The Current State of Modeling

by Randall J. Hunt1 and Chunmiao Zheng2,3

1Corresponding author: U.S. Geological Survey, WisconsinWater Science Center, Middleton, WI 53562; rjhunt@usgs.gov2Department of Geological Sciences, University of Alabama,Tuscaloosa, AL 35487.3Center for Water Research, Peking University, Beijing, China.

Any philosophy that in its quest for certainty ignoresthe reality of the uncertain in the ongoing processesof nature denies the conditions out of which itarises.—John Dewey, The Quest for Certainty, 1929

With great power comes great responsibility.—Voltaire

Today’s groundwater modeling tools are character-ized by power, capability, and sophistication that wasunthinkable even a few years ago. Boundary conditions(lakes, streams, wetlands) have advanced modules thatallow more realistic depictions of the natural world. Mod-els can simulate multiple scales conjunctively (Mehl andHill 2005; Hunt 2006), or combine different formula-tions of the underlying mathematical governing equations(Haitjema et al. 2010). The unsaturated zone can be rigor-ously included (Jones and Woodward 2001; Radcliffe andSimunek 2010), even on a large watershed scale usingkinematic wave approximations (Niswonger et al. 2006).The ability to efficiently simulate unsaturated zone flowhas been a critical advance to allow models to explic-itly simulate groundwater and surface water interactionsat the watershed scale (Therrien et al. 2006; Markstromet al. 2008).

At the same time groundwater flow modeling hasattained an advanced state, contaminant transport modelshave continued to grow to provide improved simulationcapabilities for complex field conditions. These includesimulation of transport processes in highly heterogeneousmedia based on the dual-domain mass transfer formula-tion (Zheng et al. 2011), accommodation of a full suiteof biogeochemical reactions through fully coupled multi-component geochemical-transport models (Prommer et al.2009; Ma et al. 2010; Parkhurst et al. 2010), and consid-eration of multiphase and multimedia processes (Pruesset al. 2011). Additionally, numerous efforts are ongoingto develop new or improved mathematical formulationsthat may deal more effectively with non-ideal contaminanttransport behaviors arising from strong aquifer hetero-geneity (Berkowitz et al. 2002; Zhang and Benson 2008).One example of such heterogeneity by Bianchi et al.(2011) shows decimeter-scale preferential flow paths witha varying degree of connectivity within a small aquifercube (Figure 1).

Groundwater flow and contaminant transport model-ing have been greatly facilitated by rapid technologicaladvances on two fronts: (1) the development of compactand large-memory field sensors that have yielded richdatasets for model calibration, (2) the exponential growthin computing power, which has substantially strengthened

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Figure 1. One realization of the hydraulic conductivity fieldfrom the MADE site described by Zheng et al. (2011). Thefield is generated using the geostatistical program TPROGSconditioned to hydraulic conductivity values estimated fromgrain-size data at 1741 points. Such detail in the subsurface isoften critical for transport model predictions (from Bianchiet al. 2011). This figure is reproduced/modified by permissionof the American Geophysical Union.

our ability to simulate and understand hydrologic pro-cesses and water quality evolution at unprecedented res-olution and detail across multiple spatial and tempo-ral scales. For example, Hammond and Lichtner (2010)

discussed the application of a massively parallelized codethat employed more than 130,000 CPU cores to simulatethe fate and transport of a uranium plume. Kollet et al.(2010) presented the results of a proof-of-concept studyof regional scale hydrologic simulations based on a max-imum number of approximately 8 × 109 grid cells. Thesestudies demonstrated that regional scale hydrologic andgeochemical simulations on the order of 103 km2 are fea-sible at fine spatial resolution (∼100 to 101 m laterally,10−2 to 10−1 m vertically) and an hourly time interval.

Calibration of flow and contaminant transport modelscan include thousands of parameters and hundreds of thou-sands of observations. As a result, parameter estimationapproaches have become sophisticated enough that multi-day conferences can be held on a single companion code(for example, http:/ /www.lulu.com / product / ebook / pest-conference-2009-proceedings/17376714). These largeparameter estimation problems can be solved using par-allel computing, either locally or distributed to satelliteoffices, or even using cloud computing (Hunt et al. 2010).Moreover, freely available software suites include tradi-tional nonlinear regression as well as advanced mathemat-ical formulations and global methods (e.g., Shuffle Com-plex Evolution, Covariance Matrix Adaptation Scheme).For example, technologies ported from other industriessuch as singular value decomposition (Figure 2) are allow-ing more robust and efficient mathematical formulationsof groundwater models. Graphical user interfaces now

Figure 2. An example of singular value decomposition of a photograph image. When the matrix is perfectly known (as is thecase with pixels in the original image), the highest resolution for a given number of singular values can be shown visually.For reference, the image with 20 singular values represents less than 10% of information contained in the original imagein the upper left, yet it contains enough information that the subject matter can be easily identified. Although informationof groundwater systems is not as well-known as that in this image, a similar concept applies: if too few singular values areselected, a needlessly coarse and blurry representation of the groundwater system results. Moreover, when the informationcontent of the calibration dataset is increased, a larger number of data-supported singular values can be included, resulting ina sharper “picture” of the groundwater system (from Doherty and Hunt, 2010; image from and SVD processing by MichaelN. Fienen, USGS).

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(a) (b)

(d)(c)

Figure 3. Groundwater model-derived recharge and discharge patterns visualized using a GIS post-processor. The figureshows: (a) raw model output; (b) results processed using a normalization algorithm; (c) a two-dimensional moving averagealgorithm; and (d) a sophisticated iterative low-pass filter algorithm (from Lin et al. 2009).

routinely include these advances, and with GeographicInformation Systems, a full-featured modeling environ-ment is available where a modeler can harness thisextensive capability using common tools and approaches(Figure 3). This, in turn, reduces learning curves and typo-graphic input errors. In short, the advances of the past haveprovided today’s modeler with a vast array of powerfulenvironmental simulators.

At the same time, philosophical limitations of modelshave become more widely understood. Early approachesof “as simple as possible” were supplanted by those focus-ing on true parsimony— not only as simple as possible,but also including the often overlooked corollary “butno simpler” (Hunt et al. 2007). Simply including thou-sands of parameters in a model does not mean that theresulting calibrated model must be highly heterogeneous(Fienen et al. 2009). Moreover, if a model is oversimpli-fied, salient details are omitted. These shortcomings colorand in some cases confound a model’s ability to representthe natural world, and they can even make estimations ofuncertainty uncertain (Moore and Doherty 2005). But, thenatural world is more complex than can ever be includedin a model, even if it were possible to characterize theentirety of that complexity in the field. Uncertainty ofthe model’s ability to capture natural world complexityimportant for a model prediction, as well as imperfectknowledge of what future salient stress regimes will be,are key drivers of future prediction.

Therefore, models can never be considered crystalballs predicting the future, no matter how well constructed(Doherty 2009). That does not mean that models do nothave utility today, however. The key is to recognizethat models are created for a specific objective or setof objectives, thus all models have a societal decision-making context that can elucidate what is appropriatesimplicity. That is, a model need not reflect all aspectsof the natural world perfectly; rather, it must encapsulate

enough of the natural world to be useful for thespecific question being asked or the specific purposefor which the model was designed (NRC 2007). In thisway model expectations have evolved from constructing“true” models of the incomprehensibly complex naturalworld to “adequate” models, a view that reflects theunknowable aspects inherent to models as well as the factthat modeling endeavors do not have unlimited funding(Haitjema 2011).

In many ways, current modeling has moved beyonda focus on computer codes and enhancing code tobetter reflect the natural world (indeed, unlike the past,a master’s level graduate student will likely never becalled on to write their own groundwater modeling code).Models are instead now better thought of as heuristicscience-based tools to assess what has happened, what isin the realm of possible for the future, and how uncertainthese conjectures are. Heuristic (to find or discover) refersto experience-based techniques for problem solving andlearning. Where an all-encompassing search is impossible,heuristic methods are used to speed up the process offinding a satisfactory solution. In this way, a model is notthe natural world captured in the computer, rather it is aform of “computer-aided thinking” (Molz et al. 2011), atype of calculator that allows exploration of a problem andthe bounds of what might happen using the quantitativeframework and physics that approximate our world. In thiscontext, one who builds a model is always expected to bemindful of the larger world where the model is to be used.Therefore, today’s modeler can be thought of as part of alarger team encompassing many aspects outside the realmof pure hydrology, such as ecology, economics, policy,regulation, and decision-support information technology.

With this in mind, it is worth restating the possibleroles of models in today’s decision making. As Doherty(2011) points out, “a decision often must address the factthat something bad may happen. We may be willing to

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pay a price to reduce the likelihood of its occurrence.How much we are prepared to pay depends on the cost ofits occurrence, and on the amount by which its likelihoodcan be reduced through preemptive management.” In thisview, the current role of modeling is to provide decisionmakers with a science-based estimate of likelihood thatsomething might happen, not predicting the future. Rather,modeling is better thought of as showing what we donot know, as well as what we do. Or put another way,although modeling cannot guarantee the right answerregardless of the advances we make, it can relate wherewithin the uncertainty limits the answer should lie givenexpert knowledge and observations from the site. Acaution for current models is, therefore, that the powerof running sophisticated models using parallel computingon many CPUs can in fact result in simply getting badanswers faster.

This line of reasoning suggests that groundwatermodel uncertainty also interacts with the decision-makingprocess in less obvious ways (Hunt and Welter 2010).As noted by many, the model-construction processorganizes and formalizes potential conceptual models ofa groundwater system. This in and of itself has utilitybecause it raises the discussion of contrasting professionalopinions to discussion of reasonableness of process andranges of model inputs. Even models that fail to reproduceobservations may provide useful insight into the utility orfutility of the conceptual model—an insight that oftenis more useful than partially successful model results.Moreover, quantitative hydrologic models often feed lessquantitative ecological, economic, and societal elementsof decision making. What else is there to use in theabsence of admittedly heuristic insights gained fromthese groundwater models? Although we cannot calculatehard and fast error bounds around a completely accuratemodel prediction, attempts at such calculations can stillhave value—for example, subtracting the predictionuncertainty for various scenarios of future monitoringand data collection. This type of model output facilitatesfocusing on efficient use of current and future monitoringresources—something valued by many decision makersregardless of background, system managed, and socialcontext.

Thus, despite the plethora of sophisticated tools andcapabilities, a good modeler of today is no different thanone of the past. All present, past, and future modelingproblems can be considered mathematically ill-posed andunder-constrained by observations from the field. There-fore, although we have the ability to create very complexand realistic looking models, there remains a great mod-eling responsibility to distill the complexity of the siteto what is truly important. That is, the ability to decom-pose a societal problem to its component parts is still ofthe utmost importance now as it was in the past whenthese advanced capabilities did not exist. Or put anotherway, it does not matter how “real” a model looks if salientprocesses are missing, confounded, or misrepresented; theonly thing real is the model is not good.

As in the past, the quality of current modelingdepends more on hydrosense than horsepower! Thishydrosense—the intuitive feel of what is and what isnot reasonable for a system that is difficult to observedirectly—is critical because that is still the primary mech-anism to assess if the model is a reasonable simulator,or is suffering from GIGO (garbage in, garbage out).Moreover, knowing the cost-benefit trade-offs of modelpower/complexity is needed to avoid unnecessary, andoften expensive, modeling ornamentation—that whichmakes a model look real but adds cost without benefitin the best case, or in the worst case, so obfuscates modelerrors that the model is not even an adequate simulator forthe question asked. Developing a modelers’ hydrosense isnot an exact science, unfortunately. Clearly, the ability toconceptually frame real problems into mathematical con-structs such as back-of-the-envelope calculations (Hait-jema 2006) is more than an academic exercise. The bestmodelers today are still those that can intuit fundamentalprocesses and concepts (such as mass balance, water flows“downhill” from higher to lower total head, transport timescale), and they then relate these to complex model con-struction and critical assessments of model output. Use ofhand calculations, analytical solutions, and simpler mod-eling techniques such as analytic element methods (forexample, see Ground Water special issue volume 44, num-ber 1) allow a modeler to develop insight without undueamounts of time and funding. Hydrosense pays many div-idends, as this critical thinking is necessary to constructand vet all the powerful modeling tools of today, as wellas the modeling advances of tomorrow.

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