Global and Planetary Change 39 (2003) 271 – 284 www.elsevier.com/locate/gloplacha
Variations in ground surface temperature histories in the Thompson Belt, Manitoba, Canada: environment and climate changes Chantal Gosselin, Jean-Claude Mareschal * GEOTOP-UQAM-McGill, Centre de recherche en ge´ochimie et ge´odynamique, Universite´ du Que´bec a` Montre´al, C.P. 8888, succ. ‘‘Centre-Ville’’, Montre´al, QC, Canada H3C3P8 Received 4 December 2002; received in revised form 12 May 2003; accepted 15 May 2003
Abstract Several temperature – depth profiles recorded at Pipe Mine, 32 km southwest of Thompson, Manitoba, in central Canada, exhibit a marked departure from the equilibrium gradient. These profiles could be interpreted as indicating strong warming (up to 4.5 K) of the ground surface during the last 200 years. All the temperature profiles at Pipe Mine show perturbations stronger than at the others sites in the Thompson Nickel Belt. Temperature profiles recorded near the town of Thompson show a moderate warming ( c 1 – 2 K) trend, while temperature profiles at Soab, 45 km southwest of Pipe Mine, indicate very moderate cooling ( c 0.5 K). There was little human activity in this part of Manitoba before the development of the mining camp of Thompson in the late 1950s. Our study shows the variability of ground surface temperature histories at a very local scale (i.e. < 1 km) with much stronger signals at some of the Pipe Mine drill holes than at others. These holes are located within 500 m of the highway and a power line built after 1955, at c 3 km from the now abandoned open pit mine. The ground surface temperature history (GSTH) obtained by the inversion of Pipe Mine temperature profiles suggests that a recent (50 years) and strong ( c 1 – 2 K) ground surface warming is superimposed on a 1 – 2 K warming trend that started 200 years ago, without any indication of a cold (little ice ages) episode before. The recent warming (40 years) at Pipe Mine is only a local effect and is likely to be related to the presence of the highway. Before 1960, the ground surface temperature history for Pipe is similar to other sites in the Thompson region. Ground surface temperature histories from other profiles within and near the city of Thompson seem less affected by environmental perturbations and their trends are parallel to that of the meteorological records in the Canadian Prairies. D 2003 Elsevier B.V. All rights reserved. Keywords: Thompson Belt; Pipe Mine; Ground surface temperature
1. Introduction The temperature regime of the shallow part of the Earth’s crust is controlled by the (time varying) bound* Corresponding author. E-mail address:
[email protected] (J.-C. Mareschal). 0921-8181/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-8181(03)00120-6
ary condition at the surface and by the heat emanating from the Earth interior. In order to determine the heat flow and the energy balance of the Earth, geophysicists carry out temperature measurements in boreholes and analyze temperature – depth profiles. From the temperature measurements made today, it is possible to extract some information on the past surface boundary conditions. In other words, the Earth’s
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sub-surface contains a record of temperature changes at the surface. As surface temperature changes are propagated downward by heat conduction, any periodic temporal variation of the temperature at the surface is propagated as a damped wave downward. The amplitude of this wave is attenuated exponentially with depth and the skin depth d where the wave is attenuated by a factor 1/e depends on its frequency x and on the rocks thermal diffusivity j as follows d ¼ pffiffiffiffiffiffiffiffiffiffiffi 2j=x . Because the thermal diffusivity of rocks is very low j c 10 6 m2 s 1, the short period oscillations have a small skin depth (a few centimeters for the diurnal variations, a few meters for the annual cycle). The variations of the past 200 years are recorded in the topmost 100 m of the temperature – depth profiles, the post glacial warming can be seen in the 1000– 2000 m depth range. It is possible to infer recent centennial scale variations of the Earth’s surface temperature from the temperature profiles measured in boreholes, such as those drilled for mineral exploration. If heat is transferred only by conduction, the crust is homogeneous with no thermal conductivity variations, and heat sources can be neglected, the equilibrium temperature profile is characterized by a linear increase with depth. The total amount of warming or cooling in the ground after a recent change in surface boundary conditions can be determined from the difference between the measured temperature profile and the upward continuation of the deeper part of the temperature profile (geothermal gradient). The temperature variation recorded by the ground is the difference between the temperatures of these two profiles. The timing of the change is related to the depth where the measured profile departs from steady state. Recently, there has been considerable interest in studying temperature –depth profiles to infer climate changes. This surge of interest in borehole temperature studies followed the study by Lachenbruch and Marshall (1986) who suggested that the temperature profiles from permafrosted regions on the Alaskan North slope show clear signs of warming and are a strong indication that global warming is on its way. Following this study, borehole temperature data have been used to reconstruct the ground surface temperature history (GSTH) in many parts of the world (e.g. see the papers edited by Lewis, 1992; Beltrami and Harris, 2001).
The southern part of Canada has been a particular focus for such studies because there is a large collection of borehole temperature data available. In addition, many of the temperature profiles in Canada were obtained in the Shield from holes drilled through crystalline rocks, which are less likely to be affected by groundwater circulation. In eastern and central Canada, these studies have suggested relatively consistent trends with warming of the ground surface starting around 1800 A.D. after a cold episode identified as the ‘‘little ice age’’ (Nielsen and Beck, 1989; Beltrami and Mareschal, 1992; Shen and Beck, 1992; Guillou-Frottier et al., 1998). The recent climatic warming appears to have been delayed in the prairies and in western Canada where it may have started around 1900 AD, i.e. 100 years later than in the east (e.g. Wang et al., 1994; Majorowicz et al., 1999; Majorowicz and Safanda, 2001). Regional studies of the GSTH, such as those from Canada, usually assume that the variations in ground surface temperature remain correlated at the regional scale. This assumption is to some extent supported by: (1) analyses of the air surface temperature trends that remain correlated over distances c 500 km (Hansen and Lebedeff, 1987; Jones et al., 1999) and (2) observations that ground surface temperature follows the same trends as air surface temperature (e.g. Putnam and Chapman, 1996; Harris and Chapman, 1998; Harris and Gosnold, 1999). However, differences between temperature perturbations from boreholes that supposedly recorded the same GSTH have been documented in several studies (Huang et al., 1996). Researchers who use several borehole temperature profiles to determine the regional ground surface temperature history and its implications for recent climate change are quite aware that changes in surface boundary conditions could have many other causes that are not related to climate (Lewis and Wang, 1992; Cˇerma´k et al., 1992; Majorowicz and Skinner, 1997; Lewis, 1998; Lewis and Wang, 1998). Also, the interpretation of borehole temperature data is based on the assumption that an uniform boundary condition is applied on a plane surface (at least on a scale comparable to the borehole depth). It is possible to account for any departure from this condition (e.g. Blackwell et al., 1980), but this is never done because the uncertainty on the correction is too large. In order to determine a regional GSTH for northern Manitoba and Saskatchewan (Canada), Guillou-
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Frottier et al. (1998) eliminated all the temperature profiles where the assumptions above were not verified. They retained only 10 profiles eliminating all the profiles where the surface boundary condition was not uniform (e.g. near lakes) and all the profiles where recent non-climatic variations of the conditions at the surface (such as forest fires) had been documented. The region investigated in that study is of particular interest because there is little effects from human activity. Over an area 500 500 km, the only settlements are the less than a dozen mining camps, developed after 1950, with some already abandoned. However, the majority, but not all, of the exploration boreholes are close to these mining camps. The study by Guillou-Frottier et al. (1998) confirmed the trends observed in eastern Canada: a warming of c 2 K after 1800 AD following a cold period (Little Ice Age) with a minimum around 1800 AD. Among the profiles that were rejected, we should point out the two profiles measured at Pipe Mine, near Thompson (Manitoba). They were considered suspect because they exhibit an extremely strong warming of the ground surface, much higher than the regional average. But Guillou-Frottier et al. (1998) had no explanation for this ‘‘anomaly’’. In the years following the first measurements at Pipe Mine, new data were collected and a total of 12 profiles are now available from the same site, covering an area of < 0.5 km2. The initial objective of the current study was to analyze all the data from the Pipe Mine site and to reconstruct its GSTH and attempt to discriminate between natural variations in surface temperature and those due to man made environmental changes. The second objective is to look at the variability of ground surface temperature history at the scale of the Thompson Belt and to compare the GSTH with that obtained for the whole northern Manitoba and Saskatchewan region.
2. Description of data Fig. 1 shows the location of Pipe Mine and of the other sites in the Thompson Belt where temperature – depth profiles have been measured. In addition to the 12 profiles from Pipe Mine, 10 other profiles are available in the Thompson Nic-
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kel Belt, over an approximately rectangular region c20 100 km. These data could be used to determine the regional GSTH. There are three profiles available at Moak Lake (57 km northeast of Pipe Mine), two at Mystery lake (44 km northeast of Pipe Mine) and four suitable profiles at Thompson (32 km northeast of Pipe Mine). There is also one profile at Soab Mine (45 km southwest of Pipe Mine). The exact location and depth measured in each profile is given in Tables 1 and 2. In 2001, we logged to the end of the hole (at depth 1600 m) one of the boreholes (0114) in Pipe where previously we had made measurements to 350 m (9815). Except for the profiles measured at Pipe Mine in 1998, 2000 and 2001, all the temperature profiles used for this study have been acquired for heat flow determinations and are described in several papers (Guillou-Frottier et al., 1996; Mareschal et al., 1999; Rolandone et al., 2002; Mareschal et al., 2003). So far, only two profiles at Moak Lake have been interpreted for ground surface temperature history and are included in the study by Guillou-Frottier et al. (1998). For all the profiles, temperature measurements were made at 10 m intervals using a probe equipped with a thermistor. The precision of the temperature determination is 0.002 K and the overall accuracy is better than 0.02 K. Thermal conductivity was measured on core samples collected at every 80– 90 m on the entire depth of each studied borehole with the method of divided bars (Misener and Beck, 1960). We also measured heat generation, which is important for heat flow studies, but has little influence on the shallow part of these temperature profiles. All the temperature depth profiles from Pipe Mine (Fig. 2) suggest strong recent warming with inversion of the temperature gradient in the top 80 m. These perturbations appear about twice as large as those observed at other sites throughout northern Manitoba and Saskatchewan. Other temperature profiles in the region indicate either moderate warming (1 – 2 K) near the town of Thompson (Fig. 3) and at Mystery Lake and Moak Lake (Fig. 4) or a cooling of 0.5 K like at Soab Mine (Fig. 5). The surface warming (or cooling) for all these holes was estimated as above and the results are listed in Table 2. Note that Guillou-Frottier et
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Fig. 1. Location of the sites in the Thompson Belt where temperature – depth profiles show recent perturbations of the ground surface temperature. The study area is the small square south west of Hudson Bay on the map of Canada (inset).
al. (1998) used only the Moak Lake data for their study: they rejected the profiles at Thompson because they might be contaminated by heat refraction
(see also the discussion in Rolandone et al., 2002); the profiles at Mystery Lake and Soab were not available to them.
Table 1 Drill holes at Pipe Mine and inferred ground surface temperature change above the reference level Pipe Mine Hole
Latitude
Longitude
Dip (j)
Dh (m)
DT (K)
Tref (jC)
9410 9411 9814 9815 9816 9817 0015 0020 0021 0022 0114a 0115
55j29 V17W 55j29 V10W 55j29 V10W 55j29 V10W 55j29 V20W 55j29 V12W 55j29 V17W 55j29 V10W 55j29 V09W 55j29 V30W 55j29 V10W 55j29 V20W
98j07 V50W 98j07 V54W 98j07 V35W 98j07 V42W 98j07 V42W 98j07 V47W 98j07 V50W 98j08 V11W 98j07 V54W 98j07 V51W 98j07 V42W 98j07 V54W
84 86 82.5 85 90 87 83 78.5 81.3 70 85 76.25
387 840 345 347 380 220 377 325 343 375 1610 335
4.5 3 3 2.5 4.3 1.6 3.7 1.8 2.5 2.6 2.5 1.8
1.2 0.7 1.1 1.1 1.1 1.6 1.0 1.2 1.2 1.1 0.6 0.9
For each borehole, the location, dip at the collar of the drill hole, vertical depth measured and the total amount of surface warming calculated by upward continuation of the equilibrium geothermal gradient. a Repeat of 9815.
C. Gosselin, J.-C. Mareschal / Global and Planetary Change 39 (2003) 271–284 Table 2 Location of all the sites in the Thompson Belt, with the inferred ground surface temperature change from the reference level Site Hole
Latitude
Longitude
Dip (j)
Dh (m)
DT (K)
Thompson 9405 9406 9407 0017
55j41 V59W 55j42 V15W 55j44 V25W 55j40 V17W
97j53 V50W 97j51 V58W 97j49 V22W 97j51 V35W
71 80 85 82
521 742 991 916
1 2.3 1.6 1.8
1.3 1.1 1.3 0.2
Moak Lake 9408 55j54 V21W 9409 55j53 V53W 0016 55j55 V32W
97j40 V06W 97j40 V41W 97j37 V09W
76 77 72
267 470 860
1 1.4 1
1.2 0.8 1.0
Mystery Lake 9812 55j49 V40W 9813 55j49 V40W
97j45 V40W 97j46 V36W
70 65
898 672
1.3 1.2
0.9 0.1
Soab Mine 9702 55j10 V14W
97j27 V28W
85
680
0.5
1.0
Tref (jC)
For each borehole, the location, dip at the collar of the drill hole, vertical depth measured and the total amount of surface warming or cooling calculated by upward continuation of the equilibrium geothermal gradient.
The warming at the ground surface and at a depth of 50 m was estimated as the difference between the measured temperature and the reference temperature at the same depth obtained by upward continuation of the deeper part (>200 m) of the temperature profiles, where the geothermal gradient is undisturbed. The values obtained are listed in Table 1 and displayed on the location map of the site (Fig.
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6). Note that the open pit mine, which operated between 1969 and 1985 is located c 3 km to the southwest of the drill holes. The inferred ground surface warming varies between 1.8 and 4.5 K in an area 200 600 m and warming at 50 m depth varies between 0.6 and 1.8 K. The estimated reference ground surface temperature (i.e. prior to the most recent changes) and the changes in ground surface temperature for each profile at the Pipe Mine site are listed in Table 1. The most important perturbations are seen at 9410, 9816, 0015 and 9411 with DT = 4.5, 4.3, 3.7 and 3 K, respectively. The former three holes are in the cleared area near the road; the latter is in an area covered with trees. It is worth noting that the dispersion on the reference surface temperature values is small (hTi = 1.1, rT = 0.26) and that it is much larger for the present surface temperatures (hTi = 3.9, rT = 0.95).
3. Inversion results The goal of the inversion is to obtain from one or several temperature profiles, the GSTH, reference surface temperature(s) and reference background heat flow(s). The method, which has been described in several papers (e.g. Mareschal and Beltrami, 1992; Clauser and Mareschal, 1995), is briefly summarized in Appendix A. The mean thermal conductivity for all the samples at Pipe Mine is 3.20 F 0.38(r) W m 1 K 1. Thermal conductivity and diffusivity were assumed
Fig. 2. All the temperature depth profiles recorded at the Pipe Mine site, translated as indicated.
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Fig. 3. Temperature depth profiles recorded within and near the city of Thompson (temperature scale shifted as indicated).
constant for the inversions because the lithology recorded in the drilling logs is sufficiently homogeneous (gneiss) and the geothermal gradient is the same below 200 m in all boreholes. The tempera-
ture profiles were first inverted individually, all profiles with the same depth range were inverted jointly, and finally we used the shallowest 350 m of all profiles for simultaneous inversion.
Fig. 4. Temperature depth profiles at Mystery Lake and Moak Lake, north of Thompson (temperature scale shifted as indicated).
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the little ice ages are masked and cannot be resolved because of the strong recent warming.
4. Discussion and conclusions
Fig. 5. Temperature depth profile near Soab Mine, c 80 km south of Thompson. The abandoned mine is c 5 km north of the drill hole.
The GSTHs obtained by the individual inversions (Fig. 7) show consistent trends but a lot of dispersion, mostly in the last 40 years. The GSTH obtained by simultaneous inversion of temperature data measured in all the shallow drill holes, 1000 m deep drill holes and finally all the drill holes (Fig. 8a– c) show consistent results (i.e. a continuous warming (c 2 K) between 1800 and 1950, followed by strong warming of 2 K after 1960). We have compared the results of the inversion at Pipe Mine with the GSTH obtained at the other sites in the Thompson Belt. Because of the conflicting records of Soab and the other sites, the results of inversion for all the profiles in the Thompson Belt, including Thompson and excluding Pipe, appears noisy (Fig. 9a). Without the Soab profile, the inversion gives results very similar to the regional average for northern Manitoba and Saskatchewan obtained by Guillou-Frottier et al. (1998) (Fig. 9b and c, respectively). It suggests a cold period with minimum at 1800 followed by warming of about 1.5 K. At the Pipe Mine site, the warming between 1800 and 1960 is comparable to that inferred from other sites in the Thompson Belt. It is only after 1960 that the two GSTH diverge. The GSTH before 1960 at Pipe Mine is also comparable to that inferred from other sites in Manitoba and Saskatchewan but without evidence for a cold episode before 1800 as inferred for the rest of Manitoba and Saskatchewan (GuillouFrottier et al., 1998). It is likely that, at Pipe Mine,
Except for the railway to Churchill, the region where this study was conducted was totally undeveloped until 1960. The highway and the power line were built in the late 1950s before the first mine in the city of Thompson opened in 1961. The railway connecting the various mines in the Thompson area was built between 1967 and 1969. Several of the mines in and around Thompson, including Pipe mine, are open pit mines that might have serious environmental impact. Pipe mine operated between 1965 and 1985. Surprisingly, the environmental perturbations were not at all apparent for us on the ground when we were making the measurements near the highway, the power line and the railroad. The very recent warming of the ground surface around the Pipe Mine site is unusually high. There are significant differences in surface warming from individual GSTHs on an horizontal scale of < 100 m (Table 1, Figs. 6 and 8). There seems to be a pattern with the strongest warming in cleared areas, used as gravel pit, near the highway. Because of the similarity of the Pipe Mine and of the regional GSTH before 1960, we believe that the strong apparent warming of the ground surface is caused by recent environmental changes. The indications of ground surface warming are much less pronounced near the city of Thompson, although the environmental perturbations due to mining seem at least as important as at Pipe. Two of the Thompson sites (9405, 9406) are within the perimeter of the Birchtree mine and a third one 9407 is less than 50 m from the city of Thompson train station. Only for the site 0017 (Owl), which is c 5 km south of the city, there is no obvious local environmental factor that might have affected the GSTH. Our interpretation is that the ’’Pipe Mine anomaly’’ is very local and is only due to environmental changes following the highway construction. If the mining activity had affected the GSTH, the effect would have been larger in Thompson than at Pipe Mine. On the scale of 100 km, there are differences between GSTHs between different sites in the
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Thompson Belt. It is evident that the profile at Soab has recorded cooling while all the other profiles have recorded warming. It is worth pointing out that the dispersion on reference ground surface temperature values (i.e. on ground surface temperature before the recent perturbations) is small (r = 0.46) for sites that are up to 100 km apart. The dispersion on present values is larger (r = 0.82) than on the reference level, indicating that local factors are important in these non-uniform perturbations.
The regional GSTH (Fig. 9), which probably represents the natural ground surface temperature history for the region, can be compared with the meteorological records from the Canadian Prairies. The location of the weather stations that we are using for comparison is shown on Fig. 10. The surface air temperature records from these stations are shown on Fig. 11. Unfortunately, there was no weather station in the Thompson area before 1970. Recent surface air temperatures recorded at Thompson are much colder
Fig. 6. Relative location of all the drill holes logged at Pipe Mine and estimated temperature changes at: (a) the surface and (b) 50 m depth. Vegetation has been cleared over 5 m on both sides of the highway and over a 40-m wide corridor around the power line. At sites 9410, 0015, 9816 and 9814, vegetation had been cleared. At all the other sites, vegetation had not been removed, except over the drilling area.
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Fig. 6 (continued).
( 3.5 jC) than the present ground surface temperatures ( c 3.5 jC). The short record of air surface temperature shows a warming trend parallel to that in the GSTH and that seen in other weather stations. Large differences between air and ground surface temperature have been noted elsewhere and are often explained by the snow cover. However, the two time series appear to be correlated (Harris and Gosnold, 1999). The closest weather station with a longer record than Thompson is at The Pas, 350 km SW of Thompson, which started operating in 1910. The longest continuous records in the Canadian Prairies are from
Winnipeg, Manitoba, 650 km south of Thompson and Prince Albert, Saskatchewan, 650 km SW of Thompson. The record at Churchill, which starts in the late 1800s, is not continuous. All available records show clear warming between 1880 and 1940, followed by some cooling, and a new warming trend starting in 1960. At Winnipeg, the mean temperature went from 0.36 jC for the period 1872– 1894 to 1.63 jC for the period 1970– 1992. At Prince Albert, the mean temperature went from 1.53 jC for the years 1885 –1907 to 2.10 jC for 1970 –1992. The GSTH for the Thompson region indicating a 1.5 K warming between 1800
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Fig. 7. Ground temperature histories obtained by individual inversions of the temperature profiles at the Pipe site. The same value of the singular value cutoff e was used in all inversions.
and 2000 is within the range determined from these meteorological records. It is also consistent with regional trends in annual surface temperature in the northwest forest region of Canada, which shows 1.4 K warming between 1895 and 1991 (Gullett, 1992).
Acknowledgements We are grateful to our friends and colleagues, Ge´rard Bienfait, Laurent Guillou-Frottier, Claude Jaupart, Andre´ Poirier and Fre´de´rique Rolandone, who stoically worked in hot and freezing cold weather and snow, and faced the Canadian wildlife (black flies and mosquitoes) to collect these data with us. INCO granted us permission to make measurements in their holes and provided us with (almost) all the information we requested. We thank particularly Bob Lyons and Steve Mooney for their help. Comments from Jacek Majorowicz and two anonymous reviewers have improved the presentation of this paper. The data collection was funded by LITHOPROBE. We also very gratefully acknowledge the continuous and generous support of NSERC (Canada).
Appendix A . Inversion of ground surface temperature history We solve this inverse problem using a singular value decomposition (SVD) method described previously by Mareschal and Beltrami (1992) and Clauser and Mareschal (1995). Here, we outline the main points. The temperature at depth z, T(z), is the superposition of the quasi-equilibrium temperature and of Tt(z), the temperature perturbation due to variations in ground surface temperature: T ðzÞ ¼ Tref þ qref RðzÞ þ Tt ðzÞ
ðA1Þ
where Tref is a reference ground temperature, qref is the reference surface heat flow density and R(z) is the thermal depth, Z z dz V ; ðA2Þ RðzÞ ¼ kðz VÞ 0 and k(z) is the thermal conductivity. The thermal conductivity is usually measured in core samples and/or estimated from the lithology. The inverse problem consists in determining Tref, qref and
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Fig. 8. Pipe Mine Ground Surface Temperature History obtained by simultaneous inversion of temperature data. (a) Results from all the shallow drill hole ( < 350 m); (b) results from two 1000-m deep drill holes; (c) results from the shallowest 350 m for all holes. The singular value cutoff used in the inversion is e.
the GSTH from T(z). The steady state geothermal heat flux can be approximately determined from the deepest part of the profile, least affected by recent Fig. 9. Results of the simultaneous inversion of (a) all the temperature depth profiles from the Thompson Belt, excluding those at Pipe; (b) all the profiles excluding those at Pipe and Soab; and (c) the 10 selected temperature profiles from northern Manitoba and Saskatchewan (Guillou-Frottier et al., 1998).
281
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Fig. 10. Location of weather stations in Manitoba and Saskatchewan that have been used for comparison with the GSTH for the Thompson area.
surface temperature variations, or it can be retrieved directly by simultaneous inversion. The GSTH can be approximated by a series of step heat flux changes at the surface, such that the temperature at depth z is given by Tt ðzÞ K X
"
z ¼ Tk erfc pffiffiffiffiffiffi 2 jtk k¼1
z erfc pffiffiffiffiffiffiffiffiffiffiffi 2 jtk1
#
ðA3Þ T0 ðtÞ ¼ Tj ;
tk1 VtVtk ; k ¼ 1; . . . ; K; t0 ¼ 0: ðA4Þ
Eqs. (A1) and (A3) are evaluated for each depth where temperature has been measured, forming a system of linear equations with K + 2 unknowns, which must be solved to obtain the geothermal steady state heat flux qref, the surface reference temperature Tref and a series of K surface temperature model parameters representing the GSTH at the site. The linear system of equations is ill-conditioned as in many other geophysical inversion problems. In order to regularize its solution, we use the singular value decomposition algorithm (Lanczos, 1961; Jackson, 1972). It consists of rotating the basis of the data and model space so that the linear system is represented by a diagonal matrix. The solution is stabilized because the small diagonal elements (singular values) are neglected. The resolving power and some practi-
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Fig. 11. Meteorological records from weather stations in Manitoba and Saskatchewan. No station operated in the Canadian Prairies before 1870. In order to better demonstrate the trends, we have calculated the average temperature over an 11 years moving window.
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