AVARI-based relative greenness from MODIS data for...

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Remote Sensing of Environmen

AVARI-based relative greenness from MODIS data for computing theFire Potential Index

P. Schneider ⁎, D.A. Roberts, P.C. Kyriakidis

Department of Geography, University of California, Santa Barbara, CA, 93106, USA

Received 18 September 2006; received in revised form 25 July 2007; accepted 26 July 2007

Abstract

The Fire Potential Index (FPI) relies on relative greenness (RG) estimates from remote sensing data. The Normalized Difference VegetationIndex (NDVI), derived from NOAA Advanced Very High Resolution Radiometer (AVHRR) imagery is currently used to calculate RGoperationally. Here we evaluated an alternate measure of RG using the Visible Atmospheric Resistant Index (VARI) derived from ModerateResolution Imaging Spectrometer (MODIS) data. VARI was chosen because it has previously been shown to have the strongest relationship withLive Fuel Moisture (LFM) out of a wide selection of MODIS-derived indices in southern California shrublands. To compare MODIS-basedNDVI-FPI and VARI-FPI, RG was calculated from a 6-year time series of MODIS composites and validated against in-situ observations of LFMas a surrogate for vegetation greenness. RG from both indices was then compared in terms of its performance for computing the FPI usinghistorical wildfire data. Computed RG values were regressed against ground-sampled LFM at 14 sites within Los Angeles County. The resultsindicate that VARI-based RG consistently shows a stronger relationship with observed LFM than NDVI-based RG. With an average R2 of 0.727compared to a value of only 0.622 for NDVI-RG, VARI-RG showed stronger relationships at 13 out of 14 sites. Based on these results, daily FPImaps were computed for the years 2001 through 2005 using both NDVI-RG and VARI-RG. These were then validated against 12,490 firedetections from the MODIS active fire product using logistic regression. Deviance of the logistic regression model was 408.8 for NDVI-FPI and176.2 for VARI-FPI. The c-index was found to be 0.69 and 0.78, respectively. The results show that VARI-FPI outperforms NDVI-FPI indistinguishing between fire and no-fire events for historical wildfire data in southern California for the given time period.© 2007 Elsevier Inc. All rights reserved.

Keywords: Fire Potential Index; MODIS; VARI; Wildfire risk; Wildfire susceptibility

1. Introduction

Wildfires are a major natural disturbance mechanism inMediterranean regions and have been a threat to human societyfor centuries (Pyne et al., 1996). As the wildland–urbaninterface intrudes further into wilderness areas, wildfires arebecoming an increasingly important issue not only affectingnatural ecosystems but also imposing a risk of high economicdamage to society. An example of this growing vulnerability isthe October 2003 fire complex in southern California. 15 firesburned 300,000 ha, destroyed 3300 structures and cost the livesof 24 people, thus making it one of the most destructive fire

⁎ Corresponding author.E-mail addresses: [email protected] (P. Schneider), [email protected]

(D.A. Roberts), [email protected] (P.C. Kyriakidis).

0034-4257/$ - see front matter © 2007 Elsevier Inc. All rights reserved.doi:10.1016/j.rse.2007.07.010

events in US history (Blackwell & Tutle, 2005; Keeley et al.,2004). In a landscape such as southern California, wildfiresdirectly threaten human lives and properties to a major extent.Indirect consequences include soil erosion and the resultingextreme surface runoff, increased emission of CO2, degradationof wildlife habitat, alteration of species composition, anddecrease of air quality (Barro & Conard, 1991; DeBano et al.,1998). It is therefore important to understand the physical andenvironmental processes that lead to increased wildfire risk, andto use this knowledge to develop accurate models for estimatingthe spatial and temporal patterns of risk. A spatial awareness ofwildfire risk can help mitigate the environmental and economicimpact of fire events especially at the wildland–urban interface.This can be accomplished by issuing warnings about spatial andtemporal patterns of fire potential to population and firemanagement authorities. Wildfire managers see great value in

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http://dx.doi.org/10.1016/j.rse.2007.07.010

1152 P. Schneider et al. / Remote Sensing of Environment 112 (2008) 1151–1167

fire risk maps for allocation and planning of firefightingresources. Wildfire risk assessment is further useful for taskssuch as evacuation planning or insurance estimates.

Systems for rating wildfire susceptibility that utilize weatherstation data have existed for many decades (San-Miguel-Ayanzet al., 2003). Examples include the National Fire Danger RatingSystem (NFDRS) in the United States (Burgan, 1988; Deeming,1972) and the Canadian Forest Fire Danger Rating System(CFFDRS) (Forestry Canada Fire Danger Group, 1992; Stockset al., 1989; Van Wagner, 1987). However, all of these systemsrequire the use of spatial interpolation algorithms for generatingspatially exhaustive maps of pertinent variables. This introducesconsiderable uncertainty as oftentimes the station network is notas dense as would be desirable for interpolation. Further stationslocated in inhomogeneous areas might not be representative oftheir surroundings, in particular with respect to elevation andfuels. Remote sensing offers comprehensive spatial informationabout fuel type, fuel properties, and fuel condition (Chuvieco,2003; Dennison, 2003). However, while remote sensing is avaluable tool for estimating the quantity and state of live fuels(e.g. Bowyer & Danson, 2004; Ceccato et al., 2001; Keane et al.,2001; Roberts et al., 2006; Verbesselt et al., 2007; Viegas et al.,2001), meaningful fire susceptibility assessment also requiresinformation about dead fuel moisture. Although some attemptshave been made to utilize remote sensing methods for this task(Camia et al., 2003), it remains challenging as dead fuels are oftenobscured by a canopy of live fuels and exclusively controlled byatmospheric conditions. Meteorological data will thus always berequired for estimating fire susceptibility (Aguado et al., 2003).The state of live fuels is much less dynamic in nature as it isaffected by plant physiology and soil moisture. Observing livefuel state using weather data is possible using long-term moisturecodes (Viegas et al., 2001), but can be more easily performedusing remote sensing data (Chuvieco et al., 2003).Meteorologicaland remote sensing data therefore complement each other inproviding a comprehensive assessment of overall fuel status.

Only a few attempts have beenmade to date to integrate remotesensing data with information from weather stations for wildfiresusceptibility assessment. Examples include Vidal et al. (1994)and more recently the introduction of the Fire Potential Index(FPI) by Burgan et al. (1998). The FPI was originally formulatedfor and tested on NOAA Advanced Very High ResolutionRadiometer (AVHRR) data. It has been validated with historicalwildfire data by several authors (Sebastián López et al., 2002;Sudiana et al., 2003) and exhibits a strong relationship with firefrequency (R2≈0.72 according to Burgan et al. (1998)). It iscurrently offered as a nationwide experimental product throughthe Wildland Fire Assessment System (WFAS) at http://www.wfas.net/. Overmore recent years new remote sensing technologysuch as the Moderate Resolution Imaging Spectroradiometer(MODIS) has emerged, which has the potential of providingbetter characterization of fuels than AVHRR imagery. In additionto a finer spatial resolution of 250/500 m, the MODIS sensor alsosamples more wavelengths than AVHRR, thus allowing theapplication of potentially more appropriate vegetation indicesthan the Normalized Difference Vegetation Index (NDVI)(Goward et al., 1991). The FPI product as offered by WFAS

employs the NDVI for deriving the fuel condition using RelativeGreenness (RG) (Burgan&Hartford, 1993). Several authors haveshown, however, that other vegetation indices, such as theNormalized Difference Water Index (NDWI) (Gao, 1996) or theVisible Atmospherically Resistant Index (VARI) (Gitelson et al.,2002), exhibit stronger relationships with fuel condition and LFMthan NDVI (Dennison et al., 2005; Roberts et al., 2006; Stowet al., 2005). It appears therefore valuable to investigate the effectof using such an index in the calculation of the FPI for a study sitein southern California. The objectives of this study are 1) toevaluate the performance of VARI-based RG against NDVI-based RG as a reference using in situ data and 2) to investigate ifusing VARI-based RG can improve the performance of FPI inassessing wildfire susceptibility in southern California.

2. Background

2.1. Terminology

Avariety of terms are used in the literature for characterizingthe likelihood of wildfire events. Wildfire danger, wildfire risk,wildfire hazard, wildfire susceptibility, and wildfire potential areall used to describe similar concepts. The most widely usedterms are wildfire danger and wildfire risk. The term fire dangerhas been criticized as being subjective since it implies a negativeconnotation regardless of fires also having positive effects inmany regions. Adopting concepts of risk analysis in engineering,wildfire risk is generally defined as the product of the occurrenceprobability of a fire and its expected outcome (Bachmann &Allgöwer, 2001). In this paper we use the term fire risk onlywhen we refer to a general context and when we explicitly intendto include a connotation of fire outcome. Since we neither studyignition probability, which is a requirement for determiningoccurrence probability, nor perform an analysis of the expectedfire outcome in this research, we avoid the term risk otherwiseand instead adopt the term wildfire susceptibility as recentlyintroduced by Parisien et al. (2005) and Dasgupta et al. (2006).The term is objective and focuses on the vulnerability of fuels tofire at the pre-ignition stage, which is exactly what the FPI wasdesigned for.

2.2. Vegetation indices

A vegetation index is a measure that reduces spectralinformation from several bands of remote sensing imagery intoone number. It maximizes sensitivity to biophysical parameters ofvegetation preferably with a linear response, normalizing external(solar zenith, viewing angle, etc.) and internal effects (background,topography, soil, etc.), and is coupled with a measurablebiophysical parameter such as biomass, Leaf Area Index (LAI)or fuel moisture for validation purposes (Jensen, 2005). The mostwidely used index is the Normalized Difference Vegetation Index(NDVI) suggested by Rouse et al. (1973), which is given forMODIS bands as

NDVI ¼ q857 � q645q857 þ q645

: ð1Þ

http://www.wfas.net/

http://www.wfas.net/

1153P. Schneider et al. / Remote Sensing of Environment 112 (2008) 1151–1167

In Eqs. (1) and (2), ρx represents the reflectance for thewavelength x given in nanometers. Despite being widely used,the NDVI has been shown to be associated with severalproblems (Huete et al., 2002): as all ratio-based indices it isinherently non-linear and it is further impacted by substratebrightness and atmospheric contamination. The NDVI alsoshows scaling problems saturating in high-biomass conditions.Other vegetation indices such as the Normalized DifferenceWater Index (NDWI) introduced by Gao (1996), or theNormalized Difference Infrared Index (NDII) (Hardisky et al.,1983; Hunt & Rock, 1989), which uses NIR and short-waveinfrared (SWIR) bands, have been developed. More recently,indices based entirely on the visible part of the spectrum havebeen suggested, such as the green vegetation index VIg and theVisible Atmospherically Resistant Index (VARI) (Gitelsonet al., 2002). VARI is calculated as

VARI ¼ q555 � q645q555 þ q645 � q469

ð2Þ

and has been shown to provide the best overall results for fuelmoisture estimation in Mediterranean shrublands (Roberts et al.,2006; Stow et al., 2005). This study is based on these results andadopts VARI as a promising greenness index for southernCalifornia. VARI is minimally sensitive to atmospheric effectsand was developed for estimating green vegetation fraction,which is precisely the purpose of using relative greenness in theFPI algorithm. The bands used for VARI have been specificallyselected for their sensitivity to vegetation fraction (Gitelson et al.,2002). In contrast to NDVI, which is sensitive to changes forsmall vegetation fractions and insensitive for changes atmoderate and high vegetation fractions, VARI shows a linearresponse to vegetation fraction throughout the entire range.Based on work by Kaufman and Tanré (1992), VARI reducesatmospheric effects by subtracting the blue channel in thedenominator. Gitelson et al. (2002) showed that VARI allowedthe estimation of green vegetation fraction with an error of lessthan 10%.

2.3. The Fire Potential Index

The Fire Potential Index (FPI) was first introduced by Burganet al. (1998) and revised by Burgan et al. (2000). A modifiedversion of the FPI adapted to a European context was alsosuggested by Sebastián López et al. (2002). The inputs to the FPIconsist of three raster layers, namely a fuel model map, a map of10-hour dead fuel moisture, and a RG map. In the original paperby Burgan et al. (1998), the fuel model map was derived througha combination of NOAA-AVHRR data and expert knowledge.This map was used for deriving the dead fuel moisture ofextinction MXd for each pixel. The map of 10-hour dead fuelmoisture is generated by interpolating the NFDRS estimates atweather stations using weighted inverse distance squaredinterpolation. Finally, a RG map is used to partition each fuelmodel into live and dead fractions. RG was introduced byEidenshink et al. (1990) and Burgan and Hartford (1993). It putsany current NDVI value for a pixel into perspective by

normalizing it against the historical range of NDVI values forthat particular pixel. It is given as

RG ¼ NDVIcurr � NDVImin

NDVImax � NDVImind100%: ð3Þ

where RG is the relative greenness for a particular pixel,NDVIcurr is the current NDVI value and NDVImin and NDVImax

are the overall historical minimum and maximum values for thispixel computed over the entire period of the time series. A similartechnique based on inter-annual variability of NDVI has recentlybeen used by Gabban et al. (2006) in their introduction of theDynamic Relative Greenness Index (DRGI). Furthermore Chéretand Denux (2007) proposed an annual relative greenness. Whilea comparison of RG with DRGI and annual relative greennesswould be interesting for future research, in this study we focussolely on the impact of VARI on the computation of RG and thusthe FPI. In the revised version of Burgan's paper (Burgan et al.,2000), a maximum live ratio map was also derived from thehistorical maximum greenness by scaling it between 35% and75%, in order to avoid similar live ratios for fuel modelsrepresenting very different vegetation types as it occurred for theoriginal formulation of the FPI algorithm. Finally, the FirePotential Index was computed as

FPI ¼ 1� FM10 � 2MXd � 2

� �d 1� RGdLRmax

104

� �d100 ð4Þ

where FM10 is the 10-hour time lag fuel moisture, MXd is thedead fuel moisture of extinction derived from the fuel modelparameters, RG is the relative greenness, and LRmax is themaximum live ratio. All variables have units of percent. Theresulting FPI values range from 0 to 100, where 0 is equivalent tovery low fire susceptibility and 100 represents extremely highfire susceptibility.

3. Data and methods

3.1. Study area

Southern California was selected as a study site. Fig. 1 showsits geographic location and extent. The northern border wasarbitrarily chosen as the northern boundary of the San LuisObispo, Kern and San Bernadino counties, forming anapproximately straight line from west to east at 35 47′ N. Allother borders follow the political boundaries of California. Thearea of the test site is 148,079 km2. Southern California is anideal test area for this study: its Mediterranean climate andvegetation make it very vulnerable to wildfires. In addition, withmany parts of southern California densely populated, wildfirerisk is a serious concern especially at the wildland–urbaninterface. The size of the test site is small enough to provide ahomogenous climate, but large enough for research on a regionalscale. A large amount of high-quality geospatial data is availablefor southern California. Most data sets required for firesusceptibility assessment are available at high spatial resolutionsand the network of weather stations is very dense, particularly inareas of high fire risk. The southern California climate provides

Fig. 1. Location and extent of the southern California test site with fuel model data set from FRAP using the Albini (1976) fuel models and additional classes of non-vegetated surfaces.


generally cloud-free skies during the fire season, thereforeenabling extensive use of optical remote sensing data. Thevegetation of the study site, especially in the fire-prone coastalmountain ranges, consists mostly of evergreen shrub speciessuch as chamise (Adenostoma fasciculatum) and ceanothus(Ceanothus megacarpus and Ceanothus crassifolius) as well asdrought deciduous shrub species such as sage (Salvia mellifera,Salvia leucophylla) and sage brush (Artemisia californica).

3.2. Data

The primary data set for this study was a 6-year time series ofMODIS Terra 16-day surface reflectance composites for theyears 2000 to 2005. These composites were generated asdescribed by Dennison et al. (2005). Median reflectance foreach band during a 16-day period was computed using theMODIS 500 m spatial resolution daily surface reflectanceproduct (MOD09GHK version 4). The masking of clouds,cloud shadow and snow was performed using the 1 kmresolution MOD09GST product resampled to 500 m. Thenumber of low-quality pixels included was minimized byapplying a screening process for removing extreme off-nadirviews using the look angle data layer. At the stage of dataacquisition, each composite was already georectified andatmospherically corrected. Only the image tile h08v05approximately covering the areas of southern California, partsof Nevada, Arizona and Northern Mexico, was considered here.

Ideally the reference data for validating RG would consist ofin situ measurements of live and dead vegetation fraction.Unfortunately such a data set was not available to us for ourstudy area. However, vegetation greenness is closely related toLFM and Roberts et al. (2006) have demonstrated a strongrelationship between green vegetation fraction and LFM. Wetherefore validated relative greenness against a data set of LFMwithin Los Angeles County provided by the Los Angeles

County Fire Department (LACFD). The samples were takenapproximately every two weeks at 14 sites following protocolsby Countryman and Dean (1979). Fig. 2 shows the locations ofthe sites and Table 1 lists their geographic coordinates as well assampled species. The sites are spatially homogeneous andrepresentative of southern California shrubland as they includeall dominant species such as A. fasciculatum, S. leucophylla, S.mellifera, C. crassifolius, and C. megacarpus. According to thesampling protocol, leaves and small stems (3.2 mm or less) fromold and new foliage were collected from each site. All deadplant material and reproductive plant parts were removed fromthe sample before weighing. Furthermore, only branches thatincluded live foliage and stems were sampled. After weighingthe samples, drying them at 104 °C for 15 hours, and re-weighing them, LFM was subsequently calculated as a per-centage of dry mass as

LFM ¼ mw � md

mdd100 ð5Þ

where mw is the original wet mass of a fuel sample and md is thedry mass. Table 1 lists the number of samples per year for eachsite. Two sites burned during the study period, namely PicoCanyon in 2003 and Sycamore Canyon in 2002. They werereplaced by Glendora Ridge in 2002 and Peach Motorway in2003. Only samples for the first half of 2005 were available.

A fuel model data set of southern California was availablefor computing the FPI. It was produced by the Fire ResourceAssessment Program (FRAP) of the California Department ofForestry and Fire Protection and has been derived from a varietyof sources including a Landsat Thematic Mapper classificationof primary and secondary vegetation types in conjunction withvegetation size and density, topographic information, andsuccession pathways based on fire history. While the fuelmodel data set was delivered at a 30 m spatial resolution, it was

Fig. 2. Locations of the live fuel moisture sample sites in northern Los Angeles County.


resampled at a 500 m resolution by assigning to a coarser pixelthe fuel model of the majority of fine-resolution pixels. The fuelmodel map is based on the classification scheme described byAlbini (1976) and includes additional classes for non-vegetatedsurfaces (classes 15 through 99). Table 2 gives an overview ofthe fuel models and land cover types occurring in the study area.Values for dead fuel moisture of extinction were taken fromBurgan et al. (1998) after crosswalking the fuel model classes tothe NFDRS classification (Bradshaw et al., 1983; Deeminget al., 1978) as described in Anderson (1982).

In order to generate a raster of 10-hour dead fuel moisture,daily weather data from time series of all Remote AutomatedWeather Stations (RAWS) in southern California were used.These data were acquired from the Western Regional ClimateCenter in Reno, Nevada. A total of 178 stations were available,with the majority located in California and 9 stations situated inNevada and Arizona. 126 stations recorded data during theentire validation period from 2001 through 2005. 48 additionalstations were added between 2001 and 2002 and were includedin the interpolation procedure as soon as the data became

available. While the interpolation results for 2003 through 2005are thus slightly more reliable than for the first two years of thestudy period, this does not affect the conclusions drawn from arelative comparison between NDVI-based FPI and VARI-basedFPI as both models use identical weather inputs.

Validation of a fire index requires data on historical fireevents. For this study, MODIS-derived annual cumulative firedetection data sets for 2001 through 2005 were acquired fromthe MODIS Active Fire Mapping Program, which is run by theRemote Sensing Applications Center (RSAC). The firedetections are based on daily Terra and Aqua MODIS imagerythat is collected and processed as a joint effort between RSAC,NASA Goddard Space Flight Center and the University ofMaryland. The fire detections are collected using MODISthermal bands at a spatial resolution of 1 km. The minimumdetectable fire size is approximately 100 m2 for a firetemperature of 600 K or 1 m2 at 1100 K. The algorithm usedfor creating this data set is given by Justice et al. (2002). Sincethe exact sub-pixel location and the size of the fire within thepixel are not known, the data set used for this study records the

Table 1LFM sample site description including geographic location, sampled species, and number of available samples

Site Species Latitude Longitude 2000 2001 2002 2003 2004 2005 Total

Bitter Canyon 1 S. leucophylla 34°30′ N 118°36′ W 16 21 21 21 21 10 110Bitter Canyon 2 Adenostoma fasciculatum 34°31′ N 118°36′ W 16 21 21 21 21 10 110Bouquet Canyon Salvia mellifera 34°29′ N 118°29′ W 16 19 21 21 21 10 108Clark Motorway Ceanothus megacarpus 34°05′ N 118°52′ W 16 21 21 21 21 11 111La Tuna Canyon A. fasciculatum 34°15′ N 118°18′ W 15 20 21 21 21 10 108Laurel Canyon A. fasciculatum 34°08′ N 118°22′ W 16 20 21 21 21 10 109Pico Canyon A. fasciculatum 34°22′ N 118°35′ W 16 21 21 18 0 0 76Placerita Canyon A. fasciculatum 34°22′ N 118°29′ W 16 21 21 21 20 10 109Schueren Road A. fasciculatum 34°05′ N 118°39′ W 16 21 19 21 21 11 109Sycamore Canyon Ceanothus crassifolius 34°09′ N 117°48′ W 15 20 16 0 0 0 51Trippet Ranch S. mellifera 34°06′ N 118°36′ W 16 21 21 21 21 10 110Woolsey Canyon A. fasciculatum 34°14′ N 118°40′ W 16 21 21 21 21 10 110Peach Motorway A. fasciculatum 34°22′ N 118°32′ W 0 0 0 3 21 10 34Glendora Ridge C. crassifolius 34°10′ N 117°52′ W 0 0 2 21 20 10 53


centroid of the pixel for which a fire has been detected. A totalnumber of 12,804 fire detections were available within the studyarea for the entire 5-year validation period. The majority of firedetections occurred during summer and fall, so daily FPI mapswere only computed between April 1 and November 31 for eachyear and only fire detections within this period were used. Somefire detections also were located within data gaps in the FPImaps. Thus the usable number of MODIS fire detections wasslightly reduced to 12,490.

3.3. Computing and validating VARI-based RG

While current applications of the FPI use the NDVI tocalculate RG, this is not necessarily a requirement. RG can becomputed using any remote sensing index that shows arelationship with vegetation greenness. For this paper, RGwas computed using VARI such that Eq. (3) simply becomes

RGVARI ¼ VARIcurr � VARImin

VARImax � VARImind100%: ð6Þ

where RGVARI is the VARI-based relative greenness for aparticular pixel, VARIcurr is the current VARI value at thatlocation and VARImin and VARImax are the actual overallhistorical minimum and maximum VARI values for the givenpixelas they occurred over the entire span of the time series(2000 through 2005).

The 129 available MODIS surface reflectance compositeswere subset to cover the southernCalifornia study site. For each ofthe composites, both NDVI and VARI were then computed.Finally, RG was derived from both indices for all 6 yearsaccording to Eqs. (3) and (6) and stored as an image stackconsisting of 129 bands. For the statistical analysis, values of RGcomputed for the pixels at each LFM sampling location wereextracted from the stack of RG images. A variety of differenttechniques exist for performing this task. The most intuitiveconcept would be to extract exactly that 1 pixel in which thesample location falls.While this is a valid approach (Roberts et al.,2006), many authors have either used the average value of3×3 pixel windows around each site (Dennison et al., 2005) ormanually selected individual pixels in the vicinity of the site,

which were located in homogeneous areas identified from aerialphotography (Stow et al., 2005). For this project we chose to useboth a single pixel and a 3×3 average approach and comparedtheir respective performances. Several sites are situated close tourban areas making the use of a 3×3 pixel window potentiallyproblematic. However, with the exception of Laurel Canyon andSchueren Road (Table 1, Fig. 2) all sites are located withinsufficiently large and homogeneous patches of vegetation torender the impact of urban land cover negligible for a 3×3 pixelwindow. After extracting the NDVI-based RG and VARI-basedRG using both strategies for all test sites, the resulting four datasets were regressed against LFM data sampled by LACFD, inorder to evaluate their respective relationships. The pairingbetween the LFM samples and the MODIS composites wasperformed using temporal proximity to the midpoint of thecompositing period as a measure. Relationships at all sites werelinear, so only linear models were tested in the regression. Thesignificance of the increase in R2 was evaluated following themethodology of Dennison et al. (2005) by normalizing thecorresponding correlation coefficients using a Fisher z-transform(Fisher, 1915; Papoulis, 1990) given as

zf ¼ arctanhðrÞ ¼ 12dln

1þ r1� r

� �ð7Þ

where r ¼ffiffiffiffiffiR2

pis Pearson's correlation coefficient. After

computing the difference between zf for VARI-r and NDVI-raccording to

Zdiff ¼ zfVARI � zfNDVIffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

nVARI�3 þ 1nNDVI�3

q ð8Þ

(Papoulis, 1990), where nVARI and nNDVI indicate therespective number of available samples, the significance ofthe increase in correlation strength was evaluated using a one-tailed test.

3.4. MODIS-based FPI for Southern California

In order to test the applicability of MODIS imagery andVARI for computing the FPI, a system for generating FPI maps


using MODIS data was developed. For validation purposes,daily FPI maps of southern California were generated usingboth traditional NDVI-RG and VARI-RG for the summer andfall seasons (April 1 through November 30) for 5 years (2001through 2005) using daily weather data and the latest availablesurface reflectance composite. Active fire data for the year 2000were not available. Meteorological data were utilized tocompute spatially exhaustive estimates of dead fuel moisturefor the entire study site. Measurements of daily maximum airtemperature and daily minimum relative humidity were used torepresent the generally high fire susceptibility in the earlyafternoon. In order to work with a clean meteorological data set,outliers of more than three standard deviations from the meanwere marked and the associated stations removed from the poolof stations for the particular day. Kriging with external drift(KED) was applied for spatially interpolating the station data torasters (Kyriakidis et al., 2001). KED is a variant of traditionalgeostatistical interpolation that incorporates auxiliary informa-tion within the interpolation process. For air temperature thisapproach resembles topographically informed interpolationwhich has been used by several authors (e.g. Dodson &Marks, 1997; Willmott & Matsuura, 1995), but distinguishesitself by providing a stochastic link between the variables andaccounting for uncertainty in the trend estimation. In contrast tosimple DEM-assisted interpolation, which reduces air temper-ature at each station to sea level using an average environmentallapse rate, then interpolates the de-trended data and finallyadjusts the result by elevation using a DEM, KED can be usedindependently of the nature of the variable. In this study wetherefore used KED for interpolating relative humidity usingtemperature and elevation as the auxiliary information. Usingthe interpolated raster data sets of air temperature and relativehumidity, 10-hour timelag fuel moisture was then computed foreach pixel following Fosberg and Deeming (1971) andSebastián López et al. (2002) as

FM10hr ¼ 1:28� emc ð9Þwhere emc is the equilibrium moisture content (i.e. the moisturecontent at which the net exchange of moisture between fuel andenvironment is equal to zero), given as

emc ¼

2:22749þ 0:160107� RH

� 0:014784� Tair

if 10% V RH V 50%

21:0606þ 0:005565� RH2

� 0:00035� RH� Tair� 0:483199� RH

if RH N 50%

0:03229þ 0:281073� RH

� 0:000578� RH� Tair

if RH V 10%

8>>>>>>>>><>>>>>>>>>:

ð10Þ

where RH is the relative humidity in % and Tair ¼ 95 dTc þ 32

with Tc being the air temperature in degrees Celsius. Theseempirical equations were developed for non-metric units, thusSI units need to be converted accordingly prior to application.

The FRAP fuel model data set for California was used toproduce a raster of the Dead Fuel Moisture of Extinction as it is

required for the FPI. This was accomplished by assigning valuesof extinction moisture to each fuel model type according to thedata given in Burgan et al. (1998) (see Table 2). FPI wascomputed following Eq. (4) using the input rasters of 10-hourfuel moisture, dead fuel moisture of extinction, NDVI-RG andVARI-RG derived from MODIS composite time series, andmaximum live ratio.

3.5. Validation of FPI using logistic regression

Validation of a fire susceptibility index is challenging as it isimpossible to directly measure the quantity in question at agiven location and time directly in the field. An indirectalternative approach adopted by most researchers thus relies onan analysis of the statistical relationship between the index anddata on historical wildfire events. Such an approach has beenadopted by Burgan et al. (1998) in the original suggestion of theFPI, as well as for validating the FPI in Mediterranean areas ofEurope (Sebastián López et al., 2002) and in Indonesia (Sudianaet al., 2003). A variety of other indices based on remote sensingand weather data have been validated with ground data forsavanna ecosystems by Verbesselt et al. (2006). Viegas et al.(2000) investigated the performance of several fire susceptibil-ity indices for France, Italy, and Portugal. Lasaponara (2005)studied the performance of AVHRR-derived indices with fireactivity data in southern Italy. Various components of theNFDRS have been validated with ground data by severalauthors including Haines et al. (1983), Mees and Chase (1991),Andrews et al. (2003), and Peng et al. (2005).

When using fire activity data for regression-based validationof fire susceptibility indices, the response variable is generallydichotomous (i.e. the outcome is binary). Logistic regression(Collett, 2003; Harrell, 2001; Hosmer & Lemeshow, 2000) ismost often used in such cases. It has been successfully appliedin validating wildfire susceptibility indices in the past.Examples include the evaluation of the performance ofNFDRS fire danger indices (Andrews & Loftsgaarden, 1992;Andrews et al., 2003), the comparison of fire risk indicators insavanna ecosystems (Verbesselt et al., 2006), and fireoccurrence probability modeling (Lozano et al., 2007). Logisticregression was also applied in this study for evaluating theperformance of VARI-based FPI. The specific form of thelogistic regression model used here is

pðxÞ ¼ EðY ¼ 1jxÞ ¼ eb0þb1x

1þ eb0þb1x¼ 1

1þ e�b0�b1xð11Þ

where π(x) expresses the conditional probability of a fireoccurring (i.e. the binary response variable Y is equal to 1) for agiven FPI value x and β0 and β1 are the regression coefficients.The logit transformation g(x) is defined as

gðxÞ ¼ lnpðxÞ

1� pðxÞ� �

¼ b0 þ b1x ð12Þ

and thus has many of the desirable properties of a linearregression model (Hosmer & Lemeshow, 2000).

Table 2Fuel models (1–12) and non-vegetated classes (15–99) of the study site using the Albini (1976) classification with corresponding NFDRS fuel models, description,dead fuel moisture of extinction, and area of study site covered by class

Fuel model/class NFDRS fuel model(s) Description Extinction moisture [%] Area [km2]

1 A,L,S Grass 15 17,0092 C,T Pine/Grass 20 74714 B,O Tall Chaparral 15 76755 – Light Brush 15 11,4876 F,Q Intermediate Brush 15 21388 H,R Hardwood/Conifer Light 15 25809 U,P,E Medium Conifer 20 85110 G Heavy Conifer 25 85412 J Medium Slash – 15915 – Desert – 72,19028 – Urban – 866197 – Agriculture – 11,90098 – Water – 135099 – Rock/Barren – 2584

Fuel models not listed did not occur within the study area.


A data set of compiled MODIS Active Fire detections (seeSection 3.2) was used as the response variable with the predictorvariable being the FPI. In contrast to the validation of RG withLFM observations, which was limited to shrub vegetation, thevalidation of FPI using historical fire data was carried out usingfire detections for all vegetated areas, in order to evaluate theoverall model performance. Daily FPI maps were generated at a500m spatial resolution betweenApril 1 andNovember 31 for theyears 2001 through 2005 for both the NDVI-based and the VARI-based method. Otherwise identical inputs were used for bothmethods, ensuring that all differences can be attributed to theimpact of the vegetation index used. For each of the 12,490MODIS fire pixel centroids the spatially closest FPI value wasextracted for the same day as the fire detection. To generate the no-fire data set, an equal number of unburned pixels were randomlysampled from the entire study area and all 5 years and theirrespective FPI value was recorded. In contrast to previousapplications of logistic regression within the context of firepotential validation, the explicitly spatial nature of the FPI makesthe size of the no-fire sample somewhat arbitrary. The vastmajority of pixels are not associated with actual fire, thus thepotential no-fire sample size is only limited by the overall numberof pixels generated for the entire validation period (roughly 109 inthis case). While it would have been possible to sample a muchlarger number of no-fire pixels, we chose the no-fire sample sizeto be equal to the number of available fire pixels. The resultingtotal sample size (fire and no-fire) of 24,980 is high enough to berepresentative while preserving reasonable fire/no-fire propor-tions for the logistic regression and drastically limiting thecomputational expense. However, it is important to note that thefire/no-fire proportions presented here are therefore onlyapplicable for statistical analysis but do not allow any meaningfulphysical interpretation in the sense of a fire probability.

For this study logistic regression was performed using thefollowing steps:

(1) A total of 100 FPI classes corresponding to floating-pointFPI values between 0–1, 1–2,…, 99–100 were defined forthe analysis.

(2) For each class the proportion of fire pixels was computed.Only classes containing a minimum number of 25 pixelswere considered for the subsequent analysis in order toderive a representative sample.

(3) A logistic model was fitted to the data using a maximumlikelihood approach (Hosmer & Lemeshow, 2000). Theregression coefficients were obtained iteratively bymaximizing the likelihood function Lðb0; b1Þ ¼jn

i¼1 pðxiÞyi ½1� ðxiÞ�1�yi where xi denotes the indepen-dent variable and yi the dichotomous outcome variable fori=1,…, n and (πi) denotes the conditional probabilityobtained from Eq. (11).

(4) The regression was weighted by the total number ofavailable fire/no-fire pixels in each class.

In contrast to ordinary linear regression, there is no widelyaccepted equivalent to R2 as a measure of the overall model fitfor logistic regression. It is possible to compute several differentpseudo-R2 values, but since low values are the norm for them,Hosmer and Lemeshow (2000) suggest limiting their use tocomparing competing models and to avoid interpretation in anabsolute way as in linear regression. The low pseudo-R2 valuesfor logistic regression are easily misinterpreted by those who areaccustomed to R2 values obtained from ordinary linearregression (Andrews et al., 2003; Hosmer & Lemeshow,2000). Out of 12 studied pseudo-R2 measures for logisticregression Mittlböck and Schemper (1996) recommend usingeither the squared Pearson correlation coefficient or a linearregression-like sum-of-squares R2

SS computed as

R2SS ¼ 1�

Pni¼1 ðyi � piÞ2Pni¼1 ðyi � yÞ2 ð13Þ

where yi are the binary values of dependent variable, πi denotethe estimates from the logistic regression, and y denotes theoverall proportion.

The c-index, which is identical to the area under the ROC(Receiver Operating Characteristic) curve (Harrell, 2001;Hosmer & Lemeshow, 2000), was used to evaluate the

Fig. 3. Scatter plots illustrating the relationship between RG calculated using NDVI and Live Fuel Moisture for all 14 sampling sites. The RG values were extractedusing a 3×3 pixel window. For all correlations pb10−11.


discrimination power of the logistic model. It is computed bypairing all no-fire samples with all fire samples and comparingthe fitted probabilities for each pair. The c-index results fromdividing the sum of all cases for which the fitted probability ofthe fire sample is greater than the fitted probability of the no-fire sample by the total number of pairs. A c-index value of 0.5indicates no discrimination of the model while a c-index valueof 1 indicates perfect discrimination. The model likelihoodratio χ2 statistic and its associated p-value was used to

evaluate the significance of the predictor for each individualmodel.

4. Results and discussion

In this section we first present the results obtained from aregression analysis of NDVI-RG and VARI-RG with LFM at 14sites in Los Angeles County. We then present a case studyapplying MODIS-derived VARI-RG for computing FPI in


southern California and compare its performance to NDVI-FPIvalidating both products with historical fire detections usinglogistic regression.

4.1. Performance of VARI-based RG

Fig. 3 shows scatter plots of NDVI-based RG againstmeasured LFM at all 14 sample sites for the 3×3 pixelextraction window case. With R2 values greater than 0.7, foursites showed a very strong correlation with LFM, namely BitterCanyon 1, Clark Mountainway, Peach Motorway, and Glendora

Fig. 4. Scatter plots illustrating the relationship between RG calculated using VARIusing a 3×3 pixel window. For all correlations pb10−11.

Ridge. Several other sites have acceptable R2 values between0.5 and 0.7. Two sites, namely Laurel Canyon and SchuerenRoad have weak correlations. Caution needs to be applied ininterpreting the high correlation coefficients for Peach Motor-way and Glendora Ridge. These sites were established recentlydue to other sites being burned, and thus have a smaller numberof data points than the other sites (see Table 1). Therelationships for these two sites are therefore not necessarilyrepresentative.

Fig. 4 illustrates the corresponding results for VARI-basedRG. The scatter plots show stronger relationships between RG

and Live Fuel Moisture for all 14 sampling sites. The RG values were extracted


and measured LFM than for the NDVI-based case. The R2

values are higher for all sites, with the exception of BitterCanyon 2 and Peach Motorway. Eight out of 14 sites have verystrong correlations with R2 values greater than 0.7. No site hadan R2 value of less than 0.5. This indicates that VARI-based RGhas a stronger relationship with LFM and might be a goodsubstitute for NDVI-RG in calculations of the FPI for southernCalifornia.

Table 3 confirms this conclusion and in addition showscomparable results for the 1 pixel extraction window. In nearlyall cases, VARI-based RG shows a stronger relationship withobserved LFM than NDVI-based RG. This is true independentof the size of the extraction window. However, we can alsoobserve a trend showing an increase in R2 with an increasingsize of the extraction window if we look at each indexindividually. This trend can be attributed to an elimination ofgeorectification issues and to averaging of potential siteinhomogeneities. For the majority of sites (11 out of 14),VARI-based RG for a 3×3 pixel window showed the strongestcorrelation with LFM. Only 3 sites showed a different behavior,2 of which still showed the optimum R2 for VARI-RG but for a1×1 pixel window. Only the Peach Motorway site had itsmaximum R2 for the 3×3 pixel NDVI-RG case, but asmentioned above needs to be treated with caution due to asmaller sample size. Table 3 also shows the difference in Fisherz-scores and the corresponding p-values. For the 1×1 pixelwindow, 9 out of 14 sites showed improvements that werestatistically significant at the 0.95 level. Seven sites showedsignificant improvements for the 3×3 pixel window. The twosites that showed slightly lower R2 values for the VARI case

Table 3R2 values between RG based on NDVI and VARI for all 14 LFM sample sites fortwo different extraction window sizes

1 pixel window 3×3 pixel window

NDVI VARI Zdiff p NDVI VARI Zdiff p

Bitter Canyon 1 0.775 0.848 1.59 0.05 0.809 0.866 1.42 0.07Bitter Canyon 2 0.631 0.642 0.14 0.44 0.640 0.615 −0.30 0.62Bouquet Canyon 0.641 0.711 0.95 0.16 0.637 0.692 0.72 0.23Clark Mountainway 0.606 0.737 1.79 0.03 0.734 0.800 1.19 0.11La Tuna Canyon 0.490 0.657 1.88 0.02 0.611 0.777 2.40 0.00Laurel Canyon 0.175 0.483 2.99 0.00 0.353 0.525 1.69 0.04Pico Canyon 0.592 0.771 2.10 0.01 0.657 0.798 1.87 0.03Placerita Canyon 0.512 0.661 1.72 0.04 0.526 0.681 1.85 0.03Schueren Road 0.315 0.462 1.41 0.07 0.339 0.543 2.02 0.02Sycamore Canyon 0.565 0.762 1.80 0.03 0.629 0.836 2.32 0.01Trippet Ranch 0.338 0.587 2.53 0.00 0.503 0.669 1.94 0.02Woolsey Canyon 0.577 0.721 1.88 0.02 0.634 0.733 1.40 0.08Peach Motorway 0.732 0.803 0.69 0.24 0.838 0.833 −0.07 0.52Glendora Ridge 0.689 0.702 0.12 0.44 0.791 0.810 0.27 0.39Average R2 0.546 0.682 – – 0.622 0.727 – –

The best overall R2 value for each site is highlighted in bold. For all correlationspb10−11. The regressions included all available data sets from 2000 to 2005.See Table 1 for detailed number of data points. The table also shows thedifference in Fisher z-scores Zdiff (see Section 3.3) and the correspondingsignificance level (p). p-values indicating a significance of 0.95 or more areshown in italics.

(Bitter Canyon 2 and Peach Motorway, each for the 3×3 pixelwindow) were found to have an insignificant R2 decrease at the0.99 level.

The relationships between RG and LFM are obviously sitespecific. One of the major factors contributing to the differencesis the number of available samples. The newly established sites(Peach Motorway and Glendora Ridge) with fewer availablesamples tend to have very high R2 values due to exclusion ofthe 2002 data, which decreased the strength of the correlationsin most cases. The sites with the weakest relationships overallare Laurel Canyon, Schueren Road, and Trippet Ranch. Thefirst two sites are influenced by the presence of urban landcover, in particular for the 3×3 extraction window. While onlysamples of C. crassifolius were used for Trippet Ranch, the siteis co-dominated by A. fasciculatum, thus resulting in a relativelyweak overall relationship compared to the other sites.

Figs. 3 and 4 show two general classes of relationships. Thelinear models for Bitter Canyon 1, Bouquet Canyon, andTrippet Ranch have substantially steeper slopes than those ofthe other sites. This difference can be attributed to the impact oftwo different plant functional types. Most sites are dominated byevergreen shrub species such as chamise (A. fasciculatum) andceanothus (C. megacarpus and C. crassifolius). Bitter Canyon 1is dominated by a drought deciduous shrub (S. leucophylla)while Bouquet Canyon and Trippet Ranch include S. melliferaas a co-dominant with an evergreen shrub (Table 1). The ob-served importance of plant functional type is consistent with thefindings by Roberts et al. (2006).

Fig. 5 illustrates the relative change in R2 values when VARIis used for the computation of RG. It shows the results for boththe 1×1 pixel window case as well as the 3×3 pixel windowcase. All percentage values presented here can be interpreted asthe relative change in the proportion of LFM variance explainedby using VARI-RG in lieu of NDVI-RG as the predictorvariable, e.g. a 100% relative increase is equivalent to adoubling of the percentage of variance explained by theindependent variable. It is obvious from Fig. 5 that the majorityof sites show a relative increase in the strength of thecorrelation. Only two sites, namely Bitter Canyon 2 andPeach Motorway, showed a slight weakening of the relationshipfor the 3×3 pixel window case, with values of −3.8% and−0.6%, respectively. The greatest relative improvements overallwere found for those sites that showed weak correlations forNDVI-RG, indicating that VARI-RGcan substantially improvethe relationships for some problematic NDVI-RG cases. This istrue for both Laurel Canyon and Schueren Road with increasesof 49%–175% (Laurel Canyon) and 47%–60% (SchuerenRoad) over the NDVI-RG R2. Trippet Ranch also showed asubstantial strengthening of the correlation by 33% to 73%. TheMODIS footprint for Schueren Road and Laurel Canyon is tosome extent affected by urbanization. The strong improvementsfor these sites with VARI-RG thus indicate that VARI ispotentially less sensitive to the impact of urban surfaces thanNDVI. This agrees with the hypothesis by Stow et al. (2005),who suggest that VARI might be less sensitive than othervegetation indices to background material reflectance andspatial inhomogeneities at the subpixel level.

Fig. 5. Bar graph showing the relative change in R2 for all test sites by using VARI instead of NDVI for the computation of RG. The 1×1 pixel window bar for LaurelCanyon reaches a value of 175%, but was clipped for this figure at 95% in order to highlight the differences for the remaining sites.


The remaining sites (i.e. mostly those for which NDVI-basedRG already achieved fairly high R2 values) showed smallerrelative improvements between 2% (Glendora Ridge) and 34%(La Tuna Canyon). Fig. 5 furthermore indicates that themagnitude of relative R2 increase is higher for the 1×1 pixelwindow case for 11 sites. Only a few sites, namely PlaceritaCanyon, Schueren Road, and Glendora Ridge showed strongerimprovements for the 3×3 pixel window. The unusual behaviorof Laurel Canyon with extreme differences between the NDVI-

Fig. 6. Box plots comparing the summary statistics of the FPI values for NDVI-basedand upper quartile values. The whiskers shows the extreme values defined as 1.5 tim

and VARI-based approaches can again be attributed to the sizeand location of the site. The Laurel Canyon site is only around250 m×600 m in size and is surrounded by a densely populatedresidential area. It is thus severely affected by subpixel mixingeffects. In this case the extraction approach using 1 pixel ispreferable over the 3×3 pixel window case, for which the signalis contaminated by urban land cover surrounding the site.

Overall, while RG is generally derived using NDVI (Aguadoet al., 2003; Burgan & Hartford, 1993; Burgan et al., 1998),

FPI (left) and VARI-based FPI (right). The box indicates lower quartile, median,es the interquartile range.


VARI-based RG appears to show a stronger correlation withmeasured LFM for shrubland ecosystems. It might thus bevaluable to integrate VARI into remote sensing-supportedwildfire susceptibility assessment in such areas. The physicalreason for the better performance of VARI-based RG comparedto NDVI-based RG is not yet fully understood. VARI operatesentirely in the visible part of the spectrum and several authors(e.g. Boyer and Danson (2004)) have shown that visiblereflectance is not sensitive to changes in moisture status at theleaf-scale (Roberts et al., 2006). At canopy scales, however,visible reflectance is correlated with vegetation cover and LAIas shown by Gitelson et al. (2002) and Davis and Roberts(1999). The good correlation of VARI with LFM appears to beassociated with green vegetation fraction. VARI was developedfor estimation of vegetation cover and Gitelson et al. (2002)have shown for wheat that VARI exhibits a linear relationshipwith green vegetation fraction while the same relationship forNDVI becomes nonlinear above a fraction of 50% (Robertset al., 2006). While not tested within the scope of this study, apotential equally linear relationship between VARI and greenvegetation fraction for Mediterranean shrublands could explainthe higher correlations obtained for VARI-based RG and LFM.These findings are consistent with those by Stow et al. (2005)who hypothesized that the temporal variability of greenvegetation fraction co-varies with LFM making VARI a usefulpredictor of LFM.

4.2. Validation of VARI-based FPI using historical fire data

Fig. 6 shows box plots comparing the summary statistics offire pixels and no-fire pixels for VARI-based FPI with NDVI-based FPI as a reference. As would be anticipated, the medianfor fire pixels is greater than the median for no-fire pixels inboth cases. There is a substantial overlap between fire and no-fire classes, which is due to the fact that high fire susceptibilitydoes not necessarily result in fires if there is a lack of an ignitionsource. The VARI-based FPI produces slightly higher FPIvalues overall. The median of the VARI no-fire class (62.5) lies5.3 units above that of the NDVI no-fire class (57.2). While for

Fig. 7. Histograms for fire and no-fire pixels for ND

the NDVI case the difference between the fire/no-fire medians isonly 10.2 units, the same difference is 16.0 units for the VARIcase, indicating a better separability between the two classes forVARI-based FPI. It is also evident that the extreme values forthe fire pixels show a smaller range for the VARI-FPI case (47units) than for the NDVI-FPI case (68 units). Active fire pixelsare therefore less likely to be associated with low index valuesfor the VARI case.

The better separability between the fire/no-fire classes isfurther supported by histograms for fire and no-fire classes ofthe NDVI-based and the VARI-based FPI (Fig. 7). While thehistograms for no-fire pixels have similar shapes in both cases,the fire pixel histograms show obvious differences. The VARI-based FPI confines the actual fire pixels to a smaller range ofhigher FPI values.

Fig. 8 shows logistic regression models fitted to theproportion of MODIS active fire pixels for each FPI class forboth NDVI-FPI and VARI-FPI. The proportion describes thefraction of fire pixels out of all pixels for an FPI class, i.e. avalue of 1 indicates that all pixels of a given class were detectedas burning. The fitted models are given for the NDVI-FPI caseas

pNDVI ¼ e�3:1779þ0:0485dFPIðNDVIÞ

1þ e�3:1779þ0:0485dFPIðNDVIÞ

¼ 1

1þ e3:1779�0:0485dFPIðNDVIÞ ð14Þ

and as

pVARI ¼ e�5:4157þ0:0757dFPIðVARIÞ

1þ e�5:4157þ0:0757dFPIðVARIÞ

¼ 1

1þ e5:4157�0:0757dFPIðVARIÞ ð15Þ

for the VARI-FPI case. A visual inspection of Fig. 8 suggests anoverall better fit for the VARI-FPI case. The model probabilityrange is an important indicator of overall model performance.Ideally, the logistic regression curve would start at 0 for FPI=0and reach 1 for FPI=100. While neither model achieves this

VI-based FPI (left) and VARI-based FPI (right).

Fig. 8. Fitted logistic regression models for NDVI-based FPI (left) and VARI-based FPI (right). Only data points with a minimum of 25 available pixels per class aredisplayed.

Table 4Number of available pixels and statistics of model fit for logistic regressionmodels of NDVI-FPI and VARI-FPI with historical wildfire data from theMODIS active fire product

Statistic NDVI-based FPI VARI-based FPI

N 24,980 24,980Deviance 408.8 176.2Rss2 0.166 0.267

c-index 0.69 0.78χ2 2826.7 6142.1Model at FPI=0 0.0400 0.0044Model at FPI=100 0.8430 0.8964Probability range 0.803 0.892

Deviance and the likelihood ratio χ2 statistic both were highly significant withpb0.001.


goal, the model fitted for VARI-FPI comes closer to the idealcase. For FPI=0 the y-axis offset for the VARI-FPI model isonly 0.0044 while the traditional NDVI-FPI case shows anoffset of 0.0400. For FPI=100 the NDVI-FPI model reachesonly 0.8430 while the VARI-FPI model has a slightly highervalue of 0.8964.

The higher y-axis intercept of the NDVI-FPI model indicatesa greater number of fire detections for low FPI values than forthe VARI-FPI case. For example, the NDVI-FPI range between0 and 50 corresponded to 34% of the burned pixels. Consideringthat a low FPI should be an indicator of low fire probability, thefact that over a third of the fires were associated with a lowNDVI-FPI is an indicator of poor performance. In contrast, aVARI-FPI range between 0 and 50 translated to 17% burnedpixels, thus indicating that a low VARI-FPI is less likely to beerroneously associated with a fire event than NDVI-FPI. Themodel fitted to VARI-FPI also has a steeper slope than that forNDVI-FPI, in particular for a range of index values between 50and 90. VARI-FPI thus appears to have a greater sensitivity tofire events for moderately high index values. Fig. 8 also showsthat high VARI-FPI values are more likely to be associated withan actual fire event than NDVI-FPI values. The five highestNDVI-FPI classes present in the data account for only 63% ofthe fire pixels on average, while the five highest VARI-FPIclasses can explain 78% of the fire pixels on average.

The regression statistics (see Table 4) confirm the bettermodel fit for the VARI-FPI. The most commonly used measureof model fit in logistic regression is deviance, which is similar tothe residual sum of squares in ordinary linear regression.Essentially, a smaller deviance value suggest a better fit of themodel. For the given data set, deviance in the NDVI-FPI case is408.8 and the deviance for the VARI-FPI case is 176.2,indicating that the VARI-based FPI performs better at distin-guishing between fire and no-fire events for the actual historicalfire data.

The RSS2 for the NDVI-based FPI was estimated as 0.166

while the one for VARI-based FPI resulted in a value of 0.267.Just as for deviance, this measure also confirms that VARI-FPI

agrees better with historical fire data. It is important to note oncemore that the given RSS

2 values are helpful as relative measuresfor evaluation of competing models but are not comparable toR2 values from ordinary linear regression.

The c-index for the NDVI-FPI model reached a value of0.69, while the VARI-FPI model achieved a c-index of 0.78 andthus displayed greater discriminatory power. c-index values of0.7 or greater are generally considered to offer acceptablediscrimination, while a value of 0.8 or greater is considered tohave excellent discriminatory power (Hosmer & Lemeshow,2000). While both NDVI-FPI and VARI-FPI offer acceptablediscrimination of fire susceptibility in southern California (withNDVI-FPI being at the lower end of the range of acceptablevalues), VARI-FPI is more reliable and is even close to offering’excellent’ discriminatory power. The model likelihood ratio χ2

test and its associated p-value of pb0.001 indicate that FPI is asignificant predictor variable for each individual model.

While a validation of a fire susceptibility index such as theFPI with historical fire event data is certainly valuable it is alsosomewhat problematic since even extremely high index valuescannot guarantee a fire outbreak because an ignition sourcemight be lacking. This fact is evident in the relatively largeoverlap between the fire and no-fire classes in Figs. 6 and 7.


The MODIS Active Fire product is a valuable data set forvalidating fire susceptibility indices, but there is a potential issuerelated to its use. Larger fires are comprised of several firedetections, which are likely to have similar environmental con-ditions and thus are spatially and temporally correlated. Treatingthese independently can possibly cause over- or underestimationof model performance. However, this issue should not affect therelative comparison of model performance of NDVI-FPI versusVARI-FPI assuming that the effect is identical for bothexplanatory variables. Further research will be necessary tounderstand the impact of this issue on model performance.

The VARI-based approach to computing the FPI ispromising overall, but also has limitations. While VARI is asuitable greenness index for the Mediterranean ecosystems ofsouthern California, it is unlikely to perform as well on anationwide scale. However, the use of MODIS imagery and itsfiner spectral resolution as the remote sensing input to the FPIallows for the application of a greater variety of differentvegetation indices than NOAA-AVHRR imagery as it is used byWFAS for computing the FPI. Thus a user interested incomputing regional FPI maps has the possibility to select thevegetation index that has been shown to perform best for theparticular area.

Another drawback of our approach is the limited length ofthe MODIS time series for computing relative greenness.MODIS data have only been available since the year 2000,while the time series of NOAA-AVHRR data currently used byWFAS ranges from 1979 to 2000 and can thus give morereliable estimates of relative greenness. However, more MODISdata will be integrated within the current system as they becomeavailable, so the RG estimates will improve over time.Alternatively, computation of RG could be replaced by fuelcondition estimates from spectral mixture analysis (SMA) asdescribed by Roberts et al. (1993) or Roberts et al. (2003). Byapplying SMAwith endmembers for green vegetation and non-photosynthetic vegetation the live ratio of the vegetation couldbe computed directly and used as an input for the FPI algorithm.Such an approach would eliminate the need for calculating RGusing a long time series of remote sensing imagery.

5. Conclusions

This study investigated the use ofMODIS remote sensing datafor assessing the Fire Potential Index in southern California.Compared to the NOAA-AVHRR data traditionally used for thistask, the MODIS sensor offers a finer spectral resolution andtherefore facilitates the use of other vegetation indices besidesNDVI. The first part of this paper thus focuses on using thevegetation index VARI for the computation of relative greenness(RG), which is a fundamental component of the FPI algorithm.Utilizing LFM measurements sampled at various locationsthroughout Los Angeles County for validation, it was shownthat for the typical shrub vegetation of southern California VARI-derived RG corresponds more closely to changes in live fuelmoisture than NDVI-derived RG. It has therefore the potential toprovide better results than the latter in the computation of the FPIin such areas.

Based on the conclusions from the first part, the second partof the paper focuses on the implementation of a MODIS-basedsystem for computing the FPI in southern California. Usinghistorical wildfire data from the MODIS active fire product as areference, FPI based on both the traditional NDVI-RG andVARI-RG was validated over a 5 year period. Analysis of fireand no-fire classes for both approaches indicate that VARI-based FPI performs better at distinguishing between fire and no-fire events. It shows a better separability between the medians ofthe classes and in addition the FPI values for the fire class arelimited to a narrower range of high FPI values. Furthermore alogistic regression was carried out and showed that the modelfitted to VARI-FPI was superior to that fitted to NDVI-FPI. Themodel deviance was 176.2 for the former and 408.8 for thelatter. The c-index was computed as 0.78 and 0.69, respectively.Overall MODIS imagery appears to have the potential forimprovements in existing wildfire susceptibility algorithms byproviding access to locally more appropriate vegetation indicesthan NDVI for computing relative greenness. Using the VARIvegetation index can improve maps of Fire Potential Index forsouthern California.

Acknowledgements

This work was supported by NASA Headquarters under theEarth System Science Fellowship Grant NNG-04GQ77H. Thefirst author would like to thankUCSB'sVIPERLab for providingtheMODIS composites aswell as advice and support. The authorswould like to express their gratitude to Bob Burgan (retired fromMissoula Fire Sciences Lab) for the FPI source code and valuableadvice. Furthermore, the authors also acknowledge the contribu-tion of four anonymous reviewers, whose comments substantiallyimproved the quality of the manuscript.

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