Wind, shear and turbulence are important in quantifying and forecasting weather. Wind can be measured either by Doppler or interferometry techniques. Weather radars such as WSR-88D measure only the Doppler velocity (i.e., the radial component of wind). But NCAR's Multiple Antenna Profiler Radar (MAPR), a Spaced Antenna (SA) interferometer, also measures the crossbeam wind components (i.e., the component parallel to the baseline connecting two receivers) as well as the along beam wind component obtained from the mean Doppler. Wind measurements using SA interferometry was developed based on the fact that the motion of interference patterns formed on antenna plane is associated with scatterers' motion. The SA technique has been limited mainly to the Mesosphere-Stratosphere-Troposphere (MST) and wind profiler communities.

Recently, the SA technique has received attention in the weather radar community. MAPR was mounted on a pedestal and tilted to a slant angle to function as a scanning radar. An X-band dual-polarization SA (DPSA) system has been built and has collected data for crossbeam wind measurement. Neither the scanning MAPR nor DPSA has produced satisfactory crossbeam wind results due to various limitations. One fundamental issue is the requirement of a long dwell time at each beam direction for accurate wind measurements using the SA technique. This is contrary to the idea of fast scanning weather radar for a large coverage. NSSL's Phase Array Radar (PAR) offers opportunity to advance the SA technique for crossbeam wind measurements within radar resolution volume. Turbulence and shear are also obstacles in accurate measurement of crossbeam wind. The effect of shear on wind measurement has not been fully understood.

Turbulence is usually calculated from spectrum width data, which can be corrupted by wind shear. On the other hand, shear itself is an important parameter in weather studies and in determining hazards to aircraft ascending or descending into airports. With the availability of PARs and its capability of having multiple beams, the separation of shear and turbulence effects becomes feasible. PAR has pulse-to-pulse beam steering capability that allows adjustable dwell time for specific beam directions, and it allows weather radar interferometry to measure crossbeam wind, shear and turbulence. A complete theory for such application has not been developed although a series of theoretical studies were performed for SA wind measurement in profiler community. The previous studies have been based on the assumption of wave scattering from a statistically homogenous medium of refraction index fluctuation, and no shear effects have been accounted.

In this paper, we formulate weather radar interferometry for measurements of crossbeam wind, shear and turbulence for a SA configuration. Auto- and cross-correlation functions are derived based on wave scattering by randomly distributed particles in the presence of wind, turbulence, and shear. It is found that antenna separation, mean wind, shear and turbulence all contribute to the signal de-correlation. In the case of near ranges or weak shear, crossbeam wind measurement using SA technique is feasible. The cross beam wind components can be obtained from the cross-correlation function and the along beam component from the usual mean Doppler measurement. At farther ranges, however, the shear term could dominate and crossbeam wind measurement becomes difficult. Because the shear term depends on beam width, the auto-correlation function of the signals from any one of the spaced receiving antennas is different from that for the combined signal from two or more receiving arrays. By comparing two autocorrelation functions for different-sized beams, shear can be estimated. Turbulence can be determined as well. Although accurate measurement of crossbeam wind is difficult, separation of shear from turbulence is possible using SA technique. The SA weather radar interferometry can be used to measure shear and turbulence, measurements that cannot be made with conventional Doppler weather radars.