ASTM D5981/D5981M-18

Standard Guide for Calibrating a Groundwater Flow Model Application

SIGNIFICANCE AND USE
5.1 Most site-specific groundwater 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's predictions.  
5.2 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.  
5.3 This guide is not meant to be an inflexible description of techniques for calibrating a groundwater flow model; other techniques may be applied as appropriate and, after due consideration, some of the techniques herein may be omitted, altered, or enhanced.
Note 1: Users of the inverse method should be aware that the method may have several solutions, all equally well calibrated. (1)4
SCOPE
1.1 This guide covers techniques that can be used to calibrate a groundwater 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 groundwater modeling code to a site-specific problem (see Guide D5447). 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 groundwater 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) groundwater flow models. However, these techniques, suitably modified, could be applied to other types of related groundwater models, such as multi-phase models, non-continuum (karst or fracture flow) models, or mass transport models.  
1.5 Guide D5447 presents the steps to be taken in applying a groundwater modeling code to a site-specific problem. Calibration is one of those steps. Other standards have been prepared on environmental modeling, such as Guides D5490, D5609, D5610, D5611, D5718, and Practice E978.  
1.6 Units—The values stated in either SI units or inch-pound units (given in brackets) are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system shall be independently of the other. Combining values from the two systems may result in non-conformance with the standard.  
1.7 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.8 This guide offers an organized collection of information or a series of options and does not recommend a specific course of action. This document cannot replace education or experience and should be used in conjunction with professional judgment. Not all aspects of this guide may be applicable in all circumstances. This ASTM standard is not intended to represent or replace the standard of care by which the adequacy of a given professional service must be judged, nor should this document be applied without consideration of a project's many unique aspects. The word “Standard” in the title of this document means only that the...

General Information

• Status: Published
• Publication Date: 31-Dec-2017
• ICS: 13.060.10 - Water of natural resources
• Technical Committee: D18 - Soil and Rock
• Drafting Committee: D18.21 - Groundwater and Vadose Zone Investigations

Relations

• Replaces: ASTM D5981-96(2008) - Standard Guide for Calibrating a Groundwater Flow Model Application (Withdrawn 2017)
• Effective Date: 01-Jan-2018
• Refers: ASTM D5447-17 - Standard Guide for Application of a Numerical Groundwater Flow Model to a Site-Specific Problem
• Effective Date: 15-Dec-2017
• Refers: ASTM D5609-16 - Standard Guide for Defining Boundary Conditions in Groundwater Flow Modeling
• Effective Date: 01-Mar-2016
• Refers: ASTM D5611-94(2016) - Standard Guide for Conducting a Sensitivity Analysis for a Groundwater Flow Model Application
• Effective Date: 01-Jan-2016
• Refers: ASTM D653-14 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Aug-2014
• Refers: ASTM D5718-95(2012) - Standard Guide for Documenting a Groundwater Flow Model Application
• Effective Date: 01-May-2012
• Refers: ASTM D653-11 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Sep-2011
• Refers: ASTM D5447-04(2010) - Standard Guide for Application of a Groundwater Flow Model to a Site-Specific Problem
• Effective Date: 01-Aug-2010
• Refers: ASTM D653-09 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Jan-2009
• Refers: ASTM D653-08a - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Dec-2008
• Refers: ASTM D653-08 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Nov-2008
• Refers: ASTM D5609-94(2015)e1 - Standard Guide for Defining Boundary Conditions in Groundwater Flow Modeling
• Effective Date: 15-Sep-2008
• Refers: ASTM D5490-93(2008) - Standard Guide for Comparing Groundwater Flow Model Simulations to Site-Specific Information
• Effective Date: 15-Sep-2008
• Refers: ASTM D5609-94(2008) - Standard Guide for Defining Boundary Conditions in Groundwater Flow Modeling
• Effective Date: 15-Sep-2008
• Refers: ASTM D5611-94(2008) - Standard Guide for Conducting a Sensitivity Analysis for a Groundwater Flow Model Application
• Effective Date: 15-Sep-2008

Overview

ASTM D5981/D5981M-18: Standard Guide for Calibrating a Groundwater Flow Model Application provides comprehensive guidance on techniques for calibrating groundwater flow models. Calibration is the process of adjusting model parameters so that model outputs align with observed or measured groundwater data. This step is essential before using a model for prediction purposes, increasing confidence in its results. The standard, published by ASTM International, is developed according to internationally recognized best practices and serves as a reliable reference for hydrogeologists, environmental engineers, and modeling professionals who work on site-specific groundwater studies.

Key Topics

• Calibration Process: Methods and best practices for matching model simulations to historical field data, including both manual (trial-and-error) and automated (inverse) calibration techniques.
• Conceptual Model Validation: Emphasizes reviewing and refining the underlying model assumptions, hydraulic properties, and construction whenever calibration targets cannot be matched realistically.
• Calibration Targets: Guidance on selecting and establishing measured or estimated hydraulic heads and groundwater flow rates as calibration benchmarks, with discussions on handling measurement errors and data quality.
• Parameter Identification: Strategies for defining and grouping model inputs such as hydraulic conductivity, recharge zones, and boundary conditions for effective calibration.
• History Matching: Process of iteratively adjusting model parameters to minimize the residuals (differences) between observed and simulated data.
• Uniqueness and Verification: Addresses non-uniqueness in inverse methods, suggesting the importance of multiple hydrologic conditions and verification datasets to increase the robustness of calibration.
• Reporting and Documentation: Recommends thorough documentation practices for calibration methods, targets, parameter selections, and comparison results to ensure transparency and replicability.

Applications

ASTM D5981/D5981M-18 is applicable in a variety of practical scenarios:

• Site-Specific Groundwater Investigations: Provides a framework for tailoring groundwater flow models during remediation, resource evaluation, or impact assessment projects.
• Environmental Compliance: Supports regulatory submissions by ensuring groundwater models are credibly calibrated before being used to project future site conditions.
• Model Refinement and QA/QC: Guides professionals in identifying data gaps, revising conceptual models, and systematically documenting every calibration step as part of broader quality assurance efforts.
• Training and Professional Development: Offers a structured reference for introducing new professionals to industry-standard calibration procedures and terminology within hydrogeology and environmental modeling fields.

Related Standards

Users of ASTM D5981/D5981M-18 are encouraged to reference other ASTM standards for comprehensive groundwater model development and review, including:

• ASTM D5447 - Guide for Application of a Numerical Groundwater Flow Model to a Site-Specific Problem
• ASTM D5490 - Guide for Comparing Groundwater Flow Model Simulations to Site-Specific Information
• ASTM D5609 - Guide for Defining Boundary Conditions in Groundwater Flow Modeling
• ASTM D5610 - Guide for Defining Initial Conditions in Groundwater Flow Modeling
• ASTM D5611 - Guide for Conducting a Sensitivity Analysis for a Groundwater Flow Model Application
• ASTM D5718 - Guide for Documenting a Groundwater Flow Model Application

Practical Value

Implementing ASTM D5981/D5981M-18 ensures groundwater models:

• Reflect realistic site conditions
• Incorporate verified hydraulic properties and boundary condition data
• Achieve robust calibration suited to prediction and regulatory requirements
• Adhere to recognized international groundwater modeling standards

Adopting this guide results in technically sound, transparent, and defensible groundwater modeling that meets both professional and regulatory expectations.

Keywords

calibration, groundwater flow model, inverse method, trial-and-error calibration, model verification, hydrogeology, environmental modeling, ASTM D5981/D5981M-18, model documentation, conceptual model, site-specific groundwater modeling

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: D5981/D5981M − 18
Standard Guide for
Calibrating a Groundwater Flow Model Application
This standard is issued under the fixed designation D5981/D5981M; 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope* responsibility of the user of this standard to establish appro-
priate safety, health, and environmental practices and deter-
1.1 This guide covers techniques that can be used to
mine the applicability of regulatory limitations prior to use.
calibrateagroundwaterflowmodel.Thecalibrationofamodel
1.8 This guide offers an organized collection of information
is the process of matching historical data, and is usually a
or a series of options and does not recommend a specific
prerequisite for making predictions with the model.
course of action. This document cannot replace education or
1.2 Calibration is one of the stages of applying a ground-
experience and should be used in conjunction with professional
water modeling code to a site-specific problem (see Guide
judgment. Not all aspects of this guide may be applicable in all
D5447). Calibration is the process of refining the model
circumstances. This ASTM standard is not intended to repre-
representation of the hydrogeologic framework, hydraulic
sent or replace the standard of care by which the adequacy of
properties, and boundary conditions to achieve a desired
a given professional service must be judged, nor should this
degree of correspondence between the model simulations and
document be applied without consideration of a project’s many
observations of the groundwater flow system.
unique aspects. The word “Standard” in the title of this
document means only that the document has been approved
1.3 Flow models are usually calibrated using either the
manual (trial-and-error) method or an automated (inverse) through the ASTM consensus process.
method. This guide presents some techniques for calibrating a
1.9 This international standard was developed in accor-
flow model using either method.
dance with internationally recognized principles on standard-
ization established in the Decision on Principles for the
1.4 This guide is written for calibrating saturated porous
Development of International Standards, Guides and Recom-
medium (continuum) groundwater flow models. However,
mendations issued by the World Trade Organization Technical
these techniques, suitably modified, could be applied to other
Barriers to Trade (TBT) Committee.
types of related groundwater models, such as multi-phase
models, non-continuum (karst or fracture flow) models, or
2. Referenced Documents
mass transport models.
2.1 ASTM Standards:
1.5 Guide D5447 presents the steps to be taken in applying
D653 Terminology Relating to Soil, Rock, and Contained
a groundwater modeling code to a site-specific problem.
Fluids
Calibration is one of those steps. Other standards have been
D5447 Guide for Application of a Numerical Groundwater
prepared on environmental modeling, such as Guides D5490,
Flow Model to a Site-Specific Problem
D5609, D5610, D5611, D5718, and Practice E978.
D5490 Guide for Comparing Groundwater Flow Model
1.6 Units—The values stated in either SI units or inch-
Simulations to Site-Specific Information
pound units (given in brackets) are to be regarded separately as
D5609 Guide for Defining Boundary Conditions in Ground-
standard. The values stated in each system may not be exact
water Flow Modeling
equivalents; therefore, each system shall be independently of
D5610 GuideforDefiningInitialConditionsinGroundwater
the other. Combining values from the two systems may result
Flow Modeling
in non-conformance with the standard.
D5611 Guide for Conducting a Sensitivity Analysis for a
1.7 This standard does not purport to address all of the
Groundwater Flow Model Application
safety concerns, if any, associated with its use. It is the
D5718 Guide for Documenting a Groundwater Flow Model
Application
This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rock
and is the direct responsibility of Subcommittee D18.21 on Groundwater and
Vadose Zone Investigations.
Current edition approved Jan. 1, 2018. Published February 2018. Originally For referenced ASTM standards, visit the ASTM website, www.astm.org, or
approved in 1996. Last previous edition approved in 2002 as D5981 – 96 (2008), contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
which was withdrawn January 2017 and reinstated in January 2018. DOI: 10.1520/ Standards volume information, refer to the standard’s Document Summary page on
D5981_D5981M-18. the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5981/D5981M − 18
E978 Practice for Evaluating Mathematical Models for the 5. Significance and Use
Environmental Fate of Chemicals (Withdrawn 2002)
5.1 Most site-specific groundwater flow models must be
calibrated prior to use in predictions. In these cases, calibration
3. Terminology
is a necessary, but not sufficient, condition which must be
obtained to have confidence in the model’s predictions.
3.1 Definitions:
3.1.1 For definitions of technical terms in this standard,
5.2 Often, during calibration, it becomes apparent that there
refer to Terminology D653.
are no realistic values of the hydraulic properties of the soil or
3.2 Definitions of Terms Specific to This Standard: rock which will allow the model to reproduce the calibration
3.2.1 application verification—using the set of parameter targets. In these cases the conceptual model of the site may
values and boundary conditions from a calibrated model to need to be revisited or the construction of the model may need
approximate acceptably a second set of field data measured to be revised. In addition, the source and quality of the data
under similar hydrologic conditions. used to establish the calibration targets may need to be
3.2.1.1 Discussion—Application verification is to be distin- reexamined.Forexample,themodelingprocesscansometimes
identify a previously undetected surveying error, which would
guished from code verification, which refers to software
testing, comparison with analytical solutions, and comparison results in inaccurate hydraulic head targets.
withothersimilarcodestodemonstratethatthecoderepresents
5.3 This guide is not meant to be an inflexible description of
its mathematical foundations.
techniques for calibrating a groundwater flow model; other
3.2.2 calibration targets—measured, observed, calculated, techniques may be applied as appropriate and, after due
or estimated hydraulic heads or groundwater flow rates that a
consideration, some of the techniques herein may be omitted,
model must reproduce, at least approximately, to be considered altered, or enhanced.
calibrated.
NOTE 1—Users of the inverse method should be aware that the method
3.2.2.1 Discussion—The calibration target includes both the 4
may have several solutions, all equally well calibrated. (1)
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 groundwater head or flow rate. Establishment of
3.2.3 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
model application. This, in turn, depends strongly upon the
3.2.4 hydraulic properties—properties of soil and rock that
objectives of the modeling project. All else being equal, in
govern the transmission (for example, hydraulic conductivity,
comparing a low-fidelity to a high-fidelity model application,
transmissivity,andleakance)andstorage(forexample,specific
the low-fidelity application would require fewer calibration
storage, storativity, and specific yield) of water.
targets and allow larger acceptable residuals.
3.2.5 inverse method—solving for independent parameter
values using knowledge of values of dependent variables.
NOTE 2—Some low-fidelity models are not necessarily intended to
make specific predictions, but rather provide answers to speculative or
3.2.6 residual—the difference between the computed and
hypothetical questions which are posed so as to make their predictions
observed values of a variable at a specific time and location.
conditional on assumptions. An example might be a model that answers
the question: “If the hydraulic conductivity of the soil is 50 feet per day,
3.2.7 sensitivity (model application)—the degree to which
will the drawdown be more than 3 m [10 ft]?”This model will not answer
the model result is affected by changes in a selected model
the question of whether or not the drawdown will, in reality, be more than
input representing hydrogeologic framework, hydraulic
3 m [10 ft] because the value of hydraulic conductivity was assumed.
properties, and boundary conditions.
Since the answer is conditional on the assumption, this “what-if” type of
model does not necessarily require calibration, and, therefore, there would
be no calibration targets.
4. Summary of Guide
6.2 For a medium- to high-fidelity model application, estab-
4.1 The steps to be taken to calibrate a flow model are:
lish calibration targets by first identifying all relevant available
establishing calibration targets and associated acceptable re-
data regarding groundwater heads (including measured water
siduals or residual statistics (as described in Section 6),
levels, bottom elevations of dry wells, and top of casing
identifying calibration parameters (as described in Section 7),
elevations of flowing wells) and flow rates (including records
and history matching (as described in Section 8). History
of pumping well or wellfield discharges, estimates of baseflow
matching is accomplished by using the trial-and-error method
to gaining streams or rivers or recharge from losing streams,
to achieve a rough correspondence between the simulation and
discharges from flowing wells, springflow measurements,
the physical hydrogeologic system, and then using either the
and/or contaminant plume velocities). For each such datum,
trial-and-error method or an automated method to achieve a
include the error bars associated with the measurement or
closer correspondence.
estimate.
3 4
The last approved version of this historical standard is referenced on The boldface numbers in parentheses refer to a list of references at the end of
www.astm.org. this standard.
D5981/D5981M − 18
6.3 Establish calibration targets before beginning any simu- hydrologic conditions, if the conditions are truly distinct.
lations. Matching different hydrologic conditions is one way to address
nonuniqueness, because one set of heads can be matched with
6.4 For any particular calibration target, the magnitude of
the proper ratio of groundwater flow rates to hydraulic con-
the acceptable residual depends partly upon the magnitude of
ductivities; whereas, when the flow rates are changed, repre-
the error of the measurement or estimate of the calibration
senting a different condition, then the range of hydraulic
target and partly upon the degree of accuracy and precision
conductivitiesthatproduceacceptableresidualsbecomesmuch
required of the model’s predictions. All else equal, the higher
more limited.
the intended fidelity of the model, the smaller the acceptable
6.5.1.1 Otherwaystoaddresstheuniquenessproblemareto
absolute values of the residuals.
include groundwater flows with heads as calibration targets,
6.4.1 Head measurements are usually accurate to within a
and to use measured values of hydraulic properties as model
few tenths of a foot. Due to the many approximations em-
inputs.
ployed in modeling and errors associated therewith (see Guide
6.5.2 Verification (Similar Hydrologic Conditions)—When
D5447),itisusuallynotpracticabletomakeamodelreproduce
data are available for two times of similar hydrologic
all heads measurements within the errors of measurement.
conditions, only one of those data sets should be used as
Therefore, the modeler must increase the range of acceptable
calibration targets because they are not distinct. However, the
computed heads beyond the range of the error in measurement.
other data set can be used for application verification. In the
Judgment must be employed in setting these new acceptable
verification process, the modeled data are compared, not to the
residuals. In general, however, the acceptable residual should
calibration data set, but to the verification data set. The
be a small fraction of the difference between the highest and
resultingdegreeofcorrespondencecanbetakenasanindicator
lowest heads across the site.
or heuristic measure of the uncertainty inherent in the model’s
NOTE 3—Acceptable residuals may differ for different hydraulic head predictions.
calibration targets within a particular model. This may be due to different
NOTE 5—When only one data set is available, it is inadvisable to
errors in measurement, for example, when heads at some wells are based
artificially split it into separate “calibration” and “verification” data sets.
on a survey, but other heads are estimated based on elevations estimated
It is usually more important to calibrate to data spanning as much of the
from a topographic map. In other circumstances, there may be physical
modeled domain as practicable.
reasons why heads are more variable in some places than in others. For
NOTE 6—Some researchers maintain that the word “verification”
example, in comparing a well near a specified head boundary with a well
impliesahigherdegreeofconfidencethantheverificationprocessimparts
near a groundwater divide, the modeled head in the former will depend
(4). Used here, the verification process only provides a method for
lessstronglyupontheinputhydraulicpropertiesthantheheadinthelatter.
heuristically estimating the range of uncertainty associated with model
Therefore, acceptable residuals near specified head boundaries can be set
predictions.
lower than those near divides.
NOTE 7—Performing application verification protects against over-
NOTE 4—One way to establish acceptable hydraulic head residuals is to
calibration. Over-calibration is the fine-tuning of input parameters to a
use kriging on the hydraulic head distribution. Although kriging is not
higher degree of precision than is warranted by the knowledge or
usually recommended for construction of hydraulic head contours, it does
measurability of the physical hydrogeologic system and results in artifi-
result in unbiased estimates of the variance (and thus standard deviation)
cially low residuals. Without performing application verification, the
of the hydraulic head distribution as a function of location within the
artificiallylowresidualsmightotherwisebeusedtooverstatetheprecision
modeled domain. The acceptable residual at each node can be set as the
of the model’s predictions.
standard deviation in the hydraulic head at that location. Some researchers
question the validity of this technique (2). An alternative is to perform
6.6 In transient modeling, it is often easier to match changes
trend analysis of regions of similar heterogeneity. Since a model will
in heads (that is, drawdowns) rather than the heads themselves.
usually only be able to represent trends over length scales larger than the
Ifprojectobjectivesandrequirementsallow,considerrecasting
scaleoflocalheterogeneitythatiscausingvariations,themagnitudeofthe
the calibration targets as drawdowns rather than heads.
residuals from the trend analysis should approximate the magnitude of
residuals in the model in that region.
6.7 In some cases, the circumstances under which data were
6.4.2 Errors in the estimates of groundwater flow rates will
collected do not correspond exactly to those for which the
usually be larger than those in heads (3). For example,
model may be computing values. For example, the steady-state
baseflow estimates are generally accurate only to within an
water level in a pumping well may be affected by turbulent
order of magnitude. In such cases, the upper and lower bounds
well losses whereas the model will usually be computing the
on the acceptable modeled value of baseflow can be equal to
formation head at that location.To make a fair comparison and
the upper and lower bounds on the estimate.
to avoid skewing calibrated hydraulic parameters to compen-
sate for the discrepancy, either the calibration target or the
6.5 Multiple Hydrologic Conditions—When more than one
computedvalueinthesimulationshouldbeadjustedtoaccount
set of field measurements have been collected, identify the
forthedifference.Tomaintaintheproperperspectiveregarding
different hydrologic conditions that are represented by the
the relative importance between measured data and modeling
available data sets. Include only one data set from each
results, it is recommended that the computed value be adjusted
hydrologic condition in the set of calibration targets. Use the
prior to making the comparison, and that the calibration targets
remaining data sets for verification.
remain unaltered.
6.5.1 Uniqueness (Distinct Hydrologic Conditions)—The
number of different distinct hydrologic conditions that a given
7. Identifying Calibration Parameters
set of input aquifer hydraulic properties is capable of repre-
senting is an important qualitative measure of the performance 7.1 Calibration parameters are groups of hydraulic proper-
of a model. It is usually better to calibrate to multiple ties or boundary conditions whose values are adjusted as a
D5981/D5981M − 18
group during the calibration process. Examples of calibration 8.2 Early in the calibration process it is often advisable to
parameters for some hypothetical model applications could be: conducta“calibrationsensitivityanalysis”byvaryingdifferent
inputs systematically to determine which inputs have the
7.1.1 The horizontal hydraulic conductivity of a kame
greatest effect on computed groundwater heads and flow rates.
terrace deposit;
In early stages of calibration, this analysis allows the modeler
7.1.2 The ratio of recharge at each node in the springtime to
to avoid spending time varying inputs which will have little
the average annual recharge at a particular node;
effect on the results. In later stages of cal
...