Dynamics of coupled human-landscape systems

Geomorphology 91 (2007) 393 – 407 www.elsevier.com/locate/geomorph

Dynamics of coupled human-landscape systems B.T. Werner ⁎, D.E. McNamara Complex Systems Laboratory, Cecil and Ida Green Institute of Geophysics and Planetary Physics, University of California-San Diego, La Jolla, California 92093-0225, United States Received 15 March 2007; accepted 30 April 2007 Available online 10 August 2007

Abstract A preliminary dynamical analysis of landscapes and humans as hierarchical complex systems suggests that strong coupling between the two that spreads to become regionally or globally pervasive should be focused at multi-year to decadal time scales. At these scales, landscape dynamics is dominated by water, sediment and biological routing mediated by fluvial, oceanic, atmospheric processes and human dynamics is dominated by simplifying, profit-maximizing market forces and political action based on projection of economic effect. Also at these scales, landscapes impact humans through patterns of natural disasters and trends such as sea level rise; humans impact landscapes by the effect of economic activity and changes meant to mitigate natural disasters and longer term trends. Based on this analysis, human-landscape coupled systems can be modeled using heterogeneous agents employing prediction models to determine actions to represent the nonlinear behavior of economic and political systems and rule-based routing algorithms to represent landscape processes. A cellular model for the development of New Orleans illustrates this approach, with routing algorithms for river and hurricane-storm surge determining flood extent, five markets (home, labor, hotel, tourism and port services) connecting seven types of economic agents (home buyers/laborers, home developers, hotel owners/ employers, hotel developers, tourists, port services developer and port services owners/employers), building of levees or a river spillway by political agents and damage to homes, hotels or port services within cells determined by the passage or depth of flood waters. The model reproduces historical aspects of New Orleans economic development and levee construction and the filtering of frequent small-scale floods at the expense of large disasters. © 2007 Elsevier B.V. All rights reserved. Keywords: Complexity; Modeling; Emergence; Human-landscape coupling; New Orleans

1. Introduction Groups of humans began to significantly alter aspects of their surrounding natural environment thousands of years ago (e.g., Yellow River diversions: Xu, 1993; kelp forest overfishing in California: Steneck et al., 2002). These human impacts on natural processes were mainly characterized by short-lived changes to their microenvironment, without lasting changes to the way humans interacted with the landscape. Similarly, environmental ⁎ Corresponding author. E-mail address: [email protected] (B.T. Werner). 0169-555X/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2007.04.020

processes prompted human responses (e.g., the determination of global settlement patterns by climate: Davis, 2002; retreat of North Carolina coastal cottages in response to an eroding shoreline: Pilkey et al., 1998). In essence, humans and landscapes were interacting linearly, with strongly coupled interactions localized in space and time and without the development of regional or global feedback loops that tend to expand or propagate coupled behavior. The scale of human impacts on the natural environment, however, is now considerably larger than at any point in history (Vitousek et al., 1997). The annual weight of permanently displaced soil owing to human

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modification of the landscape exceeds natural processes (Hooke, 2000). The atmospheric concentration of carbon dioxide and other greenhouse gases has increased from the nineteenth century as a result of fossil fuel combustion (Schimel et al., 1995) and is driving increased temperatures worldwide (Barnett et al., 2005). Regulation of nearly two-thirds of the world's rivers has significantly interrupted the terrestrial leg of the global hydrological cycle (Abramovitz, 1996). Fundamental alterations to oceanic ecosystem dynamics have resulted from overfishing, with functional or permanent loss of many species (Jackson et al., 2001). Similarly, increases in population and engineering capabilities have led people, especially the economically disadvantaged, to occupy increasingly marginal land subject to an array of natural disasters such as hurricanes, landslides and floods (e.g., Davis, 2006a), thereby amplifying the effect of environmental processes on human activities. The increasing strength of these interactions gives rise to the possibility that human agency and landscape processes can no longer meaningfully be treated separately, but rather only as an inter-weaved, coupled system. Possible examples include: levees along the Mississippi River contributing to wetland loss along the Gulf coast, thereby reducing the dampening effect on storm surge levels and possibly enhancing the economic damage from Hurricane Katrina (Stokstad, 2005); increased damage from wildfires linked to fire prevention practices (Goldstein et al., 2003); and overfishing of cod in the North Atlantic leading to the collapse of fishing economies (Kurlanski, 1997). Given the growing strength of these interactions, several questions arise, including: how to describe and analyze these coupled systems, how to model them, and what sorts of new, emergent behaviors might lie on the horizon? A number of investigators have attempted to grapple with aspects of these and related questions. For example, in one set of approaches, measurements are used to map out the possible range of types of interactions between humans and landscape processes, and then regression techniques are employed to project future behavior (e.g., Lent et al., 1999; Smith and Wilen, 2003). In a second approach utilized specifically for climate change, integrated assessment models treat the interaction between simplified aspects of economic development, greenhouse gas emissions and changing climate (e.g., Toth et al., 2003). In a third approach, humans are incorporated into an existing framework for natural systems, such as geological/geomorphic systems (Haff, 2003) or ecological systems (Arrow et al., 1995; Holling, 2001). In a fourth approach, the effect of

economical or political actors on land use is simulated in the context of an agent-based model (Parker et al., 2003). These groundbreaking contributions currently suffer from some limitations. The first approach cannot project significantly beyond currently observed behavior nor treat the possible emergence of novel behaviors, a serious limitation inasmuch as human impacts are unprecedented. To date, the second approach mostly has employed economic and climate sub-models that exclude such nonlinear behaviors as multiple stable states and bifurcations (e.g., Schneider and KuntzDuriseti, 2002; DeCanio, 2003). The path to predictive models using the third approach is unclear, and possibly could be limited by fundamental differences between human behavior and natural systems. The fourth approach, although promising, has not been developed to the point of treating the human-landscape system in a fully coupled manner. Here, our goal is to address these limitations by taking a small step towards generating an overarching framework and methodology for describing and modeling fully coupled human-landscape systems. Our starting point is a modified version of a previously developed picture of landscapes as complex systems (Werner, 2003). We adapt that picture for human and then human-landscape systems, apply the framework to modeling the historical and future development of New Orleans, and then discuss some of the difficulties and challenges for predicting how coupled human-landscape systems might develop in the future. 2. Landscapes as complex systems Complexity is a property of a system that refers to the simultaneous presence of simple and complicated behaviors. A central challenge in the study of complex systems is to find ways to identify and model commonalities of simple behaviors amongst a broad range of systems while also treating the diverse behaviors that distinguish one system from another. A trip to a dune field with aerial photos in hand makes obvious the multiplicity of ways that the state of the dune field can be specified: for example, positions and velocities of grains of sand; morphology of the surface; trace and height of crestlines; mean of crestline spacing, orientation and defect (ends of crestlines) density, averaged locally or over the entire dunefield. These descriptions can be supplemented by a determination of how each of these different variable sets change through time, the system dynamics. These four independent ways of describing the state of the

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dunefield and how it changes through time are dynamically significant: the response time (“time scale”) of variables in each of the descriptions to a perturbation or change in external conditions is different and scale-separate, ranging from a fraction of a second at the grain level to perhaps thousands of years for a dunefield-wide description (Werner, 2003). Nonlinearity and dissipation play critical roles in mediating the dynamical relationship between these differing descriptions. Nonlinearity is the flavor of dynamics that indicates strong two-way coupling between elements, as in the interaction between moving sand grains or sand grains and the wind. Nonlinearity also characterizes transformative, spikey interactions undergoing sharp transitions, as for stream piracy, where one channel loses its upstream source and another augments its flow within a short time interval. In contrast, linear interactions are weak and one-way, such as the effect of a mid-ocean storm in generating swell on beach morphology. Nonlinearity serves to connect variables whose behaviors span a wide range of time scales: for example, the interaction between individual sand grains comprising a dune and dune migration. Dissipation is the irreversible behavior that tends to reduce differences in space or time, as in topographic smoothing processes such as hillslope creep. Dissipation also tends to mix and randomize coherent motions, as in the flow of water through riparian vegetation during a flood. Dissipation underlies the distinct separation of differing descriptions of systems by damping the motion of short-time-scale descriptions over the response time of long-time-scale descriptions: for example, the dissipation of turbulent eddies over the time scales of channel cross-sectional or trace evolution. A complete dynamical representation of the landscape system then consists of specifying its state and behavior with a hierarchy of descriptions, arranged by time scale, along with the connections between levels of the hierarchy. Specification of what lies within the system or in the external world is not arbitrary; the boundaries of a system enclose the smallest set of elements that are nonlinearly coupled, with only weak, linear interactions crossing boundaries. System boundaries increase in spatial extent with time scale: nonlinearly coupled sand grains might stretch over only a small patch of a dune, but strong coupling of spacing and orientation of dunes can encompass tens of square kilometers. The range of possibilities for the state and dynamics of a system can be mapped out using a phase space, in which each variable, describing the system at a particular level in the hierarchy, is graphed along an

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axis in the space; the state of the system through time at that level is traced by a trajectory. Each point in the phase space has an associated vector showing the direction and magnitude of change from that state; bundles of converging or diverging vectors and trajectories indicate the structure of the phase space, the general behavior of the system. Areas of phase space into which all trajectories converge are attractors, and generally are associated with the development of patterned or other ordered behaviors. Each level in the hierarchy is associated with an independent phase space defined by differing axes and structure. If the state of the external environment (at the time scale of that level) changes, then the structure of corresponding phase space changes, possibly resulting in a smooth shift of an attractor to a neighboring location or the destabilization of a previously stable attractor and a rapid transition to a new state, termed a bifurcation for low-dimensional systems. Rapid transitions can be accompanied by a collapse of part or all of the dynamical hierarchy, with some long-time-scale behaviors and patterns disappearing and possibly reforming in a different configuration. For example, slow or small shifts in long-term wind direction over a dune field are accommodated by reorientation of existing dunes by differential migration of crestline defects. A swift, large shift in direction, say by 70°, however, can result in the breakup of long dunes into short segments, which then rapidly reorient and grow in length through annihilation of defects (Werner and Kocurek, 1997). In the first case, the dune field retains its long-time-scale dynamical elements – crestlines and pattern characteristics – whereas in the second case, these levels of the hierarchy largely are temporarily removed from the system. Over the time scale of a particular level in the hierarchy, the levels above provide a context for its shorter-time-scale dynamics, in essence operating as an extension of the external environment through strictly linear/one-way coupling: for example, saltating sand grains on a dune operate within the context of dune morphology, which itself operates within the context provided by the trace and height of dune crestlines. Over longer time scales, however, the dynamics of variables at the shorter-time-scale level are related to the dynamics at levels further up in the hierarchy via nonlinear/two-way interactions. These nonlinear connections are a description of how short-time-scale variables behave over the longer time scales of higher levels and can be specified in two ways. First, the dynamical description can be cast entirely using shorttime-scale variables, with longer-time-scale variables

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and behavior implicit in the specification of dynamics. Aspects of the dynamics that relate to the long-term ordered motion of the short-time-scale variables are termed feedbacks, and the way they lead to development of higher levels in the hierarchy from their initial absence, as in the formation of dunes or river channels from flattish landscapes, is termed self-organization. Second, the dynamical description can focus on longtime-scale variables and processes in well-developed or stable systems, and the way in which long-timescale variables provide the long-term context for (or slave) short-time-scale variables, as in the constraints of a slowly varying river channel on fluid flow (Werner, 2003). Both descriptions refer to the same phenomenon, and are equivalent. The first description emphasizes the effect of short-time-scale variables in the interaction, the second the effect of long-time-scale variables. The two-way, nonlinear nature of the interaction makes clear that two common end-member pictures, a bottom-up, reductionist casual relationship in which short-time-scale, fundamental dynamics exclusively affect longer-time-scale variables and processes and a top-down, universalist picture in which overall, long-time-scale variables and processes common amongst many systems determine everything that is interesting about a system, are erroneous (Werner, 2003). Within this framework, emergent behavior (Holland, 1997) refers to the independent dynamical characteristics of each level of the hierarchy; the variables at one level are tied to the long-time-scale behavior of the short-time-scale variables of the next level down through a separate set of dynamics that depends on both levels. In this sense, emergent behavior is not an unusual curiosity to be debated by philosophy students, but rather a fundamental property of all systems that exhibit a hierarchical structure. The geometrical character of landscapes, being surficial features primarily expressed in two dimensions, leads to significant commonalities in the level structure of hierarchies amongst a diverse set of landforms, which can be summarized with a basic four-level hierarchy, and can be elaborated with detail to fit a broad range of landscapes (Fig. 1a): grains/ fluid parcels or other fundamental constituents; morphology; boundaries or traces of transition zones; pattern characteristics. For example, in a catchment: positions and velocities of soil and sediment particles and water parcels; channel and hillslope elevations; trace or boundaries of river channels; scaling exponents of river networks.

3. Humans as complex systems Our hypothesis is that human behavior can be treated as a dynamical system across a broad range of scales. Within this hypothesis, much of the framework described in the last section for landscapes can be applied in a straightforward manner to human systems. An incomplete hierarchy for human systems might include the following levels, in rough order of increasing time scale (with fuzziness, overlaps: Fig. 1b): neuron-level processes (milliseconds), stream of consciousness, feelings, communication via language, emotions (many seconds), moods (minutes to hours), rational thought/analysis, personality (years), friendships, patterns of economic relations (years to decades), beliefs, world view, laws, customs, culture (decades to hundreds of years), genetic evolution (thousands to hundreds of thousands of years). This picture of human behaviors, organized in a temporal hierarchy, is reflected somewhat in the range of academic disciplines concerned with aspects of human systems, including: neurology, psychiatry, psychology, sociology, economics, history, philosophy and anthropology. However imprecise and inadequate this tentative human hierarchy might be judged, it can serve as a starting point for discussing human complex systems. As for landscape systems, nonlinearity is present at all scales in human systems: for example, feedbacks between feelings and emotions, moods and personality development (Lewis, 2000; DeLanda, 2006, Chap. 3); coordination and sharp transitions in group behavior, as in clapping, laughing or mobs (e.g., Sumpter, 2006); positive feedback mechanisms in concentration of wealth (Glaeser and Shleifer, 2002); and nonlinear fluctuations in stock prices (owing to herding behavior: Feigenbaum, 2003). Dissipation also appears to be pervasive: damping of intensity of feelings with time (possibly related to limited memory capacity); homogenization of behavioral traits and customs, including language (DeLanda, 1997) and gender expression (Bender, 1990); and the dissipative effects of economic transaction costs (Tobin, 1978). Boundaries enclosing human systems increase in extent with level in the hierarchy. Neuron-level processes are generally confined within a single human, but some aspects of stream of consciousness, as well as emotions, moods, feelings and personality, evolve through strongly coupled, nonlinear interactions with other humans, and so, even on time scales of hours to days, individual humans cannot be treated as distinct open systems. At the level of small groups of humans in a world with global communications and transportation

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Fig. 1. General hierarchies for (a) landscape and (b) human systems.

for people from economically prosperous regions, system boundaries bear little relationship to geographical boundaries, and, as illustrated by the “small world” effect (Watts and Strogatz, 1998), these systems potentially can encompass large numbers of individuals. Because of inexpensive transportation, effective communications and expanding commodification, market mechanisms have enlarged system boundaries over time scales characterizing economic development to extensive regions, or, in some cases, globally (Tomlinson, 1999; Robinson, 2004: Chap. 1). The dynamics of human systems generally have much greater potential for diverse and intricate dynamics than do landscapes, because of the greater range of levels and the potential for fast-scale regional and even global connections. Therefore, the structure of phase space at many of the levels should be more complicated,

and the tendency to decay towards well-defined, fixed attractors in the context of an unchanging external environment, common for landscape systems including soil profiles, drainage catchments and coastlines, is suppressed, especially at low to mid-range levels. So, for example, the dance an individual's feelings, emotions, and moods performs in interacting with other humans follows a tortuous pathway in phase space, but personalities and world views typically evolve to a small and relatively stable range of categories (Digman, 1990). At economic and political levels, aspects of behavior also resemble a progression more than a decay to a steady state, driven, in part, by destabilizing positive returns (where increasing sales leads to increasing demand via nonlinear market dominance and standardization, a type of positive feedback, as reflected in VHS vs. betamax or Microsoft

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vs. Apple: Arthur, 1994). The rise and fall of economic, political and cultural systems in the long term (Tainter, 1988) is suggestive of well-defined fixed point, cyclic or chaotic attractors at the highest levels of the human system hierarchy, with less of the confounding aspects of shifting boundaries and external conditions characteristic of the lower levels. Changes in the state of a human system can proceed as part of its internal dynamics as smooth changes in the position of an attractor with drift in the external environment, or as sharp transitions induced by external environmental changes. For example, mood shifts can be prompted by memories of events; the marketing strategy of a firm and product price can evolve smoothly as demand changes; and a political revolution can occur as economic circumstances of workers worsen and awareness of the power of the proletariat increases (as in Europe in 1848: Jones, 1991). The relations between levels in the human hierarchy similarly are restricted to tying the long-time-scale dynamics of lower level variables with behavior at higher levels via a two-way interaction. The long-term effect of a succession of emotions, moods and rational thoughts is to play a role in the constitution of personality, even as personality and identity provide the context in which these faster scale behaviors occur. Higher up in the hierarchy, economic and social interactions provide a basis for rules and laws, whereas the slowly varying form of these laws act to constrain patterns of economic and social behavior. Individuals acting within the context of a market economy exhibit a narrowed range of behaviors stemming from the overriding goal of maximizing profit that drives the key players in market interactions (capitalists). Prediction of system dynamics can be formulated as a problem in which heterogeneous individuals all individually attempt to solve an optimization problem in a single quantity: profit. In contrast, the key players of other types of systems, such as planned, feudal or participatory economies, pursue disparate aims that are difficult to specify or quantify. Political decisions exhibit a parallel range of possibilities, with studies (Valverde et al., 1999; Johnson et al., 2005) suggesting that political decisions largely are based on an assessment of their economic impact, as in the frequently cited cost-benefit analyses (Psuty and Ofiara, 2002). Treating human behaviors as deterministic dynamical systems in this way raises fundamental questions about human consciousness and free will (Dennett, 1991; Penrose, 1991; Searle, 1992; Tegmark, 2000). If genuinely free will, in the sense of conscious beings

making decisions that are not predetermined, exists, it would seem to negate the view that human affairs can be represented as a dynamical system, unless the impact of free will is bounded. The exercise of free will is a behavior within fast-scale stream-of-consciousness dynamics. In a scale-separated hierarchy, where fast-scale dynamics dissipates over the time scales of higher levels, free will would have no impact on slower-scale human behaviors, except on the brink of sharp transitions, where a flattish phase space structure (near, for example, broad peaks) at multiple levels renders the system amenable to pre-meditated kicks in particular directions in phase space, which are associated with free will decisions that lie outside the deterministic dynamics of the system. These free will decisions potentially can affect long-term outcomes by pushing the system towards one of multiple diverging pathways. Therefore, the treatment of human systems as hierarchical complex systems must be supplemented by the caveat that this approach could break down near such transitions, which could be mapped out using numerical models in some cases. More extensive investigation of human dynamics as a hierarchical complex system is warranted (e.g., Allen and Ahl, 1996), but the few examples discussed here suggest that, as with landscapes, this framework appears to be at least superficially applicable to human systems, and, therefore, can serve as a candidate approach for investigating coupled human-landscape systems. 4. Coupled human-landscape systems Humans and landscapes are coupled via a range of mechanisms. Humans impact landscapes by directly transporting sediment, indirectly through enhancing erosion by agriculture and construction or deposition by damming streams and flood control, by altering vegetation and animal life through harvesting and manipulation, by modifying the chemical and microbiological context for landscape processes, and by changing climate. Landscape processes impact humans in two primary ways: at short time scales, natural disasters such as hurricanes, floods, slope failures and earthquakes cause widespread economic damage and human suffering. At long time scales, landscape processes and configurations provide a context for human settlement patterns (Davis, 2002), cultural development (Fagan, 2004) and genetic evolution (Hewitt, 2000). The strength of human impact on landscapes is significantly enhanced at the economic and political levels, where mechanisms that concentrate wealth can

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permit focused and sustained application of resources in ways that are not possible for average individuals or whole societies. The results of resource investment can then lead to further wealth concentration (via profits) that permits more focused application of resources in a positive feedback loop. For example, beach replenishment for protection against storms is focused along coastline segments that, because of recreational value and proximity to population centers, generate significant private profits and tax revenues (see data in: Trembanis et al., 1999). Beach replenishment enhances property values and increases profits from tourism, thereby facilitating further protection measures. The impact of landscape processes on humans is focused where large populations are affected by events and trends, from hurricanes to sea level rise, but particularly where economic damage exhausts aid and disaster relief reservoirs, perhaps partially explaining the difference between the cautious approach in protecting the Netherlands against storm flooding that could devastate much of the country (Rijswaterstaat, 2006) and the more casual approach taken in protecting New Orleans, a small part of a much larger country, against hurricane storm surge (Coltan, 2005; Kelman, 2006). In addition to considering the range of ways that humans and landscapes can be coupled and the strength (nonlinearity) of that coupling, it is necessary to probe the scales and types of dynamics for which humanlandscape coupled systems spread and become pervasive. A geomorphologist with a shovel can interact with a landscape nonlinearly by digging a hole. The aspect ratio and rate of progress are dependent on the stability of the walls, which in turn can depend on the characteristics of the hole. This relatively fast-scale example of human-landscape coupling, except under extraordinary circumstances, however, does not spread to affect large swaths of the landscape nor significant fractions of the population: the hole is isolated and nonreplicating, and people can avoid it. The scales and types of dynamics for which the effects of human-landscape coupling could spread and become pervasive are easier to identify in terms of separate human and landscape systems than for coupled systems, which have not been extensively studied. In some landscape systems, self-organized disturbances and patterns can grow and propagate locally via positive feedbacks in ways that overcome dissipative tendencies. For example, for large-scale coastal cuspate features, disturbances can be amplified through positive feedbacks and replicated, via the medium of wave action that permits a rapid and uniform communication along the

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shoreline (Ashton et al., 2001). Similarly, transfer of seeds from an invasive plant species to a favorable environment can facilitate replication and spread (Higgins et al., 1996). At regional and global levels, changes to landscapes can be triggered by changes to large-scale forcing mechanisms, such as bleaching of coral reefs worldwide owing to increased ocean temperatures (Knowlton, 2001). Changes in forcing could be associated, for example, with stream networks, such as flooding frequency or sediment supply; oceans, such as waves, temperature or sea level; and the atmosphere, such as temperature, precipitation or wind. Rather than acting exclusively as properties of external environments, over a sufficiently long time scale these mechanisms themselves might be elements of feedback loops, such as in the coupling between atmospheric temperature and solar insolation, sea level, ice cover and albedo. In human systems, ideas and behaviors can spread locally by direct observation and mimicry. But in an economic world now dominated by mass communication and inexpensive transportation, ideas and cultural trends are predominantly transmitted through centralized outlets, such as the corporate media (McChesney, 2004); price and investment information is spread rapidly through a globalized, computerized trading system (Mantegna and Stanley, 1999); and capital and agricultural and manufactured goods travel around the globe with little cost or hindrance. Slower changing organizational and physical structures, such as buildings, corporations, and managerial and labor skills, however, act as rate limiting steps that tend to slow responses (e.g., Dixit, 1992). Therefore, humans-landscape coupling should be strongest where fluvial, oceanic or atmospheric processes render significant stretches of human-occupied land vulnerable to large changes and damage, and where market processes assign value to the land and drive measures to protect it from damage. These processes typically operate over the (human) medium scale of perhaps many years to decades over which landscapes become vulnerable to change and over which markets drive investment in structures, evaluate profits from those investments and respond to changes in conditions. 5. Modeling Putting these ideas into a practical simulation with which to investigate coupled human-landscape systems involves analyzing human and landscape subsystems in terms of the hierarchical structure, specifying coupling at different time scales and identifying those levels at

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which coupling is nonlinear, and then determining the coupled dynamics for the variables at the strongly coupled level(s) and ways to represent these efficiently in computer code. Focusing at the time scales where coupling is expected to be greatest in present-day market-based economies, this procedure results in a model structure that specifies (Fig. 2): 1. The state of the landscape with variables defined on a one-dimensional array of cells (for problems involving coastlines) or a two-dimensional array covering a tightly coupled landmass (as in a river floodplain). 2. The state of the economy within that landmass using variables associated with those cells that specify supply, demand and price of product as well as revenues and profits for economic actors and their predictions for the future. 3. The impact of the landscape on the economy through the effect of repeated fast-scale damage events and slowly varying changes to the landscape. 4. The impact of the economy on the landscape through the effect of economically driven alterations to the landscape to mitigate damage. For landscapes, the attributes of cells might include elevation and sediment, water, fire and vegetation characteristics. Dynamics might include sediment routing rules (e.g., Murray and Paola, 1994; Werner, 1995) and algorithms to determine where surface water flows or fire spreads, without including faster-scale grain dynamics, detailed fluid mechanics or fire chemistry. For economics, the attributes of cells might include product price, local demand and supply. Traditional equilibrium economic theory is inadequate for treating nonlinear behaviors of markets, which are characterized by instability and positive returns (Arthur, 1994). For simple examples, such as a one-price stock market, some nonlinear behaviors, such as bubbles and crashes owing to herding, have been modeled at this time scale without reference to representative individual economic actors (using an adaptation of the theory of critical phenomena: Sornette, 2003). In multiproduct markets subject to changing external conditions, however, the range of nonlinear features and behaviors is less clear, and generalizations of this approach have not been developed. As an alternative, models simulating the actions of economic agents in the market have been shown to reproduce nonlinear behaviors of actual markets (Arthur et al., 1997a,b; Tesfatsion, 2002). The employment of these agent-based models can be thought of as a rough analogue of the use of discrete element models for granular materials (e.g., Vu-Quoc et al., 2000), in the absence of a theory for mean grain flow and fluctuations (as is available for some aspects of

turbulent fluid flow). Whether the use of agent-based models ultimately stems from a lack of scale separation between economic agents and prices, as has been asserted (Arthur et al., 1997a,b), or simply from the lack of an appropriate longer-time-scale theory remains to be seen. Agent-based economic models generally simulate agents making decisions about whether to produce, sell or buy a product based on their projections of its effect on their utility, which often is related directly to revenue or profits (revenue minus costs). To project the effects of their decisions on utility, agents employ a series of prediction models, which can include various ways of linearly or nonlinear projecting the recent past into the future, linear projections combined with market (threshold) conditions, which add nonlinearity, or using one or more similar situations in the past to predict the future (local nonlinear projection, as in nonlinear time series forecasting: e.g., Sugihara, 1994). The decision is based on using the model that has the best record for predicting the future (lowest average prediction error). Different agents develop and favor different prediction models, and so they act differently in identical situations. This scheme leads to an overall market that follows a pathdependent trajectory, with multiple attractors and unstable behaviors, as seen in modern markets (Feigenbaum, 2003). The effect of landscape processes on the economic system is simulated in two steps. First, the influence of various events or natural disasters on the landscape is calculated. For example, landscape cells that are flooded because of storm surge along a coast or a flood of given discharge and duration are determined by water routing algorithms that determine where water goes but not the details of how it gets there (excluding fast-scale water flow dynamics). Similarly, the path a fire takes is modeled, but not the chemistry and fluid mechanics of fire. Second, the impact that these influences make on economic structures is assessed using rules: a flood moving through a cell destroys all structures or standing water of a given depth destroys the structure with a certain probability. External environmental processes, such as subsidence and sealevel rise, impact economies indirectly through their effect on natural disasters. The economic system impacts landscapes incidentally as structures are built: for example, increases in runoff from buildings and pavement, an effect that can be modeled using rules that alter landscape processes. The political system marshals resources and uses economic criteria to force changes in landscape processes for the protection of economic structures, based on

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Fig. 2. Form of strongly coupled human-landscape systems: landscape processes (left) dominated by water, sediment or biological routing and transformation, with morphology, vegetation, river channel, ocean, fire and surface water flow sketched; human processes (right) dominated by economic and political dynamics, showing homes and businesses; landscapes impact humans (top) through damage (to buildings shown here) from natural disasters and slowly varying changes to landscape; humans impact landscape (bottom) through effects of economically driven landscape modifications to mitigate damage, with a levee and a water drop on a fire sketched.

a calculation comparing construction costs to likely benefits. These decisions are made by political agents employing prediction models for future revenues, and are implemented using rules that alter the landscape without explicitly treating the fast-scale processes of damage protection construction: for example, levees are emplaced in favorable locations, but the dynamics of levee construction is excluded. In the coupled system, landscape processes impact the economy directly by changing construction costs and by causing losses and indirectly by influencing market behavior, feeding back on prediction models and thereby altering economic agent decisions down the line. Economic and political activity alters landscape processes directly by changing the shape and character of the land (and structures) on which these processes operate. The result is a nonlinearly coupled system in which hierarchical levels and associated dynamics not present in either system in isolation are possible. The coupled system can be analyzed in the same way as its components: level structure, variables and dynamics at each level, system boundaries, attractors and response to changing external conditions.

6. Example: New Orleans Following storm-surge related flooding in the wake of Hurricane Katrina in August, 2005, renewed interest has developed in the system by which New Orleans, a city mostly close to or below sea level, is protected from flooding (Stokstad, 2005; Travis, 2005) and the economic, social and cultural factors surrounding the response to the flood (e.g., Davis, 2006b). The general approach has been to consider the human elements (economic growth through shipping, tourism, etc; scientific approach to damage mitigation; corruption, cronyism; racism) separately from landscape processes (river floods, hurricane storm surge, wetlands degradation) or to focus only on the impact of humans on landscape processes or vice versa. For example, considerable attention has been devoted to understanding the impact of levees on subsidence (Dixon et al., 2006) or increased channelization on wetland degradation (Bourne, 2000). New Orleans has developed as a city, however, largely through strong, coupled interactions between economic development, surface morphology, flooding and levees (Kelman, 2003; Coltan, 2005). Here, we present a preliminary model for the development of New Orleans that illustrates some of the

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characteristics of coupled human-landscape complex systems discussed above and the challenges of developing models for these coupled systems. The initial model domain is taken from a 17 km × 17 km section of the 2001 USGS 24,000:1 DEM for New Orleans East quadrangle resampled on a grid of 100 × 100 m cells, projected backwards to 1788 using a 5 mm/yr subsidence rate (Dixon et al., 2006), and diffused slightly and limited to a maximum 3 m in elevation to eliminate artificial levees and other constructed features. Time progresses in increments of one year, in which economic activity, floods from the Mississippi River and hurricane storm surge, damage to economic structures and construction of artificial levees for flood mitigation (in cells adjacent to the Mississippi River and Lake Pontchartrain) are simulated. Artificial levees can be constructed in cells immediately adjacent to the Mississippi River and Lake Pontchartrain. (For further details, see: McNamara, 2006). 6.1. Landscape model To simulate subsidence, elevations are lowered 5 mm/yr where elevation is less than 3 m, and 10 mm/ yr otherwise (Dixon et al., 2006). Maximum flood discharge from the river is chosen randomly from a power law distribution, with flood stage related empirically to discharge and increasing with mean levee height along the Mississippi (Criss and Shock, 2001). Flood stage is set to its maximum value and a breach in a river levee is created at the first downstream artificial levee cell at which stage exceeds levee height. Flood velocity through the breach is related to the height of flood waters (Wood et al., 2005) and, along with breach cross-section and flood duration, is used to calculate discharge into the domain. Water moves through the breach for four hours (calibrated to match the 1850 New Orleans flood), flowing down the steepest gradient (amongst eight neighbors on the square grid) and filling (and potentially overtopping) local basins within the domain. Time intervals between hurricanes of each Saffir-Simpson category are randomly chosen from independent exponential distributions calibrated to measured return intervals for the U.S. east and gulf coasts. For each hurricane, storm surge is chosen from a normal distribution with mean and standard deviation calculated for each Saffir-Simpson category from hurricane landfalls on the U.S. east and gulf coasts. If storm surge exceeds levee height along Lake Pontchartrain (for simplicity, ignoring overland and artificial channel induced flooding from the south), a breach (with discharge calculated as for river floods) lasting eight hours (to match flood volume following Hurricane

Katrina) is created at a randomly chosen lake levee cell, with water moving down the steepest gradient and filling local basins as in river flooding. To simulate the effect that river channelization has on sediment losses and consequent erosion of storm-surge dampening coastal wetlands, coastal erosion is related to the height of the river levees using historical records (Bourne, 2000; Reyes et al., 2000). For category 3 hurricanes and below, storm surge is reduced by 2.85 mm for every square kilometer of wetland above the 2005 value of 2137 km2 (Stokstad, 2005). 6.2. Economic model The economic model connects seven sets of agents (home buyers/laborers, home developers, hotel owners/ employers, hotel developers, tourists, port services developer, port services owners/employers) through five markets (home, labor, hotel, tourism, port services). Except for port services developers (one agent), the agents are heterogeneous, employing differing prediction models or using differing utility functions to determine actions, thereby resulting in path dependent, multiple-stable-state economic dynamics. Home developer agents determine whether and where to build homes based on expected profit, projected sale price minus elevation-dependent costs. Home buyer agents calculate utility for every available home as a function of projected price and quality (related to prior selling prices of nearby homes). In the home market connecting the two, developers sell constructed homes in random order. The selling price is the highest amount for which at least one home buyer has marginally positive utility. The labor market connects laborers (home buyers) with employers (hotel owner and port services owner agents). Offered wages change incrementally in response to the difference between demand and supply for labor. Labor supply (pool of home buyers) increases incrementally in response to a rise in wages relative to average home selling price. Hotel developer agents decide whether and where to build hotels based on expected profits: projected sale price minus cost, dependent on elevation and preexisting cell state. Hotel owning agents project their willing purchase price based on expected room rental revenue and appreciation, compared to a safe investment (Clayton, 1997). The hotel market connects developers who have built hotels with the hotel owners with the highest willing purchase price. Hotel owning agents offer rooms at a price based on a derivative following strategy (Dasgupta and Das, 2000). Tourists rent rooms at a location using a utility that is a function of availability, quality and price (Sairamesh and

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Fig. 3. Home (white), hotel (dark gray), port service (black), and empty (light gray) cells in model year 1817 (a), 1863 (b) and 2000 (c), with hatched gray areas indicating Mississippi River and Lake Pontchartrain. Extent of development in New Orleans is indicated by checkered lines, traced from historical maps manually overlain and matched to the model domain, follows the patterns of modeled expansion. Remaining undeveloped area in model year 2000 fills in slowly as lowland characterized by high building costs and low property value hinders development. (d) Modeled (solid) and historically measured (asterisks) Mississippi river levee height and modeled (dashed) and historically measured (circle) Lake Pontchartrain levee height. Modeled increase in levees along the river and lake fall within the range of increases observed in historical measurements, except for measured river levee increases beyond spillway construction (1931), related to efforts to stabilize Mississippi River meanders (Barry, 1998). Tax revenue collected in model domain as a fraction of property value and market revenue versus time (e) and flood frequency (yr− 1) for model years 1780–1880 (f) and 1881–1980 (g). Flood frequency is reduced once levee construction is effective in preventing floods (beyond 1881): small floods are filtered out by levee construction, at the expense of large, less frequent disasters.

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Kephart, 2000). The tourism market connects tourists with hotel owners by iteratively matching randomly chosen tourists to hotel rooms that maximize their utility. Construction of port services, as an expensive, long-term investment, is expected to respond only to slowly varying, exogenously determined demand, not shorter-scale collective market dynamics; therefore, a single port developer agent constructs port services in cells where profit, calculated as projected selling price minus costs related to elevation and distance from the river, is maximum. Port services owner agents bid on port services cells in a manner similar to hotel owner agents. The economic model is initialized with a random assortment of home, hotel, port services and empty cells within the confines of the 1788 city (Campanella, 2002). 6.3. Coupling Home, hotel or port services cells through which floods pass are converted to empty cells. Standing water in cells causes conversion to empty cells with an empirically determined probability that depends on water depth (Dutta et al., 2003). Flood mitigation proceeds in two phases. First, levees are constructed independently in individual nonempty cells adjacent to the river or lake to an elevation 1 m above the most recent flood if that flood caused damage exceeding the cost of levee construction in that cell. Second, if total damage from a flood exceeds the cost of building a levee 1 m above flood elevation along the entire length of the river or lake in the model domain, “federal flood protection” is instituted, meaning that levee construction is uniform along the river or lake using that criterion. Additionally, a spillway can be constructed to divert river flood water from New Orleans if damage from the last flood exceeds spillway construction cost. 6.4. Results The modeled growth of New Orleans begins on the higher elevation natural levees, and then, facilitated by economically driven flood mitigation, progresses towards filling in the lower elevation bowl, lagging slightly behind the observed expansion of the city (Fig. 3a–c). Profitable port services remain at higher elevations along the river, because of higher inland costs; hotels also are more profitable than homes, and preferentially are situated on the natural levees until floods at lower elevation become infrequent enough that lower costs make these sites amenable to hotel development. Artificial river levee height increases stochastically in response to damaging floods in a

manner similar to the historical record (Fig. 3d; Kelman, 2003) until construction of the spillway (the last two observed increases in river levees correspond to attempts to address meander migration, not floods: Barry, 1998). Lake levee height increases lag river levees because of the delayed effect of river channelization on coastal wetland erosion and consequent larger storm surges (Fig. 3d). As illustrated with a graph of tax revenue with time (Fig. 3e) and flood frequency (Fig. 3f-g), the effect of increasing protection is to filter out small frequent floods at the expense of rare large disasters. This preliminary model for coupled development of New Orleans omits some aspects that might be dynamically significant, including flooding from precipitation or storm surge from the south, canal building and water pumping, but it does illustrate some of the general aspects of modeling human-landscape coupled systems discussed above, including: (1) Human-landscape interactions are amenable to specific dynamical modeling and analysis; (2) Use of dynamics at the middle levels of the hierarchy, flood routing and market forces, provides a basis for realistic simulation of strongly coupled human-landscape dynamics in New Orleans; and (3) The long-time-scale dynamics of the modeled system appears to be characterized by an attractor with emergent dynamics in which small scale floods are filtered out at the expense of amplifying the impact of large floods to be significant disasters, because protection from small scale floods facilitates development in areas prone to disaster and increased channelization causes an increase in flood size that results in enhanced damage from the low frequency flood events. 7. Discussion The procedures for describing and modeling coupled human-landscape systems presented here constitute a first step toward developing a prediction system for the future of the surface of Earth in which new, emergent behaviors perhaps can be foreseen and the possible outcomes of applying free will decision making to the limited situations where it might have an effect can be investigated. Aspects of this methodology, particularly with regard to human systems, might prove inadequate. For example, markets currently are dominated by decision making based on profit, a behavior that is well-described by the agent-based models used here. Widespread concern about accelerating alterations to physical and ecological life support systems, as in current alarm about global climate change (Dessler and Parson, 2006),

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