Comparison of tropospheric delay correction methods for InSAR analysis using a mesoscale meteorological model: a case study from Japan

Abstract

A major source of error in interferometric synthetic aperture radar (InSAR), used for mapping ground deformation, is the delay caused by changes in the propagation velocity of radar microwaves in the troposphere. Correcting this tropospheric delay noise using numerical weather models is common because of their global availability. Various correction methods and tools exist; selecting the most appropriate one by considering weather models, delay models, and delay calculation algorithms is essential for specific applications. We compared the performance of two tropospheric delay correction methods applied to Advanced Land Observing Satellite-2 (ALOS-2) data acquired over Japan, where the atmospheric field is complex with significant seasonal variation. We tested: (1) a method of delay integration along the slant radar line-of-sight (LOS) path using the mesoscale model (MSM) provided by the Japan Meteorological Agency and (2) the Generic Atmospheric Correction Online Service (GACOS) for InSAR, which estimates delay using the high-resolution forecast (HRES)-European Centre for Medium-Range Weather Forecasts (ECMWF) products along with an iterative decomposition approach. The results showed that the tropospheric delay correction using the slant-delay integration approach with MSM, which has a finer temporal and spatial resolution, performed slightly better than GACOS. We further found that the differences in the refractivity models would have limited significance, suggesting that the difference in performance mainly originates from differences in the numerical weather models being used. This study highlights the importance of using the best-available numerical weather model data for tropospheric delay calculations.

Graphical Abstract

Introduction

Satellite-based interferometric synthetic aperture radar (InSAR) provides millimeter-scale measurements of ground surface deformation that can be used to identify surface deformations as well as their temporal variations on land (Massonnet et al. 1993; Bürgmann et al. 2000; Ferretti et al. 2001; Lanari et al. 2004; Colesanti and Wasowski 2006), sub-surface tectonic and anthropogenic processes such as fluid extraction and injection (Bekaert et al. 2017; Campbell et al. 2018; Murray and Lohman 2018), earthquakes, fault modeling (Hamiel and Fialko 2007; Xu and Zhu 2019; Ghayournajarkar and Fukushima 2020; Fukushima and Ishimura 2020), and volcanic inflation and deflation (Hooper et al. 2004, 2007; Gong et al. 2011), among others.

The phase of each pixel of an interferogram is a function of several factors, including surface displacement, orbital geometry of the satellite, topography, delay of the microwave in the atmosphere, and other noise (Massonnet and Feigl 1998). The topographic contributions are accounted for using the digital elevation model (DEM) (Massonnet and Feigl 1998). The orbital inaccuracy creates ramp-type artifacts, which can be corrected by simply removing the ramp assuming a polynomial function or using the long-wavelength displacement field measured by a GNSS network (Bekaert et al. 2016; Takada et al. 2018). Atmospheric delays remain as a major source of errors in InSAR because of the difficulty associated with their correction. Moreover, they often exhibit patterns similar to those due to earthquakes, volcanic activities, and land subsidence, limiting the signal detectability of InSAR (Zebker et al. 1997; Jolivet et al. 2014).

The propagation velocity of microwaves changes as the refractivity varies within the ionosphere and troposphere layers. In the ionospheric layer, the free electron density fluctuations in the ionized atmosphere alter the refractivity. The free electrons interact with electromagnetic waves as a dispersive medium, with inverse effects on the phase and group velocities with stronger effects at lower frequencies such as L-Band ALOS-2 data (Meyer et al. 2006; Wegmüller et al. 2006; Pi et al. 2011). In the tropospheric layer, fluctuations in the temperature, dry pressure, and water vapor pressure alter the refractivity. Tropospheric delay is typically divided into two components based on the physical origin, stratified and turbulent components. Stratified components are highly correlated with topography, affecting mountainous regions. Turbulent components are caused by disturbance processes in the troposphere. The tropospheric delay appears as a function of the refractivity along the path between the satellite and the ground (Shehaj et al. 2020). The state of the atmosphere is generally different at the times when the two images used in InSAR processing are obtained. Consequently, a difference in the amount of delay appears in the interferogram, unrelated to the deformation.

Numerous studies have focused on mitigating tropospheric delay noise using various approaches. The first approach does not use external data; when multiple interferograms are available, noise can be mitigated by stacking or temporal filtering of the InSAR time series to separate tropospheric delay noise from the deformation signal (Ferretti et al. 2001; Hooper et al. 2004). Deriving the relationship between the phase delay and elevation is another simple and effective way to reduce tropospheric noise (Bekaert et al. 2015a; Murray et al. 2021). The second approach uses external datasets, such as meteorological data (Yu et al. 2018a), multispectral satellite imagery data, such as those from the MODerate resolution Imaging Spectroradiometer (MODIS) aboard the Terra and Aqua satellites (Li et al 2005, 2009), and the MEdium Resolution Imaging Spectrometer (MERIS) onboard ENVISAT (Li et al. 2006, 2009), or distributed Global Navigation Satellite System (GNSS) network data (Shamshiri et al. 2020). These two types of approaches can also be used simultaneously.

In the present study, we explored and compared the characteristics of different tropospheric delay correction methods using numerical weather models and evaluated their suitability in Japan. Most of Japan is in a temperate climate zone and exhibits notable seasonal changes. Temperature and humidity are typically high during summer for most of central and western Japan. Since ~ 70% of the Japanese landmass is mountainous, the troposphere above it experiences extensive spatiotemporal variations compared to other places in the world. For these reasons, different tropospheric delay correction methods tend to lead to significantly different outputs, highlighting the importance of choosing a suitable correction method (Bekaert et al. 2015b).

The refractivity models, the weather model dataset, and the delay calculation algorithm should be considered for this comparison. Here, refractivity models refer to mathematical relationships wherein delay is expressed as a function of the dry pressure, partial pressure of water vapor, and temperature of the atmosphere.

The refractivity model proposed by Bevis et al. (1994) (hereafter BV94) is used by the Radar INterferometry Calculation (RINC) software used by the Japanese research community (Ozawa et al. 2016), the model of Berrada-Baby et al. (1988) (hereafter BB88) has been adopted by the Generic Atmospheric Correction Online Service (GACOS) for InSAR (Yu et al. 2018b), and the model of Smith and Weintraub (1953) (hereafter SW53) is used by the open-source package Toolbox for Reducing Atmospheric InSAR Noise (TRAIN) (Bekaert et al. 2015b). There are other refractivity models, such as those proposed by Bevis et al. (1992) or Aparicio and Laroche (2011), but we focused on the models used by widely available software for InSAR tropospheric delay correction in the present study.

As for the algorithm, many studies and software packages, including RINC and TRAIN, calculate the delay along the radar line-of-sight (LOS) direction, whereas GACOS calculates the delay in the vertical direction using an iterative tropospheric decomposition (ITD) method (Yu et al. 2018a), which is later projected into the LOS direction by the users.

As for the dataset, the mesoscale model (MSM), which is published by the Japan Meteorological Agency (JMA), has relatively dense sampling (with horizontal grid spacing of 5 km and temporal resolution of 3 h), is available for the whole area in Japan, and is compatible with the RINC software. On the other hand, GACOS uses the HRES-ECMWF, a 10-day forecast product, which covers the worldwide area with spatial and temporal resolutions of 14 km and 6 h, respectively.

As explained by the diagram in Fig. 1, we made two comparisons, first on the differences in the performance of tropospheric noise correction obtained from the three refractivity models mentioned above (BV94, BB88, and SW53) (“Comparison of the three refractivity models”), and second on those obtained from RINC and GACOS (“Comparison of tropospheric correction of RINC and GACOS”). We made these comparisons on ionospheric-corrected interferograms.

Fig. 1

Framework of this study to perform the comparison of different tropospheric correction methods. BV94, BB88, and SW53 refer to the refractivity models of Bevis (1994), Berrada-Baby et al. (1988), and Smith and Weintraub (1953), respectively

Data and methods

Study area

We selected two areas on Honshu Island, Japan, as the study area (Fig. 2a). The first study area was in the Tohoku region, located in the northern part of the island; the relief in this area consists of plains and mountainous areas (Fig. 2b). Trending north to south, the Ou Mountains greatly influence airflow in the troposphere above it. The mitigation of tropospheric delay in this area is motivated by the fact that this tectonically active zone hosts large earthquakes and volcanoes, including the Mw 6.9 2008 Iwate-Miyagi Nairiku Earthquake (Ohta et al. 2008; Okada et al. 2010). The second study area was in the Kansai region of western Honshu (Fig. 2c); this region has a sharper contrast in topographic relief than the first study area. The region is traversed by major active faults, such as the Arima-Takatsuki, Ikoma, and Uemachi faults. This area also includes the location of the 2018 northern Osaka earthquake (Mw 5.6), a shallow crustal earthquake on the northeastern edge of the Osaka Plain (Kato and Ueda 2019). The tectonic deformation signals expected from the above-mentioned earthquakes and other tectonic processes are less than a few mm; hence, the present study neglected the ground deformation and assumed that the coherent phase changes in the interferograms were mainly due to tropospheric and ionospheric noise.

Fig. 2

a Map of Japan with two study areas shown with red rectangles. a, c Elevation maps for the Tohoku and Kansai regions

InSAR processing

To evaluate the performance of tropospheric delay correction in the study areas, we used SAR images from Advanced Land Observing Satellite-2 (ALOS-2)/Phased Array type L-band Synthetic Aperture Radar (PALSAR-2) in the StripMap (SM1) mode. Detailed information on the SAR observations is summarized in Table 1. For the Tohoku region, we used 10 images from 2014 to 2018 from Path 18, Frame 2830 (descending orbit), and 12 images from 2015 to 2019 from Path 124 and Frame 770 (ascending orbit); the incidence angles were 35.9° for both datasets. We used 12 images from 2015 to 2019 from Path 128 and Frame 680 (ascending) for the Kansai region, with an incidence angle of 38.2°.

Table 1 SAR images information for the Tohoku and Kansai regions

An interferogram is calculated from a pair of SAR images by taking the difference between the phases of the first (primary) and second (secondary) acquisitions to measure the surface displacement that occurred between acquisitions in the LOS direction as well as atmospheric delay effects and other noise terms. We processed the interferograms for each study area using the RINC software (Ozawa et al. 2016) with range and azimuth look numbers of 8 and 10, resulting in a spatial resolution of approximately 20 × 20 m. A spectrum filter with a 32 × 32-pixel window size was applied to reduce decorrelation (Baran et al. 2003). We used ellipsoidal height data generated from a 10-m mesh digital elevation model, published by the Geospatial Information Authority of Japan (GSI), and the Earth Gravitational Model 96 (EGM96) geoid model (Lemoine et al. 1997) to remove topographic fringes and geocode the interferograms. The differential phase values were unwrapped using Statistical-Cost, Network-Flow Algorithm for Phase Unwrapping (SNAPHU) (Chen and Zebker 2000).

Tropospheric correction methods

Slant delay integration

The total tropospheric delay can be estimated by integrating the delay along the propagation path of the microwave in the slant LOS direction (Additional file 1: Fig. S1). The total tropospheric delay is calculated in the straight line from topography to the upper limit of the tropospheric layer. The geometric delay due to the bending effect was not considered in this study (Ozawa et al. 2019). The slant-delay integration method generally involves three processing steps. The first step is to resample meteorological data to a regular latitude-longitude-height grid. The next step is the interpolation of the data along the path, and the final step is the integration of refractivity from ground $({r}_{1})$ to the upper limit of troposphere (${r}_{2})$, using the following general equations (Hanssen 2001):

$$N = N_{\text{dry}} + N_{\text{wet}} = \left( {k_{1} \frac{P}{T}} \right) + \left( {k_{{2}} \frac{e}{T} + k_{{3}} \frac{e}{{T^{{2}} }}} \right)$$

(1)

$$\Delta L = 10^{ - 6} \int_{{r_{1} }}^{{r_{2} }} {\left[ {Nds} \right]} = 10^{ - 6} \left[ {\mathop \smallint \limits_{{r_{1} }}^{{r_{2} }} \left( {k_{1} \frac{P}{T} + k_{2} \frac{e}{T} + k_{3} \frac{e}{{T^{2} }}} \right)ds} \right]$$

(2)

where N is the refractivity index, ΔL is the total delay, $P$ is the dry pressure of the atmosphere, $T$ is the temperature, and $e$ is the partial pressure of the water vapor. Different values of the constants ${k}_{1}$,${k}_{2}$, and ${k}_{3}$ have been proposed in different refractivity models (Table 2).

Table 2 List of the coefficients for each refractivity model

In this study, we used the RINC software (Ozawa et al. 2016) to read and resample MSM data. We then computed the delay after linear interpolation of the data and applied Eqs. 1 and 2 with different constant values. The sets of constants ${k}_{1}$, ${k}_{2}$, and ${k}_{3}$ corresponding to the models of BV94 (used by RINC), BB88 (used by GACOS), and SW53 (used by TRAIN) were used to calculate the delay (Table 2) and the results are compared in “Comparison of the three refractivity models”:

GACOS method

Yu et al. (2018a) proposed a method to incorporate delay data estimated using GNSS data into numerical weather model data. The authors provided a GACOS correction that delivers delay estimates computed by the method, although the website (http://www.gacos.net, last accessed on 9 September 2022) stated that only the numerical weather model is used. GACOS uses the HRES-ECMWF numerical weather model, which has a grid spacing of 0.125° with 137 vertical levels and temporal sampling of 6 h. To better estimate the stratified and turbulent delay components, GACOS uses the iterative tropospheric decomposition (ITD) method (Yu et al. 2018a). For the refractivity model, GACOS uses the equation proposed by Berrada-Baby et al. (1988), neglecting the bending effect, which is as follows:

$${\text{ZTD}} = 10^{ - 6} \mathop \smallint \limits_{{r_{1} }}^{{r_{2} ^{\prime}}} \left[ {Ndz} \right]{ } = 10^{ - 6} \left[ {\frac{{k_{1} R_{1} }}{gm}P_{{\left( {Z0} \right)}} + \mathop \smallint \limits_{{r_{1} }}^{{r_{{2{^{\prime}}}} }} \left( {k_{2} ^{\prime}\frac{e}{T} + k_{3} \frac{e}{{T^{2} }}} \right)dz} \right]$$

(3)

where the integral is calculated vertically between the ground surface, ${r}_{1}$ and upper boundary of the troposphere (or the height above the ground), r₂′. ${P}_{(Z0)}$ is the surface pressure at the topography, ${R}_{1}$ is the ideal gas constant, $gm$ is the gravitational acceleration averaged over the troposphere, and ${k}_{1}$ and ${k}_{3}$ are the same constants as defined in Eq. 2. The constant k₂′ is related to ${k}_{2}$ with k₂′ $={k}_{2}-0.622{k}_{1}$ (Berrada-Baby et al. 1988). The ZTD was projected to the LOS direction, and the bending effect was neglected.

Results

Interferograms with ionospheric correction

L-band interferograms are often severely affected by ionospheric disturbances. The ionospheric noise in the original interferograms is depicted as irregular fringes (Additional file 1: Figs. S2a, S2b, and S3). The application of the split-spectrum method (Gomba et al. 2015) effectively mitigated the ionospheric noise in the two study areas, shown as flattened fringe patterns in the interferograms (Fig. 3, Additional file 1: Fig. S4, and S5).

Fig. 3

Examples of ionosphere-corrected descending interferograms obtained using the split-spectrum method for the Tohoku region. The acquisition dates are shown above each interferogram. The incoherent pixels with a coherence threshold < 0.12 were masked in this figure

We calculated the standard deviation of each of the 51 interferograms, before and after the corrections, to assess the performance of the ionospheric correction method (Additional file 1: Tables S1, S2, and S3). If the standard deviation decreased after the correction, it means that the correction was effective. After applying the ionospheric corrections, the mean standard deviation of the interferograms decreased from 2.33 to 1.19 cm for the Kansai ascending dataset, 2.97 to 1.71 cm for the Tohoku ascending dataset, and 3.42 to 0.87 cm for the Tohoku descending dataset. We also assessed the spatial correlation of noise before and after the correction using a semi-variogram, a regression curve of semi-variogram at different distances (Liebhold et al. 1991). The semi-variogram is defined as the following equation:

$$\gamma \left( h \right) = \frac{1}{2N\left( h \right)}\mathop \sum \limits_{i = 1}^{N\left( h \right)} \left[ {Z_{{x_{i} }} - Z_{{x_{i} + h}} } \right]^{2}$$

(4)

where ${Z}_{{x}_{i}}$ is the observation value at the $i$-th location ${x}_{i}$, ℎ is the distance, and N(h) is the number of point pairs at that distance. Semi-variograms showed that the long-wavelength variations were significantly reduced by ionospheric correction (Additional file 1: Fig. S6). For the remainder of this paper, we have used ionospheric-corrected interferograms to evaluate tropospheric delay corrections.

Comparison of the three refractivity models

Tropospheric delays were predicted using the Bevis (1994) (BV94), Smith and Weintraub (1953) (SW53), and Berrada-Baby et al. (1988) (BB88) models. The difference between BV94 and SW53 is the value of the constant, and the difference between BV94 and BB88 is in the hydrostatic component calculations.

We used an identical MSM dataset to compare tropospheric correction terms estimated from the three refractivity models. In this experiment, we adopted the slant range integration method (“Slant delay integration”). Since the RINC software can only be used with the BV94 model, we programmed a code whose algorithm (except for the refractivity model) is the same as RINC and used it to make the calculations assuming the three refractivity models. Our codes were verified to produce results identical to the RINC outputs, with a difference of less than 0.01 mm.

Examples of the delay calculation results of the Tohoku and Kansai regions are shown in Figs. 4 and 5 and Additional file 1: Figs. S7 and S8, respectively. In these figures, a darker color indicates a smaller delay in higher-altitude areas and thus reflects a shorter propagating path. In some cases, the estimated tropospheric delay in a single epoch could exceed 3 m, indicating a significant tropospheric effect. The correction term for InSAR tropospheric delay was calculated by subtracting the delay of the primary acquisition from that of the secondary acquisition. Results indicated that the calculated correction terms in both study areas were up to 24 cm for all refractivity models; differences in the correction terms ranged up to a few centimeters. The variation in the differences within a scene, which is directly related to the difference in the effectiveness of the correction, was even smaller (0.55–1.55 cm) in the example shown in Fig. 6.

Fig. 4

Examples of tropospheric delay predicted in the Tohoku region obtained using the slant-delay integration method from the refractivity models of Bevis (1994) (top), Smith and Weintraub (1953) (middle), and the differences between the two models (bottom). a Delay predicted for the primary image obtained on 19 May 2016. b Delay predicted for the secondary image obtained on 16 June 2016. c Correction term calculated by the difference in the delay on the two acquisition dates

Fig. 5

Examples of tropospheric delay predicted in the Tohoku region obtained using the slant-delay integration method from the refractivity models of Bevis (1994) (top) and Berrada-Baby et al. (1988) (middle) and the difference between the two models (bottom). a Delay predicted for the primary image. b Delay predicted for the secondary image. c Correction term calculated by subtracting the delay on the two acquisition dates. The acquisition dates are identical to those shown in Fig. 4

Fig. 6

a Examples of corrected interferograms obtained using the models of Bevis (1994) and Smith and Weintraub (1953) in the Tohoku region. b Examples of corrected interferograms obtained using the models of Bevis (1994) and Berrada-Baby et al. (1988) in the Tohoku region. The acquisition dates are identical to those shown in Fig. 4

Differences were statistically evaluated by calculating the mean standard deviation over the entire interferogram of all the tested interferograms. The standard deviation among the three refractivity models shows minor differences (Additional file 1: Figs. S9 and S10), but the BV94 model produced the lowest mean standard deviation (Table 3). In the Kansai region, tropospheric corrections using the models of BV94, BB88, and SW53 reduced the standard deviation from 1.19 to 1.09, 1.09, and 1.09 cm, respectively. This result indicated that tropospheric correction using the aforementioned method is effective, and the difference in the mean standard deviation after corrections was less than 0.01 cm, which is consistent with the findings of a study by Aparicio and Laroche (2011), who found that the differences between their refractivity model and other models, including BV94 and SW53, were within 0.1% RMS (root mean square). Similarly, tropospheric noise correction using the three models all reduced the mean standard deviation from 0.87 to 0.78 cm in the Tohoku region.

Table 3 Mean standard deviation of interferograms, before and after correction

Comparison of tropospheric correction of RINC and GACOS

We compared the tropospheric correction products derived from the RINC (Ozawa et al. 2016) and GACOS (Yu et al. 2018a). The RINC calculates delay along the slant direction connecting the ground and satellite using the equations provided by the refractivity model BV94 and the MSM data of JMA. The GACOS adopts the zenith integration approach and uses the HRES-ECMWF and the refractivity model of BB88.

Figure 7 shows the absolute delay distributions obtained using the RINC and GACOS methods. In most cases, RINC predicted a greater delay and less detailed topographical variation than GACOS, with differences of up to 4 cm (Fig. 7).

Fig. 7

Correction terms from RINC and GACOS and the differences between the two methods were calculated for two interferograms in the Tohoku region. The acquisition dates are shown on the left side of the figures

The RINC and GACOS correction products were compared by calculating the tropospheric noise term (i.e., the difference between the delays of the first and second acquisitions) and subtracting it from the ionosphere-corrected interferogram, as shown in Fig. 8. The results showed that both methods reduced the tropospheric delays in 68% of the interferograms in both areas; however, a significant amount of tropospheric noise was still present in the corrected interferograms. We statistically assessed the performances of the RINC and GACOS methods. In most interferograms, correction reduced the standard deviation of the LOS displacements, but this was not always the case (Fig. 9). Tropospheric correction was effective in mountainous areas (i.e., stratified components) but not in flat areas (i.e., turbulent components) (“Evaluation of tropospheric delay in mountainous and flat areas”). The mean standard deviation of all interferograms in the Tohoku region decreased from 0.87 to 0.78 cm for both correction methods. The assessment of the Kansai region data led to a slightly different result; the mean standard deviation decreased from 1.19 to 1.09 and 1.10 cm after applying the RINC and GACOS corrections, respectively, indicating a slightly better performance from the RINC correction.

Fig. 8

a Example of an ionosphere-corrected interferogram in the Tohoku region. b Interferogram with GACOS correction applied on a. c Interferogram with RINC correction applied on a. The decorrelated parts shown in these interferograms were excluded from the statistical comparison. The primary image was obtained on January 15, 2015. The secondary image was acquired on February 12, 2015

Fig. 9

Standard deviations after tropospheric corrections using RINC and GACOS in the two study areas plotted against the standard deviations before the tropospheric corrections (reference). Marks below the broken line (standard deviations before and after correction are equal) indicate that the corrections worked as expected

Discussion

Evaluation of tropospheric delay corrections in the Tohoku and Kansai regions

The Kansai and Tohoku regions analyzed in the present study had different conditions depending on topographic relief (Fig. 2b, c), atmospheric conditions during the acquisition time, and coherence of the interferogram data. Therefore, the effectiveness of these corrections was expected to vary. The mean standard deviation of signals before tropospheric correction in ascending interferograms in the Kansai region was smaller than that in the Tohoku region, as shown in Table 3.

The effectiveness of the tropospheric delay correction was at a similar level for the two regions if the same correction software (RINC or GACOS) was used. With respect to different topographical features, it is possible that the effectiveness of the correction may be different in mountainous and flat areas, as discussed further in “Evaluation of tropospheric delay in mountainous and flat areas”.

Evaluation of tropospheric delay in mountainous and flat areas

Mountainous areas contain both stratified and turbulent components of tropospheric delay, while flat areas contain only a turbulent component. This section separately focuses on the flat and mountainous areas and compares them (Additional file 1: Fig. S11). Similar to what has been found in previous studies, our results showed higher standard deviations in mountainous areas (Table 4) (Yu et al. 2018b). In the Kansai region, tropospheric correction improved the interferogram by reducing the mean standard deviation from 0.98 to 0.89 cm in mountainous areas; the mean standard deviation decreased from 0.29 to 0.25 cm in the plains. In the Tohoku region, the mean standard deviation decreased from 1.37 to 1.30 cm for ascending interferograms and 1.71 to 1.53 cm for descending interferograms by tropospheric correction in the mountainous areas. In the flat areas in Tohoku, the mean standard deviation decreased from 0.49 and 1.14 cm to 0.47 and 0.92 cm for ascending and descending interferograms, respectively. Based on these results, it can be concluded that: (1) tropospheric delay is more substantial in mountainous areas, (2) tropospheric correction is more effective in mountainous areas, and (3) correction is imperfect yet effective in the flat areas.

Table 4 Mean standard deviation of mountainous and flat areas in interferograms

Comparison of atmospheric delay on ascending and descending interferograms

Atmospheric conditions over the same areas vary significantly with time. This study compared atmospheric delays in the ascending and descending interferograms in the Tohoku region. Ascending and descending interferograms were acquired at 11:42 and 23:58 local time, respectively. Table 3 shows the values of the mean standard deviation before correction, i.e., 1.71 cm and 0.87 cm for ascending and descending interferograms, respectively, indicating greater noise in the ascending interferograms. The tropospheric delay correction reduced the mean standard deviation of both the ascending and descending interferograms (Table 3) but still indicated the presence of greater noise in the ascending interferograms. In the ascending interferograms, after corrections (Additional file 1: Fig. S4), long-wavelength noise and altitude did not have a direct correlation. We infer that this is mainly due to greater difficulties for the numerical weather model in reproducing turbulence around noon local time.

Comparison with other studies

Stephens et al. (2020) found that the applicability of the correction method is highly case-dependent, showing there is no global weather model that can accurately capture the tropospheric delay. In our study, the tropospheric correction reduced the standard deviation up to 33% in 68% of interferograms in the Tohoku region and up to 41% in 66% of interferograms in the Kansai region (Additional file 1: Tables S1, S2, S3). These results showed that the corrections using RINC and the MSM weather model are as effective as the case studies over the Usu volcano in Japan that successfully reduced standard deviation in 45% of the interferograms using the GACOS product (Wang and Aoki 2019). The reduction in the standard deviation varied from approximately 35% to 45% over the Agung Volcano in Bali, Indonesia, which was obtained using GACOS with HRES-ECMWF data (Albino et al. 2019) and is comparable to our results. Our results using GACOS, reducing the standard deviation up to 40% in 73% of interferograms, indicate better performance than other studies that indicated insignificant improvement using GACOS (Guo et al. 2019). This suggests that the approach of using numerical weather models is effective over Japan.

Conclusions

This study confirmed that ionospheric delays heavily impact ALOS-2 L-band interferograms in Japan and that the mitigation of ionospheric delays works effectively using the split-spectrum method.

Tropospheric correction using three models—Bevis (1994), Berrada-Baby et al. (1988), and Smith and Weintraub (1953)—was applied to 51 interferograms in 2 different regions. Performance assessment of the three refractivity models showed insignificant differences in mean standard deviation and semi-variance. We concluded that all three refractivity models can be used to calculate tropospheric delay.

Tropospheric correction terms obtained using the RINC and GACOS methods showed differences up to 4 cm, and the mean standard deviation after RINC correction in the two studied areas was slightly smaller than the GACOS result; this indicates a slightly better performance of RINC correction. This can be either due to the use of the MSM mesoscale model, which has higher temporal and spatial resolutions or to the difference in the calculation scheme.