Dear Recep
You provided an example where the variability is order of magnitude
change. Yes, infiltration rate might vary from one point to
another even for two points very close to each other. Here, the initial
condition is very important for quantifying infiltration rate. If you
found a difference for two points near each other, you cannot say for sure
whether it is due to error in measurement or change in initial
condition(s) or ..... Furthermore, you are working with a spatiotemporal
process not a spatial process. At the very beginning, infiltration rate
may be governed by rainfall timing and then by soil. One has to be very
careful when he or she is resorting to replication to minimize random
error. BTW, by replication, you CANNOT delineate and finally eliminate
systematic error. Replication can only delineate and possibly eliminate
random error.
I made a cc to the list for their possible consideration and feedback.
Thanks
Abedini
On Sun, 26 Feb 2006, Recep kantarci wrote:
Dear Prof. Abedini
Thak you very much for the reply.
Please let me ask the question more specifically.
Assume that you are planning to measure a parameter, say soil infiltration
rate, at some spatial locations in a field, then to estimate the value of this
parameter at unsampled locations. On the other hand, you are thinking that
while measuring this parameter in the field, you are worrying about that you
can do a measurement error due to human or instrument. In order to minimize to
this measurement error at any spatial location, you repeat the measurement
several times at locations very close to target location, assuming that these
several locations have the same conditions with the target location, then
compare the results and discard, if exists, the extreme one, then take the
aritmatic average of the rest, take this as the value of the parameter for the
target location.
For example, if you have 30 target locations and you do this procedure for
all target location, 2 more times for each target location, then you will have
90 number of data for 30 target location.
Does this make sense in geostatistical concepts? Or, is this logical?
best regards
Recep
"M.J. Abedini" <[EMAIL PROTECTED]> yazd??:
Recep
In classical statistics, your data have to satisfy the following two basic
assumptions:
1. Identically Distributed (ID): This assumption implies that you can
repeat the experiment infinite number of times UNDER the same
condition(s).
2. Independent (I): The result of each experiment will be independent from
previous and next trials.
Sometimes, statisticians refer to these two assumptions as IID assumptions.
Unfortunately, none of earth science data satisfies these two assumptions.
One cannot measure rainfall at a single spatial point several times under
the same condition(s). Even though, one may conceptualize the whole domain
to be generated by a random function (i.e., a collection of random
variables), one cannot characterize this random function as only ONE
realization of this RF is available. As such, one has to imposed various
assumptions such as isotropy, stationarity and ergodicity to be able to
exit this dead end. You may want to refer to archieve (previous postings)
to get more info. regarding your original enquiry. In short, replication
has no meaning in earth science data because you cannot keep the
situation for two experiments similar.
Hope this helps.
Thanks
Abedini
On Mon, 20 Feb 2006, Recep kantarci wrote:
Dear list members
My question is about the practice of replications.
As you know, in order to avoid measurement/analysis errors, one may wish to
replicate his/her measurement at the same spatial point in the field or his/her
analysis for the same sample in the laboratory many times. For example, it is a
usual practice to do three times, and discard the extreme one, if exists, then
take the average of the rest.
How can we use or treat these kind of replicated data for the same spatial
point within framework of geostatistical concepts?
Reagrds
Recep
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