The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
3. THE VARIATION OF MEAN REDIUS OF 
CURVATURE AND THE INFLUENCE ON HEIGHT 
SURVEY 
We choose a scene of ERS-1/2 satellite image data of HerBei 
ShangYi areaed about 50Km* 50 Km . We measure the 
coordinates of longitude and latitude on the maps, and caculate 
the mean redius of curvature of earth with Krassovsky ellipsoid 
parameters by 1954 BeiJing coordinate system ,and then gain 
the variety of the earth’s mean redius of curvature. 
The coordinates of longitude and latitude of the area is as 
follows: 
Picture 2 : the selected area’s coordinates of longitude and 
latitude 
It can be seen from picture 3 that the variety of earth’s mean 
redius of curvature with change of latitude : 
While the latitude adds, the changes of the earth’s mean redius 
of curvature is linear. When the latitude adds 0.1 degree, the 
earth’s mean redius of curvature adds nearly 100 meters . So the 
earth’s mean redius of curvature changes very much along with 
latitude. How much influence is brought on spomebome InSAR 
height survey by so much change? Then it is analyzed 
quantificationally in detail. 
Base on InSAR height survey principle, the formula is as 
follows: 
R? + (R e + H) 2 - 2cos6K,(^ +H) = (R e + hf (1-1) 
Caculate the differential coefficient of h to R e , 
dh _ H-2cos9R l -h 
~dR e ~ h + R e 
We think Re has errors, and the rest parameters are true. 
From the law of propagation of mean square errors ,we can get 
the expression: 
While 9 = 20.8° > B = 354.56m( the baseline parameter of 
ERS-1/2 ) , h = 1400m (the area’s mean ground height) , Re = 
6374732.39m (the local earth’s mean redius of curvature ) , 
when m Re = 1 m, you can get m h - ±0.87 m. So 1 meter’s error 
of mean redius of curvature can bring the mean square error of 
0.87m . Thus it can be seen, ignoring the variation of earth’s 
mean redius of curvature will cause quite much the height 
survey errors. It is required that on InSAR height survey, it 
need to require that the corresponding ellipsoid radius to the 
different image coordinates is different too. 
Then it proves whether we can take the earth’s surface as 
spherical surface on InSAR Height surcey in selected area . 
From picture 4, it can be seen that in that way it will cause 
much more errors, and the errors distribut long the direction of 
latitude. So it is not feasible to take the earth’s surface as 
spherical surface in that area coverage . 
Picture 4 DEM comparisons true DEM with DEM taken 
ellipsoidal radius as constant. 
Picture 3 : Variation of earth’s mean redius of curvature with 
change of latitude