Palaeogeography, Palaeoclimatology, Palaeoecology (Global and Planetary Change Section), 98 (1992) 219-223
219
Elsevier Science Publishers B.V., Amsterdam
Recent climate change recorded in the underground: evidence from Cuba V l a d i m i r (~ermfik a, L o u i s e B o d r i
b and
Jan Safanda a
Geophysical Institute, Czechoslovakian Academy of Sciences, 141-31 Prague 4, Czechoslouakia b Geophysical Department, Hungarian Academy of Sciences, c / o L. EStuSs University, H-1083 Budapest VIII, Hungary
(Received January 3, 1992;revised and accepted June 26, 1992)
Underground borehole temperatures were measured in Cuba as part of routine heat flow investigations. The negative temperature gradient in the near-surface layer and the pronounced "U-shape" of the t e m p e r a t u r e - d e p t h curve seem to be a general phenomenon in the greater part of the island. As it does not depend on the depth of the water table or the conductivity contrast, it is bound to reflect the changing surface conditions. According to the theory of heat conduction in a semi-infinite body, temperature changes at the surface propagate into the subsurface with an amplitude attenuation and time delay which increase with depth. With the application of this theory to the individual T(z)-records, important information on the changes in the surface (soil) temperature could be obtained. Taking into account the effect of the vegetation cover and relating the surface and air temperatures, we can see that the recent climate in Cuba has undergone a pronounced warming of 2-3°C within the last 200-300 years. The climatic effect has been obviously combined with the agricultural effect produced by clearing forests in most parts of Cuba 100-200 years ago.
More than thirty t e m p e r a t u r e - d e p t h records from nine areas of Cuba (See Fig. 1), ((~ermfik et al., 1984, 1991) show an anomalous curvature in their uppermost sections. The temperature decreases with depth to reach a minimum between 100-200 m depth, then gradually increases, and only below 250-300 m does the temperature gradient attain its "undisturbed" value (Fig. 2). The uppermost section from 200 to 500 m is commonly limestone with limy clays and sandstones of Quaternary to Eocene ages. Despite a certain lack of conductivity data, the general geological structure of the studied depth interval reveals a relatively homogeneous composition with little conductivity variation. A detailed analysis of the observed data together with the fact that the temperature gradient actually reverses its sign indicate that a transient change in surface conditions is the most plausible explanation. The problem was treated as a one-dimensional transient conductive heat transfer in a homogeneous medium, the initial conditions corresponding to the steady-state undisturbed temperature field, i.e. a constant temperature gradient, and the boundary conditions for z = 0 expressed as follows:
T(O,t ) = To + AT(t/t*)
"/2
(1)
Correspondence to: V. Cerm~k, Geophysical Institute,
Czechoslovakian Academy of Sciences, 141-31 Praha 4, Czechoslovakia.
for n = 0,1,2 . . . . and for 0 < t ~
0921-8181/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
220
C E R M A K ET AL.
v.
80
76
where F(x) is the gamma function of argument x and i" erfc(x) is the n-th integral of the error function of argument x, and K is the thermal diffusivity. Two slightly different procedures were tested, below referred to as method M1 and method M2. Method M1 treated T*, AT, and t* as unknown parameters, which were evaluated by the application of nonlinear least-squares analysis; the power n was assumed to be a known quantity. In minimizing the sum of the squares of the differences between measured and computed temperature values, we used the method of conjugated gradients in the form proposed by Fletcher and Reeves (1964). The degree of approximation was tested by means of the F-test at the 95% significance level. The mean value of the measured gradient in the lowermost part of the temperature record was used as a value of the undisturbed gradient Go, which also served for the determination of the heat flow value ((~ermfik et al., 1991). Method M2 differs from method M1 in the
Fig. 1. Locations (Table 1) at which temperature was measured in boreholes in Cuba.
is temperature, t is time, z is depth, T 0 is the original undisturbed surface temperature and t* is the time inte~al during which the surface temperature attained the value T * , T * = T0 + AT. This equation corresponds to a simple threep a r a m e t e r power law, which for n = 0 gives a step function, and for n = 2 a linear increase of the surface t e m p e r a t u r e in time. The corresponding solution at time t = t* can be expressed as (Carslaw and Jaeger, 1962):
T( z) = To + Goz + ATZ"F(½n + 1)
×i"
erfc(z/4~4Kt*
)
(2)
TEMPERATURE .°C | 0
•
!
.o
f
//.-"
4-5
"1" F--
e
6
10
,
,
,
,
,
4,
UJ
£3
3-1
/o0
3-3
Fig. 2. The upper part (0-250 m) of t e m p e r a t u r e - d e p t h records. The arrows show the depth of water level in holes. The individual records are labelled by the group/serial number (Table 1).
RECENT CLIMATE CHANGE RECORDED IN UNDERGROUND FROM CUBA
way in which the undisturbed temperature gradient was determined. In this case, G o was taken as the temperature gradient immediately below the obviously disturbed near-surface part of the temperature record. The extrapolated surface temperature was used in defining T0. The other difference concerns the application of the leastsquares inversion theory proposed by Tarantola and Valette (1982a,b) to finding the optimum values of the unknown parameters T*, AT and /'*.
If there is no information on the surface temperature history at all, method M1 may be more suitable as it relates the calculated surface change to the conditions averaged for a long prior period. The use of the G0-value from the first (uppermost) linear T(z)-section, immediately below the disturbed part of the temperature record (method M2), relates the investigated temperature change directly to the previous conditions and may give a better insight into what really happened. The latter method is thus better if the investigated temperature change on the surface was preceded by a more complicated climatic pattern or if the thermal conductivity along the drilled hole is not constant and the use of the " d e e p " gradient may be inappropriate due to the complicated lithological structure at depth.
221
The results obtained by the two methods (Table 1), are generally in good agreement, the only substantial difference concerns the results from boreholes S-7 and S-8 (Punta Alegre). In this case, method M1 suggests that the disturbances of the observed temperature log correspond to a mild cooling while method M2 testifies to a mild recent warming. These two boreholes represent a special case and the reason for the observed disagreement is the sharp contrast in conductivity of the drilled strata (salt tectonics) which produces different temperature gradients in the upper and lower parts of the borehole ((~ermfik et al., 1991). On the basis of agreement with all the other data, preference was given to the M2-resuits ((~ermfik et al., 1992). However, the soil temperature, identical to the surface temperature, T(z = 0), can differ substantially from the air temperature, which characterizes the climate. As shown by Murtha and Williams (1986), the vegetation cover as well as the soil moisture regime may have had a significant effect on the soil temperature, which could be lower by as much as several degrees than the mean annual air temperature. All the boreholes investigated were subdivided into nine groups according to their geographical location. Although for individual boreholes the
TABLE 1 Comparison of the mean values of the individual parameters corresponding to nine groups calculated by methods M1 and M2 Group
1 2 3 4 5 6 7 8 9
Method 1
Method 2
T* (°C)
AT (K)
t* (yr)
To (°C)
T* (°C)
AT (K)
t* (yr)
T~I (°C)
25.2 28.5 29.7 26.7 29.8 26.6 26.0 28.1 25.6
1.9 6.3 7.2 4.7 7.9 ( - 1.2) 1.8 3.8 2.6
111 275 126 69 156 210 63 77 29
23.2 22.2 22.5 22.0 21.9 27.8 24.2 24.3 23.0
25.2 28.8 29.7 26.5 29.9 27.4 25.9 28.4 25.4
3.6 6.3 7.8 5.3 8.0 1.6 1.9 5.5 25
253 235 167 105 158 25 74 117 34
21.6 22.5 21.9 21.2 21.9 25.7 24.0 23.3 22.9
Group 1: Pinar del Rio (number of holes in group, n = 2), 2: Via Blanca and Boca de Jaruco (n = 4), 3: Varadero (n = 4), 4: Jatibonico (n = 4), 5: Majagua (n = 7), 6: Punta Alegre (n = 2), 7: Camaguey (n = 1), 8: Cobre and Hierro (n = 7), 9: Puriales (n = 3). For locations see Fig. 1.
222
V. (~ISRMAK ET AL. Observed p,esent day
calculated increases in the surface temperature (AT) range from 1 to 12 K, and the onset of the recent warmer period varies from 15-20 yr to nearly 400 yr B.P. (before present), the ranges of these values for boreholes in any one group are smaller. The earliest warming occurred in the vicinity of Habana (Via Blanca and Boca de Jaruco group), i.e. in western Cuba, approximately 250 years ago (first half of the 18th century), and the most recent warming, less than 20 years ago, in the region of Puriales, the easternmost part of Cuba. On the whole, there was a tendency of the onset of warming to proceed from west to east (compare Fig. 1 and Table 1), coinciding with the progress of human activities during the Spanish colonization of the island. The other quantities to be determined were the original surface temperatures T0 and their present values T* (Table 1). The T0-values, ranging from 21°C to 26°C have as the most common value 23°C (mean 23.1 + 1.7°C), and the calculated present surface temperatures T* range from 25°C to 30°C, with a mean of 27.4 _+ 1.7°C. The mean difference for soil and air temperatures of about 4.5 K between the rainforest and bare soil (Murtha and Williams, 1986) was used to account for the estimated surface temperature increase as a consequence of deforestation in Cuba. The sequence rainforest-pine forestshrub-cultivated land-grassland-bare soil reached a total 4.5 K temperature difference in relation to the air temperature, and was formally applied to assessing the corresponding correction (Table 2).
S{:I
I{'rl ~){ ';]]U[ e
e3
I
130
~ / ~/ Range / / of presenl / r~ay a,r te~peratare / / / // / /• /
I7
,x.,9
\
26
z I--
,i\.~, ~
i ~:
,
22
,%" t
I
I
!
t
250
200
150
100
50
YEARS
BEFORE
d9 0
PRESENT
Fig. 3. Modelling of the past climatic history in Cuba (see text). Results of methods M1 and M2 are presented together, data are labelled by the number corresponding to the locality-group (see Fig. 1 and Table 1), and primed numbers mark the results of method M2. Open triangles are observed surface (soil) temperatures extrapolated from the temperature logs, solid triangles are the corresponding air temperatures after a correction for the vegetation cover, and large dots correspond to the calculated past climatic conditions at each site visited.
After application of the correction for the vegetation cover, the above mean present-day temperature T* gave a mean air temperature of 25.5_+ 1.3°C, and fits the range of typical air temperatures in Cuba (24-27°C) (Rego-Vazques, 1978). The To (= T* - A T ) temperatures plotted against the corresponding t* data (Fig. 3) show an increase of surface temperature in the last 250 years from about 22°C to the present 24°C (i.e. an
TABLE 2 Characteristic vegetation cover, m e a n annual air temperature and proposed correction for conversion of soil into air temperature No.
Group
Vegetation cover type
Tai r
Corr.
1 2 3 4 5 6 7 8 9
Pinar del Rio Via Blanca Varadero Jatibonico Majagua Punta Alegre Camaguey Cobre/Hierro Puriales
pine forest, dense shrubs bare soil, sparse grass grass, single fields grass, sugar-cane, sparse trees shrubby grassland, cultivated land coastal shrubs, single trees shrubs, sparse forest shrubby grassland to forest tropical forest, dense vegetation
24-25 25-26 25-26 25 25-26 26 26 25-26 23
- 1.0 -4.5 -2.5 - 1.5 - 2.0 - 2.0 - 2.0 - 2.0 0
R E C E N T C L I M A T E C H A N G E R E C O R D E D IN U N D E R G R O U N D FROM CUBA
increase of 0.9°C/100 yr). As there is generally little difference between air temperature and the temperature of the soil under a dense vegetation cover, this result would correspond to climate conditions in Cuba when it was totally forested. However, even though cultivation of the land and deforestation have spread over the country in the past 100-200 yr, such a presumption is problematic. Aridic or semi-aridic areas are unlikely to have been covered by the tropical forest (even though the climate was more humid). Thus, the past soil temperatures differed (were higher) compared with the past air temperature. The position of the "calculated trend" line, which corresponds to the past soil temperatures in the investigated holes should be moved to lower temperatures. This presumption seems to be especially true for the Via Blanca/Boca de Jaruco data group (no. 2), which belongs to the only typically ustic moisture regime area, and its dryness is evident. If the calculated data gave past soil temperatures of about 22°C for this location, grass or shrub vegetation rather than the dense tree cover would correspond to the air temperature in this region of 20-21°C. Then the rate of the assessed climatic warming in Cuba would be slightly higher, about 1-1.2°C/100 yr in the past 200-300 years. This value is well compatible with data from other parts of the world.
223
This is contribution no. 92 of the Geophysical Institute, CSAS, Praha.
References
Carslaw, H.S. and Jaeger, J.C., 1962. Conduction of Heat in Solids. Clarendon Press, Oxford, 510 pp. (~erm~k, V., Kre~l, M., Safanda, J., N~ipoles-Pruna, M., Tenreyro- P6rez, R., Torres-Paz, L.M. and Vald~s, J.J., 1984. First heat flow density assessments in Cuba. Tectonophysics, 103: 283-296. (~erm~k, V., Kre~l, M., Safanda, J., Bodri, L., N~poles-Pruna, M. and Tenreyro-P~rez, R., 1991. Terrestrial heat flow in Cuba. Phys. Earth Planet. Int., 65: 207-209. (~erm~ik, V., Bodri, L. and Safanda, J., 1992. Underground temperature fields and changing climate: evidence from Cuba. Palaeogeogr., Palaeoclimatol., Palaeoecol., (Global Planet. Change Sect.), 97: 325-337. Fletcher, R. and Reeves, C.M., 1964. Function minimization by conjugate gradients. Comput. J., 7: 149-154. Murtha, G.G. and Williams, J., 1986. Measurement, prediction and interpolation of soil temperature for use in soil taxonomy: Tropical Australian experience. Geoderma. 37: 189-206. Rego-Vazques, J., 1978. Temperatura media anual del aire. In: Atlas de Cuba. Inst. Cubano Geod. Cartogr., La Habana, p. 32. Tarantola, A. and Valette, B., 1982a. Generalized non-linear inverse problems solved using least squares criterion. Rev. Geophys., 20: 219-232. Tarantola, A. and Vallete, B., 1982b. Inverse problem--quest for information. J. Geophys., 50: 159-170.