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" <abedini@...> yazdÄ±:

> 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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>

>

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