Sterling, VA Research Region Map Types and Lightning Frequencies

1. Sterling, VA Research Region Map Types and Lightning Frequencies Henry Fuelberg Pete Saunders

2. Map Typing (Pattern Classification) • In developing the model for lightning probability forecasts, we created pattern-type lightning frequencies that will be used as candidate predictors. As in Shafer and Fuelberg (2006), we believe these predictors will provide detailed information on local lightning enhancements that are not adequately resolved by the NCEP models. The goal is to capture local interactions between the low-level winds and thermal circulations. • A correlation technique described by Lund (1963) and Reap (1994a) was used to develop what we call “map-type predictors”. The correlation technique was applied to 3-hourly observed 850-hPa geopotential height fields from RUC analyses. The time period is the warm season months (May-September) from 2001 to 2007. We believe that the 850-hPa level provides the best indication of low-level flow in terms of both direction and speed. • The RUC-20 and RUC-40 geopotential height values were interpolated onto a coarser 50-km grid in order to smooth the smaller-scale variations and to capture the regional characteristics of the low level flow.

3. Map Typing (Pattern Classification) • Only time periods when the geopotential height maps could be correlated at 0.8 or greater (Lund 1963; Reap 1994a) were used in creating the map types. However, unclassified maps were assigned to the map type in which they were most correlated for model equation development. This also is represented in the map type means and frequencies. • For each map type and 3 hourly period, relative lightning frequencies were then calculated. • The unconditional mean number of flashes also were calculated for every 3-h period and map type. • Details of these procedures follow.

4. Map Typing Procedures We used the following procedures to determine pattern type classification: • Gathered RUC-20 and RUC-40 data for geopotential heights at various levels. RUC-40 data was used for the years 2001 through 2004. RUC20 data was used for the years 2005 through 2007, giving a total of 7 years of height data. • Grid points for the Sterling, VA research region were subset for the following lat/lon coordinates: Latitude: 33 N through 42 N Longitude: -72.0 W through -82.5 W

5. Map Typing Procedures • 3-h geopotential height data were extracted from the grib files for each day through the 7 year period to create a total of 8298 maps. • Each 3-h period then was interpolated to a 50-km grid from the initial 20-km and 40-km grids. • From here, each 3-h RUC geopotential height map was correlated with every other map in the sample to determine the map types. For example, maps correlated at the R=0.8 threshold were placed into Map Type A. Then, every map that was determined to be of Type A was removed and a new correlation matrix was created to determine Map Type B at the same threshold. This correlation process then was repeated to produce 5 total map types (A – E).

6. Map Type Frequencies and Means • We then completed the following steps to relate lightning to the map types that had been created: 1. Read in the list of lat/lon grid values. 2. Read in the time and lat/lon location of each flash in the monthly .lga file. 3. Created a program that determined if the flash lies within the specified radius of each grid point by computing the separation distance (km) between the flash and the grid point. The calculation of separation distance used a formula for the great circle distance on a sphere. 4. If the computed separation distance was <= to the specified counting radius, then the flash count for the grid point for the particular hour was incremented by one. 5. Hourly grids were written to separate output files for each month. 6. Created a program that read the monthly grid files and summed the hourly flashes into 3-hourly totals

7. Map Type Frequencies and Means • Finally, we created a program that computes map type lightning frequency values as well as the mean number of flashes for each grid point for each 3-hr period, using data for the 7-yr period 2001-2007. - We should note that a simple mean number of flashes can be heavily influenced by single events with a large number of flashes (i.e. outliers), which can result in the plots being somewhat noisy. As an alternative, a "trimmed" mean will be calculated whereby the upper and lower 2% of the data is excluded from the calculation. The resulting mean is much more resistant to outliers. - The computed frequencies represent the following: - Likewise, the computed “trimmed” means represent the following:

8. A Few Statistics * 8298 Total Maps

9. Lightning Percentiles Percentile of flash count for each 3-h period

10. Map Types L • High pressure (ridging) to the south and low pressure to the north inducing predominately zonal flow across the region H

11. Map Types H • High pressure (ridging) to the northe and low pressure to the south. This induces more easterly flow across the Mid-Atlantic states L

12. Map Types • Low pressure (troughing) over much of the Mid-Atlantic; especially in parts of Maryland and the Washington, D.C. and Baltimore metropolitan areas. L H

13. Map Types • High pressure (ridging) over much of the area, especially over Maryland and most of Virginia. Further to the south, an easterly wind component is induced. H

14. Map Types L • High pressure (ridging) centered over south central/southwestern Virginia, and weak troughing to the north of the region. H

15. Map Type Frequencies

16. Map Type Frequencies

17. Map Type Frequencies

18. Map Type Frequencies

19. Map Type Frequencies

20. Map Type Means Sum Flashes/Total # of Maps in Map Type A

21. Map Type Means Sum Flashes/Total # of Maps in Map Type B

22. Map Type Means Sum Flashes/Total # of Maps in Map Type C

23. Map Type Means Sum Flashes/Total # of Maps in Map Type D

24. Map Type Means Sum Flashes/Total # of Maps in Map Type E

25. Additional Predictors • The map type means and frequencies will be the candidate predictors for the lightning probability model, and likely will be selected as final predictors. The following parameters also will be tested statistically using the SPSS software to determine their legitimacy for inclusion in the final predictor set. Binary logistic regression techniques will be implemented to determine the significance of each parameter and how much weight it should be assigned. • Equivalent Potential Temperature • Theta-E Advection • Thickness • Price Rind (Lightning Frequency in flashes per minute based on cloud top height(km) ) • Convective Inhibition • Divergence • Most unstable CAPE • Mean Wind Speed • Precipitable Water • Showalter Stability Index • Vorticity • Lapse Rates • Moisture Flux Convergence • Temperature Advection