ASTM D5981-96(2002)
(Guide)Standard Guide for Calibrating a Ground-Water Flow Model Application
Standard Guide for Calibrating a Ground-Water Flow Model Application
SIGNIFICANCE AND USE
Most site-specific ground-water flow models must be calibrated prior to use in predictions. In these cases, calibration is a necessary, but not sufficient, condition which must be obtained to have confidence in the model’predictions.
Often, during calibration, it becomes apparent that there are no realistic values of the hydraulic properties of the soil or rock which will allow the model to reproduce the calibration targets. In these cases the conceptual model of the site may need to be revisited or the construction of the model may need to be revised. In addition, the source and quality of the data used to establish the calibration targets may need to be reexamined. For example, the modeling process can sometimes identify a previously undetected surveying error, which would results in inaccurate hydraulic head targets.
This guide is not meant to be an inflexible description of techniques for calibrating a ground-water flow model; other techniques may be applied as appropriate and, after due consideration, some of the techniques herein may be omitted, altered, or enhanced.
SCOPE
1.1 This guide covers techniques that can be used to calibrate a ground-water flow model. The calibration of a model is the process of matching historical data, and is usually a prerequisite for making predictions with the model.
1.2 Calibration is one of the stages of applying a ground-water modeling code to a site-specific problem (see Guide D 5447). Calibration is the process of refining the model representation of the hydrogeologic framework, hydraulic properties, and boundary conditions to achieve a desired degree of correspondence between the model simulations and observations of the ground-water flow system.
1.3 Flow models are usually calibrated using either the manual (trial-and-error) method or an automated (inverse) method. This guide presents some techniques for calibrating a flow model using either method.
1.4 This guide is written for calibrating saturated porous medium (continuum) ground-water flow models. However, these techniques, suitably modified, could be applied to other types of related ground-water models, such as multi-phase models, non-continuum (karst or fracture flow) models, or mass transport models.
1.5 Guide D 5447 presents the steps to be taken in applying a ground-water modeling code to a site-specific problem. Calibration is one of those steps. Other standards have been prepared on environmental modeling, such as Guides D 5490, D 5609, D 5610, D 5611, D 5718, and Practice E 978.
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation:D5981–96 (Reapproved 2002)
Standard Guide for
Calibrating a Ground-Water Flow Model Application
This standard is issued under the fixed designation D 5981; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope a given professional service must be judged, nor should this
document be applied without consideration of a project’s many
1.1 This guide covers techniques that can be used to
unique aspects. The word “Standard” in the title of this
calibrate a ground-water flow model. The calibration of a
document means only that the document has been approved
model is the process of matching historical data, and is usually
through the ASTM consensus process.
a prerequisite for making predictions with the model.
1.2 Calibration is one of the stages of applying a ground-
2. Referenced Documents
water modeling code to a site-specific problem (see Guide
2.1 ASTM Standards:
D 5447). Calibration is the process of refining the model
D 653 Terminology Relating to Soil, Rock, and Contained
representation of the hydrogeologic framework, hydraulic
Fluids
properties, and boundary conditions to achieve a desired
D 5447 Guide for Application of a Ground-Water Flow
degree of correspondence between the model simulations and
Model to a Site-Specific Problem
observations of the ground-water flow system.
D 5490 Guide for Comparing Ground-Water Flow Model
1.3 Flow models are usually calibrated using either the
Simulations to Site-Specific Information
manual (trial-and-error) method or an automated (inverse)
D 5609 Guide for Defining Boundary Conditions in
method. This guide presents some techniques for calibrating a
Ground-Water Flow Modeling
flow model using either method.
D 5610 Guide for Defining Initial Conditions in Ground-
1.4 This guide is written for calibrating saturated porous
Water Flow Modeling
medium (continuum) ground-water flow models. However,
D 5611 Guide for Conducting a Sensitivity Analysis for a
these techniques, suitably modified, could be applied to other
Ground-Water Flow Model Application
types of related ground-water models, such as multi-phase
D 5718 Guide for Documenting a Ground-Water Flow
models, non-continuum (karst or fracture flow) models, or
Model Application
mass transport models.
E 978 Practice for Evaluating Mathematical Models for the
1.5 Guide D 5447 presents the steps to be taken in applying
Environmental Fate of Chemicals
a ground-water modeling code to a site-specific problem.
Calibration is one of those steps. Other standards have been
3. Terminology
prepared on environmental modeling, such as Guides D 5490,
3.1 Definitions:
D 5609, D 5610, D 5611, D 5718, and Practice E 978.
3.1.1 application verification—using the set of parameter
1.6 This standard does not purport to address all of the
values and boundary conditions from a calibrated model to
safety concerns, if any, associated with its use. It is the
approximate acceptably a second set of field data measured
responsibility of the user of this standard to establish appro-
under similar hydrologic conditions.
priate safety and health practices and determine the applica-
3.1.1.1 Discussion—Application verification is to be distin-
bility of regulatory limitations prior to use.
guished from code verification, which refers to software
1.7 This guide offers an organized collection of information
testing, comparison with analytical solutions, and comparison
or a series of options and does not recommend a specific
withothersimilarcodestodemonstratethatthecoderepresents
course of action. This document cannot replace education or
its mathematical foundations.
experienceandshouldbeusedinconjunctionwithprofessional
3.1.2 calibrated model—a model that has achieved a de-
judgment. Not all aspects of this guide may be applicable in all
sired degree of correspondence between the model simulations
circumstances. This ASTM standard is not intended to repre-
and observations of the physical hydrogeologic system.
sent or replace the standard of care by which the adequacy of
3.1.3 calibration (model application)—the process of refin-
ing the model representation of the hydrogeologic framework,
This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rock
and is the direct responsibility of Subcommittee D18.21 on Ground Water and Annual Book of ASTM Standards, Vol 04.08.
Vadose Zone Investigations. Annual Book of ASTM Standards, Vol 04.09.
Current edition approved July 10, 1996. Published November 1996. Annual Book of ASTM Standards, Vol 11.05.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D5981–96 (2002)
hydraulic properties, and boundary conditions to achieve a reexamined.Forexample,themodelingprocesscansometimes
desired degree of correspondence between the model simula- identify a previously undetected surveying error, which would
tions and observations of the ground-water flow system. results in inaccurate hydraulic head targets.
3.1.4 calibration targets—measured, observed, calculated, 5.3 This guide is not meant to be an inflexible description of
or estimated hydraulic heads or ground-water flow rates that a techniques for calibrating a ground-water flow model; other
model must reproduce, at least approximately, to be considered techniques may be applied as appropriate and, after due
calibrated. consideration, some of the techniques herein may be omitted,
3.1.4.1 Discussion—The calibration target includes both the altered, or enhanced.
value of the head or flow rate and its associated error of
measurement, so that undue effort is not expended attempting 6. Establishing Calibration Targets
to get a model application to closely reproduce a value which
6.1 A calibration target consists of the best estimate of a
is known only to within an order of magnitude.
value of ground-water head or flow rate. Establishment of
3.1.5 fidelity—the degree to which a model application is
calibrationtargetsandacceptableresidualsorresidualstatistics
designed to resemble the physical hydrogeologic system.
depends on the degree of fidelity proposed for a particular
3.1.6 ground-water flow model—an application of a math-
model application. This, in turn, depends strongly upon the
ematical model to represent a site-specific ground-water flow
objectives of the modeling project. All else being equal, in
system.
comparing a low-fidelity to a high-fidelity model application,
3.1.7 hydraulic properties—properties of soil and rock that
the low-fidelity application would require fewer calibration
govern the transmission (for example, hydraulic conductivity,
targets and allow larger acceptable residuals.
transmissivity,andleakance)andstorage(forexample,specific
NOTE 1—Some low-fidelity models are not necessarily intended to
storage, storativity, and specific yield) of water.
make specific predictions, but rather provide answers to speculative or
3.1.8 inverse method—solving for independent parameter
hypothetical questions which are posed so as to make their predictions
values using knowledge of values of dependent variables.
conditional on assumptions. An example might be a model that answers
3.1.9 residual—the difference between the computed and
the question: “If the hydraulic conductivity of the soil is 50 feet per day,
observed values of a variable at a specific time and location.
will the drawdown be more than 10 ft?” This model will not answer the
3.1.10 sensitivity (model application)—the degree to which question of whether or not the drawdown will, in reality, be more than 10
ft because the value of hydraulic conductivity was assumed. Since the
the model result is affected by changes in a selected model
answerisconditionalontheassumption,this“what-if”typeofmodeldoes
input representing hydrogeologic framework, hydraulic prop-
not necessarily require calibration, and, therefore, there would be no
erties, and boundary conditions.
calibration targets.
3.1.11 simulation—in ground-water flow modeling, one
6.2 For a medium- to high-fidelity model application, estab-
complete execution of a ground-water modeling computer
lish calibration targets by first identifying all relevant available
program, including input and output.
data regarding ground-water heads (including measured water
3.2 Forotherdefinitionsusedinthisguide,seeTerminology
levels, bottom elevations of dry wells, and top of casing
D 653.
elevations of flowing wells) and flow rates (including records
4. Summary of Guide
of pumping well or wellfield discharges, estimates of baseflow
to gaining streams or rivers or recharge from losing streams,
4.1 The steps to be taken to calibrate a flow model are:
discharges from flowing wells, springflow measurements,
establishing calibration targets and associated acceptable re-
and/or contaminant plume velocities). For each such datum,
siduals or residual statistics (as described in Section 6),
include the error bars associated with the measurement or
identifying calibration parameters (as described in Section 7),
estimate.
and history matching (as described in Section 8). History
6.3 Establish calibration targets before beginning any simu-
matching is accomplished by using the trial-and-error method
lations.
to achieve a rough correspondence between the simulation and
6.4 For any particular calibration target, the magnitude of
the physical hydrogeologic system, and then using either the
the acceptable residual depends partly upon the magnitude of
trial-and-error method or an automated method to achieve a
the error of the measurement or estimate of the calibration
closer correspondence.
target and partly upon the degree of accuracy and precision
5. Significance and Use
required of the model’s predictions. All else equal, the higher
5.1 Most site-specific ground-water flow models must be the intended fidelity of the model, the smaller the acceptable
calibrated prior to use in predictions. In these cases, calibration absolute values of the residuals.
is a necessary, but not sufficient, condition which must be 6.4.1 Head measurements are usually accurate to within a
obtained to have confidence in the model’s predictions. few tenths of a foot. Due to the many approximations em-
5.2 Often, during calibration, it becomes apparent that there ployed in modeling and errors associated therewith (see Guide
are no realistic values of the hydraulic properties of the soil or D 5447),itisusuallyimpossibletomakeamodelreproduceall
rock which will allow the model to reproduce the calibration heads measurements within the errors of measurement. There-
targets. In these cases the conceptual model of the site may fore, the modeler must increase the range of acceptable
need to be revisited or the construction of the model may need computed heads beyond the range of the error in measurement.
to be revised. In addition, the source and quality of the data Judgment must be employed in setting these new acceptable
used to establish the calibration targets may need to be residuals. In general, however, the acceptable residual should
D5981–96 (2002)
be a small fraction of the difference between the highest and tions, only one of those data sets should be used as calibration
lowest heads across the site. targets because they are not distinct. However, the other data
set can be used for application verification. In the verification
NOTE 2—Acceptable residuals may differ for different hydraulic head
process, the modeled data are compared, not to the calibration
calibration targets within a particular model. This may be due to different
data set, but to the verification data set.The resulting degree of
errors in measurement, for example, when heads at some wells are based
on a survey, but other heads are estimated based on elevations estimated correspondence can be taken as an indicator or heuristic
from a topographic map. In other circumstances, there may be physical
measure of the uncertainty inherent in the model’s predictions.
reasons why heads are more variable in some places than in others. For
NOTE 4—When only one data set is available, it is inadvisable to
example, in comparing a well near a specified head boundary with a well
artificially split it into separate “calibration” and “verification” data sets.
near a ground-water divide, the modeled head in the former will depend
It is usually more important to calibrate to data spanning as much of the
lessstronglyupontheinputhydraulicpropertiesthantheheadinthelatter.
modeled domain as possible.
Therefore, acceptable residuals near specified head boundaries can be set
lower than those near divides. NOTE 5—Some researchers maintain that the word “verification” im-
NOTE 3—One way to establish acceptable hydraulic head residuals is to plies a higher degree of confidence than the verification process imparts
use kriging on the hydraulic head distribution. Although kriging is not (3). Used here, the verification process only provides a method for
usually recommended for construction of hydraulic head contours, it does heuristically estimating the range of uncertainty associated with model
result in unbiased estimates of the variance (and thus standard deviation) predictions.
of the hydraulic head distribution as a function of location within the
NOTE 6—Performing application verification protects against over-
modeled domain. The acceptable residual at each node can be set as the
calibration. Over-calibration is the fine-tuning of input parameters to a
standard deviation in the hydraulic head at that location. Some researchers
higher degree of precision than is warranted by the knowledge or
question the validity of this technique (1). An alternative is to perform
measurability of the physical hydrogeologic system and results in artifi-
trend analysis of regions of similar heterogeneity. Since a model will
cially low residuals. Without performing application verification, the
usually only be able to represent trends over length scales larger than the
artificiallylowresidualsmightotherwisebeusedtooverstatetheprecision
scaleoflocalheterogeneitythatiscausingvariations,themagnitudeofthe
of the model’s predictions.
residuals from the trend analysis should approximate the magnitude of
6.6 In transient modeling, it is often easier to match changes
residuals in the model in that region.
in heads (that is, drawdowns) rather than the heads themselves.
6.4.2 Errors in the estimates of ground-water flow rates will
Ifprojectobjectivesandrequirementsallow,considerrecasting
usually be larger than those in heads (2)
...
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