# Predicted Subsurface Temperature Distribution Maps for Turkey

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2 of a value decreases as the distance increases from the prediction location (ESRI, 2004) Kriging Method Kriging is based on geostatistical techniques that are based on statistical models that include autocorrelation (statistical relationships among the measured points). Kriging is similar to IDW in that it weights the surrounding measured values to derive a prediction for each location. However, the weights are based not only on the distance between the measured points and the prediction location, but also on the overall spatial arrangement among the measured points. It uses models of spatial correlation, which can be formulated in terms of covariance or semivariogram functions. Prediction maps are created by contouring many interpolated values, systematically obtained throughout the region (ESRI, 2004). Figure 3: Statistics of Data Set 1 for 500 m depth In Data Set 1, a clustered distribution is dominant in the north western and south eastern parts of Turkey. But, although Data Set 2 is distributed more homogeneously than Data Set 1, Data Set 1 is more reliable because the values are coming from deeper sources, so that they can not affected by the surface near surface effects. In this study, in the generations of maps, ordinary prediction method is used. Simple, ordinary and universal predictors are all linear predictors meaning that prediction at any location is obtained as a weighted average of neighboring data. These three models make different assumptions about the mean value of the variable under study: simple requires a known mean value as input to the model, while ordinary assumes a constant, but unknown mean, and estimates the mean value as a constant in the searching neighborhood. 3. REGIONAL INVESTIGATOIN In order to investigate maps are generated regionally. This will help to construct regional temperature maps in more detail and compare with the whole picture. In regional maps, Data Set 1 representing deeper wells is used. Data Set 1 obtained coming from the deeper parts is believed to reflect more realistic values than Data Set 2. Two regional maps for Northwest (Thrace) and Southeast (Southeast ) are generated. Thrace : 80 temperature data values are selected for the analysis of Thrace region both for 500 m and 1000 m depths. These data are mostly collected from natural gas wells with a few geothermal wells. In Figure 5, the distribution of data is shown. Figure 4: Statistics of Data Set 2 for 500 m depth 2.2 Methods There are two main groupings of interpolation techniques: deterministic and geostatistical. All methods rely on the similarity of nearby sample points to create the surface. Deterministic techniques use mathematical functions for interpolation. Geostatistics rely on both statistical and mathematical methods which can be used to create surfaces and assess the uncertainty of the predictions. In this study Inverse Distance Weighting and (ordinary) Kriging are used to generate subsurface temperature distribution maps Inverse Distance Weighting Method (IDW) IDW, is one of the deterministic techniques because they are directly based on the surrounding measured values or on specified mathematical formulas that determine the smoothness of the resulting surface. To account for the distance relationship, the values of closer points are weighted more heavily than those farther away. The weight 2 In this data set (for 500 m depth), there is only one high temperature value, Tuzla that is located in South-western edge of the map. This data is the only data that can be characterized as outlier. Rest of the data is normally distributed. The statistical properties of Thrace data both for 500 m and 1000 m depths are shown in Figure 6 and 7 respectively. Figure 5: Location points of Thrace region

3 In this data set (for 500 m depth), minimum, maximum, mean temperature, and standard deviation are as follows: 26 o C, 95 o C, 33 o C, 7 o C. The median is found to be 32 o C that shows the outlier does not statistically affect distribution. As can be seen from the locations of data, they are not distributed homogeneously. Most of them are gathered in the north and north-eastern parts. The statistical properties of Southeastern data both for 500 m and 1000 m depths are shown in Figure 9 and 10 respectively. For Southeastern (for 500 m depth), nearly normal distribution is dominant. Minimum, maximum, mean temperature and standard deviation are as follows: 19 o C, 47 o C, 30 o C, 4 o C. Figure 6: Statistics of Thrace region for 500 m depth For the data set (for 1000 m depth) minimum, maximum, mean temperatures and standard deviation are as follows: 37 o C, 174 o C, 51 o C and 15 o C. The median is found to be 49 o C, again showing that the outlier does not statistically affect distribution. Figure 9: Statistics of Southeastern region for 500 m depth For Southeastern (for 1000 m depth), minimum, maximum, mean temperature, and standart deviation are as follows: 24 o C, 79 o C, 45 o C, 8 o C. Figure 7: Statistics of Thrace region for 1000 m depth Southeast : 255 temperature data values are selected for the analysis of Southeast region both for 500 m and 1000 m depths. These data are mostly collected from oil and natural gas wells with a few geothermal wells. In Figure 8, the distribution of data is shown. Figure 10: Statistics of Southeastern region for 1000 m depth The chosen parameters in the generation of IDW maps are shown in Table 1. Figure 8: Location points of Southeast 3

4 Table 1: Chosen Parameters for and Southeast n in IDW Temperature Distribution Maps. Parameters 500 m 1000 Southeastern 500 Southeastern 1000 Optimize Power Neighbors to include Include at least Sector 8 slice 8 slice 4 slice 4 slice Type Major Minor Anizotropy Factor RMS Figure 12: 1000 m depth temperature distribution map The explanations of the chosen parameters used in Table 1 are as given below. Optimized power value is determined by minimizing the root-mean-square prediction error (RMSPE). The RMSPE is a summary statistic quantifying the error of the prediction surface. Neighbors to include are the neighbors that will be used to estimate the value at the unknown location. Include at least is the minimum number of points to be used (in each sector) to estimate the value at the unknown location. Sector type is the number and geometry of sectors used in the search. Major/minor semi axis is the radius of the circle or ellipse. Anisotropy factor is the ratio of the major to minor axis. RMS (Root mean squared) is an indication of how good (closely) the predictions are. The generated temperature distribution maps (IDW method and method) for Thrace region are shown in Figures 11, 12, 13 and 14 respectively. The maps for the Southeastern region are shown in Figures Figure 13: 500 m depth temperature distribution map Kriging Data Set 1 The chosen parameters in the generation of maps are shown is Table 2. The explanations of chosen parameters used in Table 2 are given below. Figure 11: 500 m depth temperature distribution map 4 Figure 14: 1000 m depth temperature distribution map Data Set 1 Lag size (binning) is the size of a distance class into which pairs of locations are grouped in order to reduce the large number of possible combinations. Nugget is a parameter of covariance or semivariogram model that represents independent error and measurement error that is too fine to detect. Range is the distance where the model first flattens out. Sill is the value that the semivariogram model attains at the range (the value on the y axis). Partial sill is the sill minus nugget. ASE (average standard error) and RMSS (root mean square standardized) are indications of how good (closely) the predictions are.

5 Table 2. Chosen Parameters for and Southeast n in Kriging Temperature Distribution Map. Parameters 500 m 1000 m Southeast 500 m Southeast 1000 m Type of Kriging ordinary ordinary ordinary ordinary Direction Partial Sill Figure 17: 500 m depth temperature distribution map with Data Set 1 Nugget Lag Size Number of Lags Neighbors to include Include at least Sector 4 slice 4 slice 4 slice 4 slice Type Major Minor Anizotropy Factor RMS Average Standard Error RMSS Figure 18: 1000 m depth temperature distribution map with Data Set 1 4. GENERAL ASSESSMENT In order to make a general assessment for the whole country, two data sets (deep and shallow well information, a total of 968 values) are combined and used as a one data set. Ordinary prediction (Figure 20) and standard error (uncertainty) temperature (Figure 21) maps are generated using this data set. The statistical summary of 968 data points is given in Figure 19. For combined data set (for 500 m depth), nearly log normal distribution is dominant. In the generation of temperature distribution for whole country, we did not want to disturb the data set so in this case no transformation is implemented. Minimum, maximum, mean temperatures and standard deviation are as follows: 15 o C, 150 o C, 31 o C, 14 o C. Figure 15: 500 m depth temperature distribution map Figure 16: 1000 m depth temperature distribution map Figure 19: Statistics of Data Set 1 and 2 for 500 m depth 5

6 Ilkisik (1992) and Tezcan (1979) studies, and relatively a hot region in central. It also illustrates recent volcanic activity areas in central and eastern where volcanoes were formed. On the other hand, error distribution map is also meaningful since it represents higher errors where there is scarce data. Figure 20: 500 m depth temperature distribution map with Data Set 1 and Data Set 2 Figure 21: 500 m depth temperature prediction standard error distribution map with Data Set 1 and Data Set These statistics serve as diagnostics to indicate whether the model and/or its associated parameter values are reasonable for map production. They also serve as diagnostics to evaluate a model and find its optimal parameters (semivariogram/covariance, search neighborhood, trend, and so on). Geostatistical methods of data interpolation also provide measure of the uncertainty of the prediction (Average Standard, Mean Standardized, and Root-Mean-Square Standardized prediction errors), giving an indication of how good the predictions are. If the prediction errors are unbiased, the mean prediction error should be near zero. However, this value depends on the scale of the data, so the mean standardized prediction error gives the prediction errors divided by their prediction standard errors. This value should also be as close to zero as possible. The root-mean-squared prediction error indicates how closely the model predicts the measured values. Smaller the root-mean-squared prediction error is, better the predictions are. RESULS AND DISCUSSIONS Temperature maps for Thrace, Southeastern and the whole country both for 500 m and 1000 m depths are generated and compared using deterministic (IDW) and geostatistical () methods. In the comparison the prediction error (PE) values are taken into consideration. Temperature distribution of 500 m of Turkey prepared by combining one shallow data set (Data Set 2) and one deep data set (Data Set 1) presents a meaningful map in the sense that it reflects some particular features of Turkey (Figure 12). It shows hot Aegean which was indicated by 6 As for the regional maps both are sedimentary basins with relatively higher amount of data because of sufficient number of oil and natural gas wells. It is interesting that some relatively hot spots appear in maps of Southeastern. They are related to semi thermal areas formed in that basin. On the other hand, no such occurrences can be found in Thrace basin. Hot spot observed in the southeastern part of that basin is related to a hydrothermal resource which can be considered as an outlier. REFERENCES Cermak, V. Hurtig, E., Kutas, R.I., Lodo, M., Lubimova, E.A., Mongelli, F., Morgan, P., Smirnov, Ya. B. and Tezcan, A.K.:Heat Flow Map of Southern Europe and the Meditarrenean, Proceedings, International Congress on Thermal Waters, Geothermal Energy and Vulcanism of Mediterranean Area, Athens, October (1977). EPRI: Geothermal Energy Prospect for the Next 50 Years, EPRI ER-611-SR, Palo Alto, Ca (1978). ESRI: Using ArcGIS Geostatistical Analyst, Training and Education ArcGIS 9.2.,USA (2004). Ilkisik, O.M.: Personal Communication, Istanbul (2008). Ilkisik, O.M.: Silica Heat Flow Estimates and Lithospheric Temperature in, Proceedings, 11th Congress of World Hydrothermal Organisation, Istanbul, May (1992). Korkmaz Basel, E.D., Serpen, U. and Satman, A.: Geothermal Potentials of the Fields Utilized For District Heating Systems in Turkey, Proceedings, 30th New Zealand Geothermal Workshop & NZGA Seminar, New Zealand, November (2008 a). Korkmaz Basel, E.D., Cakin, K. and Satman, A.: Subsurface Temperature Map and Estimated Geothermal Resource for Turkey, (in Turkish) VII. Ulusal Temiz Enerji Sempozyumu (VII. National Clean Energy Symposium), Istanbul, December (2008 b). Korkmaz Basel, E.D., Serpen, U. and Satman, A.: Turkey Geothermal Resource Potential, (in Turkish), TESKON 2009, IX. Ulusal Tesisat Muhendisligi Kongresi, Izmir 6-9 May, (2009a). Korkmaz Basel, E.D., Serpen, U. and Satman, A.: Turkey s Updated Geothermal Energy Potential, Seventeenth International Petroleum and Natural Gas Congress and Exhibition 2009, Ankara, May (2009 b). Mihcakan, I.M. and Ocal, M.: A Survey on Geothermal Gradient Distribution in Turkey, Eleventh International Petroleum and Natural Gas Congress and Exhibition 1998, Ankara, October (1998). Mihcakan, M., Onur, M., Ercelebi, S.G., Okay, A., Yilmazer, M.: Map of Subsurface Temperature Gradient Distribution of Turkey Using Deep Well Temperatures and Variogram Analysis, TUBİTAK, Report No: YDABCAG-100Y040, November (2006).

7 MIT Report: (Edited by Tester, J.W.), The Future of Geothermal Energy, Massachusetts Institute of Technology (2006). Tezcan, A.K: Geothermal Studies, Their Present Status and Contribution to Heat Flow Contouring in Turkey, Terrestrial Heat Flow in Europe, Springer-Verlag, Berlin (1979). Unalan, G. and Ongur T.: Geothermal Gradient and Temperature Investigation at 1000 m Depth at Some Basins of Turkey, Firsth Geological Congress of the Middle East GEOCOME-I, Ankara, 4-7 September (1979). 7

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