AI-GEOSTATS: Re: polygon kriging
What a lot of work when you can just krige the poygon directly! Try polygon kriging with my absolutely free, public domain, kriging game which works with any data set in a suitable format. This Windows based program provides he kriging equations and weights for the solution, so you can see how things work. Download from http://geoecosse.bizland.co/softwares along with tutorial data sets. Isobel --- Pierre Goovaerts <[EMAIL PROTECTED]> wrote: > Dear Lorenz, > > The easiest way to proceed would be to discretize > your polygon > using a grid, use stochastic simulation to simulate > values within > the polygon, and estimate the block value as the > arithmetical average > of these simulated point values. > > The advantage is that you can empirically estimate > the variance of > your block estimate from the distribution of > simulated block values. > > It would be fairly easy to implement this procedure > using gslib > simulation routines. You just need to make sure that > only the > grid nodes within the boundaries of the polygon are > being simulated > (you can not just simulate a rectangular grid and a > posteriori > eliminate the values simulated outside the limits). > This requires > a "if statement" inside sgsim or sisim to skip any > grid node > falling outside the boundarie (just define a grid of > indicator values > that would be one if inside and zero if outside the > limits of > the polygon, and read this grid at the beginning of > the simulation). > > Best regards, > > Pierre > <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> > > Dr. Pierre Goovaerts > President of PGeostat, LLC > Chief Scientist with Biomedware Inc. > 710 Ridgemont Lane > Ann Arbor, Michigan, 48103-1535, U.S.A. > > E-mail: [EMAIL PROTECTED] > Phone: (734) 668-9900 > Fax: (734) 668-7788 > http://alumni.engin.umich.edu/~goovaert/ > > <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> > > On Fri, 20 Feb 2004, Lorenz Dobler wrote: > > > hello list, > > > > i would like to assign the principles of > block-kriging to user defined > > (=irregular) polygons. some questions about it: > > > > 1. what do you think about this idea ? > > 2. is there any software that can do this allready > ? > > 3. does anyone of you have practical experiences > with this approach ? > > 4. is there a realistic possibility to change > existing gslib libraries to do > > kriging with irregular polygons instead of regular > blocks (problem: finding > > center [of gravity] for each irregular polygon and > defining appropriate > > search neigbourhood !!) ? > > > > hope someone can help > > > > kind regards > > > > Lenz Dobler > > > > Universität Münster > > Institut für Geoinformatik > > Robert-Koch-Strasse 26-28 > > D-48149 Münster > > > > Tel.: 0251/83-30089 > > Fax: 0251/83-39763 > > email: [EMAIL PROTECTED] > > > > > > -- > > * 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 > > > > > > > -- > * To post a message to the list, send it to > > * 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 ___ Yahoo! Messenger - Communicate instantly..."Ping" your friends today! Download Messenger Now http://uk.messenger.yahoo.com/download/index.html -- * 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
Re: AI-GEOSTATS: Re: polygon kriging
Following Pierre and Isobel's replies, an alternative way is to use a GIS. You may do the kriging (or another method) in the ordinary way, and then overlay your interpolated surface with your polygons. Each of the irregular polygons should cover several (or tens or hundreds or more, depending on the resolution of your grid) values from your interpolated surface, and then you can do whatever calculation you like (mean, min, max, stddev, ...). Of course you need to be aware that all these values are "interpolated/predicted", not real values. Cheers, Chaosheng --Dr. Chaosheng ZhangLecturer in GISDepartment of GeographyNational University of Ireland, GalwayIRELANDTel: +353-91-524411 x 2375Fax: +353-91-525700E-mail: [EMAIL PROTECTED]Web 1: www.nuigalway.ie/geography/zhang.htmlWeb 2: www.nuigalway.ie/geography/gis/index.htm - Original Message - From: "Isobel Clark" <[EMAIL PROTECTED]> To: "Pierre Goovaerts" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Saturday, February 21, 2004 6:41 PM Subject: AI-GEOSTATS: Re: polygon kriging > What a lot of work when you can just krige the poygon> directly! > > Try polygon kriging with my absolutely free, public> domain, kriging game which works with any data set in> a suitable format. This Windows based program provides> he kriging equations and weights for the solution, so> you can see how things work. Download from> http://geoecosse.bizland.co/softwares along with> tutorial data sets. > > Isobel> > > --- Pierre Goovaerts <[EMAIL PROTECTED]>> wrote: > Dear Lorenz,> > > > The easiest way to proceed would be to discretize> > your polygon> > using a grid, use stochastic simulation to simulate> > values within> > the polygon, and estimate the block value as the> > arithmetical average> > of these simulated point values.> > > > The advantage is that you can empirically estimate> > the variance of> > your block estimate from the distribution of> > simulated block values.> > > > It would be fairly easy to implement this procedure> > using gslib> > simulation routines. You just need to make sure that> > only the> > grid nodes within the boundaries of the polygon are> > being simulated> > (you can not just simulate a rectangular grid and a> > posteriori> > eliminate the values simulated outside the limits).> > This requires> > a "if statement" inside sgsim or sisim to skip any> > grid node> > falling outside the boundarie (just define a grid of> > indicator values> > that would be one if inside and zero if outside the> > limits of> > the polygon, and read this grid at the beginning of> > the simulation).> > > > Best regards,> > > > Pierre> >> <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>> > > > Dr. Pierre Goovaerts> > President of PGeostat, LLC> > Chief Scientist with Biomedware Inc.> > 710 Ridgemont Lane> > Ann Arbor, Michigan, 48103-1535, U.S.A.> > > > E-mail: [EMAIL PROTECTED]> > Phone: (734) 668-9900> > Fax: (734) 668-7788> > http://alumni.engin.umich.edu/~goovaert/> > > >> <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>> > > > On Fri, 20 Feb 2004, Lorenz Dobler wrote:> > > > > hello list,> > >> > > i would like to assign the principles of> > block-kriging to user defined> > > (=irregular) polygons. some questions about it:> > >> > > 1. what do you think about this idea ?> > > 2. is there any software that can do this allready> > ?> > > 3. does anyone of you have practical experiences> > with this approach ?> > > 4. is there a realistic possibility to change> > existing gslib libraries to do> > > kriging with irregular polygons instead of regular> > blocks (problem: finding> >
Re: AI-GEOSTATS: Re: polygon kriging
Chaosheng This is very true that if you grid a grid of points inside a polygonal area then average them, you get exactly the same answer as if you kriged the polygon average directly. The differences are two: (1) you have to do at least 64 krigings to get within 1% of the correct average answer (see my paper at the first Geostat Congress in 1975) (2) if you do one kriging for the polygon average, you get the kriging variance for the polygon average. You can derive this from the discretised point kriging variances but you have to do even more work (64 squared) than in (1). Isobel http://geoecosse.bizland.com/whatsnew.htm ___ Yahoo! Messenger - Communicate instantly..."Ping" your friends today! Download Messenger Now http://uk.messenger.yahoo.com/download/index.html -- * 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
