1、Designation: D 5611 94 (Reapproved 2008)Standard Guide forConducting a Sensitivity Analysis for a Ground-Water FlowModel Application1This standard is issued under the fixed designation D 5611; the number immediately following the designation indicates the year oforiginal adoption or, in the case of
2、revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide covers techniques that should be used toconduct a sensitivity analysis for a ground-w
3、ater flow model.The sensitivity analysis results in quantitative relationshipsbetween model results and the input hydraulic properties orboundary conditions of the aquifers.1.2 After a ground-water flow model has been calibrated, asensitivity analysis may be performed. Examination of thesensitivity
4、of calibration residuals and model conclusions tomodel inputs is a method for assessing the adequacy of themodel with respect to its intended function.1.3 After a model has been calibrated, a modeler may varythe value of some aspect of the conditions applying solely tothe prediction simulations in o
5、rder to satisfy some designcriteria. For example, the number and locations of proposedpumping wells may be varied in order to minimize the requireddischarge. Insofar as these aspects are controllable, variation ofthese parameters is part of an optimization procedure, and, forthe purposes of this gui
6、de, would not be considered to be asensitivity analysis. On the other hand, estimates of futureconditions that are not controllable, such as the recharge duringa postulated drought of unknown duration and severity, wouldbe considered as candidates for a sensitivity analysis.1.4 This guide presents t
7、he simplest acceptable techniquesfor conducting a sensitivity analysis. Other techniques havebeen developed by researchers and could be used in lieu of thetechniques in this guide.1.5 This guide is written for performing sensitivity analysesfor ground-water flow models. However, these techniquescoul
8、d be applied to other types of ground-water related models,such as analytical models, multi-phase flow models, non-continuum (karst or fracture flow) models, or mass transportmodels.1.6 This guide is one of a series on ground-water modelingcodes (software) and their applications, such as Guide D 544
9、7and Guide D 5490. Other standards have been prepared onenvironmental modeling, such as Practice E 978.1.7 The values stated in inch-pound units are to be regardedas standard. The values given in parentheses are mathematicalconversions to SI units that are provided for information onlyand are not co
10、nsidered standard.1.8 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to u
11、se.1.9 This guide offers an organized collection of informationor a series of options and does not recommend a specificcourse of action. This document cannot replace education orexperience and should be used in conjunction with professionaljudgment. Not all aspects of this guide may be applicable in
12、 allcircumstances. This ASTM standard is not intended to repre-sent or replace the standard of care by which the adequacy ofa given professional service must be judged, nor should thisdocument be applied without consideration of a projects manyunique aspects. The word “Standard” in the title of this
13、document means only that the document has been approvedthrough the ASTM consensus process.2. Referenced Documents2.1 ASTM Standards:2D 653 Terminology Relating to Soil, Rock, and ContainedFluidsD 5447 Guide for Application of a Ground-Water FlowModel to a Site-Specific ProblemD 5490 Guide for Compar
14、ing Ground-Water Flow ModelSimulations to Site-Specific Information1This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rockand is the direct responsibility of Subcommittee D18.21 on Ground Water andVadose Zone Investigations .Current edition approved Sept. 15, 2008. Published Nove
15、mber 2008. Originallyapproved in 1994. Last previous edition approved in 2002 as D 5611 94 (2002)2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Docum
16、ent Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.E 978 Practice for Evaluating Mathematical Models for theEnvironmental Fate of Chemicals33. Terminology3.1 Definitions:3.1.1 boundary conditiona math
17、ematical expression of astate of the physical system that constrains the equations of themathematical model.3.1.2 calibrationthe process of refining the model repre-sentation of the hydrogeologic framework, hydraulic proper-ties, and boundary conditions to achieve a desired degree ofcorrespondence b
18、etween the model simulations and observa-tions of the ground-water flow system.3.1.2.1 DiscussionDuring calibration, a modeler mayvary the value of a model input to determine the value whichproduces the best degree of correspondence between thesimulation and the physical hydrogeologic system. This p
19、ro-cess is sometimes called sensitivity analysis but for thepurposes of this guide, sensitivity analysis begins only aftercalibration is complete.3.1.3 calibration targetsmeasured, observed, calculated,or estimated hydraulic heads or ground-water flow rates that amodel must reproduce, at least appro
20、ximately, to be consideredcalibrated.3.1.4 ground-water flow modelan application of a math-ematical model to represent a ground-water flow system.3.1.4.1 DiscussionThis term refers specifically to model-ing of ground-water hydraulics, and not to contaminant trans-port or other ground-water processes
21、.3.1.5 hydraulic propertiesintensive properties of soil androck that govern the transmission (that is, hydraulic conduc-tivity, transmissivity, and leakance) and storage (that is, spe-cific storage, storativity, and specific yield) of water.3.1.6 residualthe difference between the computed andobserv
22、ed values of a variable at a specific time and location.3.1.7 sensitivitythe variation in the value of one or moreoutput variables (such as hydraulic heads) or quantities calcu-lated from the output variables (such as ground-water flowrates) due to variability or uncertainty in one or more inputs to
23、a ground-water flow model (such as hydraulic properties orboundary conditions).3.1.8 sensitivity analysisa quantitative evaluation of theimpact of variability or uncertainty in model inputs on thedegree of calibration of a model and on its results or conclu-sions.43.1.8.1 DiscussionAnderson and Woes
24、sner4use “calibra-tion sensitivity analysis” for assessing the effect of uncertaintyon the calibrated model and 88prediction sensitivity analysis”for assessing the effect of uncertainty on the prediction. Thedefinition of sensitivity analysis for the purposes of this guidecombines these concepts, be
25、cause only by simultaneouslyevaluating the effects on the models calibration and predic-tions can any particular level of sensitivity be consideredsignificant or insignificant.3.1.9 simulationone complete execution of a ground-water modeling computer program, including input and output.3.2 For defin
26、itions of other terms used in this guide, seeTerminology D 653.4. Significance and Use4.1 After a model has been calibrated and used to drawconclusions about a physical hydrogeologic system (for ex-ample, estimating the capture zone of a proposed extractionwell), a sensitivity analysis can be perfor
27、med to identify whichmodel inputs have the most impact on the degree of calibrationand on the conclusions of the modeling analysis.4.2 If variations in some model inputs result in insignificantchanges in the degree of calibration but cause significantlydifferent conclusions, then the mere fact of ha
28、ving used acalibrated model does not mean that the conclusions of themodeling study are valid.4.3 This guide is not meant to be an inflexible description oftechniques of performing a sensitivity analysis; other tech-niques may be applied as appropriate and, after due consider-ation, some of the tech
29、niques herein may be omitted, altered, orenhanced.5. Sensitivity Analysis5.1 The first step for performing a sensitivity analysis is toidentify which model inputs should be varied. Then, for eachinput: execute calibration and prediction simulations with thevalue of the input varied over a specified
30、range; graphcalibration residuals and model predictions as functions of thevalue of the input; and determine the type of sensitivity that themodel has with respect to the input.5.2 Identification of Inputs to be Varied:5.2.1 Identify model inputs that are likely to affect com-puted hydraulic heads a
31、nd ground-water flow rates at the timesand locations where similar measured quantities exist, andthereby affect calibration residuals.Also, identify model inputsthat are likely to affect the computed hydraulic heads uponwhich the models conclusions are based in the predictivesimulations.5.2.2 Usuall
32、y, changing the value of an input at a singlenode or element of a model will not significantly affect anyresults. Therefore, it is important to assemble model inputs intomeaningful groups for variation. For example, consider anunconfined aquifer that discharges into a river. If the river isrepresent
33、ed in a finite-difference model by 14 nodes, thenvarying the conductance of the river-bottom sediments in onlyone of the nodes will not significantly affect computed flowinto the river or computed hydraulic heads. Unless there arecompelling reasons otherwise, the conductance in all rivernodes should
34、 be varied as a unit.5.2.3 Coordinated changes in model inputs are changesmade to more than one type of input at a time. In ground-waterflow models, some coordinated changes in input values (forexample, hydraulic conductivity and recharge) can have littleeffect on calibration but large effects on pr
35、ediction. If themodel was not calibrated to multiple hydrologic conditions,3Withdrawn. The last approved version of this historical standard is referencedon www.astm.org.4Anderson, Mary P., and Woessner, William W., Applied GroundwaterModelingSimulation of Flow and Advective Transport, Academic Pres
36、s, Inc., SanDiego, 1992.D 5611 94 (2008)2sensitivity analysis of coordinated changes can identify poten-tial non-uniqueness of the calibrated input data sets.5.3 Execution of Simulations:5.3.1 For each input (or group of inputs) to be varied, decideupon the range over which to vary the values. Some
37、inputvalues should be varied geometrically while others should bevaried arithmetically. The type of variation for each input andthe range over which it is varied are based on the modelersjudgment, with the goal of finding a Type IV sensitivity (see5.5.1.4) if it exists.NOTE 1If the value of a model
38、input (or group of inputs) wasmeasured in the field, then that input need only be varied with the rangeof the error of the measurement.5.3.2 For each value of each group of inputs, rerun thecalibration and prediction runs of the model with the new valuein place of the calibrated value. Calculate the
39、 calibrationresiduals (or residual statistics, or both) that result as aconsequence of using the new value. Determine the effect ofthe new value on the models conclusions based on using thenew value in the prediction simulations.5.4 Graphing Results:5.4.1 For each input (or group of inputs), prepare
40、 a graph ofthe effect of variation of that parameter upon calibrationresiduals and the models conclusions. Figs. 1-4 show samplegraphs of the results of sensitivity analyses.5.4.2 Rather than display the effect on every residual, it maybe more appropriate to display the effect on residual statistics
41、such as maximum residual, minimum residual, residual mean,and standard deviation of residuals (see Guide D 5490).5.4.3 In some cases, it may be more illustrative to presentcontours of head change as a result of variation of input values.In transient simulations, graphs of head change versus timemay
42、be presented.5.4.4 Other types of graphs not mentioned here may bemore appropriate in some circumstances.5.5 Determination of the Type of Sensitivity:5.5.1 For each input (or group of inputs), determine the typeof sensitivity of the model to that input. There are four types ofsensitivity, Types I th
43、rough IV, depending on whether thechanges to the calibration residuals and models conclusionsare significant or insignificant. The four types of sensitivity aredescribed in the following sections and summarized on Fig. 5.NOTE 2Whether a given change in the calibration residuals orresidual statistics
44、 is considered significant or insignificant is a matter ofjudgment. On the other hand, changes in the models conclusions areusually able to be characterized objectively. For example, if a model isused to design an excavation dewatering system, then the computed watertable is either below or above th
45、e bottom of the proposed excavation.5.5.1.1 Type I SensitivityWhen variation of an inputcauses insignificant changes in the calibration residuals as wellas the models conclusions, then that model has a Type Isensitivity to the input. Fig. 1 shows an example of Type IFIG. 1 Sample Graph of Sensitivit
46、y Analysis, Type I SensitivityFIG. 2 Sample Graph of Sensitivity Analysis, Type II SensitivityD 5611 94 (2008)3sensitivity. Type I sensitivity is of no concern because regard-less of the value of the input, the conclusion will remain thesame.5.5.1.2 Type II SensitivityWhen variation of an inputcause
47、s significant changes in the calibration residuals butinsignificant changes in the models conclusions, then thatmodel has a Type II sensitivity to the input. Fig. 2 shows anexample of Type II sensitivity. Type II sensitivity is of noconcern because regardless of the value of the input, theconclusion
48、 will remain the same.5.5.1.3 Type III SensitivityWhen variation of an inputcauses significant changes to both the calibration residuals andthe models conclusions, then that model has a Type IIIsensitivity to the input. Fig. 3 shows an example of Type IIIsensitivity. Type III sensitivity is of no co
49、ncern because, eventhough the models conclusions change as a result of variationof the input, the parameters used in those simulations cause themodel to become uncalibrated. Therefore, the calibrationprocess eliminates those values from being considered to berealistic.5.5.1.4 Type IV SensitivityIf, for some value of the inputthat is being varied, the models conclusions are changed butthe change in calibration residuals is insignificant, then themodel has a Type IV sensitivity to that input. Fig. 4 shows anexample of Type IV sensitivity. Type IV sens
