques [17]. In a previous study that assimilated InSAR-derived water vapor information into a meso-scale weather model, precipitation prediction improved by up to 9 h [7]. In addition, a continuous use of InSAR water vapor information for short-term weather forecasting at the Iberian Peninsula using Sentinel-1 indicated a positive impact for improving precipitation prediction [18]; however, InSAR water vapor information has not yet been put into practical use for operational weather forecasting, and thus it is necessary to further investigate the potential of InSAR water vapor observation for the improvement of precipitation prediction.

The statistical evaluation of the accuracy and precision of InSAR water vapor observation is indispensable, especially for each type of microwave frequency band used in SAR systems. This is due to the fact that noise characteristics largely differ depending on the microwave center frequency; however, in previous studies, only the observation accuracy of C-band SAR was evaluated. (e.g., [19,20]). Currently, three frequency bands are used for SAR satellites: X-band (e.g., 9.65 GHz), C-band (e.g., 5.40 GHz), and L-band (e.g., 1.25 GHz). L-band SAR observations are typically less sensitive to the surface cover change due to, for example, the vegetation change rather than a higher frequency SAR, such as C-band SAR. Therefore, L-band SAR has the advantage that the phase information of the received data in two observations can easily interfere with each other, even in the case of mountainous and richly vegetated areas such as Japan.

When microwaves pass through the ionosphere in the upper atmosphere, the phase velocity of the microwaves changes and appears in the InSAR data as an apparent change in line-of-sight distance. The phase variation due to the ionosphere (hereafter referred to as ionospheric delay) is caused by free electrons in the ionosphere, which has a dispersive nature within the microwave frequency range. Therefore, the lower the center frequency is, the larger the change in the wave phase velocity becomes. In particular, the ionospheric delay effect is significant in L-band SAR compared to other SAR systems. In order to utilize L-band InSAR data for meteorology, it is necessary to separate the ionospheric delay from the neutral atmospheric delay.

We need to clarify the error level of the water vapor observation in L-band SAR systems, which has not been evaluated in previous studies. In this study, we statistically evaluated the L-band InSAR observation error of water vapor, with the aim of improving the precipitation forecast accuracy by using InSAR water vapor information, especially under extreme weather situations. This paper is organized as follows. In Section 2, we introduce atmospheric delay physics. In Section 3, we describe methods to estimate the InSAR PWV error level. In Section 4, we present outlines of the SAR and GNSS data used in this study. In Section 5, results of the error estimation are shown. Section 6 and Section 7 are the discussion and the conclusion.

2. Atmospheric Delay Physics

The basic InSAR observable is the phase difference of microwaves obtained from two SAR acquisitions. The observed phase difference ${\varphi }_{InSAR}$ contains several contributions, which can be expressed as follows:

$${\varphi }_{InSAR}={\varphi }_{disp}+{\varphi }_{orb}+{\varphi }_{topo}+{\varphi }_{ion}+{\varphi }_{neutral\_atm}+{\varphi }_{noise}$$

(1)

where ${\varphi }_{disp}$ represents the phase change due to the surface displacement that occurred during the two observations, ${\varphi }_{orb}$ is the phase variation due to possible orbital errors, and ${\varphi }_{topo}$ is the residual topographic phase due to errors in the digital elevation model (DEM) data. ${\varphi }_{ion}$ and ${\varphi }_{neutral\_atm}$ are the atmospheric propagation delays in the ionosphere and the neutral atmosphere, respectively. ${\varphi }_{noise}$ represents all other sources of noise.

From the previous study [21], the propagation distance $L$ of microwaves can be expressed as follows:

$$L={\int }_s^{}nds$$

(2)

where $n$ is the refractive index and $ds$ is the path increment at an arbitrary location in the atmosphere.

The atmospheric delay $\Delta L$ is given as follows:

$$\Delta L={\int }_s^{}nds-G={\int }_s^{}\left(n-1\right)ds+\left[S-G\right]$$

(3)

where $S$ is the actual propagation path length, and $G$ is the geometric distance between the satellite and the Earth’s surface. In sum, the bending effect expressed in the second term of the right-hand side is negligibly small in the range of the SAR incidence angle from 20° to 50°. Therefore, we can ignore the term $S-G$.

The ionospheric delay is due to the existence of electrons, and the ionospheric range delay ($L_{ion}$) at frequency (f) can be written as follows:

$$L_{ion}=\alpha \ast \mathrm{STEC}/f$$

(4)

where α is a constant value used to convert the total election content unit (TECU) to the unit of length, and $\mathrm{STEC}$ represents the slant total election content [22].

The refractive index of the neutral atmosphere is a function of temperature $T$ (Kelvin), partial pressure of dry air $P_d$ (hPa), and partial pressure of water vapor $P_v$ (hPa), which is expressed as follows [23]:

$${10}^6\left[n-1\right]=k_1\left(\frac{P_d}{T}\right)Z_d^{-1}+k_2\left(\frac{P_v}{T}\right)Z_v^{-1}+k_3\left(\frac{P_v}{T^2}\right)Z_v^{-1}$$

(5)

where $Z_d$ and $Z_v$ are the compressibility factors of dry air and water vapor, respectively, which can be assumed as equal to the unit value in the ordinary air condition. $k_1=77.6$ (K/hPa), $k_2=70.4$ (K/hPa) and $k_3=3.739\times {10}^5$ (K²/hPa) are the coefficients determined by laboratory experiments. These specific values were given by [24].

In particular, the neutral atmospheric delay integrated from the surface to the top of the atmosphere in the zenith direction is called the “zenith total delay” (ZTD) and can be written as follows:

$$\begin{array}{c}ZTD={10}^{-6}[{\int }_{Zenith}^{}{k}_1\left(\frac{R_a}{m_d}\right)\rho dz+k_2^{\prime }{\int }_{Zenith}^{}\left(\frac{P_v}{T}\right)Z_v^{-1}dz+\\ k_3{\int }_{Zenith}^{}\left(\frac{P_v}{T^2}\right)Z_v^{-1}dz],\end{array}$$

(6)

where $\rho$ is the total density of the atmosphere, $m_d$ is the molecular weight of dry air (28.9644 kg/kmol), $z$ is the height and $R_a$ is the universal gas constant (8314.34 J/kmol∙K). In the equation, we introduced a new coefficient, $k_2^{\prime }\equiv \left(k_2-k_1\frac{m_v}{m_d}\right)$, where $m_v$ is the molecular weight of water vapor (18.0152 kg/kmol). The first term on the right-hand side of Equation (6) is the effect of the molecular weight of air in the atmosphere, and the second and third terms on the right-hand side are the delay due to water vapor alone in the atmosphere. The first term is denoted as the “zenith hydrostatic delay” (ZHD), and the latter as the “zenith wet delay” (ZWD).

The ZHD can be modeled accurately using the surface pressure $P_0$, the latitude at the point $\phi$ and the ellipsoidal height $H$ as follows [25]:

$$ZHD=\left(2.2779\pm 0.0024\right)\frac{P_0}{f\left(\phi , H\right)}$$

(7)

and

$$f\left(\phi , H\right)=\left(1-0.00266cos2\phi -0.00028H\right).$$

(8)

The uncertainly given for the ZHD (${\sigma }_{ZHD}$) is approximately 2.41 mm [25].

The ZWD is the residual of the ZTD subtracted by the ZHD (ZWD = ZTD − ZHD). Therefore, the ZWD can be expressed as follows [26]:

$$\begin{array}{c}ZWD={10}^{-6}\left[k_2^{\prime }{\int }_{Zenith}^{}\left(\frac{P_v}{T}\right)Z_v^{-1}dz+k_3{\int }_{Zenith}^{}\left(\frac{P_v}{T^2}\right)Z_v^{-1}dz\right]\\ ={10}^{-6}{R}_v\left(k_2^{\prime }+k_3\frac{{\int }_{Zenith}^{}\left(\frac{P_v}{T^2}\right)dz}{{\int }_{Zenith}^{}\left(\frac{P_v}{T}\right)dz}\right)·{\int }_{Zenith}^{}\frac{P_v}{R_{v}T}{Z}_v^{-1}dz.\end{array}$$

(9)

PWV is the total amount of water vapor contained in the atmospheric column over a unit area. The relationship between ZWD and PWV is given as follows:

$$ZWD={\mathsf{\Pi }}^{-1}·PWV,$$

(10)

here

$$\mathsf{\Pi }=\frac{{10}^6}{{\rho }_w{R}_v\left(k_2^{\prime }+\frac{k_3}{T_m}\right)}$$

(11)

and

$$T_m=\frac{{\int }_{Zenith}^{}\left(\frac{P_v}{T^2}\right)dz}{{\int }_{Zenith}^{}\left(\frac{P_v}{T}\right)dz},$$

(12)

where $R_v$ is the gas constant of water vapor, ${\rho }_w=1000\mathrm{kg}/{\mathrm{m}}^3$ is the density of water vapor, and $T_m$ is the average air temperature weighted by the partial pressure of water vapor above the surface (weighted average air temperature) [26]. Fortunately, $T_m$ can be approximated by the ground temperature $T_s$ as follows [21]:

$$T_m\approx 70.2+0.72T_s.$$

(13)

In sum, $\mathsf{\Pi }$ can be approximately regarded as a function of the ground temperature.

3. Error Evaluation Method

InSAR originally observes the phase change ${\varphi }_{InSAR}$, which reflects the differences in microwave propagation path lengths. ${\varphi }_{InSAR}$ is the linear sum of phase changes due to several factors, as shown in Equation (1). Regarding the neutral atmospheric delay, InSAR observes the relative difference in atmospheric delays between two acquisition times. In this study, we estimated the “InSAR zenith total delay difference” ($dZT{D}_{InSAR}$), whose offset was calibrated using the “GNSS zenith total delay difference” ($dZT{D}_{GNSS}$) according to the formulae provided in previous studies [19,20]. Hereinafter, “InSAR initial value” ($IV$) denotes the phase delay in the zenith direction converted from the satellite line-of-sight direction using the incidence angle $\theta$ and a simple trigonometric function. $IV$ was derived through the following equation as follows:

$$I{V}_{\left(i\right)}={\varphi }_{neutral\_atm\left(i\right)}\times \cos {\theta }_{\left(i\right)}\times \lambda /4\pi$$

(14)

where $i \left(=1, 2, \dots ,n\right)$ is the colocation point number of the GNSS and InSAR observation point in the target area. Here, it should be noted that InSAR observations reflect the delay along the line-of-sight (narrow tube), but GNSS ZTDs reflect the average of the delay within the inverse cone space above GNSS stations. This indicates that GNSS-derived atmospheric values are representative values within the inverse cone, whose radius at the tropopause (approximately 12 km around Japan) was approximately 100 km, with the cut-off angle of 7 degrees, in our case. On the other hand, the InSAR phase is only affected by the atmosphere along the microwave path, indicating that the InSAR PWV signal reflects the atmospheric heterogeneity within a narrow tube (radius ranging from a few to a hundred meters depending on multilooking and filtering processes) between the ground and the satellite. In this context, we should keep in mind that the spatial representativeness of InSAR PWV observation is intrinsically different from that of GNSS. Therefore, to compensate for this representativeness gap between InSAR and GNSS, even if only slightly, we applied significantly large multilooking and strong spatial filtering to all interferograms, resulting in values of the actual spatial resolution of several hundred meters or larger. Details of the InSAR processing are described in Section 4.1.

The $IV$ must be calibrated to be converted into $dZT{D}_{InSAR}$. The amount of an offset in a specific scene ($Offset$) is determined by the non-weighted average of estimated differences between the $IV$ and $dZT{D}_{GNSS}$ at each station $i$ within the scene:

$$dZT{D}_{GNSS\left(i\right)}=ZTD{2}_{GNSS\left(i\right)}-ZTD{1}_{GNSS\left(i\right)},$$

(15)

$$Offset=\frac{1}{n}{\sum }_{i=1}^n\left(dZT{D}_{GNSS\left(i\right)}-I{V}_{\left(i\right)}\right),$$

(16)

where $ZTD{1}_{GNSS}$ and $ZTD{2}_{GNSS}$ represent the ZTD observed by GNSS at times closest to the reference SAR observation and the secondary one, respectively. Using the estimated offset, we could obtain $dZT{D}_{InSAR}$ at an arbitrary pixel $i$ ($dZT{D}_{InSAR\left(i\right)}$) by adding it to $IV$:

$$dZT{D}_{InSAR\left(i\right)}=I{V}_{\left(i\right)}+Offset.$$

(17)

The standard deviation of residuals between $dZT{D}_{GNSS}$ and $dZT{D}_{InSAR}$ represents the relative error of $dZT{D}_{InSAR}$ from $dZT{D}_{GNSS}$. As previous studies that evaluated measurement errors of other kinds of water vapor measurement techniques estimated these absolute errors by assuming the radiosonde observation technique as the most accurate, our study finally estimated the absolute error of the L-band InSAR PWV measurement by considering the radiosonde-derived PWV values as the true value. In sum, we considered the relative error of the InSAR PWV measurement against the radiosonde PWV measurement as the absolute error of the InSAR PWV observation. To estimate the standard deviation of residuals between $dZT{D}_{InSAR}$ and $dZT{D}_{GNSS}$, we defined the residual ($R_{\left(i\right)}$) at a location $i$ between $dZT{D}_{GNSS\left(i\right)}$ and $dZT{D}_{InSAR\left(i\right)}$ as follows:

$$R_{\left(i\right)}=dZT{D}_{GNSS\left(i\right)}-dZT{D}_{InSAR\left(i\right)}.$$

(18)

Then, its standard deviation (${\sigma }_R$) was calculated as follows:

$${\sigma }_R=\sqrt{\frac{1}{N}\sum \sum {\left(\overline{R}-R_{\left(i\right)}\right)}^2},$$

(19)

where $\overline{R}$ represents the mean of $R_{\left(i\right)}$ in a specific interferogram.

Then, we could reasonably assume that errors of $ZTD{1}_{GNSS\left(i\right)}$ and $ZTD{2}_{GNSS\left(i\right)}$ had no correlation and could be set as equal (${\sigma }_{ZTD1\_GNSS}={\sigma }_{ZTD2\_GNSS}={\sigma }_{ZTD\_GNSS}$) since the time interval of these two observations was larger than 14 days, which is the recurrence interval of the ALOS-2 satellite. Under this assumption, we could express the error of $dZT{D}_{GNSS}$ using the law of error propagation as follows:

$${\sigma }_{dZTD\_GNSS}=\sqrt{2}\ast {\sigma }_{ZTD\_GNSS}.$$

(20)

In our study, we adopted ${\sigma }_{ZTD\_GNSS}$ as 17.0 mm, as obtained in a previous study [27].

The absolute dZTD error of InSAR, which is the relative error against the radiosonde dZTD, is equal to the root of the square sum of (1) the relative error of the GNSS dZTD (${\sigma }_{ZTD\_GNSS}$), (2) the processing error of the GNSS ZTD (${\sigma }_{Sys\_GNSS}$), and (3) the relative error of $dZT{D}_{InSAR}$ from $dZT{D}_{GNSS}$ (${\sigma }_R$). Using Equation (20), ${\sigma }_{dZTD\_InSAR}$ can be expressed as follows:

$${\sigma }_{dZTD\_InSAR}=\sqrt{2{\sigma }_{ZTD\_GNSS}^2+2{\sigma }_{Sys\_GNSS}^2+{\sigma }_R^2}$$

(21)

Here, ${\sigma }_{Sys\_GNSS}$ is fixed as 3.0 mm, which is the rough average from the processed GNSS ZTD data [28].

As Equation (21) represents the error of difference of two InSAR ZTD observations, its decomposition into the error of InSAR ZTD measurements at a single observation is required. Assuming that there is no correlation between atmospheric delays in each SAR acquisition time, the error of InSAR ZTD (${\sigma }_{ZTD\_InSAR}$) can be introduced using the law of error propagation from ${\sigma }_{dZTD\_InSAR}$ in Equation (21). From the assumption, standard deviations (errors) of InSAR ZTDs at reference and secondary observations can be regarded as equal. As the $dZT{D}_{InSAR}$ is derived from two independent InSAR ZTDs ($dZT{D}_{InSAR}=ZTD{2}_{InSAR}-ZTD{1}_{InSAR}$), ${\sigma }_{dZTD\_InSAR}$ can be decomposed as the root of the square sum of two standard deviations of $\sqrt{2{\sigma }_{ZTD\_InSAR}^2}$. This can be expressed as follows:

$${\sigma }_{dZTD\_InSAR}=\sqrt{2}\ast {\sigma }_{ZTD\_InSAR}.$$

(22)

To estimate the PWV error, we further needed to decompose ${\sigma }_{dZTD\_InSAR}$ into errors of dry and wet components. From the relationship between ZWD and ZTD, the error of InSAR ZWD (${\sigma }_{ZWD\_inSAR}$) can be expressed as follows:

$${\sigma }_{ZWD\_InSAR}=\sqrt{{\sigma }_{ZTD\_InSAR}^2+{\sigma }_{ZHD}^2},$$

(23)

where ${\sigma }_{ZHD}$ is the estimation error of ZHD in Equation (7), and as introduced in Section 2, we set this value as 2.41 mm from the previous study [25]. Using Equation (23), we could remove the contribution of the dry air and obtain the error of InSAR ZWD measurements, which was used to obtain the error of the InSAR PWV measurements.

The relationship between ZWD and PWV is provided by Equations (10) to (13). According to [24], the PWV conversion factor Π can be estimated with good accuracy using the surface temperature. As the sensitivity of Π to $T_s$ is small, in this study, we used a fixed value of surface temperature, $T_s=299.30\left(K\right)$, which was estimated from the average temperature from June to September (hereafter referred to as the wet season) in 2020 in the Kyushu region, where heavy rainfall events are especially likely to occur in this season. The reason that we chose this period is that a large amount of SAR data we used were obtained in Kyushu during the wet season. Specifically, we used $\mathsf{\Pi }=0.163$, and thus the absolute error of the InSAR PWV (${\sigma }_{PWV\_InSAR}$), which we aimed to estimate, is expressed as follows:

$${\sigma }_{PWV\_InSAR}=0.163\ast {\sigma }_{ZWD\_InSAR}.$$

(24)

4. Data

4.1. InSAR Data

The SAR data used in this study were acquired by the phased array L-band SAR 2 (PALSAR-2) onboard the Advanced Land Observing Satellite-2 (ALOS-2), which is operated by the Japan Aerospace Exploration Agency (JAXA). The observation mode used here was the strip map (SM) ultrafine mode with a spatial resolution of 3 m in both range and azimuth directions. The single SAR scene in the SM mode covers an area of approximately 50 × 50 km². All interferograms were generated from level-1.1 Single Look Complex (SLC) images using the Radar Interferometry Calculation Tools (RINC) software ver. 0.41r [29]. ${\varphi }_{orb}$ was estimated from the high-precision satellite orbit data provided by JAXA, and ${\varphi }_{topo}$ was removed by simulating the terrain fringes with the 3-arcsecond Shuttle Radar Topography Mission (SRTM) DEM provided by the United States Geological Survey (USGS). Multilook processing resulted in an improvement in the interferometric coherence by sacrificing the spatial resolution of the InSAR data to approximately 100 m in both range and azimuth directions. We used the Goldstein and Werner filter with the alpha value of 0.7 and the filter window size of 32 pixels to reduce small-scale phase noises [30]. After removing these phase contributions, we could obtain the phase difference due to the neutral atmospheric delay. The statistical-cost, network-flow phase-unwrapping algorithm (SNAPHU) software was used for phase unwrapping [31]. For the calculation of residuals, we used $IV$, where the interferometric coherence was greater than 0.3.

The ionospheric delay ${\varphi }_{ion}$ was estimated and removed by the range split-spectrum method (SSM) [32]. As Gomba et al. [32] demonstrated, SSM can largely reduce ionospheric delay phase contaminations by splitting the range spectrum into higher and lower parts. Although several papers have reported the effectiveness of SSM to mitigate the ionospheric delay signal [33,34,35], to the best of our knowledge, none of the reviewed papers reported its statistical performance. According to the derivation of Gomba et al. [32], the theoretical estimation accuracy of the ionospheric delay by SSM is an order of centimeters or less depending on the interferometric coherence and the multilooking size. We visually checked all interferograms and found that the application of SSM to interferograms with serious ionospheric delay contaminations showed a significant reduction, especially for long-wavelength phase variations.

We selected four areas in Japan—southern Ibaraki, western Tokyo, Osaka and southern Kyushu—where a significant number of GNSS stations and ALOS-2 SM1 mode SLCs are available (Figure 1). The orbit is ascending in southern Ibaraki and descending in the other areas. Detailed information of the SAR observations is summarized in

Table 1. Detailed information of SAR observations in four Japanese areas.

Area	Path-Frame	Orbit	SLCs	Interferograms	Period
Southern Ibaraki	125-710	Ascending	14	7	13 September 2015–14 June 2020
Western Tokyo	18-2900	Descending	20	10	15 February 2015–2 April 2020
Osaka	20-2920	Descending	12	6	5 October 2014–20 January 2019
Southern Kyushu	23-2970	Descending	46	23	9 February 2015–17 August 2020

.

Japan is well known as a tectonically active area, and thus several kinds of phenomena, such as earthquakes, land subsidence, and volcanic activities, cause surface deformation. In this study, we assumed that there was no surface displacement (${\varphi }_{disp}=0$) as no large earthquakes (>M6) were reported among all pairs of reference and secondary SAR acquisitions. Note that recent studies reported that earthquakes with magnitudes not only larger than 6 but also smaller than 6 can cause geodetically detectable surface displacements if source depths are close to the surface (depths of a few kilometers) [36,37,38]. To assess the possible impacts due to both larger- and smaller-magnitude earthquakes, we checked the earthquake source catalog developed by the Japan Meteorological Agency. As a result, we confirmed that all interferograms used in this study contain no possible impacts due to co-seismic fault slips. In addition, as we chose interferometric pairs by using two subsequently acquired SLCs, all interferograms have time intervals of shorter than 210 days (most parts of the interferograms have time intervals shorter than four months), which would be significantly short to neglect secular surface displacements, such as the plate tectonic motion and land subsidence (ranging from a few millimeters per year to centimeters per year).

4.2. GNSS Data

GNSS data were derived from the GNSS Earth Observation Network System (GEONET), the operational GNSS network in Japan. We used the 5 min-interval tropospheric parameters estimated by the Geodesy Laboratory at the University of Nevada (NGL) [28]. The analysis method for the GNSS was the precise point positioning method using the International GNSS service precise orbit information and Earth rotation parameters. In order to avoid the effect of surface displacements caused by volcanic activity, GNSS observation data near Mt. Kirishima in southern Kyushu (blue circles in Figure 2d) were excluded in our analysis. ${\sigma }_{Sys\_GNSS}$ shown in Equation (21) is provided by NGL. As a result, there were 18 stations in southern Ibaraki, 15 stations in western Tokyo and Kanagawa, 15 stations in Osaka and 7 stations in southern Kyushu (red triangles in Figure 2).

5. Result

Figure 3 shows the distribution of residuals between $dZT{D}_{GNSS}$ and $dZT{D}_{InSAR}$ ($R$) in each area. The average values of residuals $R$ were 0.00 mm in each area. Standard deviations of $R$ were 6.35 mm in southern Ibaraki, 8.59 mm in western Tokyo, 6.69 mm in Osaka and 7.29 mm in southern Kyusyu, respectively. We also plotted the distribution of the residuals between $dZT{D}_{GNSS}$ and $dZT{D}_{InSAR}$, combining all four areas in Figure 4. For the residuals of all four areas, the mean and standard deviation (${\sigma }_R$) became 0.00 and 7.36 mm, respectively. Based on the estimated standard deviation of the residuals including all areas, we evaluated the errors in Equations (21) (${\sigma }_{dZTD\_InSAR}$), (22) (${\sigma }_{ZTD\_InSAR}$), (23) (${\sigma }_{ZWD\_InSAR}$) and (26) (${\sigma }_{PWV\_InSAR}$) step by step using the error propagation theory. First, we calculated the absolute error of InSAR dZTD (${\sigma }_{dZTD\_InSAR}$) using Equation (21), resulting in 25.50 mm based on GNSS processing and the ZTD error values introduced in Section 3. In the next step, we calculated ${\sigma }_{ZTD\_InSAR}$ in Equation (22), which was estimated as 18.03 mm. After calculating ${\sigma }_{ZWD\_InSAR}$ using the ZHD error (${\sigma }_{ZHD}$) through Equation (23), we could finally obtain the absolute error of InSAR PWV (${\sigma }_{PWV\_InSAR}$) as 2.96 mm through Equation (24). The estimated ${\sigma }_{PWV\_InSAR}$ was slightly larger than the PWV errors of other observation techniques evaluated in previous studies [12,20,39,40,41] (Figure 5 and Figure 6).

In the previous study [42], the PWV in July was greater than in January in Japan. Shoji [42] also showed the same tendency in the root mean square (RMS) difference between the GNSS and radiosonde PWV. Moreover, the GNSS PWV has a seasonal variation in Japan [43]. We checked whether the error of the InSAR PWV becomes larger in the wet season as with the error of the GNSS PWV. Figure 7 shows the $R$ distribution of data that were acquired during the wet season. As a result, the mean of GNSS ZTD was larger in the wet season than in other months (hereafter referred to as the dry season) in our case. The mean and standard deviation of $R$ were 0.00 and 8.16 mm, respectively, during the wet season. ${\sigma }_{PWV\_InSAR}$ in the wet season became 2.99 mm. On the other hand, the mean and standard deviation of $R$ were 0.00 and 5.84 mm, respectively, in the dry season. ${\sigma }_{PWV\_InSAR}$ in the dry season became 2.91 mm. Our results indicate that ${\sigma }_R$ was larger in months when the GNSS ZTD was also larger than that in other months. We concluded that ${\sigma }_{PWV\_InSAR}$ was greater in the wet season than that in the dry season.

We compared the error of the L-band InSAR PWV (${\sigma }_{PWV\_InSAR}$) estimated from this study with that of the C-band InSAR PWV estimated by other studies [12,20] (Figure 5). Note that previous studies only estimated the standard deviation of residuals between $PW{V}_{GNSS}$ and $PW{V}_{InSAR}$. Therefore, Figure 6 shows the relative PWV errors of InSAR against GNSS. The error of the L-band InSAR PWV compared with the GNSS PWV (${\sigma }_{PWV{\left(GNSS\right)}_{InSAR}}$) can be estimated by Equation (24) with ${\sigma }_R$ (=7.4mm) instead of ${\sigma }_{ZTD\_InSAR}$. In the previous study [20], the ENVISAT difference PWV error was 0.675 mm, which was the average of the mean absolute error (MAE) of difference PWVs between InSAR and GNSS for 10 interferograms in the United States (US). Here, we divided their PWV errors by $\sqrt{2}$ using Equation (22) and replaced the ZTD with PWV to obtain the above error values, resulting in the ENVISAT PWV error in [20] becoming 0.48 mm. The Sentinel-1 PWV error was 0.65 mm, which was the average of the root mean square error (RMSE) between the InSAR and GNSS PWV of 10 interferograms in the US [12]. The L-band InSAR PWV error in this study was found to be 0.93 mm by solving the following equation:

$${\sigma }_{PWV\left(GNSS\right)\_InSAR}=0.163\ast \sqrt{{\sigma }_{ZHD}^2+({\sigma }_R^2/2)}.$$

(25)

Figure 6 summarizes the observation errors of other kinds of PWV observations and the error of the L-band InSAR PWV estimated in this study. These observation errors are relative errors to the radiosonde observation. In [39], the GNSS error was 3.7 mm, which was the RMSE with 10 radiosonde stations observed for one year in Japan. The radiometer error was 1.29 mm, which was the RMSE against the radiosonde PWV in the US [40]. The Geostationary Operational Environmental Satellite (GOES) error was 2.7 mm, which was the RMSE against the radiosonde PWV in the US [41]. Comparing the estimated L-band InSAR PWV error with those of other techniques, as shown in Figure 6, the L-band InSAR PWV observation showed relatively worse accuracy than others. Nonetheless, the PWV error level of 2.96 mm in the L-band InSAR would be too small for meteorological use as PWV in Japan ranges from 10 to 50 mm in ordinary conditions, and sometimes exceeds 80 mm in extreme weather conditions [43].

We investigated the relationship between the interferometric coherence and the InSAR atmospheric observation accuracy. Although we used InSAR observation values with an interferometric coherence greater than 0.3 to estimate the amount of offset in a specific InSAR scene, we also plotted the absolute values of estimated $R$ with a coherence lower than 0.3. Figure 8 shows the scatterplot of absolute dZTD residuals ($R$) as a function of the interferometric coherence. We also plotted the regression line and the moving average line (the black dashed line and the solid red line in Figure 8) to visually elucidate the relationship between the interferometric coherence and absolute values of estimated $R$. The correlation coefficient between the scatterplot of absolute dZTD residuals and the coherence was −0.27, indicating a weak negative correlation between the residuals and the coherence. If the interferometric coherence is lower, InSAR observation becomes less precise, which may be due to the decorrelation noise.

In addition, we investigated the height dependence of the ZTD residual between InSAR and GNSS. Figure 9 shows the scatter plot of the residuals of all four areas as a function of observation altitude and a fitting line with a correlation coefficient of 0.218. Similar to the relation between the interferometric coherence and absolute values of estimated $R$, we found a weak positive correlation between the elevation and absolute values of estimated $R$. Possible explanations for the existence of this weak positive correlation may be that (1) at higher altitudes (around 1000–2000 m), atmospheric turbulence is more severe and highly variable, and (2) some GNSS stations in mountainous areas were affected by topographic configurations by, for example, blocking lower-elevation microwave paths. However, these possible explanations are only speculation, and the number of samples and survey areas seem to be insufficient to derive any conclusions. Therefore, the height dependence of the ZTD residuals and its mechanism should be further investigated in future works.

6. Discussion

The comparison of different seasons in Figure 7 shows interesting features. ${\sigma }_R$ during the wet season was 1.50 times larger than that during the dry season. This result indicated that in the wet season, when the ZTD was large, the discrepancy between GNSS and InSAR atmospheric observation also increased. Furthermore, the shapes of the histograms in Figure 7 visually suggest that the shape in the wet season deviated further from the fitted Gaussian distribution than that in the dry season. InSAR observations reflect the delay along the line-of-sight (within a narrow tube extended between the satellite and the ground pixel), but GNSS ZTDs reflect the average of the delay within the inverse cone space above GNSS stations. These different characteristics may affect ZTD observation when atmospheric water vapor largely varies over small distances (for instance, orders of from hundreds to thousands of meters). If this difference was a reason that the residual became greater in the wet season than in the dry season, then water vapor may severely fluctuate in the wet season compared to in the dry season.

We evaluated the relative error of the L-band InSAR PWV against the GNSS as 0.93 mm, which was comparatively worse than the C-band InSAR PWV error in previous studies [12,20]. We summarized possible factors of the difference between previous studies and our study as follows: (1) We performed a comparison between GNSS data and a collocated InSAR pixel, but the average of multiple InSAR pixels (for example, the radius of a few kilometers) surrounding GNSS stations was used in previous studies. As our method compared the dZTD of one InSAR pixel (resolution of several hundred meters or larger by multilooking and filtering) with GNSS dZTD, residual pixel-scale noises may affect the error level estimation. Here, note that extending the averaging radius would make the interpretation more complex in terms of the pixel height and the associated stratified delay effect. Especially in mountainous areas, if we set a large radius for averaging, the averaged pixel value would make the InSAR delay value more suitable for the comparison to GNSS in terms of horizontal representativeness but may represent a delay value at a different height due to variable topography height. This causes another problem for the comparison of InSAR and GNSS. Therefore, we need to determine the averaging radius carefully. According to our understanding, both too large and too small radii would be inappropriate, although we do not have an idea of how to determine the radius for averaging. (2) While we removed ${\varphi }_{ion}$ from the total phase differences of the L-band InSAR, it should be noted that our ionospheric correction cannot perfectly remove the effect of the ionosphere, and thus the residual in the ionospheric correction may have had a negative impact on the InSAR PWV error estimation in this study. Previous studies have not removed it as they considered its effect to be negligible as in the case of C-band InSAR, which has a higher microwave frequency and, thus, lower ionospheric phase contamination. (3) Previous studies [12,20] used SAR images acquired during drier seasons than the Japanese summer season. The larger the PWV values are, the larger the InSAR PWV errors might be [42]. On the other hand, there is no difference between the GNSS atmospheric processing in our study and that in the previous two studies. Due to the above-described reasons, the error of L-band InSAR PWV estimated in this study may, to some extent, become larger than the error of C-band InSAR.

We also compared the L-band InSAR PWV error with other PWV observation errors in Figure 6. Contrary to our intuition, the GNSS PWV error was larger than the L-band InSAR PWV error evaluated in this study. Among the reasons for such a contradiction may be that we could not compare the InSAR observation with the radiosonde directly as no available data existed; however, the estimated L-band InSAR error included the GNSS observation error. Therefore, our estimated InSAR error included errors of both the GNSS and the radiosonde, resulting in the tendency towards larger estimation to some extent. Nevertheless, the estimated L-band InSAR PWV error was approximately the same order as other PWV observation errors. In the future, the InSAR PWV error should be directly compared with radiosonde PWV. Another reason for this may be that the GNSS PWV error was derived at the end of the 20th century. Recently, GNSS processing techniques have been further improved, and the number of available GNSS satellites is increasing. Therefore, the GNSS PWV observation would be more accurate than that at the time of the previous study.

We evaluated the relationship between $R$ and the interferometric coherence. In Figure 8, the smaller the interferometric coherence was, the larger the absolute value ($R$) tended to be. Especially in the range of coherence values lower than 0.3, the number of samples was small, and there were some extraordinarily large $R$. Our method did not use pixels with a coherence of less than 0.3 for offset estimation. Therefore, the absolute values of $R$ with a coherence of less than 0.3 tended to largely deviate and may have had bias. It is important to define the threshold of the interferometric coherence appropriately when estimating offsets.

7. Conclusions

We estimated the dZTD distribution using L-band ALOS-2 InSAR data and calculated the residuals between $dZT{D}_{GNSS}$ and $dZT{D}_{InSAR}$ using the error propagation theory. The estimated standard deviation of residuals was 7.36 mm, which was used to estimate the observation error of PWV derived from InSAR data, which was finally found to be 2.96 mm. The estimated L-band InSAR PWV error was comparable to that of other InSAR observations evaluated in previous studies. We investigated the dependences of the observation season and altitude and found that the standard deviation of the residual increased in the wet season, which may be due to the high variability and a larger amount of water vapor in this season. The height dependence was not suggested in our analysis. This study clarified that the InSAR water vapor observation using L-band InSAR has significant accuracy compared to C-band InSAR, which showed its usefulness for the data assimilation into meso-scale weather prediction [7,9,18,44], indicating that L-band InSAR also has the potential for improving the precipitation forecast. At present, there are no experiments on the precipitation forecast using the L-band InSAR data assimilation. In the near future, high-spatial resolution water vapor mapping by InSAR may be utilized for operational meso-scale weather forecasting to enhance its prediction ability, especially against localized severe rainfall. The number of SAR satellites from both governmental space agencies and private companies is expected to increase in the coming decades, and thus, more InSAR data will be available for meteorological applications. The use of high-spatial and -temporal density InSAR data for weather forecasting would improve precipitation prediction for localized heavy rainfall, which is currently difficult to predict accurately, and contribute to mitigating the social damages caused by hydrological disasters related to heavy rainfall.