Re: [ai-geostats] Kriging along streams

[Donald E. Myers]

Additional space-time references


  2003, De Iaco, S, Myers, D.E., and Posa, D., The Linear
Coregionalization Model and the Product-Sum Space-Time Variogram.
Mathematical Geology 35, 25-38
  
  
  2002, S. De Ioca, D.E. Myers and D. Posa, 
Space-time variograms and a funct\
ional form for total air pollution measures. Computational
Statistics and Da\
ta Analysis 41, 311-328.
  
  
  2000, S. De Iaco, D.E. Myers and D. Posa, Total Air Pollution and
Space-Tim
e Modeling. in Monestiez P., Allard D. and Froidevaux R., Eds, geoENV
III, Geostatistics for Environmental Applications, Kluwer Academic
Publ., 45-56
  
  
  
  2002, D.E. Myers, Space-time correlation models and contaminant
plumes. 
Environmetrics 13, 535-554 (papers from the Fourth Int. Conference
on Envi
ronmetrics and Chemometrics, Las Vegas, NV Sept. 2000)
  2002, S. De Iaco, D.E. Myers and D. Posa, Nonseparable space-time
covariance models:some parametric families. Mathematical Geology
34, 23-42
  
  2002,
D.E. Myers, S. De Iaco, D. Posa and L. De Cesare, Space-Time
Radial Basis Functions, in a special
issue of 
Computers and Math. Applications34, 539-549
  
  

   2000, L. De Cesare, D.E. Myers and D. Posa, 
FORTRAN Programs for Space-Time\ Modeling.ACM
citation Computers  Geosciences28, 205-212
  2001, 
S. De Iaco, D.E. Myers and D. Posa,Space-time
analysis using a general product-sum model. Statistics and
Probability Letters 52, 1, 21-28.
  
  2001, 
L. De Cesare, D.E. Myers and D. Posa, 
Estimating and Modeling Space-Time Correlation Structures, Statistics
and Probability Letters 51/1, 9-14
  
  
  
  2000, L. De Cesare, D.E. Myers and D. Posa, Product-sum
covariance for space-time modeling: an environmental application. Environmetrics12,
11-23
  
  
  1997, L. De Cesare, D. E. Myers and D. Posa, Spatial Temporal
Modeling
of SO2 in the Milan District. in Geostatistics Wollong '96,
E.Y. Baafi and N.A. Schofield (eds), Kluwer academic Publishers,
1031-1042
  

Also see Cressie-Huang in JASA and Gneiting in JASA

Donald E. Myers

Noemi Barabas wrote:

  Dear Oscar,

It sounds like you need kriging in a single dimension.  If so, I think what
you need to do is a kind of coordinate transformation, for example using
river mile as your distance vector.  You would also need to pay attention to
the dates of the samples.  Variation in time might obscure spatial trends
along the river's course if you just have a few sampling events at different
times for the stations.  

If you have data in space as well as time, there are several methods for
space-time interpolation.  Constructing correlograms for data vs time on
paired stations could give you an idea of what constitutes a data pair for
kriging purposes in terms of the time lag between them.  Methods will differ
depending on whether it is the time or space dimension that is more densely
sampled.

References on techniques include the following:

For straightening rivers (which might be more involved than you need):

Barabas, N., Goovaerts, P. and P. Adriaens. 2001. Geostatistical assessment
and validation of uncertainty for three-dimensional dioxin data from
sediments in an estuarine river. Environmental Science  Technology, 35(16):
3294-3301. 

For space-time data:

Pebesma and de Kwaadsteniet (1997) Mapping spatial and temporal variation of
groundwater quality in the Netherlands.  In GeoENVI - Geostatistics for
Environmental Applications, eds., Soares et al, pp. 139-151.  Kluwer
Academic Publishers, Netherlands.

Kyriakidis and Journel (1999) Geostatistical space-time models: A review.
Mathematical Geology (not sure which volume etc.)

Heuvelink et al (1996) Spatio-temporal kriging of soil water content. In
Geostatistics Wollongong '96, eds Baafi and Schofield. pp. 1020-1030.
Kluwer Academic Publishers,Netherlands.


Nomi



-Original Message-
From: oscar garcia [mailto:[EMAIL PROTECTED]]
Sent: Thursday, February 24, 2005 11:56 AM
To: ai-geostats@unil.ch
Subject: [ai-geostats] Kriging along streams


Dear list members,

I want to perform kriging of water quality indicators
measured in stations along a river course, so Can you
help me with references about kriging along streams in
a river basin?? is there software to perform this kind
of analysis??? 

Thanks in advance for your help,

Oscar Javier Garca-Cabrejo
Master in Hydrosystems, Civil Engineering Department
Pontificia Universidad Javeriana 
Bogota, Colombia
South America

_
Do You Yahoo!?
La mejor conexin a internet y 25MB extra a tu correo por $100 al mes.
http://net.yahoo.com.mx


  
  

* By using the ai-geostats mailing list you agree to follow its rules 
( see http://www.ai-geostats.org/help_ai-geostats.htm )

* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED]

Signoff ai-geostats



* By using the ai-geostats mailing list you agree to follow its rules 
( see http://www.ai

[ai-geostats] Continuing discussion on F and t tests

[Donald E. Myers]

The sample variance (assuming that you use the n-1 divisor) is an 
unbiased estimator of the population variance provided you use random 
sampling. Note the ing on the word sampling,  it is not quite correct 
to talk about random samples or independent samples. or at least it 
may be mis-leading. Random sampling pertains to how the data is 
collected, not the end result.

Note moreover that one can always compute a sample variance for a given 
data set but this does not show that the random variable or random 
function has a finite variance.

The sample variance (even when sampling from a normal population) is 
relatively speaking more variable as an estimator of the variance than 
the sample mean is as an estimator of the population mean.  The sampling 
distribution in this restricted case is chi-square, the chi-square 
distribution has a fat tail (as contrasted with a normal distribution).

If correctly (or maybe you would want to say adequately ) estimated, 
the sill of a second order stationary random function would be the 
variance of the random function. In general, the sample variance will 
not estimate the sill (because you are not using random sampling).

Donald Myers
http://www.u.arizona.edu/~donaldm
* By using the ai-geostats mailing list you agree to follow its rules 
( see http://www.ai-geostats.org/help_ai-geostats.htm )

* To unsubscribe to ai-geostats, send the following in the subject or in the 
body (plain text format) of an email message to [EMAIL PROTECTED]

Signoff ai-geostats

AI-GEOSTATS: re:samples in a block

[Donald E. Myers]

Unfortunately as Mark has noted, if nothing is known then one will have
to design a sampling plan using other criteriia, i.e., essentially
meaning non-statistical criteria.

Even if there were no spatial correlation and one only wanted to
estimate the average value for the block one would need the variance. In
such a case one might iterate, i.e., randomly select sample locations
(the number being determined perhaps by budget and difficulty of
sampling). After sampling at those locations, compute the sample
variance and use this to predict a sample size (which will almost
certainly be larger than the original size). One can of course use the
data obtained at this stage to estimate the mean and also obtain a
confidence interval, the new sample size will be related to the desired
confidence interval width and desired confidence level. Having
determined a new sample size, repeat the process (combining the
original sample with the new data would not correspond to random
sampling), if after several iterations it appears that the predicted
sample size stablizes then you are through. Note that this process only
focuses on the number of sample locations, the actual locations being
selected randomly.

This process can be improved on by using the theory of sequential
sampling.

With respect to geostatistics, we need to remember that the data (in
common practice) is used for two different purposes.The first being the
estimation/modeling of the variogram or covariance function, the second
being the kriging (of whatever form or type). An optimal sampling plan
for the one will generally not be an optimal plan for the other.

There is an old issue of GEOSTATISTICS, the NACOG newsletter, that has
a long list of papers on sampling design. A number of papers have been
written since then as well. There is no definitive answer to the
question since it depends on the question, i.e., what is the data to be
used for?

Donald E. Myers
Department of Mathematics
University of Arizona
Tucson, AZ 85721
http://www.u.arizona.edu/~donaldm


--
* To post a message to the list, send it to [EMAIL PROTECTED]
* As a general service to the users, please remember to post a summary of any useful 
responses to your questions.
* To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe 
ai-geostats followed by end on the next line in the message body. DO NOT SEND 
Subscribe/Unsubscribe requests to the list
* Support to the list is provided at http://www.ai-geostats.org