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Probabilistic Lightning Forecasts Using Deterministic Data. Evan Kuchera and Scott Rentschler 16 Aug 2007. Motivation. Air Force operators require skillful and objective probabilistic weather information to maximize efficiency and minimize loss
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Probabilistic Lightning Forecasts Using Deterministic Data Evan Kuchera and Scott Rentschler 16 Aug 2007
Motivation • Air Force operators require skillful and objective probabilistic weather information to maximize efficiency and minimize loss • Typically this is accomplished with ensembles for grid scale phenomena • However, sub grid scale processes are probabilistic in nature even with deterministic data • We believe that ensemble forecast skill will be higher if a probabilistic approach is taken with each ensemble member for sub grid scale phenomena • Addresses both sub-grid scale and flow uncertainties
Motivation • Example—lightning forecast with SPC SREF method • 10 ensemble members • CAPE values of 130,125,120,115,110,105,103,102,101,101 • With a forecast threshold of 100 J/kg, this gives a 100% chance of lightning • However, with values so close to the threshold, the true probability is likely much closer to 50% than 100% • This can be accounted for somewhat with real-time calibration after the ensemble is created (as SPC does with success), but this is not necessarily an option for the Air Force (resource constraints, lack of calibration data)
Background • Lightning background: • Need graupel and ice particle collisions to transfer negative charge to the larger particles • Thunderstorm updrafts need to grow large graupel particles with enough fall speed to cause a separation of charge in the vertical • The theoretical value of CAPE required to do this is only 25 J/kg
Background • CAPE background: • Accepted parcel theory assumption is that as the parcel rises, all condensate is immediately removed, and that there is no latent heat of freezing • However, lightning is caused by frozen condensates in an updraft! • We decided to test CAPE both ways—the traditional way, and with condensates/latent heat of freezing
Methodology • Goal: create a probabilistic lightning algorithm using a large set of CONUS observations and physical assumptions relevant worldwide • 2006 3-hourly 20 km RUC analyses • NLDN lightning in the RUC grid box (0-3 hr after analysis) • 3 hour precipitation from METARS • Find which forecast parameters are the best, then curve fit the probability of lightning given a binned value of that parameter
NLDN 3-hourly lightning climatology for a 16 km grid box (2003-2006)
Results GL CAPE is calculated from the LFC to -20C Set to zero if equilibrium level is warmer than -20C TEST is condensate and latent heat of freezing included
Results Climatology=0.155
Results Perfect Reliability
Results No Skill Forecast
Results SPC method: forecast 100% chance of lightning if GL CAPE is greater than 100 J/kg and precipitation is greater than 0.01 inches. Forecast 0% otherwise. NULL method: Always forecast 0% chance of lightning. TEST method: Algorithm presented here. BSS: Brier skill score, compares mean squared error of forecast to mean squared error of climatology. 1 is perfect, 0 is no skill, negative is worse than climatology. ROC area: Total integrated area underneath ROC curve. 1 is perfect, 0.5 is no skill.
Summary • Algorithm has been developed to forecast lightning probability given observed instability (RUC analysis) and precipitation (METARS) • Algorithm is somewhat sharp, reliable at all forecast probabilities, and has good resolution of events and non-events • Buoyancy calculations probably need to account for condensate and latent heat of freezing—but our data are not conclusive on this point
Other/Future Work • Equations have been developed (not shown here) to forecast strikes per unit area for application to any model resolution • After knowing strikes per unit area, can forecast probabilities for smaller areas (i.e. Air Force base warning criteria area) based on downscaling climatology—equation has been developed for this purpose as well • Just beginning to look at algorithm with model data and in ensembles—issues with model precipitation forecasts • Acknowledgments: ARM data archive, Dr. Tony Eckel, Stephen Augustyn, Bill Roeder, Dr. David Bright, Jeff Cunningham
Questions? GFS 66 hour grid point lightning probability forecast valid this afternoon
Backup Slides • Adjustments for changes in model resolution or area of interest • First, re-calculate total number of strikes for the new model grid box area • If model grid is finer than RUC, re-calculate probabilities using inverse of strikes equation • If model grid is coarser than RUC, increase probabilities using special upscaling equation • If area of interest is smaller than area of model grid, recalculate strikes and use downscaling equation to get probabilities
Backup Slides • Downscaling equation details • Inputs: • Strikes (S) • horizontal resolution of coarse area in km (C) • horizontal resolution of fine area in km (F) • Equation: 1-[1-(F^2/C^2)]^(S^A) • Where A is a “fudge factor” depending on F • A=1-0.17*LN(F-1) • A equals unity when F is 2 km, and slowly decreases toward zero as F approaches ~350 km • In nature, lightning tends to be randomly distributed at 2 km (storm scale) but more clustered at higher resolutions. “A” attempts to account for this • Best to use this equation from 2 to 128 km grid sizes • If strikes is less than one, calculate equation using 1 strike, then multiply result times number of strikes
Backup Slides • Upscaling • Probability added to: • [1-probability]*[1-(F^2/C^2)]*downscaled probability • This ensures high probabilities will only occur when the original probability was high, or the area has increased substantially with moderately high initial probabilities • No testing as to whether this is calibrated
NWS Topeka forecast taken from the web on 15 Aug: Friday, August 17 at 7pmTemperature: 89°FThunder: <10% Backup Slides
