Moving and Morphing Polygons with Splitting and Merging

During the development of occluded fronts, the splitting and merging of individual convective areas always occurs, as well as a shift in the main precipitation areas within the front. For this reason, it is important that an animated presentation format on a traffic situation display can also reproduce these developments as realistically as possible. The mapping of polygons in the splitting case to perform the interpolation of their transformation is shown in Figure 6. The polygon *Polt*|<sup>1</sup> at the current time t decomposes over the time period Δ*t* in four parts, namely *Polt*+Δ*t*|1(*t*|1) , ... , *Polt*+Δ*t*|4(*t*|1) , as illustrated in Figure 6. However, the splitting contours are unknown and, as a consequence, the space between appearing parts is not safe. Therefore, as was mentioned in the previous subsection, the current polygon *Polt*|<sup>1</sup> is mapped to all four forecasted polygons *Polt*+Δ*t*|1(*t*|1) , ... , *Polt*+Δ*t*|4(*t*|1) . The morphing of the polygon *Polt*|<sup>1</sup> into each forecasted polygon *Polt*+Δ*t*|1(*t*|1) , ... , *Polt*+Δ*t*|4(*t*|1) is then performed simultaneously in the way described above. Figure 6 shows interpolation lines, additional points, and the constellation of the polygons at the time period *t* + <sup>Δ</sup>*<sup>t</sup>* <sup>2</sup> . Colors correspond to the mapping of the polygons. An approach to transform one polygon into several polygons, and vice versa, is hereby developed.

**Figure 6.** Illustration of interpolation without decomposition of the current polygon. On a radar screen, only the envelope curve is presented. Corresponding mapping is visualized in different colors.

The mapping of whole polygons can be also used to perform a transformation in the case of the simultaneous splitting and merging of the current and forecasted polygons, i.e., when a part of one polygon splits from the polygon and another part merges with some other polygon at the same time. Figure 7 illustrates this mapping example without decomposition.

**Figure 7.** Assignment of polygons for interpolation in the case of simultaneous splitting and merging.

Consequently, the presented morphing approach is applicable for general interpolation of the transformation between two sets of closed polygons representing current and forecasted adverse weather areas over a short period of time.

#### **4. Meteorological Modeling**

The three new meteorological forecasting techniques, i.e., Weather Research and Forecasting (WRF), the PHAse-diffusion model for STochastic nowcasting (PhaSt), and the Radar Nowcasting Density of the Vertical Integrated Liquid (RaNDeVIL) model, were developed and extended to better nowcast severe weather events affecting tactical approach operations. For this purpose, short-range severe weather forecasts with very high spatial resolution were elaborated, starting from radar images, through an application of nowcasting techniques combined with the Numerical Weather Prediction (NWP) model and data assimilation.
