Darius Mottaghy, Jacek Majorowicz, Volker Rath –
[email protected],
[email protected],
[email protected]
Czeszewo observed calculated
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We present results from ground surface temperature histories (GSTH) reconstructed from two deep boreholes in Poland. Our main interest lies in the magnitude of the Pleistocene-Holocene Warming (PHW). One data set comes from the Udryn borehole, located in northeastern Poland, where heat flow of the norite anorthozite massif is only 40 mW m−2. The second data set originates from Czeszewo which is situated further west.(Fig. 1). Here, heat flow is considerably higher (¿80 mW m−2).
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Figure 2: Determination of boundary conditions (Table 1) for the inversion by forward modeling.
Since the present ground surface temperature and the basal heat flow enter the inversion as predetermined boundary conditions, we ran forward models with a simple step function representing the GSTH. As a result, we obtain a first, rough fit of the modeled temperatures (Fig. 2) to the data with boundary conditions as in Table 1. For the actual inversion, the specification of a prior model is necessary. If there is information on the GSTH from other sources, this can be taken into account within the prior. Otherwise, a zero prior is used.
The lower right panel shows the a posteriori GSTH, where the iteration process is made visible by different colors. The models for every iteration are obtained with an optimized regularization parameter τ , found by the minimum of the GCV function, which is plotted in Fig. 3 (upper right) versus τ . Here, the iteration number is given by the color-code. 25 inverse iterations were necessary to reach the final model. The lower left panel demonstrates the influence of the regularization parameters on the reconstructed GSTH in the last iteration: the red line is the model determined by using the regularization parameter found at the minimum of the GCV function. However, the other models are plotted in different gray scales, the darker the closer to the minimum. The GST history shows that there was a large PHW with about 17 K. Thus, mean GST during the last glacial maximum (LGM) was about -9 ◦C. Because in a low heat flow region (40 mW m−2) the effects of permafrost formation strongly influence the results. Details on this interpretation have already been published [5]. 0 -1.4
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Figure 1: Location of the boreholes Czeszewo and Udryn on a heat flow map (cite?) of eastern Europe (mW m−2), uncorrected for paleoclimatic effects.
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The forward model used in the inversion takes latent heat effects into account. The freezing and thawing of pore water can have a substantial influence on the thermal regime [5], in particular in regimes with higher porosities, such as studied here. All thermal parameters are functions of temperature. Table 1: Present mean annual GST and air surface temperature, and basal heat flow at 5 km, as used in the inversion. Location
Present GST Present mean annual SAT Basal heat flow ◦ ◦ C C (mW m−2) Udryn 8 6 37.2 Czeszewo 10 8 81.5
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Figure 4: Results from GSTH reconstruction for the Czeszewo borehole with an optimized regularization parameter. Description of panels see Fig. 3
We conclude that there has been large differences in temperatures during the LGM within a few hundred kilometres on the East European Platform. Besides the general increase of the continental component of the climate from west to east, the advance and retreat of the glacier during the Vastulian (Weichselian) glaciation caused a large spatial variability. For a reliable characterization of the PHW magnitude within such a regional scale more modeling is necessary. Our results contribute provide valuable information for larger scaled climate and glacier models.
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We invert borehole temperatures for ground surface temperature histories (GSTH) using the Tikhonov method. For this, a choice of the regularization parameter is necessary. This parameter controls the trade-off between the data fitting error and and the model seminorm applied for inversion. In particular when comparing different data sets, methods, or results, it is important to give a repeatable and objective way of choosing its value. Common methods for the choice of this parameter are the L-curve [2] or the GCV [9] criterion. Here, we use the latter one, its application on GSTH inverisons is described in detail in [6].
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Figure 5: Locations of the boreholes on a map showing the movement directions of the ice sheet of the Main Stadial of the Vistulian (Weichselian) Glaciation in Poland, as reconstructed from the orientation of glacial morpholineaments according to [4]. Additionally, temperature logs and extrapolations of the studied boreholes are plotted, together with another one in Torun (taken from [3]).
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tral Europe[1, 7]. Besides this, a longer exposure to cold air masses (katabatic winds) at the rim of the glacier is likely to be the reason for the very low mean GST at the Udryn location during the LGM.
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1 Introduction
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Ground surface temperature histories reconstructed from boreholes in Poland: implications for spatial variability?
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Figure 3: Results from GSTH reconstruction for the Udryn borehole with an optimized regularization parameter. The upper left panel shows the temperature log, porosity, and the thermal conductivity along the borehole. Upper right: GCV functions for each inversion iteration. Lower left: reconstructed GSTH for the last iteration, combined with the results for the regularization parameters used for associated GCV function. Lower right: reconstructed GSTH for each inversion iteration.
The inversion method is applied to data from Udryn, shown in the upper left panel of Fig. 3. As using a constant prior implies an unrealistic assumption of mean temperatures before the initiation of the simulation, a smooth transition is chosen from the recent GST of 8 ◦C to an initial value of -8 ◦C. This particular prior model entering the regularisation was inspired by the results of [8]. Test runs with a zero prior yield similar results, however, the numerical stability was not sufficient.
The same procedure is performed using the data from Czeszewo. Here, we used the depth interval 100-2400 m. As seen from Fig. 4, the result stabilizes after 15 iterations. From the inversion, the PHW is about 10 K which means that the mean GST during the LGM was around 0◦C. Although with both locations being only about 400 km apart, temperatures in Czeszewo were much higher during the LGM. This and the high heat flow in the Czewzewo region prohibited very likely the formation of permafrost. The higher temperatures during the LGM are confirmed by recently published results from Torun [3]. Its location (120 km NE of Czeszewo) is shown in Fig. 5 where the movement directions of ice lobes during the main state of the Vistulian Glaciation. This figure suggests explanations for the different temperatures during the LGM. The advance of the ice sheet in the western part of Poland extents further to the south. One the one hand this may imply a longer period of ice coverage in Czeszewo, and on the other hand a ”protection” of the Udryn location by the warmer, marine influence. This general fact, the transition from moderate to colder climates from west to east and thus a PHW in the range from 711 K is supported by GSTH reconstructions from boreholes in cen-
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