1500 1600 1700 1800 1900 2000 TIME, year A.D.

Fig. 39. Comparison of the annually resolved five-century multiproxy reconstructions for the Northern Hemisphere by Mann et al. (1998), Esper et al. (2002), and Huang (2004). Pattern by Huang (2004) integrates also borehole data. Temperatures are shown as anomalies with respect to the 1961-1980 mean.

1500 1600 1700 1800 1900 2000 TIME, year A.D.

Fig. 39. Comparison of the annually resolved five-century multiproxy reconstructions for the Northern Hemisphere by Mann et al. (1998), Esper et al. (2002), and Huang (2004). Pattern by Huang (2004) integrates also borehole data. Temperatures are shown as anomalies with respect to the 1961-1980 mean.

multiproxy time series could at least in part arise from the significant role that tree-ring information plays in the former reconstructions (Huang et al., 2000). As known, centennial trends are expressed very weakly in tree-ring series (see Figure 9 and Section 1.2.3, Chapter 1). For that very reason Esper et al. (2002) applied a powerful method for the regional calibration of tree-rings that keeps long-term trends better than the method used by Mann et al. (1998) and thus obtained larger variability in the past temperature time series. The early seventeenth century SAT anomaly estimates of these authors diverge by about 0.7 K from those by Mann et al. (1998). Later re-calibration of the data has reduced these differences to only 0.35 K (Briffa and Osborn, 2002). Even bearing in mind turbid complex of reconstruction uncertainty, the curve by Esper et al. (2002) contains evidence for more pronounced climate oscillations in the past millennium than has been previously accepted by the multiproxy reconstructions.

Because the divergence in the amplitude of the temperature variation is an extremely important difference, detection of a fair scatter among various published estimates was followed by lengthy discussions. Their effect can be found in the works by Mann and Hughes (2002), Cook et al. (2004), and Esper et al. (2005). The researchers have exchanged their views at numerous conferences (e.g. Session PP19: Climate Change in the Recent

Past: Integrating Meteorological, Proxy, Borehole, and Modeled Climate Reconstructions; AGU Fall Meeting, December 2005, San Francisco, CA;, as well as on the different web sites of professional climatologists, e.g. the Real Climate (, and/or more descriptive the ClimateAudit (CA) and the European Tribune: The argument on the subject "Borehole versus proxies" has represented only a part of the above "big discussion" on the reliability of different paleoclimate reconstructions. Mann et al. (2003) have optimized the Huang et al.'s (2000) data and partly corrected them later (Jones and Mann, 2004). However, Pollack and Smerdon (2004) did not accept their optimization (for more details see Section 3.2, Chapter 3). Guiot et al. (2005) on the basis of 222 borehole temperature profiles inferred averaged GST history for Europe that indicated ~0.5K higher temperature rise in comparison with their reconstruction based on multiproxy sources. The average of the multiproxy temperature anomalies for the 1500-1700 A.D. segment is -0.1 ± 0.5 K. The average borehole temperature for this period equals to -0.45K; thus, it is still within the lower boundary of the confidence interval. The amount of warming calculated for Europe is somewhat smaller than Huang et al.'s (2000) value for the Northern Hemisphere. In spite of the higher coincidence obtained after 1750 A.D., Guiot et al.'s (2005) statement was that "borehole temperature reconstruction is not perfect".

The main benefit of this trenchant discussion was probably that it has impelled the researchers to re-assess the skill of different methods for the past climate reconstruction. The most advantageous testing strategies for the ability of the "borehole" method to draw out past GST changes from T-z profiles were applied in the recent works by Beltrami et al. (2006) and González-Rouco et al. (2006), whose authors used simulated subsurface T-z profiles forced by the GCM as a substitute of the real climate and applied inversion technique to reconstruct GST histories from calculated profiles.

Modern 1000-years long ECHO-g ocean-atmosphere GCM models were used as a surface forcing to the forward models of heat conduction. These models have included the 1000-years long external forcings (solar irradiance, radiative effects, and volcanic aerosols) as well as the anthropogenic influence (greenhouse gas concentration increase) and were complex enough to provide insight into intrinsic properties/possibilities of the inversion technique and to test the correctness of the GST reconstruction. Control and two trial simulations with the same external forcing and different initial conditions were considered. The 600 m deep T-z profiles were gained from the 898 land terrestrial grid boxes and reflected averaged Northern Hemisphere land conditions. To investigate influence of the spatial distribution and surface coupling of borehole sites similar profile was calculated also on the base of the 177 grid boxes reflecting the real borehole distribution. The SVD inversion was applied to these T-z profiles to infer GST history. Recovered from simulated T-z profiles GST histories were compared with the climate model variations used as a surface forcing. Results have shown that in spite of different disturbing factors (e.g. dating of the temperature logs and non-equal depth) and irregular (somewhere sparse) geographical distribution, GST histories return adequately the filtered version of the real climate change.

The numerical experiment described above has proved that the SVD inversion technique is powerful enough to reproduce the main features of the multi-century climatic trends. In the case of satisfactory quality of the borehole temperature logs and the proper treatment of possible uncertainties, borehole method itself could detect major climatic excursions of the past. It is extremely important that none of the reconstructions based on different models show any evidence of an overestimation of the magnitude of the past climatic change, while it was this difference that has inspiredthe discussion as well as the additional testing of the "borehole" method mentioned above.

For the recent two-three decades boreholes distributed over the entire continents were recognized as a great tantamount source for new information in numerous "white spots" of the global map of the paleoclimatic change. Researchers from many countries mastered routine application of the geothermal method and a sizeable number of results have been published. It appears that the boreholes can provide information previously unavailable in character and spatial distribution. Further investigations, however, have added a grain of salt to initial enthusiasm for the "geothermal" climate reconstruction. No doubt, in many cases different inversion methods gave equally good coherent results. However, in a number of situations inversion techniques gave poor results. These failures were attributed to an impact of numerous non-climatic influences on subsurface temperatures that can disturb the ideal heat conduction regime described by Eq. (4). That time potential environmental disturbances to the subsurface climatic archive were recognized as well as the necessity of the careful analysis of the potential perturbations for each individual temperature log. An influence of terrain on the GST has been discussed in detail by Lewis and Wang (1992), and examples of the effects on ground temperatures of spatial distribution of differing terrains, temporal changes in terrain, and subsurface fluid flow have been presented. Since then numerous investigations have been carried out concerning the influence of different local effects on the subsurface temperatures and the ways to recognize these anomalies and reveal reliable GST histories from disturbed temperature logs. The next sections contain the summary of these efforts.

2.4.5 Interpreting ensembles of borehole temperature logs

The above sections were devoted to the techniques of the GST inversion from the temperature-depth profiles measured in individual boreholes. As in all branches of geophysics, an extraction of climatic signal from borehole temperature logs is complicated by the presence of noise in the data. The principal sources of noise are of three types: (1) the measurement errors, (2) the representation errors, i.e. the simplification of the mathematical model and its departure from the conditions existing in the real geophysical systems, and (3) terrain effects causing both secular and provisional changes on the ground-air boundary. Since in most of the field situations detailed information that permits sure correction of measured profiles is not available, the development and application of various techniques for suppression of noise and enhancement of the signal have received special importance. Numerous studies in other geophysical branches have shown that the analysis of multiple observations can be more preferable to suppress the effect of the random noise in the data than the use of single measurements. The basic idea of this approach is that the signal can be enhanced and/or noise can be attenuated by the interpretation of the available data together as an ensemble. This approach is widely employed as simultaneous inversion using weighted staking of seismic reflection data (Fatti et al., 1994; Larsen et al., 1999; Margrave et al., 2001; Ryberg et al., 2005). Results have shown that in the presence of random noise the combination of the data volumes provides more accurate results than the techniques using individual data. Joint processing effectively suppresses the noise without unnecessary suppression of the signal. The unknown parameters are better constrained and, in spite of the noise present, are more reliably estimated.

The advantage of such approach in borehole climatology can be illustrated as follows. Let us assume that the climate in some wide area is characterized by a secular change in temperature that is archived in the underground. It is this signal that should be recovered by the GST reconstruction procedure. Generally, borehole site represents a variety of environmental conditions. Boreholes are drilled into different rock types, on the heights or valleys, embracing a variety of hydrologic regime and surface conditions from bare soil to the dense vegetation. Thus, temperature-depth profiles from different boreholes may contain local non-climatic perturbations to the long-term transient climate signal. All boreholes would unlikely have the same topography and vegetation cover, subsurface structure, and hydrologic regime. If different kinds of noise appear randomly in the data ensemble, an analysis of combined T-z profiles would likely result in the common regional signal enhancement and suppression of noise. A signal common to all the boreholes can safely be attributed to the regional climate change. Combined analysis of borehole data can be performed using two different strategies: (1) simultaneous inversion of the temperature logs from several boreholes, and/or (2) averaging of the individual GST histories. Both procedures differ conceptually. Simple averaging of the GST histories inverted from the single-hole logs can be accomplished without limitations, while the simultaneous inversion of several T-z profiles can be performed exclusively under assumption of the presence of common transient climate signal in all jointly analyzed temperature logs.

Beltrami and Mareschal (1993) have extended conventional SVD technique and suggested the multi-inversion approach. The method was verified using 21 temperature logs sampled across the whole eastern and central Canada and yielded generalized GST history for this region. Later Clauser and Mareschal (1995) have performed the testing of this method by the simultaneous inversion of borehole temperature logs from Central Europe. Both studies have supported an increase in the resolution under multi-inversion approach, when common climatic signal can be fully unraveled. Beltrami et al. (1997) has presented detailed description of the simultaneous inversion of borehole temperature data for reconstruction of the GST history in the SVD context. Pollack et al. (1996) have extended the simultaneous inversion approach for the FSI technique. Their method was used for the joint processing of the borehole temperature logs in numerous studies. Thus, Majorowicz and Safanda (2001) have constructed composite surface temperature history from simultaneous inversion of T-z profiles from 43 boreholes located at the western Canadian Basin.

The field situations favorable for the simultaneous inversion strategy include: (1) repeated temperature logs from a single borehole, (2) a suite of boreholes from a single site, and (3) a suite of boreholes from a wider region with similar climatologic and environmental changes. The mathematical procedure is especially obvious in the case of the SVD inversion. As previously (see Section 2.3.4), an unknown GST history V0(t) is approximated by N intervals of constant temperature (Eq. (18)). In the case of a single borehole the matrix Ak (Eq. (20)) contains M rows and N columns, where M is the number of temperature measurements in the single-hole. For L holes with Mi measurements in each of them, the matrix A will consist of Mi rows and N columns, containing series similar to Eq. (13) calculated for all given depths in each given borehole. When parameters of initial (equilibrium) temperature field for each borehole U0 and Qm are estimated simultaneously with the GST history V0(t), the vector Vi will consist of (N + 2L) unknowns, and the matrix A will contain two additions (see Section 2.3.4). The first M1 elements of the (N + 1) column will be equal to 1 and all other to 0, the following M2 elements in (N + 2) column are 1 and all other elements are 0, and so on. Similar addition can be constructed for the thermal resistances4 to the depths zi in all given boreholes. Further inversion procedure is the same as for the single-hole SVD case.

The efficiency of a simultaneous inversion in the noise suppression is clear. Of course, the GST histories obtained by merging data sets that simultaneously combine a number of T-z profiles and conductivity data with different terrain/microclimate effects and noise level, have typically larger data misfits than the individual holes. In the cases when obtained data misfits are too large, it can mean that a common climatic signal may not present in the data. On the other hand, testing of the simultaneous inversion technique conducted in the work by Beltrami et al. (1997) using SVD approach for both synthetic noisy and noise-free data as well as for the field examples containing common climatic signal have shown that staking temperature perturbations from L boreholes can increase the stability of the solution and resolution of the inversion and improve the signal to noise ratio by a factor VZ. Calculations by Beltrami et al. (1997) revealed the dependence of the resolving power from the noise level. Generally, composite surface temperature history obtained by simultaneous inversion was comparable with the GST curve obtained by inversion of the single log with the lowest noise. A definite problem for the simultaneous inversion represents the fact that not all available borehole temperature logs were measured using the same sampling interval. In this case the composite GST history was not close to anyone of the individual surface temperature histories and was weighted to the temperature logs with the finer sampling. Thus, temperature logs with similar sampling should be used for simultaneous inversion to avoid possible bias. Temperature logs with large sampling intervals can be interpolated for finer distances. On the other hand, the simultaneous use of the temperature logs of different lengths does not represent serious restriction. Such temperature-depth profiles contain the surface climate history of different time spans. Numerical experiments by Beltrami et al. (1997) have shown that because shallow boreholes does not archive an information on remote GST changes, merging of the shallow- and deep-hole data for simultaneous inversion does not improve the course of the past GST history obtained from the deep holes. On the other hand, this procedure can specify better the recent GST history and/or to improve the estimates of the heat flow obtained from the shallow-borehole data.

An averaging of the GST histories reconstructed from the individual borehole temperature logs represents another possible kind of the ensemble interpretation and suppression of the random noise in the geothermal data. As mentioned above, the principal difference between simultaneous inversion and averaging of the individual GST histories is that the averaging can be performed without restrictions, whereas the former procedure provides good results only for boreholes that contain common climatic signal. On the other hand, the simultaneous inversion takes into account the data uncertainties

4Thermal resistance is the ability of a material to resist the flow of heat. It represents the reciprocal of thermal conductivity and is measured in km/W.

and the borehole sampling and depth. These effects cannot be easily captured in the simple averaging of the single GST histories. Comparing both techniques, Pollack et al. (1996) have concluded that for the three field situations enumerated above they yield closely identical results. Diverging GST histories were obtained when merging a suite of boreholes from the vast areas that have experienced different surface temperature variations over their different parts. The simultaneous inversion estimate in this case appears to give biased GST history. If both procedures, the GST averaging and simultaneous inversion, exhibit different results it generally notifies that an assumption of a common transient climatic signal in processed boreholes may be invalid.

Numerous examples of the application of both procedures to the worldwide database of borehole temperature logs are presented in Section 3.2 (Chapter 3). Recently Chouinard and Mareschal (2006) have compared again different approaches of the GST inversion from ensembles of borehole T-z profiles. They used temperature logs measured in boreholes in two Canadian regions: northwestern Ontario and northern Manitoba/Saskatchewan. Using these data the authors have performed three experiments: (1) simultaneous inversion of all available profiles, (2) screening of the profiles for the possible non-climatic disturbances and simultaneous inversion of the undisturbed profiles, and (3) averaging of the individual inversions. Results of experiments have shown that at least for above two regions the averaging of the individual inversions gives less resolved GST histories than the simultaneous inversion of the same temperature-depth profiles. For example, well resolved by the simultaneous inversion the Little Ice Age appears much weaker in the GST curve calculated by averaging the individual GST reconstructions. Similarly less visible is the fingerprint of the recent warming. On the other hand, the difference between results of the simultaneous inversion of all temperature logs and only selected profiles, which were assumed to be free of the non-climatic influences, was far not so significant than the authors had anticipated. Generally, the most informative results with maximum resolution were obtained from the simultaneous inversion of a few noise-free profiles.

2.5 Ground-Air Temperature Coupling: Pre-Observational Mean Temperature (POM)

Borehole temperature measurements contain direct information on the GST history. The GSTs represent important climatic variable; thus, in principle they need no calibration with the independent data. On the other hand, it is the air column temperatures, including the most important surface air temperatures (SAT) taken at screen height (1.5 m above the ground surface), that are typically of interest in discussions of climate variability. The SAT responds to the convective heat transfer in an atmospheric boundary layer, while the GST represents a continuously integrated ground temperature variations in the vicinity of the borehole that occur mainly by conduction process. Thus, both massifs of the data are complementary, but independent data sets that provide measure of the surface temperature and its change through the time in different frequency domains. Once we are sure that we have reliable methods to infer the GST history from borehole logs, further task should be the relation of the GST to the SAT changes. This ensures that the climate change will be tackled with more confidence.

The problem of coupling of the GST and SAT has arisen from the very beginning of the borehole climatology. The fact of the systematic difference between the GST and SAT, namely that the soil may be warmer than the air has been revealed already in the early work by Chang (1958), who demonstrated that a greater part of the solar radiation is absorbed by the Earth's surface rather than by the atmosphere. The micrometeorological processes near the Earth's surface causing higher "thermal capacity" of the ground were investigated in the work by Deacon (1969). Figure 14 (Chapter 1) illustrates the air and ground temperature oscillations measured during 12-year temperature monitoring at several shallow depths in the experimental borehole Prague-Sporilov (the Czech Republic) (Cermak et al., 2000). The annual wave is seen as the most important variation. In addition to an annual cycle, ground temperature exhibit a daily cycle and variations associated with changes in weather. These variations are confined to the near-surface zone. The filtering of the high-frequency components and the lag of the ground response with respect to air temperature variations is apparent in the temperature record presented in Figure 15 (Chapter 1). The daily temperature wave and the weather cycles are practically not observable below about 0.5 m and approximately 1 m depth, respectively.

Figure 40 shows monthly averaged GST change in Eilat area (Israel). Ground temperatures were measured at 2 cm, 20 cm, and 1 m depth during the years 1957-1963 (data source: Temperatures were recorded at 8, 14, and 20h. This example represents ideal case of the air-ground temperature coupling in warm dry environment without snow cover or freezing. As shown, the coherency of the general course of the near-surface and deeper ground temperatures is practically perfect. On the other hand, deeper ground temperature is higher than the near-surface temperature in winter and is lower in summer. This creates definite attenuation of the total annual range of variation of the GST in comparison with air temperature variations. Due to the fact that the GST is higher than the SAT in winter and is lower in summer, the ground represents potential storage capacity and a source for the heating/cooling. Heat flows out and/or into the ground in the cold and warm seasons, respectively. This phenomenon is referred as the "heat-valve" effect (Gilpin and Wong, 1976). Factors connected to the movements and/or diffusion of air and/or moisture masses (wind, evaporation/transpiration, vertical soaking of soil moisture, and precipitation) tend to equalize air and soil temperatures (Arya, 1988).

One of the first empirical long-term relationships between annual mean GST and SAT has been presented by Kukkonen (1987) for the territory of Finland. It is based on the combination of air and ground temperatures measured on the meteorological stations all over the country and borehole temperatures extrapolated to the surface

where TG and TA (°C) are annual mean ground and air temperatures, respectively. As seen on the annual scale ground is warmer than the air. On the other hand, the ground temperature fluctuations are approximately 30% attenuated in respect to the air temperature. The fact that generally the mean annual SAT is lower than the corresponding GST was corroborated by numerous later measurements. Comparison of soil and air temperatures by Chisholm and Chapman (1992) for the Salt Lake City Airport meteorological

Fig. 40. Monthly averaged ground temperatures measured in Eilat area, Israel. Data are averaged through 1957-1963 period. Ground temperatures were measured at 8, 14, and 20h at the depths 2, 20, and 100 cm, respectively. (Data source: id23_m.htm.)

Fig. 40. Monthly averaged ground temperatures measured in Eilat area, Israel. Data are averaged through 1957-1963 period. Ground temperatures were measured at 8, 14, and 20h at the depths 2, 20, and 100 cm, respectively. (Data source: id23_m.htm.)

station have shown that the ground is generally warmer than the air by 1-2K. Similar results was obtained in the work by Schmidt et al. (2001) for Fargo (North Dakota). For the nine-year long record the mean annual average ground temperature was ~2 K higher than the air temperature. The same difference was obtained for 1997-1998 years GST-SAT monitoring at the station Pomquet (Nova Scotia). In most of the mentioned locations this difference occurs mainly due to the insulating effect of the snow cover, although such factors as evaporation also play a role. As demonstrated by the regional investigations in Canada, in the regions with insignificant snow cover (e.g. coastal areas) the mean annual GST-SAT difference equals to only 1K, while in the areas with deep and long duration snow cover (e.g. described below Kapuskasing site) it may reach as much as 5 K.

A comparison of mean monthly air and soil temperatures recorded during 1984-1989 period at Salt Lake City Airport has shown that the soil temperatures at all recorded depth (10, 20, 51, and 102 cm) almost perfectly repeat the annual air temperature variations, however, with considerable offset (Chisholm and Chapman, 1992). Repeated model studies have revealed that on the long scale mean annual GST corresponds linearly to the mean annual surface temperature (Baker and Ruschy, 1993; Putnam and Chapman, 1996; Gosnold et al., 1997; Harris and Gosnold, 1999; Majorowicz and Safanda, 2005). This statement can be confirmed by the Granger causality test (see Section 3.4.5, Chapter 3). For this analysis we have used reconstructions of the annual global surface temperature over the last five centuries (1500-1980), based on the mul-tivariate calibration of the high-resolution proxy climate indicators (tree-rings, ice cores, corals, and historical documents) combined with the long-term instrumental records by Mann et al. (1998) (Figure 39 of this chapter) and similarly long GST reconstruction based exclusively on the terrestrial borehole data (Mann et al., 2003; Figure 98, Chapter 3). Application of the Granger causality test to these records have shown that on the long scale the SAT series is the Granger cause of the examined GST, and has thus supported strong long-scale GST-SAT coupling (for details see Section 3.4.5, Chapter 3). All above-mentioned investigations have given the confidence that it seems reasonable to consider borehole temperatures as filtered versions of the surface air temperature (SAT).

The complementary nature of the GST and SAT has inspired the idea of coupling of the measured temperature logs and the SAT time series for the joint processing. To estimate the magnitude of recent climate change, specifically the amount of the recent global warming, paleoclimate reconstruction from the temperature-depth records can be suitably completed with a long-term meteorological SAT series monitored at the weather stations. This idea was introduced by Harris and Chapman (1995, 1997) and provided a useful tool for the assessment of the so-called pre-observational mean temperature (POM) that represents the temperature conditions existing before the routine instrumental observations actually started some 100-250 years ago, i.e. the value against which the twentieth century climate warming is usually referenced. Coupling the inverted borehole temperature logs with the SAT series provides a more realistic benchmark than the models based on the inverted borehole data themselves.

For the 1-D case of the purely conductive heat transfer POM can be obtained by comparing the temperature log measured in a borehole with synthetic temperature-depth profile, corresponding to the solution of the 1-D heat conduction equation in a horizontally layered half-space that describes purely conductive heat transport with no heat sources taken into account (Eq. (4), Section 2.2). The surface boundary conditions corresponding to the observed SAT series are where TSAr is the SAT temperature time series, and t0 the time when the SAT record started. It is assumed that the interval (0, t0) is long enough. Thus, at constant temperature before t0 and for an absence of other effects the initial temperature-depth profile, T-z, at time t0 represents a steady-state temperature field corresponding to the constant heat flow from depth. The approximate duration of t0 can be estimated from the expression for the characteristic time of the thermal relaxation t0~L2/4k, where L is the characteristic length and k the thermal diffusivity. When k equals to 10~6m2/s for a 100-200 m deep borehole t0 achieves approximately 100-300 years. As in the previous processing examples, measured temperatures can be converted into reduced temperatures by removing the quasi-steady state part from the measured temperature log. The reduced temperatures contain only temperature "disturbances", ideally in absence of substantial topographic elevation and other disturbing factors the subsurface climate recollection alone. Since the boreholes have different depths, the measurements to the depth z = where t* is the time from the beginning of the meteorological record to the date of borehole logging, are generally taken for the inversion. This procedure avoids the biasing due to different borehole depths (Harris and Chapman, 1997).

To estimate the POM-value, the standard least-square inversion analysis can be used, which minimizes the sum of the squared differences between reduced and synthetic temperature-depth profiles. Inverted data are sensitive to the calculated POM-value; in the absence of non-climatic disturbances the POM-value can be assessed quite accurately, which is otherwise not possible by using the SAT record alone. Below we illustrate the application of the method to the data from Canadian borehole Hearst (49.69°N, 83.54°W), the GST reconstructions for which were presented in the Section 2.4.3.

Generally, results of the meteorological temperature measurements are representative of extensive areas; thus, making POM estimates, there is no need to get results of SAT measurements of especially close to investigated boreholes meteorological stations and/or to reject from consideration borehole temperature logs where such data does not exist. According to investigations by Hansen and Lebedeff (1987), the correlation coefficient between the annual mean temperature variations for pairs of stations selected at random from among the station pairs with at least 50 common years in their record is above 0.5 within 750 km distances at latitudes 23.6-44.4°N and within 1250 km distances for latitudes 44.4-64.2°N for each direction defined by 45° intervals. At middle and high latitudes the correlations approach unity as the separation between the stations becomes small. Of course, local specific conditions, such as vegetation cover, slope orientation, presence of large water body, etc., may produce lateral variations in the GST of up to several degrees over a short distance (e.g. Blackwell et al., 1980). In such cases the SAT records from the nearby meteorological station should be used to calculate the POM-value (Harris and Chapman, 1997).

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