A mathematical model for non-Rayleigh microwave sea echo is developed which describes explicitly the dependence of statistical properties of the radar cross section on the area of sea surface illuminated by the radar. In addition to the first probability distribution of the scattered radiation, its temporal and spatial correlation functions are also considered. It is shown that, in general, these correlation functions decay on at least two scales, the second, non-Rayleigh, contributions being strongly dependent on the properties of a "single scatterer." Predictions of the model are found to be in qualitative agreement with existing experimental data. A new class of probability distributions, the " K -distributions," is introduced, which may prove useful for fitting such data.

A model for non-Rayleigh sea echo

I describe an algorithm for retrieving geophysical parameters over the ocean from special sensor microwave/imager (SSM/I) observations. This algorithm is based on a model for the brightness temperature T(sub B) of the ocean and intervening atmosphere. The retrieved parameters are the near-surface wind speed W, the columnar water vapor V, the columnar cloud liquid water L, and the line-of-sight wind W(sub LS). I restrict my analysis to ocean scenes free of rain, and when the algorithm detects rain, the retrievals are discarded. The model and algorithm are precisely calibrated using a very large in situ database containing 37,650 SSM/I overpasses of buoys and 35,108 overpasses of radiosonde sites. A detailed error analysis indicates that the T(sub B) model rms accuracy is between 0.5 and 1 K and that the rms retrieval accuracies for wind, vapor, and cloud are 0.9 m/s, 1.2 mm, and 0.025 mm, respectively. The error in specifying the cloud temperature will introduce an additional 10% error in the cloud water retrieval. The spatial resolution for these accuracies is 50 km. The systematic errors in the retrievals are smaller than the rms errors, being about 0.3 m/s, 0.6 mm, and 0.005 mm for W, V, and L, respectively. The one exception is the systematic error in wind speed of -1.0 m/s that occurs for observations within +/-20 deg of upwind. The inclusion of the line-of-sight wind W(sub LS) in the retrieval significantly reduces the error in wind speed due to wind direction variations. The wind error for upwind observations is reduced from -3.0 to -1.0 m/s. Finally, I find a small signal in the 19-GHz, horizontal polarization (h(sub pol) T(sub B) residual DeltaT(sub BH) that is related to the effective air pressure of the water vapor profile. This information may be of some use in specifying the vertical distribution of water vapor.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/96JC01751

A well‐calibrated ocean algorithm for special sensor microwave / imager

Publisher Summary The basic concept of satellite altimetry is to measure the range from the satellite to the sea surface. The altimeter transmits a short pulse of microwave radiation with known power toward the sea surface. The pulse interacts with the rough sea surface and a part of the incident radiation reflects back to the altimeter. The chapter emphasizes on the correction algorithms applied to the dual-frequency altimeter onboard the TOPEX/POSEIDON (T/P) satellite. This state-of-the-art altimeter sets the standard for future altimeter missions as it is significantly more accurate than any of the other altimeters that have been launched to date. To provide assurance that the performance requirements for altimeter measurement accuracy are met or exceeded, extensive calibration and validation (cal/val) are important elements of altimeter missions. Cal/val embraces a wide variety of activities, ranging from the interpretation of information from internal-calibration modes of the sensors to the validation of the fully corrected sea-level estimates using in situ data. The chapter concludes with a summary of the T/P mission design and an assessment of the performance of the T/P dual-frequency altimeter in addition, as well as an overview of future altimeter missions.

Chapter 1 Satellite Altimetry

A method to model tropospheric radiowave propagation over land in the presence of range-dependent refractivity is presented. The terrain parabolic equation model (TPEM), is based on the split-step Fourier algorithm to solve the parabolic wave equation, which has been shown to be numerically efficient. Comparisons between TPEM, other terrain models (SEKE, GTD, FDPEM), and experimental data show predominantly excellent agreement. TPEM is also compared to results from an experiment in the Arizona desert in which range-dependent refractive conditions were measured. Although horizontal polarization is used in the implementation of the model, vertical polarization is also discussed. >

A terrain parabolic equation model for propagation in the troposphere

A theoretical foundation for the use of the parabolic wave equation/Fourier split-step method for modeling electromagnetic tropospheric propagation is presented. New procedures are used to derive a scalar Helmholtz equation and to subsequently transform to a rectangular coordinate system without requiring approximations. The assumptions associated with reducing the resulting exact Helmholtz equation to the parabolic wave equation that is used for computations are then described. A similar discussion of the error sources associated with the Fourier split-step solution technique is provided as well. These discussions provide an important indication of the applicability of the parabolic equation/split-step method to electromagnetic tropospheric propagation problems. A rigorous method of incorporating an impedance boundary at the Earth's surface in the split-step algorithm is also presented for the first time. Finally, a few example calculations which demonstrate agreement with other propagation models are provided.

Theoretical description of the parabolic approximation/Fourier split-step method of representing electromagnetic propagation in the troposphere

Propagation of short radio waves: edited by Donald E. Kerr.728 pages, drawings and photographs, 16 × 24 cm. New York, McGraw-Hill Book Co., Inc., 1951.Price, $9.00

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Propagation of short radio waves: edited by Donald E. Kerr.728 pages, drawings and photographs, 16 × 24 cm. New York, McGraw-Hill Book Co., Inc., 1951.Price, $9.00