AI-GEOSTATS: re: sampling
I agree with both Marcel and Don that the first question, before any sampling strategy can be chosen, should be what the data is going to be used for, i.e. what is the sampling objective. Of course, Marcel was talking from a mining perspective, I am talking from a soil science perspective. In my sampling optimization software, I tried to include as many different optimization criteria as possible. There are at least three fundamentallydifferent objectives for spatial studies that I have come across: 1) to describe spatial variability. Sometimes finding certain variogram parameters can be an aim by itself (e.g. to detect periodicity or anisotropy). In my opinion, this might be one of the most difficult optimization criteria to formulate (although some people definitely tried, Don among others in a 1987 paper). 2) to optimize spatial interpolation. In my case, this would be important in precision agriculture, in order to produce high quality maps of soil/crop parameters and use those for remedial action. My previous e-mail was mainly focussed on this - minimizing the kriging variance is one of the optimization criteria you could try for this case. I gave this a shot in my Geoderma papers that I referred to earlier. 3) to detect hot-spots or low-spots. In my case, this is very important in soil pollution studies, where your very precisely want to delineate polluted areas (because remediation costs money, and there are health risks involved), but you are not very interested in the areas that are well below the environmental threshold. I suspect that this is quite often the case in minin studies. I tried to tackle this sort of optimization criterion in my environmetrics paper. Of course, one cannot always go without the other. In order to optimize spatial interpolation, you probably need at least an indication of the nature of the spatial variability, and preferably a variogram. I agree with Don that a phased approach is probably best for such cases. However, I don't think I would go for a purely random approach. In my case, I would probably in the first stage lay out a coarse grid over the whole area, and include some short-distance observations (either randomly selected, or somehow clustered). This should give me an idea about the nature of the spatial variability, which I could use to optimize my second stage, additional sampling scheme for minimal kriging variance. Also, the spatial simulated annealing algorithm would allow me to make full use of the first stage samples. Hope this helps, JW. ** Jan Willem van Groenigen University of California - Davis Dept. of Agronomy and Range Science 1 Shield Avenue Davis, CA 95616 - 8515, U.S.A. -- e-mail: [EMAIL PROTECTED] http://agronomy.ucdavis.edu/groenigen tel. (530) 752-3457 fax. (530) 752-4361 * -- * 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
AI-GEOSTATS: Samples in a block
Hi Mark, it seems you have already realized the paradox of sampling in geostatistics: the more you know about the variable in question, the better you can optimize a sampling scheme for it. It isn't easy to break out of this paradox, and that's probably the reason that sampling has received relatively little attention in the geostatistical literature. You will not find much about it in most textbooks. You have probably already found a number of papers by Webster and McBratney from the beginning of the 80's (mainly in the Journal of Soil Science, I think). They described an algorithm for calculating the optimum grid spacing for a sampling scheme, given the maximum allowed kriging variance and a variogram. These papers, although relatively old, are still often quoted. Another paper from those days dealing with the optimal type of grid is Yfantis, E.A., Flatman, G.T. and Behar, J.V., 1987. Efficiency of kriging estimation for square, triangular and hexagonal grids. Mathematical Geology, 19(3): 183-205. I normally don't like to advertize my own work this much, but hey this was my Ph.D. thesis. I developed a simulated annealing - based algorithm that (among other things) optimizes for the same criterion as the Webster/McBratney papers, but that optimizes the optimal location of individual points, rather than optimal grid spacing. Although this might not be very useful in large, contiguous sampling areas, it considerably improves your sampling efficiency when you already have preliminary samples and/or many sampling constraints. Again, you need (to assume) a variogram. A couple of references to my work: -Van Groenigen, J.W. and Stein, A., 1998. Constrained optimization of spatial sampling using continuous simulated annealing. Journal of Environmental Quality, 27(5): 1078-1086. -Van Groenigen, J.W., Siderius, W. and Stein, A., 1999. Constrained optimisation of soil sampling for minimisation of the kriging variance. Geoderma, 87: 239-259. -Van Groenigen, J.W., Pieters, G. and Stein, A., 2000. Optimizing spatial sampling for multivariate contamination in urban areas. Environmetrics, 11: 227-244. Also, you can download a preliminary software implementation of this algorithm from my website (see below). Of course, there is a lot a controversy in the geostatistical community about the use of kriging variance as a measure for interpolation error, since it does not take into account the actual values of the measured variable, which can give you problems when the intrinsic hypothesis doesn't hold (and it often doesn't). Although this has some truth to it, my philosophy is that that is exactly what makes it interesting for sampling optimization, since you don't have those values before sampling anyway However, the last of my references used an optimization criterion that doesn't involve kriging variance. Cheers, Jan Willem. ** Jan Willem van Groenigen University of California - Davis Dept. of Agronomy and Range Science 1 Shield Avenue Davis, CA 95616 - 8515, U.S.A. -- e-mail: [EMAIL PROTECTED] http://agronomy.ucdavis.edu/groenigen tel. (530) 752-3457 fax. (530) 752-4361 * -- * 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: spatial stats in ecology
Hi Tom, just a few thoughts from your neighbours at UC Davis. Is there any particular rule of thumb I should follow...or am I in the realm of opinion. I think that a lot of subjects in geostatistics are in the realm of opinion, and I'm sure you will receive many from the list' participants. Without having looked at your data at all, I think you should probably do some sort of transformation (lognormal or indicator) on your data, in order to normalize your dataset. I think that other members will probably recommend some papers or texts on that subject. If not, you can always send me an e-mail. I was, however, more interested in your research itself. We recently got a paper accepted for Soil Science Society of America Journal, entitled 'short-range spatial variability of nitrogen fixation by chickpea'. Although this is a study in an agroecosystem rather than a natural one, it might be of interest to you. In short, we measured N-fixation using the N15 natural abundance isotope dilution method, and tried to relate it to a range of soil factors. We sampled at 0.3 m distance, but the range of spatial variability was extremely short, i.e. 3-4 meters. My guess would be that nodule biomass and type might be even more variable. If you would be interested in a copy of the manuscript, let me know. The prof. I currently work for, Chris van Kessel, has published a number of papers in SSSAJ during the 80-s and 90-s on spatial variability of nitrogen fixation and some related microbiology. I grant that there is not many (if any) geostatistical analysis, but I think these papers might still be of interest to you. He found strong correlations between N fixation and hydrological characteristics. The availability of water controls various crucial processes of the N cycle (denitrification, nitrification, leaching), and will therefore dictate the need for the plant to fixate N. In addition, you need water to transport the inorganic N to the roots. In short, I think it would be a good idea to include hydrology somehow in your analysis, even if it is as simple as elevation. Next to that, I think you should definitely try some multivariate geostatistical techniques (like cokriging), because N fixation is an extremely complex process, controlled by many biotic and abiotic variables that all can vary considerably within a few meters. On a different note, I was interested in the performance of your ion exchange membrane. In another study, we linked N uptake in plants to N availability indices from anion exchange membranes, and compared that to results from total N, mineral N, incubations, hot KCl extractable N, etc. The membrane performed terrible, just total N in the soil was much better (and cheaper). I was wondering what your experiences were. Sorry to divert a bit from the main topic of this list JW. Jan Willem van Groenigen University of California - Davis Dept. of Agronomy and Range Science 1 Shield Avenue Davis, CA 95616 -- * 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
