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1934RE: [ai-geostats] Kriging along streams

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  • Noemi Barabas
    Feb 24, 2005
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      You are right about river networks.

      I do think that the uni-directionality of flow is not necessarily a problem
      in terms of what can inform what. Statistically, a downstream station can
      inform an upstream station because what is downstream is there because of
      what happened upstream, and the same for past and future. While there may
      not be a *physical* link from future to past, there will still be a
      *statistical* link from future to past as long as there was a statistical
      link from past to future. [That is the idea in inverse modeling for example
      (which are a combination of physical and statistical modeling)].

      Intuitively, kriging backwards might have to be done according to a
      different model than forward, but, I am open to surprises. It is worth a
      try, anyway.


      -----Original Message-----
      From: Edzer J. Pebesma [mailto:e.pebesma@...]
      Sent: Thursday, February 24, 2005 5:19 PM
      To: Noemi Barabas
      Cc: oscar garcia; ai-geostats@...
      Subject: Re: [ai-geostats] Kriging along streams

      Noemi, the idea of transforming to a one-dimensional situation,
      distance along river, was the first one I got. Then, I rejected
      it because it will not work for river networks; it will for a
      single sections without joints though. Space-time modelling may
      be complicated by the fact that there will be a strong
      correlation with future observations downstream, but not with
      observations upstream because water flows down; this may call
      for another translation of space-time using flow speed to get
      to a space-time coordinate system where the usual models make

      Noemi Barabas wrote:
      > Dear Oscar,
      > It sounds like you need kriging in a single dimension. If so, I think
      > 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
      > 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
      > 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
      > depending on whether it is the time or space dimension that is more
      > 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
      > and validation of uncertainty for three-dimensional dioxin data from
      > sediments in an estuarine river. Environmental Science & Technology,
      > 3294-3301.
      > For space-time data:
      > Pebesma and de Kwaadsteniet (1997) Mapping spatial and temporal variation
      > 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.
      > Noémi
      > -----Original Message-----
      > From: oscar garcia [mailto:osgarcia@...]
      > Sent: Thursday, February 24, 2005 11:56 AM
      > To: ai-geostats@...
      > 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 García-Cabrejo
      > Master in Hydrosystems, Civil Engineering Department
      > Pontificia Universidad Javeriana
      > Bogota, Colombia
      > South America
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