A Decision Framework for Minimum Levels of Model Complexity

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1 Precipitation Precipitation Preface for Groundwater Modeling Advisory Panel White Papers Modeling groundwater in the subsurface environment gives us a view and insight of what cannot be easily seen nor readily observed. The U.S. Geological Survey anticipates future modeling demands will be greater, especially addressing multi-disciplinary factors and applied to landscape-level science as scientific questions and resource issues become more complex. The National Ground Water Association (NGWA) determined that to further support the many interests affected by groundwater, it should mobilize its members to collaborate to improve groundwater modeling and its application. On April 14, 2016, NGWA convened nearly 40 prominent groundwater modelers to form the Groundwater Modeling Advisory Panel (GMAP). The goal of GMAP is to advance the state of groundwater modeling through cooperative information exchange and outreach to groundwater professionals. The GMAP objectives are to address groundwater modeling practice and to research questions and identify alternative/best techniques and responses. GMAP members intend to provide the scientists and engineers involved in groundwater modeling applications professionals and interested members of the public with our collective understanding of the subject matter and observations for consideration in professional practice. We decided not to develop standards, as our members saw the modeling field on a path of continuing and rapid evolution. The members of GMAP identified 33 topics of interest and categorized them into five groups for development. Each group had eight to 15 members and two Co-Leads who facilitated discussions and NGWA WHITE PAPER A Decision Framework for Minimum Levels of Model Complexity 10/4/2017

2 organized preparation of modeling practice white papers. The five initial topic groups were: field complexity, stepwise/analytical element modeling, uncertainty in modeling, model applications, and integrated groundwater/surface water modeling. The papers are written as discussion documents to be updated. The groups met monthly, distributed document development responsibilities, drafted sections of papers, completed their selected modeling practice topic papers, and conducted peer review from approximately June 2016 to June The NGWA Board of Directors approved the papers in October The papers address questions of: How should decision makers consider groundwater modeling in project development and solution? How should the complexity of the subsurface be considered in developing groundwater models? What considerations should be made in moving from simple to more complex model development? How can uncertainty be included in modeling to inform decisions for groundwater supply and remediation? What approaches can be followed to address interaction of groundwater and surface water in decisions? GMAP members believe sharing their knowledge and experience will assist both long-time practitioners and newly-graduated modelers in applying their skills and expertise. The Advisory Panel also hopes modelers will bring other questions forward for consideration and development in future groundwater modeling practice white papers. Future discussions and papers are already planned. A Decision Framework for Minimum Levels of Model Complexity The individuals who gave of their time and expertise on this paper were: Authors Reviewers Bruce Hensel Eve Kuniansky Vikas Tandon Peter Schulmeyer David Bean Jaco Nel Jim Finegan Steve Luis Melissa Hill Jill Van Dyke Michael Alfieri Introduction Groundwater models are valuable tools that can be utilized to make better decisions regarding water resource management and/or remediation of groundwater resources. With advances in technology and the wide variety of sophisticated software codes, groundwater models are being used more frequently to evaluate very large, highly complex hydrogeologic environments. However, building complexity (i.e., incorporating many hydrogeologic features and processes) into a groundwater model is relatively time-consuming and typically requires large amounts of data, which can be costly to collect. Site models require both observed flow and water level data sets for calibration along with mapping of rock properties to avoid the non-uniqueness inherent in the mathematical equation for flow (Hill and Tiedeman 2007; Anderson et al. 2015). Furthermore, there are cases where a simpler, less complex model using less data can achieve overall project objectives. The National Research Council (NRC 2007) advocated the principle of parsimony for model construction, which they defined as the preference for the least complicated explanation for an observation. That is not to say all models should be simple; rather, as stated by NRC (2007), Parsimony does not justify simplicity for its own sake. It instead demands that a model capture all essential processes for the system under consideration but no more. 2

3 The objective of this paper is to provide a general framework for achieving parsimony by leading the reader to the minimum level of model complexity necessary for common groundwater modeling applications. A set of three tables (A, B, C) were developed to form a Model Complexity Framework that presents general considerations for degrees of complexity or detail needed, based on the model type and model objective. This framework provides a tool that can be used in the model selection process to establish parsimony or the appropriate complexity based on the objectives of the model, hydrogeologic characteristics of the site, and characteristics of the constituents of concern when fate and transport will be modeled. Note that this framework only establishes a minimum level of model complexity. A specific model that may appear to call for a lower level of complexity, based on these three tables, may actually require greater complexity, based on factors (for example, legal considerations or statutory requirements) that are not considered by the framework. Such determinations can be made and justified by the modeler. The target audience for this framework consists of the modelers and the stakeholders in the modeling process. The experienced modeler will provide input on which sets of conditions apply to a specific model and make a recommendation consistent with this framework, or provide explanation for why the level of complexity differs from the framework. The framework therefore provides a reference that stakeholders who may not be groundwater-model savvy can use to better understand model selection decisions made by the modeler. Note that this framework does not consider data availability. It is the modeler s responsibility to determine and describe any limitations of the model as a result of data availability restrictions and to determine the acceptable model uncertainty based on model objectives. A scientifically defensible modeling project requires sufficient data be collected to achieve the project objectives, and this framework is organized such that project objectives and technical observations related to hydrogeology and contaminant transport drive model selection (Reilly and Harbaugh 2004). The assumption of the framework is that sufficient data collection has or will be performed to meet project objectives and to sufficiently define hydrogeology and contaminant transport for modeling purposes, in order to avoid the garbage in garbage out situation. [For further perspective on uncertainty, please refer to the NGWA Groundwater Modeling Advisory Panel paper Uncertainty in Groundwater Modeling. ] Using the Framework The Framework has three tables incorporating general, hydrogeologic, and fate and transport factors. A description of the tables follows. Table A provides general guidance, where a relatively simple model may be viable if all applicable rows fall within the column labeled Less Detailed, while a more complex model may be required if the response to any single row falls within the More Detailed column. Tables B and C show increasingly more complex types of models, which require increasingly more complex codes or simulators from left to right. 1 The modeler selects the appropriate response for each applicable row on the table, and the left-most type of model that all responses fall under is the minimum build that achieves parsimony (Figure 1). 1 A code or simulator is the program with mathematical equations, such as MODFLOW or MT3DMS, which is used to build the model. The model is the representation of the hydrogeologic system of interest. 3

4 Model Complexity, Table B. Hydrogeologic Drivers Figure 1. Example use of Table B, where red ovals indicate attributes of the planned model. The yellow line is added to this example to show that the minimum level of flow model capable of simulating all attributes is three-dimensional with zoned properties. All of the red ovals are intersected by or to the left of the yellow line, indicating a model with 3D zoned properties is capable of adequately representing the problem of interest. Table A: General Considerations The level of model complexity is dependent on how the model will be used and the overall objectives of the project, just as much as it is dependent on hydrogeologic and transport factors. For example, a back-of-theenvelope calculation to demonstrate a point to an internal team can contain simplifications and rounding assumptions that would not be acceptable in a report, where the context of those simplifications might be lost. Similarly, additional detail, which is represented in a model by adding complexity, can add to the level of confidence and understanding of the conceptual system based on a balanced, calibrated model result, when the model will be used as a basis for critical decisions such as evaluation and selection of groundwater remediation systems. However, too much complexity may obscure the true drivers of the groundwater system and confuse the modelers, clients, and public stakeholders when attempting to ground-truth the model results. Six general considerations that can affect model complexity are listed in Table A. These considerations are typically developed by the modeler and stakeholders early in the project. It is important to involve all stakeholders, including regulators, in this process so that when the model is presented in a report, all parties go in with a reasonable expectation of the model complexity. Examples of how a model may be more complex or less complex are then provided, based on each consideration. This table is designed to be used in conjunction with Table B, and Table C if contaminant transport will be modeled, to meet the principle of parsimony (as defined in the introduction). 4

5 Table A lists common considerations, but modelers and stakeholders are encouraged to add additional considerations appropriate to their specific application. For example, one consideration not listed in Table A is whether or not the model will be used in litigation. In some cases, a less complex model that is easy for non-technical jurists to understand may be preferable, while in other cases a more complex model may hold up better under scrutiny from technical experts representing an opposing litigant. Model Complexity, Table Table A. General A. General Considerations Considerations Degree of Detail Needed Based on Model Use Model Use Less Detailed Screening Level: analytical or numerical models using layers with uniform properties may provide sufficient detail and complexity More Detailed Decision Making: Additional detail and complexity may be warranted to improve conceptual site model, site data, calibration, and acceptance by outside stakeholders Model Relevancy Model outcome is one of many inputs to decision: analytical models or numerical models using layers with uniform properties may provide sufficient detail and complexity Outcome Drives Decision: Additional detail and complexity generally warranted to improve conceptual site model, data incorporation, model calibration, and confidence in model Flow Model Objective Water Supply Evaluation: simulation of aquifers using a single layer; individual, uniform hydrogeologic parameters or zones that cover large areas and can be correlated to facies changes; confining layers do not need to be discretely modeled and can be simulated using leakance between layers Complex Flow and/or Transport Evaluation: aquifers are subdivided into multiple layers; multiple zones to define hydraulic conductivity and other properties that may or may not be based on hydrogeologic facies, cell-based property distributions may be considered if calibration cannot be achieved using zones; confining units discretely modeled as separate layers Particle Tracking Model Objective Wellhead Protection: uniform hydrogeologic parameters or zones that cover large areas and can be correlated to facies changes Identification of upgradient sources or downgradient receptors: Additional flow model detail and complexity may be warranted to improve model calibration and confidence in model results Transport Model Objective Understand Uncertainty Prediction of migration distance, and/or concentration at potential receptors: Concentration calibration data may be sparse; analytical model or numerical model with few property zones may provide sufficient detail Regional Assessment or Limited Data: Analytical codes, some of which have predefined values based on hydrogeologic environments may be appropriate for screening level assessments Evaluation of remedial alternatives: Additional flow model detail and complexity may be warranted to improve model calibration and confidence in model results Site-Specific: Stochastic analysis can provide in-depth information on uncertainty for a specific site. Table B: Hydrogeologic Drivers A groundwater flow model is a device that represents an approximation of a field situation (Anderson and Woessner 1992; Anderson et al. 2015). In order to determine the type and complexity of the model that may adequately and appropriately represent a site or field situation, the model developer should perform an assessment of the hydrogeologic features that need to be incorporated in the site model. Most models will be built to represent a combination of hydrogeologic features that generally reflect the local and regional hydrogeologic properties, the applicable hydraulic stresses and boundaries, and the physical properties of the groundwater or other fluids under consideration. The number and complexity of the site-specific features the model is designed to replicate determine the minimum level of model complexity necessary to effectively represent the field situation. Table B lists 11 hydrogeologic features that may be considered when making a decision regarding the type of model necessary to represent a field situation. Data on these hydrogeologic features are typically available from site visits, site investigation reports, and publicly available information published by local, state, and federal agencies. A review of boring logs, geologic cross-sections, local or regional geologic and hydrogeologic reports, land use records, maps, aerial photographs, and satellite images will provide information necessary to characterize each of these features. For each hydrogeologic feature, the table provides possible options in a row, ranging from simplest manifestation of the hydrogeologic feature in a model at the left to the most complex manifestation at the right end of the row. The hydrogeologic characteristics fall under column headings in the table that represent the type of model capable of simulating that feature, increasing in complexity from left to right. 5

6 Some of the simpler manifestations of the hydrogeologic features, such as an unconsolidated and relatively homogeneous aquifer with a uniform flow direction, may be simulated using an analytical model. As complexities and non-uniformities increase with depth or laterally, or boundaries and external hydraulic controls influence groundwater flow, more complex numerical models may be needed. Lateral nonuniformities are typically represented by increasing model complexity to incorporate two dimensions (2D), one along the dominant flow path and the other being the horizontal axis perpendicular to the dominant groundwater flow, resulting in plan-view models. The addition of vertical heterogeneities, confining units, leakage between hydrogeologic units, vertical hydraulic gradients, partially penetrating wells, and barriers to flow are typically represented by increasingly complex three-dimensional (3D) models, which may have multiple layers, zones of similar aquifer properties, or in some situations cell-by-cell variations in hydrogeologic properties. In some situations, the presence of hydrogeologic complexities may not be sufficient reason for selecting a more detailed model to represent those complexities, especially if model objectives or the decisions that will be made using the model predictions do not support the additional complexity. For example, if a review of hydrogeologic factors indicate an analytical or a 2D numerical model is generally sufficient to represent the site except for the presence of a confining unit, and the model purpose is to evaluate groundwater flow or extraction well yields without considering flow or contaminant transport across the confining unit, then a 3D model that incorporates the vertical heterogeneity or the confining unit may not be necessary. Specialized models, such as for discrete-fracture flow or for large conduits in karst aquifers, may require detailed field data and be constrained to a relatively small scale or can use statistical evaluations to estimate aquifer characteristics. In addition, groundwater models typically assume laminar-flow conditions, but turbulent flow and multi-phase movement may also be modeled using solutions such as computational fluid dynamics and others. Model Complexity, Table B. Hydrogeologic Drivers Model Complexity, Table B. Hydrogeologic Drivers Hydrogeologic Feature Analytical Type of Model Needed to Simulate Feature 1,2 Analytical Element / 2D Numeric 3D Uniform Layers 3D Zoned Properties 3D Cell by Cell Properties Specialized Number of Aquifers Single aquifer of interest Multiple aquifers of interest Hydrostratigraphy Relatively Homogeneous Mapable Facies Changes Complex, Not Mapped Time Varying Recharge Distribution Not Considered or Uniform Variable across model domain Porosity Equivalent Porous Media Fracture/Dual Porosity Flow Groundwater Flow Direction Uniform Groundwater flow direction is not uniform within model domain Temporal Groundwater Flow Variability Uniform Groundwater flow direction and/or velocity changes over time Wells for groundwater extraction or injection, barrier walls, and other anthropogenic or natural barriers to flow Wells & Barriers None 3 are integral to the hydrogeologic system or modeling objectives Intersecting Lakes, Rivers, Streams None Groundwater interaction with surface water features is integral to hydrogeologic system or model objectives Confining Units Not Modeled Include in model if flow model will be coupled to transport model, quasi-3d models OK for flow only. Density- or Heat- driven flow Not Considered Multi-Phase Flow Simulators Subsidence Not Modeled Include in model for 3-D flow models only. 1. Model complexity increases from left to right, and with darker shading greater complexity. 2. Determine type of model needed to capture hydrogeologic complexity by using the left-most model type that fits hydrogeologic features to be modeled. 3. For non-transport applications, there are analytical models that solve for radial flow to a well 6

7 [For further perspective in adding complexity to models, please refer to the NGWA Groundwater Modeling Advisory Panel paper A Stepwise Approach to Groundwater Modeling. ] Table C: Fate and Transport Drivers Like groundwater flow models, fate and transport models are an approximation (simplification) of the physical, chemical, and biological processes that affect the movement of dissolved solutes from one point to another, and how these solutes may be altered while they are transported (Wireman 2012). Dissolved solutes are transported by physical processes (primarily advection), while chemical and biological processes redistribute (and/or reduce) solute mass among different phases (solid, dissolved, vapor) and forms (reduced/oxidized, parent/daughter products). Table C lists eight physical, chemical, and biological processes that should be considered when deciding what type of fate and transport model is required to represent a project site. Steady-state flow in a single homogeneous aquifer system with a constant solute source term (and sink) may be solved with a simple analytical solution, while transient flow in a multi-layer heterogeneous aquifer system with multiple or variable source terms (and sinks) will require a much more complex analytical or numerical solution. Secondary mechanisms controlling solute transport include sorption/desorption on aquifer materials, where the transport of the solute(s) will be slower (retarded) compared to groundwater flow; hydrodynamic dispersion, where the solute mixes and spreads in groundwater due to the pore-scale variation in groundwater velocity; and chemical reactions resulting in mass loss/production. In some cases, solutes also undergo chemical or biological reactions (i.e., redox reaction, precipitation, hydrolysis decay, reductive decay, etc.). In a simple uniform flow system these processes may be solved for with analytical solutions. However, in many aquifer systems solutes will undergo a combination of chemical and biological reactions that will require the use of more complex numerical solutions to solve. Specialized Model Complexity, Table C. C. Fate Fate and and Transport Drivers Drivers Type of Model Needed to Simulate Characteristic 1,2 Transport Purpose / Characteristic Analytical Particle Tracking Numeric Specialized Groundwater velocity Constant/Uniform Variable over time or distance Sources of COI 3 Single Multiple Source Concentration Relatively Constant Concentration not simulated Changes over time Dependent on ph, redox, and or other constituents Phase of COI Dissolved NAPL / Soil Gas Groundwater Geochemistry ph & redox relatively constant ph and/or redox may change over time ph and/or redox change along flow path COI Sorption None/Linear reversible Non-Linear reversible Not reversible / dependent on other constituents COI Decay First-Order First-Order / Sequential Dispersion Yes Yes 1. Model complexity increases from left to right, and with darker shading greater complexity. 2. Determine type of model needed to capture transport complexity by using the left-most model type that fits hydrogeologic features to be modeled. 3. COI = Constituent of interest, i.e., constituent that will be modeled 7

8 simulators for geochemical reactions (e.g., PHREEQC) may be used independently or as integrated into numerical and other models. In Summary Decisions to move from simple to complex models are challenging. The decisions are influenced by project objectives, field conditions, and availability of and ability to collect field data. The success of model planning to inform project decisions may be affected by the decision makers understandings of the range of model capabilities and their applicability to the objectives of the project given site characteristics. References Anderson M.P., W.W. Woessner, and R.J. Hunt Applied Groundwater Modelling, Simulation of Flow and Advective Transport, 2nd edition. Academic Press, San Diego, USA. Anderson M.P., and W.W. Woessner Applied Groundwater Modelling, Simulation of Flow and Advective Transport. Academic Press, San Diego, USA. Hill, M.C., and C.R. Tiedeman Effective Groundwater Model Calibration: With Analysis of Data, Sensitivities, Predictions, and Uncertainty. John Wiley & Sons Inc., Hoboken, New Jersey, USA. doi: / index National Research Council Models in Environmental Regulatory Decision Making. National Academies Press, Washington D.C. Reilly, T.E., and A.W. Harbaugh Guidelines for evaluating ground-water flow models. U.S. Geological Survey Scientific Investigations Report Spitz, K., and J. Moreno A Practical Guide to Groundwater and Solute Transport Modeling. John Wiley & Sons Inc. Wireman, M Transport and Fate of Contaminants in the Subsurface. Ground Water Protection Council, September Zheng, C., and G. Bennett Applied Contaminant Fate and Transport, 2nd edition. John Wiley & Sons Inc. Suggested Reading Hunt, R.J., J. Doherty, and M.J. Tonkin Are models too simple? Arguments for increased parameterization: Ground Water 45, no. 3:

9 Disclaimer: This White Paper is provided for information purposes only so National Ground Water Association members and others using it are encouraged, as appropriate, to conduct an independent analysis of the issues. NGWA does purport to have conducted a definitive analysis on the topic described, and assumes no duty, liability, or responsibility for the contents of this White Paper. Those relying on this White Paper are encouraged to make their own independent assessment and evaluation of options as to practices for their business and their geographic region of work. Trademarks and copyrights mentioned within the White Paper are the ownership of their respective companies. The names of products and services presented are used only in an education fashion and to the benefit of the trademark and copyright owner, with no intention of infringing on trademarks or copyrights. No endorsement of any third-party products or services is expressed or implied by any information, material, or content referred to in the White Paper. The National Ground Water Association is a not-for-profit professional society and trade association for the global groundwater industry. Our members around the world include leading public and private sector groundwater scientists, engineers, water well system professionals, manufacturers, and suppliers of groundwater-related products and services. The Association s vision is to be the leading groundwater association advocating for responsible development, management, and use of water by National Ground Water Association ISBN NGWA SM The Groundwater Association Press Published by: NGWA Press National Ground Water Association Address 601 Dempsey Road, Westerville, Ohio U.S.A Phone (800) * (614) Fax (614) ngwa@ngwa.org Website NGWA.org and WellOwner.org 9