Fig. 53. Annual means of the difference between air and soil temperature at 50 cm depth for weather station 1 108487, British Columbia. (Drawn from Beltrami and Kellman, 2003.)

To assess the GST-SAT coupling on the decadal timescale Beltrami and Kellman (2003) have examined 30-year measurements of the air and soil temperatures for the 10 weather stations across Canada. Stations have represented open field locations. Soil temperatures were measured at depths of 5, 10, 20, 50, 100, 150, and 300 cm. Figure 53 illustrates annual means of the differences between air and soil temperature at 50 cm depth at the station 1108487 (British Columbia). As seen, the differences between soil and air temperature randomly oscillate within approximately 1 K range. This phenomenon was observed at all investigated in the work by Beltrami and Kellman (2003) stations. The linear fitting of the data has revealed insignificant increasing/decreasing trends varying from approximately — 9 X 10—2 to 6 X 10—3K/year. If revealed trends are persistent over the longer periods of time, they could certainly obscure the GST-SAT coupling at a single location, thus affecting an interpretation of the SAT trends based on the GST reconstruction data. However, as seen in Figure 53, the inter-annual variability of detected differences is quite high and the total length of the temperature records is insufficient for definite decisions about long-term persistence of detected trends. If departures from perfect GST-SAT tracking which have been calculated by Beltrami and Kellman (2003) are systematic, they are likely to complicate the comparison of the GST and SAT records spanning decades or centuries.

Fortunately, (1) because of spatial variability of the signs of observed trends they will probably compensate each other on the large-scale spatial averaging, and (2) in nature many factors that violate perfect GST-SAT coupling tend to compensate each other and/or vanish under large-scale averaging. The investigations by Smerdon et al. (2004, 2006) have revealed significant site-to-site variability in both the magnitude and the nature of the GST-SAT differences as well as their highly irregular distribution between years of observations. Due to the former property, all successful attempts to suppress the "noise" in the GST reconstructions were based on the spatial averaging and/or on the simultaneous inversion of numerous temperature logs (see Section 3.2, Chapter 3). An absence of the secular trends represents the common feature of all examined records. This hints that limits, within which the soil-air temperature differences will fluctuate, may be quite narrow. As shown by Jones and Mann (2004), despite the various possible sources for the GST-SAT decoupling, the apparent discrepancies appear to be diminished when attempts are made to account for spatial sampling biases and/or when estimates of the large-scale century-long SAT trends from the borehole data are performed using spatial regression.

The conclusions of the above-mentioned studies were based on over decade and 30-years long temperature monitoring results. Clearly, for the correct detection of the long scale GST-SAT coupling longer time series are indispensable. The waiting for the accumulation of the sufficiently longer data series monitored at the microclimatic stations is not a promising task. Thus, the understanding of the centennial or longer term GST-SAT coupling can be performed by either of two ways:

(1) Development of the powerful numerical models to simulate long scale active processes at the level of the air-ground interaction and in the subsurface and comparison between observed and modeled temperatures. Consistency between observed subsurface anomalies and anomalies simulated using meteorological forcing will serve as a good verification of the assumption of one-by-one long-term GST-SAT tracking.

(2) The GST reconstructions inferred from borehole data can be compared with the SAT measurements as well as with the proxy sources available in the same locations during periods of overlap. Again, the correspondence of the reconstructed and observed climate changes will help to validate the use of borehole temperature logs for paleoclimate reconstruction.

The possibility of the application of the first approach was discussed in the work of Bartlett et al. (2004), who have developed two-layered forward numerical model of snow-ground interactions using the EPO monitoring results. Their calculations have verified the applicability of the developed model for the broad spectrum of snow conditions and have confirmed its suitability for the simulation of the GST changes in different environments (see above). Smerdon et al. (2004, 2006) have estimated the multivariate empirical regressions for the GST-SAT differences and meteorological variables and detected that the amplitude of the GST-SAT decoupling during summer and/or winter can be used to describe quantitatively their tracking on the annual scale. On the basis of these conclusions Pollack et al. (2005) have worked out an effective method for modeling of observed GST-SAT differences using daily meteorological observations. Developed in this work numerical model applies an assumption of the pure 1-D conductive heat transfer with the time-dependent forcing on the surface boundary that equals the SAT. Spatially this model represents thin surficial layer of the variable thermal diffusivity superimposed on the homogeneous half-space. In the work by Pollack et al. (2005) meteorological influences are captured as temporal variations of the thermal diffusivity in the surficial zone by empirically determined values of winter snow cover insulation and the annual variations of latent heat of freezing/thawing, evapotranspiration, and seasonal changes in vegetation. The thermal diffusivity represents the ratio of the thermal conductivity to the volumetric heat capacity. The presence of the snow cover, e.g. is equivalent to a decrease of the thermal conductivity, while the latent heat influence increases the volumetric heat capacity. Both effects thus lead to a decrease in the thermal diffusivity of the shallow subsurface. Modeling results have shown that the attenuation of the temperature signal passed through the surficial layer depends on the cause of the thermal diffusivity decrease. Reduction of conductivity, increase of volumetric heat capacity, or a combination of both effects produces different signal attenuation. Validation/testing of this method has proved that the model suggested by the authors provides quite high coincidence between simulated and observed subsurface temperatures, while its parame-trization is much simpler than for the most complex land surface processes models that are traditionally used in such studies (Pollack et al., 2005). Because records of various meteorological variables (air temperature, rain, and snow cover) are available on much larger time and spatial scales than the present-day results of temperature monitoring, Pollack et al.'s model can be attested as an extremely useful tool for the future investigations of the effect of the long-term trends in the meteorological time series on the GST-SAT coupling. In their most recent work, Pollack and Smerdon (2006) have examined the influence of the subsurface layer with reduced thermal diffusivity on the downward propagation of the temperature signal with different periods. Preliminary calculations have revealed considerable attenuation of the short-term (daily to monthly) signals, while on the annual scale the ratio of the amplitude of the temperature wave that enters the half-space beneath the layer with reduced thermal diffusivity to that of the signal at the same depth in a homogeneous medium varied in the range of only 0.68-0.95. This ratio was even closer to 1 at the decadal (0.86-1.0) and centennial (0.95-1.0) scales. The major conclusion of this study is that the daily and seasonal GST-SAT decoupling has only little impact on the downward propagation of the temperature signals with decadal to centennial characteristic times relevant to the climate change studies. On the whole, this study thus has corroborated perfect long scale GST-SAT tracking.

Typical examples of the second-kind research of the long-term tracking of the surface climate changes by underground temperatures are presented in the works by Huang et al. (2000), Harris and Chapman (2001), Beltrami and Bourlon (2004), and Pollack and Smerdon (2004). All these studies have shown that notwithstanding the short-scale GST-SAT decoupling borehole T-z profiles averaged for the Northern Hemisphere have yielded results consistent with the meteorological SAT records and multiproxy reconstructions (for details see Section 3.3, Chapter 3). Obtained results indicate that on the large temporal/spatial scales ground and air temperatures track each other.

Merging of both approaches was performed in the work by Beltrami et al. (2005), whose authors have compared precise temperature logs measured in the cluster of four boreholes in northern Quebec (Canada) with the 70-year long SAT series and records of precipitation from the weather station located only 130km away from the borehole site. Earlier examination has shown that all temperature logs are generally similar and contain stable and consistent climatic signals (Beltrami et al., 1997). The SAT record exhibits warming trend of about 0.9 K during the last 70 years. The region under investigation is characterized by both significant snow cover in the winter (~3m in average) and the summer rainfall (~700mm). Thus, on the shorter scales GST changes could be perturbed by both influences. Because similar climatic conditions exist over the wide regions of central and eastern Canada, investigated boreholes may be regarded as a representative sample of this vast area. The authors have modeled subsurface temperature anomalies by the 1-D pure conductive equation similar to Eq. (17) (see Section 2.3.3) using SAT record as a forcing function. Comparison of measured and simulated T-z profiles was performed by the calculation of the pre-observational mean temperature (POM) that represents background long-term mean temperature prior to the beginning of the meteorological record (for details see Section 2.5 of this chapter). Comparison of the measured and calculated temperature-depth profiles have revealed their almost perfect coincidence. Estimated POM-value was 2.3 K below the SAT mean; thus, it indicated pronounced twentieth century warming. Obtained accurate fit of both measured and calculated temperature profiles using the SAT course as an upper boundary condition means that the SAT forcing is responsible for the major part of the subsurface temperature anomalies, and thus proves that in the investigated location ground has tracked the SAT variations for at least last 70 years. Perfect GST-SAT tracking was not obscured either by high amount of summer precipitation or by the thick snow cover. This and similar studies (see Bodri et al., 2001; Harris and Chapman, 2001) corroborate an assumption that GST follows SAT at least on several decades long temporal scales.

This interval can be further prolonged. Described in Section 2.4.4 of this chapter comparisons of the last millennium long GST histories inferred from measured temperature logs (210 logs all over Canada) and from T-z profiles simulated using the state-of-the-art General Circulation Model ECHO-g, which takes into account both the anthropogenic and natural external forcings (Beltrami et al., 2006; González-Rouco et al., 2006), proves that the ground follows the SAT trends even in the millennium-long timescales.

Summarizing results of existing studies one can conclude that the GST-SAT differences are apparent only on annual and shorter timescales. The long-term relationships between GST and SAT generally support the hypothesis of their one-by-one coupling and validate the assumption that GST histories can be regarded as a source of information about air temperature changes at times prior to the beginning of the instrumental record.

2.6.6 Other possible terrain effects

Except for the above-described meteorological influences and vegetation, subsurface temperature distribution may be affected by many local factors that the researchers generally refer to as "terrain". This term embraces the topography of given location, type of bedrock, hydrological conditions (water table, rivers, lakes, and swamps), moisture effects, etc. All these factors distort the curvature of the temperature-depth profile and thus can bias the reconstructed GST history. Various possible influences of terrain on the subsurface temperatures were summarized by Lewis and Wang (1992), who have called attention of the "borehole" community to the complex terrain-dependent relationships on the GST at any location and time period and emphasized the need of screening each borehole site and their data for possible terrain effects. These studies were continued in the subsequent years. Topography and the groundwater flow represent probably the most often occurring and/or important of the terrain effects. This section is devoted to the former factor, while the latter effect will be discussed in the next section.

An extraction of the past climate changes from the borehole temperature measurements contaminated by various terrain effects represents typical "signal-in-noise" problem. The extraction of a useful signal from the noisy measurements is a basic endeavor in all branches of geophysics. The principal sources of noise are of two types: (1) the measurement errors and (2) the representation errors, i.e. the simplification of the mathematical model and its departure from the conditions existing in the real geophysical systems. In the unique problem of the reconstruction of the boundary condition (climatic history) from the subsurface temperature profiles to what this book is devoted, the first kind of noise embraces of the usual errors in the measurement of temperatures, depths, and thermal parameters of the medium. Influence of these errors on the reconstructed GST history is discussed in Section 2.3. Effects of the topography and groundwater flow are typical kinds of the representational errors in the GST history reconstructions. These types of errors arise from the fact that all forward and/or inverse methods of the GST reconstruction are based on the assumption of the exclusive heat conduction (no advec-tion) in a one-dimensional, laterally homogeneous medium. Topography characterizes the land surface in terms of elevation, slope, and orientation. It should be described by at least 2-D models. Such modeling can be easily performed by the forward calculations, while present-day GST reconstruction techniques are developed for the 1-D situation and thus cannot capture effects of topography and/or groundwater flow in principle.

However, it should be emphasized that the use of the 1-D approach does not represent unnecessary simplification only. As described in Section 2.3.6 of this chapter, the development of the 2-D techniques will not necessarily improve the GST histories. The 2-D approach will significantly raise the number of the degrees of freedom of the inverse problem (underground structure, thermophysical parameters, and pattern of the steady-state temperature field), while we may only handle finite amount of measured data. The application of a 2-D approach means that we use more parameters to describe the unknowns than could be uniquely determined by the data. In practice the use of the 2-D approach implies severe limitation of a priori parameter range treated. In all inversion problems some optimal relation between resolution and variance should be established. In other words, one should answer the question, what is the effective number of degrees of freedom in the data and what parameters can be independently estimated with an acceptable variance. This was the reason that plausible attempts to minimize an effect of noise included development of different correction techniques or at least qualitative assessment of the reliability of the reconstructed GST histories and possible error sources.

The perturbations of a vertical heat flow field by topographical effects have played an important role in the interpretation of the geothermal data since the beginning of the terrestrial heat flow measurements. The works by Konigsberger and Thoma (1906) and by Lees (1910) represent the earliest 2-D quantitative analyses of the effect of differently dipping slopes based on forward calculations. Jeffreys (1938) have proposed the method to correct measured temperature gradients for local topography. Bullard (1938) has shown that correction is unnecessary in the case of shallow boreholes and relatively low elevations, while high alpine terrains can produce deep disturbances of the underground temperature field. Lachenbruch (1968), Bodmer et al. (1979), and Turcotte and Schubert (1982) have suggested their own techniques for the calculation of temperature patterns below typical topographical profiles. For a flat rectangle with a sinusoidal surface temperature variation calculated from sinusoidal topography these authors have shown that the amplitude of the perturbation decreases with depth z as exp(-2^z/X), where X is the wavelength of the surface altitude variation. Thus, in the case of topographical variation at the surface with an amplitude A = 100 m and X = 1 km the ground temperature would have been reduced to approximately 0.2 K magnitude at 1km depth. Blackwell et al. (1980) developed a correction method based on a 3-D approach that has taken into account not only elevation, but also other topographic variables: slope angle and orientation.

In addition to the steady-state topography effect Birch (1950) has estimated transient effects due to uplift and erosion. These effects, however, represent meaningful correction for terrestrial heat flow, but because they occur on much longer timescales, they are not so important for the GST history reconstruction. The work by Sclater et al. (1970) was among the first attempts to solve the problem numerically, while present-day estimations of the topographic effect are almost exclusively based on the 2- and/or 3-D numerical simulations of the subsurface temperature field (Safanda, 1994; Kohl and Rybach, 1996; Kohl, 1999).

To investigate terrain effects on the subsurface T-z profiles an experimental 150 m deep borehole was drilled in the campus of the Geophysical Institute in Prague-Sporilov, the Czech Republic (Safanda, 1994). The borehole is located in the slightly elevated terrain with the height difference of ~60m along 1200m long slope; thus, measured temperature logs clearly need the topographic correction. Topography effect on the subsurface temperature field was simulated by numerical solution of the 2-D steady-state equation of conductive heat transfer in the heterogeneous medium. The radioactive heat production in the medium was assumed to be zero. Thermal conductivity distribution used in the calculations has corresponded to the real in situ structure. It was anisotropic and represented a mean bedding inclination of 50° to the north and a mean conductivity of 3.2W/mK along the bedding and a conductivity of 2.2W/mK in perpendicular direction. The real shape of local topography was used as the surface boundary condition, when the GST was assumed to depend on the altitude and the slope of the surface. An atmospheric lapse rate12 of 5 K/km was applied at the upper surface, while constant heat flow of 60mW/m2 was assigned at the lower boundary at 5.5km depth. This value can be interpreted as undisturbed heat flow characteristic for the region under investigation.

Figure 54 illustrates an effect of topography on the Sporilov site. Isolines represent the values of the vertical heat flow normalized by the value of the basal heat flow at 5.5 km depth. As shown, even relatively flat topography can significantly distort subsurface heat flow field. Except for the parallel isolines characteristic for the horizontally layered medium, one can observe quite complex heat flow pattern. The southern (higher) edge is 0.5K warmer, while the northern (lower) edge is 0.5K cooler that the borehole site. The heat flow pattern is rather complicated with the concentration of isolines at the middle plateau, where the borehole is located. The largest gradients occur in the upper 100 m depth interval directly under the borehole site. The disturbances of less than 0.5% appear only below 500 m depth. This depth thus represents characteristic distance of the penetration of topography effect in the case of the relatively smooth relief and low elevation. Calculated normalized heat flow steadily increases with depth from 0.86 at 25 m to 0.93 at 150 m. These values are 7-14% lower than the basal undisturbed heat flow.

Figure 55 illustrates possible influence of different slope configurations and subsurface structure on the vertical heat flow profiles at the borehole site (Safanda, 1994). As previously, all models implied 2-D conduction in the complex layered medium. Curve 1a corresponds to the position below Sporilov borehole shown in Figure 54, and thus represents south-north inclined topography with subsurface layers inclined by 50° to north. Curve 1b illustrates the influence of the opposite subsurface inclination.

12The adiabatic lapse rate means the temperature decrease in the atmosphere as a function of elevation, assuming that air behaves adiabatically. The atmospheric lapse rate varies with temperature and pressure. In the air saturated with water vapor it is generally near 4.9K/km.

Fig. 54. Effect of topography simulated for the GFU-1 site. Isolines represent the pattern of the vertical heat flow normalized to the basal heat flow at 5.5 km depth (Data by Safanda, 1994). The southern/northern slopes are 0.5K warmer and/or cooler, respectively, compared with the flat terrain.

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