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	Kriging Interpolation
		The goal of this project is to implement an ordinary kriging module for IBM Data Explorer 2.0 using C language.
		Kriging is also the method that is associated with the acronym B.L.U.E. best linear unbiased estimator.) It is "linear" since the estimated values are weighted linear combinations of the available data.
		The difference of kriging and other linear estimation method is its aim of minimizing the error variance.
	www.nbb.cornell.edu /neurobio/land/OldStudentProjects/cs490-94to95/clang/kriging.html (1064 words)

	GIS in Public Health - Kriging
		Overview of Kriging Methodology: Kriging is a statistical technique that posits a certain statistical model for the data, namely that the response at a given location is the sum of two components: an unknown underlying surface, which we are trying to estimate, plus some additional noise.
		Kriging produces an estimate of the underlying (usually assumed to be smooth) surface by a weighted average of the data, with weights declining with distance between the point at which the surface is being estimated and the locations of the data points.
		Among the advantages of the implementation of kriging in Geostatistical Analyst relative to that in Spatial Analyst are the ability to use the Matern covariance model favored by many statisticians, the ability to handle directionality in the data, and the ability to make plots of prediction errors as a way of assessing uncertainty.
	www.hsph.harvard.edu /biostats/research/divisions/env_stat/GISinLMA/kriging.htm (2346 words)

	Kriging
		Kriging provides a means of interpolating values for points not physically sampled using knowledge about the underlying spatial relationships in a data set to do so.
		Kriging is based on regionalized variable theory and is superior to other means of interpolation because it provides an optimal interpolation estimate for a given coordinate location.
		Kriging with an external drift is an extension of kriging with trend.
	www.gammadesign.com /GSWinHelp/kriging_and_cokriging/kriging.htm (569 words)

	Recursive Spatio-Temporal Function Estimation
		The stochastic models used in each of these methods are combined into a state equation representation we call the "kriging update model" that permits a recursive solution, akin to Kalman filtering, for estimating a function.
		The state equation representation preserves the principle assumption of kriging, that the mean is deterministic but unknown.
		Kriging models a function as z(x) = u(x) + m(x), where u(x) is a zero-mean random component and m(x) is an unknown, deterministic mean function.
	iacl.ece.jhu.edu /projects/filtint (739 words)

	A computer program for interpolation of geohydrologic data using the method of "kriging"
		Although kriging techniques have potential applicability to a variety of fields, we particularly ask that this memo be brought to the attention of those persons involved in ground-water studies.
		The kriging procedure determines the n weights, gamma(subscript i), such that these conditions hold: (1) the estimate is unbiased--in the sense that the average error will be zero for a large number of such estimates, i.e., (see original), where E[] is the expectation; and (2) the variance of the estimation, i.e.
		The criteria used to obtain kriging estimates are that the estimation be unbiased and the variance of the estimation be minimized.
	water.usgs.gov /admin/memo/GW/gw81.01.html (1346 words)

	International Journal of Health Geographics \| Full text \| Exploratory disease mapping: kriging the spatial risk ...
		Furthermore, universal kriging is based on a polynomial trend surface model which is to be removed prior to estimation of the semivariogram from the residuals, i.e.
		Due to the constant mean assumption ordinary kriging is the appropriate spatial prediction method and without nugget effect this leads to direct interpolation of the data at the counties centres and to smoothed values shrunken towards the global mean for the rest of the study area.
		Kriging is known to be a smoothing method and it may be argued that the proposed mapping method results in double or over-smoothing.
	www.ij-healthgeographics.com /content/3/1/18 (5478 words)

	Mathematical Interpolation
		Kriging assigns low weights to distant samples and vice versa, but also takes into account the relative position of the samples to each other and the site or area being estimated.
		Indicator kriging is used when it is desired to estimate a distribution of values within an area rather than just the mean value of an area.
		Ordinary kriging was selected for this study based on how well it has performed on prior years data and because the statistical characteristics of the data in 2000 and 2003 make Ordinary Kriging the appropriate choice of estimator.
	www.asl-associates.com /kriging.htm (2016 words)

	USGS Open-File Report 2004-1026_sec4
		Kriging techniques assume the source data have regionalized errors of estimation and generalize the data to minimize estimation variance.
		Kriging tends to eliminate local anomalies from the interpolation grid to portray a more general trend for the data.
		The use of universal kriging in this geochemical study is supported by the geochemical variation in the stream sediment and water chemistry data categorized by bedrock lithology group across the study area (box plots by bedrock lithology in Section 6.0).
	pubs.usgs.gov /of/2004/1026/geochem_4.htm (1733 words)

	WWRC 96-04 : Estimation of Mean Annual Precipitation in Wyoming Using Geostatistical Analysis
		Kriging with external drift represents the kriging estimate Z*(x) as a sum of a trend component m(x) and a residual R(x), where the trend component m(x) is a linear function of the external drift variable y(x):
		Since external drift kriging with three topographical variables and geographical coordinates produced the best cross-validation results, it was used as a procedure to construct the precipitation distribution maps of the subregions and the entire state.
		Mean kriging variances obtained from the external drift kriging with topographical information and geographical coordinates for subregions were equal to 4.29, 4.10, 1.78 and 5.41 for the northeastern, northwestern, southeastern and southwester subregions, respectively.
	library.wrds.uwyo.edu /wrp/96-04/96-04.html (2411 words)

	KRIGING
		Kriging is the estimation procedure used in geostatistics using known values and a semivariogram to determine unknown values.
		A variety of kriging which assumes that local means are not necessarily closely related to the population mean, and which therefore uses only the samples in the local neighborhood for the estimate.
		The kriged estimate for a point will usually be quite similar to the kriged estimate for a relatively small block centered on the point, but the computed kriging standard deviation will be higher.
	ewr.cee.vt.edu /environmental/teach/smprimer/kriging/kriging.html (1687 words)

	SAS FAQ: How can I perform spatial Kriging in SAS?
		Kriging is a technique used in the analysis of spatial data.
		It is not rigorous in its presentation of kriging nor exhaustive in its presentation of proc krige2d, but hopefully illustrates the basic use of the technique and procedure.
		In ordinary kriging, we allow the variable values from the measured locations to act as covariates for the values at unmeasured locations.
	www.ats.ucla.edu /stat/sas/faq/SAS_kriging.htm (1065 words)

	Air Resource Management
		Kriging is a family of estimators used to interpolate spatial data.
		The choice of which kriging to use depends on the characteristics of the data and the type of spatial model desired.
		The ordinary kriging programs used for this study were modified to calculate the new error variance, named the Ordinary kriging interpolation variance (NKVAR) and output it along with the traditional kriging variance.
	webcam.srs.fs.fed.us /ozone/spatial/kriging.htm (922 words)

	kriging (Site not responding. Last check: )
		This could be desirable if ordinary point kriging results in surfaces that have many sharp spikes or pits at the data points, a phenomenon often occurring when sample values change very fast within short distances.
		Universal kriging can produce good local estimates in the presence of a trend, especially in situations where the estimate is extrapolated rather than interpolated from the local sample values.
		Though universal kriging can calculate a trend automatically, you should resist to use it as a fl box, particularly when it is used to extrapolate beyond the available data.
	sun1.giac.montana.edu /geog501/kriging6.htm (345 words)

	The GLOBEC Kriging Software Package - EasyKrig3
		The parameters of the variogram or correlogram needed in the kriging operation are automatically passed from the Variogram window to the Kriging window.
		Note that the station positions on the kriging map are color-coded to reflect the level of the agreement of the kriged results with the original data.
		There are blank regions on the kriging map, where the normalized kriging variance (normalized by the variance) exceeds specified “Relative Variance”, i.e.
	globec.whoi.edu /software/kriging/easy_krig/easy_krig.html (5603 words)

	MAPKriging.html
		Kriging is an optimal, linear estimation method that produces an UNBIASED, MINIMUM ESTIMATION ERROR VARIANCE estimate of a function of an unknown random field Z(u), The form of the estimator is,
		Following is an example of the application of Kriging in the estimation of the two kinds of functions indicated above.
		Thus, Kriging can be used as an alternative to other commonly used methods for numerical approximation of definite integrals.
	www.engr.colostate.edu /~ramirez/ce_old/classes/ce522_ramirez/MAPKriging1.html (532 words)

	Linear Kriging
		Because the semivariogram is isotropic, the ordinary kriging estimator for the value at any point x in the plane depends on x only through its distances a, b, and c to the three vertices, respectively.
		In the case of kriging with three neighbors, the contours are all infinite in extent, because we cannot simultaneously have all three coefficients 1-2z, z-2, and 1+z greater than or equal to zero.
		It is evident from the form of equation [1] that the kriged surface is continuous everywhere, but it is not necessarily differentiable everywhere: in the example with z=2, the contours for r=0 and r=2 cover the points where the surface does not have a unique slope.
	www.quantdec.com /Articles/geostat/linear.htm (792 words)

	International Journal of Health Geographics \| Full text \| How does Poisson kriging compare to the popular BYM model for ...
		Poisson kriging was combined with stochastic simulation to generate multiple realizations of the spatial distribution of cancer mortality risk, allowing the propagation of uncertainty through the detection of cancer clusters and outliers [24].
		Point Poisson kriging, which assigns each measured rate to the geographic centroid of the unit over which it has been recorded, was later replaced by Area-to-Area (ATA) Poisson kriging that accounts for the geometry of administrative units and the spatial repartition of the population at risk in semivariogram estimation and kriging [25].
		The trade-off cost for the simplicity of Poisson kriging is that, unlike the full Bayesian approach, the uncertainty attached to the parameters of the correlation function is ignored in the analysis, which should lead to smaller prediction variances in general [26].
	www.ij-healthgeographics.com /content/7/1/6 (10492 words)

	Designing optimal sampling configurations with ordinary and indicator kriging
		Kriging is, in basis, a form of weighted average estimator.
		The weights are assigned on the basis on the form of a model fitted to a function, such as the variogram, which represents spatial variability in the property of interest.
		The poor fit of the model at the origin of the variogram is due to the necessity of increasing the nugget variance to prevent negative OK variances.
	www.geovista.psu.edu /sites/geocomp99/Gc99/065/gc_065.htm (3912 words)

	KRIGING
		Kriging is the estimation procedure used in geostatistics using known values and a semivariogram to determine unknown values.
		A variety of kriging which assumes that local means are not necessarily closely related to the population mean, and which therefore uses only the samples in the local neighborhood for the estimate.
		The kriged estimate for a point will usually be quite similar to the kriged estimate for a relatively small block centered on the point, but the computed kriging standard deviation will be higher.
	www.cee.vt.edu /ewr/environmental/teach/smprimer/kriging/kriging.html (1687 words)

	Assesment of Kriging Accuracy in the GIS Environment
		The sensitivity of ordinary Kriging interpolation in the GIS environment was evaluated with respect to the resolution of the predicted grid and conclusions were drawn for applications in spatial analysis.
		In this paper Kriging was applied to a low vacillating elevation data set and the errors from Kriging were evaluated using fundamental statistical parameters such as root mean square error, variance of errors, mean absolute error, etc. In addition, the Kriging errors were compared between two different software systems.
		The ordinary Kriging results from Idrisi and Arc-Info yielded the mean absolute error 8.57 and 8.53 ft. Interpolation from Thiessen polygons indicated the mean absolute error of 9.2 ft and IDW 12.6 ft. The trend surface interpolation error was on average 34.8 feet, the highest error from all interpolation methods.
	gis.esri.com /library/userconf/proc01/professional/papers/pap280/p280.htm (1520 words)

	ArcGIS Geostatistical Analyst Exercise
		Kriging was developed in the 1960s by the French mathematician Georges Matheron.
		For kriging estimation, the semivarogram model (the yellow line in figure 2) is used to obtain estimates for the weighting parameters of Equation 1.
		The ability of kriging to produce a prediction standard error map is what separates it from other spatial interpolation methods (like inverse distance weighting).
	www.ce.utexas.edu /prof/maidment/giswr2005/geostat/GeostatisticExercise.htm (3243 words)

	Ordinary Kriging
		The first step in ordinary kriging is to construct a variogram from the scatter point set to be interpolated.
		An important feature of kriging is that the variogram can be used to calculate the expected error of estimation at each interpolation point since the estimation error is a function of the distance to surrounding scatter points.
		When interpolating to an object using the kriging method, an estimation variance data set is always produced along with the interpolated data set.
	www.ems-i.com /gmshelp/Interpolation/Interpolation_Schemes/Kriging/Ordinary_Kriging.htm (579 words)

	kriging
		Ordinary kriging is linear, because its estimates are weighted linear combinations of the sample values.
		Ordinary kriging is "best", because it aims at minimizing the variance of the error for each interpolated point.
		In addition to this, kriging is capable of estimating the reliability of each interpolated point.
	www.giac.montana.edu /geog501/kriging2.htm (310 words)

	Kriging
		Kriging is a method of interpolation named after a South African mining engineer named D. Krige who developed the technique in an attempt to more accurately predict ore reserves.
		Kriging is a set of linear regression routines which minimize estimation variance from a predefined covariance model.
		Since kriging is a rather complex interpolation technique and includes numerous options, a complete description of kriging is beyond the scope of this reference manual.
	www.ems-i.com /gmshelp/Interpolation/Interpolation_Schemes/Kriging/Kriging.htm (259 words)

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