ANOMALOUS GROUND WARMING VERSUS SURFACE AIRWARMING IN THE CANADIAN PRAIRIE PROVINCES

JACEK A. MAJOROWICZNorthern Geothermal Consult., 105 Carlson Close, Edmonton, Alberta, Canada, T6R 2J8,

MAJOROWI@FREENET.EDMONTON.AB.CA.

WALTER R. SKINNERClimate Research Branch, Atmospheric Environment Service, Environment Canada, 4905 Dufferin

Street, Downsview, Ontario, Canada, M3H 5T4, WSKINNER@DOW.ON.DOE.CA.

Abstract. Modelling results of precision temperature logs made to depths of up to several hundredmeters in numerous wells in the Canadian Prairie provinces (mostly Alberta) show evidence of averagewarming at the ground surface (GST) of 2.1 K (standard deviation = 0.9 K) mostly in the second halfof this century. The GST warming signal for which higher frequency noise is cut off by the earth,which acts as a low-pass filter, correlates with the surface air warming (SAT) measured at screenlevel. A spatial comparison is made between the SAT warming and the GST warming for the last fourdecades in this region. A GIS (Geographic Information System) area cross tabulation was performedthrough the intersection of the classes of the ground and surface warming maps with a resultingcontingency coefficient C = 0.805. Identical grid samples extracted from the ground warming andsurface warming maps were related statistically with a resulting correlation coefficient of r = 0.75.Differences in the magnitudes of the warming exist due to the limited number of compatible datasets, errors in ground warming and air warming reconstructions, and land surface changes affectingthe energy balance and subsurface heat fluxes. The influence of these effects requires further study. Itis unlikely that all of the sites for which GST warming has been proven to correlate with air warmingwould have identical topography, vegetation, and hydrogeological disturbances for an area as largeas the one under study (about 720,000 km2). The warming effect in the study area, as preserved bythe ground, is mainly climate related.

1. Introduction

In the absence of significant water movement climate-induced variations in surfaceair temperature at the ground level propagate downwards following the laws ofconduction. A profile of temperature with depth has been shown to contain infor-mation of past surface air temperature variations (Birch, 1948; Lachenbruch andMarshall, 1986). The relationship, however, between the surface air temperature(SAT), (recorded at the screen level, 1.5 m above the ground) changes and groundsurface temperature (GST) changes below the surface is complex. The effects ofsnow, ice and surface water can be significant (Lewis and Wang, 1992; Outcalt etal., 1994; Taylor, 1995). A large part of the high frequency random distortion influ-encing surface temperature variation will be cut off by the earth acting as a low passfilter. In addition, long-term processes such as land clearing, vegetation changesand surface and subsurface moisture changes, some of which are anthropogenic,can affect subsurface temperatures.

Climatic Change 35: 485–500, 1997.c 1997 Kluwer Academic Publishers. Printed in the Netherlands.

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Evidence from several studies show that warming trends described by geother-mal methods are in good agreement with long-term trends computed from airtemperature time series. This has been shown for eastern Canada (Ontario, Que-bec) and western Canada (British Colombia, southern Yukon) by Wang et al.(1994) and also for mid-western U.S.A. (western Utah by Chisholm and Chapman(1992), Colorado Plateau of eastern Utah in U.S. by Harris and Chapman (1994)and Oklahoma by Deming and Borel (1995)). Also, long-term studies of groundtemperature variations versus air temperature variations have proven the value ofground temperatures as an indicator of long-term climate trends (Baker and Rushy,1993). The recorded ground signal is essentially a low-pass filtered version of thesurface air signal in which the higher frequency ‘noise’ is reduced or removed. Alarge scatter of the warming magnitudes is evident from individual wells spreadthroughout Ontario and Quebec in Canada (Beltrami et al. (1992) and Wang et al.(1992)).

A large number of ground temperature measurements exists for undisturbed con-ditions in observational hydrogeological and abandoned oil wells mostly in centralAlberta, Canada (Majorowicz, 1993). It has been recently expanded to the north andsouth. This provides a good opportunity to compare ground warming trends fromthe geothermal method with air warming trends of daily surface air temperatureover a large region with diverse landscape and terrain properties extending from theCanada–USA border to Northwestern Territories and from the Rocky Mountains inthe west to the Canadian Shield in the east. The availability of this unique groundtemperature data set allows us to determine how well air temperature history canbe obtained from ground temperature history. If GST warming from geothermaldata and SAT warming trend from climatological records give comparable resultsfor recent century, the geothermal method can be used to reconstruct past surfaceair temperatures for previous centuries for which climatological observations arescarce. In addition, the varying influence of terrain conditions can be addressedbecause of the wide variety of locations from which the data are derived.

2. Ground Warming from the Analysis of Well Temperatures

A change in temperature at the earth’s surface results in the deviation of thetemperature depth profile from the straight line gradient controlled by deep heatflux. Examples of such typical disturbances for northern and southern Alberta areshown in Figures 1a and 1b, respectively.

In the case of the Prairie Provinces in Canada, the upper 70 m +/- 30 m of thetemperature profile commonly show near-surface inversions (Majorowicz, 1993).The model of a linear increase of temperature with time at the ground surface (called‘ramp’ function model) starting some 50 years ago can explain typical curvature ofthe temperature depth profile as shown for the site north of Edmonton (Figure 2).The background (steady–state) thermal gradient G is usually established from the

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Figure 1. Two typical examples of the temperature depth profiles in (a) northern and (b) southernAlberta. The difference between transient departure of temperature – depth curve from the backgroundsteady-state thermal regime is shaded and is due to surface temperature change in the second half ofthis century.

Figure 2. Temperature depth profiles at 0, 10, 20, 30, 40 and 50 years after the onset of the groundwarming of 0.6 K per decade. The thermal conductivity used is 1.6 W/m K, diffusivity is 0:8�10�0:6 SI.Crosses mark measured temperatures at two wells at one site north of Edmonton (Sion).

deeper section of the profile and the thermal conductivity is uniform. An anomaly,dT (z), is calculated as a departure of the temperature from the steady state thermalregime:

dT (z) = T (z)� (To +Goz) (1)

where To and Go are the extrapolated surface T and gradient of a linear fit to T (z)data in the linear section of the borehole.

Assuming that the ground surface (GS) temperature (T ) varies with time t

according to a simple three-parameter power law (Lachenbruch and Marshall,1986):

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dT (0; t) = D(t=t�)n=2 (2)

for 0 < t < t� and n = 0, 1, 2, : : :

where the GS temperature increase is D at the end of time t = t�, the temperaturedisturbance with depth is described by the equation:

dT (z) = D2nF (1=2n+ 1)inerfc(z=(4Kt�)1=2) (3)

for the initial boundary condition dT (z; t) = 0 where K is diffusivity, F is thegamma function and inerfc is the nth integral of error function.

The best fit results were obtained using a numerical trial and error procedure fordifferent apriori models for n = 0, 1, 2, 4. Ideal fits to the data can be obtained asshown in Figure 3, though the solutions are not unique. The simple model of linearincrease of GST (‘ramp model’) used also by Lachenbruch and Marshall (1986),Wang et al. (1994), Majorowicz (1993) and Majorowicz and Judge (1994) is usedin this paper for comparison with the surface air warming trends for which also‘ramp function’ model was assumed (Figure 4). In this case the ‘ramp function’model is the most convenient one.

The above described method has proven to be ideal for the study of recentGST warming characterised by strong dT (z) signals observed in the subsurface.However, for more complicated reconstructions of older past GST histories, mod-ern inversion techniques using the singular value decomposition method can beused (Beltrami and Mareschal, 1992; Beltrami and Taylor, 1995). This method hasbeen tried for the six deepest temperature-depth profiles in Alberta (Beltrami andMajorowicz, 1995; Majorowicz and Safanda, 1996; unpublished results in prepa-ration) and, in general the obtained results agreed well with the method describedabove.

3. Ground Warming Pattern for the Prairies in Canada

The linear ‘ramp’ function fitting of the ground temperature warming history forthis century was applied to model the anomaly in the temperature-depth profilesfor 56 wells from the sites shown in Figure 5. Since most of the GST warmingevident in the Prairie Province wells has been in the last 4 decades, as found frommodelling and statistical analysis of the data, ground warming magnitudes for the1950–1990 period were used in contouring and then compared with the magnitudesof surface air temperature warming for the same period.

A contour map of well-estimated GST warming was generated using carefullyselected data to avoid sites affected by very recent clear cutting in the forested areasof northeastern Alberta. Excluded data are from wells at five sites located north ofFort McMurray and Cold Lake where clear cutting took place around 1980 +/- 5yrs. Each of these sites indicated unusually large warming exceeding 3.5 K. Theirregularly spaced data for the area with the largest well density were transformed

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Figure 3. Examples of the best fit of the curve based on the ‘ramp function’ increase of surfacetemperature with time to the temperature data (crosses) from the wells in (from left to right); anagriculture area in the boreal forest zone (54.57� N, 110.81� W), boreal forest area converted bypetroleum exploration (58.29� N, 116.22� W) and grassland area (51.57� N, 110.48� W). The fit isbetter than 0.05 K. Shaded a rea shows the area of disturbance due to the surface temperature change.

to a regular grid by the kriging method and then contoured using SPANS GIS. Asshown in Figure 5, GST warming varies from less than 1.0 K in the Foothills ofthe Rocky Mountains in southern Alberta to values exceeding 2.0 K in northernand northeastern Alberta and southwestern Saskatchewan. The GST warming islarger for the Boreal Forest ecozone than for the southern Alberta Prairie Grasslandecozone.

4. Climate Warming from Surface Air Temperature Data

A selection of 29 stations in and closely adjacent to the Alberta study area wereextracted from the Historical Canadian Climate Database (HCCD). Canadian cli-matologists have been involved with ongoing work on the construction of a his-torical database containing monthly, seasonal and annual mean maximum, meanminimum, and mean temperatures for 131 locations dating back to 1895 (Gullett etal., 1992; Skinner and Gullett, 1993). These locations, and their spatial distribution,

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Figure 4. Annual temperature departures for the HCCD station Peace River in Alberta. The bestlinear trend is shown by the dashed line (magnitude of warming = +2.0 K).

Figure 5. Map of the GST warming for 1950–1990 based on the modelling of the temperature profilesusing ‘ramp’ function of surface temperature change. Map also shows the distribution of the wellsites used in the analysis.

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have been identified as representative of the Canadian land mass for regional andnational scale climate variability and change studies.

The HCCD was constructed from the National Climate Data Archive (NCDA)of the Atmospheric Environment Service (AES), utilizing climate stations thatwere selected on the basis of spatial distribution, length of record, data continuity,homogeneity assessments and other factors. The HCCD was assembled to providea collection of historical data sets that have been tested for homogeneity (Gullett etal., 1991), and adjusted where necessary, to ensure regional representativeness. Thedata adjustments that were carried out had the effect of removing some of the locallyinduced noise, or discontinuities, in the series resulting from changes in observingprogramme, instrumentation, site conditions, and other non-climatic effects. Thesedata adjustments resulted in more representative series that are suitable for use inregional scale analyses.

Best-fit linear trends were calculated for individual HCCD station time series forthe 1950–1990 period. An example is shown in Figure 4 for the HCCD station PeaceRiver (see Figure 6 for the location). A contour map of mean annual SAT warmingwas then generated. The irregularly spaced station data within and immediatelyadjacent to the area delineated for well-estimated warming were transformed toa regular grid by the kriging method and then contoured using SPANS GIS. Asshown in Figure 6, the largest increase in mean annual SAT was about 2.0 K incentral Alberta, with peaks over the Peace River and Cold Lake areas. Smallerincreases of less than 1.5 K occurred in the extreme southern and northern parts ofthe province.

5. Comparison of Ground Warming and Surface Air Warming

Maps of GST warming and mean annual SAT warming were analyzed for rela-tionships/similarities in three ways: pattern differences, area cross tabulation, andspatial correlation.

Comparison of the warming maps (Figures 5 and 6) shows similarities in thepatterns of warming through the study area. In both maps the smallest warming isin southwestern Alberta in the Prairie Grassland ecozone and the greatest warm-ing is in the central part of the study area. The largest differences (greater than0.5 K) between GST warming interpreted from well temperature profiles and meanannual SAT warming are evident in the northern area of the Boreal Forest ecozone(Figure 7). In central and southern Alberta, differences are less than 0.5 K andessentially vanish in the Prairie Grassland ecozone.

A GIS cross tabulation was performed through the intersection of the map classes(both maps contoured with a 0.2 K interval) of GST warming and SAT warming.The cross tabulation provides a calculation of areas of intersection and also theChi square coefficients to summarize statistical relationships between the twomaps (Sachs, 1984). The contingency coefficient (C) is a statistic of the degree of

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Figure 6. Map of annual near-surface air temperature warming for 1950–1990 based on best-fit lineartrend analysis applied to HCCD station time series. Location of the SAT stations used in the analysisare shown by black circles. Locations of the cities of Cold Lake and Peace River coinciding withlocations of the SAT stations there are shown by silver dots.

Figure 7. Map of differences between ground warming and air warming shown in previous two maps.

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association, or consistency, between two characteristics of manifold tables (Sachs,1984), and is derived from the Chi square value. A value C = 0.805 indicates a closeassociation between the class structures of the two maps. Identical grid samples(points 100 km apart) were extracted from the ground warming and air warmingmaps (yielding 701 points in the study area) and related statistically (PearsonProduct Moment Correlation). The resulting correlation coefficient r = 0:747 isstatistically significant at a confidence level of 0.05.

6. Longitudinal and Latitudinal Variations in Ground Surface Warming

The prairie data on GST warming (Figure 5) show weak dependence on the latitude(correlation coefficient less than r = 0:5) as shown in Figure 8. However, a clearerlatitudinal variational is evident from comparison of the magnitude of GST warmingfrom Alaska (Lachenbruch and Marschall, 1986) and the Mackenzie Delta withthe magnitude of ground warming from the Prairie Provinces south of 63� N; thelarger GST warming is in the north (Figure 9). Temperature measurements in thepermafrost of northeastern Alaska showed anomalous curvature in the upper 100 mrevealing that near-surface permafrost has warmed 2.0–4.0 K during the last 50–100 years. Much less GST warming (1.0–2.0 K) was observed further southeast, inOntario and Quebec in Canada (Beltrami et al., 1992; Wang et al., 1992) and evensmaller GST warming in Utah (0.3 K in this century according to Chisholm andChapman (1992)). This suggests that the magnitude of the GST warming decreasesfrom north to south as first suggested by Pollack and Chapman (1993). Preliminarydata from South Dakota and Texas (Gosnold, 1994) showed GST warming of 2.0 Kand 0.5 K, respectively, again suggesting that the magnitude of the ground warmingdecreases from north to south.

A north-south gradient of GST warming is accompanied by an east-west gradientin Canada, as shown in Figure 10. Our data show later onset of GST warming thanin eastern Canada. Lewis et al. (1994) reported that geothermal data reveal entirelydifferent patterns of GST warming in eastern (Ontario, Quebec) and western Canada(British Columbia and southern Yukon). In eastern Canada the temperature increaseat the ground surface began over a century ago (average 110 years ago) and had beenpreceded by a relatively cold period in the previous century. Temperature profiledepartures from steady state in western Canada are of lesser magnitude (0.8 K)than in the east and began later in time (mostly 20th century). The data from theCanadian Prairie Provinces fit well between these patterns, between eastern andwestern Canada with a GST warming magnitude of about 2.0 K (Figure 10) andlate onset of significant warming. Statistical analysis of the onset time of GSTwarming (best fitted by a ramp ground surface function) gives an average of 4decades (S.D. = 14 yrs) for our prairie data and 5 decades (S.D. = 21 yrs) for theAlaska data of Lachenbruch and Marshall (1986) showing that the warming eventpertains to this century. In eastern Canada onset of ground warming is earlier;

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Figure 8. Ground warming magnitude (K) from the Prairie Provinces for this century from forwardmodelling of temperature-depth logs versus latitude in �N.

however, in some parts recent cooling has been taking place (Lewis and Wang,1992; Allard et al., 1994).

7. Discussion

A statistically significant spatial correlation coefficient between GST warmingpatterns and SAT warming patterns for the same time intervals has been found forthe area of the western Prairie Provinces of Canada. This indicates that the GSTwarming history is primarily a reflection of the SAT warming history. The area ofanalysis is a large region, extending over 1000 km from north to south and includes

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Figure 9. Histograms of magnitude of recent ground warming interpreted from temperature versusdepth logs for the Alaska and Mackenzie delta area (Lachenbruch and Marshall, 1986; Taylor, 1995,personal comm.) and in the Prairie Provinces.

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Figure 10. Typical examples of borehole temperatures from eastern (Ontario), central (PrairieProvinces) and western (B.C.) Canada. The deep reversal caused by climate warming that startedover a century ago is present only in eastern Canada (modified from Lewis, Wang and Majorowicz,1994).

major portions of two separate ecozones. Comparatively, we have used a large database which has made possible contouring and spatial correlations not attemptedpreviously on such a scale.

The differences between the magnitudes of warming based on near-surfaceground temperature reconstruction from well temperature profiles and historical airtemperature warming are most evident over northern Alberta in the Boreal Forestecozone. A characteristic difference is 0.6+/-0.2 K. The difference in southernAlberta is much less than the error of the methods (0.3 K) and therefore GST andSAT warming can be considered to be in very good agreement. The comparisonis based on the data from wells and climate stations with different locations anddistributions. Differences between these data can therefore be expected. Climatestations have been located, in many cases, in the vicinity of airports (large openspaces) or major population centres, while the location of the wells in whichtemperature logs were taken are more random with a majority of the sites locatedin remote areas within unspoiled landscapes. Therefore, reconstruction of the pasthistory of the GST from temperature data measured in wells gives an independentconfirmation of the SAT warming, seen here and elsewhere (Skinner and Gullet,1993), in the latter part of this century in the western Prairie Provinces. It alsosuggests that the city-warming effect (as an artifact in long-time series of SAT) isnot overwhelmingly important.

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A systematic difference between GST warming from the geothermal methodand SAT warming from observations for 1950–1990 is observed over the northernAlberta area and also in the extreme southeastern portion of the study area. Onepossible contributing factor could be long-term changes in snow cover and theassociated effect upon the ground temperature history. Although the snow bothinsulates the ground in the cold period and reduces the warming in the spring,which are competing effects, the widely recognized systematic tendency for themean ground surface temperature to exceed the mean air temperature by severaldegrees clearly in cold regions indicates that the winter-insulating effect is thedominant one. An increase in snow cover with time in the north would explainlarger GST-SAT warming difference. Latent heat effects associated with near-surface freezing can significantly complicate the relationship between air plusground temperatures, and give rise to the so called ‘zero curtain’ as observed atsome sites farther north in the Mackenzie Valley (Taylor, 1995). However, therehas been a general trend towards decreasing total precipitation since 1950 overthe entire study area (Mekis and Hogg, 1996), with a significant decrease in snowcover reported in the Western Canadian Basin after 1970 (Brown et al., 1995)which fails to explain discrepancies shown in Figure 7. The recent decrease insnow cover due to warmer climate can be also seen for two locations (northernAlberta and southern Alberta) shown in Figure 11. The observed annual snowcover decrease over the past 30 years (Brown et al., 1995) gives approximately 40days extra without insulation and greater heat absorption at the ground surface. Itappears clear that at this time little explanation can be offered from the analysis ofprecipitation trends for the larger deviations shown in Figure 7.

One possible cause for the observed differences between GST warming andSAT warming in the north could be the terrain effects caused by widespread landclearing, forest fires and agriculture in the northern Boreal Forest ecozone startingapproximatelly in the mid-century. Such changes have altered the environmentof the sites used to observe ground temperature changes. The effects of temporalterrain changes like the clearing of forests for agriculture in North America occurredin many areas at the turn of the century, just prior to the hypothesized warmingdue to increased carbon dioxide and the related ‘greenhouse effect’. In Alberta,the land was also cleared in many areas in the former boreal region. This processis continuing. It is extremely difficult to estimate the increase of GST due to suchprocesses. However, a GST increase is expected due to an increase in solar radiationabsorbed by the earth’s surface after clear cutting of the forest or cultivation of theland (Angstrom, 1916; Lewis and Wang, 1992). It is unlikely, however, that such aneffect could explain entirely the observed regional ground warming. The wells inour study are located across hundreds of kilometers of continental terrain and havecommon perturbations in their temperature profiles. The high spatial correlation ofGST warming and SAT warming patterns makes it unlikely that all of the boreholeswould have identical terrain related disturbances. However, the observed differencein the north showing that ground warming is larger by at least 20% than air surface

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Figure 11. Variations in the snow cover depth based on end of the month data for the northern Albertasite of Peace River and the southern Alberta site of Lethbridge.

warming makes the changes to the land a likely explanation of this difference.The changes to the surface in this century could have caused sudden changesin surface temperature, which superimposed on the climate warming signal, couldhave caused larger ground warming than air warming in this area. The southern areaof Alberta (grassland ecozone) has not been altered significantly in this century,and as expected, the GST and SAT warming are similar there. As suggested by

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the above study, the method of precise borehole temperature analysis is usefulin delineating climatic trends, but it may offer quantitative warming data only inrelatively unaltered terrain.

Acknowledgements

We are grateful to Metro Magas and Dal Withers from Environment Alberta fortheir great help in accessing observational wells. We thank anonymous re-reviewersfor their very helpful comments.

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(Received 1 December 1995; in revised form 17 September 1996)

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