The geoid is a representation of the surface of earth that assumes the sea is covered the earth, also known as surface of equal gravitational attraction and mean sea level. The main function of the geoid in geodesy is to serve as a reference surface for leveling. The elevation measured by leveling is relative to the geoid. Three dimensional coordinates that are easily obtained by GPS easily; are widely used in such applications as large-scale map production and engineering applications. The latitude and longitude values obtained by GPS are used directly, but ellipsoidal height (h) values must be transformed into orthometric heights (H). In many surveying and engineering applications, orthometric heights are required. Ellipsoidal heights have geometric meanings in practical surveying, engineering, and geophysics and in other applications, and they bear no physical meanings. For the transformation from ellipsoidal heights to orthometric heights, which are used in applications, geoid heights (N) must be known with required accuracy. Several techniques can be used for determination of geoid heights. Most commonly used method for the determination of geoid is the combination of GPS data and leveling measurements. The by laws for large scale map production is required to be changed and allow to GPS applications, as parallel to the augmentation in application of the GPS technique. The new draft bylaw contains observation and calculation methods for obtaining orthometric heights by GPS, as well. One of them is determining the height of the geoid by GPS/Nivelman method. In this study, compared with classical methods by the deterministic and Kriging interpolation methods for determining the geoids by GPS/Nivelman method in Istanbul Metropolitan Surface deterministic and Kriging interpolations were calculated by known geoid undulation (NMEASURE) values performed by using ArcGIS 8.3 Geostatistical Analyst software. Geostatistical Analyst provides deterministic and geostatistical interpolation methods. Deterministic interpolation techniques (inverse distance weighted, radial basis functions, and local polynomial interpolation) should not be used for decision making, because they do not provide information on how good their predictions are. Geostatistical interpolation techniques (e.g., kriging) can be chosen based on the result of exploratory spatial data analysis and diagnostics (cross validation and validation). Deterministic methods use predefined mathematical functions for interpolation. Geostatistical methods rely on statistical features of the data. Geostatistical Analyst provides the necessary tools for data exploration and variography analysis. Kriging is based on the assumption that the parameter being interpolated can be treated as a regionalized variable. A regionalized variable is intermediate between a truly random variable and a completely deterministic variable in that it varies in a continuous manner from one location to the next and therefore points that are near each other have a certain degree of spatial correlation. Kriging is a set of linear regression routines which minimize estimation variance from a predefined covariance model. This method uses variogram to express the spatial variation, and it minimizes the error of predicted values which are estimated by spatial distribution of the predicted values. Besides, while the Geoid Model was forming; the effect of control point frequency to computed geoid height values was investigated. To study the effect of point frequency to the counting of geoid, geoid surfaces were formed with 50(~one point to 100 km2), 200(~one point to 25 km2), 393 (~one point to 13 km2) and 434(~one point to 12 km2) points in Istanbul. For testing with interpolations, 50 test points were chosen and NCALCULUS values were counted by various deterministic and geostatistical interpolations. NCALCULUS-MEASURE distinction values were found by subtracting NCALCULUS values from measurement values that were found by NGPS/NİVELMAN method. Mean square errors and maximum, minimum and mean error values were calculated for all methods. By comparing of these values, the method that gives the most suitable surface was chosen. It was found that the results of determining geoid by Kriging method were more precise than deterministic methods. The results of Ordinary Kriging method were more precisely than Simple Kriging method’s results but the maps produced by Simple Kriging method were more esthetic than the other equal geoid height maps. The results found by multiquadratic method between deterministic methods were close to the results found by Kriging method and multiquadratic method gave the best results. For increasing precession augmentation of survey quality is better than augmentation of model points. Keywords: Geostatistic, deterministic, interpolation, geoid. Geoit, ağırlık potansiyelinin sabit olduğu ortalama deniz yüzeyine yakın bir yüzeydir. GPS ile bulunan enlem ve boylam değerleri doğrudan kullanılmakta ancak elipsoidal yükseklik (h) değerlerinin ortometrik yüksekliğe (H) dönüştürülmesi gerekmektedir. Dönüşüm için yeterli doğrulukta geoit yüksekliklerinin bilinmesi gerekmektedir. Geoit yükseklikleri belirleme teknikleri içerisinde en yaygın kullanılanı GPS/Nivelman tekniğidir. BÖHHBÜY dönüşüm için yerel GPS/Nivelman geoidi kullanılmasını öngörmektedir. Bu çalışmada, İstanbul Metropoliten alanlarında GPS/Nivelman yöntemi ile geoit belirlemek için deterministik ve Kriging enterpolasyon yöntemleri karşılaştırılarak, Kriging yönteminin geoit yüzeyi modellemesinde kullanılabilirliğinin araştırılması yapılmıştır. Uygulamada, ArcGIS 8.3 Geostatstical Analyst yazılımı kullanılmıştır. Dayanak nokta yoğunluğunun geoit hesabına etkisini araştırmak için İstanbul’ da 50 (~ 100 km2’ye bir nokta), 200 (~ 25 km2’ye bir nokta), 393(~ 13 km2’ye bir nokta) ve 434 (~ 12 km2’ye bir nokta) noktalı geoit yüzeyleri oluşturulmuştur. Test için 50 nokta seçilmiş ve bu noktaların deterministik ve geoistatistik enterpolasyonla NHESAP değerleri hesaplanmıştır. NHESAP-ÖLÇÜ fark değerlerinden, farkların maksimum, minimum ve ortalama değerleri ile karesel ortalama hatalar karşılaştırılarak en uygun yüzeyi veren yöntem seçimi yapılmıştır. Çalışmalar sonunda, Kriging yöntemi ile geoit belirleme sonuçlarının deterministik yöntemlerden daha presizyonlu olduğu, Ordinary Kriging yönteminin Simple Kriging yönteminden bulunan sonuçlardan daha presizyonlu olduğu saptanmıştır. Multiquadratik yöntemle bulunan sonuçların Kriging yöntemlerinden bulunan sonuçlara çok yakın olduğu ve multiquadratik yöntemin en iyi sonucu veren deterministik yöntem olduğu, presizyonu arttırmak için nokta yoğunluğunu arttırmaktan çok veri kalitesini arttırmak gerektiği saptanmıştır. Anahtar Kelimeler: Geoistatistik, deterministik, enterpolasyon, geoit
