# Heuristic and Bayesian Tornado Prediction in Complex Terrain of Southern Wyoming

## Abstract

**:**

## 1. Introduction

## 2. Research Motivation and Goal

#### Hypothesis Test

## 3. Materials and Methods

#### 3.1. Surface Observations

#### 3.2. Doppler Weather Radar Observations

## 4. Topography

## 5. Results

#### 5.1. Environmental Conditions: (t − 2) h

#### 5.2. Supercell Thunderstorm Formation: (t − 1) h

#### 5.3. Tornado Formation: (t − 5) min

## 6. Discussion

## 7. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of hypothesis illustrating the interaction of saturated air parcels and environmental wind flow over modeled complex terrain with a thunderstorm updraft from 2-D (bottom graphic) and 3-D (top graphic) perspectives: elevation contours (solid brown lines), air parcels (P1, P2), thunderstorm updraft (red “U” symbol), ambient wind flow (solid green arrows) affecting parcels, and parcel motion over time (solid blue arrows).

**Figure 2.**Monthly distribution of tornadoes in Albany County, Wyoming from January 1950 to December 2022.

**Figure 3.**Topography of southern Wyoming including Albany County with black geographical labels for various regions, distance legend, compass heading, and terrain elevation key (grey tones: m MSL). Mesonet identifiers are indicated by yellow squares with labels in the domain. The brown horizontal line at the bottom of the figure is the Wyoming-Colorado border. The city of Laramie (dark brown cross symbol and label) is situated at the western foot of the Laramie Range. The WSR-88D KCYS radar tower (dark blue radar dish symbol) is located just east of mesonet station, CYS.

**Figure 4.**Dryline boundary computed as the vector magnitude of the gradient of the surface dewpoint depression (solid brown and green lines with slanted green regions for higher relative humidities) (${10}^{-4}$ °C m${}^{-1}$) and surface divergence of the horizontal (u, v) wind (dashed blue contours) (${10}^{-4}$ s${}^{-1}$) for Cases (

**a**) A at 2000 UTC, (

**b**) B at 2203 UTC, (

**c**) C at 1902 UTC, and (

**d**) D at 2200 UTC.

**Figure 5.**WSR-88D KCYS N0Q (Long Range Base Reflectivity at 0.5 degrees) (dBZ) (dotted color table from 20 (dark blue) to 75 (white) dBZ), surface moisture flux divergence (${10}^{-6}$ g kg${}^{-1}$ m s${}^{-1}$) (negative: purple dashed contours with “M” symbols for local minima), Jacobian matrix determinant (${10}^{-7}$ s${}^{-2}$) (negative: solid blue and positive: solid orange contours), surface observations (red: drybulb temperature (°C), dark green: dewpoint temperature (°C), 10-m AGL wind barbs (brown: every 5 knots), and 3-km interpolated 10-m AGL wind vectors (vanilla: every 5 knots)) for Cases (

**a**) A at 2000 UTC, (

**b**) B at 2203 UTC, (

**c**) C at 1902 UTC, and (

**d**) D at 2200 UTC. Storm identifiers are labeled with black capital letters (e.g., “A”, “B”, “C”, “D”, or “E”).

**Figure 6.**WSR-88D KCYS N0S (Storm Relative Velocity at 0.5 degrees) (knots) (solid color table from −75 (inbound green) to +75 (outbound red) knots), extrapolated mean sea-level pressure (hPa: dotted vanilla contours), and surface observations (red: drybulb temperature (°C), dark green: dewpoint temperature (°C), and 10-m AGL wind barbs (brown: every 5 knots)) for Cases (

**a**) A at 2000 UTC, (

**b**) B at 2203 UTC, (

**c**) C at 1902 UTC, and (

**d**) D at 2200 UTC. The outline of the 20 dBZ echo is a dark blue contour. Locations of high and low air pressure extrema are indicated by blue “H” and red “L” symbols, respectively.

**Figure 7.**Same data as in Figure 5 but for Cases (

**a**) A at 2100 UTC, (

**b**) B at 2302 UTC, (

**c**) C at 1930 UTC, and (

**d**) D at 2330 UTC. Storm identifiers are labeled with black capital letters.

**Figure 8.**Same data as in Figure 6 but for Cases (

**a**) A at 2100 UTC, (

**b**) B at 2302 UTC, (

**c**) C at 1930 UTC, and (

**d**) D at 2330 UTC. Storm identifiers are labeled with black capital letters.

**Figure 9.**Same data as in Figure 5 but for Cases (

**a**) A at 2116 UTC, (

**b**) B at 2340 UTC, (

**c**) C at 2003 UTC, and (

**d**) D at 0003 UTC (next day). Storm identifiers are labeled with black capital letters.

**Figure 10.**Same data as in Figure 6 but for Cases (

**a**) A at 2116 UTC, (

**b**) B at 2340 UTC, (

**c**) C at 2003 UTC, and (

**d**) D at 0003 UTC (next day). Storm identifiers associated with tornadoes are labeled with black capital letters; tornado vortexes are marked by upside-down dark brown triangles. The pressure drop associated with storm inflow acceleration is solid white contours at 1 and 3 hPa intervals and indicates the vortex location.

**Figure 11.**Bayesian posterior probability (smoothed) due to shearing effects (%) of a tornado based on the negative (dotted vanilla and filled dotted colored contours) Jacobian determinant and moisture flux divergence for Cases (

**a**) A at 2116 UTC, (

**b**) B at 2340 UTC, (

**c**) C at 2003 UTC, and (

**d**) D at 0003 UTC (next day). Storm identifiers associated with tornadoes are labeled with black capital letters. Outlines of 20, 35, 50, and 65 dBZ echoes are indicated by dark blue, dark green, dark yellow, and light red contours, respectively.

**Figure 12.**Bayesian posterior probability (smoothed) due to stretching effects (%) of a tornado based on the positive (dotted vanilla and filled dashed colored contours) Jacobian determinant and moisture flux divergence for Cases (

**a**) A at 2116 UTC, (

**b**) B at 2340 UTC, (

**c**) C at 2003 UTC, and (

**d**) D at 0003 UTC (next day). Storm identifiers associated with tornadoes are labeled with black capital letters. Outlines of 20, 35, 50, and 65 dBZ echoes are indicated by dark blue, dark green, dark yellow, and light red contours, respectively.

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**MDPI and ACS Style**

Andretta, T.A.
Heuristic and Bayesian Tornado Prediction in Complex Terrain of Southern Wyoming. *Meteorology* **2023**, *2*, 239-256.
https://doi.org/10.3390/meteorology2020015

**AMA Style**

Andretta TA.
Heuristic and Bayesian Tornado Prediction in Complex Terrain of Southern Wyoming. *Meteorology*. 2023; 2(2):239-256.
https://doi.org/10.3390/meteorology2020015

**Chicago/Turabian Style**

Andretta, Thomas A.
2023. "Heuristic and Bayesian Tornado Prediction in Complex Terrain of Southern Wyoming" *Meteorology* 2, no. 2: 239-256.
https://doi.org/10.3390/meteorology2020015