Designation: D5611 − 94 (Reapproved 2016)Standard Guide forConducting a Sensitivity Analysis for a Groundwater FlowModel Application1This standard is issued under the fixed designation D5611; the number immediately following the designation indicates the year oforiginal adoption or, in the case of 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 groundwater 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 groundwater flow model has been calibrated, asensitivity analysis may be performed. Examination of thesensitivity 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 order 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 guide, 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 the 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 groundwater flow models. However, these techniques couldbe applied to other types of groundwater related models, suchas analytical models, multi-phase flow models, non-continuum(karst or fracture flow) models, or mass transport models.1.6 This guide is one of a series on groundwater modelingcodes (software) and their applications, such as Guide D5447and Guide D5490. Other standards have been prepared onenvironmental modeling, such as Practice E978.1.7 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 considered 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 use.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 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 project’s manyunique aspects. The word “Standard” in the title of thisdocument means only that the document has been approvedthrough the ASTM consensus process.2. Referenced Documents2.1 ASTM Standards:2D653 Terminology Relating to Soil, Rock, and ContainedFluidsD5447 Guide forApplication of a Groundwater Flow Modelto a Site-Specific ProblemD5490 Guide for Comparing Groundwater Flow ModelSimulations to Site-Specific InformationE978 Practice for Evaluating Mathematical Models for theEnvironmental Fate of Chemicals (Withdrawn 2002)31This guide is under the jurisdiction of ASTM Committee D18 on Soil andRockand is the direct responsibility of Subcommittee D18.21 on Groundwater andVadose Zone Investigations.Current edition approved Jan. 1, 2016. Published January 2016. Originallyapproved in 1994. Last previous edition approved in 2008 as D5611 – 94(2008).DOI: 10.1520/D5611-94R16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3The last approved version of this historical standard is referenced onwww.astm.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13. Terminology3.1 Definitions:3.1.1 boundary condition—a mathematical expression of astate of the physical system that constrains the equations of themathematical model.3.1.2 calibration—the process of refining the model repre-sentation of the hydrogeologic framework, hydraulicproperties, and boundary conditions to achieve a desireddegree of correspondence between the model simulations andobservations of the groundwater flow system.3.1.2.1 Discussion—During calibration, a modeler may varythe value of a model input to determine the value whichproduces the best degree of correspondence between thesimulation and the physical hydrogeologic system. This pro-cess is sometimes called sensitivity analysis but for thepurposes of this guide, sensitivity analysis begins only aftercalibration is complete.3.1.3 calibration targets—measured, observed, calculated,or estimated hydraulic heads or groundwater flow rates that amodel must reproduce, at least approximately, to be consideredcalibrated.3.1.4 groundwater flow model—an application of a math-ematical model to represent a groundwater flow system.3.1.4.1 Discussion—This term refers specifically to model-ing of groundwater hydraulics, and not to contaminant trans-port or other groundwater processes.3.1.5 hydraulic properties—intensive properties of soil androck that govern the transmission (that is, hydraulicconductivity, transmissivity, and leakance) and storage (that is,specific storage, storativity, and specific yield) of water.3.1.6 residual—the difference between the computed andobserved values of a variable at a specific time and location.3.1.7 sensitivity—the variation in the value of one or moreoutput variables (such as hydraulic heads) or quantities calcu-lated from the output variables (such as groundwater flowrates) due to variability or uncertainty in one or more inputs toa groundwater flow model (such as hydraulic properties orboundary conditions).3.1.8 sensitivity analysis—a 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 Discussion—Anderson and Woessner4use “calibra-tion sensitivity analysis” for assessing the effect of uncertaintyon the calibrated model and prediction sensitivity analysis”for assessing the effect of uncertainty on the prediction. Thedefinition of sensitivity analysis for the purposes of this guidecombines these concepts, because only by simultaneouslyevaluating the effects on the model’s calibration and predic-tions can any particular level of sensitivity be consideredsignificant or insignificant.3.1.9 simulation—one complete execution of a groundwatermodeling computer program, including input and output.3.2 For definitions of other terms used in this guide, seeTerminology D653.4. Significance and Use4.1 After a model has been calibrated and used to drawconclusions about a physical hydrogeologic system (forexample, estimating the capture zone of a proposed extractionwell), a sensitivity analysis can be performed 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 having 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 dueconsideration, some of the techniques herein may be omitted,altered, or enhanced.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 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 and groundwater 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 model’s conclusions are based in the predictivesimulations.5.2.2 Usually, 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 isrepresented 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 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 groundwaterflow models, some coordinated changes in input values (forexample, hydraulic conductivity and recharge) can have littleeffect on calibration but large effects on prediction. If themodel was not calibrated to multiple hydrologic conditions,4Anderson, Mary P., and Woessner, William W., Applied GroundwaterModeling—Simulation of Flow and Advective Transport, Academic Press, Inc., SanDiego, 1992.D5611 − 94 (2016)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 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 modeler’sjudgment, with the goal of finding a Type IV sensitivity (see5.5.1.4) if it exists.NOTE 1—If the value of a model 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 calibrationresiduals (or residual statistics, or both) that result as aconsequence of using the new value. Determine the effect ofthe new value on the model’s 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 a graph ofthe effect of variation of that parameter upon calibrationresiduals and the model’s 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 statisticssuch as maximum residual, minimum residual, residual mean,and standard deviation of residuals (see Guide D5490).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 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 through IV, depending on whether thechanges to the calibration residuals and model’s conclusionsare significant or insignificant. The four types of sensitivity aredescribed in the following sections and summarized on Fig. 5.NOTE 2—Whether a given change in the calibration residuals or residualstatistics is considered significant or insignificant is a matter of judgment.On the other hand, changes in the model’s conclusions are usually able tobe characterized objectively. For example, if a model is used to design anexcavation dewatering system, then the computed water table is eitherbelow or above the bottom of the proposed excavation.5.5.1.1 Type I Sensitivity—When variation of an inputcauses insignificant changes in the calibration residuals as wellas the model’s conclusions, then that model has a Type IFIG. 1 Sample Graph of Sensitivity Analysis, Type I SensitivityFIG. 2 Sample Graph of Sensitivity Analysis, Type II SensitivityD5611 − 94 (2016)3sensitivity to the input. Fig. 1 shows an example of Type Isensitivity. 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 Sensitivity—When variation of an inputcauses significant changes in the calibration residuals butinsignificant changes in the model’s 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 will remain the same.5.5.1.3 Type III Sensitivity—When variation of an inputcauses significant changes to both the calibration residuals andthe model’s 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 concern because, eventhough the model’s 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 Sensitivity—If, for some value of the inputthat is being varied, the model’s 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 sensitivity caninvalidate