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1、EasyKrig3.0的说明 文档(kriging插值) 精品文档 收集于网络，如有侵权请联系管理员删除 The GLOBEC Kriging Software Package EasyKrig3.0July 15, 2004 Copyright (c) 1998, 2001, 2004 property of Dezhang Chu and Woods Hole Oceanographic Institution. All Rights Reserved. The kriging software described in this document was developed by Dez
2、hang Chu with funding from the National Science Foundation through the U.S. GLOBEC Georges Bank Projects Program Service and Data Management Office. It was originally inspired by a MATLAB toolbox developed by Yves Gratton and Caroline Lafleur (INRS-Ocanologie, Rimouski, Qc, Canada), and Jeff Runge (
3、Institut Maurice-Lamontagne, now with University of New Hampshire). This software may be reproduced for noncommercial purposes only. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY. Contact Dr. Chu at dchuwhoi.edu with enhancements or suggestions for changes.
4、 Table of Contents: 1. INTRODUCTION 1.1 General Information 1.1.1 About kriging 1.1.2 Brief descriptions of easy_krig3.0 1.2 Getting started 1.2.1 Operating systems 1.2.2 Down-load the program 1.2.3 Quick start 2. DATA PROCESSING STAGES 2.1 Data Preparation 2.2 Semi-variogram 2.3 Kriging 2.4 Visuali
5、zation 2.5 Saving Kriging Results 3. EXAMPLES 3.1 Example 1: An Aerial Image of Zooplankton Abundance Data 3.2 Example 2: A Vertical Section of Salinity Data An Anisotropic Data set 3.3 Example 3: Batch Process of Pressure (dbar) at Different Potential Density Layers 3.4 Example 4: 3-Dimensional Tem
6、perature Data 4. REFERENCES 精品文档 收集于网络，如有侵权请联系管理员删除 1. INTRODUCTION 1.1 General Information 1.1.1About kriging This section provides a brief theoretical background for kriging. If the user(s) is not interested in the theoretical background, he/she can skip this section and go to section 1.1.2 direct
7、ly. Kriging is a technique that provides the Best Linear Unbiased Estimator of the unknown fields (Journel and Huijbregts, 1978; Kitanidis, 1997). It is a local estimator that can provide the interpolation and extrapolation of the originally sparsely sampled data that are assumed to be reasonably ch
8、aracterized by the Intrinsic Statistical Model (ISM). An ISM does not require the quantity of interest to be stationary, i.e. its mean and standard deviation are independent of position, but rather that its covariance function depends on the separation of two data points only, i.e. E (z(x) m)(z(x) m
9、) = C(h),(1) where m is the mean of z(x) and C(h) is the covariance function with lag h, with h being the distance between two samples x and x: h = | x x | = (2).)()()( 2, 3 3 2, 2 2 2, 1 1 xxxxxx Another way to characterize an ISM is to use a semi-variogram, = 0.5* E (z(x) z(x) )2.(3) . )(h The rel
10、ation between the covariance function and the semi-variogram is = C(0) C(h).(4) . )(h The kriging method is to find a local estimate of the quantity at a specified location, . This estimate is a . L x weighted average of the N adjacent observations: (5) . )() ( 1 xx N L zz The weighting coefficients
11、 can be determined based on the minimum estimation variance criterion: . (6) . )()(2) 0 () ( )( 2 xxxxxxCCCzzE LLL subject to the normalization condition . (7) . N 1 1 Note that we dont know the exact value at , but we are trying to find a predicted value that provides the . L x minimum estimation v
12、ariance. The resultant kriging equation can be expressed as 精品文档 收集于网络，如有侵权请联系管理员删除 ,(8) . 1 )()( 1 1 N Lnn N CCxxxx where is the Lagrangian coefficient. In addition, we have replaced the covariance function with the normalized covariance function normalized by C(0). Equivalently, by using Eq. (4),
13、the kriging equation can also be expressed in terms of the semi-variogram as ,(9) . 1 )()( 1 1 N Lnn N xxxx where we have used normalized semi-variogram, i.e., semi-variogram normalized by C(0) as we did in deriving Eq. (8). Having obtained the weighting coefficients ( ) and the Lagrangian coefficie
14、nt ( ) by solving either Eq. . . (8) OR Eq. (9), the kriging variance, Eq. (6), can be expressed as: .(10) . ) 0 ()( )() 0 ()( )( 22 L LLLL CCzzE xx xxxx The above equations are the basis of the Easykrig software package. 1.1.2Brief description of EasyKrig3.0 The EasyKrig program package uses a Grap
15、hical User Interface (GUI). It requires MATLAB 5.3 or higher with or without optimization toolbox (see section 2.2) and consists of five components, or processing stages: (1) data preparation, (2) variogram computation, (3) kriging, (4) visualization and (5) saving results. It allows the user to pro
16、cess anisotropic data, select an appropriate model from a list of variogram models, and a choice of kriging methods, as well as associated kriging parameters, which are also common features of the other existing software packages. One of the major advantages of this program package is that the program minimizes the users requirements to guess the initial parameters and automatically generates the require
