# Probabilistic Analysis as a Method for Ground Freezing Depth Estimation
## 3 Results
### Validation of Chosen Model of Estimation ([PERSON])
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Gumbel Distribution Parameters for Chosen Estimation Models:**} & \multicolumn{2}{c}{**Correlation**} \\ \cline{3-10}
**No.** & **Localization** & \multicolumn{2}{c}{**LSM**} & \multicolumn{2}{c}{**Max. LM**} & \multicolumn{2}{c}{**MM**} & \multicolumn{2}{c}{**Lieblein**} & \multicolumn{2}{c}{**Coefficient**} \\  & & \(\mathbf{\alpha}\) & \(\mathbf{u}\) & \(\mathbf{\alpha}\) & \(\mathbf{u}\) & \(\mathbf{\alpha}\) & \(\mathbf{u}\) & \(\mathbf{\alpha}\) & \(\mathbf{U}\) & \(\mathbf{R}^{2}\) **for [PERSON]** \\ \hline
1. & Bialystok & 4.980 & 0.404 & 5.895 & 0.410 & 5.515 & 0.407 & 5.717 & 0.408 & 0.980 \\
2. & Bielsko-Biala & 8.958 & 0.212 & 10.479 & 0.214 & 10.019 & 0.214 & 10.133 & 0.213 & 0.984 \\
3. & Chojnice & 4.460 & 0.400 & 5.334 & 0.407 & 5.005 & 0.405 & 5.130 & 0.404 & 0.990 \\
4. & Elblag & 5.902 & 0.363 & 6.182 & 0.362 & 6.617 & 0.366 & 5.999 & 0.360 & 0.992 \\
5. & Gorzów & 4.664 & 0.302 & 5.647 & 0.307 & 5.150 & 0.305 & 5.555 & 0.306 & 0.977 \\
6. & Jelenia Gó & 5.831 & 0.320 & 5.826 & 0.316 & 6.385 & 0.322 & 5.733 & 0.315 & 0.971 \\
7. & Kalisz & 4.864 & 0.347 & 5.014 & 0.346 & 5.419 & 0.351 & 4.894 & 0.343 & 0.985 \\
8. & Katowicz & 7.291 & 0.201 & 8.759 & 0.204 & 8.199 & 0.204 & 8.584 & 0.203 & 0.986 \\
9. & Ketrzyn & 6.506 & 0.352 & 6.726 & 0.349 & 7.178 & 0.354 & 6.643 & 0.347 & 0.973 \\
10. & Kielce & 4.645 & 0.399 & 5.351 & 0.404 & 5.157 & 0.402 & 5.191 & 0.402 & 0.979 \\
11. & Klodzko & 6.541 & 0.281 & 6.865 & 0.280 & 7.284 & 0.284 & 6.663 & 0.278 & 0.985 \\
12. & Kolo & 5.973 & 0.336 & 5.809 & 0.334 & 6.658 & 0.339 & 5.687 & 0.332 & 0.983 \\
13. & Koszalin & 6.065 & 0.313 & 6.669 & 0.316 & 6.817 & 0.317 & 6.449 & 0.313 & 0.991 \\
14. & Kraków-Balice & 6.670 & 0.261 & 6.721 & 0.258 & 7.328 & 0.263 & 6.565 & 0.256 & 0.972 \\
15. & Leba & 7.097 & 0.275 & 6.643 & 0.268 & 7.079 & 0.276 & 6.498 & 0.268 & 0.958 \\
16. & Legnica & 4.592 & 0.327 & 4.952 & 0.328 & 5.136 & 0.332 & 4.790 & 0.325 & 0.987 \\
17. & Lesko & 7.026 & 0.234 & 8.079 & 0.237 & 7.875 & 0.237 & 7.897 & 0.235 & 0.986 \\
18. & Leszno & 5.208 & 0.350 & 5.459 & 0.349 & 5.826 & 0.354 & 5.294 & 0.347 & 0.992 \\
19. & Lublin & 5.682 & 0.333 & 6.244 & 0.335 & 6.364 & 0.337 & 6.099 & 0.332 & 0.991 \\
20. & Lód��{z} & 4.699 & 0.386 & 4.905 & 0.386 & 5.284 & 0.391 & 4.736 & 0.382 & 0.992 \\
21. & Mikolajki & 6.024 & 0.311 & 6.656 & 0.312 & 6.718 & 0.315 & 6.510 & 0.311 & 0.986 \\
22. & Nowy Sacz & 8.851 & 0.202 & 8.788 & 0.199 & 9.776 & 0.203 & 8.526 & 0.198 & 0.977 \\
23. & Opole & 5.006 & 0.324 & 5.689 & 0.327 & 5.607 & 0.328 & 5.475 & 0.325 & 0.988 \\
24. & Resko & 5.888 & 0.245 & 6.623 & 0.247 & 6.539 & 0.248 & 6.537 & 0.246 & 0.982 \\
25. & Rzeszów & 8.658 & 0.351 & 7.514 & 0.344 & 9.415 & 0.351 & 7.498 & 0.344 & 0.959 \\
26. & Sandomierz & 5.560 & 0.434 & 6.095 & 0.436 & 6.141 & 0.436 & 6.014 & 0.434 & 0.974 \\
27. & Shubice & 5.857 & 0.298 & 6.476 & 0.300 & 6.544 & 0.301 & 6.290 & 0.297 & 0.991 \\
28. & Suwalki & 6.276 & 0.442 & 6.343 & 0.441 & 6.969 & 0.445 & 6.236 & 0.439 & 0.982 \\
29. & Swinoujšie & 5.232 & 0.433 & 5.322 & 0.432 & 5.860 & 0.437 & 5.205 & 0.429 & 0.988 \\
30. & Szczecin & 4.253 & 0.282 & 4.616 & 0.279 & 4.622 & 0.284 & 4.633 & 0.280 & 0.961 \\
31. & Tarmów & 6.189 & 0.322 & 6.494 & 0.321 & 6.884 & 0.325 & 6.323 & 0.319 & 0.984 \\
32. & Torun & 4.528 & 0.446 & 5.095 & 0.450 & 5.079 & 0.450 & 4.978 & 0.447 & 0.989 \\
33. & Warszawa & 5.986 & 0.401 & 6.066 & 0.402 & 6.647 & 0.404 & 6.109 & 0.401 & 0.985 \\
34. & Wlodawa & 3.726 & 0.507 & 4.476 & 0.515 & 4.188 & 0.513 & 4.334 & 0.512 & 0.992 \\
35. & Zakopane & 5.450 & 0.378 & 5.050 & 0.372 & 6.008 & 0.380 & 4.998 & 0.370 & 0.975 \\
36. & Zielona Góa & 3.553 & 0.421 & 3.589 & 0.416 & 3.915 & 0.425 & 3.516 & 0.413 & 0.972 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of calculation for all localizations. Figure 7: Comparison of predicted and measurement value for chosen location: Bialystok (**left**) and Elblag (**right**) station.