K

¡rs^/i

FSI method

True model

1000 1200 1400 1600 1800 2000 TIME, years A.D.

Fig. 27. Method FSI: Effect of varying parameter a (standard deviation characterizing the a priori constraint imposed on the GST history; Eq. (27)) on the noise-free "gate" model (G1) (bottom) and on a sinusoidal model (top). The correlation time rc in both cases is 100 years.

shown below, the effect of both parameters on the reconstructed GST history depends on the level of noise in the data. As seen in Figure 26c, the influence of the correlation time Tc is not so strong when the noise level in the data is low. The influence of the standard deviation a is illustrated in Figure 27 (bottom). In the ideal case, when the T-z profile and the values of thermophysical parameters are noise free and inversion procedure does not introduce discretization/roundoff errors, one may set relatively large value for standard deviation without the risk that the instability of the solution will occur. For the G1 temperature profile (Figure 27, bottom) the instability threshold is as high as 500 K. In the real cases the optimal values for a should be much lower and can be established experimentally. Numerical trial runs have shown that for usual field temperature logs the optimal value is close to 100 K (see also Shen and Beck, 1991, 1992). However, the solution can be regarded as reliable and/or reasonable over a wide range of values for a within this interval.

Results of similar calculations for the noise-free "sinusoidal" model are shown in Figures 27 (top) and 28. This model was calculated by the expression V0(t) = 4°C + sin(ftt/400—5tc/2) with period of 800 years; t is the time in the years B.P. The oscillations of the surface temperature roughly correspond to the Medieval Warm Period, the Little Ice Age, and the warming since then. Corresponding temperature-depth profile is shown as the inset to Figure 28. Synthetic T—z profile used for the GST inversion is completely noise free. This example illustrates the possibility to reconstruct past harmonic oscillations and demonstrates how the damping of high-frequency climatic signal with depth manifests

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