International Telemetering Conference Proceedings / October 25-28, 1993 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Spaceborne wind scatterometers are designed principally to measure radar backscatter from the ocean's surface for the determination of the near-surface wind direction and speed. Although measurements of the radar backscatter are made over land, application of these measurements has been limited primarily to the calibration of the instrument due to their low resolution (typically 50 km). However, a recently developed resolution enhancement technique can be applied to the measurements to produced medium-scale radar backscatter images of the earth's surface. Such images have proven useful in the study of tropical vegetation3 as well as glacial5 and sea6 ice. The technique has been successfully applied2 to Seasat scatterometer (SASS) data to achieve image resolution as fine as 3-4 km. The method can also be applied to ERS-l scatterometer data. Unfortunately, the instrument processing method employed by SASS limits the ultimate resolution which can be obtained with the method. To achieve the desired measurement overlap, multiple satellite passes are required. However, with minor modifications to future Doppler scatterometer systems (such as the NASA scatterometer [NSCAT] and its follow-on EoS-era scatterometer NEXSCAT) imaging resolutions down to 1-2 km for land/ice and 5-10 km for wind measurement may be achieved on a single pass with a moderate increase in downlink bandwidth (from 3.1 kbps to 750 kbps). This paper describes these modifications and briefly describes some of the applications of this medium-scale Ku-band imagery for vegetation studies, hydrology, sea ice mapping, and the study of mesoscale winds.

The hyperbolic conservation laws model the phenomena of nonlinear waves including discontinuities. The coupled nonlinear equations representing such conservation laws may lead to discontinuous solutions even for smooth initial data. To solve such equations, developing numerical methods which are accurate, robust, and resolve all the wave structures appearing in the solutions is a challenging task. Among several discretization techniques developed for solving hyperbolic conservation laws numerically, Finite Volume Method (FVM) is the most popular. Numerical algorithms, in the framework of FVM, are broadly classified as upwind and central discretization methods. Upwind methods mimic the features of hyperbolic conservation laws very well. However, most of the popular upwind schemes are known to suffer from the shock instabilities. Many upwind methods are heavily dependent on eigen-structure, therefore methods developed for one system of conservation laws are not straightforwardly extended to other systems. On the contrary, central discretization methods are simple, independent of eigen-structure, and therefore, are easily extended to other systems. In the first part of the thesis, a hybrid central discretization method is introduced for Euler equations of gas dynamics. This hybrid scheme is then extended to other hyperbolic conservation laws namely, shallow water equations of oceanography and ideal magnetohydrodynamics equations. The baseline solver for the new hybrid scheme, Method of Optimal Viscosity for Enhanced Resolution of Shocks (MOVERS), is an accurate scheme capable of capturing grid aligned steady discontinuities exactly. This central scheme is free from complicated Riemann solvers and therefore is easy to implement. This low diffusive algorithm produces sonic glitches at the expansion regions involving sonic points and is prone to shock instabilities. Therefore it requires an entropy fix to avoid these problems. With the use of entropy fix the exact discontinuity capturing property of the scheme is lost, although sonic glitches and shock instabilities are avoided. The motivation for this work is to develop a numerical method which exactly preserves the steady contacts, is accurate, free of multi-dimensional shock instabilities and yet avoids the entropy fix. This is achieved by constructing a coefficient of numerical diffusion based on pressure gradient sensor. The pressure gradients are known to detect shocks and they vanish across contact discontinuities. This property of pressure sensor is utilized in constructing the coefficient of numerical diffusion. In addition to the numerical diffusion of the baseline solver, a numerical diffusion based on the pressure sensor, scaled by the maximum of eigen-spectrum, is used to avoid shock instabilities. At contact discontinuities, pressure gradients vanish and coefficient of numerical diffusion of MOVERS is automatically retained to capture steady contact discontinuities exactly. This simple hybrid central solver is accurate, captures steady contact discontinuities exactly and is free of multi-dimensional shock instabilities. This novel method is extended to shallow water and ideal magnetohydrodynamics equations in a similar way. In the second part of the thesis, an entropy stable central discretization method for hyperbolic conservation laws is introduced. In a quest for optimal numerical viscosity, development of entropy stable schemes gained importance in recent times. In this work, the entropy conservation equation is used as a guideline to fix the coefficient of numerical diffusion for smooth regions of the flow. At the large gradients, coefficient of numerical diffusion of baseline solver is used. Switch over between smooth and large gradients of the flow is done using limiter functions which are known to distinguish between smooth and high gradient regions of the flow. This simple and stable central scheme termed MOVERS-LE captures grid aligned steady discontinuities exactly and is free of shock instabilities in multi-dimensions. Both the above algorithms are tested on various well established benchmark test problems.