1034 VOLUME 17W E A T H E R A N D F O R E C A S T I N G

q 2002 American Meteorological Society

A Lightning Prediction Index that Utilizes GPS Integrated Precipitable Water Vapor*

ROBERT A. MAZANY1 AND STEVEN BUSINGER

University of Hawaii, Honolulu, Hawaii

SETH I. GUTMAN

NOAA/Forecast Systems Laboratory, Boulder, Colorado

WILLIAM ROEDER

Patrick Air Force Base, Florida

(Manuscript received 8 March 2001, in final form 26 February 2002)

ABSTRACT

The primary weather forecast challenge at the Cape Canaveral Air Station and Kennedy Space Center islightning. This paper describes a statistical approach that combines integrated precipitable water vapor (IPWV)data from a global positioning system (GPS) receiver site located at the Kennedy Space Center (KSC) withother meteorological data to develop a new GPS lightning index. The goal of this effort is to increase theforecasting skill and lead time for prediction of a first strike at the KSC. Statistical regression methods are usedto identify predictors that contribute skill in forecasting a lightning event. Four predictors were identified outof a field of 23 predictors that were tested, determined using data from the 1999 summer thunderstorm season.They are maximum electric field mill values, GPS IPWV, 9-h change in IPWV, and K index. The GPS lightningindex is a binary logistic regression model made up of coefficients multiplying the four predictors. When timeseries of the GPS lightning index are plotted, a common pattern emerges several hours prior to a lightning event.Whenever the GPS lightning index falls to 0.7 or below, lightning occurs within the next 12.5 h. An indexthreshold value of 0.7 was determined from the data for lightning prediction. Forecasting time constraints basedon KSC weather notification requirements were incorporated into the verification. Forecast verification resultsobtained by using a contingency table revealed a 26.2% decrease from the KSC’s previous-season false alarmrates for a nonindependent period and a 13.2% decrease in false alarm rates for an independent test season usingthe GPS lightning index. In addition, the index improved the KSC desired lead time by nearly 10%. Althoughthe lightning strike window of 12 h is long, the GPS lightning index provides useful guidance to the forecasterin preparing lighting forecasts, when combined with other resources such as radar and satellite data. Futuretesting of the GPS lightning index and the prospect of using the logistic regression approach in forecastingrelated weather hazards are discussed.

1. Introduction

Space launches and landings at the Kennedy SpaceCenter (KSC) are subject to strict weather-related con-straints (see, e.g., Bauman and Businger 1996). Nearly75% of all space shuttle countdowns between 1981 and1994 were delayed or scrubbed, with about one-half ofthese due to weather (Hazen et al. 1995). Of the various

* School of Ocean and Earth Science and Technology ContributionNumber 5930.

1 Current affiliation: 17th Operational Weather Squadron, Joint Ty-phoon Warning Center, Pearl Harbor, Hawaii.

Corresponding author address: Prof. Steven Businger, Dept. ofMeteorology, University of Hawaii, 2525 Correa Rd., Honolulu, HI96829.E-mail: businger@hawaii.edu

weather constraints, the primary weather challenge isto forecast lightning 90 min before a first strike andwithin a 20 n mi radius of the launch complexes (Fig.1a). The National Lightning Detection Network indi-cates that this region has one of the highest lightningflash densities in the country, averaging 10 flashes persquare kilometer per year, confirming that lightning hasa significant impact on the Kennedy Space Center (Huf-fines and Orville 1999; Orville and Huffines 1999). Thefirst concern is the safety of personnel working on thecomplex, and the next is protection for $10 billion rocketlaunching systems and platforms that include the spaceshuttle, Athena, Pegasus, Atlas, Trident II, and Titan IV.Last, delay costs can run anywhere from $90,000 for a24-h delay to $1,000,000 if the shuttle must land atanother facility and be transported back to the KSC(Bauman and Businger 1996).

Modeling and observational studies conclude that pat-

OCTOBER 2002 1035M A Z A N Y E T A L .

FIG. 1. (a) Map of the Cape Canaveral Air Station and Kennedy Space Center vicinity showinglocations of special meteorological sensors. Circle indicates primary area of concern for lightningstrikes (adapted from Bauman and Businger 1996). (b) Current and planned GPS IPWV sites inFlorida.

terns and locations of Florida convection are related tothe interaction of the synoptic wind field with the me-soscale sea breeze (Estoque 1962; Neumann 1971; Piel-ke 1974; Boybeyi and Raman 1992). The sea-breeze

circulation and patterns of convection have differentcharacteristics dependent on whether or not the low-level flow has an onshore, offshore, or alongshore com-ponent with respect to Florida’s east coast (Arritt 1993).

1036 VOLUME 17W E A T H E R A N D F O R E C A S T I N G

Onshore easterly flow typically generates less vig-orous convection than offshore westerly flow (Foote1991). However, onshore flow is characterized by a shal-low low-level maritime moist layer, capped by a sub-sidence layer with dry conditions aloft, creating diffi-culties in predicting convection associated with this typeof regime (Pielke 1974; Bauman et al. 1997). Blanchardand Lopez (1985) show that the majority of convectiontakes place in the sea-breeze and lake-breeze conver-gence zones. They state that deep convection is sparseand requires low-level forcing, which generally occursonly when the east coast sea breeze has advanced west-ward and merges with the west coast sea breeze. Al-though convection can develop independently of a sea-breeze frontal merger, it is usually weaker than whenthe fronts merge.

Reap (1994) found that southwesterly flow tends tobe unstable and produce more lightning strikes alongthe Florida east coast than easterly flow. The south-westerly flow also contains deeper moisture and ac-counts for two-thirds of the lightning strikes during thesummer at KSC. In contrast, easterly flow accounts forless than 5% of the total lighting flashes (Watson et al.1991).

The International Station Meteorological ClimateSummary (NCDC 1996) for the KSC (March 1968–February 1978) indicates an annual average of 76 dayswith thunderstorms. Most of the thunderstorms (81.2%)occur from May through the end of September. In fact,the 45th Weather Squadron (WS) at Patrick Air ForceBase (AFB) issues more than 1200 lightning watchesand warning per year.

The 45th WS uses numerical weather prediction mod-els and many observation systems to detect and predictlightning in support of the space center needs. The latterinclude satellite data, weather radars, rawinsondes, andfive lightning detection systems. The lightning detectionand ranging (LDAR) is a seven-antenna radio-wavetime-of-arrival system that provides a three-dimensionalpicture of in-cloud, cloud-to-cloud, cloud-to-clear-air,and cloud-to-ground lightning. The cloud-to-groundlightning surveillance system is a five-antenna magneticdirection finding system. The launch pad lightningwarning system (LPLWS) is a network of 31 surfaceelectric field mills. The National Lightning DetectionNetwork (NLDN) is a national network of magneticdirection finding and time-of-arrival antennas. The A.D. Little, Inc., sensor is an older system using one an-tenna to estimate the lightning distance from the mag-netic pulse change. Most of these lightning detectionsystems are more fully described by Harms et al. (1997).

For the 1999 thunderstorm season, the 45th WeatherSquadron’s capability to forecast thunderstorms detect-ed by the NLDN and LPLWS is 97.5%, of which 79.1%meet the desired 90-min lead time (NCDC 1996). TheKSC false alarm rate is 43.2%. There is room for im-provement in these statistics, particularly in reducingthe false alarm rate.

GPS and the role of water vapor

The water molecule has an asymmetric distributionof charge that results in a permanent dipole moment.This unique structure results in the large latent heatassociated with changes of phase, it makes possible thephenomena of lightning, and also makes possible theability to monitor integrated precipitable water vapor(IPWV) using the global positioning system (GPS).

Several mechanisms have been proposed to accountfor the generation of electrical charge separation inclouds. In general, theories that have been forwardedto explain the separation of charge in clouds recognizethe importance of microphysical processes involvingwater in its various phases (e.g., Willis et al. 1994).

Bevis et al. (1992, 1994) describe the methodologyfor using GPS to monitor atmospheric water vapor fromground-based GPS sites and present an error analysis.Duan et al. (1996) provide the first direct estimation ofIPWV by eliminating the need for any external com-parison using water vapor radiometer observations(Rocken et al. 1993). Businger et al. (1996) describemeteorological applications of atmospheric monitoringby GPS for use in weather and climate studies and innumerical weather prediction models.

The National Oceanic and Atmospheric Administra-tion (NOAA) Forecast Systems Laboratory (FSL) estab-lished the first GPS network dedicated to atmosphericremote sensing of water vapor (Wolfe and Gutman 2000).Since its inception in 1994, the NOAA GPS network hasbeen steadily expanding, with GPS receivers sited orplanned in all 50 states. Florida, like many other states,has plans to develop a relatively large network of GPSreceivers for applications other than weather forecasting(Fig. 1b). The dual use of these sites, however, is expectedto provide valuable data for the improvement of short-term cloud and precipitation forecasts, with consequentimprovements in transportation safety. Recently, a slidingwindow technique for processing the GPS was developedjointly at the University of Hawaii and the Scripps In-stitution of Oceanography, University of California at SanDiego. The method has been implemented operationallyat FSL and provides estimates of IPWV every 30 min,with about 18-min processing time or latency, and an rmsaccuracy of ;3.5% of the mean value of IPWV (Fig. 2).GPS IPWV data are available in near–real time on theWeb (courtesy of NOAA/FSL at http://gpsmet.fsl.noaa.gov/realtimeview/jsp/rti.jsp).

In this paper we describe a statistical approach thatcombines IPWV data from a GPS site located at theKennedy Space Center with other meteorological datato develop a new GPS lightning index. The goal of thiseffort is to improve the skill in forecasting a first strikeat the Kennedy Space Center.

2. Data resources

The thunderstorm season at the KSC is from Maythrough September. Data for the 1999 summer season

OCTOBER 2002 1037M A Z A N Y E T A L .

FIG. 2. Comparison of column integrated water vapor from rawinsondes launched by the 45thWeather Squadron at Patrick AFB, FL (circles), with GPS observations made at the U.S. CoastGuard differential GPS site (CCV3) at Cape Canaveral, FL (Julian day 5 yearday).

TABLE 1. Initial predictors.

Predictors Source of data

1) GPS IPWV2–13) DIPWV* from 1 to 12 h

14) 30-min field mill averages15) 30-min field mill maxima16) Temperature17) Pressure18) Dewpoint temperature19) Total totals20) Freezing level21) Wind direction22) K index23) 700-mb vertical velocity

GPS sensorGPS sensorElectric field millElectric field millGPS sensorGPS sensorSurface observationRaobRaobSurface observationRaobEta Model

* D means change.

were divided into two periods: period A (14 April–9June) and period B (10 June–26 September). These par-ticular dates were chosen on the basis of the distributionof thunderstorms and the data availability associatedwith instrumentation down time.

The period B data were used to create the logisticregression model that composes the GPS lightning in-dex. Period B data contained 46 event days and providedrobust predictor data. During this period, GPS IPWVvalues are much higher and show more variability thanin the winter and are somewhat higher than during pe-riod A. The period A data were reserved for an inde-pendent test using the GPS lightning index results.

The Kennedy Space Center has a dense array ofweather sensors. One of the challenges of this researchis determining which meteorological variables wouldadd skill in a lightning prediction index. Twenty-threepotential predictors were initially evaluated (Table 1).

The availability of real-time GPS IPWV was the pri-mary motivation for undertaking the research presentedin this paper. Since October 1998, GPS IPWV data havebecome available with 30-min temporal resolution fora GPS site located at 28.488N, 80.388W, roughly thecenter of the Cape Canaveral landmass just north of theprimary landing strip. Data for this research cover 1 yrfrom October 1998 to October 1999. The GPS site hadmissing data, mostly due to communications problemsbetween the site and the facility that collects the datafor NOAA/FSL. Any day that had a total of more than4 h of missing data was eliminated from the analysis.

The Kennedy Space Center data resources offeredbenefits that make this study possible (Fig. 1a). Upper-air soundings are often taken more than twice a daypending various launches and weather conditions, sothere is a slight increase in the temporal resolution. Also,there are U.S. Air Force weather observers at Cape Can-averal Air Station 24 h a day. Adding a human elementto the observation codes, especially in the remarks sec-tion, provided an increase in understanding of the me-teorological conditions. Electric field mills provided an-other source of data in this investigation. There are 31field mills that measure the electric potential of the at-mosphere in volts per meter (V m21) every 5 min. Themaximum field mill value was used for the 30-min win-dow ranging from the top of the hour until the half-hourmark. This maximum value was assigned to the GPSIPWV value taken 15 min after the hour. From the half-hour mark to the top of the hour, that value was assignedwith the GPS IPWV value taken 45 min after the hour.Typical fair weather electric field mill values rangedfrom 70 to 800 V m21. During inclement weather when

1038 VOLUME 17W E A T H E R A N D F O R E C A S T I N G

the potential for lightning existed, values would increasesubstantially, sometimes reaching values of 12 000 Vm21 during a lightning event. The only suspect valueswere around 1000 UTC [0500 eastern standard time(EST)]. From a normal field of 100–200 V m21 justbefore 1000 UTC, field mill values would jump, some-times up to 3000 V m21 for what appeared to be nometeorological event. Marshall et al. (1999) explain thissunrise effect as the local, upward mixing of the denser,low-lying, electrode-layer charge.

Other variables investigated for the GPS lightningindex include 700-mb vertical velocity from the EtaModel, total totals (TT) index, K index (KI), freezinglevel from rawinsondes, and surface temperature, dew-point, pressure, and wind direction taken from stationobservations. The KI considers the static stability of the850–500-mb layer. The KI is given by

KI 5 T 2 T 1 T 2 (T 2 T ),850 500 d850 700 d700 (1)

where T850 and Td850 are the dry-bulb temperature anddewpoint temperature at 850 mb, and T500 is the dry-bulb temperature at 500 mb. The quantity T700 2 Td700

is the 700-mb dewpoint depression. In order for the KIto correspond with the 30-min GPS temporal resolution,KI values were interpolated linearly between soundingtimes.

Lightning detection and ranging (LDAR) data provide80%–90% detection efficiency of cloud-to-groundstrokes (Cummins et al. 1998). LDAR was used asground truth to verify when and where a lightning eventoccurred. LDAR data are voluminous; the sensors detectpoint discharges. With a time resolution on the order ofmilliseconds, one lightning flash can have up to 20 000LDAR points, and one thunderstorm can have thousandsof flashes, so one thunderstorm can have up to tens ofmillions of LDAR points. These LDAR points (in me-ters) are ranged from a central site in the x, y, and zdirections (Maier et al. 1996). A point is classified asa new flash if the new point is 300 ms later or 5000 mfrom the previous point. Also, two or more points makea flash, presuming they meet the above criteria, occur-ring within 300 ms in time and nearer than 5000 m inspace. These are the same criteria that the NationalWeather Service, Melbourne, Florida, uses to verifystep-leader points as a lightning flash. In the researchpresented in this paper, the first strike was verified usingLDAR data and was matched to the nearest correspond-ing GPS IPWV data.

3. Development of a lightning prediction index

a. Logistic regression

Regression methods provide the best opportunity fordata analysis concerned with describing the relationshipbetween a response variable and one or more predictorvariables. Since the event to be forecast was the firststrike of a lightning event, a binary logistic regression

model was chosen as opposed to a linear regressionmodel.

What distinguishes a logistic regression model froma linear regression model is that the outcome variablein logistic regression is binary or dichotomous (Hosmerand Lemeshow 1989). The two outcomes are yes thelightning event occurred or no it did not.

The quantity p j 5 E(Y | xj) represents the conditionalmean of a lightning strike (Y) given a predictor (x) whenthe logistic distribution is used. The specific form of thelogistic regression model is

(b 1bx )0 jep 5 , (2)j (b 1bx )0 j1 1 e

where p j is the probability of a response for the jthcovariate, b0 is the intercept, b is a vector of unknowncoefficients associated with the predictor, and xj is apredictor variable associated with the jth covariate.Next, Hosmer and Lemeshow (1989) use a logit trans-formation of pj defined as

g(p ) 5 ln[(p )/(1 2 p )] 5 b 1 b X .j j j 0 j j (3)

The importance of this link function is that g(pj) hasmany of the desirable properties of a linear model. Thelogit g(x) is linear in its parameters, may be continuous,and may range from 2` to 1`, depending on the rangeof x.

b. The predictors

The initial set of predictors included 23 variables (Ta-ble 1), which were tested for their potential contributionto the regression. In the table, changes in IPWV withtime (DIPWV) for periods ranging from 1 to 12 h aredesignated as variables 2 through 13. The purpose ofincluding changes in IPWV is to capture differences inthe airmass moisture over a number of time intervals.Positive values indicate that IPWV has increased overthe time interval.

The logistic regression model applied to these variousdata provides estimates of the coefficients, standard er-ror of the coefficients, p values, t ratio, and odds ratio.The coefficient of each predictor is the estimated changein the link function with a one-unit change in the pre-dictor, assuming all other factors and covariates are thesame. The last three statistics are described briefly be-low. The reader is referred to Wilks (1995) for additionaldiscussion and examples.

The p value, also known as rejection level or levelof the test, is a probability with values ranging from 0to 1. If the p value is small, it means that the differencebetween the sample means is unlikely to be a coinci-dence and that the parameter may have a statistical sig-nificance. Statistical hypothesis testing is carried out bysetting up a null hypothesis. The null hypothesis is re-jected if the probability of the observed test statistic isless than or equal to the test level. The test level ischosen in advance of the computations; commonly, the

OCTOBER 2002 1039M A Z A N Y E T A L .

TABLE 2. Logistic regression table.

Predictor Coefficient Std dev t ratio p value Odds ratio

ConstantMax (V m21)IPWV9-h DIPWVK index

26.78660.001 135 90.060 630.323 410.067 28

0.72080.000 292 30.014 670.029 610.020 81

29.423.894.13

10.923.23

0.0000.0000.0000.0000.001

1.001.061.381.07

FIG. 3. (a) Average time series of GPS IPWV and maximum electricfield mills values for the hours leading up to a lightning strike. (b)GPS IPWV 24-h average time series for nonevent weather days.

5% level is chosen. In the work described in this paper,a more stringent test level of 1% (99% significance lev-el) was chosen. Predictors that did not meet the 99%significance level, as determined by the p value in themodel results, were eliminated.

Of the initial 23 variables, this test left only fourpredictors that met the 99% significance level: electricfield mill maximum (V m21), GPS IPWV, 9-h DIPWV,and KI (Table 2). If we set the coefficients to zero asthe null hypothesis, the estimated coefficients show thatthe four remaining predictors all have a p value # 0.01.This indicates that the parameters are not zero with a99% significance level, and we can reject the null hy-pothesis and use the estimated coefficients. Given thefact that three of the variables are sensitive to moisture,it important to note that they are not well correlated.The highest correlation coefficient was 0.47 betweenIPWV and KI.

The t ratio, also known as the t test or z value, is animplicit test that bears directly on the meaningfulnessof the fitted regression. The t ratio is obtained by di-viding the coefficient by its standard deviation. Dividingby the standard deviation weights the accuracy of the

coefficient. Smaller standard deviations lead to larger tratio, positive or negative. If the estimated t ratio (orslope) is too small, then the regression is not infor-mative. The magnitude of the t ratios in Table 2 providesevidence that the coefficients are significant and belongin the GPS lightning index.

The odds ratio is a fundamental method for studyingcategorical data. In this approach, one first calculatesthe odds of success instead of failure for one group andthe odds of success instead of failure for the other group,and then the ratio of the two sets of odds is taken. Theodds ratio is a measure of association in this research.It approximates how much more likely (or unlikely) itis that a predictor contributes to the outcome of a light-ning strike (Hosmer and Lemeshow 1989). Review ofthe odds ratios in Table 2 indicates that some predictorshave a greater impact than others. An odds ratio veryclose to 1 indicates that a one-unit increase minimallyaffects a lightning event. A more meaningful differenceis found with 9-h DIPWV. An odds ratio of 1.38 indi-cates that the odds of a lightning event increase by 1.38times with each unit increase in 9-h DIPWV. The oddsratios calculated for changes in IPWV over shorter andlonger time intervals are less and are discussed in thenext section.

c. Relationship between predictors and predictand

The relationship between time series of discreteevents can be studied by a technique known as the su-perposed epoch method (Panofsky and Brier 1958). Thefirst strike of lightning is defined as a discrete eventsince it is the critical component of the forecast for theKSC. Since lightning occurs at various times of the day,the superposed epoch method creates composites of thedata surrounding the 27 lightning events during thethunderstorm period. For each lightning event the timeof first strike was denoted as T0. Hours prior to that keytime were denoted as T0–1, T0–2, T0–3, and so on. Figure3a depicts the composite GPS IPWV values leading upto the first strike. The general increase in IPWV suggestsa correlation between increasing IPWV values and thetime of the first strike. Contrary to GPS IPWV, electricfield mill values show random fluctuations leading rightup to the first strike when the field mill values spike upto indicate a lightning event has occurred. In this case,there is very little warning time for forecasting lightningevents. This predictor remains in the model because of

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FIG. 4. (a) Scatterplot of average electric field mill values and GPS IPWV. (b) Scatterplot ofaverage electric field mill values and K index. (c) Scatterplot of average electric field mill valuesand GPS 1-h DIPWV. (d) Scatterplot of average electric field mill values and GPS 9-h DIPWV.White diamonds denote lightning detected; black asterisks denote no lightning detected.

its relationship with lightning 90 min prior to the firststrike (Fig. 3a). Although this figure shows slight in-creases up until the first strike itself, in the 5-min res-olution (raw), the increases are much more dramatic (notshown).

Days containing no lightning at all, nonevent days,have IPWV values that hover around 35 mm. The non-event graph depicts average GPS IPWV values for 20days during the thunderstorm period (Fig. 3b). As seenin the graph, the 24-h run is relatively flat, exhibitingminor fluctuations, including subtle nocturnal declinefrom 0315 UTC (2215 EST) until 1115 UTC (0600EST) and a rise to 1815 UTC (1315 EST), that can beattributed to solar heating.

A series of scatter diagrams was used to documentrelationships between the predictors and the lightningevents. The scatterplots show data for all thunderstormdays. Only the 30-min data up to the time of the firstlightning strike are plotted. No data following the firststrike are included in the plots. Lightning events wereconsidered independent if there was a 12-h period be-tween the end of one lightning event and the start ofanother. Figure 4a shows GPS IPWV values .35 mmare more conducive for lightning strikes. Conversely,no first-strike events were noted when the GPS IPWVvalues were ,33 mm.

When the KI is plotted with electric field mill data(Fig. 4b), a clear bias is present. Lightning events aremuch more likely to occur when the KI was $26. Thisstability index proved more relevant than the TT index.A study on nowcasting convective activity for the KSCconducted by Bauman et al. (1997) concluded that of

all the stability indices, only the KI was found to havea modest utility in discriminating convective activity.This can be attributed to the fact that the KI captures amoisture layer from 850 to 700 mb, as opposed to justone reference point of 850-mb dewpoint temperature inthe TT index. Typical Cape Canaveral KI values rangingfrom 26 to 30 yield an airmass thunderstorm probabilityof 40%–60%. A value of 31–35 yields a probabilityrange of 60%–80%, and 36–40 yields a probability of80%–90%. Values for this study hover around 50%–60%, which represent odds similar to that of flipping acoin.

Initially, changes of IPWV over 1 h were used (1-hDIPWV). Eventually, the time interval was extended to12 h (12-h DIPWV). Again, the superposed epoch meth-od was applied to the data. Use of the 1- to 12-h DIPWVpredictors enabled the GPS lightning index to capturethe IPWV changes of the air mass. As it turned out, the9-h DIPWV predictor had more impact statistically thanthe other DIPWV predictors. Figure 5a shows that theodds ratio reaches a convincing maximum for 9-hDIPWV, with lower odds ratios associated with bothlonger or shorter time intervals over which the changein IPWV is taken. Looking at field mill values and 1-h DIPWV (Fig. 4c), values associated with lightning arescattered on either side of the zero line with the averagevalue around 2.5 mm. When compared with the 9-hDIPWV plot (Fig. 4d), average 9-h DIPWV values aredouble the D1-h averages and indicate no lightningstrikes occurred below the zero line. Other intervals,such as 6-h DIPWV (not shown), do show a tendencyof increased lightning as IPWV increased. However, the

OCTOBER 2002 1041M A Z A N Y E T A L .

FIG. 5. (a) Odds ratios associated with each DIPWV for increasingtime intervals over which the change in IPWV is taken. (b) Compositetime series of the average change in GPS 9-h DIPWV from one hourto the next, using the superposed epoch method with the time of thefirst strike defined as the zero hour.

FIG. 6. Histogram of time of day of first lightning occurrence atCape Canaveral. Histogram includes data from both test periods.

9-h DIPWV exhibits the most prominent increase ofIPWV in the 5 h prior to the first strike (Fig. 5b), andthe 9-h DIPWV prevails statistically as the best predictorin the logistic regression model (Fig. 5a).

The 9-h DIPWV examines changes in IPWV asso-ciated with meteorological events that span the courseof 9 h. Figure 6 shows that most of the first lightningevents occur during the mid- to late afternoon. Mech-anisms linked to this time frame may include effectsassociated with the diurnal cycle of solar heating andmoisture properties associated with the sea breeze and,as discussed in the introduction, the impact of synopticcirculations. The relationship between change in GPSIPWV and lightning occurrence proves a little morechallenging to explain. Increases in the 9-h DIPWV like-ly indicate an increase in midlevel moisture, which playsan important role in the stability of convective clouds.Moist air (as opposed to dry air) entrained into devel-oping cumulus clouds results in less reduction of buoy-ancy from evaporative cooling.

A possible mechanism for increased midlevel mois-ture is the interaction of various mesoscale boundariesassociated with the geography and diurnal circulationsover central Florida. Sea breezes originating along thewest coast advance and interact with east coast sea

breezes, resulting in enhanced convergence when theymeet. The 9-h DIPWV predictor could be detecting theincreased moisture associated with sea-breeze fronts.

Other mechanisms that affect changes in IPWV includedeeper moisture associated with southwesterly flow re-gimes, indicating an increase in the maritime moist layer(Reap 1994). Another important mechanism is diver-gence aloft associated with the passage of weak jet streaksor flow enhancements aloft (Bauman et al. 1997). Di-vergence aloft is associated with jet entrance and exitregions and draws moisture up to midlevels in the tro-posphere. These events create environmental conditionsfavorable to convective activity and lightning, which aremodulated by the diurnal cycle. It should be noted thatthe current analysis does not definitively identify the un-derlying physical processes that select for 9-h DIPWVas a predictor; consequently, the current analysis has notruled out the possibility that the selection of 9-h DIPWVas a predictor could be the result of random variability.This remains a goal for future research.

4. Assessing the utility of the GPS lightning index

To determine the effectiveness of the GPS lightningindex in describing the outcome variable, the fit of theestimated logistic regression must now be assessed. Thisis referred to as goodness of fit. Hosmer and Lemeshow(1989) recommend three methods to determine good-ness of fit: Pearson residual, deviance residual, and the

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TABLE 3. Goodness-of-fit tests.

Method p value

Pearson residualDeviance residualHosmer–Lemeshow test

1.0001.0000.605

TABLE 5. Measures of association.

Pairs No. Percent

ConcordantDiscordantTies

146 42424 299

331

85.614.20.2

Total 171 054 100

TABLE 4. Observed (Obs) and expected (Exp) frequencies.

Group

1 2 3 4 5 6 7 8 9 10 Total

YesObsExp

00.3

01.1

22.7

66.2

1611.2

1517.5

2625.8

3835.2

4247.6

7673.3

221

NoObsExp

9998.7

10098.9

9796.3

9493.8

8387.8

8582.5

7373.2

6264.8

5751.4

2426.7

774

Total 99 100 99 100 99 100 99 100 99 100 995

Hosmer–Lemeshow test (Table 3). They also introducea decile-of-risk method for observed and expected fre-quencies (Table 4), as well as measures of associationbetween the response variable and the predicted prob-abilities (Table 5).

The p values range from 0.605 to 1.000 for the Pear-son and deviance residuals and for the Hosmer–Le-meshow tests (Table 3). This indicates that there is suf-ficient evidence for the model fitting the data adequately.If the p values were less than the accepted level (0.05),the test would indicate sufficient evidence for a con-clusion of an inadequate model fit.

The results of applying the decile-of-risk groupingstrategy to the estimated probabilities computed fromthe model for lightning strikes are given in Table 4. Thedata in Table 4 are grouped by their estimated proba-bilities from lowest to highest in 0.1 increments. Thus,group 1 contains the data with the lowest estimatedprobabilities (#0.1) while group 10 contains data withthe highest estimated probabilities (.0.9). Since the to-tal number of lightning strikes is 995, each decile grouptotal must be evenly distributed for proper comparison.Therefore, the Hosmer and Lemeshow strategy breaksdown each group into a total of 99 or 100 events.

The following will help to explain the meaning ofTable 4. The observed frequency in the yes (y 5 0, alightning strike) group for the seventh decile (,0.7) ofrisk is 26, meaning that there were 26 lightning eventsactually observed from the seventh decile group. Theseare the events that have an estimated probability of oc-curring of #0.7. In a similar fashion the correspondingestimated expected frequency for this seventh decile is25.8, which is the sum of the modeled probabilities forthese lightning events to occur. The observed frequencyfor the no lightning (y 5 1) group is 99 2 26 5 73,and the estimated frequency is 99 2 25.8 5 73.2. Table4 provides sufficient evidence that the model does fit

the data well because the observed and expected fre-quencies are very close.

The values in Table 4 are calculated by pairing theobservations with different response values. Here 221yes lightning strikes and 774 no lightning events wererecorded during the thunderstorm period. This resultsin 221 3 774 5 171 054 pairs with different responsevalues. Based on the GPS lightning index, a pair isconcordant if the yes lightning event has a higher prob-ability by the sum of its individual estimated probabil-ities of occurrence being greater than the observed light-ning events, discordant if the opposite is true, and tiedif the probabilities are equal. These values are used asa comparative measure of prediction. Measures of as-sociation (Table 5) show the number and percentage ofconcordant, discordant, and tied pairs. These valuesmeasure the association between the observed responsesand the predicted probabilities.

a. Testing the GPS lightning index

The lightning index was tested on data from periodB. In order to obtain the proper predictand (index value),Wilks (1995) suggests using

1y 5 , (4)

1 1 exp(b 1 b x 1 b x 1 b x 1 b x )0 1 1 2 2 3 3 4 4

where y is the predictand (index value), b is the coef-ficients for each predictor, x is the value of the predictor,and the subscripts indicate which predictor it is for. Inthis case, using the GPS lightning index coefficients foreach predictor listed in Table 2, Eq. (5) now becomes

OCTOBER 2002 1043M A Z A N Y E T A L .

1y 5 . (5)

1 1 exp(26.7866 1 0.001 135 9x 1 0.060 63x 1 0.323 41x 1 0.067 28x )1 2 3 4

FIG. 7. Time series of GPS lightning index for (a) a nonevent day, 5 Jul; (b) a nonevent day, 15 Jul; (c) a noneventday, 18 Jul; (d) a lightning event on 3 Jul; (e) a lightning event on 10 Jul; and (f ) a lightning event on 1 Aug 1999.The horizontal line is the lightning index threshold value of 0.7.

The meaning of this equation is most easily understoodin the limits, as (b0 1 b1x1 1 b2x2 1 b3x3 1 b4x4) →6`. As the exponential function in the denominatorbecomes arbitrarily large, the predicted value approach-es 0, indicating a lightning strike. As the exponentialfunction in the denominator approaches 0, the indexvalue approaches 1, indicating a nonevent. Thus, it isguaranteed that the logistic regression will produceproperly bounded probability estimates. The index valuewas calculated for the entire dataset for both test periods.

The index time series for each day during the thun-derstorm period were reviewed to identify recurring pat-terns and the best index threshold value (ITV). Indexvalues for nonevent days typically fluctuate very closeto 1.0 (Fig. 7). When the index value falls below 0.7,lightning events follow, with few false alarms (discussedlater in section 4d). An ITV of 0.7 proved to be bestsuited for a forecast threshold. A level of 0.8 often re-

covered to 0.9, indicating a nonlightning event, whilea level of 0.6 provided insufficient lead time before thefirst strike. A running mean time series of index values10–12 h prior to the first strike graphically captures thepredictive value of the GPS lightning index. Figures 7c–e depict typical lightning-event days. In these cases, theITV of 0.7 was reached up to 10 h prior to the firststrike.

b. Categorical forecasts for period B

Forecast verification is needed to test the predictiveaccuracy of the GPS lightning index. Anytime the indexvalue fell below the ITV of 0.7 and up to 90 min priorto first strike (meeting 90-min desired lead time), it wascounted as a yes forecast. A contingency table (Table6) is used to evaluate the GPS lightning index’s pre-diction capabilities (Wilks 1995). For the thunderstorm

1044 VOLUME 17W E A T H E R A N D F O R E C A S T I N G

TABLE 6. Contingency table for categorical forecast of discretepredictands, giving relationship between counts (letters a–d ) of fore-cast event pairs for the dichotomous categorical verification. Quadranta denotes the occasions when the lightning was forecast to occur anddid. Quadrant b denotes the occasions when the lightning was forecastto occur but did not. Quadrant c denotes the occasions when thelightning was not forecast to occur but did. Quadrant d denotes theoccasions when the lightning was not forecast to occur and did not.Subscripts n and i indicate dependent test (thunderstorm period) andindependent test (period A).

Observed

Yes No

Model forecastYes an 5 25

ai 5 7bn 5 5bi 5 3

No cn 5 3ci 5 1

dn 5 13di 5 10

TABLE 7. Period-B test results (10 Jun–26 Sep 1999).

GPS lightningindex results

(%)

KSC resultsfrom 1999season (%)

False alarm rateHit rateThreat scoreProbability of detection

16.782.675.889.3

43.2——

97.5

TABLE 8. Independent test results (period A, 14 Apr–9 Jun 1999).

GPS lightningindex results

(%)

KSC resultsfrom 1999season (%)

False alarm rateHit rateThreat scoreProbability of detection

3080.963.687.5

43.2——

97.5

period (subscript n), a total of 46 days were evaluated.Twenty-five thunderstorms days were observed andforecast by the GPS lightning index (quadrant a). Fivethunderstorms days were forecast to occur but did not(quadrant b). Three storm days were observed to occurbut the model failed to respond (quadrant c). In 13 re-maining days the model did not forecast a lightningevent and none was observed (quadrant d). The datafrom these quadrants are now used to determine theaccuracy measures for a binary forecast. In particularthe false alarm rate (FAR) is a measure of the forecastevents that fail to materialize: FAR 5 b/(a 1 b). Theprobability of detection (POD) is a measure of the fore-cast events that did occur: POD 5 a/(a 1 c). The mostdirect measure of the accuracy of categorical forecastsis the hit rate: hit rate 5 (a 1 d)/n. A frequently usedalternative to the hit rate, particularly when the eventto be forecasted (as the ‘‘yes’’ event) occurs substan-tially less frequently than the nonoccurrence (‘‘no’’event), is the threat score (TS): TS 5 a/(a 1 b 1 c).The results of these calculations are shown in Table 7.The GPS lightning index proved its utility, particularlyin the area of FARs.

Although period-B data are not statistically indepen-dent, the application of the GPS lightning index to thesedata reduced the FAR to 16.6%. This is a decrease of;27% of the KSC’s previous FAR. The POD result wasonly 8% less than the KSC POD for the 1999 season.In making these comparisons it should be noted that thetime window of the GPS lightning index is 12.5 h. Thetime window associated with KSC forecasts varies withsynoptic situation but is 4–6 h on average.

c. Categorical forecasts for the independent period A

Using the same 90-min desired lead time and the ITVcriteria of 0.7 for the independent period A (subscripti, Table 6), a total of 21 days were evaluated. Seventhunderstorms days were observed and forecast by theGPS lightning index (quadrant a). Three thunderstorm

days were forecast to occur but did not (quadrant b).One storm day was observed to occur but the modelfailed to respond (quadrant c). In 10 remaining days themodel did not forecast a lightning event and none wasobserved (quadrant d). The data from these quadrantsare again used to determine the accuracy measures fora binary forecast (FAR and POD). The results of thesecalculations are shown in Table 8.

GPS lightning index results for FAR in the indepen-dent period A were 13.2% lower than KSC results of43.2% (Table 8). POD was down by only 10%. Thesemeasures could easily be improved by adding a fore-caster’s input of additional knowledge. Reference to sat-ellite and Doppler radar data would give a forecasterthe benefit of knowing the tracks and intensities of thun-derstorms moving into the area. The GPS lightning in-dex’s capability to improve FARs would enhance mis-sion readiness. Mission functions that cease for light-ning would not be delayed by a forecast of lightningthat does occur.

Results for period B are slightly better than for periodA. This is attributed to seasonal availability in the mois-ture of the atmosphere during the summer season. TheGPS trends show an increase in the amount of IPWVas well as more fluctuations during period B.

As with any attempt to forecast a meteorologicalevent, timing is critical. The lightning model outputindicates a potential when the ITV is met. To get a betterunderstanding of how the GPS lightning index performswith regard to the timing of the first strike, the distri-bution of lead times once the ITV is met is plotted inFig. 8a. A wide range of lead times (0–12 h) is observed.The lead times display an approximately normal distri-bution. The majority of the lead times fall between 3and 7.5 h.

d. Missed events

During the independent test the first missed eventoccurred on 19 May 1999 (Fig. 8b). The GPS lightning

OCTOBER 2002 1045M A Z A N Y E T A L .

FIG. 8. (a) Time (h) prior to first strike that the ITV of 0.7 was met for all thunderstorms. Time series of GPSlightning index for (b) a lightning event in which the desired lead time was not met on 19 May, (c) a false alarm eventon 13 May, (d) a day with no lightning event on 20 May, (e) a nocturnal lightning event on 21–22 Jul, and (f ) back-to-back lightning events on 9 Aug 1999. The horizontal line in (b)–(f) is the lightning index threshold value of 0.7.

index forecast the lightning event, but only 1 h prior tofirst strike, thus not meeting the 90-min required leadtime. An event on 13 May 1999 is a prime example ofa false alarm (Fig. 8c). Observations on this day showearly morning fog that may have inhibited developmentof convection. However, the ITV was met and no light-ning occurred.

The GPS lightning index was checked to see how ithandled rain showers with no lightning, nocturnalevents, and back-to-back events. Figure 8d depicts aday marked by distant nocturnal lightning (.30 n mifrom KSC), morning fog, and afternoon towering cu-mulus in all quadrants. Although the index shows fluc-tuations, the ITV was never met, and the lightning indexcorrectly handled this event. During a nocturnal ex-ample (Fig. 8e), the ITV was met 7 h prior to the firststrike around 0500 UTC (midnight EST). Although theindex successfully predicted this event, it should be not-ed that the increase in the index roughly 2 h prior tothe lightning strike could confuse forecasters. Last, thelightning index captured back-to-back events (Fig. 8f).In this case, a nocturnal thunderstorm ended just around0600 UTC (0100 EST). Nine hours later the ITV wasmet, and the first strike followed 4.5 h later.

An interesting phenomenon that occurs frequently inthe time series after the ITV is met is the tendency fora flatness or increase in the index prior to the first strike(e.g., Figs. 7e,f and Fig. 8e). This may be a reflectionof compensating mesoscale subsidence associated withdeveloping thunderstorms drying out the atmosphereabove the GPS site.

5. Summary and conclusions

A new GPS lightning index is developed to providea tool for the Kennedy Space Center’s primary weatherforecast challenge. Two periods were chosen, period A(14 April–9 June 1999) and period B (10 June–26 Sep-tember 1999), to develop and evaluate the GPS lightningindex after examining a year’s worth of operational GPSIPWV data with reference to the climatology of light-ning occurrence in southern Florida. A binary logisticregression model was used to identify which of a set of23 predictors contributed skill in forecasting a lightningevent. Four predictors proved important for forecastinglightning events: maximum electric field mill values,GPS IPWV, the 9-h change of IPWV (9-h DIPWV), andK index.

Maximum electric field mill values increased substan-tially during inclement weather when the potential forlightning existed, sometimes reaching values of 12 000V m21 during a lightning event. However, this variablelacked sufficient long-term (90 min plus) predictability.Composites of GPS IPWV and 9-h DIPWV several hoursprior to an initial lightning strike show an increase ofprecipitable water for the site. By using current GPSIPWV and 9-h DIPWV values, the model captures thecurrent IPWV of the atmosphere but also changes inmidlevel moisture associated with diurnal and synoptic-scale circulations. The KI diagnoses convective activityby examining the moisture in the layer from 850 to 700mb and the stability of the lapse rate. Given the fact thatthree of the variables are sensitive to moisture, it is im-

1046 VOLUME 17W E A T H E R A N D F O R E C A S T I N G

portant to note that they are not well correlated. Thehighest correlation coefficient was 0.47 between IPWVand KI.

The GPS lightning index is a binary logistic regres-sion equation that includes the four predictors multipliedby their coefficients. When a time series of the GPSlightning index is plotted, a common pattern emerges.Whenever the lightning index drops to 0.7 or below,lightning almost always follows within 12.5 h. An indexthreshold value (ITV) of 0.7 was identified, and light-ning events are forecast whenever the ITV is met. Fore-cast verification results obtained by using a contingencytable revealed a 26.6% decrease from the KSC’s pre-vious-season false alarm rates during period B and a13.2% decrease in false alarm rates for period A. Forthe KSC, a decrease in false alarm rates means thatmissions will not be halted for a forecast lightning eventthat does not occur. In addition, the KSC met their de-sired lead time (90-min notification) 79.1% of the timeduring 1999. Because the forecast verification was setup with reference to the 90-min desired lead-time cri-teria, POD results from the thunderstorm test period(89.2%) and period A (87.5%) also reflect the desiredlead-time statistic. In this research, if a storm failed tomeet the desired lead it was counted as a missed event.Thus, the GPS lightning index also improves the pre-vious lead time at KSC by 10%.

The primary utility of the GPS lightning index is inalerting a forecaster to the possibility of lightning.Armed with the lightning index time series, a forecastercan improve the lead time and false alarm rate in light-ning forecasts. However, the lightning index has a fairlylarge time window within which the lightning can occur.At the time the GPS lightning index falls below thethreshold value, the atmosphere may not yet display thesigns of a thunderstorm and imminent lightning. There-fore, the forecaster needs to rely on other resources suchas radar and satellite to help to refine the timing of thelightning event.

Future work will consist of testing the GPS lightningindex using data from future thunderstorm seasons. Itmay be possible to refine the index with the addition ofpredictor variables not included in this study, such aslow-level divergence, thunderstorm motion, radar data,and so on.

If the GPS lightning index fulfills its early promise,it may be useful to consider a similar statistical approachto help to predict related weather phenomena. Obser-vations show a correlation between increases of GPSIPWV and heavy precipitation (Businger et al. 1996),suggesting that a logistic regression model could pro-vide the basis for a new flash-flood index.

Acknowledgments. The data resources and collectionthat went into this research were substantial and couldnot have been accomplished without assistance fromJames Foster and Mike Bevis (GPS data) and SusanDerussy (radiosonde data). We thank Gary Barnes, Pao-

Shin Chu, and three anonymous reviewers for numeroussuggestions for improvements to the manuscript. NancyHulbirt provided assistance with the figures. This re-search was supported by the U.S. Air Force through itsAir Weather program and NOAA Grant NA67RJ0154.

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