Groundwater Protection Area Delineation Using AnAqSim

Public water supply wellfields provide water for a variety of beneficial uses in homes, businesses and industries, and for farmland irrigation in many communities. To protect those water supplies, water purveyors often perform analyses to determine the area over which water enters and flows though the aquifer supplying a well or wellfield, so that measures can be taken to prevent and/or minimize the potential contamination of groundwater in those areas.

 

Often referred to as “wellhead protection areas”, a number of state and local governments have regulations and guidelines on how to delineate these groundwater protection areas.  For instance, in the Commonwealth of Massachusetts, regulations require that the groundwater protection area for a well (referred to as a “Zone II Area”) be delineated under severe hydrologic conditions.  Specifically, Massachusetts regulations describe the Zone II Area as follows:

“Zone II is that area of an aquifer which contributes water to a well under the most severe pumping conditions that can be realistically anticipated (180 days of pumping at safe yield with no recharge from precipitation). “

https://www.mass.gov/how-to/ws-07-zone-2-pumping-test

Typically, one of the most common methods utilized to delineate Zone II Areas (and groundwater protection areas in general) is a groundwater flow model.  AnAqSim is particularly well-suited for this type of analysis because it has a number of special features and tools that make it easy to delineate pumping well Zones of Contribution in general, and Zone II Areas in particular, including the following:

• AnAqSim’s ability to automatically calculate recharge or leakage over an area (this is useful in confirming that the model area determined from pathline tracing to be contributing recharge to the well matches the specified withdrawal rate at the well; this area can also  be used as a basis for pathline tracing for the Zone II);
• the ability to capture a snapshot of heads for a selected time step in a transient aquifer simulation (e.g. “freeze” calculated heads on the 180th day following termination of recharge as is required for a Zone II analysis), and then perform pathline tracing;
• easy setup of a grid of pathline starting locations over some area of the aquifer surface for forward tracing toward the pumping well; and
• constraining the display of pathlines, so that only those pathlines captured by selected model features (e.g. wells for which wellhead protection areas are to be delineated) are shown on the plot.

As the first installment of our new AnAqSim Example Application Series, which was developed to provide a set of practical modeling application examples that demonstrate how common groundwater modeling analyses can be accomplished using AnAqSim, our Simple Zone II Example Application  demonstrates how AnAqSim can be used to delineate a Zone II groundwater protection area consistent with Massachusetts 310 CMR 22 and guidance documents.

Although the example is focused on the delineation of a Zone II area in Massachusetts, the techniques used in delineating the Zone of Contribution (ZOC) and Area Contributing Recharge (ACR) for the well can also be applied for delineating groundwater protection zones under other regulatory programs.

The example, which comes with a detailed guide on model set up and Zone II delineation with AnAqSim(and all associated modeling files), can be downloaded for free HERE.

flexAEM Remediation Calculator Toolkit's new Transform Calculator Utility

Recently, the flexAEM Remediation Calculator Toolkit was updated and expanded to reflect the new features and software enhancements included in the latest version of AnAqSim (2019-1). The expanded Toolkit now includes the “Transform Calculator” utility, which allows the user to take one of the 15 calculators and manipulate the calculator geometry to better match your site’s spatial coordinates and groundwater flow direction.    

The Transform Calculator utility translates the lower left corner of the calculator to match the entered coordinates, it then rotates and scales the calculator to the desired angle and size to fit with site x-y coordinates (we recommend using feet or meters).

Each input to the Transform Calculator utility is briefly described below:

Select Calculator:

·         Select 1 of the 15 calculators provided in the toolkit.

X Translation:

·         Moves the calculator along the x-axis.

Y Translation:

·         Moves the calculator along the y-axis.

Rotation (degrees):

·         Rotates your calculator counterclockwise from the x-axis around the origin (lower left corner) of the selected calculator.

X Dimension:

·         Sets the length of your calculator along its no-flow boundary (the selected calculator’s x-axis). All base calculators start out as 5000 x 5000. Negative numbers will mirror the model around the y-axis (this may create some issues, rotating by 180 degrees is better).

Y Dimension:

·         Sets the length of your calculator along its constant head boundary (the selected calculator’s y-axis). All base calculators start out as 5000 x 5000. Negative numbers will mirror the model around the x-axis (this may create some issues, rotating by 180 degrees is better).

Output File Name:

·         Enter a name for your calculator (saves in the flexAEM Remediation Calculator Toolkit folder) or Browse to save your calculator in a different location.

Transform:

·         Transforms the selected calculator and saves it with the Output File Name.

Once the calculator transformation is complete, a .dxf map of key site features can be imported into AnAqSim to quickly and easily visualize the transformed calculator for your site, and produce report ready graphics. Below, the Funnel & Gate calculator has been rotated by 15 degrees and adjusted in the X and Y directions to match site coordinates. Finally, a .dxf site map has been brought into the transformed Funnel & Gate calculator using Plot Input / What to Plot and selecting color from the Basemap drop down menu and then Selecting the Basemap_File for the site.

To learn more, or to purchase the newly updated and expanded Remediation Calculator Toolkit (including the Calculator Transform utility), visit the flexAEMCalculator Toolkits page today!

Groundwater Modeling with AEM – A Look Back, and a Look Ahead to the Future

Introduction

The analytic element method (AEM) approach to groundwater modeling is efficient, powerful, easy to implement, fast to run, and provides the analyst a means for gaining insight at various steps of the modeling process that can guide data collection and subsequent model development. It is also a method that is apparently underutilized by groundwater modelers today. (We say apparently because there is some hope that modelers employ the method more than they report it in their final project documentation.)

This article will briefly describe the AEM groundwater modeling approach and how it evolved to its present state.

Definition of AEM groundwater modeling method

The Analytic Element Method is often described as being based on (1) mathematical solutions for the groundwater flow equation written in terms of discharge potential, and (2) the principle of superposition.

What that means in practical terms is that the flow equation is not written in terms of hydraulic head; it is written and solved in terms of discharge potential, which for a constant thickness aquifer is essentially head multiplied by hydraulic conductivity and aquifer thickness (Brikowski 2013). This allows the AEM, by superposition (adding of individual solutions), to be applicable to both confined and unconfined flow conditions as well as to aquifers that include heterogeneities (Strack and Haitjema 1981).

A mathematical solution, in terms of strength coefficients, is generated for the space around each element in the model; with each element representing a hydraulic or hydrologic feature - - a well, infiltration basin, or river reach for example. Then all of the element solutions are added at each point in model space to develop a 2D or 3D picture of the discharge potential field, and hydraulic head field. That field can be contoured to produce a head distribution map, or used as a basis for pathline tracing, or processed to calculate the groundwater flux though a boundary or user-defined transect.

The AEM is newer than FD and FE

Several authors have pointed out that the AEM is newer than finite-difference (FD) and finite-element (FE) methods. While that is technically true - - FD methods late 1960s; FE methods early 1970s; AEM about 10 years later in the late 1970s / early 1980s - - AEM is hardly the “new kid on the block.” It has been developed, applied and tested for almost 40 years now. And AEM was originally developed to address the limitations of prior FD and FE techniques. (To read the story of how AEM’s inventor Dr. Otto Strack first applied AEM on a large US Army Corps of Engineers project see Deming 2003. For more information on the history, applications, and strengths of AEM in general see Hunt 2006.)

While computer power has, in recent years, made up for some of the inefficiencies of FD and FE groundwater flow modeling methods, the continued development of AEM over the past four decades provide it with a number of advantages that still make it the method of choice in many situations. That development, and those advantages, are discussed in the following sections.

Brief history and progress in the field of AEM method of groundwater modeling

As mentioned above, the AEM groundwater modeling method that was originally developed in the Netherlands came to be first used in the United States by Dr. Otto Strack on a large-scale USACE dewatering project. Dr. Strack was assisted on the project by Henk Haitjema. Together these two PhD hydraulicians and mathematicians would go on to expand the capabilities of the method and make it available to groundwater modelers in the form of widely used AEM software packages. They also trained dozens of students (see figure below) who rose to prominence in the AEM field and developed their own methods and software.

    (from Kraemer 2007)

Some examples of the more popular and widely used AEM groundwater modeling software include:

Table 1. AEM Groundwater Modeling Software
Software / Solver	Author
SLAEM / MLAEM	Dr. Otto Strack
GFLOW	Dr. Henk Haitjema
Split - Visual AEM	Dr. Igor Jankovic
TimML / TTim	Dr. Mark Bakker
Bluebird / Cardinal / Ostrich – Visual AEM	Dr. James Craig
AnAqSim	Dr. Charles Fitts

(For more information see:  http://www.analyticelements.org/mw/index.php/AEM_Software  )

Advantages of AEM

The Analytic Element Method in general, and all of the AEM codes described above (and others not described here), allow the modeler to develop groundwater flow models with the following advantages:

1. Easy and accurate setup in representing hydrologic features and boundaries
• As simple as drawing points and lines on the screen; works well with GIS representation of hydrologic features.
• Accurate, fine-scale, representation of model boundaries, river features, etc. There is no need to construct million-grid-cell models to represent curved watershed boundaries or sinuous river channels; and thus there is no corresponding computational penalty.
2. Faster more accurate simulations
• Fewer equations in simple to moderately complex AEM models mean faster run times.
• Continuity of flow within the model domain, and between model subdomains is assured by virtue of the underlying solution techniques.
3. The AEM model is capable of providing a wide “range of view” with accurate results one foot from an infiltration basin or at the far reaches of the watershed. Heads and velocities can be calculated at any location within the model space.
4. Model post-processing for pathline tracing, flux through transects, and zone budgets can be accomplished accurately and efficiently using the calculate discharge potential generated by the AEM model.
5. The AEM groundwater modeling method provides the perfect tool for application of the Stepwise Modeling approach recommended by many investigators and organizations.
• When starting simple with a finite difference model you often start with a coarse grid. This can cause problems in representing model features and inaccuracy in the results.
• AEM moves smoothly from a “back of the envelope” or analytic solution in easily implemented steps (no grid to refine or rearrange) to a fairly complex model; with insight gained at each step in the process.

The Future

Significant advancements in the field of AEM modeling of groundwater flow have been in progress over the past several years, and are likely to continue into the future. New, more flexible, elements are being developed (e.g. Ranjram and Craig 2018), and new solver methods are being implemented to address difficult modeling problems such as the instabilities that can occur when severely dewatering multilayer aquifer models (e.g. Fitts 2018). There are developments underway that will expand analytic element flow modeling into the area of contaminant fate and transport simulation (e.g. Majumder and Eldho 2019), and research into rapidly and efficiently solving large complex AEM models in the cloud (Fullerton 2017).

Conclusion

As Steve Kraemer (2007) noted, “There is a small but active community of ground water modelers who use an innovative solution technique known as the analytic element method.” That method has evolved over the years, and its use and publications describing its use continue to grow.

For the reasons outlined in this brief summary, AEM presents an ease of use, flexibility and power that make it ideally suited for a wide variety of groundwater modeling applications; and the perfect tool for Stepwise Modeling. For more on that subject see the National Groundwater Association White Paper on Groundwater Modeling (https://www.ngwa.org/publications-and-news/industry-resource-library/White-papers -  free to NGWA members). In addition, we are planning an article on AEM and Stepwise Modeling in an upcoming flexAEM blog post.

flexAEM

At McLane Environmental, we have been using a variety of AEM groundwater modeling tools since the early 1990s, and have applied them successfully in dozens of hydrogeologic investigations. To hopefully foster the wider use of AEM techniques in the modeling community, we have published a series of AEM modeling exercises, and model development software tools, centered around AnAqSim modeling software.

These exercises demonstrate the usefulness and accuracy of results generated by AEM models. While focused on AnAqSim, the concepts and tools are applicable to other AEM software and to groundwater modeling in general. For more information please visit the flexAEM website (http://www.flexaem.com/).

References

Brikowski, T. 2013. Introduction to the analytic element method (GEOS-5311 Lecture Notes). 23 p. http://utdallas.edu/~brikowi/Teaching/Applied_Modeling/GroundWater/LectureNotes/analytic_element.pdf

Deming, D. 2003. Autobiographical sketch of Otto D.L. Strack. Ground Water Vol. 41, No. 4:550 – 554. https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1745-6584.2003.tb02391.x

Fitts, C.R. 2018. Modeling dewatering domains in multilayer analytic element models. Ground Water Vol. 56, No. 4:557 – 561.

Fullerton, J.B. 2017. Cloud-based analytic element groundwater modeling. Masters Thesis, Brigham Young University, 54 p. https://scholarsarchive.byu.edu/etd/6319/

Hunt, R.J. 2006. Ground water modeling applications using the Analytic Element Method. Ground Water Vol. 44, No. 1:5 – 15. https://onlinelibrary.wiley.com/doi/full/10.1111/j.1745-6584.2005.00143.x

Kraemer, S.R. 2007. Analytic element ground water modeling as a research program (1980 to 2006). Ground Water Vol. 45, No. 4:402 – 408. https://onlinelibrary.wiley.com/doi/10.1111/j.1745-6584.2007.00314.x

Majumder, P. and T.I. Eldho 2019. Reactive contaminant transport simulation using analytic element method, random walk particle tracking and kernel density estimator. Jour. Contam. Hydrol. Vol 222, p. 76-88. https://www.sciencedirect.com/science/article/pii/S0169772218302821

Ranjram, M. and J.R. Craig 2018. Closed analytic elements with flexible geometry. Ground Water Vol. 56, No. 5:816 – 822. https://onlinelibrary.wiley.com/doi/abs/10.1111/gwat.12649    

Strack, O.D.L and H.M. Haitjema 1981. Modeling double aquifer flow using a comprehensive potential and distributed singularities. 2. Solution for inhomogeneous permeabilities. Water Resources REsearch, Vol. 17, No. 5:1551-1560. http://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/WR017i005p01551

Harnessing the Power of AEM to Develop Quantitative Conceptual Site Models

Since the late 1980s, the development and use of a Conceptual Site Model (CSM) has been described in regulatory guidance and the technical literature as a sound platform for developing a qualitative (narrative and pictorial) description of contamination sources and groundwater flow conditions at a contaminated site. CSMs have typically been used for identifying data needs; for performing very preliminary receptor identification; and for providing a qualitative basis for decision making regarding site cleanup planning and implementation.

Linkage between the CSM and quantitative analysis of key aquifer and contaminant processes, however, is typically either not discussed, or mentioned briefly in the context of risk assessment.  To remedy this issue,  the development and use of a Quantitative Conceptual Site Model (QCSM) is warranted, as it provides a functional tool for project leaders to support data collection, conceptual model testing, receptor impact analysis, and remedy evaluation, selection and design.

What is a QCSM?  Whereas a traditional CSM is typically defined as a written and/or illustrative representation of the various processes that control the transport, migration, and potential impacts to receptors via soil, air, groundwater, surface water, and/or sediments (and is typically qualitative in nature), a QCSM consists of merging quantitative analysis results with the framework of a sound conceptual site model to form a proper basis for high level decision making.  Although there are many quantitative tools that can be utilized to facilitate QCSM development, groundwater models, and AEM models in particular, provide a fast, efficient tool that can be utilized to better understand site conditions, guide site investigations, and evaluate remedial options.

When describing CSM development, regulatory and technical guidance is typically vague with regard to the application of computer models, and if and when it is discussed, modeling typically appears to be an ancillary, not integral process.  In contrast, the QCSM approach integrates modeling into the decision-making process, explicitly calling for the use of groundwater (and soil zone) flow and transport models to develop a quantitative representation of the flow system, and provide answers to problems that are primarily hydraulic in nature ( e.g. capture zone, mounding, etc.) and/or related to the transport of contaminants (e.g., evaluation of potential receptors, monitored natural attenuation evaluations, etc.).

Click Graphic to Enlarge

As an example of developing and applying a QCSM, the approach was effectively utilized at an industrial site in New Jersey, where it was important to understand how both regional pumping influences and site-specific features may affect groundwater flow conditions at the local scale, which in turn was important to investigate the nature and extent of groundwater at the site. Accordingly, a groundwater flow model was developed using AnAqSim, which allowed for the computationally efficient incorporation of large-area regional flow features (which have an effect on flow patterns at the site-scale), while still allowing for detailed analysis of flow conditions at the local scale.  The AnAqSim model was constructed in the early phases of investigations at the site, and once calibrated to site conditions, was integrated into the decision-making process.  Specifically, the model was used by the project team to better understand:

• Groundwater flow conditions in the complex, multi-layer aquifer beneath the Site;
• Groundwater-surface water interactions;
• The effects of pumping from regional public supply wells and site production wells;
• Hydraulic communication between hydrostratigraphic units at the site; and
• Potential contaminant migration pathways.

Once this quantitative information was conveyed, it facilitated a discussion between the analysis team and the field investigation Project Manager that led to quickly identifying data and information gaps, and effectively planning additional investigation activities to address those data gaps.  Information collected from additional investigation activities (e.g., groundwater and surface water elevations) was incorporated back into the model, which allowed for an improved model calibration, and a higher degree of confidence not only in the model, but for the QCSM of the site and surrounding area.

As this example illustrates, a QCSM can be integrated and utilized at every stage of the project, and provides a strong clear basis for higher level decision making in a manner that is scientifically supported and transparent.

To learn more about the QCSM approach, download McLane Environmental’s recent White Paper entitled “A Quantitative Conceptual Site Model Approach for Environmental and Engineering Decision Making” HERE. 

Using PEST with AnAqSim

Overview of the Process

AnAqSim, an easy to use Windows-based analytic element groundwater flow model, can also be run from the command line or a batch file. This ability allows the user to move beyond AnAqSim’s built-in manual model calibration features (maintaining a calibration target data set, and plotting a
map of residuals) to employ the power of PEST for automated model calibration.

PEST is a general-purpose parameter estimation software tool that has been widely used for calibrating MODFLOW models and other groundwater flow models. To use PEST with AnAqSim the user is required to create a batch file to run AnAqSim from the command line and create a template file for the AnAqSim model and an instruction file to read the AnAqSim output into PEST.

The creation of a simple AnAqSim script file described in section 4 of the AnAqSim User Guide (http://www.fittsgeosolutions.com/AnAqSimUserGuide.pdf) allows the user to automate AnAqSim runs from the command line. Specifically the user can specify where the run log should be written and what analysis commands should be executed. A list of the analysis commands is included in
Section 2 below. Using this command line functionality for AnAqSim, an automated PEST calibration can be performed for any AnAqSim model. A typical PEST run will include the following user created files:

• The PEST control file (*.pst)
• Any template files (*.tpl) that PEST needs (for AnAqSim there is only one template file because all of the AnAqSim inputs are stored in the *.anaq file in xml format).
• Any instruction files (*.ins) for reading the output (for AnAqSim there is only one instruction file because all of the output will be written to the same *.out file).
•  (Optional) A parallel run management file (.rmf) if you wish to use multiple processors on your own computer or across a network of computers.

To get started, PEST  is freely available from the USGS website at https://www.usgs.gov/software/pest-parameter-estimation-code-optimized-large-environmental-models-version-3

AnAqSim analysis commands

• initialheadsfile <name.hds> (Optional) name of the initial heads file if the model is
  set up to use an initial heads file
• outputfile <name.out> file where AnAqSim will write the results of all
  subsequent commands
• headspecifiedwells writes the discharges of any head-specified wells to the output file
• dischargespecifiedwells writes the heads at discharge-specified wells to the output file
• headspecifiedlines writes the discharges of internal head-specified line boundaries to the output
  file
• rivers writes the discharges of river line boundaries to the output file
• calibration writes the calibration results to the output file (includes the modeled
  head at each calibration target)
• verticalleakage writes the vertical leakages over polygon areas to the output file
• headoutputfile <name.csv> writes the heads to a csv file based on the current contour settings and plot window
• exit instructs AnAqSim to close the current model window

Simple Example

To illustrate the use of PEST with AnAqSim we will present a simple model parameter fitting example. The following description is intended only to show the kinds of things that AnAqSim is capable of when coupled with PEST. It is not intended to be a step-by-step tutorial or set of instructions.

The example provided below is a simple box model that only requires the free educational version of AnAqSim, available from http://www.fittsgeosolutions.com/downloads-licensing/ (be sure to download the AnAqSimEDU version unless you have purchased a license for the full version of AnAqSim).

The box model is a 5000 ft x 5000 ft square area of homogeneous sandy aquifer material with flow from left to right and three pumping wells located near the center. The box model was initially set up with a specified hydraulic conductivity and pumping rates for the wells to calculate the hydraulic head field within the model. From within that head field, we recorded the head elevations at six observation well locations.

The goal of this example will be to have PEST work from the six recorded head values as its inputs to find the “unknown” pumping rates of the three wells and hydraulic conductivity of the aquifer. The model domain and observation well locations are shown in the figure below.

Starting Model

Starting AnAqSim Model

Observation wells (calibration targets) are added to an AnAqSim model by selecting Analysis Input/Calibration Targets/Head and entering the names and locations of the monitoring wells as well as the observed (measured) head at each location. For PEST runs, the observed head value entered is not important, only the locations of the observation wells. This is so we can extract the modeled heads from AnAqSim after each model run using the command line; the observed heads are input directly into the PEST .pst file and are not extracted from the AnAqSim model.

The first PEST file that we need to create is the PEST control file (ExtracWells.pst). A brief discussion of the relevant sections of the file will be included here, but we suggest that those interested in a more detailed description of the PEST input variables read the information contained
in the USGS report describing PEST++ Version 3 (https://pubs.usgs.gov/tm/07/c12//tm7c12.pdf), specifically Appendix 1.

PEST Files

The ExtracWells.pst file is shown below, select parameters that need to be changed to adapt this example to other AnAqSim models are emphasized in blue. The remaining parameters affect how the
calibration is carried out by PEST and are considered beyond the scope of this example.

ExtracWells.pst

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

pcf * control data restart estimation 4 6 1 0 1 1 1 single point 1 0 0 10.0 -3.0 0.3 0.03 10 10.0 10.0 0.001 0.1 100 0.005 4 4 0.005 4 1 1 1 * parameter groups kh relative 0.01 0.0 switch 2.0 parabolic * parameter data kh_1 log factor 100.0 1.0 300.0 kh 1.0 0.0 1 p_well1 none factor -4000.0 -25000.0 -1.0 kh 1.0 0.0 1 p_well2 none factor -4000.0 -25000.0 -1.0 kh 1.0 0.0 1 p_well3 none factor -4000.0 -25000.0 -1.0 kh 1.0 0.0 1 * observation groups heads * observation data cal1 89.34256 1.0 heads cal2 80.57272 1.0 heads cal3 97.98874 1.0 heads cal4 82.09399 1.0 heads cal5 93.70227 1.0 heads cal6 95.60841 1.0 heads * model command line run_anaq.bat * model input/output ExtracWells.tpl ExtracWells.anaq ExtracWells.ins run1.out

The first line, pcf, indicates that this is the “PEST control file”. The next section contains the control data variables. The first blue variable, 4, is the number of parameters that PEST will be trying to calibrate, the second blue variable, 6, is the number of observation points that PEST will use to assess each run’s performance. These two variables must agree with the number of entries for 

* parameter data and * observation data.

The entries in each row under * parameter data contain the unique name of each parameter that will be adjusted during calibration; whether the variable should be adjusted using a log transform or not (for hydraulic conductivities, where values can range over several orders of magnitude, a log transform is recommended); the starting value that the parameter will take; the allowable minimum parameter value; and the allowable maximum parameter value.

The entries under * observation data contain the unique name for each observation point; the measured value for each observation point; the weight of each observation point; and what kind of observation it is (this can be named anything).

The command beneath * model command line is the command or batch file that is run for each model call. In this case, we are using the batch file run_anaq.bat.

The commands beneath * model input/output contain instructions for how to update the parameter data and how to read the observation data. The first line uses the PEST template ExtracWells.tpl to write the new AnAqSim file ExtracWells.anaq for the next model run. The second line uses the PEST instruction file ExtracWells.ins to read the model output from run1.out. PEST interfaces with the AnAqSim model using the instructions in these two files.

The DOS batch file used for this example is the command line call of our AnAqSim model.

run_anaq.bat

1	"C:\program files\fitts geosolutions\anaqsim\anaqsim.exe" ExtracWells.anaq run_anaq.txt

This instructs the computer (from the DOS command prompt) to run anaqsim.exe on the file ExtracWells.anaq and execute the commands in run_anaq.txt.

run_anaq.txt

1 2 3

outputfile run1.out calibration exit

The text file run_anaq.txt contains three lines, a line to use run1.out as the outputfile, a line to execute the calibration command so the modeled heads at each of our calibration targets are recorded for each model run, and a line to exit and close the model.

ExtracWells.tpl

The template file is a replica of AnAqSim XML model input file ExtracWells.anaq with the addition of ptf @ at the beginning and each instance of one of our parameters replaced with @<parameter name>   @. The @ symbol (or whatever symbol follows ptf) is used by PEST to identify locations where parameter data should be written. A snippet of the template file is shown below with the relevant sections in blue.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

ptf @ <?xml version="1.0" standalone="yes"?> <ModelInput> <Release> <ReleaseNo>AnAqSim release 2015-1 beta 30 Jan 2015</ReleaseNo> </Release> <General> <Steady>true</Steady> <Length_unit>feet</Length_unit> <Time_unit>day</Time_unit> <Comments>AnAqSim Remediation Toolkit</Comments> </General> <Solution> <Underrelaxation>0.9</Underrelaxation> <Maximum_iterations>20</Maximum_iterations> <Starting_heads_source>file</Starting_heads_source> <Almost_dry_fraction>0.01</Almost_dry_fraction> <Interface_leakage_option>false</Interface_leakage_option> </Solution> <Check> <Head_check_tolerance>1e-3</Head_check_tolerance> <Q_check_tolerance>1e-3</Q_check_tolerance> <Qn_check_tolerance>1e-4</Qn_check_tolerance> <Extraction_check_tolerance>1e-6</Extraction_check_tolerance> </Check> <ConfinedUnconfinedDomains> <Label_unique>aquifer</Label_unique> <Level>1</Level> <Domain_Type>confined</Domain_Type> <Top_elevation>50</Top_elevation> <Bottom_elevation>0</Bottom_elevation> <Average_head>87</Average_head> <Porosity>0.25</Porosity> <Storativity>0.10</Storativity> <Specific_yield>0.1</Specific_yield> <K1_horizontal>@kh_1 @</K1_horizontal> <K2_horizontal>@kh_1 @</K2_horizontal> <Angle_K1_to_x_axis>0</Angle_K1_to_x_axis> <K3_vertical_top_half>30</K3_vertical_top_half> <K3_vertical_bottom_half>30</K3_vertical_bottom_half> </ConfinedUnconfinedDomains> …

The parameter kh_1 is inserted for both the K1_horizontal and K2_horizontal in the confined aquifer domain for our model. PEST recommends that the variable name be padded by multiple spaces to allow enough space to enter variables (e.g. if the number of desired significant digits for kh_1, above, is less than the space provided, kh_1 will be rounded to fit within the allocated space – 14 digits in the example above).

ExtracWells.ins

1 2 3 4 5 6 7 8

pif @ @Label@ l1 w !cal1! l1 w !cal2! l1 w !cal3! l1 w !cal4! l1 w !cal5! l1 w !cal6!

The instruction file is used by PEST to read any output files and extract the relevant observation data. The @ symbol is used to identify characters in the output file that PEST will place the cursor. The following ExtracWells.ins is used to read run1.out.

ExtracWells.ins begins with pif @ indicating that this is a PEST instruction file and the @ symbol is used to identify characters. The second line, @Label@, lets PEST know that the next command should be run with the cursor placed after the characters Label. In our run1.out file this is the line before the calibration target results. The next line, l1 w !cal1!, indicates that PEST should move down 1 line (l1) place the cursor just after the 1^st white space (w) and read the next uninterrupted set of characters to cal1 (!cal1!). The next 5 lines do the same thing for cal2 through cal6.

run1.out

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ExtracWells.anaq opened Start solving system 11/20/2018 9:16:42 AM 80 equations and unknowns in system Iteration 1 2 3 4 5 Converged within the specified solution check values. Solve complete 11/20/2018 9:16:42 AM Head Calibration: Label Modeled Head Observed Head Residual Time c-1 89.34256 89.34256 -3.870564E-08 0 c-14 80.57272 80.57272 -4.054981E-06 0 TP-5 97.98874 97.98874 -2.511405E-06 0 MW1 82.09399 82.09399 -1.832374E-06 0 MW-2a 93.70227 93.70227 2.057103E-06 0 TW-84 95.60841 95.60841 2.81206E-06 0 Average residual = -5.94717E-07 Sum of residuals squared = 3.824847E-11 Root mean square error (RMSE) = 2.524826E-06

The final PEST file that may be needed is the parallel run management file, ExtracWells.rmf. This file is used to assign any number of PEST slaves (i.e. the individual processors that will run instances of the AnAqSim model) to run in parallel across a range of locations. For this example problem we used two slaves. These are in the folders slave_1 and slave_2 as subdirectories of the folder where ExtracWells.rmf is located. Each folder that is being used for PEST slaves needs to have a copy of the model, and all of the previous files mentioned. A command prompt then needs to be opened in each of these locations and the command pslave needs to be run to set up these locations to receive instructions from parallel PEST (PPEST) followed by the model command line call (run_anaq.bat in this case). The parallel pest run can then be executed in the main file location by entering ppest ExtracWells into the command line (no extension needs to be provided and the .rmf file and .pst file must share the same name).

ExtracWells.rmf

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prf 2 0 0.2 0 'S1' .\slave_1\ 'S2' .\slave_2\ 1 1

The first line of ExtracWells.rmf indicates that this is a PEST run file, the second line has four entries: the number of slaves (2), whether files are individually named for each slave (1) or not (0), the time to wait for machines to catch up in seconds (0.2) (this should be longer when slaves are distributed over multiple nodes on a crowded network), and whether the lambda search is undertaken using partial parallelization (1) or in serial (0). The third and fourth lines contains the name and location of each slave. For this example the slaves are located in subfolders slave_1 and slave_2. The final line is an estimate of the amount of computation time the model requires to finish on each slave in seconds (if the time is unknown use a ratio of computation times). This is useful when running on nodes of different computational power (e.g. different processors on multiple computers).

PEST Run Results

Pest Run Results

For the box model presented above, PEST performed 68 model runs and was able to complete the optimization with a final phi of 0! The lower the phi value, the better is the estimation of the sought parameters. PEST is telling us that, for this simple ideal model example, the parameter estimation is close to perfect.

The comparison of the calibrated model that was used to set the observations heads and the final PEST calibration is presented below. PEST as able to almost perfectly reproduce the original calibrated model.

Final Calibrated Model

Helpful Tips

PEST utilities are available at http://www.pesthomepage.org/PEST_Utilities.php. These commands can help ensure that the input files are formatted correctly and provide debugging information. The most important one is PESTCHEK <name.pst> which checks that the PEST input files are formatted correctly and consistent.

We hope this simple example has shown you how easy it can be, with a few data and instruction files, to set up and execute a PEST parameter estimation process for an AnAqSim model. If you have questions, please contact us.

The files used for this tutorial are available from FlexAEM at: http://www.flexaem.com/downloads/PEST AnAqSim Example.zip

Exploring the power of AnAqSim using QGIS

FlexAEM recently announced the addition of a new set of exercises to the AnAqSim Instructional Series! The new set of exercises demonstrates how groundwater professionals can use the spatial data management and analysis features of QGIS, a free and powerful open-source geospatial information system (GIS) software package to enhance the groundwater modeling capabilities of AnAqSim. 

The series illustrates how QGIS can generate spatial data describing hydrologic and hydrogeologic features to facilitate groundwater model construction, and then import and process AnAqSim model output data to display model results such as water level contours and flow pathlines in both 2D and 3D. For AnAqSim users who may be less familiar with QGIS, the series includes an overview of QGIS and its capabilities, including compatible file formats, vector and raster analysis tools, editing and management tools, and much more.

The new series includes exercises that demonstrate how to perform a number of useful functions with QGIS, including the digitization of site features to create model elements. For example, river or ocean boundaries, or groundwater divides, can be digitized and transferred to AnAqSim to represent model boundary conditions (Figure 1). The boundaries of other features, such as lakes and ponds, can also be digitized in QGIS and placed in the AnAqSim model using appropriate element properties (Figure 2).

Figure 1

Figure 2

The exercises also demonstrate how QGIS can be used to create rivers and assign elevation data to points along a river system. Users will learn how to digitize a river system using a basemap, and then use a raster file to obtain elevation values for the selected points along the river. Users also learn how to easily format the river data and import it into AnAqSim.

Basemaps for digitizing model elements or preparing river data can also be created in QGIS for use in AnAqSim, or basemap images from other sources can be imported into QGIS to facilitate basemap creation. There is a multitude of freely available GIS data available online, which can be downloaded, viewed, and analyzed in QGIS. The exercises included in the set demonstrate how to use these data to create custom basemaps, and then export those basemaps as a DXF file for use in AnAqSim. For example, the set include an exercise that provides a step-by-step tutorial on how to obtain a web map hosted by the USGS, digitize the boundary of a feature using the web map, and then export the digitized boundary to AnAqSim to help establish model boundary conditions.

Figure 3

Figure 4

Finally, the exercise set demonstrates how to export water level contours (Figure 3) or groundwater flow pathlines (Figure 4) generated from an AnAqSim model run, import the results into QGIS, and view them in 3D. Any model result from AnAqSim that contains elevation values can be viewed in 3D in QGIS, which allows users to easily visualize model scenarios.

To learn more about QGIS and how it can be used with AnAqSim, check out the new addition to the AnAqSim Instructional Series at http://www.flexaem.com/tutorials-tools/Instructional-Set-7.