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Fig. 60. Left: Synthetic temperature logs. "Conductive" indicates the solution obtained for pure conductive regime. Other T—z profiles correspond to combined conductive plus advective regimes with different up- and down-flow velocities. Right: Reduced temperature logs. Reduced temperatures for advectively disturbed temperature field were obtained for reducing parameters of T0 = 0°C, G = 20K/km.

induced convection such velocity corresponds to a hydraulic flow driven by a surface head difference of 100-200m along 1-3km long profile in a medium with permeability of ~10~15m2. At higher fluid velocities of (1-5) X 10~8m/s the temperature field is dominated by advection ("strong" convection), which may considerably distort the purely conductive geotherms. The typical T-z profile associated with downward groundwater flow exhibits expressive curvature. Being "corrected" in our case for a constant geothermal gradient (reduced temperature, Figure 60, right) it shows temperature changes similar to the recent warming in the upper part of the profile and cooling in its deeper section. The paleoclimatic signal is not necessarily washed out, but may be significantly distorted (0.5-1 K or even larger differences from the purely conductive geot-herm). In case of downward fluid flow the advection lowers the existing temperature gradient and vice versa. Produced by the "moderate" convection hydraulic disturbances to the temperature log are very similar to the purely conductive conditions, and it is not easy to recognize which effect dominates.

Bodri and Cermak (2005a) have made an attempt to include advective disturbances due to vertical subsurface fluid flow in the usual 1-D inversion procedure for POM estimates (Section 2.5). This approach seems capable of yielding good results in major groundwater recharge or discharge areas. The series of tests on both synthetic and field examples indicated that the advective/conductive joint inference of the POM-temperature improves the earlier pure conductive models and provides more reliable estimates, thus making possible the use of a vast amount of the previously rejected temperature logs for past climate reconstructions. In this approach the impact of hydraulic flow on the paleoclimatic temperature signal was investigated for a simple 1-D model in case of the semi-infinite medium. Even though it may be far from the realistic 3-D and/or 2-D case presented in Figure 57, such model has a potential to be used as a general approach when fluid flow is suspected to exist in boreholes where temperature log were measured.

The 1-D representation of Eq. (37) with constant velocity of fluid was used as the mathematical model. Negative velocity corresponds to the fluid flow towards the surface. The surface boundary conditions remain the same, as in the pure conductive approach; at large depth (reduced) temperature gradient equals zero and the temperature disturbance due to surface climate variations tends to be negligible. As previously, initial T-z profile can be obtained from the assumption of the original steady-state temperature conditions. The unknown parameters are the POM-value and the fluid velocity (v). Similarly to the pure conductive case, both parameters can be estimated by comparing reduced temperatures with synthetic temperature logs using least squares inversion technique. Certain shortcomings of the method are: (1) the assumption of the purely vertical flow, (2) the assumption of constant velocity, which likely is not the case for the most of field situations, and (3) the assumption that the fluid flow conditions have been constant for a long time (at least during the last 100 years or so). The influence of the first assumption is investigated in Bense and Kooi (2004) and Bodri and Cermak (2005a) by means of synthetic models describing the areas where considerable vertical ground fluid flow and surface warming occur simultaneously. As shown, in the discharge and recharge areas estimated with the 1-D approach velocities coincide well with the average vertical velocities of the fluid circulation in the whole investigated depth interval. Modeling results by Lu and Ge (1996) and Reiter (2001) have revealed that horizontal groundwater flow can also produce temperature anomalies that can further be misinterpreted as the result of past GST changes. According to the calculations by Bodri and Cermak (2005a), the velocity estimated in zones of sub-horizontal rather than vertical directions of flow is comparable with the mean value of total velocity of the fluid movement in such regions. The differences between the real POM-value and estimated from 1-D model were relatively insignificant even in zones of generally sub-horizontal water movements, where the declination from the pure vertical flow reaches its maximum. As third shortcoming of the method, the fluid flow conditions depend on many factors. They are closely related to recharge of precipitation and can show wide fluctuations; in the media composed of more soluble rocks the dissolution of the material under the fluid flow can increase the permeability of the strata with time; on the contrary, the flow of fluid with high degree of the mineralization can significantly lower the primary high permeability of rocks with time, thus retarding fluid flow, etc. However, as shown by Fetter (1988), most of the local and/or regional flow systems with relatively flat water table in the less permeable strata can be generally considered as possessing a dynamic equilibrium. Drastic changes of the hydrological properties would have to occur before this becomes an important factor. Thus, the third assumption does not present a serious problem.

An example in Figure 61 presents a synthetically generated noise free temperature log in a homogeneous half-space described by K = 2.5W/mK, (pc)m = 2.5MJ/m3 K, and G = 20K/km. To simulate the surface conditions we used POM of 9.2°C before year 1900 and the surface air temperature since then corresponding to the SAT record observed at the meteorological station Prague-Klementinum (Figure 64). The mean SAT-value for Klementinum for the twentieth century equals to 9.71°C, so the chosen

Fig. 61. Left: Synthetic temperature logs. "Conductive" indicates the solution obtained for a pure conductive regime. Solid black line corresponds to the combined conductive plus advective regimes (down-flow velocity 1CT9m/s). Right: Reduced temperature logs. Reduced temperature for advec-tively disturbed temperature field was obtained for reducing parameters of TC = 9.2°C, G = 20K/km. "Best-fit" temperature corresponds to conductive regime (for details see text).

Fig. 61. Left: Synthetic temperature logs. "Conductive" indicates the solution obtained for a pure conductive regime. Solid black line corresponds to the combined conductive plus advective regimes (down-flow velocity 1CT9m/s). Right: Reduced temperature logs. Reduced temperature for advec-tively disturbed temperature field was obtained for reducing parameters of TC = 9.2°C, G = 20K/km. "Best-fit" temperature corresponds to conductive regime (for details see text).

POM-value corresponds to 0.5K as the last century warming. To calculate synthetic temperature log Tsynt(POM,v) (Figure 61), we used down-flow fluid velocity of 1 X 10~9m/s. For comparison the geotherm calculated for pure conductive conditions is also presented. As seen, the downward fluid flow lowers the existing temperature gradient.

As the calculated synthetic temperature-depth profile is noise free, the estimation of the POM-value and of the fluid velocity, taking into account the advective heat transport, should return the input values. The degree of conformity between the real and synthetic models is usually characterized by the sum of the squares of deviations between measured and synthetic temperature logs. We have calculated root mean square (rms) misfits for wide spectra of possible POM and fluid velocity (v) combinations to determine the bestfit parameters. Generally, preferred values of estimated parameters correspond to the minimum of rms misfits. Figure 62 shows the respective map of the rms misfit as a function of parameters POM and v. As in the previous case of single POM estimation (Section 2.5), the relatively small differences in the estimated parameters can produce significant misfits of the calculated model from the measured temperature log. A single sharp minimum on the rms misfit map implies the stability and uniqueness of the solution and indicates the robustness of the method of joint POM-v estimate.

Applying the purely conductive approach to estimate POM-value from the advectively disturbed temperature log we obtain POM-temperature that can differ from its real value. In the above case the POM-value estimated with conductive approach equals to 9.7°C; thus,

Fig. 62. Map of the rms misfit (in Kelvin) as a function of POM-values and fluid velocities for synthetic example shown in Figure 61.

it is 0.5K higher that the real value 9.2°C used for the calculation of the synthetic temperature log. Such discrepancy may lead to a misleading interpretation of the twentieth century warming. The value of 9.2°C (used as the pre-1900 temperature) means a 0.5K warming relatively to 9.71°C, the mean value corresponding to the period 1900-1992, that can be used as the characteristic of the average twentieth century temperature, while the value of 9.7°C calculated under conductive conditions suggests no twentieth century warming at all. The rms misfit between simulated and best-fit calculated temperature logs reaches 0.91 K. As shown in Figure 61 (right), a satisfactory fitting can be achieved only in the uppermost part (40-50m) of the reduced temperature log.

Numerical trial runs with synthetic temperature logs have shown that if the pure conductive approach is used to estimate POM-value from the advectively disturbed temperature log, the corresponding error of the POM estimate depends on the direction and velocity of the hydraulic flow. In the case of fluid up-flow with velocity of 1X 10—9m/s, the estimated POM-value is 8.4°C, which indicates ~1.3 K for the twentieth century warming (rms misfit is high and equals 1.3 K). If the pure conductive approach is applied to estimate POM-value in an advection-dominated system of fluid velocities of 1 —5X10—8m/s, the deviation of the estimated pure conductive POM-value from the real values corresponding to the down-flow fluid movement may be 1-1.5 K above its true value. Similar, but even more pronounced results could be obtained for the case of upward flow. With the present assumption the maximum permitted velocities of the up-flow movement should not exceed 10—8m/s; higher velocities cannot be applied as such a situation would lead to heating up of the surface and would violate the chosen surface boundary condition.

When pure conductive approach is applied to temperature logs affected by strongly advective dominated temperature field, the graph of the rms misfit as a function of POM-can be more complex than a single sharp minimum, presented in Figure 42. It may contain a "flat" extreme and/or two or more local minima, indicating an unstable or a non-unique solution. If such rms pattern is obtained in a practical case, this may indicate a presence of advective disturbances in the measured temperature log.

The joint POM-v estimation using field examples is presented below. Temperature-depth measurements were performed for four closely spaced 150 m deep holes near Tachlovice, the site located about 15km SW of Prague (50.01°N, 14.24°E, 350 m asl). All boreholes penetrated relatively homogeneous stratum of Silurian and Devonian shales. Temperature measurements were taken at 2.5 m depth intervals to the depth 20 m and at 5 m intervals below 20 m. Thermal conductivity was estimated (Bodri and Cermak, 1995) on the basis of the geological survey and amounts to 2.5W/mK, the value characteristic for typical rocks of the Bohemian massif.

All four temperature records are practically identical, all showing a clear "U-shape" (Figure 63), which suggests a recent warming. Minor distortions of the U-shape can be indicative of water movement effects in the top section of the drilled strata of a topographic depression representing a discharge area among surrounding low hills. The borehole sites are located in the slightly undulated terrain on the gently sloping side of the small river. The water flow in pores and in small fractures is driven by a surface head difference of ~ 30-50 m across 3-5 m distance. Relatively low hydraulic conductivity of shales (10—8-10—4m/day, Fetter, 1988) retards the flow; thus, relatively low Darcy velocities may be expected in the area.

TEMPERATURE, deg.C 9 10 11 12 13

TEMPERATURE, deg.C 9 10 11 12 13

Fig. 63. Temperature logs measured in four holes at site Tachlovice (Tach-I to Tach-IV), Czech Republic.

As a representative SAT record we used mean annual temperatures measured at meteorological station Prague-Klementinum (Figure 64). As mentioned above, the mean temperatures corresponding to 1900-1992 and 1960-1992 periods equal 9.71 and 10.07°C, respectively. For inversion we used temperature-depth data only from below 15 m depth to exclude any seasonal temperature variations. The reducing parameters (T0 - surface temperature and G - temperature gradient) were calculated by the linear regression of the deepest part of the T-z records.

The estimated POM-values prior to year 1900, taking into account the advective influence, are presented in Table 4. The obtained best-fit values correspond to single minimum in the rms misfit maps (presented in Figure 65) indicating the uniqueness of the solution obtained for the given model formulation. Figure 66 shows the comparison of observed reduced temperatures with the best-fit temperatures calculated for both approaches. As shown, in all cases the inclusion of fluid circulation significantly improved the rms misfit; thus, temperature logs calculated with "conductive plus advective" approach almost perfectly reproduce the observed temperatures. Values of the rms misfit in Table 4 range between 0.06 and 0.08 K. They are 2.5-4 times lower than the rms misfits obtained when we used pure conductive model for the parameter estimation. An additional test of significance of both models can be provided by comparison of the variance of the

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