EFFECT OF THE SURFACE ROUGHNESS OF THE WATER AND ICE BOUNDARY ON LAKE ICEPACK THICKNESS MEASUREMENT USING WIDEBAND AUTOCORRELATION RADIOMETRY Seyedmohammad Mousavi1∗ , Roger De Roo2 , Kamal Sarabandi1, and Anthony W. England3 1
Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor, MI Email:
[email protected],
[email protected] 2 Climate and Space Sciences and Engineering Department, University of Michigan, Ann Arbor, MI Email:
[email protected] 3 College of Engineering and Computer Science, University of Michigan, Dearborn, MI Email:
[email protected] ABSTRACT
Wideband autocorrelation radiometry (WiBAR) is a new method to remotely measure the vertical extent of low loss layered media such as dry snowpack and freshwater lake icepack. This technique measures the pack thickness by sensing the microwave propagation time τdelay of multi-path microwave emission of the pack. The presence of a surface roughness can affect the ability of this technique to measure the τdelay correctly. In this paper, the effect of the surface roughness is discussed, and it is shown that the surface roughness can be measured for lake icepack by understanding the surface roughness effect.
Fig. 1. Remote sensing of microwave travel time within the pack using Wideband Autocorrelation Radiometry (WiBAR). derived from the coherent part of the reflectivity is given by 2
Index Terms— icepack, remote sensing, microwave radiometry, surface roughness 1. INTRODUCTION Lake icepack and dry snowpack thickness measurement using wideband autocorrelation radiometric remote sensing has been previously discussed in [1–3]. This method directly measures the microwave propagation time τdelay through the low loss terrain covers and other layered surfaces. This τdelay relates to the vertical extent of the pack.
ec =
2
(1 − |R01 | )(1 − |Rc12 | ) 1 + |R10 |2 |Rc12 |2 + 2R10 Rc12 cos(2πf τdelay )
(1)
where R01 is the Fresnel reflection coefficient of air to ice, Rc12 = R12 exp(−2k12 σb2 cos2 θp ) is the coherent reflection coefficient of ice to water, k1 is the wavenumber in ice, and σb is the rms roughness of the ice-water boundary. In this model, it is assumed that the volume scattering and absorption in the pack are negligible, and the ice-air boundary is smooth, as shown in Fig. 1. 3. FIELD MEASUREMENTS AND RESULTS
2. EFFECT OF THE SURFACE ROUGHNESS ON WIDEBAND AUTOCORRELATION RADIOMETRY Electromagnetically, the surface roughness is measured relative to the wavelength, λ, using kσ, where k = 2π λ is the wavenumber, and σ is the physical rms roughness of the surface. It has been shown that a surface with kσ < 0.2 may be considered perfectly flat [4]. For surface with kσ > 0.2, 2 2 the coherent reflectivity, |Rc | = |R| exp(−4k 2 σ 2 cos2 θ), 2 should be used, where |R| is the Fresnel reflectivity, and θ is the angle of propagation in the medium. The emissivity
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Field measurements for lake icepack were conducted on Douglas Lake at the University of Michigan Biological Station (UMBS) in March 2016. The measurements were in H-pol. The measurement setup is shown in Fig. 2(a). Using the ground truth measurements, the icepack thickness was found to be 14 inches (dice =35.5 cm), as shown in Fig. 2(b). Using the calibration and the post processing techniques mentioned in [2], the autocorrelation response of the measurement and the expected value of the autocorrelation response for the icepack is shown in Fig. 3. The first delay peak after
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Measurement
Autocorrelation Response (dB)
10
(a)
Expected value of the autocorrelation response (σ b=0) Expected value of the autocorrelation response (σ b=3.2 mm)
0
Expected value of the autocorrelation response (σ b=5 mm)
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(b) -60
Fig. 2. (a) Measurement setup of the lake icepack measurement using a wideband autocorrelation radiometer (WiBAR) on a tripod (a motorcycle battery was used as a power source) and (b) ground truth measurement of the lake icepack (dice = 35.5 cm).
0
5
10
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Time Delay (ns)
Fig. 3. The autocorrelation function of the lake icepack measured on Douglas Lake on March 02, 2016. The Hamming window was used (θair = 0.9◦ , dice = 35.56 cm). 5. ACKNOWLEDGMENT
the zero delay peak is at 4.44 ns. There is about 9 dB difference in the first delay peak after zero between the model for smooth surfaces and measurement autocorrelation response, which could be due to the surface roughness at the ice-water boundary, given the gain variations due to temperature drift of electronics, the volume scattering, and absorption in the pack are negligible. During the field measurement, we were not able to cut a piece of icepack and measure the rms roughness of the water-ice boundary due to the lack of equipment; however, by testing different rms roughness for water-ice boundary, we found that for σb = 3.2 mm, the autocorrelation delay peaks of the model and measurement are matched as shown in Fig. 3. This coherence effect can be suppressed if the scale of roughness is greater than 4.5 mm at X-band, as shown in Fig. 3. Swift et al. [5] attributed their inability to observe the interference fringes in measurements on Lake Erie to surface roughness caused by ship traffic. It can be observed that there is a relationship between the surface roughness and the amplitude of the delay peak, which may be used to measure the surface roughness. However, exploring this potential is beyond the scope of this paper and will be discussed in more details in future publications.
The authors hereby express their gratitude to NASA for its support via contracts NNX15AB36G and NNX17AD66G. We also thank Bob Vande Kopple and the University of Michigan Biological Station for their assistance in the field campaign. 6. REFERENCES [1] S. Mousavi, R. De Roo, K. Sarabandi, and A. W. England, “Sampling requirements for wideband autocorrelation radiometric (wibar) remote sensing of dry snowpack and lake icepack,” in 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), July 2017, pp. 1004–1007. [2] S. Mousavi, R. D. De Roo, K. Sarabandi, A. W. England, S. Y. E. Wong, and H. Nejati, “Lake icepack and dry snowpack thickness measurement using wideband autocorrelation radiometry,” IEEE Transactions on Geoscience and Remote Sensing, vol. PP, no. 99, pp. 1–15, 2017. [3] A. W. England, “Wideband autocorrelation radiometric sensing of microwave travel time in snowpacks and planetary ice layers,” IEEE Trans. Geosci. Remote Sens., vol. 51, pp. 2316–2326, Apr. 2013.
4. CONCLUSIONS The effect of the surface roughness of the water and ice boundary on icepack thickness measurement using WiBAR was discussed in this paper. A simple forward model considering the surface roughness at the ice-water boundary was introduced. In this model, it is assumed that the ice-air boundary is smooth, and the volume scattering and absorption in the pack are negligible. It was shown that the presence of a surface roughness can suppress the coherence effect needed to observe the quarter wave oscillation in the emissivity. Experiments were conducted in H-pol at X-band on a lake icepack.
[4] R. D. De Roo and F. T. Ulaby, “Bistatic specular scattering from rough dielectric surfaces,” IEEE Transactions on Antennas and Propagation, vol. 42, no. 2, pp. 220– 231, Feb 1994. [5] C. T. Swift, D. C. Dehority, A. B. Tanner, and R. E. Mcintosh, “Passive microwave spectral emission from saline ice at C-band during the growth phase,” IEEE Transactions on Geoscience and Remote Sensing, vol. GE-24, no. 6, pp. 840–848, Nov 1986.
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