Numerical modeling of lava flow cooling applied to the 1997

Okmok eruption: Comparison with advanced very high resolution

radiometer thermal imagery

M. R. Patrick,1 J. Dehn, and K. DeanAlaska Volcano Observatory, Geophysical Institute, University of Alaska Fairbanks, Fairbanks, Alaska, USA

Received 11 April 2003; revised 6 October 2004; accepted 5 November 2004; published 24 February 2005.

[1] Throughout February and March 1997, Okmok Volcano, in the eastern AleutianIslands of Alaska, erupted a 6-km-long lava flow of basaltic 0a0a within its caldera. In thefirst part of the study a numerical model for lava flow cooling was developed by Patrick etal. and applied to the flow to better understand the nature of its cooling. In this second partof the study, the model predictions for lava surface temperature over a 200-day coolingperiod were compared to advanced very high resolution radiometer (AVHRR) thermalimagery. Various methods were used to extract the subpixel lava temperature from theAVHRR pixel-integrated values, including the dual-band method and pixel merging.Inherent to these approaches is the multicomponent modeling of the lava surfacetemperature. Whereas active flows have been shown to have several thermal components,so, too, do flows undergoing extended cooling. Because of the dependence of the methodson the AVHRR instantaneous field of view (IFOV), the scan-dependent IFOV dimensionsand overlap values were considered. Results from Patrick et al. indicate thatconvective heat loss from the surface largely controls surface temperature during extendedcooling, but the functions governing this heat loss mechanism are poorly understood.AVHRR-derived temperatures from this part of the study suggest that values for theconvective heat transfer coefficient for this flow were most commonly between 50 and100 W m�2 K�1 and generally above 25 W m�2 K�1. These results are in agreement withpreviously measured values from the field but are significantly higher than those assumedin other remote sensing studies of cooling lava. Also, the AVHRR data corroborate themodeled prediction of seasonal warming of the lava surface.

Citation: Patrick, M. R., J. Dehn, and K. Dean (2005), Numerical modeling of lava flow cooling applied to the 1997 Okmok

eruption: Comparison with advanced very high resolution radiometer thermal imagery, J. Geophys. Res., 110, B02210,

doi:10.1029/2003JB002538.

1. Introduction

[2] The modeling of active lava flow cooling has ad-vanced recently to a high level of sophistication [e.g.,Kesthelyi and Denlinger, 1996; Neri, 1998; Harris andRowland, 2001], yet the modeling of long-term flow cool-ing has not been commensurate. Perhaps one reason for thisdisparity is the difficulty in obtaining reliable temperaturedata throughout the flow’s cooling history, which may lastyears. This is especially true at remote volcanoes. A partialremedy to this problem is to concentrate on surface tem-perature, which can be measured routinely with satelliteremote sensing instruments. The benefits of satellite data forthis purpose include the high temporal resolution andrelatively inexpensive procurement, even for the mostremote volcanoes.

[3] In this second part of the study, the numerical modeldescribed by Patrick et al. [2004] was applied to the 1997Okmok lava flow and the predicted lava surface temper-atures were compared with surface temperature measure-ments made by advanced very high resolution radiometer(AVHRR) thermal imagery throughout the course of thecooling period. Several techniques, including the dual-bandapproach and pixel merging, were compared for extractingreliable measurements of the lava surface temperature fromthe infrared imagery.

2. Background

[4] The National Oceanographic andAtmospheric Admin-istration (NOAA) AVHRR data used in this study originatedfrom the image archive at the Geophysical Institute of theUniversity of Alaska Fairbanks (UAF). Data are recorded byup to three polar-orbiting satellites (NOAA 12, 14, and 15)and are received directly at the Institute in near real time.The Alaska Volcano Observatory Remote Sensing group atUAF analyzes these AVHRR data on a daily basis overAlaska, Kamchatka, the Cascades and the Kurile Islands for

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, B02210, doi:10.1029/2003JB002538, 2005

1Now at Hawai’i Institute of Geophysics and Planetology, School ofOcean and Earth Science and Technology, University of Hawaii at Manoa,Honolulu, Hawaii, USA.

Copyright 2005 by the American Geophysical Union.0148-0227/05/2003JB002538$09.00

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remote monitoring of the North Pacific region’s numerousactive volcanoes [Dean et al., 1998; Dehn et al., 2000].[5] AVHRR collects data in five spectral bands (Table 1),

all having a nadir (vertically down looking) pixel size ofabout 1.1 km [Kidwell, 1991]. The repeat period for eachsatellite over the equator is approximately 12 hours, butowing to multiple satellites and the convergent orbits overhigh latitudes, Okmok (Figure 1) and the rest of theAleutian volcanoes can have up to eight passes a day.Analysis of volcanism using AVHRR data is typicallyperformed with bands 3 (3.55–3.93 mm) and 4 (10.3–11.4 mm). Band 3 (B3) data are especially useful as thisband’s wavelengths approach the peak emittance wave-lengths of erupting lava while the band 4 (B4) wavelengthsmore closely match those of normal ground. Converting theat-satellite radiance to actual ground radiance requirescorrecting for the effects of surface emissivity, atmospherictransmissivity, upwelling radiance, and reflected radiance,described in detail by Harris et al. [1997b]. The emissivitiesof numerous substances have been measured usingspectroradiometry [Salisbury and D’Aria, 1994], andtransmissivity can be estimated with an atmosphericmodeling program such as MODTRAN4 [Berk et al.,1999]. Upwelling radiance in band 4 can also be calcu-lated with MODTRAN4, while its contribution in band 3is often assumed to be negligible [Harris et al., 1997b].Reflected radiance in band 3 is often estimated fromnearby pixels in daytime scenes [Wooster and Kaneko,2001], or taken as insignificant in nighttime scenes, and itis assumed to be negligible in band 4 in general [Harris etal., 1997b]. Ground radiance in these bandwidths can thenbe converted to ground temperature using the inversePlanck function. It is especially important to appreciatethat this temperature value is a composite of the actualrange of temperatures within the pixel footprint, as afunction of the fractional area and temperature of thevarious thermal components as well as the wavelength ofthe channel.

3. Model Comparison With AVHRR Imagery

3.1. AVHRR Measurements of the1997 Okmok Eruption

[6] In order to measure lava surface temperature, theUAF AVHRR archive was scanned by eye for anomaliesover Okmok in the period February-December 1997. From

this set, nighttime, cloud-free images with low scan angles(<40�) were selected and, fortuitously, all of these nighttimeimages were in the ideal predawn hours, when solar heatingof the surface is at a minimum. Only those images whichsaw the caldera completely cloud free were used, and thisstringent criterion reduced the total number of useableAVHRR scenes acquired throughout 1997 to 65. Of these,47 were acquired during the eruption and 18 were from theposteruption cooling stage. To provide a rough representa-tion of the vigor of the eruption the highest AVHRR B3pixel value and the highest B4 pixel value (not necessarilyspatially coincident) from each image have been plotted(Figure 2). These values are uncorrected pixel temperatures,and are meant only for a qualitative synopsis. A morerigorous extraction of surface temperatures, suitable for

Figure 1. AVHRR band 3 image over Okmok on15 March 1997. This image was acquired toward the endof the eruption, with the white region (thermal anomaly)indicating increased radiance from the active lava flow.Coastlines are also shown in white. Note the faint plumetrailing to the west.

Table 1. AVHRR Characteristicsa

Band Wavelength, mm IFOV, mrad

1 0.58–0.68 1.392 0.725–1.1 1.413 3.55–3.93 1.514 10.3–11.3 1.415 11.4–12.4 1.3

Other Characteristics Value

Maximum scan angle 55.4�Total swath width �3000 kmRadiometric resolution 10 bitsInfrared NEDT <0.12 KInfrared saturation �49�C (channel 3),

�50–60�C (channels 4 and 5)

aAdapted from Harris et al. [1997b]. IFOV = Instantaneous field of view; NEDT = Noise equivalent DT.

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comparison with the model results, is discussed in thefollowing sections.[7] Figure 2 shows a sudden increase in B3 temperature

around 13 February, a plateau of saturated values for aperiod after this date, then a sudden decrease towardbackground temperatures. The rise in B3 temperature cor-responds to the first observed thermal anomaly in satelliteimagery (13 February, 1305 UTC), which was small (1–2 pixels) and located at cone A, and is interpreted tocorrespond to initial lava effusion. The first pilot report ofactivity was received the next day [Dean et al., 1998]. Theplateau of sensor-saturated pixel values reflects continuedeffusion and emplacement of the lava flow. The end of thissaturated period and the subsequent decrease in temper-atures reflects cooling of the lava after effusion has ceased.Thermal anomalies were observed in AVHRR imageryuntil mid-October 1997.

3.2. Progressive Versus Instantaneous Cooling

[8] The simplest way to apply the cooling model is toassume that the entire flow was erupted en masse and beganto cool immediately. The results shown in Figure 6 ofPatrick et al. [2004] essentially operate on this assumption.In actuality, the lava was erupted over a period of about5 weeks, from 13 February to approximately 20 March[Patrick et al., 2003], and this progressive eruption andcooling introduces a potentially serious complication.Ameliorating this concern to some degree, the AVHRRresults from Patrick et al. [2003] indicate that a largeoutflux of lava occurred between 11 March and 15 Marchand largely represents the eruption of the second lobe, whichcomprises 40% of the total flow area. Visual analysis of theimagery suggests that much of the lava on the first lobe wasalso active during this phase. Therefore it appears that in thisperiod of time the majority of the lava flow surface wasactive. Because our comparison effectively analyzes only the

upper portion of the flow (over 200 days surface coolingonly penetrates a few meters), the effective time range oferuption for most of the flow area is narrowed from 5 weeksto 5 days, reducing the influence of prior cooling in theAVHRR-derived lava surface temperature data.[9] Nevertheless, there may still be significant effects from

differential cooling of the flow surface, and we used a simplemodel to characterize of this. The aerial extent of each lobewas divided into small packets, which were erupted out in aneven temporal distribution from the emergence of the lobe toits effusive cessation, based upon the observations of lobeeruption times of Patrick et al. [2003]. In actuality, asmentioned the flow surface likely overran older portions ofthe flow thereby limiting the actual surface cooling time priorto the effusive cessation, so this simulation assumes a worst-case scenario. The surface temperature was assigned to eachpacket based on its age at each time step during the eruptionphase and subsequent cooling period, from the model resultsof Patrick et al. [2004], allowing us to create a simple lavaflow that is concurrently cooling and erupting. Because it isunrealistic that a packet begins static cooling as soon as it iserupted we assigned an arbitrary ‘active lava’ temperaturedistribution to the packet if its age is less then an assumedemplacement time. We modeled this as being spatially 1%hot cracks (1000�C), and 99% crust (200–500�C). Once thepacket age is older than the emplacement time, say 1 or2 days, it begins cooling (i.e., assigned temperatures from thecooling model).[10] In this way, we can compare how closely a more

realistic composite cooling curve (i.e., more thermal com-ponents of different ages as a result of graduated eruptionand cooling) compares with a simple, single-component(i.e., uniform temperature, instantaneous eruption and cool-ing) version. Figure 3 shows results for average lavasurface temperature from the progressive eruption modelas well as the standard model results assuming instanta-neous eruption and cooling. Differences between the pro-gressive and instantaneous models are limited to the first

Figure 2. Highest AVHRR band 3 and band 4 pixeltemperatures in each nighttime, cloud-free image acquiredduring the eruption and subsequent cooling phase. Theeruption ended around 20–26 March, and the last detectedsurface anomaly was in mid-October 1997. Reprinted fromPatrick et al. [2003] with permission from Elsevier.

Figure 3. Model results for average lava surface tempera-ture (over background) with differing assumed emplace-ment scenarios, modified from the cooling model of Patricket al. [2004]. Although unrealistic, assuming instantaneouseruption and cooling for the flow results in predicted surfacetemperatures which rapidly (within 1 month) converge onthose for more plausible emplacement times.

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month after cooling ensues, after which the results con-verge to nearly identical values. This similarity indicatesthat the instantaneous eruption and cooling scenario is areasonable assumption for long-term cooling.

3.3. Tools for Comparison

3.3.1. Dual-Band Method[11] The dual-band method was pioneered by Dozier

[1981] and Matson and Dozier [1981], first applied tovolcanic targets by Rothery et al. [1988], and subsequentlymodified for AVHRR measurements of volcanic phenomenaby Harris et al. [1997a]. Both two-component (used inmethod 1 here) and three-component (method 2) dual-bandapproaches are used here. A two-component approachmodels the pixel-integrated temperature as resulting fromthe combined thermal signature of warm lava at a temper-ature Th, occupying a fraction of the pixel area denoted by p,and cold ground at ambient temperature Tb, occupying anarea 1-p. In this case, the dual-band equations are

R3 ¼ pL3 Thð Þ þ 1-pð ÞL3 Tbð Þ

R4 ¼ pL4 Thð Þ þ 1-pð ÞL4 Tbð Þ

where R3 and R4 are the total radiance values measured bythe satellite in bands 3 and 4, respectively, L3(Th) and L4(Th)are the radiance contributions from the hot component ineach band, and L3(Tb) and L4(Tb) are the radiancecontributions from the background component in eachband. L3(T) and L4(T) are determined using the Planckfunction values for a blackbody at temperature T at the B3and B4 central wavelengths. Background temperature (Tb)can be estimated from adjacent nonanomalous pixels, andthe remaining two unknowns (Th and p) can be calculatedsimultaneously.[12] For a three-component model, the pixel area is

assumed to be composed of small, hot areas (Th) on theflow occupying a pixel fractional area of ph, areas ofmoderately warm, cooling lava (Tc) occupying a fractionalarea of pc, and areas at background temperature (Tb)occupying the remainder of the pixel area (1-ph-pc). Thedual-band equations are

R3 ¼ phL3 Thð Þ þ pcL3 Tcð Þ þ 1-ph-pcð ÞL3 Tbð Þ

R4 ¼ phL4 Thð Þ þ pcL4 Tcð Þ þ 1-ph-pcð ÞL4 Tbð Þ

With five unknowns (Th, Tc, Tb, ph and pc) at least threemust be assumed to reduce the unknowns to two.Unfortunately, for emplaced, extended cooling only back-ground temperature is known with some certainty (fromadjacent pixels), so Th and ph need to be assumed in order tosolve for Tc and pc. The hot component temperature andarea are not well known as little field work has been done to

constrain them, and they likely change dramatically as theavailable underlying heat diminishes. On a pixel-by-pixelbasis, therefore the ignorance of both the hot componenttemperature and area renders the three-component modelineffective for providing additional information.3.3.2. Pixel Merging[13] In order to reduce the number of unknowns in the

radiance equations for the three-component model, the pixelmerging method performed by Harris et al. [1999] isadapted for AVHRR imagery. In this approach, the radiancevalues for each pixel in the anomaly are essentially aver-aged to produce a larger pixel. This technique has thebenefit of encompassing the entire hot source, so that whenthe total area of the volcanic target is known (as in the caseof a lava lake or an emplaced lava flow) this area can beused to constrain the other unknowns.[14] A complication is introduced by this method, how-

ever, as a result of pixel overlap. Because the ground sampledistance (GSD) of AVHRR is less than the IFOV [Cahoonet al., 1992], substantial overlap of pixel footprints willresult [Breaker, 1990], leading to repeated incorporation ofthe hot target radiance with the merging approach. Calcu-lation of IFOV size versus scan angle was done using thesimple geometric approach of Cahoon et al. [1992] for acurved Earth surface, using the assumptions in Table 2.Along- and cross-track GSDs were taken from Cahoon etal. [1992] and B3 and B4 IFOVs were taken from Harriset al. [1997b]. To account for the oversampling, themerged area of pixel coverage was calculated taking intoconsideration the GSD and IFOV as a function of scanangle (Figure 4), as opposed to simply summing the total

Figure 4. Graphical representation of the pixel-mergingmethod. The pixel merging area is that of the black box,whose dimensions are calculated from the number of pixelsin the cross- and along-track dimensions, and their IFOVand GSD.

Table 2. Values for IFOV/GSD Calculationsa

Value, mrad

Cross-track GSD 0.95Along-track GSD 1.05Band 3 IFOV 1.51Band 4 IFOV 1.41

aFrom Cahoon et al. [1992] and Harris et al. [1997b].

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area of the individual pixels which would produce anoverestimate of the actual ground footprint. The total areaof the lava flow (8.9 km2) was then divided into this totalmerged pixel area to calculate lava fraction ( p).[15] The merged area was chosen manually in each

image based upon visually elevated pixels, making sureto encompass the entire flow. Attempts to isolate theanomalous areas using automated band-differential thresh-olding [Harris et al., 1995; Higgins and Harris, 1997]were not consistently successful, most likely because thismethod was developed for active lava in which band 3 ismore reliably raised above background.

3.4. Comparing Modeled Cooling to AVHRR Data

[16] The model results were compared to AVHRR datacollected over the flow throughout its initial cooling periodusing the selected images, covering a period from 24 Marchto 2 September. In order to extract the lava temperature fromthe AVHRR pixel-integrated temperature (a composite oflava and background temperature) two basic approacheswere used. First, the dual-band approach to calculate lavasurface temperature is attempted (in methods 1 and 2).Second, the pixel merging method of Harris et al. [1999]is used (methods 2 and 3).3.4.1. Method 1: Dual-Band, Pixel-by-Pixel Method,Two-Component Model[17] For each cooling image the two-component dual-

band approach was applied to each pixel in the thermalanomaly (Figure 5). Band 3 and 4 transmissivity valuesand B4 upwelling radiance were estimated using theMODTRAN4 atmospheric model [Berk et al., 1999]. B3

reflected radiance was negligible in these nighttime images,and background temperature (Tb) was taken from theaverage of nonanomalous adjacent pixels. The mean hotcomponent temperature (Th) solution for the anomalouspixels in each image is shown in Figure 5b, with thestandard deviation to indicate the range of values in eachimage. The plot shows an exponential-like drop andleveling similar to that exhibited by modeled temperatures(Figure 5a), but in a much higher temperature regime.[18] Whereas modeled temperatures are 5–10�C above

background throughout the majority of the 200-day cool-ing period, the hot component temperatures we measuredaverage around 50–100�C above background for theperiod. Summing the hot component area of the anoma-lous pixels in each image results in a total area (<4 km2)that is considerably less than the actual total lava flowarea (8.9 km2). Clearly, this two-component dual-bandapproach fails to characterize the temperature of thecooling crust, and likely reflects influence from small,anomalously hot areas on the flow surface (an unaccountedfor third component).[19] In dual-band calculations of active flows [e.g.,

Harris et al., 1997a] these anomalously hot areas areattributed to cracks in the nascent crust which exposeincandescent lava. For extended cooling of an emplacedflow a similar model can be applied with the small, high-temperature areas representing areas of active fumaroles,as were observed on the Okmok flow in 2001, as well ason other flows (A. Harris, personal communication, 2002).In the two-component pixel approach, however, the flow ismodeled as a single component, resulting in the extractedlava temperature being an unconstrained composite of thehot steaming areas and cooling crust.3.4.2. Method 2: Dual-Band, Pixel-Merging Method,Three-Component Model[20] To resolve this problem a three-component model

was applied to the dual-band equation to solve for thetemperature of the cooling lava. By merging the pixels overthe flow the number of unknowns in a three-componentmodel can be sufficiently reduced to make the dual-bandmethod viable. Here ph + pc accounts for the area of theentire lava flow (8.9 km2) divided into the merged pixelarea, letting us solve for pb. This leaves essentially threeunknowns: Th, Tc (for which a solution is sought) and pc( ph can then be calculated by ph = 1-pc-pb). Backgroundtemperature was determined by pixels near the flow, as inthe previous method. If a range of possible values for Th,is assumed the range of values for Tc, pc and ph can besolved for. On the basis of field observations at Okmokin 2001 (K. Papp, personal communication, 2002) andEtna in 1991–1993 (A. Harris, personal communication,2002) typical hot component temperatures could rangefrom 50�C to 300�C. Solution for the crust temperatureusing this range of hot component temperatures is shownin Figure 6. Temperature values are generally consistentwith modeled predictions, in that crust temperature dropsto within 10�C of background within 1 month and hoversat �5–10�C above background for the remainder of the200-day study period. The size of the hot component(Figure 6b) is inversely related to hot component tem-perature and generally decreases with time, with totalsizes for Th = 300�C ranging from 3 � 10�4 to 0.1 km2

Figure 5. Results of method 1 for AVHRR lava surfacetemperature extraction. (a) The model results for varyingconvective heat transfer coefficient values. (b) Method 1results, which produced spurious values. Note the differenty axes ranges.

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(for 24 March to 2 September) and for Th = 100�C rangingfrom 0.02 to 0.48 km2 (for 11 April to 2 September). Themethod yielded no solution for Th = 100�C for the periodbefore 11 April, probably because such a low assumedhot component temperature is unable to account for theactual hot component radiance in this early part of thecooling.3.4.3. Method 3: Single-Band, Pixel-Merging Method,Two-Component Model[21] Finally, we attempt extracting lava surface tempera-

ture from band 4 alone. Band 4 was chosen over band 3because of its reduced sensitivity to the small, anomalouslyhot portions of the flow which are essentially ignored in thismethod. The impact of this assumption has been estimatedand incorporated into the error discussion in section 3.5.2.The pixel-integrated radiance can then be assumed to be thesum of the background radiance (L4(Tb)) covering an area1-p and the cooling lava flow radiance (L4(Th)) coveringan area of p:

R4 ¼ pL4 Thð Þ þ 1-pð ÞL4 Tbð Þ

Background temperature is computed from the average ofpixels surrounding the hot area. In order to avoid errorsintroduced by assumptions for transmissivity and emissivityinherent in any calculation of absolute temperatures,uncorrected band 4 temperatures were used and a relativecalculation of lava surface temperature over local back-ground was performed (Figure 7). The band 4 measure-ments of the flow are mostly consistent with the range ofmodeled temperatures. Rapid exponential cooling ensuesfor approximately the first 50 days, and is followed by avery steady decrease in temperatures hovering at �5–10�C

Figure 6. Results from method 2 AVHRR lava surfaceextraction approach (dual-band, three-component, pixel-merging). (a) Surface temperature results agree well modelresults (Figure 5a) using heat transfer coefficients between50 and 100 W m�2 K�1. (b) Hot component areas forvarious assumed hot component temperatures.

Figure 7. Results from the method 3 AVHRR lava surface extraction approach (single-band, two-component) compared to modeled results using varying convective heat transfer coefficient values.The AVHRR-extracted values are most consistent with convective heat transfer coefficients between50 and 100 W m�2 K�1 and are generally above 25 W m�2 K�1. This range is in agreement withmeasured convective heat transfer coefficients over lava surfaces by Keszthelyi and Denlinger [1996]of 65–75 W m�2 K�1.

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above background temperatures. The error bars in theAVHRR-extracted values are described below.

3.5. Error Analysis

[22] The radiant signature of the lava flow is relativelysubtle compared to that of the background, and this studyattempts to extract a signal that is significantly weakerthan what has been studied with active lavas [e.g., Harriset al., 1997a, 1997b], compelling an estimate of the scaleof error in our extraction methods. For each method, thetotal error was calculated by the square root of the sumof the squares of the individual error sources. It should benoted that errors in MODTRAN-estimated upwellingradiance and assumed emissivity were estimated to benegligible.3.5.1. Method 2 Errors3.5.1.1. Error Source 1[23] Uncertainty in the MODTRAN-estimated transmis-

sivity values for bands 3 and 4 can have a significant impacton extracted lava surface temperature. The crust temperaturesolution was observed to be more sensitive to the differencebetween band 3 and 4 transmissivity values than to theirabsolute values, and therefore we varied the difference by±0.03 which slightly exceeds the variation in summer/winter transmissivity difference between B3 and B4. Thisproduced crust temperatures that varied by 0.1–2.0�C(mean = 0.7�C).3.5.1.2. Error Source 2[24] The background temperature may vary among the

background portions of the pixel merged area, and this maypresent a problem as a single background temperature wasassumed. On the basis of visual inspection of the variance inbackground around the thermal anomalies, the maximum

range in background temperature was estimated at ±1�C.The effect of this uncertainty was addressed easily bysimply varying the background by that amount and rerun-ning the method. This produced an effect of 3.2–6.7�C(mean of 4.5�C).3.5.1.3. Error Source 3[25] In the pixel-merging method the spatial extent, or

footprint, of the pixel on the ground was estimated usingan effective IFOV, as described earlier. An effective IFOVassumes a perfect response function, that is, the responseof the sensor within the IFOV is 1 and 0 anywhereoutside. In actuality, the detector response (or point spreadfunction, PSF) is a relatively smooth function, and theIFOV simply approximates this as best as possible. Inorder to estimate the error introduced by this, the AVHRRPSF was approximated numerically from the results ofMannstein and Gessell [1991] and used to perform asimulated pixel merging extraction on an idealized in-stance of the 1997 Okmok flow (Figure 8). AlthoughMannstein and Gessell [1991] provided the PSF for band5 (IFOV = 1.3 mrad) only, we take it as a reasonableapproximation for band 4 (1.41 mrad) response for thepurposes of this simulation. A digitized version of the flowwas assigned a uniform lava temperature, which was T�Cabove the uniform background temperature, at 0�C.AVHRR PSFs were placed at nadir ground sample dis-tances above the flow to replicate the actual AVHRRresponse, and the pixel merging approach was performedusing the effective IFOV values described earlier. Formethod 2, this produced errors in the crust temperaturefrom 1.7 to 5.4�C for the range of scan angles and hotcomponent temperatures (100–300�C). The simulationsalways produced higher values for crust temperature thanthe actual value, which likely reflects the pixel overlapproducing repeated incorporation of radiance into themerged value.3.5.2. Method 3 Errors3.5.2.1. Error Source 1[26] This method also suffers from uncertainties arising

from the pixel-merging method, and the pixel-mergingsimulation was performed in the context of this method,as well. The error in extracted lava temperature was within12% (again, always producing an overestimate) of thedifference between lava and background temperature, andfor numerous randomly chosen PSF positions over theflow, indicating that the method has an inherent error atthat level.3.5.2.2. Error Source 2[27] To address background temperature uncertainty, we

reran the method with background temperature deliberatelyaltered by ±1�C. This produced errors in extracted lavatemperature ranging from ±1.3 to 4.5�C, depending on thelava temperature and fractional area of background in eachimage.3.5.2.3. Error Source 3[28] Band 4 will have a much reduced sensitivity to the

anomalous hot components on the flow, compared to band3, but there may still be a significant impact. The hotcomponent temperatures and calculated areas from method2 were used to estimate the impact on the pixel mergedtemperature, and the method was rerun with altered valuesto examine the effect on the extracted lava surface temper-

Figure 8. Schematic of the ancillary model used toexamine the error inherent in the pixel-merging extractionmethod. This extraction method was simulated for anidealized surface temperature distribution in the region ofthe flow. The error in extracted lava surface temperatureswas at most 12% of the temperature difference between lavaand background. The pixel-merging method always over-estimated lava surface temperature, likely due to pixeloverlap and repeated radiance incorporation.

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ature. This effect varied from 2.9–6.7�C, with higher errorsoccurring for higher lava temperatures.

4. Discussion

[29] As mentioned, the pixel-integrated radiance is aweighted average of the radiance of several subpixelelements. The land surface surrounding the lava and thelava itself comprise the two obvious components. Refiningthis two-component model is done by then considering thelava surface as multicomponent, in which the majority ofthe lava surface is cooling conductively, and a smallerportion contains anomalously high temperature steamingareas, producing a total of three components for the pixel.Several approaches were used to extract the lava surfacetemperature component from the AVHRR pixel-integratedtemperatures, and each addressed this multicomponentthermal structure of the flow surface in a different way.The dual-band, two-component approach (method 1)ignored the multicomponent model and attempted to extracta homogenous lava surface temperature. As the resultsshow (Figure 5b), the estimated lava surface temperatureis drastically elevated over the range of plausible lavasurface temperatures predicted by the model (Figure 5a),suggesting the failure of this approach. The dual-band,three-component model (method 2) attempted to consider

the two-component nature of the lava surface and producedreasonable results in rough agreement with the modelpredictions (Figure 6). The single-band, two-componentapproach (method 3, Figure 7) assumed that the radiantcontribution of the anomalously hot areas (those areas notconducive to conductive modeling) was insignificant inlong-wave band 4 due to their very small size. In this case,the calculation is relatively simple and the combined errorsin this method were slightly lower than those in method 2.Because of the simplicity in the approach and lower errors,method 3 is taken here as the favored method for modelcomparison, but it should be noted that there is neverthelessa good overlap between the method 2 and method 3solutions.[30] These AVHRR data were originally meant for a

formal validation of the model, but the degree to whichthis was successful is arguable. In one sense, the AVHRRdata indeed show a similarity with the modeled predictions:an exponential-like drop and leveling of surface temperaturein a similar temperature range. On the other hand, thesensitivity tests of Patrick et al. [2004] indicate that the200-day model predictions for lava surface temperature arehighly dependent upon the convective heat transfer coeffi-cient (hc), which could not be established with muchconfidence because of the paucity of knowledge on itsbehavior over lava flows. This uncertainty therefore pre-cludes a definitive validation, and only a range of predictedlava surface temperatures (Figure 7) can be compared to theAVHRR-derived values.[31] If we accept the validity of the model, however, the

AVHRR-derived lava surface temperatures can be used toascertain reasonable convective heat transfer coefficients forthe flow throughout its cooling. This is possible because themodeled lava surface temperatures are relatively insensitiveto all input parameters except the convective heat transfercoefficient [Patrick et al., 2004, Table 2a]. Varying any ofthe other input parameters within a plausible range willproduce a temperature difference of up to only 3�C. Themodeled Okmok lava surface temperatures were plotted fora range of plausible convective heat transfer coefficients,spanning both natural (�5–20 W m�2 K�1) and forcedconvective (�20 + W m�2 K�1) regimes (Figure 7). AsFigures 6 and 7 show, the AVHRR-derived lava temper-atures from methods 2 and 3 are consistent with aconvective heat transfer coefficient in the realm of 50–100 W m�2 K�1, and generally above 25 W m�2 K�1.These results are in agreement with the field measurementsof Keszthelyi and Denlinger [1996] for forced convectionover lava surfaces, in which values of 65–75 W m�2 K�1

were observed for winds of 3–4 m s�1. Kesztheyli et al.[2003] found values for hc between 45 and 50 W m�2 K�1.These two studies measured hc in conditions somewhatdifferent than in this study (recently erupted pahoehoe vs.the emplaced ‘a’a studied here), suggesting that hc valuesof 50–100 W m�2 K�1 may be generally relevant forrough lava surfaces with moderate winds. Nevertheless, allof these results suggest that previous approaches forcalculating the convective heat transfer coefficient [Headand Wilson, 1986; Oppenheimer, 1991; Harris et al.,1997a; Wooster et al., 1997], which produce values around10 W m�2 K�1, may be prone to underestimating theconvective heat loss. It seems clear, however, that more

Figure 9. (a) Modeled lava surface temperature withno subtraction of background temperature. (b) AVHRR-extracted lava surface temperature. Model results use aconvective heat transfer coefficient of 75 W m�2 K�1. Bothsets of results show the seasonal warming of the lavasurface during cooling. Because these AVHRR-derivedtemperatures are not fully corrected for atmosphere, theplots are not overlaid as their absolute values are not meantto be compared to the modeled predictions directly.

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work is needed to establish definitive relations for con-vective heat transfer in a lava cooling context.[32] Finally, the modeled lava surface temperature

exhibited a secondary rise in the summer months due tohigher background temperatures which result in a decreasein cooling rate affecting the lava surface (Figure 9a). Whenshown in absolute values (i.e., without the backgroundtemperature subtracted), the AVHRR-derived lava surfacetemperatures (Figure 9b) appear to show the same phenom-enon. This is only meant to be a relative comparison,however, since a direct comparison of temperatures is notpossible due to discrepancies introduced by atmosphericcorrection and background temperature differences.

5. Conclusions

[33] The numerical model described by Patrick et al.[2004] was applied to the 1997 Okmok flow and the modelpredictions for lava surface temperature over a 200-daycooling period were compared to lava surface temperaturesmeasured by AVHRR imagery. To extract the subpixel lavacomponent from the pixel-integrated radiance, three methodswere compared: (1) a dual-band, pixel-by-pixel approachwith a two-component pixel model, (2) a dual-band, pixel-merging approach with a three-component pixel model,and (3) a single-band, pixel-merging approach with a two-component pixel model. Of these, methods 2 and 3 producedresults consistent with the range of model predictions,suggesting a convective heat transfer coefficient for the flowmost commonly between 50 and 100 W m�2 K�1, andgenerally above 25 W m�2 K�1, which agrees with valuesmeasured elsewhere. Finally, the model prediction of asecondary rise in lava surface temperatures due to seasonalwarming was corroborated by the AVHRR time trend of lavasurface temperature.

[34] Acknowledgments. Considerable assistance was provided byV. Sharpton (UAF), and K. Engle (UAF) must be thanked for his competentadministering of the AVHRR receiving station at the Geophysical Institute.Comments and shared field data from A. Harris (University of Hawaii atManoa) very much improved the paper. K. Papp (UAF) provided valuablefield data as well. Reviews by L. Keszthelyi, J. Crisp, and AssociateEditor L. Mastin are greatly appreciated. This work is supported by theU.S. Geological Survey Volcano Hazards Program and the GeophysicalInstitute at the University of Alaska Fairbanks.

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�����������������������K. Dean and J. Dehn, Alaska Volcano Observatory, Geophysical Institute,

University of Alaska Fairbanks, 903 Koyukuk Dr., P.O. Box 757320,Fairbanks, AK 99775-7320, USA.M. R. Patrick, HIGP/SOEST, University of Hawaii, 1680 East-West

Road, Honolulu, HI 96822, USA. (patrick@high.hawaii.edu)

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