1、Designation: D 5490 93 (Reapproved 2008)Standard Guide forComparing Ground-Water Flow Model Simulations to Site-Specific Information1This standard is issued under the fixed designation D 5490; 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 tocompare the results of ground-water flow mode
3、l simulations tomeasured field data as a part of the process of calibrating aground-water model. This comparison produces quantitativeand qualitative measures of the degree of correspondencebetween the simulation and site-specific information related tothe physical hydrogeologic system.1.2 During th
4、e process of calibration of a ground-water flowmodel, each simulation is compared to site-specific informa-tion such as measured water levels or flow rates. The degree ofcorrespondence between the simulation and the physical hy-drogeologic system can then be compared to that for previoussimulations
5、to ascertain the success of previous calibrationefforts and to identify potentially beneficial directions forfurther calibration efforts.1.3 By necessity, all knowledge of a site is derived fromobservations. This guide does not address the adequacy of anyset of observations for characterizing a site
6、.1.4 This guide does not establish criteria for successfulcalibration, nor does it describe techniques for establishingsuch criteria, nor does it describe techniques for achievingsuccessful calibration.1.5 This guide is written for comparing the results ofnumerical ground-water flow models with obse
7、rved site-specific information. However, these techniques could beapplied to other types of ground-water related models, such asanalytical models, multiphase flow models, noncontinuum(karst or fracture flow) models, or mass transport models.1.6 This guide is one of a series of guides on ground-water
8、modeling codes (software) and their applications. Other stan-dards have been prepared on environmental modeling, such asPractice E 978.1.7 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 est
9、ablish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.1.8 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 orexper
10、ience 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 thi
11、sdocument be applied without consideration of a projects 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:2D 653 Terminology Relating to Soil, Rock, and Cont
12、ainedFluidsE 978 Practice for Evaluating Mathematical Models for theEnvironmental Fate of Chemicals33. Terminology3.1 Definitions:3.1.1 application verificationusing the set of parametervalues and boundary conditions from a calibrated model toapproximate acceptably a second set of field data measure
13、dunder similar hydrologic conditions.3.1.1.1 DiscussionApplication verification is to be distin-guished from code verification which refers to software testing,comparison with analytical solutions, and comparison withother similar codes to demonstrate that the code represents itsmathematical foundat
14、ion.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 of1This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rockand is the direct responsibility of Subcommit
15、tee D18.21 on Ground Water andVadose Zone Investigations .Current edition approved Sept. 15, 2008. Published October 2008. Originallyapproved in 1993. Last previous edition approved in 2002 as D 5490 93 (2002).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Custo
16、mer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Withdrawn. The last approved version of this historical standard is referencedon www.astm.org.1Copyright ASTM International, 100 Barr Harbor Drive, PO
17、 Box C700, West Conshohocken, PA 19428-2959, United States.correspondence between the model simulations and observa-tions of the ground-water flow system.3.1.3 censored dataknowledge that the value of a variablein the physical hydrogeologic system is less than or greaterthan a certain value, without
18、 knowing the exact value.3.1.3.1 DiscussionFor example, if a well is dry, then thepotentiometric head at that place and time must be less than theelevation of the screened interval of the well although itsspecific value is unknown.3.1.4 conceptual modelan interpretation or working de-scription of th
19、e characteristics and dynamics of the physicalsystem.3.1.5 ground-water flow modelan application of a math-ematical model to represent a ground-water flow system.3.1.6 hydrologic conditiona set of ground-water inflowsor outflows, boundary conditions, and hydraulic properties thatcause potentiometric
20、 heads to adopt a distinct pattern.3.1.7 residualthe difference between the computed andobserved values of a variable at a specific time and location.3.1.8 simulationin ground-water flow modeling, onecomplete execution of a ground-water modeling computerprogram, including input and output.3.1.8.1 Di
21、scussionFor the purposes of this guide, a simu-lation refers to an individual modeling run. However, simula-tion is sometimes also used broadly to refer to the process ofmodeling in general.3.2 For definitions of other terms used in this guide, seeTerminology D 653.4. Summary of Guide4.1 Quantitativ
22、e and qualitative comparisons are both es-sential. Both should be used to evaluate the degree of corre-spondence between a ground-water flow model simulation andsite-specific information.4.2 Quantitative techniques for comparing a simulation withsite-specific information include:4.2.1 Calculation of
23、 residuals between simulated and mea-sured potentiometric heads and calculation of statistics regard-ing the residuals. Censored data resulting from detection of dryor flowing observation wells, reflecting information that thehead is less than or greater than a certain value withoutknowing the exact
24、 value, should also be used.4.2.2 Detection of correlations among residuals. Spatial andtemporal correlations among residuals should be investigated.Correlations between residuals and potentiometric heads canbe detected using a scattergram.4.2.3 Calculation of flow-related residuals. Model resultssh
25、ould be compared to flow data, such as water budgets,surface water flow rates, flowing well discharges, verticalgradients, and contaminant plume trajectories.4.3 Qualitative considerations for comparing a simulationwith site-specific information include:4.3.1 Comparison of general flow features. Sim
26、ulationsshould reproduce qualitative features in the pattern of ground-water contours, including ground-water flow directions,mounds or depressions (closed contours), or indications ofsurface water discharge or recharge (cusps in the contours).4.3.2 Assessment of the number of distinct hydrologiccon
27、ditions to which the model has been successfully calibrated.It is usually better to calibrate to multiple scenarios, if thescenarios are truly distinct.4.3.3 Assessment of the reasonableness or justifiability ofthe input aquifer hydrologic properties given the aquifermaterials which are being modele
28、d. Modeled aquifer hydro-logic properties should fall within realistic ranges for thephysical hydrogeologic system, as defined during conceptualmodel development.5. Significance and Use5.1 During the process of calibration of a ground-water flowmodel, each simulation is compared to site-specific inf
29、orma-tion to ascertain the success of previous calibration efforts andto identify potentially beneficial directions for further calibra-tion efforts. Procedures described herein provide guidance formaking comparisons between ground-water flow model simu-lations and measured field data.5.2 This guide
30、 is not meant to be an inflexible description oftechniques comparing simulations with measured data; othertechniques may be applied as appropriate and, after dueconsideration, some of the techniques herein may be omitted,altered, or enhanced.6. Quantitative Techniques6.1 Quantitative techniques for
31、comparing simulations tosite-specific information include calculating potentiometrichead residuals, assessing correlation among head residuals, andcalculating flow residuals.6.1.1 Potentiometric Head ResidualsCalculate the residu-als (differences) between the computed heads and the measuredheads:ri5
32、 hi2 Hi(1)where:ri= the residual,Hi= the measured head at point i,hi= the computed head at the approximate location whereHiwas measured.If the residual is positive, then the computed head was toohigh; if negative, the computed head was too low. Residualscannot be calculated from censored data.NOTE 1
33、For drawdown models, residuals can be calculated fromcomputed and measured drawdowns rather than heads.NOTE 2Comparisons should be made between point potentiometricheads rather than ground-water contours, because contours are the resultof interpretation of data points and are not considered basic da
34、ta in and ofthemselves.4Instead, the ground-water contours are considered to reflectfeatures of the conceptual model of the site. The ground-water flow modelshould be true to the essential features of the conceptual model and not totheir representation.NOTE 3It is desirable to set up the model so th
35、at it calculates heads atthe times and locations where they were measured, but this is not alwayspossible or practical. In cases where the location of a monitoring well doesnot correspond exactly to one of the nodes where heads are computed inthe simulation, the residual may be adjusted (for example
36、, computed headsmay be interpolated, extrapolated, scaled, or otherwise transformed) foruse in calculating statistics. Adjustments may also be necessary when the4Cooley, R. L., and Naff, R. L., “Regression Modeling of Ground-Water Flow,”USGS Techniques of Water Resources Investigations , Book 3, Cha
37、pter B4, 1990.D 5490 93 (2008)2times of measurements do not correspond exactly with the times whenheads are calculated in transient simulations; when many observed headsare clustered near a single node; where the hydraulic gradient changessignificantly from node to node; or when observed head data i
38、s affected bytidal fluctuations or proximity to a specified head boundary.6.1.2 Residual StatisticsCalculate the maximum andminimum residuals, a residual mean, and a second-orderstatistic, as described in the following sections.6.1.2.1 Maximum and Minimum ResidualsThe maximumresidual is the residual
39、 that is closest to positive infinity. Theminimum residual is the residual closest to negative infinity. Oftwo simulations, the one with the maximum and minimumresiduals closest to zero has a better degree of correspondence,with regard to this criterion.NOTE 4When multiple hydrologic conditions are
40、being modeled asseparate steady-state simulations, the maximum and minimum residualcan be calculated for the residuals in each, or for all residuals in allscenarios, as appropriate. This note also applies to the residual mean (see6.1.2.2) and second-order statistics of the residuals (see 6.1.2.4).6.
41、1.2.2 Residual MeanCalculate the residual mean as thearithmetic mean of the residuals computed from a givensimulation:R 5(i 5 1nrin(2)where:R = the residual mean andn = the number of residuals.Of two simulations, the one with the residual mean closest tozero has a better degree of correspondence, wi
42、th regard to thiscriterion (assuming there is no correlation among residuals).6.1.2.3 If desired, the individual residuals can be weightedto account for differing degrees of confidence in the measuredheads. In this case, the residual mean becomes the weightedresidual mean:R 5(i 5 1nwirin(i 5 1nwi(3)
43、where wiis the weighting factor for the residual at point i.The weighting factors can be based on the modelers judgmentor statistical measures of the variability in the water levelmeasurements. A higher weighting factor should be used for ameasurement with a high degree of confidence than for onewit
44、h a low degree of confidence.NOTE 5It is possible that large positive and negative residuals couldcancel, resulting in a small residual mean. For this reason, the residualmean should never be considered alone, but rather always in conjunctionwith the other quantitative and qualitative comparisons.6.
45、1.2.4 Second-Order StatisticsSecond-order statisticsgive measures of the amount of spread of the residuals aboutthe residual mean. The most common second-order statistic isthe standard deviation of residuals:s 5H(i 5 1nri2 R!2n 2 1!J12(4)where s is the standard deviation of residuals. Smaller values
46、of the standard deviation indicate better degrees of correspon-dence than larger values.6.1.2.5 If weighting is used, calculate the weighted standarddeviation:s 55(i 5 1nwiri2 R!2n 2 1!(i 5 1nwi612(5)NOTE 6Other norms of the residuals are less common but may berevealing in certain cases.5,6For examp
47、le, the mean of the absolute valuesof the residuals can give information similar to that of the standarddeviation of residuals.NOTE 7In calculating the standard deviation of residuals, advancedstatistical techniques incorporating information from censored data couldbe used. However, the effort would
48、 usually not be justified because thestandard deviation of residuals is only one of many indicators involved incomparing a simulation with measured data, and such a refinement in oneindicator is unlikely to alter the overall assessment of the degree ofcorrespondence.6.1.3 Correlation Among Residuals
49、Spatial or temporalcorrelation among residuals can indicate systematic trends orbias in the model. Correlations among residuals can beidentified through listings, scattergrams, and spatial or tempo-ral plots. Of two simulations, the one with less correlationamong residuals has a better degree of correspondence, withregard to this criterion.6.1.3.1 ListingsList residuals by well or piezometer, in-cluding the measured and computed values to detect spatial ortemporal trends. Figs. X1.1 and X1.2 present example listingsof residuals.6.1.3.2 ScattergramUse
