Seasonal and Look-directional Variation of X-band SAR Sigma Nought in Mongolian Land Surface

Abstract

This paper presents TerraSAR-X and KOMPSAT-5 sigma nought variation according to season and antenna observation configuration in Mongolia. Two types of landcover including bare surface and cropland were examined. The seasonal variation of sigma nought in cropland was about 7 dB and particularly a significant sigma nought reduction occurred after harvest. On the contrary, the Mongolia bare surface provides a consistent sigma nought values for several years with an annual variation less than 2.5 dB of standard deviation. However, the bare soil was relatively sensitive to look-direction (or ascending or descending mode) as well as incidence angle while the cropland was almost independent of antenna look-direction and small incidence angle changes. Although the look-directional variation of bare surface sigma nought was observed in this study, the look-direction anisotropic nature of the surface was not well examined. A further study would be required to account for this feature with various SAR observation configurations.

1. Introduction

Synthetic aperture radar (SAR) provides useful information on ground surface, and the information is usually obtained from radar backscattered power and phase. The radar backscattered power characterizes the properties of target or ground surface, and the radar cross section (RCS) or backscattering cross section is a measure of how detectable an object by radar. While the RCSs from the targets or certain areas of interest are main concerns of most SAR studies, not only the targets of interest but also neighbouring objects contribute to the SAR backscatter or radar return. The latter is called clutter defined as unwanted echoes in a radar return. Therefore, it is necessary for analyzing properties of a target to understand the variation patterns and characteristics of SAR clutter according to season and/or observation mode. The normalized measure of the radar return from a distributed target is called the backscatter coefficient, or sigma nought, and is defined as per unit area on the ground. The study of sigma nought variation according to season and/or observation mode is useful for discrimination of certain objects from homogeneous ground. In addition, the homogeneous and isotropic distributed target, for instance Amazon rainforest, is also mandatorily required for polarimetric SAR calibration, especially for cross talk calibration. Artificial targets for SAR absolute radiometric calibration are commonly installed on relatively flat surface of bare soil or agricultural field where homogeneous distributed targets are maintained. Consequently, the seasonal or look-directional variation of sigma nought in the area used for SAR calibration should be examined. Mongolia was used as the KOMPSAT-5 calibration site because of its low clutter level, and trihedral corner reflector were installed as passive point targets for absolute radiometric calibration (Jeong et al., 2011). In this paper, seasonal variations of X-band SAR sigma nought over the typical Mongolian land surfaces are studied. The TerraSAR-X and KOMPSAT-5 X-band SAR single-look complex (SLC) data acquired in different seasons and modes are used for this study. The variation of sigma nought with respect to acquisition mode such as ascending and descending modes is also examined.

The organization of this paper is as follows. In Section 2, the methods and data used in this study is described. Section 3 provides the results obtained from the TerraSAR-X and KOMPSAT-5 X-band SAR SLC data in the study areas, followed by a discussion about the results and conclusions in Sections 4 and 5, respectively.

2. Methods and Data

1) Radar equation and sigma nought

For a distributed target, it radar equation is well known by assuming that the distributed target is of uniform normalized cross section (Freeman and Curlander, 1989). The received antenna average power is given by (Freeman and Curlander, 1989)

\(P_{r}=\frac{P_{t} G^{2} \lambda^{2}}{(4 \pi)^{3} R^{4}} \Delta A \sigma^{0}+P_{N}\)       (1)

where P_r and P_t are the received and transmitted power, respectively, G² the two-way antenna gain, λ the radar wavelength, R the slant range, ΔA the resolution cell area, P_N additive noise, and σ⁰ the normalized cross section. In fact, it is usually difficult to directly measure the resolution cell area. Since here we are using the SAR single-look complex (SLC) data rather than raw signal, the image formation process must be considered. The image formation process primarily consists of azimuth and range compression for a phase-compensated coherent integration, and the resulting signal strength is equivalent to the summation of signal power over the number of samples integrated (Ulaby et al., 1982; Freeman and Curlander, 1989).

\(\begin{aligned} \operatorname{Pr} &=\frac{P_{t} G^{2} \lambda^{2}}{(4 \pi)^{3} R^{4}} \cdot \frac{L_{s y t h}}{V_{s}} P R F \cdot \frac{\Delta x \cdot \Delta r}{\sin \theta_{i}} \sigma^{0}+P_{N} \\ & \equiv K \sigma^{0}+P_{N} \end{aligned}\)       (2)

where L_synth is the total integration length, V_s the antenna orbit velocity, PRF the pulse repetition frequency, Δx and Δy the azimuth and range resolution, respectively, θ_i the incidence angle, and the K is the calibration factor provided by a data calibration team. In equation (2), the σ⁰ is the backscatter coefficient of the distributed target, sigma nought, defined as per unit on the ground.

Backscattering from a target is influenced by the relative orientation of illuminated resolution cell and the sensor, as well as by the distance in range between them. The derivation of sigma nought thus requires a knowledge of the local slope or local incidence angle. The TerraSAR-X sigma nought can be derived from the binary pixel values DN by

\(\begin{aligned} \sigma^{0} &=\left\{k_{s} \cdot|D N|^{2}-N E B N\right\} \times \sin \theta_{l o c} \\ &=K \cdot|D N|^{2} \cdot \sin \theta_{l o c, j}-N E S Z \end{aligned}\)       (3)

where K is the calibration factor, θ_loc,j the local incidence angle, NEBN the noise equivalent beta nought and NESZ = NEBN · sin θ_loc,j the noise equivalent sigma zero (Zinc and Bamler, 1995; Fritz et al., 2008). The noise equivalent sigma zero is the system noise and its contributions are relatively low between -19 dB and -26 dB. The calibration factor k_s and NEBN or NESZ can be read from the data header file.

The computation of backscattering coefficient, or sigma nought, from the KOMPAT-5 X-band SAR SLC data is similar to Eq. (3). The calibration constant K is provided with the image of KOMPSAT-5 in hierarchical data format (HDF). The sigma nought of the KOMPSAT-5 SLC data is given by (Shin et al., 2011)

\(\sigma^{0}=\frac{|D N|^{2}}{K} \sin \theta_{i}\)       (4)

where K is the calibration factor (or calibration scale factor) and θ_i the incidence angle. The calibration factor K can be obtained from the HDF formatted data header at an attribute of “/S01/Calibration Constant” stored in a 64-bit floating point value. In Eq. (3) and (4), the incidence angle at the area of interest is commonly required and it can be obtained through the SAR orbital geometry in Fig. 1. From Fig. 1 (Raney, 1986), the incidence angle θ_i can be computed by

Fig. 1. Space-borne SAR geometry in the range-elevation plane (after Raney, 1986).

\(\cos \left(\pi-\theta_{i}\right)=\frac{1}{2 R_{e} R}\left\{R_{e}^{2}+R^{2}-H^{2}\right\}\)       (5)

where H is the distance from the Earth centre to spacecraft, R_e the Earth radius to the point of interest, and R the slant range from the antenna to the point. The WGS 84 is commonly used for the computation.

Although the COSMO-SkyMed data are not used in this study, the data format is very similar to that of KOMSAT-5 and consequently there is some similarity in data handling in many respect between the two SAR systems. Therefore, here we introduce the sigma nought calculation from the COSMO-SkyMed SLC data. As seen in Eq. (2), the radiometric calibration of SAR images must consider the range spreading loss effect, antenna pattern gain compensation and incidence angle effect. Thus some additional steps are required to remove the effects of range and incidence angle fo a precise sigma nought from the COSMO-SkyMed SLC data.

\(\sigma^{0}=F_{t o t} \times|D N|^{2}\)         (6)

where the total scaling factor is computed as follows.

\(F_{t o t}=\left(R_{r e f}\right)^{2 R_{e x p}} \frac{\sin \theta_{i, r e f}}{K \cdot F^{2}}\)       (7)

where R_ref is the reference slant range, R_exp the reference slant range exponent, θ_i,ref the reference incidence angle, F the rescaling factor applied in the image formation, and finally K the calibration constant.

2) TerraSAR-X and KOMPSAT-5 data

TerraSAR-X and KOMPSAT-5 data have been acquired in the study area near Ulaanbaatar, Mongolia. Ulaanbaatar is located at about 1,350 m above mean sea level, slightly east of the centre of Mongolia. The forests f the mountains surrounding Ulaanbaatar are composed of evergreen pines, deciduous larches and birches while the riverine forest of the Tuul River is composed of broad-leaved, deciduous poplars, elms and willows. Most of the annual precipitation of 267 mm falls from June to September.

A total of 21 scenes of the TerraSAR-X data were acquired in HH-pol strip map mode between 2011 and 2013 (Table 1). Each of two ascending and one descending track covers the area as in Fig. 2 (left). A total of 26 scenes of the KOMPSAT-5 data were also acquired in HH-pol strip map mode between 2016 and 2017 (Table 2). A total of 13 scenes were acquired in each of ascending and descending mode as listed in Table 2. Each of ascending and descending tracks covers the area as in Fig. 2 (right). Fig. 3 and 4 contend the information of sample location of the TerraSAR-X and KOMPSAT-5 and general characteristics of areas.

Table 1. Summary of TerraSAR-X data

Fig. 2. Data coverage of the TerraSAR-X(left) and KOMPSAT-5(right) data used in this study. The yellow and blue boxes present the coverage of ascending and descending tracks, respectively.

Table 2. Summary of KOMPSAT-5 data

Fig. 3. Subareas for studying the two types of land cover in TerraSAR-X image (left). The characteristics of each sub-area are shown as bare soil area 1 (right-top), cropland (right middle), and bare soil area 2 (right bottom).

Fig. 4. Two different locations of bare soil areas in KOMPSAT-5 (left) and the characteristics of bare soil area 1 (right-top) and bare soil area 2 (right bottom).

Since here we focus on seasonal and look-directional variation of sigma nought over relatively homogenous and isotropic surface, two types of land cover including bare soil and cropland were selected for examination. We selected relatively flat and homogeneous regions as the sub-areas used for sigma nought measurement.

3. Results

1) Bare soil surface

Fig. 5 presents the variation of sigma nought on bare soil surface measured from TerraSAR-X. The annual variation of was very limited as seen in Fig. 5. The first date of year 2011 was set as day zero in Fig. 5. An annual mean of ASC-1 (or TerraSAR-X 127/010 ascending mode with an incidence angle of 37.3°) was -15.6 dB with a standard deviation of 1.00 dB, and a mean of ASC-2 (or TerraSAR-X 127/011 ascending mode with an incidence angle of 39.3°) was -15.9 dB with a standard deviation of 0.81 dB. The result obtained from descending mode DSC-1 (or TerraSAR-X 165/010 descending mode with an incidence angle of 37.3°) was also similar with a mean value of -14.5 dB with a standard deviation of 2.33 dB. These results indicate that the annual variation on bare soil in Mongolia is very limited less than 2.5 dB. It is very important to maintain a stable sigma nought on the bare surface al year long for a SAR calibration site.

Fig. 5. Variation of TerraSAR-X sigma nought on bare soil surface at Area-1. The horizontal axis presents days from the first date of year 2011. A mean and a standard deviation of DSC-1 are -14.5 dB and 2.33 dB, respectively. Those values of ASC-1 are -15.6 dB and 1.00 dB, respectively; and of ASC-2 are -15.9 dB and 0.81 dB, respectively.

It is also well worth noting that there is some systematic difference of sigma noughts acquired in ascending and descending mode even with a same incidence angle. As seen in Fig. 5, the sigma nought values measured from DSC-1 (descending mode with an incidence angle of 37.3°) were generally higher than those from ASC-1 (ascending mode with an incidence angle of 37.3°) by 1 dB to 4 dB. This effect is more clearly observed at the next site near airport in Fig. 6. Similar to the results in Fig. 5, the seasonal variation in Mongolian bare surface was very small less than 2 dB at the Area-2 summarized in Fig. 6. The results at the Area-2 also clearly show that the descending mode with an incidence angle of 37.3° consistently produces a higher sigma nought than the ascending move with an incidence angle of 39.3° by 2 dB to 4 dB.

Fig. 6. Variation of TerraSAR-X sigma nought on bare soil surface at Area-2. A mean and a standard deviation of DSC-1 are -14.5 dB and 2.34 dB, respectively, and those of ASC-2 are -15.6 dB and 1.01, respectively.

There are two possible sources of this difference of sigma nought or RCSs. The difference of incidence angle by 2° could contribute to the sigma nought variation. For a man-made trihedral corner reflector with a length of 3 m, the increase of incidence from 37.3° to 39.3° would reduce RCSs by less than 1 dBsm (Ulaby et al., 1982; Mahafza, 2013). Here we conducted a simulation using the given incidence angle and trihedral corner reflector dimension by adopting a method described by Mahafza (2013), and the simulation confirmed the reduction from -32.54 dBsm to -33.10 dBsm (i.e. 0.56 dBsm). The land surface covered with bare soil is not simple t simulate without the knowledge of soil moisture content and surface roughness modelled by the RMS height and correlation length. If the surface is composed of perfectly flat conductor, a simulation confirms that the effect of incidence variation from 37.3° to 39.3° would only contribute to 0.5 dB (Mahafza, 2013). The second possible source of the deviation might be anisotropic nature of the surface according to look direction of the antenna, i.e. ascending and descending mode. The consistent wind and surface water flows would make the bare soil surface different directional properties. Although the source of the difference is not conclusive, it is worth noting that there is a look-directional variation of sigma nought at surrounding ground surface larger than that potentially occurred at an installed trihedral corner reflector by 1 to 3 dB.

This characteristics of radar signatures is also similarly observed by the KOMPSAT-5 X-band SAR in Fig. 7. The seasonal (or annual) variation of sigma nought was very limited no larger than 1.8 dB, which strongly confirmed that the Mongolian bare surface is good for a SAR calibration site. The difference between the descending and ascending mode was consistent but less significant than that by TerraSAR-X. The KOMPSAT-5 ascending mode with an incidence angle of 27.6° provides consistently higher sigma noughts than those by the descending mode with an incidence angle of 30.0° by 1 to 3 dB.

Fig. 7. Vaiation of KOMPSAT-5 sigma nought on the bare soil at (a) Area-1 and (b) Area-2. The zero in the horizontal represents the first date of year 2011. (a) Result from Area-1: A mean and a standard deviation are -9.9 dB and 1.14 dB, respectively, for descending mode and those of -12.1 dB and 1.40 dB, respectively, for ascending mode. (b) Results from Area-2: A mean and a standard deviation are -11.0 dB and 1.8 dB, respectively, for descending mode and those of -10.6 dB and 1.33 dB, respectively, for ascending mode.

The difference of incidence angle between ascending and descending mode was 2.4° which would contribute to 1.85 dB reduction of RCSs (from -27.37 dB to -29.22 dB) for a tetrahedral corner reflector (Mahafza, 2013). Compared with the TerraSAR-X SAR data used in this study, the KOMSAT-5 data used in this study had slightly lower incidence angles both of ascending and descending mode by about 10°. The smaller incidence angle is, the difference of corner reflector’s RCSs is normally larger. However, the variation at Mongolian bare surface according to the increase of incidence angle was not that much significant but the look-directional variation plays an important role.

2) Cropland

Seasonal and/or look-directional variation of sigma nought in cropland should also be examined in Mongolian land surface when it is used for SAR calibration site. Cropland is preferred as SAR calibration site for many countries and institutes because it usually provides homogeneous and anisotropic clutter. In particular, the polarimetric calibration site requires a distributed target satisfying a condition of reflection symmetry which implies independency between co-pol and cross-pol (van Zyl and Kim, 2011). Thus cropland or tropical rainforest are utilized as for a polarimetric calibration site. However, there exists a seasonal variation in cropland or forest according to phenological cycle (Baghdadi et al., 2009; Dabiri et al., 2015; Nguyen et al., 2015). It was reported that the radar signal decreased by about 6 dB either plant drying-out or harvest (Baghdadi et al., 2009).

In our study area near Ulaanbaatar, Mongolia, seasonal variation over cropland was examined by TerraSAR-X as in Fig. 8. When Fig. 8 is compared with Fig. 5 and , seasonal variation of sigma nought in cropland is distinctive with a sigma nought reduction after harvest by about 6 to 8 dB. The result is very similar to a seasonal variation of 7 dB reported by Baghdadi et al. (2009) for monitoring sugarcane. The dashed line in Fig. 8 obtained by a cubic spline interpolation clearly showed a seasonal variation pattern. Therefore, the seasonal variation must be considered when cropland is used as a SAR calibration site. It also must be emphasized that the sigma nought reduction in cropland according to an increased incidence angle or look-direction (i.e. ascending or descending mode) is negligible. This characteristics of SAR signatures is clearly distinctive from those in bare soil seen in Fig. 5-7.

Fig. 8. Variation of TerraSAR-X sigma nought on cropland in Mongolia. The seasonal variation is typically well observed with a reduction of sigma nought by 6 to 8 dB after harvest. It is also well worth of noting that the sigma nought reduction according to incidence angle and/or look-direction is negligible in cropland. The dashed line is an interpolated line by cubic spline method for examining a seasonal variation.

When corner reflectors or transponders are installed, a homogeneous low backscattering background is mandatorily required for the site where a large signal-to-clutter (SCR) ratio is obtained. Among various land covers, cropland or bare surface has been normally considered a good candidates fr this purpose. In Mongolian terrain near Ulaanbaatar, the results shows different characteristics for the two types of land surface as summarized in Table 3. The cropland shows a typical seasonal variation with a sigma nought reduction of about 7 dB (6-8 dB) after harvest. This seasonal variation of radar signatures would seriously limit the utilization of the site particularly during winter season. However, the cropland has an advantage in that the radar returns are by far less dependent on small changes in incidence angles as well as different look-directions (ascending or descending). In addition, the reflection symmetry measured by the independency between co-pol and cross-pol is well defined. On the contrary, the Mongolian bare soil would guarantee large SCRs with a minimum seasonal variation less than 2.5 dB (Table 3). However, one should note that Mongolian bare soil is relatively sensitive to the antenna look-direction as well as incidence angle. Thus the measurements of sigma nought in ascending and descending mode must be conducted separately.

Table 3. Characteristics of sigma nought variation in Mongolian bare soil and cropland

5. Conclusions

Reference RCSs must be steadily and consistently measured for the lifetime of a space-borne SAR system. The area for a reference site should be a homogeneous low backscattering background. Seasonal variation is another factor to consider because the RCSs of point targets must e measured all year long for several years. Therefore, it is important to examine backscattering characteristics of background and its variation according to season and system parameters. This paper studied the seasonal variation of sigma nought of bare surface and cropland near Ulaanbaatar, Mongolia, using KOMPSAT-5 and TerraSAR-X. The seasonal variation of cropland was significant by about 7 dB, and abrupt changes of SAR signature match well with harvest season. However, sigma nought dependency to system parameters of the incidence angle and look-direction is limited. On the contrary, sigma naught in the Mongolian bare soil maintains near-constant values with a standard deviation of n larger than 2.5 dB for several years. The consistency of the backscattering on bare surface would be a great merit for SAR calibration site. However, the bare surface is relatively sensitive to the antenna look-direction as well as incidence angle. Therefore, the system parameters must be precisely determined when the RCSs of point targets are measured.

Although the look-direction variation of SAR signatures in Mongolian bare soil is observed in this study, the reason of directional anisotropic nature of the surface is not conclusive in this study. It would require further studies with various SAR observation parameters including look-direction and squint angle, incidence angle, etc.