J. Cent. South Univ. (2020) 27: 997-1011

DOI: https://doi.org/10.1007/s11771-020-4348-4

A review of underlying topography estimation over forest areas by InSAR: Theory, advances, challenges and perspectives

XIE Yan-zhou(лÑãÖÞ), ZHU Jian-jun(Ö콨¾ü), FU Hai-qiang(¸¶º£Ç¿), WANG Chang-cheng(Íô³¤³Ç)

School of Geosciences and Info-Physics, Central South University, Changsha 410083, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract: The paramount importance and multi-purpose applications of underlying topography over forest areas have gained widespread recognition over recent decades, bringing about a variety of experimental studies on accurate underlying topography mapping. The highly spatial and temporal dynamics of forest scenarios makes traditional measuring techniques difficult to construct the precise underlying topography surface. Microwave remote sensing has been demonstrated as a promising technique to retrieve the underlying topography over large areas within a limited period, including synthetic aperture radar interferometry (InSAR), polarimetric InSAR (PolInSAR) and tomographic SAR (TomoSAR). In this paper, firstly, the main principle of digital elevation model (DEM) generation by InSAR and SAR data acquisition over forest area are introduced. Following that, several methods of underlying topography extraction based on InSAR, PolInSAR, and TomoSAR are introduced and analyzed, as well as their applications and performance are discussed afterwards. Finally, four aspects of challenge are highlighted, including SAR data acquisition, error compensation and correction, scattering model reconstruction and solution strategy of multi-source data, which needs to be further addressed for robust underlying topography estimation.

Key words: underlying topography; microwave remote sensing; InSAR; PolInSAR; TomoSAR

Cite this article as: XIE Yan-zhou, ZHU Jian-jun, FU Hai-qiang, WANG Chang-cheng. A review of underlying topography estimation over forest areas by InSAR: Theory, advances, challenges and perspectives [J]. Journal of Central South University, 2020, 27(4): 997-1011. DOI: https://doi.org/10.1007/s11771-020-4348-4.

1 Introduction

Digital elevation model (DEM) is used to depict the shape of bare Earth and plays a significant role in geohazard prediction, flood inundation simulation and natural resource management [1, 2]. Nevertheless, over the forest covered area, large-scale (global, national and regional) underlying (sub-canopy) topography data with high-accuracy and high-resolution are still unavailable. With the development of remote sensing technique, although spaceborne and airborne light detection and ranging (LiDAR) systems can measure underlying topography, due to the very low-resolution and limited coverage, the obtained DEM data are not applicable in many applications. Optical photogrammetry technique, with the characteristics of high resolution, large coverage and high accuracy, is another powerful tool for topography mapping, but it can only measure the elevation on the forest layer surface, without the ability to detect the underlying topography. To remove forest height signals from DEM produced by the optical photogrammetry, artificial field working or artificial estimation by the height difference between forest boundaries and their neighboring bare ground is often required to estimate the average forest height, which will be subtracted from the corresponding DEM data. Such methodology has low efficiency and yields poor accuracy over forest covered areas where it is difficult to truly capture the precise terrain information under forest canopy as shown in Figure 1 [3]. Hence, more advanced methodologies need to be developed to, directly or indirectly, construct underlying topographic map over forest covered area, which is of paramount importance for obtaining high-accuracy DEM product on a large scale.

Interferometric synthetic aperture radar (InSAR) has been proved to be one of the most effective techniques for topographic mapping on regional or global scale due to its characteristics of end-to-end coverage, high-resolution, high-accuracy, all-weather monitoring [4, 5]. Operating with microwave signal, which can penetrate through the forest layer and has been the core competitiveness compared to optical remote sensing, InSAR is capable of detecting the forest vertical structure as well as the sub-canopy ground surface, and therefore outperforms over other traditional techniques in terms of underlying topography retrieval [6, 7]. Nevertheless, instead of directly ¡°seeing¡± the ground surface, the traditional InSAR measures the elevation corresponding to the scattering phase center height, which is located between the top of the forest canopy and the ground surface. The essential reason for this is that traditional InSAR, limited by insufficient observations, cannot support specific scattering model to separate the canopy and ground scattering contributions so that the location of realistic scattering phase center of underlying topography height is still ambiguous, plaguing the accurate underlying topography extraction [8]. Hence, the basic idea to achieve the underlying topography mapping is to remove the forest bias precisely and thoroughly. To that end, three types of methodologies based on adding a priori information or expanding the observation space have been developed with or without physical scattering models. The first type is based on single- polarization InSAR acquisitions, and can be divided into two groups according to different methods used to cancel the forest-layer influence. One part of methods is based on the direct subtraction of forest height product obtained by InSAR inversion itself or external auxiliary data [2, 6, 9], while the other part introduces the time-frequency analysis (TFA) [3, 10, 11], without the need to generate forest height product. The second type of methodology utilizes polarimetric InSAR (PolInSAR) acquisitions, which can be divided into three subsets. Among them, coherence optimization- based phase separation method, as the simplest way to distinguish the different scattering phase centers, is independent on specific scattering model [8, 12-14]. On the other hand, scattering model- based inversion methods [15, 16] and the polarimetric decomposition methods [17, 18] rely on scattering model to characterize the scattering process of microwave signal in complicated forest scenes. The third type of methodology to eliminate the forest bias is tomographic SAR (TomoSAR) [19], which is relied on multi-baseline InSAR/ PolInSAR dataset.

This article aims to present a systematic introduction to underlying topography mapping by analyzing the above-mentioned topography extraction methodologies along with the research status, which is organized as follows. In Section 2, the InSAR theory and development status are introduced. The methodologies and their applications for underlying topography retrieval are analyzed and discussed in Section 3. In Section 4, we introduce the challenges of underlying topography surveying, followed by our conclusions in Section 5.

Figure 1 Schematic of uncertainties and ambiguities in underlying topography mapping with traditional measuring techniques

2 Theory and current status of InSAR for underlying topography mapping

2.1 Basic InSAR theory

As an active microwave remote sensing technique, synthetic aperture radar (SAR) through transmitting and receiving the electromagnetic wave signal, records the intensity and phase information of the echo signal. During this process, shape, orientation and dielectric characteristics of the illuminated scatterers are recorded by the intensity and phase information. Integrated by SAR imaging theory and interferometry, InSAR employs two complex-valued SAR images with slightly different incidence angles to obtain more information about the illuminated target by exploiting the interferometric phase and coherence [20]. When two SAR sensors illuminate a given target at different incidence angles, interferometric processing for the acquired two SAR images (master and slave) can be utilized to measure the elevation [20], as shown in Figure 2(a). In particular, over forested areas, since the forest scatterers distribute along the vertical direction, they will be projected to the line of sight associated with the two SAR images in different ways. As a result, this phenomenon causes volume decorrelation, which reduces the interferometric coherence and elevates the interferometric phase center.

Although InSAR utilizes the geometric relationship between the two images combined with system parameters to accurately measure the spatial position of a point and monitor its subtle deformation, the lack of observation information makes it only able to measure the combined height of phase center of multiple scatterers in a given resolution pixel, and cannot distinguish the vertical distribution of certain scatterers, such as the top of canopy or the underlying surface. In view of this, polarimetry has been combined with traditional InSAR to form polarimetric synthetic aperture radar interferometry (PolInSAR) [8, 21]. Polarimetric SAR expands the observation space from single- polarization channel to dual- or full-polarization acquisitions, i.e., HH, HV, VH and VV channel, as shown in Figure 2(b). Based on the fact that polarized waves signals in different polarization states have different levels of sensitivity to the geometric information (e.g., shape, size, and spatial distribution) and physical property information (e.g., dielectric constant) of the scattering target, polarimetric SAR is capable of interpreting and characterizing the scattering mechanisms of the targets and discriminating different target components within the same resolution cell [16]. Combined with SAR interferometry, PolInSAR can be used to quantitatively investigate the scattering mechanisms and their location along the vertical direction [21]. Following this, we are able to consider the retrieval of forest structural parameters and the underlying topography information.

Different from transforming the polarization states, TomoSAR depends on expanding the observation space by increasing the number of baselines (Figure 2(c)), which is another viable strategy to make conventional InSAR capable of distinguishing different scatterers within the same resolution cell and thus removing the vegetation bias. To be more specific, integrating InSAR theory and the spectrum analysis, TomoSAR forms a second synthetic aperture in the normal direction perpendicular to the line-of-sight and azimuth directions [19]. Accordingly, the traditional two- dimensional imaging is extended to three- dimensional imaging, making TomoSAR able to separate different scattering targets within a given resolution pixel and subtly characterize the structural variation of forest scenario along the vertical direction.

Figure 2 Schematic representation of InSAR height estimation:(H denotes flight altitude of sensor; R represents distance between radar and target point referred to as slant range; h is elevation of scattering point and S denotes radar signal. The baseline configuration can be characterized by spatial baseline B, incidence angle ¦È, and baseline inclination ¦Á)

2.2 InSAR systems for underlying topography mapping

Due to the inappropriate spatial and temporal baselines as well as the wavelength limitations, dedicated campaign for underlying topography estimation has not been carried out based on spaceborne SAR systems. Nevertheless, airborne SAR systems, characterized by low development and maintaining costs and flexible operation, have been widely used in simulations and demonstrations for spaceborne missions. Currently operating and some past sensors mainly include AIRSAR, E-SAR, GEO-SAR, RAMSES-SAR, F-SAR, UAVSAR, PI-SAR1/2, CASM-SAR, CET38-SAR, and SETHI-SAR [3]. Over recent decades, a large number of airborne campaigns have been carried out exploiting these sensors over different forest covered areas. Explicit conclusions have been made from the investigations on forest parameter inversion that L- and P-band SAR acquisitions contain much more valuable information about the forest vertical structure and the sub-canopy terrain because of their strong penetration ability, which is more advantageous than the short-wavelength SAR in the forest parameter and underlying topography extraction [22-27]. In addition, the temporal variability of the polarimetric and interferometric characteristics at low frequency related to environmental conditions has been well investigated resorted to the flexible scheduling of airborne systems, which offers significant guidance for temporal baseline design of spaceborne system.

Providing the spaceborne platforms, the existing spaceborne SAR sensors are characterized by multi-band and multi-polarization acquisitions, as well as high spatial and temporal resolution. Despite this, the main problem that existing sensors face with is that they cannot simultaneously take into account the strong penetrability, the suitable spatial interferometric configuration, and the short imaging interval that small enough to suppress the impact of temporal decorrelation on interferometry. On the one hand, the ideal acquisition mode is to configure zero temporal baseline for performing topographic mapping. To that end, under the framework of shuttle radar topography mission (SRTM) in 2000, dual-antenna SAR sensor has been equipped in a space shuttle to successfully acquire DEM products in 30 m/90 m resolution covering 80% of the world [4]. Moreover, TerraSAR-X (2007) and TanDEM-X (2010) satellites have been launched successively to construct a formation flight, in which the instruments have ability to image the same target simultaneously and produce a global DEM in 12 m resolution [5]. In addition, considering the band selection and well interferometric condition, BIOMASS mission, which will be the first spaceborne P-band radar and bring about unprecedented opportunities to learn about the Earth and its dynamics, has been selected by European Space Agency (ESA) as the 7th Earth Explorer mission and will be launched in 2022 [28-30]. Furthermore, the German Space Agency (DLR) is expected to launch the L-band satellite formation TanDEM-L also in 2022, which acquires data with zero temporal baseline in bistatic mode [31-33]. Both two future missions will provide massive data suitable for operational underlying topography mapping and have planned underlying topography retrieval as one of the target scientific objectives.

3 Methodologies for underlying topography estimation

3.1 InSAR-based (single-polarization) inversion methods

As introduced above, the main challenge of traditional InSAR technique for underlying topography extraction is how to effectively remove the forest bias hidden in the inversed InSAR height. Basically, two strategies have been proposed and validated, including direct subtraction of forest height from DEM products gained from InSAR or optical remote sensing, and, on the other hand, time-frequency analysis (TFA) based on sublook decomposition.

For the first strategy, the performance strongly depends on the accurate forest height products to ensure that the inversion results based on the differential relationship are reliable. Currently, effective forest height mapping can be achieved by InSAR-only methods relied on coherent scattering model, and the hybrid methods exploiting the synergies of fusing InSAR and LiDAR, which has their own respective advantages and disadvantages in extracting large-scale forest height.

To inverse forest height by only InSAR observations, several scattering models have been developed to depict the scattering process and relate the InSAR observations to forest parameters (underlying ground phase, forest height, canopy extinction and ground-to-volume amplitude ratio). Among them, the most widely adopted model, the random volume over ground (RVoG) model, simplifies vegetated scenarios as two layers, i.e., the ground surface and the vegetation volume layer where the isotropic particles randomly distribute over ground [6, 7]. Due to the inadequate observations of InSAR data to solve the RVoG model, however, parts of the model parameters need to be determined as known information by other ways, or simplifications or modifications of the models have to be applied to perform forest height estimation with single-polarization InSAR acquisition. The widespread accepted simplified version of the RVoG model is the SINC model, which approaches the model extinction to zero and further assumes the null ground-to-volume amplitude ratio [16]. Moreover, some adaptations of SINC model have been proposed and comprehensively evaluated with respect to their performance when operated in distinct forest conditions and with different seasonal acquisitions [34-38]. It terms out that the inversion performance is closely related to the authenticity and validity of the model assumptions, where in the worst case, inversion may almost fail due to the loss of sensitivity of InSAR coherence to forest height variation.

Considering the InSAR/LiDAR fusion methods, LiDAR measurements are mainly used to provide a priori information for solving the scattering model, or as a training set for machine learning prediction model. QI et al [39, 40] explored the potential synergy of combining TanDEM-X InSAR data and simulated NASA Global Ecosystem Dynamics Investigation (GEDI) LiDAR acquisitions. Moreover, for operational applications, LEI et al [41] utilized ALOS-1 InSAR coherence data and a small airborne LiDAR strip to generate large-scale moderate-resolution mosaics of forest height over the state of Maine and New Hampshire, while HUANG et al [42] created a finer-resolution forest height map at a resolution of 30 m in China using ICESat/GLAS, ALOS PALSAR and Landsat Data. Both two large-scale forest maps have been validated and the root-mean-square errors (RMSE) are in the order of 3-4 m. Although large-scale forest height can be acquired feasibly, another potential limitation comes from the resulting height of InSAR DEM, which is associated to the effective phase center of mixed scatterers within a given resolution pixel, and not located on the surface of the canopy layer due to various degrees of penetration. Penetration depth is significantly diverse both in time and space, and affected by forest density, moisture, and terrain slope, increasing the ambiguity of underlying topography extraction by direct subtraction methods. This ambiguity, to some extent, can be reduced by introducing the penetration depth model to compensate InSAR height [43], which requires further evaluation to guarantee the stability of this strategy.

For the second strategy, the TFA is in principle based on sublook decomposition technology to obtain various sublook images with different azimuth observation angles, without depending on external data sources or methods [10]. Due to the heterogeneity of forest, presenting anisotropy in space, the backscatter acquisitions under different viewing conditions are different when the SAR sensor observes the same forest scene from different angles, leading to variation of phase center and ground-to-volume amplitude ratio for different sublook images. The sublook signal containing the strongest ground scattering contribution will be selected, whose phase center is assumed to be located on the ground surface, so as to realize the estimation of underlying topography. While TFA does not require any external data, a priori information, and even scattering models to achieve the underlying topography retrieval, the accuracy of this method may constrained by the penetration depth of the microwave signal in forest area, and therefore, it is only applicable to the topography extraction with P-band data and over sparse-forest covered area. In order to eliminate this limitation, the TFA method has been combined with the RVoG model to identify more pure ground scattering contribution [3]. One problem needs to be carefully considered is that, in the case of spaceborne InSAR data with small variation in azimuth observation angle, which may result in ill-conditioned problem, how to use the TFA method combining with the RVoG model to well estimate pure ground scattering needs to be further investigated.

3.2 PolInSAR-based inversion methods

SAR signals in different polarizations have different sensitivity levels to the geometric and physical characteristics of scattering targets [16]. For instance, SAR signals in HV and HH polarizations are sensitive to volume scattering from canopy and ground scattering, respectively. As a result, the phase centers of SAR signals in HH polarization are closer to ground surface than those of SAR signals in HV polarization. However, although SAR signals in HH polarization record significant ground scattering contributions, they still contain significant forest height signals. To solve this problem, by transforming polarizations according to polarimetric coherence optimization theory, we can extract more pure ground scattering contributions from PolInSAR data [8, 44]. As a result, we can obtain DEM product containing less forest height signals than that derived by the InSAR technique in HH polarization [12-14]. Nonetheless, we still cannot obtain or separate the pure ground scattering contributions from PolInSAR signals because the polarimetric coherence optimization theory has not consider the strict relationship between the scattering process of PolInSAR and the vegetation biophysical parameters.

To better describe the effect of biophysical parameters on PolInSAR scattering process, the RVoG model has been proposed, which models the vegetation area as a homogeneous volume layer and an impenetrable ground surface [6, 7]. As stated above, the RVoG model correlates the SAR observations (coherence) to forest parameters but cannot be solved by only single-polarization InSAR acquisition without further assumption or approximation. PAPATHANASSIOU et al [15] first introduced PolInSAR observations and combined with the RVoG model to achieve the simultaneous inversion of underlying topography and other vegetation parameters. Afterwards, a huge number of researches on forest parameter inversion have been carried out at various frequencies and under different topographic conditions as well as different vegetation types. When the RVoG model are employed to invert forest parameters from repeat-pass PolInSAR data, one important factor should be considered is the temporal decorrelation, which will distort the relationship between the PolInSAR scattering process and biophysical parameters, and bias the ground phase estimation. To solve this limitation, the RVoG model with temporal decorrelation (RVoG+TD) model, for example, is constructed to take into account the influence of dielectric constant changes and wind-induced temporal decorrelation on interferometry over vegetation covered area [45]. To further consider the wind-induced temporal decorrlation, the random motion over ground (RMoG) model is proposed, which is formulated by the assumption that wind-induced decorrelation would vary with forest height [46, 47]. In addition to the temporal decorrelation, another error source in parameter inversion process comes from the terrain slope effect, in which the S-RVoG model [48, 49] is utilized to compensate the influence of terrain slope on the penetration depth of microwave signal in vegetation layer. Furthermore, the three-layer RVoG model [18], the gaussian vertical backscatter (GVB) model [50, 51], the RVoG with varying extinction model [50, 52] as well as oriented volume over ground model [16] are used to reduce the impact caused by the heterogeneity of the vertical structure in vegetation layer. Although the slope effect and the heterogeneity may not lead to remarkable impact on ground phase inversion, they will significantly limit the accuracy of vegetation height estimation, which is not beneficial for us to obtain accurate forest height, which can also be used to estimate underlying topography as the method demonstrated in Section 3.1. The above RVoG model-based methods are mainly designed for volume decorrelation observed by repeat-pass PolInSAR system. For PolInSAR system working in bistatic configuration, such as the TanDEM-X system, whose PolInSAR observations are free from the temporal decorrelation, the RVoG model should be reconstructed to consider the different phase centers of surface and double-bounce scattering processes [53, 54].

For the above methods, polarimetric complex coherence is regarded as observation. In fact, the polarimetric coherence is estimated from polarimetric coherency matrix and polarimetric cross-covariance matrix, which contains more complete polarimetric information [16]. Considering this, the Freeman three-component decomposition, modeling the forest scattering process as surface scattering, double-bounce scattering and volume scattering, had been extended to interpret the locations of phase centers associated with the above three scattering mechanisms [17]. The obtained interferometric phase related to double-bounce scattering contribution can be used to estimate the underlying topography, but the performance of this method is relatively poor since it ignores the relationship between vegetation biophysical parameters and the PolInSAR scattering process. Similarly, NEUMANN et al [18] constructed another inversion framework based on the Neumann polarimetric decomposition model, which compared with the previous decomposition method, effectively combines polarimetric decomposition with the RVoG model. Due to the complexity of the model solution, this methodology has not been widely adopted so far. However, the inversion framework indeed paves the road towards comprehensively considering the heterogeneity of forest scenario and establishing a more accurate scattering model.

In terms of solving the model formulation,PAPATHANASSIOU et al [15] regarded the parameter inversion of the RVoG model as a 6-D nonlinear optimization problem, while CLOUDE et al [55] proposed a three-stage inversion method to avoid the local minima traps and the impact of inaccurate initial set on non-linear optimization. Nonetheless, in single-baseline PolInSAR configuration, the number of independent observations is less than the unknown parameters in the RVoG model. Consequently, without any assumption or external data, we cannot obtain reliable results from the PolInSAR data. To solve this problem, a simple idea is to increase the observation space by multi-baseline, multi-track or multi-band PolInSAR data [23, 56-59]. These methods not only improve the robustness of the parameter solution through the constraint relationship of the observation data under different geometric conditions, but also can make full use of the redundant observation information, allowing to consider more complex scattering models that can better characterize the scattering process in different forest scenarios.

While PolInSAR technology has been widely applied for forest height retrieval over diverse forest conditions, the interferometric phase of sub-canopy ground surface is only regarded as an intermediate parameter, on which dedicated application research has not been carried out in depth. For forest height inversion, at present, the highest accuracy can reach to 10% of the mean forest height, which is satisfactory enough to be used to remove the forest height bias in the DEM containing forest height signals. In addition, the underlying topography is also directly derived by the RVoG model form PolInSAR data [60]. The results show that in airborne case, the RMSE of the obtained DEMs derived by the PolInSAR data at L- and P-bands are less than 4 m, which demonstrates that it is feasible to derive underlying topography by the RVoG model [58, 60]. Despite that these methods have been proved to be capable of estimating the underlying topography, comprehensively quantitative evaluation and analysis on inversion performance have not been fully carried out.

3.3 Underlying topography retrieval methods by means of TomoSAR

The results of 3-D imaging of forest areas with airborne L-band data were first published in Ref. [19]. However, due to the traditional fast Fourier transformation (FFT) imaging method, the vertical resolution is relatively low, which is not beneficial for separating ground scattering contribution. In view of this, a large amount of research has been carried out with emphasis on tomographic spectrum estimation methods, and a series of super-resolution algorithms have been proposed, mainly including non-parametric spectrum estimation methods [61], parametric spectrum estimation methods [62] and compressive sensing imaging methods [63]. These works assume that the scatterer is a point target, whereas in forest areas, the scattering targets are distributed, resulting in the estimated bias of tomographic spectrum by these algorithms. To solve this problem, TEBALDINI [64] proposed the covariance matching estimation technique (COMET) based TomoSAR method, which can be applied to multi-baseline InSAR/PolInSAR data, and has great tolerance for the changes of the scatterers as well as the level of scattering noise. Furthermore, it is found that simply utilizing the backscattering intensity along vertical direction is not enough to support an in-depth analysis about the scattering mechanisms at different vertical positions. In response to this gap, TEBALDINI [65, 66] proposed the sum of Kronecker product (SKP) decomposition to extract volume scattering and ground scattering contributions by algebraic synthesis. By introducing polarimetry, the method allows TomoSAR to not only reflect backscattering intensity at different heights, but also analyze the occurring scattering mechanisms. This method provides the possibility for detailed analysis on the forest vertical structure and the scattering process, which is beneficial for us to better understand the vegetation scattering mechanisms.

By TomoSAR technique, several experiments had been performed for inverting underlying topography from airborne multi-baseline InSAR or PolInSAR data. The results show that over coniferous forest covered test site characterized by flat terrain, the RMSE of the underlying topography map can be less than 1 m, while for tropical forest area characterized by hilly terrain, the corresponding RMSE is less than 3 m [61, 67]. Even if the TomoSAR technique has better performance on underlying topography inversion than the PolInSAR technique, it is difficult to extract large-scale underlying topography by TomoSAR because that to secure reliable inversion, TomoSAR requires a large number of InSAR or PolInSAR images characterized by short temporal baselines and the spatial baselines with uniform distribution as well as enough diversity, which brings about great challenge for the operation of spaceborne SAR platform. Although several works [68] have been devoted to perform TomoSAR with a small amount of SAR images, how to conduct high-resolution TomoSAR with SAR images characterized by baselines in non-uniform distribution and small diversity still needs to be further investigated.

3.4 Discussions

As analyzed before, the underlying topography inversion performance of three main techniques has varying degrees of dependence on the topographic conditions, forest attributes and properties, as well as the data frequencies. A brief comparison of three main techniques for underlying topography estimation, with respect to their characteristics, advantages and disadvantages, is shown in Table 1. Selection of a certain method requires comprehensive and systematic consideration of the specific research purpose, the accuracies required, along with the a priori knowledge available in the study areas. Considering the topography inversion accuracy, TomoSAR methodologies yield the best results then followed by the PolInSAR technique, while the InSAR (single-polarization) methodologies produce the worst results compared with the former. Nevertheless, TomoSAR technology requires a large number of acquisitions covering the same area within a short period, with rigorous requirements on the spatial distribution of the baselines, which makes it difficult to tackle with operational underlying topography mapping on a large scale, but only suitable for monitoring of local or regional areas so far.

Table 1 Comparison of underlying topography estimation methods by InSAR technique

In regard to the fair comparison (equal level of the number of baselines) between InSAR and PolInSAR-based retrieval methods, the essential difference locates on the methods used to remove the vegetation bias and their levels of thoroughness, which accordingly leads to the discrepancies in the final estimation results of underlying topography. For the direct removal idea, i.e., vegetation- subtraction strategy with InSAR (single- polarization) data, these methods impose less dependence on SAR data acquisition and are suitable for global-scale underlying topography retrieval, while the performance is still limited by the quality of forest height products. On the other hand, with respect to the indirect removal ways, these methods can be generalized into two parts, according to whether the method relies on a specific model. For the first part, the TFA based on sublook decomposition, and phase separation method based on coherence optimization theory have no requirement on establishment of physical models, while both of two series of methods are vulnerable to inadequate penetration depth of microwave signal, especially for high-frequency data and in dense forest conditions. For the second part, underlying topography extraction by coherent scattering model and polarimetric decomposition with PolInSAR acquisitions are on the basis of scattering model or decomposition model, and thus, it is reasonable to expect that the successful inversion with these methods lies on the effective and precise characterization of the forest scene using the physical scattering model, and any improper models will directly deteriorate the parameter inversion. In addition, it is worth noting that all four indirect vegetation-removal methodologies above have no dependence on any external auxiliary data but are based on strong penetration of signals to fully interact with as much scatterers as possible, which is theoretically suitable for the upcoming TanDEM-L and BIOMASS mission, operating with L-band and P-band, respectively.

Despite the tremendous progress in underlying topography retrieval witnessed over past decades, the operational underlying topography mapping technique, generally, is still in the testing stage where experiments were basically carried out using airborne SAR data acquired over test sites in relatively flat-terrain conditions. For the practical applications in different fields, there is still improvement space for further development on InSAR underlying topography inversion framework, which will be highlighted in Section 4.

4 Challenges and perspectives of underlying topography estimation with InSAR

4.1 Sensor/platform design and data selection

So far, the main reason why extractions of underlying topography are mostly based on airborne SAR data rather than spaceborne data is that the existing spaceborne acquisition cannot simultaneously satisfy the three major decisive factors, strong penetration depth, appropriate spatial baseline and sufficiently short temporal baseline (or negligible temporal decorrelation). First of all, significant penetration depth through the vegetation layer is required to ensure the direct interaction between SAR signals and ground surface. Meanwhile, SAR signals with strong penetration ability can record more complete information about vegetation vertical structure, which allows us to extract reliable vegetation parameters. With this aspect, the long-wavelength SAR data should be the preference. Although the upcoming BIOMASS and TanDEM-L mission breakthrough some constraints of previous satellites with respect to penetration depth, optimization of spatial and temporal baseline still deserves careful consideration. Considering the temporal baseline design or selection, different from the bare ground, forest morphological and biophysical properties are highly dynamic in temporal space. In other words, temporal decorrelation caused by the changes in the vegetation scenario during the interferometric data acquisition will become the major decorrelation source impeding robust underlying topography inversion. However, the temporal baseline design with the consideration of vegetation dynamic property is not rigorous and adaptive. Accordingly, the zero or nearly zero temporal baseline should be in priority. However, for multi-baseline InSAR/ PolInSAR configuration, which can increase the observational space, the temporal decorrelation is inevitable and how to scale the impact of temporal deocrrelation on underlying topography inversion is still a big challenge. On the other hand, as for the design of spatial baseline, KUGLER et al [69] and LIAO et al [70] investigated and analyzed the impact of spatial baseline on vegetation height inversion and corresponding baseline optimization strategy, which requires to remain both high interferometric coherence and coherence-to-height sensitivity, leading to only a certain limited range of height that can be inverted robustly for a given baseline configuration. As far as topography inversion is concerned, however, long-baseline configuration is more sensitive to elevation retrieval, which should be the preference for underlying topography inversion. Thereby, the balance and trade-off between the vegetation removal performance and underlying topography estimation accuracy are necessary to be further addressed. To conclude, only when the three key factors are satisfied to the maximum simultaneously can the underlying topography inversion result be the most reliable, which is achieved by not only the intrinsic sensor/platform design, but also the selection and optimization from massive data acquisitions.

4.2 Orbit errors and atmospheric effect

Another significant interferometric phase error source restricting high-accuracy underlying topography mapping comes from the orbit errors and atmospheric effect. Since the principle of vegetation height inversion is based on the idea of phase difference, the above two errors would not affect the vegetation height inversion in a significant way. Although TanDEM-L constellation is not affected by atmospheric effect thanks to the bistatic acquisition mode, it is still necessary to tackle with SAR images acquired in time series when multi-baseline configuration is selected to extend the spatial baseline combination and enhance the performance of topography mapping, impacting by nonnegligible atmospheric delay required to be carefully considered. ZHU et al [71] has studied and discussed the strategies for solving these two types of errors and the corresponding limitations in detail. In addition, traditional phase calibration techniques designing for orbit error removal and spatio-temporal filtering analysis for correcting atmospheric delay are difficult to apply on underlying topography mapping, because of the strong volume scattering contribution from forest, limited number of SAR images and special combination of interferometric pairs. In view of this, orbit error and atmospheric effect correction using multi-polarization interferograms deserve to be further investigated [72].

4.3 Interpretation and modeling of forest scattering process

The refined interpretation and correct modeling of the forest scattering process is of significant importance to build the physically relationship between the forest biophysical parameters and the InSAR signals, as well as a crucial theoretical support for establishing the correlation between tomographic spectrum and forest biophysical parameters. While several scattering models have been established to describe the forest scattering process, the intrinsic relationship between the forest biophysical parameters and the SAR scattering process is not yet explicitly clear, especially for low-frequency SAR data. When the forest is illuminated by low-frequency SAR signals, the main problems include: 1) the forest medium is heterogeneous; 2) the impact of topographic slope on ground scattering process and interferometric process is not clear; 3) the existing volume scattering model is too simple without completely considering the shape and orientation distribution of forest scatterers; 4) the conventional scattering models ignore the refraction effect occurring when microwaves penetrate through the forest layer. Nonetheless, the validity of these assumptions or limitations requires further research and demonstration in different forest scenarios and at different frequencies.

4.4 Underlying topography inversion from multi- source data

Compared to single-baseline inversion, underlying topography mapping with multi-baseline configuration produces more reliable estimations and is less susceptible from different error sources due to the increased observations and diversity in interferometric configurations. FU et al [58] demonstrated the algorithms for joint solution with multi-baseline acquisitions, while the mathematical formulation tends to be more sophisticated, making it hard to be inversed stably in some certain cases. The other multi-baseline methodologies for parameter inversion in forest scenario are, essentially, to select or filter the single-baseline solutions, which is suitable for forest height estimation but cannot be applied on topography mapping due to the continuity of the terrain surface. In addition, effective frameworks of fusing inversion with multi-band and multi-track acquisitions have not been thoroughly studied, and their complementarities have not been fully exploited. Although several studies have been carried out on the InSAR DEM inversion in mountainous terrain, the underlying topography retrieval in mountainous areas presents higher uncertainties, because forest-dominated signals cannot be accurately removed due to the influence of dramatic terrain fluctuations, regardless of whether it is based on scattering model. Furthermore, while the synergy of the fusion between LiDAR and SAR acquisitions in forest height estimation has been validated and evaluated [39, 40, 73-75], the combination of LiDAR and InSAR for improved underlying topography extraction still remains to be demonstrated, especially in the case where more spaceborne LiDAR data covering most of the world has become available without commercial restrictions, such as the ICESat-2 satellite and the GEDI mission.

5 Conclusions

The vegetation-biased DEM obtained by traditional remote sensing technologies can no longer meet the urgent requirements of underlying topography surveying in many application fields. More accurate digital terrain model in forest covered area should be produced to capture the realistic elevation of the bare Earth. To that end, a variety of methodologies for underlying topography mapping based on InSAR, PolInSAR and TomoSAR have been developed, considering the penetration ability of microwave and combining theory of the interferometric altimetry. Restricted by some factors such as uncertainties in external a priori information, incomplete framework of scattering theory, unreasonable parameters of platform configuration, and uncompensated error sources, the underlying topography mapping is still in the exploration stage with various theoretical and methodological research. With the continuous upgrading of the sensors and platforms, as well as the advance of the corresponding data processing theory, the underlying topography extraction will become an essential and indispensable research directions in the field of surveying and mapping, and play an irreplaceable role in various application fields.

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Foundation item: Projects(41820104005, 41531068, 41842059, 41904004) supported by the National Natural Science Foundation of China

Received date: 2020-02-02; Accepted date: 2020-03-26

Corresponding author: ZHU Jian-jun, PhD, Professor; Tel: +86-731-88836153; E-mail: zjj@csu.edu.cn; ORCID: 0000-0001-7185-6429