# Storm Identification, Tracking and Forecasting Using High-Resolution Images of Short-Range X-Band Radar

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{®}(see [2,3]) designed by the Remote Sensing Group of the Polytechnic of Turin, Italy. It is a network of low-cost, low-power consumption, unmanned, X-band, micro-radars. Radar echoes are quantized into imagery data using eight-bit radiometric resolution resulting in a grey scale image with 1024 × 1024 image dimensions. Real-time precipitation observations are available at ( http://meteoradar.polito.it).

_{z}) and the area of this object is greater than an areal threshold (T

_{a}) [4]. Storm identification is comprised of identifying a storm’s boundaries, calculating its area, centroid, mean and maximum reflectivity where the centroid is the center of mass of the storm. Storm identification starts with segmenting the image into meaningful sub-regions (objects/storms) on the basis of some properties, such as intensities (grey levels/reflectivity), color and texture. Many storm identification techniques, like [4–8], are based on global thresholding. We have also adopted this procedure. Global thresholding can be categorized as single- and multi-level, as well as manual, semi-automated and automated. In the manual one, the user has to set the threshold value by trial and error, while in the semi-automated one, the user has to enter an initial value, and the system computes the rest of the value(s). A fully-automated system does not need user intervention and chooses the thresholds automatically.

## 2. State-of-the-Art

_{z}(minimum threshold value in dBZ); second, the grouping of all runs that are adjacent. Storms with volumes less than volumetric threshold T

_{v}are dropped. TITAN calculates storm properties, such as centroid, vertically-integrated liquid (VIL), volume, etc. TITAN is unable to identify storm cells within a cluster of storms. Beside this, if the reflectivity threshold is kept high, TITAN is not capable of identifying storm initiation and also stratiform events.

- Dur is the total life time (duration) of a track;
- The standard deviation of VIL (σ
_{v}); - The root mean square error of centroid positions from their optimal line fit.

## 3. Storm Identification

_{z}and T

_{a}. Storm identification is the recognition of individual storms’ boundaries and computes their characteristics, i.e., centroids, area, major/minor radii and orientation, etc. Most of the storm-based weather forecasting systems use a thresholding technique for the identification of storms/cells.

_{a}. The qualifying storm(s) is subjected to further processing. Storms approximated by ellipses and attributes, like the centroid, major/minor axis orientation, etc., are calculated according to the procedure discussed in [27].

#### 3.1. Thresholding

_{0}) and foreground class (C

_{1}). In the case of radar images, radar echoes are the foreground, while their absence is the background of the image. Since we are interested in rain, pixels belonging to C

_{0}are dropped, while pixels belonging to C

_{1}are kept for further processing. A single threshold only separates the background from the foreground, but it is not capable of identifying different objects (storms/cells) in the foreground. The foreground after applying a single threshold is called a cluster if it has sub-storms, as shown in Figure 2. To correctly separate the sub-storms of a cluster, multi-level thresholding, also called multi-thresholding, is required. Most of the weather forecasting systems have left the choice of selecting the initial threshold to the users of the system. Normally, the user performs some trial and error to choose the appropriate threshold. Our aim is to develop a fully-automated system capable of calculating a suitable initial threshold value and also to find out the number of appropriate levels. Many techniques have been developed for threshold calculation, such as histogram-, clustering- and entropy-based methods. Some of these techniques are parametrized and/or supervised, while others are non-parametric and unsupervised methods. We have selected two methods, which are ThresholdGW [9] and graythresh [10], which are totally automated, non-parametric and unsupervised procedures. The first method is not popular, but is easy to implement, while the second one is popular in the image processing community. These methods calculate the initial threshold in the grey scale, which is then converted into radar reflectivities. Our system also supports single thresholding and semi-automatic multi-level thresholding.

#### 3.1.1. ThresholdGW

_{z}is calculated as the average of the maximum and minimum intensities in the radar image. The image is segmented into two classes, i.e., C

_{0}and C

_{1}, using T

_{z}. The mean T

_{z}is calculated for each class, and the final T

_{z}is the average of the mean of the background and foreground.

#### 3.1.2. Graythresh

_{0}and C

_{1}on such a point that maximizes the variance between the background and foreground classes, called between class variance ${\sigma}_{B}^{2}$. The histogram of a gray scale image is computed where each bin corresponds to each gray level from zero to 255. Each gray level is considered as a dividing point for which the between class variance is computed. Finally, a gray level with maximum ${\sigma}_{B}^{2}$ is selected as T

_{z}. The detailed procedure is given in [10].

#### 3.2. Storm Labeling

_{4}(p), while p also has its four diagonal neighbors, which can be represented by N

_{D}(p). The union of N

_{4}(p) and N

_{D}(p) results in the eight-neighbors adjacency method, which can be represented by N

_{8}(p).

_{4}(p). Furthermore, p and q are said to be eight-adjacent if q is one and q ∈ N

_{8}(p). If p and q are conned pixels, q is labeled as p. When a new unconnected pixel p is found, the storm label is incremented by one, and so on. Pixels having the same label belong to the same storm. The value of the label represents the storm the number.

_{4}(p) and N

_{8}(p), we recommend using only N

_{4}(p), because N

_{8}(p) increases the probability of false mergers.

#### 3.3. Mathematical Morphology

#### 3.4. Multi-Level Thresholding

## 4. Storm Tracking

#### 4.1. Definition of Components of SALdEdA

_{i,t}, which represents a storm that is N

_{i,t}pixels large, where i = 1, 2, 3 …n, where n corresponds to the number of storms per radar scan (image/map). The current time is represented by t, while t-1 denotes the previous time instance. The current storm number is represented by i, while the previous one by j, where i = 1,2, …n

_{t}and j = 1,2, …n

_{t}

_{−1}. The radar reflectivity of the i-th storm at time t in dBZ is represented by Z

_{i,t}. The maximum reflectivity of a storm is represented by ${Z}_{i,t}^{max}$. If SALdEdA is used for precipitation objects, Z should be replaced by R.

#### 4.1.1. The Structure Component

_{t}and n

_{t}

_{−1}correspond to the number of storms at t and t-1. S is 0 ≤ S

_{i,j}≤ 1. S

_{i,j}is equal to zero if two storms are structurally the same, while S

_{i,j}= 1 indicates that the storms have totally different volumes. Volume (V

_{i,t}) is calculated as below:

_{i,t}with ${Z}_{i,t}^{max}$ is compulsory in order to distinguish the S component from the A component of SALdEdA. Z

_{i,t}can be calculated as follows:

_{x;y}is the pixel reflectivity value in dBZ.

#### 4.1.2. The Amplitude Component

_{i,t}) corresponds to mean reflectivity.

_{i,t}is the total number of pixels in the i-th storm and Z

_{x,y}is the pixel reflectivity value in dBZ. The value of the amplitude (A) is 0 ≤ A

_{i,t}≤1; where A

_{i,t}= 0 means that the i-th and j-th storms have complete agreement, while A approaching one means full disagreement between the corresponding storms with respect to amplitude. Though, theoretically, the A component can be one, practically, it cannot be, because A = 1 means one of the storms has zero mean reflectivity, which is not possible in our case (reflectivity values greater than zero are only considered).

#### 4.1.3. The Location Component

_{i,t}) represents the center of mass of the i-th storm. The value of L

_{i,j}is in the range of [0, 1]. When L

_{i,j}= 0, two storms have exactly the same position, while L

_{i,j}= 1 indicates that the two storms are the boundaries of the radar coverage area separated by distance d. Smaller values of L between two storms at two successive radar maps show that they are candidates for temporal association. Since the center of mass is a single point in a storm, therefore, tracking depending on it could be erroneous. The change in the reflectivity of storms will change its center of mass, even if it is in its old position, thus resulting in the motion of the storm.

#### 4.1.4. The Eccentricity Component

_{i,j}= 0 means that both storms have the same eccentricity, while dE

_{i,j}= 1 shows that one of the storms is perfectly circular, while the other one is a perfect line.

#### 4.1.5. The Area Component

_{i,j}ranges in [0, 1]. Practically, dA cannot be equal to one, because the area of a storm cannot be zero.

#### 4.2. Objective Function

_{i,j}is the cost when the i-th storm of the t time instance is compared with the j-th storm of t-1. C

_{i,j}is defined as:

_{i}is in the range of [0, 1]. The combinatorial optimization problem is solved by using the Hungarian algorithm [19].

#### 4.3. Handling Splits and Mergers

## 5. Storm Forecasting

_{T}represents the original observation at time T; ${\tilde{y}}_{T}$ represents the fitted value of y

_{T}; and ŷ

_{T}represents the forecasted value at T. Let us suppose that p

_{T}is the current value of a parameter pand that $\frac{dp}{Dt}$ is the temporal derivative, then:

#### 5.1. Forecasting

#### 5.2. Choosing λ

## 6. Results

_{a}is set to 10 km

^{2}for all experiments.

#### 6.1. Dataset Descriptions

#### 6.2. Automatic Storm Identification

_{z}.

_{z}is calculated by graythresh and ThreshGW, and every level has a 5-dBZ reflectivity difference.

#### 6.2.1. Storm Identification Evaluation

_{0}and ω

_{1}(respective probabilities of the background class C

_{0}and the foreground class C

_{1}) show that even in rainy radar images, 85% of the image is occupied by non-rainy pixels. The results also show that the effects of both thresholding techniques are almost the same for segmenting radar images. Therefore, any one of the two can be used for calculating the initial threshold T

_{z}.

#### 6.3. Storm Tracking

_{z}= 28 dBZ for the identification of convective and T

_{z}= 20 dBZ for the identification of stratiform events. Our main focus is to find the contribution of each variable of SALdEdA in storm tracking and to evaluate the goodness of the overall system after combining SALdEdA variables for tracking.

#### 6.3.1. Tracking Evaluation

_{3}and a new track is started at t

_{4}. A wrong association is depicted in Figure 10b,c. The fault of Figure 10c is due to the wrong threshold value of the maximum distance between them.

^{2}area with a velocity up to 50 km/h. For the convective storms, the life time may not be the actual one, because a storm can originate outside the of coverage area of our radar; therefore, the tracking in this case may be partial.

#### 6.4. Forecasting

#### 6.4.1. Forecasting Evaluation

## 7. Conclusions

^{®}presented in [2,3] is used in this investigation. Procedures for all major steps, i.e., storm identification, tracking and nowcasting, of a rain nowcasting system have been developed.

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Cluster of storms; (

**b**) hierarchical form of storms after applying different levels of thresholds.

**Figure 3.**(

**a**) The number of storms at t is less than the number of storms at t-1; storms can be tracked based on the distance between centroids and the areas of the storms; (

**b**) the reflectivity of the two candidate storms is different; storms can be associated considering the reflectivity distribution of storms; TITANmisses this aspect; (

**c**) the eccentricity of the two storms is different; storms’ association can be carried out based on eccentricity.

**Figure 5.**Comparison of automatic threshold calculation and user randomly selected threshold. (

**a**) Graythresh and ThreshGW (G stands for Gonzalez and W for Woods) calculated T

_{z}= 20 dBZ; (

**b**) user randomly (manually) selected T

_{z}= 30 dBZ.

**Figure 6.**Removal of false merger with morphological erosion. (a) Identification with erosion; (b) identification without erosion.

**Figure 8.**Histogram of K and η for checking the goodness of ThreshGW and graythresh. (

**a**) Graythresh (η); (

**b**) ThreshGW (η); (

**c**) graythresh (K); (

**d**) ThreshGW (K).

**Figure 10.**(

**a**) The tracking algorithm fails to associate storms (missed association) at t

_{3}and t

_{4}; (

**b**) storms at t

_{3}and t

_{4}are incorrectly associated; (

**c**) the storm at t

_{3}is incorrectly associated with the storm at t

_{4}, due to violating the maximum speed limitation.

**Figure 11.**Scatterplots of area vs. life time and area vs. velocity for convective and stratiform events.

**Figure 12.**Histograms of the area and life time for convective events (

**a,b**) and stratiform events (

**c,d**).

**Figure 14.**The histograms of lambda for which the minimum of the MSE is obtained while forecasting the area, mean reflectivity, major and minor axis lengths with a 5-min forecast leading time.

**Figure 15.**The black ellipse depicts the current (original) storm, while the red ellipse the forecasted one. (

**a**) Both storms overlap each other; (

**b**) underestimation; (

**c**) overestimation; (

**d**) missing location; (

**e**) missing event; (

**f**) false alarm.

**Table 1.**Selected datasets; F = Foggia, T = Turin, C = convective, S= stratiform and DID = dataset ID.

DID | Events | Start Time | End Time | Duration (Minutes) |
---|---|---|---|---|

Foggia | ||||

F_{C}_{1} | 1 April 2013 | 16:31:04 | 20:00:04 | 210 |

F_{C}_{2} | 2 and 3 April 2013 | 19:00:05 | 03:00:06 | 481 |

F_{C}_{3} | 27 April 2013 | 04:20:05 | 13:20:05 | 541 |

F_{C}_{4} | 2 May 2013 | 05:21:04 | 08:00:04 | 161 |

F_{C}_{5} | 3 June 2013 | 10:00:06 | 13:00:06 | 181 |

F_{C}_{6} | 9 August 2013 | 15:30:04 | 22:30:05 | 403 |

F_{C}_{7} | 20 August 2013 | 11:00:05 | 18:20:05 | 290 |

F_{C}_{8} | 22 August 2013 | 13:31:05 | 12:50:04 | 111 |

F_{S}_{1} | 25 November 2013 | 04:21:06 | 09:20:06 | 300 |

F_{S}_{2} | 27 December 2013 | 00:01:06 | 08:00:03 | 480 |

Turin | ||||

F_{C}_{9} | 23 and 24 April 2013 | 23:51:05 | 03:20:04 | 210 |

F_{C}_{10} | 8 August 2013 | 17:01:04 | 20:40:04 | 210 |

F_{S}_{3} | 19 December 2013 | 07:00:03 | 19:59:04 | 450 |

F_{S}_{4} | 10 February 2013 | 12:30:05 | 15:19:05 | 500 |

**Table 2.**Storm identification evaluation; mean values of η, K, ω

_{0}and ω

_{1}are given in the form of graythresh/ThreshGW up to 4 decimal places.

η | K | ω_{0} | ω_{1} | |
---|---|---|---|---|

Foggia | 0.9770/0.9720 | 0.0233/0.0279 | 0.8395/0.8407 | 0.1605/0.1592 |

Turin | 0.9478/0.9386 | 0.0522/0.0614 | 0.8915/0.8950 | 0.1085/0.1050 |

Overall | 0.9681/0.9619 | 0.0318/0.0381 | 0.8553/0.8572 | 0.1447/0.1427 |

**Table 3.**Contribution of structure, amplitude, location, eccentricity difference and areal difference (SALdEdA) variables in storm tracking; the total number of tracks is 683.

Variables | Wrong Tracks | Correct Tracks | Percentage Correct |
---|---|---|---|

S | 160 | 523 | 76.57 |

A | 554 | 129 | 18.88 |

L | 485 | 198 | 28.99 |

dE | 653 | 30 | 4.39 |

dA | 143 | 540 | 79.06 |

DID | α_{1}_{:}_{0} | α_{0}_{:}_{95} | α_{0}_{:}_{90} | α_{0}_{:}_{85} | α_{0}_{:}_{80} |
---|---|---|---|---|---|

Total | 61.32 | 73.64 | 99.34 | 78.99 | 74.93 |

DID | Total Tracks | Wrong Tracks | Correct Tracks | Percentage Correct |
---|---|---|---|---|

F_{C}_{1} | 42 | 0 | 42 | 100 |

F_{C}_{2} | 44 | 0 | 44 | 100 |

F_{C}_{3} | 123 | 3 | 120 | 97.560 |

F_{C}_{4} | 36 | 0 | 36 | 100 |

F_{C}_{5} | 38 | 0 | 38 | 100 |

F_{C}_{6} | 90 | 2 | 88 | 97.77 |

F_{C}_{7} | 83 | 0 | 83 | 100 |

F_{C}_{8} | 17 | 0 | 7 | 100 |

F_{S}_{1} | 18 | 0 | 18 | 100 |

F_{S}_{2} | 67 | 0 | 67 | 100 |

F_{C}_{9} | 22 | 1 | 21 | 95.45 |

F_{C}_{10} | 60 | 0 | 60 | 100 |

F_{S}_{3} | 30 | 0 | 30 | 100 |

F_{S}_{4} | 23 | 0 | 23 | 100 |

Total | 683 | 6 | 677 | 99.34 |

FLT | Underestimate | Hits | Overestimate | Missed Event | Missed Location | False Alarm |
---|---|---|---|---|---|---|

Convective Events | ||||||

5 | 2.11 | 89.95 | 1.16 | 6.77 | 0 | 0 |

10 | 4.06 | 84.36 | 4.49 | 7.07 | 0 | 0 |

15 | 6.38 | 78.64 | 8.26 | 6.70 | 0 | 0 |

Stratiform Events | ||||||

5 | 1.63 | 91.34 | 0.86 | 6.16 | 0 | 0 |

10 | 2.64 | 88.47 | 1.78 | 7.09 | 0 | 0 |

15 | 4.29 | 85.68 | 2.96 | 7.05 | 0 | 0 |

FLT | Hits | Overestimate | Underestimatez | False Alarm |
---|---|---|---|---|

Convective Events | ||||

5 | 88.09 | 6.89 | 3.23 | 1.78 |

10 | 78.43 | 14.56 | 4.95 | 2.04 |

15 | 68.42 | 17.49 | 9.98 | 4.10 |

Stratiform Events | ||||

5 | 97.66 | 1.04 | 0.66 | 0.62 |

10 | 93.71 | 2.89 | 2.56 | 0.82 |

15 | 88.84 | 5.29 | 5.08 | 0.77 |

© 2015 by the authors; licensee MDPI, Basel, Switzerland This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Shah, S.; Notarpietro, R.; Branca, M.
Storm Identification, Tracking and Forecasting Using High-Resolution Images of Short-Range X-Band Radar. *Atmosphere* **2015**, *6*, 579-606.
https://doi.org/10.3390/atmos6050579

**AMA Style**

Shah S, Notarpietro R, Branca M.
Storm Identification, Tracking and Forecasting Using High-Resolution Images of Short-Range X-Band Radar. *Atmosphere*. 2015; 6(5):579-606.
https://doi.org/10.3390/atmos6050579

**Chicago/Turabian Style**

Shah, Sajid, Riccardo Notarpietro, and Marco Branca.
2015. "Storm Identification, Tracking and Forecasting Using High-Resolution Images of Short-Range X-Band Radar" *Atmosphere* 6, no. 5: 579-606.
https://doi.org/10.3390/atmos6050579