Journa/ of Va/can%gy and Geothermal Research, 24 (1985) 293-313Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

SATELLITE THERMAL INFRARED OBSERVATIONS OF MT. ETNAAFTER THE 17TH MARCH 1981 ERUPTION

A. BONNEVILLE', G. VASSEUR' and Y. KERR'

'Centre Géologique et Géophysique, Place E. Bataillon, 34060 Montpellier, France'Centre National d'Etudes Spatiales, 18, Au. E. Belin, 31065 Toulouse, France

(Receivecl November 28, 1983; revised and acceptecl August 9,1984)

ABSTRACT

293

Bonneville, A., Vasseur, G. and Kerr, Y., 1985. Satellite thermal infrarecl observations ofMt. Etna after the 17th Mareil 1981 eruption. J. Vo/canol. Geotherm. Res., 24: 293­313.

The aim of this stucly is lo estimate the feasibility of monitoring the surface temper­ature of an active vo1cano, using satellite-thermal infrared data.

For lhis, the data collected by a racliometer on board the NOAA polar-orbiting satellitesover Mt. Etna were processecl (geometdcal and racliometric corrections) and merged witha Digital Terrain Model in orcier to correct for the variations of mean grouncl temper­ature ancl a tmospheric absorption with altitude.

Four piclures, or scenes, subsequent to the eruption of 17th March 1981, have beeninterpreted; and they display two thermal anomalies: one, near the summit zone; and theother, on the NNW slope where lava f10ws took place.

Sorne elementary models of thermal evolution are proposed.

INTRODUCTION

The thermal study of volcanic areas by infrared remote sensing is not anew idea, but it still presents numerous problems: technical problems in datacollection and processing but mainly theoretical problems in the interpreta­tion.

A review of previous experimental work on infrared techniques applied tovolcanic studies can be found in Friedman and Williams (1968) and Francis(1979). Among the studies made on Italian volcanoes, we can also mentionthe works of Cassinis et al. (1974) and Archambault et al. (1980). Fromthese publications it appears that, in spite of significant technical progress,infrared remote-sensing methods remain of limited use. This is partly ex­plained by the low spatial resolution of satellite radiometers and by theprohibitive cost of repetitive SUl-veys in the case of au-borne and helicopter­borne thermographies.

Among various other applications, thermal infrared surveys can be expect-

0377 -0273/85/$03.30 © 1985 Elsevier Science Publishers B.V.

294 295

---------------------------------------------TABLE 1

Characteristies of selected images

1

1

1

'"~

~411.l~-J-j

2.001.301.302.00

U.T.

2027254927612874

Orbit

NOAA7NOAA7NOAA7NOAA7

Satellite

Fig. 1. Topographie map of the stucliecl area. The dimensions are 42.4 X 42.4 km' andthe general situation is given in the inset. The broken line arouncl the summit indieatestlw limit of Valle ciel Bove. The partition into 5 zones, with the central zone (I) eoveringthe volcanie structure, Îs shown as fine dot and dashed lines.

14/11/8121/12/8105/01/8213/01/82

Date

DATA ACQUISITION AND PROCESSING

For this study, we used the data recorded on board of the NOAA polar­orbiting satellite by the Advanced Very High Resolution Radiometer (A.V.H.R.R.) in the wavelength range 10.3 to 11.3 !Jm. At closest approach of thesatellite, the resolution (pixel side) is about 1 km. These data collected bythe "Centre de Météorologie Spatiale" are available as digital information ona magne tic tape.

We have chosen a period close to the eruption of the Etna volcano ofMarch 17th, 1981. Scenes were selected according to: (a) near-verticalityabove the site; (b) the lack of clouds above the site; and (c) the time of theircollection. Only night flights were considered since the daily heating of thesoil might mask underground contributions. Unfortunately no good qualitypicture priar to the eruption was abtainable and the 4 retained scenes coverthe period from October 1981 to January 1982.

These scenes - described in Table 1 - caver the whole of Etna's valcanic

structure as a square are a (42.4 X 42.4 km2) shown on Fig. 1, except for theJanuary 13th scene which forms a rectangular area (36 X 42.4 km2). Thesouthwest corner of the area has a longitude af 14° 46'36" E and a latitude

of 37° 33' 35" N. The data were thoroughly processed far topographic andgeometrical correction in arder ta correct for distortions due to the satellite'sposition. The measured values were also resampled with steps of 250 m, Le.smaller than the nominal resolution of the radiometer, in order ta obtaincomparable pictures for each scene.

ed to provide a better knowledge of heat-transfer phenomena using surfacemeasurements. Thermal infrared data are known to be sensitive to the earth's

surface temperature. If this surface temperature reveals itself to be of someuse in the study of volcanic activity, then satellite infrared observationswould provide a unique tool for its monitoring in space and time. However,two questions must be answered before using such data:

(1) How to obtain a significant surface temperature from radiance mea­surement (which is the actual quantity obtained by satellite sensors).

(2) How to relate this surface temperature to the underlying thermalphenomena in connection with the volcanic activity.

ln this paper, we shall try to answer these questions using data obtainedin the thermal IR channel (10.3 to 11.3 !Jm) by the NOAA satellites over theEtna volcano. This volcano is a suitable subject for survey owing to itspermanent activity, its dimensions and the good knowledge that we alreadyhave of it. This method is still experimental and our work aims mainly at aninventory of thermal anomalies and their possible volcanological interpreta­tion.

Data acquisition and pre-processing

296 297

CO2

(a) Rayleigh molecular scattering;(b) selective absorption by sorne given components (C02, 03 .•• );

(c) scattering by dust, drops and aerosols; and(d) scattering and absorption by water vapor.

The transmissivity depends on wavelength (Fig. 2a); it can be evaluated fora standard atmosphere using the Lowtral1 4 model (Selby et al., 1978).

For this study, the altitude range (0-3300 m) is divided into 17 slices,each 200 m high. For each slice, the average transmissivity between 10.3 and11.3 /lm wavelength was determined using a mid-latitude winter atmospheremodel (Fig. 2b).

Radianee and temperature

The measured quantity is the radiance defined as the power emitted in agiven spectral range per solid angle unit and per apparent surface unit. Forthe thermal infrared range, this radiance is given for each pixel by:

LIR = f f[h~leF(Tp, À) + LeÀ + Lad dÀ

where fis the radiometer function (known), S À the atmospheric transmissivity,~ À the ground spectral emissivity, F(T p, À) the Planck function. LeÀ is theenviron ment contribution to the pixel radian ce and LaÀ the atmosphericradiance. Due to the pixel size (1 km2), LeÀ can be neglected.

The interesting quantity is Tb, the average temperature of the pixel. ln afirst step we compute a brightness temperature by using the normalizedresponse function of the sensor, assuming that ~le and Sie are unit y andneglecting the contribution of LaÀ (in this radiometric window and for anon-disturbed atmosphere, ~Ie is maximum and LaÀ is minimum). Usingthese assumptions, the relation between the radiance and the temperaturecan be inverted numerically and we obtain the average brightness temper­ature Tb as a function of the measured radiance:

Tb = G(LIR)

Further details about the reduction technique can be found in Bonnevilleand Kerr (1983). For each scene, this apparent temperature can be mappedat the same scale as the topographie map and used for further interpretation.

Altitude effeets

ln most IR studies, brightl1ess temperatures are used directly. However, inour case, the altitude range is very large (0 to 3000 m) and its influence onthe mapped quantity must be examined thoroughly.

Altitude variations result in two opposite effects: owing to the atmosphericcooling, a general decrease of the actual ground temperature with respect toaltitude is first noticed; at the same time, when altitude increases, the slice ofair between the satellite and the analyzed point is reduced and the actualatmospheric transrnissivity is increased, resulting in an increase of the ap­parent temperature.

Since these effeets might eventually mask the possible underground con­tribution, we attempt to apply a correction using the Digital Terrain Modelin order to "project" ail the points on the same reference level (sea level) andto obtain directly comparable temperatures.

100(f2

+-'

E!/lCco•..+-'

a

%

100

90

o

0.2 0.3 0.6

1000

a

2

b

4 6

2000 3000Zm

A tmospheric absorption

'l'he absorptÎoi1 of eleetromagnetic WaVéSpropagating through the atino­sphere depends mainly upon four causes:

Fig. 2, a. Atmospheriç transmissivity as a function of wavelength (Toyota et al. 1978).b. Inlegrated transrnissivily of the almosphere from the ground ta the satellite height as afunction of the altitude (mid-latitude winter model, Lowtran 4).

298

For each pixel, we obtain an average transmissivity ~p depending on itsaltitude and approximate its actual temperature, Ta, by:

Ta = (~p)-1/4Tb

If our assumptions are correct, Ta would be the actual ground temper­ature which could be compared with ground measurements.

Unforlunately, no ground data are available for this period, but we canuse indications given by measurements obtained two years later at thestation "Torre dei Filosofo" at 2900 m altitude near the summit zone (fig.6b, e.R.G. Garchy, 1984).

For the corresponding pixel, the values of Ta are: -5.5°e (14/11/81),-6.5°e (21/12/81), -4.5°e (5/1/82), -6°e (12/1/82) and for the sameperiod but for 1983-1984 the measured air temperatures are in the range 0to -10oe and the measured temperature at -3 cm depth in the range 0 to-6°e.

This very ctude comparison is not really satisfactory; nevertheless it seemsto indicate that the order of magnitude of Ta is correct.

Adiabatie eooling of the atmosphere

Using an estimated temperature gradient of -6 X 10-3°e m-1 leads todifferences of nearly 200e between the air temperature of the highest andlowest points of the scene. Owing to the nature of heat exchanges betweenthem, the air and sail temperatures are, in a first approach, at the sametemperature. 80 we can reasonably expect that the air cooling with altitudeis entirely reflected by the sail temperature.

This relation can be emphasized by a statistical approach. We divide eachscene into 5 parts (Fig. 1). For each part we determine the correlation be­tween the pixel temperature and its altitude. The result for the central partof each scene (with the largest altitude range) is shawn on Fig. 3a--d. Thecorrelation coefficient and regression coefficient for each scene are given inTable 2.

The correlation is excellent except for the 5/1/82 scene. The 14/11/81,21/12/81 and 13/01/82 slopes are close to the gradient of-6 X lO-3°e m-1;

that of 5/01/82 is lower in absolute value. However, Fig. 3c shows that the

TABLE 2

Correlation of temperature and altitude

T

I"cf

-1

T<'CI

·1

..:

..~~

'~" z.:"~ . )

1CXXl dQ~. ~ 1",1

» ••:.,

.......... . ~,"

a

c

TI"CI

-1 d

299

z

Scene

14/11/8121/12/8105/01/8213/01/82

Correlation coefficient

0.980.950.840.94

Regression coefficient QC m-\

-6.28 X 10-3

-6.97 X 10-3-4.54 X 10-3-6.84 X 10-3

Fig. 3. Grpund-surface temperature corrected for atmospheric absorption as a function ofaltitude in part 1 for the four scenes. The line represents the least-square straight line. (a)14lh November 1981; (b) 21st December 1981; (c) 5th January 1982; (d) 13th January1982.

300301

[] ~"

Fig. 4. Maps of the e()rrected temperature for eaeh scene using a homogeneous cooling ofatmospherie temperature -6 X 10-' °c m-I. The heavy fines are iso-altitude 2500, 1500and 500 m. Seale: 1 pixel = 1 .km'. Ail temperatures in °C. (a) 14th November 1981; (b)21st December 1981; (e) 5th January 1982; (d) 13th January 1982.

(c)

(b)

1·1

(ci)

e/ 1(1.

[J

• Ir;

"

'0

Il

[]

"L

(a)

Il .

mg. Il

ElJ'

•

1'1

points under 1000 m are colder than predicted; if we only retain the pointscorresponding to the highest altitudes, the correlation becomes better andthe slope of the regression equation comparable to that of the other scenes.The reasons for this difference are unknown (low-altitude mists?).

Lacking more precise information, we have decided to apply to ail thescenes a constant correction of -6 X 10-3°C m-1 in order to display theanomalous areas. This choice will be further discussed later; however, it isobvious that if we applied to each scene a correction too close to the data,we might in fact totally or partially mask the long-wavelength anomalies.This is a classical problem in geophysics (Kieffer et al., 1981).

For each point, we thus calculate a corrected temperature by the formula:

T = S-j;1!4 Tb + 0.006 z

where z is the altitude in meters.

At this stage, we have at our disposaI temperature maps, reduced to sea

level, comparable to each other and to volcanic structures. These maps,shown on Fig. 4a-d display thermal anomalies which will be discussedfurther.

First, it is necessary to recaII sorne theoretical notions on the groundtemperature and ta discuss the validity of the processing described previous­ly.

302

DISCUSSION ON V ARIOUS FACTORS AFFECTING THE OBSER V ATIONS

Heat budget at the ground surface

If we define heat received by the ground as positive, the heat budget canbe written as (Sekioka and Yuhara, 1974):

-Et + R t - h (13s - 0 a) = <P 1 z= 0

where Et is the evapo-transpiration flux, Rt is the net radiative budget,h(O s - fi a) is the convective exchange flow between the ground (temperaturefi s) and the air (temperature fi a), h being the exchange coefficient and <1' isthe conductive and convective heat flow of internai origin.

The radiation term, Rt can be written as:

Rt=(l-A)Ri+Wa-Ws

where Ri is the direct and diffuse solar radiative flux, A the earth 's albedo,Wa the radiative input due to sky radiation and W s the radiative heat outputdue to ground-emitted energy.

The ground acts as a grey body at a temperature around 3000K and, asshown on Fig. 5, emits its maximum energy in the thermal infrared range,between 8 and 14 /.lm, which includes the channel measured by the sensor.As indicated previously, this ground radiation can be written as:

Ws= ~afi:

Cll

Ucroc

303

Ground surface temperature at night

At night time, in the case of a cloudless sky, the term Ri can be neglectedand the heat budget equation reduces to:

Wa - W s - h (fi s - 0 a) = <P 1 z=o

Wa can be obtained from an empirical formula as a function of the airtemperature fi a (Idso et aL, 1975).

For fi s '" IJa, W scan be linearized as:

W s '" ~ a 0 ~ + 4~ a 0 ~ (0 a - IJs)

The heat budget equation reduces to:

Wa-~aO~=(plz=o +H(Oa-lJs)

with H = h + 41(1J~

We notice that the ground surface temperature IJsis determined by the airtemperature fi a and also by the heat flow in the ground. This heat flow is the

sum of several components: the most important are diurnal and annualwaves resulting from solar heating variations. Also it includes a geothermalheat flow of deep origin which is generally small enough to be neglected.According ta Cassinis and Lechi (1974), this heat flow must reach manytimes its normal value (60 mW m-2) in order to affect the surface temper­ature significantly. This point will be discussed later using a detailed analysisof our observations.

Parameters controlling the underground temperature

~ .'" ." ..

E::J

.-J UV Visible

0.3 OA7 0.9 3.5

IR

300·K

la Àin,Ltm

We assume first that conduction is the dominating heat transfer mecha­nism. The internai temperature satisfies the equation:

aopc - = 'iJ(K 'iJ1J) + a

at

pc Îs being the specifie heat pel' unit volume, K the thermal activity and athe heat production rate. Assuming no lateral heat conduction, no volumeheat production and homogeneous thermal parameters, this equation redticesto:

a21J 1 ao-----=0az2 a at

a being the diffusivity. The relevant boundary conditions are: (a) at theground surface the heat budget equation given above, with <\' = -K(afi /az),

and (b) sorne conditions at depth accounting for the deep phenomena.Therefore, the ground-surface temperature depends on thermal parameters

Fig. 5. Earth and sun spectral emittance.

304

such as ex, K, h and ~. ln the considered area we suppose that these param­eters are constant. This important approximation is supported by the factthat this study deals with the volcanic structure where sorne homogeneitycan be expected.

Discussion on the processing

If the processing of the data and the above assumptions are correct, in theabsence of thermal anomalies of deep origin, we expect that the temperaturereduced to a reference level would be uniform. On Fig. 4, we observe numer­ous fields where the reduced temperature deviates from its average value byseveral degrees; before any interpretation of these anomalies in relation withthe volcanic activity, we must check that such anomalies are not the result oferroneous corrections or wrong assumptions.

Errors due. to emissivity variation

We assumed that ~ = 1. Any variation in emissivity would result in a corre­sponding error on the ground temperature given by:

ae a~-=--e 4~

and a 1% emissivity decrease results in an error of -0.75°K on the assumedtemperature. If the emissivity varies in a wide range, this would lead tospurious anomalies. ln the case of the Etna, the studied area is vegetation­free and the approximation on ~ does not seem to be drastic.

Errors due to estimate of the adiabatie air cooling

The corrections were applied uniformly to the whole area and periods.This is obviously the weakest point of the method. lt is clear from Fig. 3that for low altitude, the correlation between altitude and apparent temper­ature is not good and the applied correction is probably inadequate. How­ever, 0 n the vo1canic structure itself (above 500 m) the correlation is m uchbetter and it seems possible to obtain meaningful anomalies there.

Error on the atmospheric radiance La /..

The computed brightness temperatures were obtained with the assump­tion La/.. = O. If La/.. was non-zero but a constant, this would approximatelyresult in a systematic bias on the brightness temperatures. ln fact, in thiscase of L -'a proximity and of severe topography, La/.. could eventual1ypresent spatial variations which could lead to spurious anomalies on thecorrected images and especially a systematic temperature difference betweenthe eastern flank of the vo1cano (close to the sea) and the western one. Sucha difference is not observed on the corrected images (Fig. 4a-d) which leadsus to believe that the errar due to this cause is quite smal!.

305

Mapping errorsSuch errors could, owing to correction depending on altitude, reveal

thermal anomalies where there are none. The precision of the localizationwas found from the coast layout to be within the scanner resolution (1 km).Moreover, the value of the temperature-altitude correlation coefficient isfound to decrease for any offset of longitude and latitude. This consistencyleads us to estimate that the location is correct to within 1 km and thetemperature reduction to within 1°C.

On the whole, errors in the reduction of data for temperature at a fixedlevel may result in spurious anomalies of a few degrees amplitude. Bearing inmind that the largest errors eventual1y arise from the altitude correction, wenow de scribe the observed anomalies and their relation with volcanic activity.

THERMAL ANOMALIES OBSERVED

Geological context (Fig. 6)

Mt. Etna is a strato-vo1cano (1,200 km2), linked to the Corn iso-Messineregional fault and to a system of deep dykes (SSW-NNE). Three types ofactivity are known: (a) continuous summit activity; (b) irregular activity onflanks with explosions and lava flows; and (c) exceptional eccentric activityaway from summit and from tectonically active areas.

The 17th March 1981 eruption, a flank eruption on the NNW slope, tookplace in this context (Romano, 1981). A fault system, between the altitudes2250 and 1130 m, spreads out nearly 7.5 km long; these faults have emitteda considerable quantity of lava, estimated at 18.6 X 106 m3, covering an areaof 4.72 km2 (Murray, 1982). A lava flow reached the Alcantara River on19th March and activity decreased until it stopped on 23th March, 1981.

Thermal anomalies

A brief investigation of the four "corrected thermographies" displays: (a)the existence of a wide positive anomaly, on the 1500 m isocontour, NNWof the central crater spreading towards the west; and (b) the existence of asummit anomaly whose shape varies according to the date.

These anomalies are also observed on Fig. 7b, obtained by taking for eachpixel the average individual temperatures of each of the four thermographies.

We have to discuss now the choice of the vertical temperature gradient inorder to correct the altitude effects. Figure 7a-c shows the "average thermo­graphies" computed for gradients a of -5 X 10 -3, -6 X 10 -3 and -8 X10-3°C m-l. The NNW slope anomaly still remains in aIl cases while thesummit one is strongly attenuated with a = -5 X 10-3°C m-I.

This NNW anomaly coincides with the area overlapped by the 17th March,1981 lava flows. A more detailed illustration of this geographical coincidence

306 307

62. '4.

Illo. ".

o <leL

Fig. 7. Maps of averHge corrected temperature using gradients of: (a) -5 X 10 -3°C rn - "(b) -6 X 1O-3°C m-I, (c) -8 X 10-30C rn-I. Scale: 1 pixel ~ 1 km'. Ail temperatures in°c.

=-

"';-l

00

.•.

.'

~:'

F :.'

F

~ •••])1JI-

Paterno

-.ft .. _

\000

,lm

R<lndazzo

~~m

: ~3JOll'; fJ)/ / /

. ,". F SE

\, .' ",' crater·'·.-Jl~ •.••• ,

'·,·', __)\00 ... _.---

,0

1 •••

2À3 - - - -

4 F

-CU

"\ 1000/fll)

__ ......• )000' •.'

(b)

Fig. 6. a. Structural scheme of Etna after Kieffer (1975). The black zone corresponds talava ernissions of l'vlarch 1981. 1 ~ situation of sumrnit area (Fig. 6b). b. Argos temper­ature network and furnarolic fields. 1 = temperature probe; 2 ~ Argos transmitter; 3 ~isocontours of altitude; 4 = fumarolic fields.

308 30"

temperatures

'-----.J

ln the previous section we described two clear positive temperatmranomalies pro bably related to volcanic activity. The second anomaly, nemthe summit is clearly related to fumarolic activity; however, the spatialresolution of satellite measurements is not sufficient for a good understanding of the origin of this anomaly and ground measurements should be usee!to define more precisely its fine structure. The NNW anomaly appears ta bl'linked to the 1981 -eruption lava flows. Yet is itpossible to account for sucha temperature anomaly 8 to 10 months after the eruption? Simple quanti­tative models of heat transfer can be used in order to give an order of magni­tude of the expected temperature anomaly.

DISCUSSION

is shown on Fig. 8, pointing out the corrected and oversampled scenes nealthe summit. Furthermore, we can see a very good coincidence between th,maximum anomaly (more than 8°C) and the exact position of the 17tl­March, 1981 eruptive faults.

So, we have to link this positive anomaly of 4 to 6°C amplitude and 01

about 30 km2 with the presence of the lava flows, either by a direct heatin~)of the ground by lavas or by heating due to a deeper source. (Dykes havin~'fed these flows for example.) Moreover, this geographical coincidence allow,us to demonstrate that, for these thermographies, the localization is bettelthan 1 km, i.e. the spatial resolution of the radiometer.

Figure 8a and b also display more information about the summit anomalywith the choice made for the value of a, it has an area of 5 km2, west of th,central crater, and an amplitude of 4°C (which decreases while a increases)!ts existence is not surprising: it is well known that in the vicinity of tlwsummit (Fig. 6b) there are numerous fumarolic fields. From 1982 to th('present, a temperature survey network has been operating in the summilarea, the data being collected by the Argos satellite system (Archambault.1982). ln fumarolic fields, measurements in shallow boreholes (120 Clll

depth) indicate temperatures reaching 80°C. This is not the radiometric surface temperature but in sorne limited areas local anomalies of several °c canbe expected at the ground surface. The extent of such anomalies is mucllsmaller th an the spatial resolution of the radiometer; in this case the temperature deduced from satellite measurements is just an average of the actualground temperature over one pixel. For this reason the mapped summitanomaly (Fig. 8) appears ta besmoothed out over a zone which is widerthan the actual thermally anomalous zone.

Inspection of Fig. 8 indicates that the position of the anomaly is slightl)shifted toward the west with respect to the summit. We do not think th althis is due to a systematic location error; this offset could be the result ofatmospheric phenomena such as the effect of major winds blowing fromthe north-northwest side.

Eruptive fauts

and lava flows~

2km

b~J~y~

a ~' january 1982

_ + 8"

~+ 6"

l±tm±J + 4"

mIIJ + 2"

c::=J reference

N

r

1000

Fig. 8. Maps of the summit area for the corrected thermographies: (a) 5th January 1982;(b) 13th January 1982.

310311

CONCLUSION

Fig. 9. a. Lava f10w cooling mode!. b. Ts - Ta (OC) as a function of time for several valuesof the thickness e.

The aim of this experiment was to assess the feasibility of studying a vol­cano using satellite infrared data with ail relevant processing.

ln spite of the poor spatial resolution of the radiometer, it proved to besuccessful since significant ground temperature anomalies related to voJcanicactivity were made conspicuous.

However the procedure used for reducing altitude effect is very empirical:we did not consider local meteorological effects (wind, rain, snow, etc .... )and slope orientatiQn effects. Improvements in the definition of temperatureanomalies would require ground·based measurements of meteorologicalparameters at various points of the volcano.

t Months121086

~l·b

e:: 1 rn

a

Lava

Ground

o

20

o

10

4()

30

T 5 ï~'C

T[ z z-e z+e]T(z t) = -.! 2 erf . c; - erf r; --erf 2 ~t' 2 2y cd 2y a. t y ex!

The cooling of a lava flow with a thickness e, an initial temperature Tl an?a fixed temperature (T = 0) for z = a is given by Carslaw and Jaeger (1959,p.62):

where Pa = air density at the ground surface, Cp = air specifie heat at con·stant pressure, Ca = drag coefficient = 0.002 + 0.lE-5 z, Vw = mean windvelocity + 2 m ç 1 in order to take into account fluctuations.

For z = 1500 m and Vw = 6 m S-I, we obtain h = 26 W m-2°C-1 The observed cooling rate is high for low values of e.

Considering lava flows issued in March 1981 and the covered area, theaverage thickness is 5 m. The results lead us to predict a temperature of 6 to8°C, 8 to 10 months after the emission, which is close to the amplitude ofthe 0 bserved ana maly.

However, there is a large difference between the are a covered by lavaflows (5 km2) and the surface of the thermal anomaly (30 km2). 1'0 explainthis, we first invoke the dimensions of pixels (1 km) which are generallywider than the lateral extension of lava flow; in this case however, the mea­sured radiance would correspond to an average temperature and the actualtemperature of lava flow would be greater. This is inconsistent with ourcomputations.

More realistic tS ta consider that the heating of the whole zone is causedby a more regional enhancement of heat: (a) either this heating is related tothe faults feeding the lava flow but this would imply strong lateral convec­tion to affect such an area; or (b) the anomaly reflects the existence ofdeeper phenomena such as a buried intrusion which would also require theexistence of strong convection.

ln fact, this is not the exact solution to our problem since we want to imposefor z = a a mixed boundary condition accounting for exchange with air (atO°C temperature):

-k aT 1 = -h T Iz=oaz z=o

where h is the convective heat exchange coefficient.Except for a few instants after the beginning of the cooling process (for

t = 0), theerror is negligible. We are therefore allowed to use the previousequation ta compute the (small) ground air temperature difference, re­placing aTjaz by its approximate value.

The resulting ground temperature anomaly is shown on Fig. 9b as a func­tion of time and thickness (e) for Tl = 1200°C. The value of h can be givenby the empirical formula (Patoureaux, 1979):

h = PaCpCa Vw

312

The following step will be to monitor the time evolution of surfacetemperatures prior ta an eruptian. Such a study is in course, using a set ofpictures corresponding to a period before the 28th March 1983 Etna erup­tion. The processed radiometric temperatures will be compared with groundmeasurements continuously recorded during the same period in the summitarea.

ACKNOWLEDGEMENTS

The authors wish to thank the "Centre National d'Etudes Spatiales" andthe "Centre National de la Recherche Scientifique" (Action ThématiqueProgrammée "Télédétection", Programme Interdisciplinaire de Recherchesur la Prévision et la Surveillance des Eruptions Volcaniques) which havesupported this work.

REFERENCES

Archambault, C., 1982. Remote sensing of Etna. Argos Newslett., Odober 1982, No. 15.Archambault, C., Stoschek, J. and Tanguy, J.C., 1980. Analyse et surveillance thermique

de volcans actifs (1978-1979). Bull. PIRPSEV, No. 11, Paris.Bonneville, A. and Kerr, Y., 1983. Réduction des observations de télédétection infra­

rouge d'un volcan actif: l'Etna. Rapp. Tech., Bull. PIRPSEV, No. 71, Paris.CarsJaw, H.S. and Jaeger, J.G" 1959. Conduction of Heat in Solids. Oxford University

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