# An Object-Based Method for Tracking Convective Storms in Convection Allowing Models

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Generic Evolution Properties of Convective Storms

#### 2.1. Data and Method

#### 2.2. Track-Based Attributes and Their Properties

#### 2.3. Object Attributes to Infer Resolvability

#### 2.4. Adaptability of Baseline Parameters for Tracking CAM-Simulated Storm

## 3. Materials and Methods

- A one-to-one track ${\mathrm{T}}^{0}\left({\mathrm{o}}_{\mathrm{t}},{\mathrm{o}}_{\mathrm{t}+\mathsf{\Delta}\mathrm{t}}\right)$ is the association of an object at $\mathrm{t}$ to another object at $\mathrm{t}+\mathsf{\Delta}\mathrm{t}$. This is the most common type of track we derive, describing the independent evolution of a storm from $\mathrm{t}$ to $\mathrm{t}+\mathsf{\Delta}\mathrm{t}$;
- A many-to-one track $\mathrm{T}\left(\left\{{\mathrm{o}}_{\mathrm{t}}^{1},{\mathrm{o}}_{\mathrm{t}}^{2},\dots \right\},{\mathrm{o}}_{\mathrm{t}+\mathsf{\Delta}\mathrm{t}}\right)$ is the association of multiple objects at $\mathrm{t}$ to one object at $\mathrm{t}+\mathsf{\Delta}\mathrm{t}$. It describes the merging of several storms at $\mathrm{t}$ into one storm at $\mathrm{t}+\mathsf{\Delta}\mathrm{t}$;
- A one-to-many track $\mathrm{T}\left({\mathrm{o}}_{\mathrm{t}},\left\{{\mathrm{o}}_{\mathrm{t}+\mathsf{\Delta}\mathrm{t}}^{1},{\mathrm{o}}_{\mathrm{t}+\mathsf{\Delta}\mathrm{t}}^{2},\dots \right\}\right)$ is the association of one object at $\mathrm{t}$ to multiple objects at $\mathrm{t}+\mathsf{\Delta}\mathrm{t}$. It describes the splitting of a storm at $\mathrm{t}$ into several storms at $\mathrm{t}+\mathsf{\Delta}\mathrm{t}$;
- A many-to-many track $\mathrm{T}\left(\left\{{\mathrm{o}}_{\mathrm{t}}^{1},{\mathrm{o}}_{\mathrm{t}}^{2},\dots \right\},\left\{{\mathrm{o}}_{\mathrm{t}+\mathsf{\Delta}\mathrm{t}}^{1},{\mathrm{o}}_{\mathrm{t}+\mathsf{\Delta}\mathrm{t}}^{2},\dots \right\}\right)$ is the association of multiple objects at $\mathrm{t}$ to multiple objects at $\mathrm{t}+\mathsf{\Delta}\mathrm{t}$. It describes the group tracking of several storms at t to several storms at $\mathrm{t}+\mathsf{\Delta}\mathrm{t}$. Because our goal is to separately track the evolutions of individual storms, this type of track is not considered in our solution.

## 4. Results and Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Dixon, M.; Wiener, G. TITAN: Thunderstorm identification, tracking, analysis, and nowcasting—A radar-based methodology. J. Atmos. Ocean. Technol.
**1993**, 10, 785–797. [Google Scholar] [CrossRef] - Johnson, J.; MacKeen, P.L.; Witt, A.; Mitchell, E.D.W.; Stumpf, G.J.; Eilts, M.D.; Thomas, K.W. The storm cell identification and tracking algorithm: An enhanced WSR-88D algorithm. Weather Forecast.
**1998**, 13, 263–276. [Google Scholar] [CrossRef] [Green Version] - Wilson, J.W.; Crook, N.A.; Mueller, C.K.; Sun, J.; Dixon, M. Nowcasting Thunderstorms: A Status Report. Bull. Am. Meteorol. Soc.
**1998**, 79, 2079–2099. [Google Scholar] [CrossRef] - Xue, M.; Kong, F.; Weber, D.; Thomas, K.W.; Wang, Y.; Brewster, K.; Droegemeier, K.K.; Kain, J.S.; Weiss, S.J.; Bright, D.R.; et al. CAPS realtime storm-scale ensemble and high-resolution forecasts as part of the NOAA Haz-ardous Weather Testbed 2007 spring experiment. In Proceedings of the 22nd Conference on Weather Analysis and Forecasting/18th Conference on Numerical Weather Prediction, Park City, UT, USA, 25–29 June 2007. [Google Scholar]
- Bentzien, S.; Friederichs, P. Generating and Calibrating Probabilistic Quantitative Precipitation Forecasts from the High-Resolution NWP Model COSMO-DE. Weather Forecast.
**2012**, 27, 988–1002. [Google Scholar] [CrossRef] - Tennant, W. Improving initial condition perturbations for MOGREPS-UK. Q. J. R. Meteorol. Soc.
**2015**, 141, 2324–2336. [Google Scholar] [CrossRef] - Schwartz, C.S.; Romine, G.S.; Weisman, M.L.; Sobash, R.A.; Fossell, K.R.; Manning, K.W.; Trier, S.B. A Real-Time Convection-Allowing Ensemble Prediction System Initialized by Mesoscale Ensemble Kalman Filter Analyses. Weather Forecast.
**2015**, 30, 1158–1181. [Google Scholar] [CrossRef] - Clark, A.J.; Bullock, R.G.; Jensen, T.L.; Xue, M.; Kong, F. Application of Object-Based Time-Domain Diagnostics for Tracking Precipitation Systems in Convection-Allowing Models. Weather Forecast.
**2014**, 29, 517–542. [Google Scholar] [CrossRef] [Green Version] - Skinner, P.S.; Wheatley, D.M.; Knopfmeier, K.H.; Reinhart, A.E.; Choate, J.J.; Jones, T.A.; Creager, G.J.; Dowell, D.C.; Alexander, C.R.; Ladwig, T.T.; et al. Object-Based Verification of a Prototype Warn-on-Forecast System. Weather Forecast.
**2018**, 33, 1225–1250. [Google Scholar] [CrossRef] - Han, L.; Fu, S.; Zhao, L.; Zheng, Y.; Wang, H.; Lin, Y. 3D Convective Storm Identification, Tracking, and Forecasting—An Enhanced TITAN Algorithm. J. Atmos. Ocean. Technol.
**2009**, 26, 719–732. [Google Scholar] [CrossRef] - Lakshmanan, V.; Smith, T. An Objective Method of Evaluating and Devising Storm-Tracking Algorithms. Weather Forecast.
**2010**, 25, 701–709. [Google Scholar] [CrossRef] - Kyznarová, H.; Novak, P. CELLTRACK—Convective cell tracking algorithm and its use for deriving life cycle characteristics. Atmos. Res.
**2009**, 93, 317–327. [Google Scholar] [CrossRef] - Judy, M. Multiple Hypothesis Tracking and Strong Point Analysis for Storm Tracking with Weather Radar. Master’s Thesis, University of Oklahoma, Norman, OK, USA, 2020. [Google Scholar]
- Gagne, D.J.; McGovern, A.; Haupt, S.E.; Sobash, R.A.; Williams, J.K.; Xue, M. Storm-based probabilistic hail fore-casting with machine learning applied to convection-allowing ensembles. Weather Forecast.
**2017**, 32, 1819–1840. [Google Scholar] [CrossRef] - VandenBerg, M.A.; Coniglio, M.C.; Clark, A.J. Comparison of Next-Day Convection-Allowing Forecasts of Storm motion on 1- and 4-km Grids. Weather Forecast.
**2014**, 29, 878–893. [Google Scholar] [CrossRef] - Smith, T.M.; Lakshmanan, V.; Stumpf, G.J.; Ortega, K.; Hondl, K.; Cooper, K.; Calhoun, K.; Kingfield, D.; Manross, K.L.; Toomey, R.; et al. Multi-Radar Multi-Sensor (MRMS) Severe Weather and Aviation Products: Initial Operating Capabilities. Bull. Am. Meteorol. Soc.
**2016**, 97, 1617–1630. [Google Scholar] [CrossRef] - Hou, J.; Wang, P. Storm Tracking via Tree Structure Representation of Radar Data. J. Atmos. Ocean. Technol.
**2017**, 34, 729–747. [Google Scholar] [CrossRef] - Zan, B.; Yu, Y.; Li, J.; Zhao, G.; Zhang, T.; Ge, J. Solving the storm split-merge problem—A combined storm iden-tification, tracking algorithm. Atmos. Res.
**2019**, 218, 335–346. [Google Scholar] [CrossRef] - Huttenlocher, D.; Klanderman, G.; Rucklidge, W. Comparing images using the Hausdorff distance. IEEE Trans. Pattern Anal. Mach. Intell.
**1993**, 15, 850–863. [Google Scholar] [CrossRef] [Green Version] - Gardner, M.W.; Dorling, S.R. Artificial neural networks (the multilayer perceptron)—A review of applications in the atmospheric sciences. Atmos. Environ.
**1998**, 32, 2627–2636. [Google Scholar] [CrossRef] - Johnson, A.; Wang, X.; Wang, Y.; Reinhart, A.; Clark, A.J.; Jirak, I.L. Neighborhood- and Object-Based Probabilistic Verification of the OU MAP Ensemble Forecasts during 2017 and 2018 Hazardous Weather Testbeds. Weather Forecast.
**2020**, 35, 169–191. [Google Scholar] [CrossRef] - Burghardt, B.J.; Evans, C.; Roebber, P.J. Assessing the Predictability of Convection Initiation in the High Plains Using an Object-Based Approach. Weather Forecast.
**2014**, 29, 403–418. [Google Scholar] [CrossRef] - Degelia, S.K.; Wang, X.; Stensrud, D.J.; Turner, D.D. Systematic Evaluation of the Impact of Assimilating a Network of Ground-Based Remote Sensing Profilers for Forecasts of Nocturnal Convection Initiation during PECAN. Mon. Weather Rev.
**2020**, 148, 4703–4728. [Google Scholar] [CrossRef] - Helmus, J.J.; Collis, S.M. The Python ARM Radar Toolkit (Py-ART), a Library for Working with Weather Radar Data in the Python Programming Language. J. Open Res. Softw.
**2016**, 4. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**(

**a1**–

**a4**) 20-min snapshots of MRMS composite reflectivity and (

**b1**–

**b4**) objects identified from 18 z to 19 z, 1 May 2019. Same-colored objects in column b imply tracks identified for 18–19 z and gray objects represent systems that initiate and/or dissipate during 18–19 z.

**Figure 2.**(

**a1**–

**a4**) 20-min snapshots of MRMS composite reflectivity and (

**b1**–

**b4**) objects identified from 19 z to 20 z, 1 May 2019. Same-colored objects in column b imply tracks identified for 19–20 z and gray objects represent systems that initiate and/or dissipate during 19–20 z.

**Figure 3.**Histogram of (

**a**) track direction ($\mathsf{\theta}$) and (

**b**) track speed (h) for a total of 8336 sample objects with valid hourly future tracks. Sample mean, one standard deviation range and sample size are listed on top of the histograms. The blue curves are (

**a**) normal and (

**b**) lognormal distribution probability density functions (PDFs) we designed to fit the histograms.

**Figure 4.**As in Figure 3, but for (

**a**) changes in track direction ($\mathsf{\Delta}\mathsf{\theta}$) and (

**b**) changes in track speed ($\mathsf{\Delta}\mathrm{h}$ ) for a total of 6531 sample objects with valid hourly future and past tracks. The blue curves in (

**a**,

**b**) are normal PDFs we designed to fit the histograms.

**Figure 5.**Object size histograms of (orange) temporally well-resolved and (blue) not well-resolved objects that appear on the hourly time frames of the 2-min MRMS composite reflectivity data from May 2019. An object is identified as temporally well resolved if it is associated with at least one future or past hourly track.

**Figure 6.**(

**a**) MRMS composite reflectivity and (

**b**) simulated reflectivity at the analysis time of a CAM forecast produced by OU MAP; (

**c**,

**d**) identified objects for observed and simulated storms from (

**a**,

**b**). Distance-matched observed and simulated objects in (

**c**,

**d**) are displayed with the same colors.

**Figure 7.**Schematic illustrations of whether to accept or reject a new ${\mathrm{T}}^{0}$ (shown as red dashed line) in three different scenarios (see text): (

**a**) the new track is independent of the already accepted track, (

**b**) the new track conflicts with already accepted tracks, and (

**c**) the new track shares an object with the already accepted track the already accepted tracks are shown as red solid lines. Circles marked by black and blue outlines represent objects at $\mathrm{t}$ and $\mathrm{t}+\u2206\mathrm{t}$, respectively.

**Figure 8.**(

**a**,

**b**) MRMS composite reflectivity and (

**c**,

**d**) identified objects for 22 z and 23 z, 1 May 2018. Blue (gray) shaded objects in (

**c**,

**d**) are objects larger (smaller) than ${\mathrm{A}}_{\mathrm{thres}}=100\mathrm{pts}$. The actual evolutions of the black contoured objects in ((

**c**), 22 z) to the blue contoured objects in ((

**d**), 23 z) is schematically shown in (

**e**) by the red lines.

**Figure 9.**(

**a**) Schematic illustration of the six steps to identify hourly tracks for the example of Figure 7, (

**b**) workflow of the algorithm and (

**c**) descriptions of selected symbols in (

**a**).

**Figure 10.**Schematic illustration of a track-object network and all the OTs to be identified. The initial object (or CI) for each identified OT is marked with a black solid triangle. Three OTs are identified from this network as marked by green shades, blue shades and black outlines.

**Figure 11.**(

**a1**–

**a6**) MRMS composite reflectivity, (

**b1**–

**b6**) MRMS objects and hourly OTs identified, and (

**c1**–

**c6**) 0–5 h MAP forecast simulated reflectivity and (

**d1**–

**d6**) forecast objects and hourly OTs during 00–05 z, 11 May 2018. CI objects of distinct hourly OTs are marked by black circles. Objects larger (smaller) than ${\mathrm{A}}_{\mathrm{thres}}$ are colored with blue (gray) shades.

**Table 1.**Track attributes for identified hourly tracks in Figure 1 (18–19 z) and Figure 2 (19–20 z) including track direction ($\mathsf{\theta}$ ), speed (h) and changes in track direction and speed ($\mathsf{\Delta}\mathsf{\theta}$ and $\mathsf{\Delta}\mathrm{h}$ ) from 18–19 z to 19–20 z of 1 May 2019.

18–19 z | $\mathsf{\theta}[\xb0]$ | $\mathsf{h}\left[\mathsf{k}\mathsf{m}{\mathsf{h}}^{-1}\right]$ | 19–20 z | $\mathsf{\theta}[\xb0]$ | $\mathsf{h}\left[\mathsf{k}\mathsf{m}{\mathsf{h}}^{-1}\right]$ | $\mathsf{\Delta}\mathsf{\theta}[\xb0]$ | $\mathsf{\Delta}\mathsf{h}\left[\mathsf{k}\mathsf{m}{\mathsf{h}}^{-1}\right]$ |
---|---|---|---|---|---|---|---|

Orange | 238.23 | 26.79 | Orange | 240.45 | 40.38 | 2.22 | 13.59 |

Blue | 207.31 | 32.1 | Blue | 358.94 | 4.17 | 151.63 | −27.93 |

Pink | 214.42 | 36.48 | 144.52 | −32.67 | |||

Green | 263.6 | 19.17 | N/A | N/A | |||

Magenta | 271.34 | 15.48 | N/A | N/A |

**Table 2.**The parameters used for hourly tracking. ${\mathsf{\theta}}_{\mathrm{p}/\mathrm{f}}$ and ${\mathrm{h}}_{\mathrm{p}/\mathrm{f}}$ denote the direction and speed of the given past or future motion. ${\mathrm{A}}_{\mathrm{res}}$ and ${\mathrm{h}}_{\mathrm{max}}$ are parameters of the likelihood criterion applied in steps 2 and 6 of the proposed tracking.

Parameters | Values |
---|---|

$\mathsf{\theta}~{\mathrm{N}}_{\mathsf{\theta}}\left({\mathsf{\mu}}_{\mathsf{\theta}},{\mathsf{\sigma}}_{\mathsf{\theta}}\right)$ (Generic PDF) | ${\mathsf{\mu}}_{\mathsf{\theta}}=250\xb0$ or MPL-based; ${\mathsf{\sigma}}_{\mathsf{\theta}}=60\xb0$ |

$\mathrm{ln}\left(\mathrm{h}\right)~{\mathrm{N}}_{\mathrm{h}}\left({\mathsf{\mu}}_{\mathrm{h}},{\mathsf{\sigma}}_{\mathrm{h}}\right)$ (Generic PDF) | ${\mathrm{e}}^{{\mathsf{\mu}}_{\mathrm{h}}}=45{\mathrm{km}\mathrm{h}}^{-1}$ or MLP-based; ${\mathrm{e}}^{{\mathsf{\sigma}}_{\mathrm{h}}}=1.8$ |

$\mathsf{\theta}~{\mathrm{N}}_{\mathsf{\theta}}\left({\mathsf{\theta}}_{\mathrm{p}/\mathrm{f}},{\mathsf{\sigma}}_{\mathsf{\theta}}\right)$ (Extrapolation-based PDF) | ${\mathsf{\sigma}}_{\mathsf{\theta}}=30\xb0$ |

$\mathrm{h}~{\mathrm{N}}_{\mathrm{h}}\left({\mathrm{h}}_{\mathrm{p}/\mathrm{f}},{\mathsf{\sigma}}_{\mathrm{h}}\right)$ (Extrapolation-based PDF) | ${\mathsf{\sigma}}_{\mathrm{h}}=30{\mathrm{km}\mathrm{h}}^{-1}$ |

${\mathrm{A}}_{\mathrm{res}}$ | $100\mathrm{pts}$ |

${\mathrm{h}}_{\mathrm{max}}$ | $120{\mathrm{km}\mathrm{h}}^{-1}$ |

**Table 3.**Sample size (number # of identified tracks), number # of incorrect tracks and accuracy rate for the selected four severe weather cases of May 2018. The verification period for each case is from 12 z to 12 z the next day.

Case | Sample Size (# Incorrect) | Accuracy Rate |
---|---|---|

May 01 | 108 (1) | 99.1% |

May 02 | 201 (0) | 100% |

May 03 | 211 (5) | 97.6% |

May 04 | 88 (1) | 98.9% |

All | 608 (6) | 99% |

**Table 4.**Sample size (number # of identified CI objects), number # of CI missed by 1 h and number of incorrect CIs for the selected 4 severe weather cases of May 2018. The verification period for each case is from 12 z to 12 z the next day.

Case | # CI | Missed by 1 h | # Incorrect |
---|---|---|---|

May 01 | 24 | 1 | 0 |

May 02 | 43 | 0 | 0 |

May 03 | 36 | 0 | 1 |

May 04 | 20 | 2 | 1 |

All | 123 | 3 | 2 |

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**MDPI and ACS Style**

Han, F.; Wang, X.
An Object-Based Method for Tracking Convective Storms in Convection Allowing Models. *Atmosphere* **2021**, *12*, 1535.
https://doi.org/10.3390/atmos12111535

**AMA Style**

Han F, Wang X.
An Object-Based Method for Tracking Convective Storms in Convection Allowing Models. *Atmosphere*. 2021; 12(11):1535.
https://doi.org/10.3390/atmos12111535

**Chicago/Turabian Style**

Han, Fan, and Xuguang Wang.
2021. "An Object-Based Method for Tracking Convective Storms in Convection Allowing Models" *Atmosphere* 12, no. 11: 1535.
https://doi.org/10.3390/atmos12111535