1、CEMP-RT Technical Letter NO. 11 10-1-175 3515781 i1734879 14b DEPARTMENT OF THE ARMY U.S. Army Corps of Engineers Washington, DC 20314-1000 ETL 11 10-1-175 Engineering and Design PRACTICAL ASPECTS OF APPLYING GEOSTATISTICS AT HAZARDOUS, TOXIC, AND RADIOACTIVE WASTE SITES Distribution Restriction Sta
2、tement 30 June 1997 Approved for public release; distribution is unlimited. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CEMP-RT Technical Letter NO. 1110-1-175 DEPARTMENT OF THE ARMY US. Army Corps of Engineers Washington, DC 2031 4-1 O00 ETL 111
3、0-1-175 Engineering and Design PRACTICAL ASPECTS OF APPLYING GEOSTATISTICS AT HAZARDOUS, TOXIC, AND RADIOACTIVE WASTE SITES 30 June 1997 1. Purpose. The principal purpose of this ETL is to introduce the reader to geostatistical techniques and to demonstrate their basic utiiity with respect to HTRW s
4、ite investigations. The ETL also will include a discussion of statistical concepts that support the science of geostatistics. Practical aspects of geostatistical techniques wili be dis- cussed in two ways. First, practical references will be made, when appropriate, during the discussion of statistic
5、al concepts, and second, examples describing several aspects of the use of geosta- tistical techniques in HTRW site investigations wili be presented and discussed in a section of this ETL specifically dedicated to providing working exam- ples. This ETL also will include a brief literature and softwa
6、re review; review of geostatistical appli- cations; comparison of information that is gener- ated with geostatistical methods to that information obtained using classical statistical methods; and some more recent geostatistical methods, such as conditional simulation. 2. Applicability. This letter a
7、pplies to all USACE commands having HTRW investigation, design, and remedial action responsibility within the military or civil works programs. 3. References. Documents referenced in this ETL are listed. Appendix A contains additional references useful in geostatistical application. b. ASTM D-5922,
8、Standard Guide for Analysis of Spatial Variation in Geostatisticai Site Investigations. c. ASTM D-5549, Standard Guide for Content of Geostatistical Site Investigations. 4. Distribution Statement. Approved for public release, distribution is unlimited. 5. Discussion. a. Geostatistics is a powerful t
9、ool to assess relationships among data obtained from various locations. It allows optimization of sample spac- ing and frequency. More importantly, geostatistics also allows one to effectively estimate parameter values in areas between actual sample points and quantify the uncertainty of the estimat
10、ed values. This can be very valuable in risk management and design decision making. This ETL builds upon the principles introduced in EM 200- 1-2. b. The ETL contains examples which illus- trate the statistical principles discussed throughout the document. Not every application of geosta- tistics to
11、 HTW projects could be illustrated, how- ever, and the user must be aware of the basic principles and seek appropriate applications. Spe- cific examples of typical cost-effective applications of geostatistics are also given here. a. EM 200-1-2, Technical Project Planning Guidance for HTRW Data Quali
12、ty Design. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-3515789 0734883 8T4 = ETL 1110-1-175 30 Jun 97 (1) Geostatistics, by the construction of a vari- ogram based on preliminary sampling, can be used to determine the typical separation of sampin
13、g points that delineate uncorrelate data. The range of the variogram is used as a basis for selec- ting a sample spacing that minimizes costs and provides independent data for determining, for example, average exposure values for risk assess- ment. First, an adequate number of preliminary samples ar
14、e analyzed from the site (refer to sec- tion 4-3). Second, a variogram is constructed using techniques described in Chapter 4. Third, the range of the variogram, as defined in section 2-3 is deter- mined. Lastly, the range or some multiple or frac- tion of it, is chosen for future sample spacing. Th
15、e variogram should be updated as new data are col- lected. For example, the variogram may indicate data spaced more than 200 ft apart are uncorrelated. Closure sampling may then be proposed to be spaced every 200 ft or more along an excavation. Smaller spacing results in unnecessary duplication of i
16、nformation and unneeed expenditure of funds. (2) Geostatistics, through block kriging, can yield estimates of the average concentrations to be encountered in a typical daily excavation area/ volume. For applications such as excavation of near surface contamination, two-dimensional block kriging coul
17、d be used to estimate mean contaminant concentration for specific excavation areas. Although this document does not address three- dimensional block kriging for estimating mean con- centrations within given volumes, additional guid- ance and tools for three-dimensional kriging are available through
18、references cited in Appendix A. Alternatively, one can use two-dimensional block kriging to estimate mean concentrations in different layers within a given volume. These estimates can then be averaged to approximate the overall average concentration within the entire volume. This assumes adequate da
19、ta exist to perform the two- dimensional block kriging at the different depths. To perform two-dimensional block kriging, adequate site characterization data are collected (refer to section 4-4). Second, the data gathered from the areas of interest are used to construct a variogram, as described Cha
20、pter 4. Third, the variogram is modeled as described in section 4-6. Lastly, the model is used to perform block kriging, as described in section 2-4 for blocks of a size com- parable to the daily excavation aredvolume. The block-kriged values can then be used for estimating the treatment plant loadi
21、ng, etc., related to that block. The kriging also quantifies the possible variance in the average concentration for each block that can be used to manage the risk of operating a treatment plant. (3) Exposure concentrations for risk assess- ment purposes can be computed, using geostatis- tics, even t
22、hough the site characterization data are somewhat clustered or were collected using biased sampling strategies. Assuming the data are already available and adequate in number (refer to section 44, the first step is to compute a sample variogram, as described in Chapter 4. Second, the variogram is mo
23、deled as described in section 4-6. Next, this model is used in performing a block kriging operation over the inferred exposure area, as described in section 2-3. Finally, the block kriging value can be used, along with the kriging variance, to determine the exposure point con- centration, assuming t
24、he data were normally distributed (or were transformed to be normally distributed). (4) The last example describes the use of geo- statistics to quantify project risk for excavation or treatment volumes. Even with ample site char- acterization point data (borings or wells), the limits of the treatme
25、nt zone are imperfectly defined. Geostatistics allows one to evaluate the risk that the size, and therefore cost, of the remediation may be larger or smaller than expected. First, site char- acterization is performed and adequate data are collected (as described in section 4-4). Second, the data are
26、 transformed by assigning a value of one or zero, depending on whether the value is above or below, respectively, a given clean-up value or other criteria. Third, the transformed data are then used to construct a variogram as described in Chapter 4. Fourth, this variogram is modeled as described in
27、section 4-6. Next, this model is used in performing indicator kriging as described in sec- tion 2-6. The kriging estimates essentially reflect a 2 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,- 351578? 0734882 730 W probability that the concentrati
28、on at the points of estimation exceed the clean-up value or other stan- dard. These kriging estimates can be contoured to define areas or volumes of material that have a certain likelihood of exceeding some cleanup value. The contour value is essentially the probability of exceedance. Lastly, the si
29、ze of the area defined by different probabilities of exceedance can be deter- mined and, using a unit cost or similar approach, a cost-versus-risk curve can be developed. This can be used in programming money for the project, as a basis for negotiating cleanup levels with regulators, or to help dete
30、rmine if the cost and time of addi- tional characterization work will be offset by less risk during construction. Alternatively, rather than transforming the data to ones and zeros, the actual values are kriged and the kriging variances can be used to determine prediction intervals on each esti- mat
31、ed value as described in section 2-6. In the vicinity of the point estimate, these prediction inter- vals can be used to define the spread of potential values expected within a given probability. This assumes the data are normally distributed or have been transformed to be normally distributed. 6. A
32、ctions Required. a. USACE elements identified in paragraph 2 shall consider applications of geostatistics as FOR THE COMMANDER: 2 Appendices App A - References App B - Notation EIL 1 11 0-1-1 75 30 Jun 97 described in this document as appropriate. This is particularly true during planning of large-s
33、cale site characterization efforts or when there are risk management or design decisions to be made that must consider the uncertainty of site characteriza- tion results. The same USACE elements should also encourage the use of geostatistics, where appropriate, by their contractors. b. USACE element
34、s shall make every effort to familiarize staff members actively supporting HTRW projects with the fundamentals and poten- tial benefits of the application of geostatistics. This letter is a good starting point for learning about the use of geostatistics for HTRW projects. Users are encouraged to att
35、end appropriate training. c. This letter sets out procedures for the tech- nically correct application of geostatistics which are consistent with current practice, such as set forth in ASTM D-5922 and D-5549. The techni- cal procedures outlined herein shall be considered when performing USACE in-hou
36、se geostatistical analysis or reviewing such analyses done by US ACE contractors. Ddectorate o Military Pr ams u 3 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ETL 1110-1-175 30 Jun 97 Chapter 1 Introduction 1-1. General a. This Engineer Technical
37、 Letter (ETL) addresses the use of geostatistics at hazardous, toxic, and radioactive waste (HTRW) sites. One very fundamental aspect of perhaps all HTRW site investigations that deal with environmental con- tamination is the need to characterize the extent and spatial distribution of contamination.
38、 Such a characterization typically would include describ- ing, using a variety of statistical or analytical tools, spatial trends and variability. A principal diff- culty in doing this is the fact that measurements may be few, or may be sparsely scattered over large regions. A question that arises n
39、aturally in this situation is how one might interpolate in order to make predictions (or estimates) at points where measurements of contaminant concentration are not available. Such interpolation will be referred to as point, or punctual, estimation in this ETL. Additionally, an investigator may nee
40、d to deter- mine a single representative value for an area that is represented by several measured or estimated values or both; this will be referred to in this ETL as block estimation. Geostatistics is a set of sta- tistical procedures designed to accomplish these ends. Geostatistics may be applied
41、 to many prob- lems, other than contamination, that occur at HTRW sites. Even though this document addres- ses only twodimensional applications, geostatistics can be used in three dimensions as well. Indeed, there are many cases in which the third dimension, usually stratification, is desirable to a
42、ddress. b. Kriging is the principal geostatistical meth- odology described in this ETL. For introductory purposes kriging can be defined as a technique for determining the optimal weighting of measure- ments at sampled locations for obtaining predic- tions, or estimates, at unsampled locations; addi
43、tional definition of kriging is provided through- out this document. Kriging is well-suited for mak- ing point and block estimates. However, much of the advantage of using geostatistical procedures, such as kriging, lies not just in the point and block estimates they provide, but in the information
44、they provide concerning uncertainty associated with these estimates. The uncertainty information is usually quantified as either the standard deviation (or variance) associated with kriging estimates and is referred to as kriging standard deviation (or kriging variance) in this ETL. c. Original geos
45、tatistical work involved making estimates for the areal extent and concen- trations of economic mineral deposits, in relation to mining. Today (1996), geostatistical techniques continue to have a function in mining. However, a welldevelope methodology that is capable of interpolating a given set of
46、measured values at dis- crete locations into estimates for new locations or developing an individual estimate for an area including many locations, or both, has attracted users from many disciplines, and there is a trend toward incorporating geostatistics as standard cur- riculum for most geo-scienc
47、e educational pro- grams. The use of geostatistical techniques as part of HTRW site investigations is becoming common because of the almost routine need for data inter- polation as part of these investigations. d. Once investigators have established that their data are adequate as to quality and qua
48、ntity, geostatistics can provide powerful analytical tools that result in quantitative characterization of areas of special interest within the study area or the entire study area. These characterizations may address spatial variation; for example, it may be determined where values for concentration
49、s of contaminants in soils are relatively high or low, are less than or greater than a specified value, or even have a high or low probability of exceeding a certain value. 1-2. Scope a. The scope of this ETL will be limited principally to discussions and examples of two- dimensional point and block estimations using a geostatistical method known as kriging. The ETL will present the technical aspects of geostatistics 1-1 Provided by IHSNot for ResaleNo reproduction or networking permitted without license f
