Evidence of ground surface temperature changes from two boreholes in the Bohemian Massif

Palaeogeography, Palaeoclimatology, Palaeoecology (Global and Planetan, Change Section), 98 (1992) 199-208

199

Elsevier Science Publishers B.V., Amsterdam

Evidence of ground surface temperature changes from two boreholes in the Bohemian Massif Jan Safanda and Jaroslav K u N k Geophysical Institute of Czechosl. Acad. Sci., 141 31 Praha 4, CzechosloL,akia (Received January 20, 1992; revised and accepted June 27, 1992)

ABSTRACT Safanda, J. and Kublk, J., 1992. Evidence of ground surface temperature changes from two boreholes in the Bohemian Massif. Palaeogeogr., Palaeoclimatol., Palaeoecol. (Global Planet. Change Sect.), 98: 199-208. The temperature profiles obtained from holes D~tfichov (north Moravia) and Holubov (south Bohemia) were investigated to extract information on climatic variations. The method of analyzing the data is based on the solution of the heat conduction equation in a horizontally stratified medium subject to a step-function change of the surface temperature, and on the generalized least squares inversion theory. The log from D~t~ichov displays a systematic gradient increase to 2 km. Its interpretation is rather ambiguous due to the uncertainty in the thermal conductivity-versus-depth function. Of the conductivity models considered, the homogeneous one yields the most probable results. They suggest the surface warming from - 6 ° C to 7°C 12,000 years ago, which can be related to the climate change at the end of the last glacial period. The curve from Holubov exhibits a gradient increase, which stops at 400 m. It can be explained as a consequence of 0.9K warming 480 years ago, possibly connected with deforestation of the region during the medieval colonization. Namely, the mean annual soil temperature is by 1K lower in a forest compared with a grass cover in these latitudes. The uppermost 80 m of the record suggest 0.5K cooling 40 years ago, followed by a warming of 1.3K 10 years ago. The two last changes, if true, do not correlate with the climatic variations observed and may reflect some local effects.

Introduction

The extraction of the past climate from the geothermal data has been attracting ever increasing attention since the beginning of the seventies. In this connection papers such (~ermfik (1971), Beck (1977 and 1982), Shen and Beck (1983, 1991), Vasseur et al. (1983), Lachenbruch and Marshal (1986), Lachenbruch et al. (1988), C;ermfik et al. (1992), Wang (1992) can be mentioned. Ground surface temperature (GST) his-

Correspondence to." J. Safanda, Geophysical Institute of Czechosl.Acad.Sci., 141 31 Praha 4, Czechoslovakia.

tory reconstructed by this approach represents an independent source of information on climatic variations. It should be noted, however, that the mean annual GST usually differs from the mean annual air temperature. The difference between these quantities may attain as much as several degrees, dependent on the slope orientation and inclination (Blackwell et al., 1980), the type of vegetation cover (Murtha and Williams, 1986; Moore and Fosberg, 1971; Kubik, 1990), the duration of snow cover (Beltrami and Mareschal, 1991), the precipitation regime and its long-term changes (Chisholm and Chapman, 1991) and probably many other factors. Nevertheless, it has recently been shown (Chisholm and Chapman,

0921-8181/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved

200

1991) that changes in the GST are generally consistent with trends in surface air temperature. Due to very slow propagation of the temperature changes in the Earth's body, the method can reveal GST changes, which occurred as far back as tens of thousands of years. The unsteady-state character of the temperature field is manifested by changes in the temperature gradient, which cannot be attributed to other effects like conductivity variations with depth, influence of topography or temperature distortion due to the ground water flow. Especially the last mentioned phenomenon cannot be in many cases ruled out, because information about hydrogeological conditions is missing in most boreholes. This uncertainty can be diminished by interpreting more drillholes located in the region investigated. The present paper deals with the GST history reconstruction at two places of the Bohemian Massif and represents the first application of the method in the area. Temperature in borehole Holubov and D~t~ichov In this first attempt of the past climate changes extraction, we have chosen two temperature curves reflecting very probably unsteady-state conditions. The first curve originates from borehole Holubov located in southern Bohemia (48°53.7'N, 14°19.1'E, 511 m a.s.1.). The borehole was logged twice in May and August 1972. The measurements were made using a thermistor thermometer (Kre~l, 1981) at intervals of 10 m with a relative accuracy better than _+0.01 K. Differences between the two logs do not exceed 0.020.04 K and do not display any trend with depth. The later measurement (Fig. 1) was used for the interpretation. It covers the depth interval 20-690 m and in the upper 350 m deflects from the line fitted to the lowermost part. On a general scale, the temperature gradient increases from 16 K / m at the depth of 100 m up to about 19 K / m , which is observed in the interval 450-690 m. The mean annual surface temperature, extrapolated from the first three measured points (20-40 m), amounts to 8°C. This value is 0.6 K lower

~mm

J. SAFANDA AND JAROSLAV KUBIK

temperature, °C 5

10 '

IN~ "

~i

'

,

15 ,

,

,

,

,

20 ,

,

,

,

I k~... Borehole Holubov 1OO

r

\.

TO = 6.7*Ck~.. 200

~?'.......

,._300

gradT:/~

400

600

Coordinates : 48°53.7'N 14° 19.1'E 511m a.s.l.

700

i

500

~k \, k

\ f

J

i

J

~

I

~

J

,

,

,

~

~,

Fig. 1. Temperature-depth profile measured in August 1972 in borehole Holubov (dotted line). Solid line is a linear fit to the data below 450 m.

than the ground surface temperature, To, computed according to the formula (Kubik, 1990) TO= 1 0 . 6 - 4.7 × 10 -3 × h -

0.33 × (1 - 50) (1)

where h is an altitude above sea level of the surface in metres and l denotes a latitude of a given place in degrees. Strictly speaking, To represents the mean annual soil temperature in °C at a depth of 0.5 m under the plain terrain covered with grass. It was compiled from observations at 48 hydrometeorological stations in Czechoslovakia. The surface conditions at borehole Holubov are very similar to those at the stations. In explaining the observed non-linear tempera t u r e - d e p t h distribution, we should examine four main causes: disturbances due to the groundwater movement, the effect of the topography, the inclination of the borehole and changes in the thermal conductivity. There are no indications of the first mentioned phenomenon in borehole Holubov. The effect of the topography was evaluated by means of the routine procedure (Safanda, 1987) suggested by Bullard (1938) and Jeffreys (1938). Topography surrounding the borehole is shown in Fig. 2. The borehole is located on a small flat

GROUND

SURFACE

TEMPERATURE

CHANGES

FROM

TWO

BOREHOLES

IN BOHEMIAN

lithnIoqy

0

/

~ 4km ~ . ~• ~ ~50o ~5ooa.

"" ~~7 ~ M ~ 2 '

201

MASSIF

temperaturegradient, mK/s

thermal

conductivity, w/~

!

2

3

40

10

20

°°

•~I

4 .o

I

•3

i p i i

o

,,

200

t

,,

el

o:'

I 'I I .I I

c~ O)

"~ 4.00

o

..'

O'

i

o

]o

o.o

. i

o

°1

TABLE 1 Temperature gradient corrections for the topography and inclination in borehole Holubov Depth

Corrections ( m K / m ) due to

Total correction

(m)

topography

inclination

(mK/m)

0 50 100 200 300 400 500 600 700

0.00 - 0.48 - 0.49 - 0.51 - 0.49 - 0.46 -0.41 - 0.34 -0.28

0 0 0 0 0 + O.10 +0.10 + 0.10 +0.15

0.00 - 0.48 - 0.49 - 0.51 - 0.49 - 0.38 -0.31 - 0.24 -0.13

•

.I

o;~,~ 8~, o

Li

elevation extending for a few hundred metres, not more than 20 m above the surroundings. On a broad scale the borehole lies in a valley. The temperature gradient topocorrections obtained in this way are shown in Table 1. With the exception of the first few tens of metres, where the influence of the close and remote terrain is compensated, the topocorrection is negative and relatively constant with depth. The corrections due to the inclination, which is negligible, and the total correction including both factors are given in the same table. We can say that taking them into account would even increase the difference between the smaller temperature gradient in the upper part of the borehole and the greater one in the lower part. It

-

o~

"m ]I

600 Fig. 2. Topography surrounding borehole Holubov. The dashed circle indicates the extent of the topography taken into account in computing the topocorrections.

30

i

correctedfor topographyand inclinationonly

[~

granulite

.....

~]

Mridotite

oooo correctedalso for conductivity

Fig. 3. Lithology, thermal conductivity and temperature gradient in borehole Holubov. Gradient values, depicted by full circles, were corrected for the topography and inclination only, data given by open circles were also corrected for the constant conductivity 3 W / m K .

means the topography does not cause the detected anomaly. The corrections were not considered in interpreting the data set. The last factor, which could account for the observed temperatures, is the thermal conductivity. This quantity was measured on drill cores from 16 different depths by the divided bar apparatus (Kre~l and Veselg, 1973). The results depicted in Fig. 3 seem to decrease with depth, which could contribute to the gradient increase observed. On the other hand, the sampling is rather sporadic and the scatter of conductivity values, as displayed in the depth interval of 500600 m is appreciably high. In Fig. 3 are also depicted two curves of the temperature gradient corrected in the first case for the topography and inclination and in the other case for the topography, inclination and thermal conductivity. The correction for the conductivity 3 W / m K , which is approximately the mean value, consists of a multiplication of the gradient by the ratio k / 3 , where k is the measured or supposed conductivity at the given depth. The depth dependence of the gradient attenuates appreciably after the application of the last correction, but does not disappear entirely. One can conclude that the gradient increase is probably to a certain degree compen-

202

J. SAFANDA AND JAROSLAV KUB[K

thermal conductivity. Measurements on 39 drill cores samples were carried out using the divided bar apparatus. The results are shown in Fig. 5. The values seem to decrease with depth, but their scatter is great. In the rough approximation, two depth intervals, 200-1200 m and 1400-2100 m, of the different conductivity can be distinguished with mean values 3.1 _+ 0.3 W / m K and 2.5 _+_+0.5 W / m K , respectively. The mean value of the whole set is 2.8 _+ 0.5 W / m K . In interpreting the curve in terms of the GST change, both homogeneous and two-layer models of the conductivity were investigated.

sated by the conductivity decrease with depth. Additional measurements would be necessary to ascribe conclusively this effect to the conductivity changes only, which is not possible because the drill cores were destroyed long ago. The second curve (Fig. 4) originates from borehole Dyetrichov located in northern Moravia (49°49.1'N, 17°23.0'E, 613 m a.s.l.). The measurement was carried out in the year 1981 to the depth of 2400 m, i.e. nearly to the bottom of the hole. The relative accuracy of the continuous log is estimated at 0.1-0.2 K. That is why we sampled the log every 100 m only. The temperature gradient increases continuously from 11-13 m K / m in the first 500 m to 22-23 m K / m below the depth of 2000 m. The mean annual GST extrapolated from the depth interval 100-200 m is 7.8°C and equals exactly the value yielded by Eq.(1). In discussing possible causes of the non-linear temperature log, effects of topography and inclination can be ruled out. There is no indication of either water circulation in the borehole or groundwater movement in its surroundings. The only "steady-state" factor that could contribute to the observed changes in the gradient is the

Method of the ground surface temperature reconstruction

It follows from the above deliberations that the observed temperature logs could reflect unsteady-state conditions caused by past GST changes. To evaluate the character of the increase, we presumed the heat conduction in a homogeneous halfspace or in a stratified medium, in which the temperature T must obey equation OT/at = gO2T/Oz:

(2)

temperature, "C 0

I0

20

30

Borehole

40

50

D~tgichov

Coordinates:

49*49.1'N 17"23.0'E 613 m a . s . l .

i000 steady-state ~

component

homogen,

model /

2-1ayer model /

2000

t

Fig. 4. Temperature-depth profile measured in borehole Detrichov in the year 1981 together with steady-state components estimated during the inversion for the two models considered.

GROUND

SURFACE

TEMPERATURE

CHANGES

conductivity,

TWO

BOREHOLES

3.0

,

,

,

O O o

O O

D~tgichov conductivity O 0

o

O

o 1000

O

o

O

o

-

IN

BOHEMIAN

MASSIF

203

To determine the parameters of the G S T change, we employed the general least-squares inversion theory proposed by Tarantola and Valette (1982a,b). This method has been recently applied to various aspects of geothermics (Vasseur et al., 1985; Nielsen, 1986; Wang and Beck, 1987; (~ermfik et al., 1992). In this approach, the set of temperature measurements T(zj), j = 1 , . . . , m is treated as an m-dimensional vector T, which is related to p a r a m e t e r vector p by the equation

W/mK

2.0 0

FROM

=3.06

o

T=g(p)

o

(6)

O

o o

O

O

O

O

o 2000

o

.

.

o

o

.

.

:2.54 .

.

.

.

.

Fig. 5. Thermal conductivity-depth values measured on the drill core samples from borehole D~tfichov together with two trend lines, fitted by the linear regression, and the mean conductivity values for the two depth intervals. The symbol t is time, z denotes depth and g represents thermal diffusivity. The initial subsurface t e m p e r a t u r e was assumed to be 7"( z, 0) = T O+ G0z

(3)

with To denoting the undisturbed surface temperature and G o the undisturbed gradient. The G S T changes with time according to a three-parameter law

T(O, t) = T O+ a T ( t / t * ) "/2

(4)

for 0 < t ~ < t * and n = 0 , 1 . . . . The symbol t* thus represents a duration of the G S T change of the amplitude AT. The solution of Eqs. (2-4) for a homogeneous halfspace, evaluated at t - - t * is (Carslaw and Jaeger, 1959)

T ( z ) = T o + Goz + A T 2 " Y ( n / 2 + 1) ×i"erfc( z / 2 V ~ t * )

(5)

where F(x) is the g a m m a function of argument x and i" erf c is the n-th time integral of the error function. Equation (5) thus enables us to calculate the subsurface t e m p e r a t u r e at the end of a G S T change. The form of the change (4) can be adjusted by the value of n; n = 0 is a step change, n = 2 represents a linear one and so on.

where g is an m-dimensional vectorial function whose components are given by (5). In our case, p contains four components AT, t*, T 0' and Go, which are to be estimated by the inversion of the non-linear system (5). The inversion is done iteratively. The advantage of the method is the possibility.of quantifying our confidence in the a priori estimates of the T and p in a form of their a priori standard deviations and the possibility of obtaining estimates of the a posteriori standard deviations of p. The a posteriori to a priori standard deviations ratio (SDR) is used in the paper to characterize the reduction of the uncertainty of the parameters estimated. To handle the problem in the case of thermal parameters varying with depth, the above mentioned least-squares inversion procedure was extended to the transient heat conduction in a stratified medium. The extension is based on a numerical solution described in Nielsen and Balling (1985). A compact and efficient computation of this formalism has been compiled for the case of a step change of the surface temperature. Provided the thermal conductivity and diffusivity are known in the individual layers, the corresponding undisturbed gradients together with the GST, the amplitude of the change and the time of its occurrence can be estimated from the measured temperature logs. Results

The Holubov borehole In order to find the parameters of the earliest change, believed to be the main source of the

204

J. SAFANDA AND JAROSLAV KUBiK

temperature, K ~0.5

-0.3

-O,1 r

i

O.l

0.3 ,

~

0.5

HOLUBOV the

residual

two jumps

curves

200 August

1972

;--

May 1972

409

600 ,

Fig. 6. Differences between the temperature measured m borehole Holubov and the computed response to the earliest warming. The residual curves are shown both for"the first measurement in May 1972 and the other in August 1972. The approximation of the latter curve by the two jumps of the surface temperature is given by the dotted line.

non-linearity of the log, the section between 100680 m was considered with the standard deviation of one measurement equal to 0.01 K. The uppermost part of the log (20-100 m) was excluded since the temperature gradient strongly varies within it (see Fig. 3), reflecting some more recent events. The value of 10 -6 m2/s was chosen as a characteristic diffusivity. The solution of Eq. (6) was sought for n = 0, 1, 2 and 3. The best fit between the log and the computed response was achieved for n = 0, i.e. for a step increase in the GST. The warming occurred 475 yr ago (SDR = 0.3) and its amplitude amounted to 0.86 K (SDR = 0.03). The estimated undisturbed GST, 6.74°C (SDR = 0.2), and the temperature gradient, 18.58 m K / m (SDR = 0.2), remain very close to the a priori values. The response of the temperature field to this warming, computed according to Eq. (5), approximates the observed temperature curve below 100 m very closely. The degree of coincidence in shown in Fig. 6 in a form of the residual curve, i.e. in a form of the difference between the non-linear part of the log and the computed response to the warming. In order to show how the difference is influenced by measurement errors, the residuals are depicted both for the former log and the later one. The residual curves

are highly correlated and vary about the zero line, i.e. about the linearly increasing temperature, by no more than 0.06 K below the depth of 80 m. Owing to an approximative character of t h e knowledge of the thermal conductivity, further interpretation of the variations is futile, except for the first 100 m, where the shape of the difference curve suggests a cooling of the surface followed by a more recent warming. To evaluate the parameters of the two changes, we used an equation analogous to Eq. (5), expressing the subsurface temperature response T to two jumps having amplitudes AT I = T 1 - T 0 and AT 2 = Z 2 - T1, which occurred Tt* = t - t~ years ago and t~ = t - t 2 years ago, respectively. The equation reads

T ( z , , ) = T o + G o z + AT, e r f c ( z / 2 f f f f t ~ ) + AT 2 erfc(z/2vFfft~)

(7)

The inversion algorithm was applied to the residual curve in the depth interval 20-140 m with an a priori value of To, G O equal to zero. The results indicate a cooling by - 0 . 5 K (SDR = 0.8) 36 years ago (SDR = 0.5) followed by a warming of 1.3 K (SDR = 0.4) 9 years ago (SDR = 0.1). The response of the subsurface field to the last mentioned changes is shown in Fig. 6.

The DYthchov borehole Due to the monotonous increase of the temperature gradient, the temperature curve was interpreted as a response to a single warming in the past. According to the measurements of the thermal conductivity, two models were considered. The homogeneous model cannot be ruled out owing to the great scatter of measured values, but the two-layer one was also taken into account. For the homogeneous halfspace, the best coincidence between the measured profile and the modelled response was achieved for the step change of the surface temperature (n = 0 in Eq. 4). The value of 1.2 × 10 -6 m2/s was adopted as a characteristic diffusivity. The solution of Eq. (6) suggests the warming from - 6 ° C (SDR = 0.6) to 7°C (SDR = 0.2) 12,000 years ago (SDR = 0.3). The difference between the measured and corn-

GROUND

SURFACE

TEMPERATURE

CHANGES

FROM TWO BOREHOLES

temperature, K -~0.5

-0.1

- 0 ..~ i

0

0.1

i

0.5

0.3 i

F

DETRICHOV residual curves

50O a~

~1000

1500

2 - l a y e r model

<:Z 2000

........

homogen

model /

2500

'

'

'

/ J

---

~

'

'

'

Fig. 7. Differences between the temperature profile measured in borehole D6tfichov and the computed response to the warming yielded by the homogeneous and two-layer models, respectively.

puted profiles is given in Fig. 7. The average difference at a single point is 0.15 K, which is less than the considered standard deviation of one temperature measurement, 0.2 K. The boundary between layers of the two-layer model is at a depth of 1300 m. Its diffusivity was 1.3 x 10 -6 mZ/s and a priori conductivity 3.1 W / mK. It was underlain by the layer with diffusivity 1.1 x 10 -6 m2/s and a priori conductivity 2.5 W/mK. Owing to the uncertainty of the estimate, the conductivity was allowed to vary by 10% during the inversion. The step change of the GST was investigated only. Under such conditions, the warming from 2°C (SDR = 0.4) to 7°C (SDR = 0.3) 5500 years ago (SDR = 0.8) is the most probable solution. The a posteriori conductivity values are 2.9 W / m K for the upper layer and 2.5 W / m K for the lower one. The difference between the temperature log and the computed response is depicted in Fig. 7. The agreement is slightly worse than for the homogeneous model. The average difference at a single point is 0.2 K.

Conclusions The interpretation of the temperature gradient increase encountered in borehole Holubov in terms of GST changes is an alternative to its

IN BOHEMIAN

MASSIF

205

explanation as a compensation for the thermal conductivity decrease with depth. On a general scale, this increase can be modelled by the sudden warming of the surface from 6.7 to 7.6°C about 475 years ago. The warming is inconsistent with the cooling, observed in Europe since the 16th century (Lamb, 1977) and known as the Little Ice Age. The weather became warmer again at the end of the 18th century with other oscillations later. The observed long-term warming of the surface can be explained as a consequence of the deforestation in the surroundings of the borehole in connection with the spreading colonization in the region and acquisition of new arable land. The effect of the vegetation cover was reported for Czechoslovakia in Kubfk (1990). According to this paper, the mean annual GST of forested grounds is approximately 1 K lower than in unforested places. This difference is sufficient to account for the estimated warming. According to the most recent results obtained by Beltrami (pers. comm., 1992), a cooling with the minimum 1 K lower than the long-term mean is discernible just prior to the above mentioned warming, when the inversion method described in Beltrami and Mareschal (1991) is applied to the Holubov data set. The minimum coincides approximately with the onset of the Little Ice Age in Europe. On the other hand, the log is too shallow to bring information about the glacial effects. They should interfere in this depth range with younger post-glacial climatic events. In order to appreciate the connection between the temperature variations in the upper 100 m and the climate oscillations, 10-year averages of the air temperature, measured in Prague since 1770 (Petrovi6, 1969; Jflek, 1990) and at Mile~ovka since 1905 (Zacharov, pers. comm., 1992) were plotted in Fig. 8. The Mile~ovka station is located 60 km northwest of Prague at an altitude of 800 m. Contrary to Prague, it is out of reach of any anthropogenic "heat island" and its record may indicate a "natural" warming trend. To be sure that the variations measured in Prague and Mile~ovka are of importance also for Holubov, located about 150 krn to the south, we compared mean annual air temperature series of the last 40 years in Prague and Brno, the distance of which

206 10.5

J. SAFANDAANDJAROSLAVKUBIK ......................

~ 6.5

PRAHA-KLEMENTINUM

10.0 r...)

1 6.0

J

d

~ 9.5

~

--

@

5.5 I L_,

r*-'

5.0

9.0 _~ 8.5 1750

I , , , 4.5 1850 1900 1950 2000 years, A.D. Fig. 8. The 10-yr averages of the air temperature measured at Prague-Klementinum (the left-hand temperature scale) and at Mile{ovka (the right-hand scale). ,

~

,

I , 1800

MII.~ S O g I ' ~

,

,

,

,

,

i

,

,

,

,

i

~

,

~

~

is about 200 kin. These records display a very good correlation. If the mean annual air temperature variations are responsible for the two detected changes which occurred 36 and 9 years ago, then the onset of the cooling should be discernible in Fig. 8 in years 1930-1940 followed by the warming in about 1960. This is not the case. The 10-year averages of the mean air temperature have been increasing since 1880 with only two short and minor coolings in decades 1920-1930 and 1950-1970. It means that the computed GST changes do not correlate with the pattern of the 10-year averages of the air temperature. If the two detected jumps are real, it is necessary to seek their source elsewhere, e.g. in the soil moisture regime or in the annual precipitation changes (Chisholm and Chapman, 1991). Another possibility is that the temperature disturbances in the uppermost 100 m are connected with the fine effects of the nearest terrain coupled with the surface temperature differences due to the varying slope inclination and orientation (Blackwell et al., 1980). Quantification of this type of disturbances would require much more information on the local conditions. To avoid these problems, it would be necessary to use boreholes located in a flat topography only. The lower accuracy of the temperature logging at the D6ffichov borehole allowed only an esti-

mate of the basic trend, explained by warming at the end of the last glacial period. The amplitude of warming resulting both from the homogeneous model, 13 K, and from the two-layer one, 5 K, is much greater than amplitudes of the post-glacial climatic oscillations and can be related to the glacial-post-glacial transition only. The homogeneous model yields better results both in the sense of the agreement between the measured and computed profiles, and in the sense of the known data about the time of glacial retreat and post-glacial warming. A tendency towards a smaller conductivity contrast between upper and lower layers of the two-layer model was revealed during the solution, when the a priori difference was 3.1-2.5 W/InK and the a posteriori one 2.9-2.5 W/mK. It suggests less contrast in the effective conductivity between the upper and lower part of the borehole than indicated in Fig. 5. The warming yielded by the homogeneous model seems to be supported also by results given in Rfi~i6ko% and Zeman (1992). They interpreted cryogenic effects detected in Badenian deposits of borehole Blahutovice-1 (northern Moravia) up to the depth of about 200 m as an evidence of permafrost occurrence in the region during the last ice age. Our results imply a ground surface temperature of - 4 ° C if we consider the present undisturbed subsurface gradient of 20 mK/m. Some of our considerations and experience obtained during the GST history reconstructions are summarized by the following points: (a) the temperature-depth distribution should be affected by climatic changes like the warming at the end of the last glacial and the temperature oscillations during the post-glacial time, e.g. the Atlantic (6000-4000 yr B.P.), the Sub-Boreal (3500-2500 yr B.P.), the Little Climatic Optimum 900-1200 AD) and the Little Ice Age (1550-1850 AD), at least all over Central Europe. There are many temperature logs, however, that do not seem to display signature of these changes. The question is why. It is of great importance to discover disturbing factors and to be able to say why the borehole is not suitable for the GST reconstruction. (b) knowledge of the thermal conductivity is of the crucial importance for the inversion. Unfortu-

G R O U N D S U R F A C E T E M P E R A T U R E CHANGES FROM T W O B O R E H O L E S IN B O H E M I A N MASSIF

nately, the scatter of values measured at the different depths, which can be characterized by the standard deviation of the mean value, is commonly of the order of 0.3-0.5 W / m K , even when estimated from measurements within a lithologically uniform depth interval. For the typical values of conductivity, 2.5 W / m K , and temperature gradient, 25 m K / m , the uncertainty of 0.3 W / I n K in the mean conductivity represents _+3 m K / m uncertainty in the gradient. It means gradient variations up to _+3 m K / m are likely to be explained as a consequence of conductivity variations within the given lithological unit, whereas the gradient disturbances caused by the above mentioned climate oscillations during the postglacial time do not exceed, according to the model computations, the value of _+ 1.5 m K / m . (c) in order to draw reliable conclusions about the GST history of the region, we are going to undertake much more extensive study using boreholes throughout the Bohemian Massif. To obtain as much information as possible we are looking for a more advanced inversion method like that of Shen and Beck (1991) or Wang (1992), which treat thermal parameters as a function of the depth and yield the GST history as a continuous time function. References Beck, A.E., 1977. Climatically perturbed temperature gradients and their effect on regional and continental heat flow means. Tectonophysics, 41: 17-39. Beck, A.E., 1982. Precision logging of temperature gradients and the extraction of past climate. Tectonophysies, 83: 1-11. Beltrami, H. and Mareschal, J.C., 1991. Recent warming in Eastern Canada: Evidence from geothermal measurements. Geophys. Res. Lett., 18: 605-608. Blackwell, D.D., Steele, J.L. and Brott, C.A., 1980. The terrain effect on terrestrial heat flow. J. Geophys. Res., 85: 4757-4772. Bullard, E.C., 1938. The disturbance of the temperature gradient in the earth's crust by inequalities of height. Mon. Not. R. Astron. Soc., Geophys. Suppl., 4: 360-362. Carslaw, H.S. and Jaeger, J.C., 1959. Conduction of Heat in Solids. Clarendon Press, Oxford, 2nd ed., 510 pp. (~erm~ik, V., 1971. Underground temperature and inferred climatic temperature of the past millenium. Palaeogeogr., Palaeoclimatol., Palaeoecol., 10: 1-19. (~erm~_k, V., Bodri, L. and Safanda, J., 1992, Underground temperature fields and changing climate: evidence from

207

Cuba. Palaeogeogr., Palaeoclimatol., Palaeoecol. (Global Planet. Change Sect.), 98: 219-223. Chisholm, T.J. and Chapman, D.S., 1992. Climate change inferred from analysis of borehole temperatures: an example from western Utah. J. Geophys.Res., in press. Jeffreys, H., 1938. The disturbance of the temperature gradient in the earth's crust by inequalities of height. Mon. Not. R. Astron. Soc., Geophys. Suppl., 4: 309-312. Jflek, J., 1990. Statistick~i ro~enka Cesk~ a Slovensk~ Federativnl Republiky 1990. SNTL, Prague, 740 pp. Kre,~l, M., 1981. Technique of heat flow measurements. In: A. Z~topek (Editor), Geophysical Synthesis in Czechoslovakia. Veda, Bratislava, pp. 449-454. Kre~l, M. and Vesel3~, I., 1973. Instrument for the automatic measurements of the coefficient of the heat conductivity of rocks. Trav. Inst. G6ophys. Tch~cosl. Acad. Sci., 461: 317-334. Kub~k, J., 1990. Subsurface temperature field of the Bohemian Massif. Stud. Geophys. Geod., 34:110-128. Lachenbruch, A.H. and Marshall, B.V., 1986. Changing climate: Geothermal evidence from permafrost in the Alaskan Arctic. Science, 234: 689-696. Lachenbruch, A.H., Cladouhos, T.T. and Saltus, R.W., 1988. Permafrost temperature and the changing climate. In: Proc. 5th Int. Conf. on Permafrost, Trondheim (preprint). Lamb, H.H., 1977. Climate: Present, Past and Future. Methuen, London, 711 pp. Moore, E. and Fosberg, M.A., 1971. Temperatures and classification of soils in Latah, Benewah and Kootenai counties, Idaho. Northwest Sci., 45: 137-144. Murtha, G.G and Williams, J., 1986. Measurement, prediction and interpretation of soil temperature for use in soil taxonomy: tropical Australian experience. Geoderma, 37: 189-206. Nielsen, S.B.. 1986. The continuous temperature tog: method and applications. Thesis. Univ. Western Ont., London. Nielsen, S.B. and Bailing, B., 1985. Transient heat flow in a stratified medium. In: A.E.Beck (Editor), Terrestrial Heat Flow and Thermal Regimes. Tectonophysics, 12l: 1-10. Petrovi(:, S., 1969. Podneb~ Ceskoslovensk~ socialistick6 republiky. Hydrometeorol. Inst., Prague, 356 pp. Rfa~ifikov~, E. and Zeman, A., 1992. Blahutovice-1 borehole near Hranice na Morav~: Weathering effect in Badenian deposits. Scr. Fac. Univ. Masaryk., Brno, in press. Safanda, J., 1987. Some remarks on the estimation of geothermal topocorrections. Stud. Geophys. Geod., 31: 284-300. Shen, P.Y. and Beck, A.E., 1983. Determination of surface temperature history from borehole temperature gradients. J. Geophys. Res., 88: 7485-7493. Shen, P.Y. and Beck, A.E., 1991. Least squares inversion in borehole temperature measurements in functional space. J. Geophys. Res., 96: 19,965-19,979. Tarantola, A. and Valene, B., 1982a. Generalized non-linear inverse problems solved using least square criterion. Rev. Geophys., 20: 219-232. Tarantola, A. and Valette, B., 1982b. Inverse problem = quest for information. J. Geophys., 50: 159-170. Vasseur, G., Bernard, P., Van de Meulebrouck, J., Kast, Y. and Jolivet, J., 1983. Holocene paleotemperatures de-

208 duced from geothermal measurements. Palaeogeogr., Palaeoclimatol., Palaeoecol., 43: 237-259. Vasseur, G., Lucazeau, F. and Bayer, R., 1985. The problem of heat flow density determinations from inaccurate data. Tectonophysics, 121: 25-34.

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Wang, K., 1992. Estimation of ground temperature histories from borehole data. J. Geophys. Res., 97: 2095-2106. Wang, K. and Beck, A.E., 1987. Heat flow measurement in lacustrine or oceanic sediments without recording bottom temperature variations. J. Geophys. Res., 92: 12837-12845.