Some traditional methods,such as the velocity-azimuth display(VAD) and the velocity-azimuth processing (VAP),have been widely used to retrieve the 3-D wind field from single-Doppler radar data because of their relative conceptual and practical simplicity.The advantage of VAD is that it is not affected by small-scale perturbations of the radial wind along the azimuth,to which the VAP method is very sensitive. Nevertheless,the spatial resolution of the VAD method is very poor compared to the VAP method. We show,in this study,that these two retrieval methods are actually related with each other and they are two special applications of a retrieval function based on the azimuthal uniform-wind assumption for a given azimuthal interval[θ1,θ2].When using this retrieval function to retrieve wind fields,the azimuthal interval used in retrieval can be adjusted according to the requirement of smoothness or resolution.The larger(smaller) the azimuthal interval is,the coarser(finer) the horizontal resolution of retrieved wind field is,and the more insensitive(sensitive) the retrieval method is to small-scale perturbations.Because the full information within the azimuthal interval[θ1,θ2],instead of the information at two terminal points only, i.e.,azimuthsθ1andθ2,is used to retrieve the wind fields,this method is referred to as the integrating VAP (IVAP) method,wherein the horizontal wind field is retrieved by using the Doppler velocity over the part of circumference,delimited by the given azimuthal interval times the scan radius.By contrast,the VAP method uses only the velocities at two terminal points of the given azimuthal interval.Therefore,the IVAP method has a filtering function,and the filtering rate can be controlled by adjusting the azimuthal interval. The filter such as that used in the pre-processing of the VAP method is no longer necessary for the IVAP method.When the retrieval azimuthal interval is as large as a whole circumference,the IVAP becomes the VAD.On the other hand,if only two neighboring azimuthal data are used,the IVAP becomes the VAP. The frequency response function of IVAP indicates that the IVAP method can filter out shortwaves,and a larger azimuthal interval leads to stronger filtering ability,therefore a smoother retrieved wind field. The shortwave filter function of the IVAP method is tested by an ideal experiment wherein the radar observations are artificially created by a uniform flow superposed with random disturbances.The VAP and IVAP methods are used in wind retrieval,respectively,and give different results for different azimuthal intervals(i.e.,6°,12°,24°,and 48°).Because the VAP method is sensitive to small disturbances,the retrieved winds have larger errors for all different azimuthal intervals.However,the retrieved wind by the IVAP method has smaller errors when the azimuthal interval is larger due to its shortwave filter function. An experiment for an idealized linear wind field is also carried out to demonstrate the effect of the retrieval azimuthal interval on the IVAP method.The results show that a short interval gives the retrieval close to the"true"wind field with a linear distribution.When increasing the interval,the retrieval is smoothed and can represent only the mean wind field.
