Simulations and Observations of GNSS Ocean Surface Reflections Per Høeg Hans-Henrik von Benzon
Ocean Surface Reflections Figure of the geometry of ocean reflections The presented simulations involve ocean scattering and the wave propagation between transmitter and receiver (a bi-static scattering system) The wave propagation is performed using a full-wave solution to the parabolic equation The wave propagation is performed using a solution to the parabolic equations, which is an approximation to the wave equation (Levy, 2000) The initial field for the wave propagation is calculated from the ocean scattering coefficients 2
Ocean Surface Reflections The theory of propagation of microwaves in the atmosphere is well established, and methods for propagation modeling range from ray tracing, numerical solutions, to the wave equation. The presented simulation tool is based on the solution of the parabolic equations. The parabolic equations in our simulator is solved using the split-step sine transformation. The ocean surface is modeled with the use of an impedance model. The value of the ocean impedance (conductivity tensor) is given as a function of the range along the surface of the ocean. This concept gives an accurate lower boundary condition in the determination of the electromagnetic field, and makes it possible to simulate reflections and the effects of transitions between different media. The analysis of both the simulated surface reflection signals and the measured reflection signals reveal spectral structures of the reflected signals leading to the extraction of sea surface roughness, surface wind speed and direction. 3
Ocean Surface Reflections Electromagnetic wave propagation in the atmosphere can be approximated by a set of parabolic equations. A spatial impedance model characterizes the surface reflection conditions, (Dockery and Kuttler, 1996). The values of the impedances are given as a function of range along the ocean surface. The split-step/sine transform solution is given by: u( x + Δx, y) = e π p ikδx( 1 ik( n 1) Δx 1 2 k S { e 2 2 1) S{ u( x, y)}} S{} represents the sine-transformation, where Δx is the distance between the phase screens, p is the spatial frequency, and k is the wave-vector. The output is either amplitude and phase of the electromagnetic field or the corresponding I,Q components. 4
Ocean Surface Reflections Measurements (2004) Measured power spectrum (Data set 1) Measured power spectrum (Data set 2) 5
Ocean Surface Reflections Measurements (2004) Measured spectrogram for data set 1, showing the direct signal and the ocean-reflected ray Measured spectrogram for data set 2 6
Ocean Surface Reflections - Simulation Ocean scattering coefficients, which are used to calculate the initial field for the wave propagation Amplitude of the sum of the direct and reflected field 7
Ocean Surface Reflections - Simulation Spectrum of the simulated signal at the receiver Spectrogram of the received signal. The direct and a reflected main signal are seen in the center of the plot. 8
Simulations of Ocean Surface Reflections In the following simulations the inclination angle is small, i.e. a low grazing angle simulation (h = 20 meter). A number of different sea states and atmospheric conditions are analyzed for this setup. 9
Wind Speed and Ocean Wave Height The correlation function for the sea surface heights z is called K (Beckmann and Spizzichino, 1987; Garrison and Katzberg, 2000). The Fourier transformation of the correlation function K, for a Philips spectrum W, is given by (Levy, 2000): W (p, q) = B for ( p 2 + q 2 ) > g ( ) 2 π p 2 + q 2 W (p, q) = 0 for ( p 2 + q 2 ) < g U 2 U 2 Here, g is the gravity acceleration, B is a constant, while U is the wind speed. Assuming a Philips spectrum, the relation between wind speed U and RMS wave height h becomes: h = 0.0051 U 2 10
Wind Speed and Ocean Wave Height Sea State Wind Speed Wave Height (rms) 0 0.00 m/s 0.000 m 1 5.14 m/s 0.135 m 2 7.72 m/s 0.304 m 3 10.29 m/s 0.540 m 4 12.86 m/s 0.843 m 5 14.01 m/s 1.002 m 11
Calculation of Ocean Surface Impedance The rough sea surface impedance can be calculated using the following equation: ( δ = sinθ 1+ ρ )δ 0 + ( 1 ρ)sinθ ( 1 ρ)δ 0 + ( 1+ ρ)sinθ where θ is the grazing angle, ρ is the roughness reduction factor and δ 0 is the smooth surface impedance (normally is a function of the wave polarization). The roughness reduction factor is given by: " $ # ρ = e γ 2 % 2 & ' " γ 2 I0 $ # 2 % ' & where I 0 is the modified Bessel function of the first kind of order 0, and γ is the Rayleigh roughness parameter, given by: γ = 2 k h sinθ Here, k is wave number of the electromagnetic wave, and h is the RMS height of the ocean waves. 12
Surface Impedance as Function of Frequency The roughness reduction factor as a function of Rayleigh roughness Rough (sea state 4) and smooth (sea state 0) surface impedance as a function of frequency 13
Wave Propagation Simulations (at 10.6 GHz) Atmospheric ducting - a wave guide between atmosphere layers and ocean Simulation performed for a 10.6 GHz wave Incoming transmitted wave at a height of 25 m Smooth water surface (sea state 0), including a standard atmosphere No atmospheric ducting condition Same simulation conditions as in the left figure. Smooth water surface (sea state 0) and standard atmosphere Atmospheric ducting (atmospheric boundary layer with an inversion layer in a altitude of 30 m) 14
Wave Propagation Simulations (at 10.6 GHz) Simulation performed for 10.6 GHz for a rough ocean surface (sea state 4) The RMS wave height is 0.843 m, with a grazing angle of 0.1 degree Atmospheric ducting is considered (boundary layer) 15
Wave Propagation Simulations Simulation performed for 10.6 GHz for a rough ocean surface (sea state 4) The RMS wave height is 0.843 m, with a grazing angle of 3.0 degree Atmospheric ducting is considered (boundary layer) The wave travels longer due to lower wave energy loss in the wave guide 16
Wave Propagation for GNSS Signals - Evaporation An atmospheric evaporation duct The modified refractivity as a function of height - given by the Paulus-Jeske model (Paulus, 1990) This model corresponds to an evaporation duct as in many boundary conditions 17
Wave Propagation for GNSS Signals - Evaporation The amplitude of the electromagnetic field The collected power at the GNSS receiver as a function of receiver code delay (measured in chips) - equaling a phase delay mapping receiver (Garrison and Katzberg, 1998; Zhang et al., 2012) 18
Summary 1. The developed simulation tool identifies the main ocean scattering processes, their characteristics, and the spectral structures related to the reflected signal. 2. The tool, based on the parabolic wave equations for a multitude set of phase screens, describes the ocean reflections through an impedance model (the conductivity tensor). 3. The simulations reveal for low-elevation measurements the nonlinear relation between the elevation angle, size of the reflections zone, and the horizontal and vertical signal attenuation. 4. The model for the sea surface roughness impedance, wind speed and rms ocean wave height show for GNSS frequencies a stronger signal damping for a smoother ocean surfaces (sea state 0) compared to a rough sea (sea state 4). While the real part of the signal shows the reverse effect. At the same time the reflection zone becomes larger for rough sea states. 5. Simulations, including a standard atmosphere boundary layer, give a significant ducting of the received signal, leading to a much larger reflection zone (and broader received power spectra). The size of the elliptical reflection area is directly linked to the grazing angle of the received signal. 6. When adding an evaporation model into the simulations, a similar ducting is observed as identified for the atmosphere boundary layer. 19