Yaron A, Felus 
  
Following the generation of experimental semivariogram in the above figures; we used an interactive method to find the 
initial function and then used weighted least squares to fit the exact corresponding semivariogram functions. We should 
mention that to compute the sample semivariogram, we choose area in out data that have no visible trend ( the selection 
was made using the contour line map). We were able to fit a Gaussian function to all the data sets that will also give us 
the required sill for equation (9) -C(0). 
The USGS fitted Gaussian function has the following parameters: Nugget=g=366; Range=r= 50330; Sill=s= 90559.7; 
The Radio Echo Sounding Data fitted Gaussian Variance function has the parameters of: Nugget=g=130; Range=r= 
61295; Sill=s= 35621 and the mutual data sets fitted Gaussian function has a Nugget=g= 500; Range=r= 88243; Sill=s= 
20000. With those variogram models we followed the process of equation (6) and (7) to grid our data at 100 meter 
resolution and produce a grid with a better accuracy. 
5 CONCLUSIONS AND FURTHER RESEARCH. 
We have designed a complete schema to integrate DEM's acquired from different sources, and we demonstrated the 
execution of this process in an actual problematic case study area - The tranantarctic mountains in Antarctica. We 
divide the integration process into two separate classes of algorithms, namely; merging of overlapping data sets and 
fusion of one data set in the other. For the first technique, we suggest an interpolation zone of 1km, this means, that we 
smooth and decrease the effect of a 140 m variance over a distance 1KM ( more then 10 times the variance is a good 
rule of thumb). For the fusion process, we propose to use a geostatistical interpolation - Least square collocation - it is 
not common to see statistical interpolations when using elevation models, those methods are being used extensively for 
potential fields, for geological analysis and spatial environmental examination. We decided to use those methods in our 
area since we assume a smooth behavior of the DEM over the ice topography of the Antarctic plateaus. More over, our 
interpolation algorithm is designed to work with small local subset or support which make it more suitable to deal with 
moderately varying data such as elevations model. The main advantage of the geostatistical mathematical scheme is that 
it fits a unique covariance/semivariogram model which encompass the measurement errors and the intrinsic data 
relationship in it, based on this analysis the algorithm interpolates the data. This is in contrast with other methods, 
which assume a certain data behavior in advance. Moreover, using geostatistics, we can get an estimate for our 
interpolation dispersion, The mathematical development of the sequential dispersion equation is long but follows the 
same line of arguments as the sequential least squares collocations. Further research is needed to evaluate the results of 
this model and compare it's performance with respect to other models. 
ACKNOWLEDGMENTS 
The authors would like to thank Dr. Terry Wilson and Dr. Burkhard Schaffrin for their useful discussions. This work 
was partially supported by an NSF grant (OPP-9615639) 
REFERNENCES 
Abidy M. A. and R. C. Gonzales 1992. Data fusion in Robotics and Machine intelligence. Academic Press, Inc., San 
Diego, CA. 
Antarctic Digital Database (ADD) Version 2.0 [1998], Mapping and Geographic Information Center British Antarctic 
Survey on behalf of the SCAR Working Group on Geodesy and Geographic Information at: 
http://www.nbs.ac.uk/public/magic/add main.html 
Bamber L. Jonathan 1994. A digital elevation model of the Antarctic ice sheet derived from ERS-1 altimeter data and 
comparison with terrestrial measurements. Annals of Glaciology, vol 20 Proceedings of the fifth international 
Symposium on Antarctic Glaciology (VISAG), Cambridge, U.K. 
Cressie N. (1993). Statistics for Spatial Data. Wiley & Sons, New York. 
Drewry J. David 1982. Ice Flow, Bedrock and Geothermal Studies from Radio-Echo Sounding Inland of McMurdo 
Sound, Antarctica. Craddock C(ed), pp 977-983. 
Hahn M. and Samadzadegen F. 1999, Integration of DTM's Using Wavelets. International Archives of photogrammetry 
and remote sensing, Vol 32 part 7-4-3 W6, Valladolid,Spain, 3-4 June 1999. 
Helmut Moritz 1970. A generalized least squares model. Studia Geophysica Et Geodaetica, Vol 14. Pp 353-362. 
  
122 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000. 
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