# A Process-Oriented Method for Tracking Rainstorms with a Time-Series of Raster Datasets
## 3 PoAIR Algorithm
### Reconstructing a Rainstorm Process by Linking Rainstorm Sequences
#### 3.3.1 The Linkage Between Rainstorm Objects and Rainstorm Sequences  
In the temporal domain, an independent rainstorm object is instantaneous, while a rainstorm sequence lasts for a specified time. These differences make the linkage strategies of rainstorm objects and rainstorm sequences different. For rainstorm objects, this paper uses an averaged moving distance, i.e., \(D_{\text{mean}}\), as a criterion to identify the rainstorm objects from previous and subsequent snapshots. If no object is found, the independent object is regarded as noise, or is linked the found objects. The found objects may be independent objects or objects belonging to a rainstorm sequence. For rainstorm sequences, this paper uses spatiotemporal topological relationships to find the candidates to be linked. If a rainstorm sequence overlaps in space and intersects with or is adjacent in time to a given rainstorm sequence, the latter is linked with the former; otherwise, the latter is regarded as a rainstorm process.  
There are three types of linkages between rainstorm objects and rainstorm sequences:  
* The linkage between rainstorm objects: Firstly, obtain the given rainstorm object and its candidates, according to the occurrence time in order, define the previous object, _preO_, and the next object, _postO_. As no motions can be obtained from the independent rainstorm objects, the PoAIR  
Figure 4: The workflow of the rainstorm reconstruction processes.  
algorithm then uses the centroid distance of the objects as a criterion to determine the presence or otherwise of linkage. If their centroid distance meets in Equation (5), a linkage is performed, and is represented in the form of \(<\)_preO_\(>\)_postO_\(>\). \[d(\textit{preO}\textit{postO})<D_{\text{mean}}\] (5) where \(\text{d}(\textit{preO},\textit{postO})\) means the Euclidean distance between _preO_ and _postO_, \(D_{\text{mean}}\) is multiplied by the time interval and 58 km/h, the mean speed of typical convective rainstorm motion [26].
* The linkage between a rainstorm object and a rainstorm sequence: Firstly, find which object within a rainstorm sequence is to be linked with the given object. Then, the same linkage as between rainstorm objects is performed. This linkage is represented as: \[O_{s}^{s}\] \  
\(O_{S}^{i_{s}-1}\) and \(O_{d}^{i_{s}-1}\) are respectively the backward speed and direction of a rainstorm sequence in snapshot \(t_{s}-1\);  
Step 3: Obtain the candidate to be linked in the _postS_, denoted as _postO_, and use Equation (8) to calculate an area overlapped degree _(AOD)_ between _postO_ and _preO_. If the _AOD_ is above a certain threshold, a linkage is performed.  
\[AOD=\frac{A(\text{Overlap})}{A(\text{preO})}+\frac{A(\text{Overlap})}{A(\text{ postO})} \tag{10}\]  
where \(A(\text{Overlap})\), \(A(\text{preO})\) and \(A(\text{postO})\) are respectively the overlapped area and the area of _preO_ and _postO_.  
_Contains_ and _Overlaps_ relationships perform linkages twice. The first linkage uses the starting time of rainstorm sequences to identify the _preS_ and _postS_, then the same linkage as in the _Finishes_ relationship is performed. The second linkage uses the end time to identify the _preS_ and _postS_, then the same linkage as in the _Starts_ relationship is performed.  
The expressions of the linkages between two rainstorm sequences are shown in Figure 6.