



QUADRAT, CENTER  Point Pattern Analysis 

AUTOCORR  Spatial Autocorrelation 
Now what is interpolation all about? These are geostatistical ways to estimate information for locations without such, by founding on known surrounding values. Easy to understand the concept, if you imagine height points for some area which you gathered in the field using modern GPS (Global Positioning System). By interpolating between the known height spots you try to build a continuous surface, a DEM. Or you already have some analog maps showing the elevation isolines  again you could rely on known values (in that case: the height lines) to interpolate the unknown elevation between them.
Getting some results is quite easy  indeed a matter of doing a few clicks!
Our computer works hard and the outputs often look very reasonable at the first glance.
 But: what did we really get? how reliable are the values compared to reality??
What may sound as a simple task has more but one trap! To achieve good results one has
to be very careful in choosing the 'right' interpolation method and in interpreting
the outputs. Those of you interested in underlying algorithms, read David F. WATSON:
'Contouring: A Guide to the Analysis and Display of Spatial Data' (Pergamon Press,
Oxford 1992) or Edward H. ISAAKS & R. Mohan SRIVASTAVA 'Applied Geostatistics' (Oxford Univ.
Press, Oxford 1989) among several others.
To give an example (very simplified): following you see a map of 453 point locations in the City of Salzburg with the attribute: number of different lichen species at this point (lichens are those strange plant organisms made up from some kind of symbiotic livingtogether fungus with algae :); rather valuable bioindicators!). For the ease of demonstration we make the assumption, that habitat quality is positively correlated with the number of different lichen species per location (data from collection in 1982, ZIEGELBERGER & TÜRK, Salzburg Univ., Dept. of Plantphysiology)
Now let us compute the trendimages:
linear, quadratic, cubic
(red = less species / green = more
species per sample location)
IDRISI finishes the TRENDcalculation by presenting you some statistics (Goodness of
fit, F ratio, degrees of freedom, ...) that can be compared between different trend orders to
proof for the significance. Goodness of fit tells about the 'amount of variation explained' through the 'fit'. It is computed by examining the residuals:
z_{i} ... observed values
... modelpredicted values
... mean of observed values
The above images show a very general pattern of the lichen distribution. Note the increasing complexity from the simple linear (left) to the cubic (right) surface. The quadratic (middle) and the cubic trend images seem to indicate a center of lower species counts in the northern half of the City of Salzburg, which very coarse reflects the situation in reality. But if you focus on the lower left corner of the right result you will notice a zone of apparently lower species counts. It is evident, that there are very few measure points arround, so extrapolation will occur, which makes this results very doubtful.
IDW: look at the formula and the line chart below  we calculate estimates of unknown values dependent on neighbouring known values. The distance acts as weight and its exponent allows further adjustment of that weight: the higher the distance exponent, the higher the influence of the nearest known feature value:
... interpolated zvalue
d ... distance from known point i
z ... zvalue of known point i
p ... distance weight exponent
n ... number of points to be included in search (in IDRISI: sixonaverage or all)
i ... number of known value points to be taken into account
These are just six random choosen sample distance values. They indicate the distance from the point to be estimated to the next six known value points in ascending order (the weights have been standardized). Note how the weights of the different distances diverge with
higher exponents.
The dialog box of INTERPOL:
The decision, which parameter combination to use isn't always easy. Look the results over very critical. Here's an excerpt from the IDRISI for WINDOWS Help on the INTERPOL function:
Do not assume that because a computer has done the interpolation that it has any strong claim to accuracy. There are
many interpolation procedures, appropriate for different surface characteristics, and this is only one. The
weightedaverage technique used produces quite smooth surfaces with maxima and minima occurring at the locations of
control points. As one moves away from these control points, the surface will tend towards the local average height,
where local is determined by the search radius.
See an example:




QUADRAT, CENTER  Point Pattern Analysis 

AUTOCORR  Spatial Autocorrelation 
last modified:  Comments to Eric J. LORUP idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis idrisi resource center idrisi gis idrisi gis