Interpolation and visualization for advected scalar fields

Doppler radars are useful facilities for weather forecasting. The data sampled by using Doppler radars are used to measure the distributions and densities of rain drops, snow crystals, hail stones, or even insects in the atmosphere. In this paper, we propose to build up a graphics-based software system for visualizing Doppler radar data. In the system, the reflectivity data gathered by using Doppler radars are post-processed to generate virtual cloud images which reveal the densities of precipitation in the air. An optical flow based method is adopted to compute the velocities of clouds, advected by winds. Therefore, the movement of clouds is depicted. The cloud velocities are also used to interpolate reflectivities for arbitrary time steps. Therefore, the reflectivities at any time can be produced. Our system composes of three stages. At the first stage, the raw radar data are re-sampled and filtered to create a multiple resolution data structure, based on a pyramid structure. At the second stage, a numeric method is employed to compute cloud velocities in the air and to interpolate radar reflectivity data at given time steps. The radar reflectivity data and cloud velocities are displayed at the last stage. The reflectivities are rendered by using splatting methods to produce semi-transparent cloud images. Two kinds of media are created for analyzing the reflectivity data. The first kind media consists of a group of still images of clouds which displays the distribution and density of water in the air. The second type media is a short animation of cloud images to show the formation and movement of the clouds. To show the advection of clouds, the cloud velocities are displayed by using two dimensional images. In these images, the velocities are represented by arrows and superimposed on cloud images. To enhance image quality, gradients and diffusion of the radar data are computed and used in the rendering process. Therefore the cloud structures are better portrayed. In order to achieve interactive visualization, our system is also comprised with a view-dependent visualization module. The radar data at far distance are rendered in lower resolutions, while the data closer to the eye position is rendered in details.