# Designing an Interactive Visual Analytics System for
## 4 IETD Analysis  
Storm events can be characterized by both directly observable parameters and derived properties that require modeling [6]. The directly observable parameters include total precipitation volume, storm duration, average intensity, antecedent dry period, peak intensities, and temporal distribution. The derived properties are determined through analysis that integrates different stormwater models to identify moisture distribution, storm structure, energy dynamics, and circulation patterns. Analyzing both observable and derived characteristics is important for understanding the complete dynamics and impacts of storm events. Although supporting both types of characteristics is important,our system currently focuses on providing multiple visualizations to examine different observable characteristics. For precipitation analysis, we applied IETD analysis [6; 29] to determine observable characteristics of storm events. It identifies clear boundaries between independent storm events by evaluating minimum dry periods, separating consecutive precipitation occurrences into distinct events. Specifically, it uses a predefined threshold value \(\theta\) to classify consecutive precipitation events as single or separate events. Figure 1 demonstrates how IETD determines storm boundaries using a threshold of \(\theta=2\) h. Two distinct storm events are identified, indicating that event A (\(E_{A}^{\theta}\)) has multiple small amounts of rainfall of less than 1 inch and event B (\(E_{B}^{\theta}\)) has a burst of rainfall in 2 h. In event A, several minor precipitation occurrences at the beginning and end are considered part of the same event, as they fall within the IETD threshold (\(\theta\)). As it identifies clear boundaries between independent storm events, it helps determine significant precipitation characteristics through statistical analysis. If each event (\(E\)) consists of a sequence of precipitation measurements \((p_{i},t_{i})\) where \(p_{i}\) is the precipitation intensity amount (inch per hour) at time \(t_{i}\), it can be represented as follows:  
\[E=\{(p_{i},t_{i})\mid t_{i+1}-t_{i}\leq\theta,p_{i}>0\},i=1,\cdots,n\]  
where \(n\) represents the total number of observations. Each event's characteristics are defined as total event duration (\(\Delta t=t_{n}-t_{1}\)), total precipitation (\(\mathcal{S}=\sum_{i=1}^{n}p_{i}\)), and average precipitation intensity (\(\overline{p_{E}}^{\text{new}}=\frac{\sum_{i=1}^{n}p_{i}}{n}\)). The average precipitation computation method we used in this study differs from the traditional approach (\(\overline{p_{E}}^{\text{old}}=\frac{\sum_{i=1}^{n}p_{i}}{\Delta t}\)). Specifically, our method computes average precipitation by dividing the total precipitation (\(\mathcal{S}\)) by the number of nonzero precipitation occurrences. In IETD analysis, events often include time steps with zero precipitation between precipitation occurrences, depending on the user-defined IETD threshold value. Thus, excluding precipitation periods that have zero intensities is important when computing average precipitation intensity. For example, 28 nonzero precipitations were observed in event A (\(E_{A}\)). As the total precipitation (\(\mathcal{S}\)) is 6.24, the computed average precipitation becomes 6.24/30 = 0.208 with the traditional method. However, our approach generates 6.24/28 = 0.222, excluding two zero hours. It shows a slightly higher precipitation intensity value. The proposed method represents  
Figure 1: Illustration of IETD analysis with threshold \(\theta=2\) h. Each vertical bar represents measured hourly precipitation. When dry periods between precipitation measurements are less than the threshold, they are grouped into a single event. This example shows two distinct precipitation events (A and B) separated by a dry period exceeding the IETD threshold. a precise average intensity during actual precipitation periods because it excludes the two zero precipitation periods.