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EOS, TRANSACTIONS, AMERICAN GEOPHYSICAL UNION

VOLUME 95 NUMBER 32

12 August 2014

PAGES 285292

2014. American Geophysical Union. All Rights Reserved.

Exploratory Modeling: ExtractingCausality From ComplexityPAGES 285286

On 22 May 2011 a massive tornado torethrough Joplin, Mo., killing 158 people. Withwinds blowing faster than 200 miles per hour,the tornado was the most deadly in the

United States since modern record keepingbegan in the 1950s.

As with any similar disaster, the eventposed a number of questions: How and whydid this happen? What forces caused the tor-nado to form? What were the properties of theair and the land that spurred it to such greatstrengths? In many cases, researchers work toanswer these questions not just for the disas-ter in question but in a general sense.

Ever-advancing computing resources temptresearchers to simulate environmental sys-tems in ever-increasing detail. An atmosphericmodel able to represent fine-scale turbulenteddies coupled to a land surface model, for

instance, could be used to reproduce theJoplin tornado to try to figure out exactly whythat storm grew so large. However, althoughsuch detailed simulations may be suitable forscenario-based predictions such as a specifichistorical event, they often are too contextu-ally dependent to investigate fundamentalcause-effect relationships. In short, advancedmodels may tell us how specifically but notwhy in general.

A major contemporary scientific challengeis to develop ways to resolve causality, notjust correlation, in large-scale, nonlinear Earthsystems. The goal is to answer the question ofwhat makes a tornado stronger rather thanwhat made the 2011 Joplin tornado so strong.

One way to attempt to resolve causality ina complex system is to adopt an exploratorymodeling approach (see Figure 1). In such anapproach, simple models are run repeatedlywith different combinations of parametervalues, governing mechanisms, or levelsof mechanistic detail. At each stage of thisiterative process, hypotheses are generated,tested, and refined in conjunction with fieldobservations.

This approach has been refined in the past20 years in the geomorphological sciences.Here we explore the new opportunities af-forded by increasing computing power andexpanding sensor networks used in conjunc-tion with exploratory modeling.

Appropriately Minimalist Modeling

Scientists who study nonlinear, dynamicsystems have long been aware that complexphenomena may arise from simple processes.Simple sets of physical interactions within cer-tain ranges of parameters can produce chaoticbehavior, spatially periodic patterning, cata-strophic shifts, phase transitions, or (multi)fractal scaling [Schertzer and Lovejoy,2011].

Exploratory modeling is, in essence, aphilosophical approach to identifying theseunderlying processes. The reduced detail andcomplexity in exploratory models enable

hypothesis testing over large spatial and timescales and enable rapid testing of many com-binations of parameters and processes with-out the need for an expensive supercomputer.

Exploratory modeling works by intention-ally leaving out or simplifying physical detailslike turbulence or the role of nutrient trans-port on detrital sediment production, notnecessarily because those details are poorlyunderstood or computationally demandingbut because doing so helps elucidate theessential causative processes.

To ensure that essential processes arerepresented in a way sufficient to reproduceobserved emergent processes, exploratorymodels may go far beyond so-called toyor

bare bonesmodels with the most minimallevel of detail. However, they remain differ-entiated from more figurative models in thatsecondary dynamics are absent or repre-sented with very low levels of detail. Key todeveloping a successful exploratory model isselection of the appropriate level of detail,which should be just sufficient to reproducethe emergent phenomena of interest and anysecondary details useful for selection betweenmultiple models. Exploratory models gener-ally work at the coarsest scale of processdescription commensurate with the problembeing investigated.

Examples of Successful Exploratory Models

In geomorphology, the use of exploratorymodels to identify fundamental cause-effectrelationships dates back 2 decades to thework ofMurray and Paola[1994]. In theirresearch the pair distilled braided streamdynamics down to an essential set of rulesin this case, how riverbed slope guides dis-crete parcels of water and sediment.

Using their simplified model, the authorswere able to resolve a long-standing question

in geomorphology. Namely, by using multiplemodel runs where different rules for sedimenttransport were switched on or off, Murrayand Paola found that readily erodible banksunencumbered by topography are a keyrequirement for the formation of braidedstreams.

More recently,Rozier and Narteau[2014]used a few simple rules representing the mo-tion of sand grains coupled to a model of air-flow to elucidate the fundamental processesguiding barchan dune formation. The modelsability to reproduce dune merging and calv-ing behavior suggests that simple rules ofsediment motion are sufficient for the devel-opment of these behaviors in a broad sense.

As computational power increases, thetendency is to want to add complex physicalprocesses into model simulations. In both ofthese examples, however, details such asspatially explicit turbulence would have beenan unnecessary complication if the goal wereto define first-order drivers and sensitivities.

Simple Models Facilitate UnderstandingCoupled Dynamics

Exploratory models are particularly pow-erful for understanding coupled physical-human-biological dynamics when there aremany potential drivers or many spatiotemporalscales that are potentially important.

For example, to understand the criticaldrivers of landscape pattern formation inthe Florida Everglades and its sensitivities tohuman stressors,Larsen and Harvey[2010]developed an exploratory model that coupledflow, vegetation, and sediment dynamics. Sothat the model could represent millennia oftime, simplifications were made in how flowwas simulated by obtaining approximatesolutions to governing equations and decoupl-ing the solution of vertical velocity profilesfrom that of horizontal flow. Phosphorus, asensitive driver of Everglades vegetation butone hypothesized not to play a major role in

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landscape patterning, was represented onlyindirectly in a term for a peat accretion rate.

Despite these simplifications, the authors

used a detailed representation of how waterflows through different vegetation communi-ties that was developed in close associationwith field experiments and supported by data[Larsen and Harvey,2010]. Consequently, res-toration managers deemed the model trust-worthy enough to use in simulating how flowaffects sediment transport and landscapedevelopment, information that continues toinfluence subsequent restoration decisions.

In another recent example that combinespaleoclimatology, hydrology, ecology, andarchaeology, Coulthard et al.[2013] used anexploratory model to test the hypothesis that

early humans were able to migrate out ofAfrica through the Sahara Desert by follow-ing green corridors along rivers. Critically, a

simplified exploratory flow model allowed fullhydrodynamic simulations of river flow andflooding at continental scales. The researchshowed that in previous wetter climates therecould have been enough water to permitmigration along these corridors.

In these and other examples, the strategiesused to simplify complex processes and in-teractions to the appropriate level of detail arewide ranging. Strategies include rule-basedcellular automata approaches, reduced spa-tial dimensionality of governing equations,decoupling equations for dynamics that areonly weakly linked, and hierarchical tech-

niques for representing cross-scale dynamics[Hewitson and Crane,1996;Royle and Dorazio,2008].

Exploratory Modeling as a Research Guide

Although predicting emergent behaviorfrom a set of known interactions can bestraightforward, ascertaining the critical in-teractions that explain observed emergent

behavior is more challenging. The problemis that several different processes or param-eter values can be combined to create thesame emergent outcome, an issue known asequifinality.

Researchers using exploratory modelingaddress equifinality by constructing a varietyof models that follow many potential path-ways to produce an emergent phenomenon.Each of these different model constructionswill behave slightly differently, and observa-tions can be used to discriminate betweenalternate explanatory mechanisms. The ben-efit of exploratory modeling is that these vari-ous model constructions can guide specificobservational research.

As an example, multiple mechanisms havebeen proposed to explain the maze-likeridge-hollow patterns ubiquitous in borealpeatlands. By turning simple formulations ofthese mechanisms on and off in a factorialdesign modeling experiment,Eppinga et al.[2009] showed that one of two mechanismswas responsible for the patterning: either awater stress feedback by itself or a water stressfeedback coupled to a nutrient accumulationfeedback. Further modeling research showedthat nutrient concentrations would be lowestunder ridges in the former scenario and high-est under ridges in the latter.

Targeted sampling, motivated by the ex-

ploratory modeling, revealed that nutrientpatterns in a continental peatland were con-sistent with the nutrient accumulation feed-back, whereas those in a maritime peatlandwere consistent with the water stress feedback[Eppinga et al.,2010]. Critically, the exploratorymodeling provided recognition that nutrientpatterns were mechanistically discriminatoryand highlighted the most efficient strategy forfield sampling.

Identifying New Causal Mechanisms

The models highlighted here were con-structed on the basis of conceptual modelsand hypotheses developed from expert knowl-

edge or from the mechanisms known to drivesimilar systems. By necessity, the causal un-derstanding that developed through the appli-cation of these models was born out of trialand error through many iterative refinements.There is no guarantee that the exploratorymodeling vetted all plausible hypotheses.

Fortunately, emerging statistical approachesin the geosciences may improve hypothesisgeneration and the efficiency with whichmodels converge on plausible causal mecha-nisms. Granger causality [Detto et al.,2012]and transfer entropy statistics [Ruddell andKumar,2009] resolve true causal relationships

Fig. 1. Exploratory modeling can play one part within a comprehensive approach to studyingcomplex environmental systems. In this conception, models and field observations become pro-

gressively more refined toward the center. The iterative refinement is complete when the model issufficient to meet specified objectives. ET means evapotranspiration.

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Eos, Vol. 95, No. 32, 12 August 2014

between variables as well as their time scaleof interaction. These analyses enable induc-tive delineation of process networks fromtime series of multiple variables. Processnetworks constitute hypotheses of potentialcausal mechanisms, which would then betested through, for example, an exploratorymodeling process.

As the iterative process of model refine-ment and field observations proceeds, ques-

tions and hypotheses become more specific.Thus, the level of detail in the later modelsmay extend beyond what one would typicallyconsider to be an exploratory model.

In their braided stream research, the ab-stract exploratory models developed byMurrayand Paola[1994] could replicate generalchannel dynamics yet exhibited scaling prob-lems and failed to replicate observed braid-ing intensity or high-sinuosity meanders[Doeschl-Wilson and Ashmore,2005;Zilianiet al.,2013]. Later research that employedsolutions to the full shallow-water equationswith secondary circulation corrections (ratherthan Murray and Paolas simplified version)

fixed these problems but necessitated the useof a supercomputer [Nicholas,2013].

In this way, the exploratory model may beperceived as a deductive counterpart to ex-ploratory statistics. Like a principal compo-nent analysis, it is useful as a way to identify themechanisms responsible for the emergence ofa large percentage of the coarse-scale streambehavior, but more detailed models maybe needed to resolve the finer detail of thatpattern.

A Foundation of Simplicity

Simplified models have flourished in thegeosciences since the advent of computer

programming. Yet progress on using simplifiedmodels to resolve causality in complex Earthand environmental systems has been uneven.

There seems to be an emerging recogni-tion that exploratory models occupy a nichedistinct from that of detailed simulation mod-

els, analogous to the way exploratory statis-tics occupy a niche distinct from predictivestatistics. Exploratory modeling and explora-tory statistics both yield a coarse, fundamentalunderstanding of primary drivers and sourcesof variability and may serve as an impor-tant precursor to more detailed subsequentmodeling.

Combined with continually advancing com-puting power and the introduction of new

statistical techniques, exploratory modelingwill provide geoscientists with ever moreopportunities to enhance their understandingof complex systems. In fact, they are rapidlyemerging as a key foundation for any endeavorthat seeks to test hypotheses to better under-stand system drivers.

Acknowledgments

This feature reflects the contributions of alarger group of participants in the NationalScience Foundationfunded workshop TheArt and Science of Reduced ComplexityModeling in the Environmental Sciences(NSF EAR-1263851). Participants names andworkshop resources, including toy models foreducational use, can be accessed online athttps://sites.google.com/site/rcmworkshop/home.We thank Norm Miller and two anon-

ymous reviewers for helpful suggestions.

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Author InformationLAURELLARSEN, University of California, Berkeley;

email: laurel@berkeley.edu; CHRISTHOMAS, BritishGeological Survey, Edinburgh, UK; MAARTENEPPINGA, Utrecht University, Utrecht, Netherlands;and TOMCOULTHARD, University of Hull, Hull, UK

https://sites.google.com/site/rcmworkshop/homehttps://sites.google.com/site/rcmworkshop/homehttps://sites.google.com/site/rcmworkshop/homehttps://sites.google.com/site/rcmworkshop/homehttps://sites.google.com/site/rcmworkshop/homehttps://sites.google.com/site/rcmworkshop/homehttps://sites.google.com/site/rcmworkshop/homehttps://sites.google.com/site/rcmworkshop/homehttps://sites.google.com/site/rcmworkshop/homehttps://sites.google.com/site/rcmworkshop/home