How big are the raster cells of the resulting raster you are calculating?
I am asking this because there is one thing you need to realize: there *usually* is a difference between your sample points locations and the raster cell's centres. It is actually the raster cell's centres that are being calculated. So although the fitted mathematical curve should pass exactly through the data points, any cell below a sample point that doesn't have an exact match between its centre and the sample point, may result in a cell value different from the sample point.
This issue will be more pronounced (and the differences between the sample points value and the estimated / calculated cell value bigger) with larger cell sizes.
Just to visualize this: imagine a soccer pitch as being a cell: the centre point of the pitch is the actual point that is being estimated in the interpolation. Now your soccer player (the sample point), might actually be in completely different position, e.g. near one of the goals, resulting in a difference between sample points value and the estimated cell.
How big are the raster cells of the resulting raster you are calculating?
I am asking this because there is one thing you need to realize: there *usually* is a difference between your sample points locations and the raster cell's centres. It is actually the raster cell's centres that are being calculated. So although the fitted mathematical curve should pass exactly through the data points, any cell below a sample point that doesn't have an exact match between its centre and the sample point, may result in a cell value different from the sample point.
This issue will be more pronounced (and the differences between the sample points value and the estimated / calculated cell value bigger) with larger cell sizes.
Just to visualize this: imagine a soccer pitch as being a cell: the centre point of the pitch is the actual point that is being estimated in the interpolation. Now your soccer player (the sample point), might actually be in completely different position, e.g. near one of the goals, resulting in a difference between sample points value and the estimated cell.
Below is my understanding of this issue. Correct me if i am wrong.
My cell size is 20m because of large area coverage.
Although my sample point might deviate from the center point of the raster cell, unless the cell itself is a rubber and it can bend itself, otherwise no matter where my sample point located in the cell, its estimated value should equal to itself value which is also the center point value because this cell passing through this point when modeling.
If it is true by saying "there *usually* is a difference between your sample points locations and the raster cell's centres. It is actually the raster cell's centres that are being calculated. ". Under this circumstance, the spline will not pass the sample point? because of the distance between the sample pt and raster center? so the algrithim will not be followed?
The bold text is a misunderstanding of the process of Spline interpolation. In fact, the sentence just before it "unless the cell itself is a rubber and it can bend itself" is closer to reality. During the actual interpolation, there IS NO raster, there is just the mathematical equations and the surface being bend with the sample points as a kind of "control points" restricting the process. Only after the actual interpolation, will a raster be generated from the mathematical surface. This means the values of sample points, and the final raster cells who's centres need to be determined / estimated from the computed surface, can and will deviate from each other UNLESS the sample point happens to be EXACTLY in the centre of a raster cell (which is an extremely rare case).
This is again a misunderstanding, the spline function will pass through the sample points, no matter what.
the smaller the cell size is, the closer the raster surface will be to the the mathmatical result, right?
So in theory i can get a very detailed raster surface (forget about the interpolated errors) even with small amount of input point data right?
Jason
So in theory i can get a very detailed raster surface (forget about the interpolated errors) even with small amount of input point data right?
Jason
No, the raster cells will always conform to the mathematical result.
*With this I mean the raster cell's centre!*, but since the raster cell's centre is the value assigned to the cell, you could say the entire cell conforms to the mathematical result.
But of course, the smaller the cells, the more the resulting raster will "look" like the computed surface if you could view both in 3D, and this is what you probably meant to say. The raster is a kind of pixelated approximation of the true computed surface.
Don't equate a "very detailed raster with small cell size" to being an accurate / reliable raster... Cell size is arbitrary in terms of accuracy, it is just a property of the output you set during the interpolation.
The more sample points you have, the better your estimate will be, so to increase the accuracy / reliability of the raster, you need more sample points, not necessarily a finer raster with smaller cell size (although setting a big cell size also doesn't make sense)
By the way, a nice introduction to interpolation methods is "Geostatistics Without Tears" by Gregg Babish. See this post:
http://forums.arcgis.com/threads/95588-Simple-Kriging-question-please-help!!?p=339687&viewfull=1#pos...