| Conventionally the scale at which mapped information is presented in earth sciences
reflects the uncertainty in this information. This partly reflects the cartographic
sources of error in printed maps, but also conventions on the amount of underpinning
observation on which the map is based. In soil surveys a convention is that the number
of soil profile observations per unit area of printed map is fixed over a range of
scales. For example, for surveys in the Netherlands, Steur (1961) suggested that there
should be 5 field observations per cm2 of map. Bie and Beckett (1970) showed that
there is a consistent relationship between map scale and the field effort of the soil
survey.
It is now common practice to map variables by geostatistical methods. The output from
kriging can be on the support of the original data (point kriging) or can be upscaled to
‘blocks’ by block kriging. The block kriging prediction is of the spatial mean of the target
variable across a block of specified dimensions. In principle the size of the block on which
data are presented can by varied arbitrarily. In some circumstances the block size may be
determined by operational requirements. However, for general purposes, predictions can be
presented for blocks of any size.
The same variable, sampled at a fixed intensity, could be presented as estimates for blocks
10 x 10 m on one map and 100 x 100 m on another map. The data user might be tempted to
assume that the predictions on smaller blocks provide more information than the larger
blocks. However, the prediction variance of the block mean diminishes with block size so
improvement of the notional resolution of the information is accompanied by a reduction in
its precision. This precision can be quantified by the block kriging variance, however
this on its own may not serve to indicate whether the block size represents a good
compromise between resolution and precision in a particular circumstance such that
the resolution reasonably communicates the uncertainty of information to the data
user.
In this presentation I show how, in place of the block kriging variance, one can use the
model-based correlation between the block kriged estimate and the true spatial mean of the
block as a readilly interpreted measure of the quality of block-kriging predictions. Graphs of
this correlation as a function of block size, for a given sampling configuration,
allow one to assess the suitability of different block sizes in circumstances where
these are not fixed by operational requirements. For example, it would be possible
to determine a new convention by which block kriged predictions are routinely
presented only for block sizes such that the correlation exceeds some threshold
value.
Steur, G.G.L. 1961. Methods of soil survey in use in the Netherlands Soil Survey
Institute. Boor Spade 11, 59–77.
Bie, S.W., Beckett, P.H.T. 1970. The costs of soil survey. Soils and Fertilizers 34, 1–15. |