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Method of calibration

 

The main aim of our project was to prepare material for further archaeological and chronological studies, so it was obvious, that we should put stress on the calibration of radiocarbon dates. The problem of calibration appears complex and controversial. Particularly we have spent a lot of time to find the best method of presentation of calibration results in a simple, numerical form (Krzanowski et al. 1994). Finally we have decided to show the calibration results in the form of intervals of calendric age which contain the real value of calendric age with probability 68.3% and 95.4% (these values correspond with 1SD and 2SD intervals for Gaussian distribution). Fig. 1 shows the method of determination these intervals. The same method is used by many well known calibration programs - e.g. calibration program by M. Stuiver and P. Reimer - CALIB 3.0 (Stuiver & Reimer 1993) or the Groningen calibration program (van der Plicht 1993).

Radiocarbon dates included in the ANDY database were calibrated using the Gliwice Calibration Program (Pazdur & Michczynska 1989) ver. 5.2. The calibration curves used for the calculation were taken from "Radiocarbon", Vol. 35 (1993) and they are practically the same as the curves used by the CALIB 3.0. The only difference is that we decided to finish the calibration curve at 9439 BC (the end of German oak and pine calibration by B. Kromer and B. Becker) and don't include the results obtained by mass spectrometry on corals, which extend the range of calibration to over 30000 years BP (Bard et al. 1993). Because measurement points building the calibration curve before 10.000 BP are located considerably rarer than earlier than this date we decided that it would be the best point to finish the calibration curve, which would be used for the treatment of radiocarbon dates from archaeological sites. Moreover, all dates were calibrated without correction for systematic age difference between the northern and southern hemisphere, estimated by Vogel et al. (1993) to be about 40 yr. We suppose that this correction, obtained for wood samples from South Africa (latitude between 25dS and 35dS), would not be valid for region near the equator.

Calibration programs written in few countries were compared in 1989 (Aitchison et al. 1989) and reasonably good agreement was found between them. All these programs use the same statistical method of calculation, and differ only in the form of result presentation. We will not discuss this problem here, presenting only an example table with the results of calibration the same radiocarbon dates by Gliwice Calibration Program and CALIB 3.0 (Tables 1 and 2). Unimportant differences between these results (2-3 years) are caused by technical aspects of programming. Moreover Fig. 1 and Fig. 2 present probability distributions of calendric age obtained by Gliwice (Fig. 1) and CALIB 3.0 (Fig. 2) programs, which differ only in the presentation form.

Gd-5695 320±40 conv BP
68.3% cal AD 1621- 1644 15.60%
  cal AD 1515- 1593 52.21%
95.4% cal AD 1482- 1654 95.56%
         
         
Gd-4662 780±80 conv BP
68.3% cal AD 1173- 1297 68.29%
95.4% cal AD 1343- 1391 7.04%
  cal AD 1152- 1318 76.11%
  cal AD 1112- 1147 4.57%
  cal AD 1044- 1105 7.88%
         
         
Gd-5682 1210±50 conv BP
68.3% cal AD 773- 890 67.37%
  cal AD 729- 731 0.94%
95.4% cal AD 908- 959 10.14%
  cal AD 692- 897 85.38%
         
         
Gd-3534 1870±45 conv BP
68.3% cal AD 117- 219- 66.52%
  cal AD 90- 92 1.62%
95.4% cal AD 63- 250 95.33%
         
         
Gd-6213 2400±80 conv BP
68.3% cal BC 547- 389 48.25%
  cal BC 758- 679 19.47%
95.4% cal BC 283- 255 1.67%
  cal BC 786- 360 93.95%
         
         
Gd-8011 3720±60 conv BP
68.3% cal BC 1996- 1986 3.41%
  cal BC 2147- 2026 51.30%
  cal BC 2193- 2155 13.59%
95.4% cal BC 2282- 1940 95.47%
         
         
Gd-3442 4405±30 conv BP
68.3% cal BC 2995- 2926 49.45%
  cal BC 3039- 3017 15.41%
  cal BC 3073- 3068 3.48%
95.4% cal BC 3047- 2921 79.50%
  cal BC 3091- 3054 16.01%
         
         
Gd-4394 5400±150 conv BP
68.3% cal BC 4357- 4041 67.87%
95.4% cal BC 3859- 3818 1.23%
  cal BC 4540- 3938 94.16%
         
         
GaK-2470 7830±180 conv BP
68.3% cal BC 6783- 6463 50.81%
  cal BC 6895- 6841 7.25%
  cal BC 6996- 6921 10.18%
95.4% cal BC 6286- 6241 1.26%
  cal BC 6328- 6295 0.90%
  cal BC 7097- 6344 91.07%
Table 1. Example results of calibrations made by the Gliwice Calibration Program.
Gd5695
Radiocarbon Age BP 320±40
% area enclosed cal AD age ran relative area under
probability distribution
68.3 (1s) cal AD 1514- 1593 .76
  1620- 1645 .24
95.4 (2s) cal AD 1481- 1654 1.00
       
       
Gd4662
Radiocarbon Age BP 780±80
68.3 (1s) cal AD 1170- 1300 1.00
95.4 (2s) cal AD 1040- 1100 .08
  1110- 1320 .84
  1340- 1390 .08
       
       
Gd5682
Radiocarbon Age BP 1210±50
68.3 (1s) cal AD 727- 732 .03
  772- 891 .97
95.4 (2s) cal AD 690- 898 .89
  908- 960 .11
       
       
Gd3534
Radiocarbon Age BP 1870±45
68.3 (1s) cal AD 89- 94 .05
  116- 220 .95
95.4 (2s) cal AD 62- 251 .99
       
       
Gd6213
Radiocarbon Age BP 2400±80
68.3 (1s) cal BC 760- 680 .29
  550- 390 .71
95.4 (2s) cal BC 790- 360 .99
  280- 260 .01
       
       
Gd8011
Radiocarbon Age BP 3720±60
68.3 (1s) cal BC 2190- 2030 .91
  2000- 1980 .09
95.4 (2s) cal BC 2290- 1940 1.00
       
       
Gd3442
Radiocarbon Age BP 4405±30
68.3 (1s) cal BC 3075- 3067 .07
  3040- 3016 .23
  2997- 2926 .70
95.4 (2s) cal BC 3094- 3051 .19
  3049- 2920 .81
       
       
Gd4394
Radiocarbon Age BP 5400±150
68.3 (1s) cal BC 4360- 4040 1.00
95.4 (2s) cal BC 4540- 3940 .99
  3860- 3820 .01
       
       
GaK2470
Radiocarbon Age BP 7830±180
68.3 (1s) cal BC 7000- 6920 .16
  6900- 6840 .12
  6780- 6460 .73
95.4 (2s) cal BC 7100- 6340 .95
  6330- 6240 .03
Table 2. Example results of calibrations made by CALIB 3.0 program.

 

Fig. 1. Probability distribution of calendric age obtained for radiocarbon date 4405±30 by the Gliwice Calibration Program.

 

Fig. 2. Probability distribution of calendric age obtained for radiocarbon date 4405±30 by CALIB 3.0.

Final remarks

We do not discuss the basic problems of database system here. The raeder may find a comprehensive introduction to the theory of databases at the manual "An introduction to database systems" written by C.J. Date (Date, 1977). On the other hand particular problems of radiocarbon databanks were discussed by Renee Kra (Kra, 1988).

We are aware of the fact, that the solutions we prefer, may be not satisfactory for all. Consequently we expect many observations, even critical reproof, about our database.

References

Aitchinson T.C., Leese M., Michczynska D.J., Mook W.G., Otlet R.L., Ottaway B.S., Pazdur M.F., van der Plicht J., Reimer P.J., Robinson S.W., Scott E.M., Stuiver M., and Weninger B., 1989, A Comparison of Methods Used for the Calibration of Radiocarbon Dates. Radiocarbon, Vol. 31, No. 3, 846-864.
Bard E., Arnold M., Fairbanks R.G., and Hamelin B., 1993. 230Th-234U and 14C Ages Obtained by Mass Spectrometry on Corals. radiocarbon, Vol. 35, No. 1, 191-201.
Date C.J., 1977. An introduction to database systems. Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, USA.
Kra R.S., 1988. Updating the past. The establishment of the International Radiocarbon Data Base. American Antiquity, Vol. 53, No. 1, 118-125.
Krzanowski A., Michczynski A., Pazdur M.F., Ziólkowski M.S., 1994. Komputerowa baza danych datowan radioweglowych rejonu Andów Srodkowych. Zeszyty Naukowe Politechniki Slaskiej, Geochronometria 10, pp. 139-151.
Pazdur M.F., Michczynska D.J., 1989. Improvments of the Procedure for Probabilistic Calibration of radiocarbon dates. radiocarbon, Vol. 31, 824-832.
Stuiver M., Long A., and Kra R.S. [ed.], 1993. Radiocarbon. Calibration 1993. Vol. 35, No. 1.
Stuiver M., and Reimer P.J., 1993. Extended 14C Data Base and Revised CALIB 3.0 14C Age Calibration Program. Radiocarbon, Vol. 35, No. 1, 215-231.
van der Plicht J., 1993. The Groningen Radiocarbon Calibration Program. Radiocarbon, Vol. 35, No. 1, 231-239.
Vogel J.C., Fuls A.M., Visser E., and Becker B., 1993. Pretoria Calibration Curve for Short-Lived Samples, 1930-3350 BC. radiocarbon, Vol. 35, No. 1, 73-87.