Probabilistic Lightning Forecasts Using Deterministic Data

I n t e g r i t y - S e r v i c e - E x c e l l e n c e

Air Force Weather Agency

Probabilistic Lightning Forecasts Using Deterministic

Data

Evan Kuchera and Scott Rentschler16 Aug 2007

2I n t e g r i t y - S e r v i c e - E x c e l l e n c e

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


Image from NASA-GHCCWorldwide lightning climatology


Traditional Lifted Index


TEST Lifted Index


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


2006 Results

METAR ObservationsNo lightning/no precip 2,014,877

No lightning/precip 147,881lightning/no precip 33,840

lightning/precip 27,143Total 2,223,741

Climatology of lightning 2.7%Climatology of lightning

given precipitation 15.5%Climatology of lightning given non-zero CAPE 4.1%

Climatology of lightning given precipitation and

non-zero CAPE 24.7%


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


CAPE > 0, Precipitation > 0.01

y = 0.14*Ln(x) + 0.005

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CAPE (J/kg) * Precipitation (inches)Bins with width 5

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CAPE=0, Precipitation > 0.01

y = 0.36x0.5

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[LI in K (from -4 to 0) + 4] * Precipitation (inches)Bins width 0.10

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CAPE > 0, Precipitation=0

y = 0.025Ln(x) + 0.03

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Results

Forecasts by bin when precipitation occurred

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0.025 0.075 0.125 0.175 0.225 0.275 0.325 0.375 0.425 0.475 0.525 0.575 0.625 0.675 0.725 0.775 0.825 0.875 0.925 0.975

Climatology=0.155


Results

Reliability--Precipitation only

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Results

ROC Curve--precipitation only (probability thresholds on curve)

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No Skill Forecast


Method BSS ROC areaSPC -0.420 0.713NULL -0.180 0.500TEST 0.362 0.888

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.

Results


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

Strikes per 400 square km

y = e4.5x

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Probability

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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


Backup SlidesNWS Topeka forecast taken from the web on 15 Aug:

Friday, August 17 at 7pmTemperature: 89°FThunder: <10%


Backup Slides


Backup Slides

Documents

Probabilistic Lightning Forecasts Using Deterministic Data