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O R I G I N A L A R T I C L E S

The Urban Funnel Model and theSpatially Heterogeneous Ecological

FootprintMatthew A. Luck,1,2,* G. Darrel Jenerette,1,2 Jianguo Wu,1 and

Nancy B. Grimm2

1Department of Life Sciences, Arizona State University West, 4701 W. Thunderbird Road, P.O. Box 37100, Phoenix, Arizona85069-7100, USA, and 2Department of Biology, Arizona State University, Tempe, Arizona 85287, USA

ABSTRACTUrban ecological systems are characterized by com-plex interactions between the natural environmentand humans at multiple scales; for an individualurban ecosystem, the strongest interactions mayoccur at the local or regional spatial scale. At theregional scale, external ecosystems produce re-sources that are acquired and transported by hu-mans to urban areas, where they are processed andconsumed. The assimilation of diffuse humanwastes and pollutants also occurs at the regionalscale, with much of this process occurring externalto the urban system. We developed the urban fun-nel model to conceptualize the integration of hu-mans into their ecological context. The model cap-tures this pattern and process of resourceappropriation and waste generation by urban eco-systems at various spatial scales. This model is ap-plied to individual cities using a modification oftraditional ecological footprint (EF) analysis that isspatially explicit; the incorporation of spatial heter-ogeneity in calculating the EF greatly improves itsaccuracy. The method for EF analysis can be further

modified to ensure that a certain proportion of po-tential ecosystem services are left for in situ pro-cesses. Combining EF models of human appropria-tion with ecosystem process models would help usto learn more about the effects of ecosystem serviceappropriation. By comparing the results for foodand water, we were able to identify some of thepotentially limiting ecological factors for cities. Acomparison of the EFs for the 20 largest US citiesshowed the importance of urban location and in-terurban competition for ecosystem services. Thisstudy underscores the need to take multiple scalesand spatial heterogeneity into consideration to ex-pand our current understanding of human–ecosys-tem interactions. The urban funnel model and thespatially heterogeneous EF provide an effectivemeans of achieving this goal.

Key words: urban funnel model; human–ecosys-tem interaction; spatially heterogeneous ecologicalfootprint; scale of resource appropriation; water;food; carbon assimilation.

INTRODUCTION

To understand how urban ecosystems work, weneed to consider the interactions between social

and ecological processes. Human systems dependon ecosystem services (Costanza and others 1997;Daily 1997), but human activities can alter the abil-ity of ecosystems to produce these services. Humanactivities affect ecosystems through multiple mech-anisms, including the direct alteration of biogeo-chemical cycles, species assemblages, and terrestrialland-cover characteristics (Vitousek 1994). For ex-ample, increases in atmospheric carbon and bio-

Received 17 October 2000; accepted 31 May 2001.*Corresponding author; current address: Center for Environmental Studies,Arizona State University, Tempe, Arizona 85287-3211, USA;e-mail: [email protected]

Ecosystems (2001) 4: 782–796DOI: 10.1007/s10021-001-0046-8 ECOSYSTEMS

© 2001 Springer-Verlag

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available nitrogen can affect primary productivity,nutrient retention capabilities, and global climate;deliberate and accidental introductions of nonna-tive species alter regional biogeographical patterns;and direct land-cover transformations such as ur-banization and agricultural conversion, as well asinduced land-cover changes such as desertification,greatly modify the patterns and processes of exist-ing ecosystems. As a result of these changes, hu-mans have now appropriated as much as 40% ofterrestrial potential net primary productivity (NPP)(Vitousek and others 1986; Haberl 1997), 26% ofterrestrial evapotranspiration, and 54% of runoff(Postel and others 1996) on a global scale. Anysynthetic universe that purports to represent theecosystem processes occurring in human-domi-nated landscapes must therefore explicitly incorpo-rate human activities.

The city is the principal socioeconomic entity thatprovides for human habitation; current estimatesindicate that over half of the global population willsoon live in urban centers (UN 1997). The US Cen-sus Bureau (1995) has defined urban areas as placeshaving 2500 or more residents and urbanized areasas places inhabited by at least 50,000 people, in-cluding the urban fringe, which is defined as havinga population density of 2590 people per squarekilometer (1000 people per square mile), althoughvarious other defining variables may also be appro-priate (McIntyre and others 2001). Along with theirhigh population density, cities are emergent struc-tures that require a high degree of land modifica-tion, including the emplacement of impermeablematerials (such as concrete, asphalt, and roofingmaterials) and the creation of an extensive infra-structure (sewage, water delivery, and transporta-tion systems). They are centers of business andculture and have well-developed political, eco-nomic, and social organizations.

For the purposes of our study, we consider theurban ecosystem to be a city at a specific point inspace that imports and consumes materials neededfor human survival, such as food and water. At thesame time, cities also are producers of other mate-rials, including finished goods, services, technology,and information, and serve as the hubs of transpor-tation networks. In the parlance of economics, citiesare net producers; but in standard ecosystem termi-nology, cities are heterotrophic—that is, they can-not support total ecosystem metabolism by internalproduction alone—because their overall consump-tion of organic matter (ecosystem respiration, in-cluding that accounted for by burning fossil carbon)vastly exceeds the production of new organic mat-ter by photosynthesis (Collins and others 2000).

Production is much less than respiration in urbanareas; they must therefore be net importers of ma-terials. Although ecosystem services do exist withina city, including the reduction of noise and airpollution, the modification of local climate and run-off characteristics, and aesthetic and recreationalbenefits (Bolund and Hunhammar 1999), these ser-vices are not sufficient to sustain the urban system’smaterial and respiratory demands or meet its needfor waste assimilation. Moreover, the importance ofthese services is secondary to the basic require-ments for human survival. Biological (or physiolog-ical) needs must be met first (Maslow 1954), andthese needs cannot be fulfilled entirely by the city’sinternal ecosystem services.

As human history has evolved, our metabolicdemands have expanded far beyond our basic bio-logical requirements. The maintenance of the struc-ture and function of advanced sociocultural systemsand technology requires the throughput of energytypical of dissipative systems (Nicolis and Prigogine1977). This additional consumption of external en-ergy, termed “technometabolism” (Boyden and Do-vers 1992), can be viewed as a positive feedbackloop for the growth of human systems. As humantechnology and consumption increased, so did ourability to procure and consume resources from ar-eas beyond our immediate surroundings. There is along standing debate among archaeologists as towhat events in human history triggered this shift;but whether it was spurred by the rise of agricultureor the advent of urbanization, it is now undeniablethat the reach of human influence in the modernworld extends to every corner of the globe (Red-man 1999).

We distinguish urban ecosystems from ruralones, which are comprised of farms, agriculture,and other inhabited or intensively managed landsoutside of cities, as well as wild lands—that is, re-gions that are not domesticated, cultivated, ortamed. Such nonurban areas are characterized bylow human population density and less developed,more pervious surfaces; however, land modificationby humans may still be high in rural systems. Incontrast to urban systems, rural and wild-land eco-systems are often autotrophic; thus, they producemany of the resources required by cities. The eco-systems of the rural and wild lands that comprisethe “hinterlands” of cities are thus appropriated tosupply them with natural resources. Althoughthese rural and wild lands are often physically dis-tant from the urban areas that consume their re-sources, the degree to which they are manipulatedand the extent of the land area that is exploited are

The Urban Funnel Model 783

determined by technology, economics, and the size,location, and demands of cities.

An examination of the ways in which a city in-teracts with rural and wild lands can provide insightinto the human–ecosystem relationship. In contrastto wild-land ecosystems, ecosystems of concen-trated human habitation are maintained throughimports of materials and energy produced in exter-nal ecosystems. The appropriation is a dynamic pro-cess and is therefore independent of any single orparticular ecosystem. Dependence on these exter-nal inputs frees human systems from ecologicalconstraints occurring at the local scale, but in ex-change it extends the impact of human influence toremote ecosystems.

The ecological footprint (EF) is the hypotheticalarea needed to provide the ecological services that ahuman or a city utilizes. It has been used to quan-tify the area from which ecosystem services areappropriated at local scales (Larsson and others1994; Kautsky and others 1997) as well as regionalor even global scales (Folke and others 1997, 1998;Young and others 1998; Jansson and others 1999).The EF concept also has been used as an indicatorthat measures the supply and demand of the re-newable resources needed to ensure the sustain-ability of human systems (Wackernagel and Rees1996; Wackernagel 1999). Because the Earth has afinite area, the sum of all EFs must be less than theplanet’s total area for the demands of the currentpopulation on ecosystem services to be sustainable.The area required to support a given system indef-initely cannot exceed the available productive area.

We developed a model to conceptualize the inte-gration of specific urban areas with their reciprocalecological processes at multiple scales and thenused EF analysis to quantify these human-ecosys-tem interactions. To do so, we looked at the importof water, the production of food, and the absorptionof emitted carbon dioxide for the Phoenix, Arizona,metropolitan area, a National Science Foundationurban Long-Term Ecological Research site, andthen extended our analysis to the 20 largest USmetropolitan areas. We hypothesized that city loca-tion would be an important factor. For example,although McDonnell and others (1997) showedthat urban ecosystems were less productive thanrural ecosystems in the eastern United States, weanticipated that the opposite would be true forPhoenix and for other cities that are embedded inharsh environments. This hypothesis was based onthe observation that the import of water and nutri-ents to the city creates an “oasis” of high vegetationbiomass in what would otherwise be an arid envi-ronment.

We examined several specific questions concern-ing the extent of influence of an urban ecosystem:(a) How does spatial heterogeneity in ecosystemservices affect the EF? We expected that the non-random distribution of resources would increase ordecrease the EF as a function of urban location. (b)How does the EF size differ for distinct ecologicalservices? We hypothesized that because the rates atwhich ecosystem services are generated are specificfor each service, the area appropriated for theseservices would be dependent on the resource. (c)How does the EF increase when the demand esca-lates for ecological services? We predicted that theEF size would increase nonlinearly in response toincreases in ecosystem service requirements be-cause the resources for their provision are not typ-ically distributed uniformly across heterogeneouslandscapes.

THE URBAN FUNNEL MODEL OF HUMAN–ECOLOGICAL INTEGRATION

We need to devise new conceptual models thatintegrate multiple-scale social and ecological pro-cesses into a single integrated system (Loucks 1994;Pickett and others 1997). To be most effective, sucha socioecological model would incorporate multi-ple-scale processes and feedback mechanisms si-multaneously and would also explicitly identify thefeedback mechanisms that integrate social and eco-logical processes. Although the effects of the socialdynamics of human systems on the environmenthave been widely documented, we still need toidentify the ecological processes that create ecolog-ical constraints on urban system or operate as feed-back mechanisms.

In the last decade, a number of approaches havebeen developed to take the activities of humans intoaccount as integral components of ecosystems;these include the urban–rural gradient (McDonnelland Pickett 1990; Pickett and others 1997), thewatershed ecosystem approach (Pickett and others1997), a landscape ecological approach (Pickett andothers 1997; Numata 1998; Grimm and others2000; Zipperer and others 2000), and a social eco-logical approach (Grove and Burch 1997). All ofthese approaches emphasize the interactions thatoccur internally or in close proximity to cities. How-ever, reciprocal ecological interactions that affectland-use dynamics are often not identified at thisscale because they are weak and difficult to detect.Because the strength of the interactions is notequal, there is a discontinuity in space betweencities and the ecological systems that affect and areaffected by them.

784 M. A. Luck and others

Although a city directly regulates the environ-ment within its boundaries, it is dependent on eco-logical services that exist at much larger scales andat substantial distances from the city. It is primarilythe acquisition of external resources for humanconsumption, driven by socioeconomics, that al-lows human systems to grow and thrive. In order torelate local human dominance of feedback withinthe physical boundaries of urban areas with re-gional, human and ecological interactions, we de-veloped a conceptual model to capture the multiplescales of these interactions, the urban funnel model(Figure 1).

The outermost ring at the top of the funnel tapsinto the entire pool of ecological resources and ser-vices that are available in the biosphere, a portion ofwhich is appropriated by the city. The funnel rep-resents the structure that channels the flow of ma-terials imported by humans into the urban system.Each city has a funnel that competes for resources;none of the funnels is allowed to overlap with thefunnel of another city competing for the identicalresources. Technology, which influences the de-mand for resources and their transportation, affectsthe funnel size. The cone of the funnel representsthe transportation network that concentrates anddelivers the appropriated resources to the city.Within the urban domain, wastes are remedied (forexample, the sewage treated in wastewater treat-ment plants), deposited and accumulated locally(for example, the solid waste dumped in landfills),or returned in a diffuse form to the biosphere (forexample, emissions of gaseous and particulate at-mospheric substances or the discharge of sewageeffluent to receiving waters). These wastes mayfeed back to affect the pool of available biospheric

resources positively (in the form of carbon andnitrogen accumulation or fertilization) or nega-tively (in the form of pollution).

Within the synthetic universe created by the fun-nel model, humans modify their effects on the en-vironment primarily by regulating the rate at whichthey consume materials and the location fromwhich their ecological services are drawn. Ourmodel has allowed us to identify a new method thatcan describe the integration of human ecologicalprocesses at regional or continental scales; only atthe scales from which ecological services are ac-quired are human practices expected to have eco-logical constraints. We use the EF to quantify thesize of the top of the funnel, which represents thescale at which integrated socioecological interac-tions occur.

A SPATIALLY HETEROGENEOUSECOLOGICAL FOOTPRINT

EFs are usually computed by determining the percapita utilization of ecological services—for exam-ple, the consumption of water and food and theassimilation of emitted carbon dioxide—and thenmultiplying this figure by the population of interestand dividing it by the local average production po-tential of ecosystem services, to arrive at a measureof unit area, commonly hectares (Wackernagel andRees 1996; Folke 1997):

EF � consumption [emission]

� population/mean production

�[assimilation] (1)

This method of calculating the EF is not without itscritics; several papers arguing for and against the EFconcept were presented in a recent forum organizedby the journal Ecological Economics (2000; 32:341–94). It has been argued, for examples, that using afigure for mean ecosystem productivity as the basisfor the calculation makes the unrealistic assumptionthat the production of ecosystem services is homoge-neous. Therefore, to address this issue, we modifiedthe method for quantifying the EF as follows: (a) Wecomputed the EF separately for individual servicesinstead of lumping all ecosystem services together,and (b) we calculated the EF in a spatially explicitmanner, using the specific spatial data that pertainedto each of the ecosystem services.

We investigated the effect of interurban compe-tition and the influence of city location on theregional distribution of resources by comparing theEF sizes for cities both independently and then in

Figure 1. Schematic diagram of the urban funnel con-ceptual model. Resources are appropriated by a city fromthe pool of available resources, transported down thefunnel to the city, and then processed and consumed.Excess materials and waste products are exported into theenvironment, where they may augment the pool of avail-able resources.


terms of the competition for resources between cit-ies—that is, individual city footprints versus non-overlapping footprints. We restricted the extent ofour study to the contiguous lower 48 US states andcomputed EFs simultaneously for the 20 largest USmetropolitan areas. We expected that EF size wouldincrease with competition for resources.

STUDY AREA

Greater Phoenix is a rapidly growing urban centerlocated in the southwestern United States and en-tirely isolated within the Sonoran Desert. The studyarea, including the 24 municipalities of the Phoenixmetropolis, is 2387 km2 in extent, and supports apopulation of over 2.9 million inhabitants (US Cen-sus Bureau 1998). The surrounding wild lands ofthe Sonoran Desert are characterized as semi-aridto arid lands with soils of low permeability andmoisture. Local rainfall averages less than 200mm/y, and actual evapotranspiration exceeds 95%.The vast majority of resources—including food, wa-ter, fossil fuels, and electricity—must be imported tomeet the demands of its growing population.

Phoenix was established in 1867 at the confluenceof two large rivers, the Gila and the Salt. In its earlyyears, the city relied exclusively on surface water, but

it made increasing use of groundwater as its popula-tion grew and agricultural activities expanded. Today,approximately 49% of the water for metropolitanPhoenix is supplied by the Salt River, 27% is pumpedfrom groundwater, and about 24% is imported fromthe Colorado River (ADWR 1994). Groundwater isbeing withdrawn at unsustainable rates due to thecombined pressures of the city’s location in the aridSonoran Desert and the rapid growth of its popula-tion. To meet long-term projections of water demand,the Central Arizona Project (CAP) canal was con-structed in 1986 to divert an allocation of water fromthe middle and upper Colorado River to the Phoenixand Tucson metropolitan areas.

For purposes of interurban comparison, we alsoobtained 1998 population and area data for the 20largest cities in the United States (Table 1) (USCensus Bureau 1998). Although per capita require-ments tend to vary from one area to another, weused the Phoenix per capita requirements for allcities to facilitate comparisons between cities andexamine the influence of regional heterogeneity.

DATA DESCRIPTION

Precipitation data were obtained from PRISM (Pa-rameter-elevation Regressions on Independent

Table 1. The 20 Largest US Metropolitan Areas

Metropolitan AreaPopulation(millions)

Area(km2) Color*

New York–N. New Jersey–Long Island, NY–NJ–CT–PA 20.1 17,534 BlackLos Angeles–Riverside–Orange County, CA 15.8 9505 BlackChicago–Gary–Kenosha, IL–IN–WI 8.8 8140 BlackWashington–Baltimore, DC–MD–VA–WV 7.3 11,425 BlackSan Francisco–Oakland–San Jose, CA 6.8 3785 DarkPhiladelphia–Wilmington–Atlantic City, PA–NJ–DE–MD 6.0 9609 LightBoston, MA–NH 5.6 13,294 DarkDetroit–Ann Arbor–Flint, MI 5.5 8363 LightDallas–Fort Worth, TX 4.8 5880 BlackHouston–Galveston–Brazoria, TX 4.4 6069 LightMiami–Fort Lauderdale, FL 3.7 2389 BlackAtlanta, GA 3.7 7955 LightSeattle–Tacoma–Bremerton, WA 3.4 5352 DarkCleveland–Akron, OH 2.9 5771 LightMinneapolis–St. Paul, MN–WI 2.8 4345 DarkSan Diego, CA 2.8 3175 LightSt. Louis, MO–IL 2.6 4102 LightPittsburgh, PA 2.3 6594 BlackPhoenix–Mesa, AZ 2.9 2387 DarkTampa–St. Petersburg–Clearwater, FL 2.3 3052 Light

*Color scheme as shown in Figure 3, B–D.


Slopes Model) and represent the mean annual pre-cipitation for 1961–90 (Daly and others 1994). Ac-tual evapotranspiration data were derived from aglobal model produced by Ahn and Tateishi (1994).The digital elevation model (DEM) used to delin-eate the CAP canal watershed in the Colorado Riverdrainage was developed by the United States Geo-logical Survey (USGS) EROS Data Center. Thedrainage basin was computed using WATERSHEDin ArcInfo 8.0.2 (ESRI 2000). The renewable watersource was calculated as the difference betweenspatially explicit maps of precipitation and actualevapotranspiration, and may take the form of sur-face water runoff or groundwater recharge. Result-ing negative values were set to zero. Water con-sumption was calculated using a 10-year (1985–94)average of the annual per capita usage of totalmunicipal water (335.83 m3/y) for the Phoenixmetropolitan area (ADWR 1994). Because the cal-culation of renewable water is confounded by itsinteraction with agriculture, a conversion figure ofan additional 2000 m3/y was included, based onestimates of crop water usage from the United Na-tions Food and Agriculture Organization (FAO)(Klohn and Appelgren 1997). We assumed that theremediation of urban wastewater (that is, sewage)occurs internally to the city and therefore did notinclude this factor in our analysis.

A spatial map of food production was generatedfrom a US Department of Agriculture (USDA) da-tabase for 1998. This database contains records ofboth the annual crop area planted and the amountof crops harvested by type for each county in theUnited States. We extracted the data for the sevendominant agricultural food crops: wheat, corn, bar-ley, rye, soybeans, potatoes, and oats. Because allcrop harvests except potatoes were reported inbushels, these values were converted from units ofvolume to mass using conversions adopted by theChicago Board of Trade. The mass of harvestedcrops was converted to kilocalories based on con-version factors used by the United Nations FAOstatistics database. Total kilocalories for each countywere converted to a sustainable human populationsize existing on a diet of 2500 kcal per person perday.

In addition to the resources required as inputsinto a city, we also examined the appropriation ofecosystem services that absorb urban waste. Carbonexport from the city was estimated on a per capitabasis using 1996 US rates of 5.61 metric tons ofcarbon annually (Marland and others 1999). Car-bon dioxide is assimilated into terrestrial biomassduring primary production. The actual measure ofecosystem carbon assimilation is net ecosystem pro-

ductivity (NEP), defined as autotrophic photosyn-thesis minus the total respiration of all organisms inthe ecosystem. This is in contrast to the rate atwhich an ecosystem obtains carbon, net primaryproduction (NPP), defined as autotrophic photosyn-thesis minus autotrophic respiration. In this analy-sis, we used 1% of NPP as an estimate of potentialcarbon assimilation (NEP) rates (Agren and Bosatta1996). We used a spatially explicit 40-year-meanestimate of NPP generated by the Century model aspart of the Vegetation/Ecosystem Modeling andAnalysis Project (VEMAP) (Schimel and others1997). Modeled data were used because accuratealternatives do not exist, and modeling is one of theprimary methods for extrapolating information be-tween scales. Estimating NPP at the plot scale isdifficult, and translating these plot estimates tolarger scales is even more so (Scurlock and others1999). The Century model has been validated re-peatedly in a variety of ecosystems where appropri-ate environmental data exist and thus may providethe best available estimates of NPP.

Spatial data sets were converted to 10 � 10 kmgrid cell sizes and projected in Albers conic equal-area using ArcInfo 8.0.2 (ESRI). Data were con-verted to grids in ASCII format; the EF algorithmswere written and compiled using Visual C�� (Mi-crosoft 2000).

METHODS

The EFs for renewable Phoenix water were com-puted from two points, the Phoenix urban centerand the CAP canal portion of the Colorado Riverwatershed. The CAP canal EF uses the connectionof the canal with the Colorado River as its startingpoint; it includes a consideration of the water ap-propriated from the watershed upstream from thispoint and takes into account the 209,780 m3/y lostto evaporation during transport. The existence ofthe CAP canal system helps to simplify the wateranalysis for Phoenix in that it is essentially a pointsource of water for the city; therefore, it is realisticto assume that water is collected from specific areasin a watershed rather than from some diffuse areasurrounding the city. The water EF was calculatedin two ways—first including and then excluding theagricultural interaction, based on the average pro-duction values for the same crops used to computethe agricultural EF. The consumption of water toproduce agricultural crops was calculated as an ad-ditional EF measure (hereafter, water EF with ag-ricultural interaction).

Using mean values and methodology developedby prior researchers (Wackernagel and Rees 1996),


we calculated a nonspatial EF for each resource intwo iterations—one based on the mean US nationalyield and the other on the mean Phoenix yield. Wealso constructed two new algorithms to calculatethe EF in a spatially explicit fashion: the mini-mum-area EF and the minimum-distance EF (Ta-ble 2). The minimum-area EF calculates the min-imum EF contiguous to a city. With the resourcesin a raster format, the algorithm begins by firstselecting the cell in which the city center is lo-cated. In the minimum-area EF, the resource val-ues for a particular ecosystem service of theneighbors of that cell are evaluated, and theneighboring cell with the highest value is addedto the EF. The resources contained in the EF aresummed, and the cells neighboring the EF are againevaluated. If the EF becomes “stuck” (that is, isolatedby another footprint and/or by geographic boundariessuch as coastlines or borders), the algorithm “jumps”by searching for and adding the available cell nearestthe existing EF. Cells with resource values of zero areadded to the EF but are not included in the EF area.The second alternative analysis we conducted, theminimum-distance EF, involved incrementally ex-panding the EF around the city in a circle while tab-ulating the resources within the EF. In both cases, thealgorithm stops and the EF is calculated when theresources in the EF are sufficient to supply the re-quirements of the urban area. Additional EFs werecomputed for the 20 largest US metropolitan areas inrank order of population using the minimum-area(contiguous) algorithm. Finally, to investigate the ef-fects of regional-scale spatial heterogeneity, the min-imum-area EF was expanded from Phoenix to theentire land area of the United States.

RESULTS

The nonspatial footprint required to generate a sus-tainable water supply for Phoenix (not including

agricultural uses) from local average runoff was102,000 km2 (Figure 2). Taking the spatial distribu-tion of resources into consideration, the minimumarea contiguous to Phoenix required to meet thecity’s total water needs was 10,500 km2, whereasthe area required to supply total water consump-tion using solely CAP canal water was 122,000 km2

(Figure 3A). Incorporating agricultural usage in-creased consumption of the renewable water sup-ply almost seven-fold; the nonspatial footprintneeded to generate a sustainable water supply thatincluded agricultural interaction was 709,000 km2.Using the spatial distribution of resources, the min-imum area contiguous to Phoenix required to sup-ply the total water consumption including agricul-tural interaction was 51,000 km2, or about fivetimes the value for nonagricultural water use. Theminimum area to support the city’s water needswas 300 km2 excluding agriculture and 1800 km2

Table 2. Various Algorithms Used to Calculate Nonspatial and Spatial EFs

Method Function

Nonspatial (U.S. mean; Phoenixmean) REQ � POP / RESmean

Minimum Area REQ � POP / RESspatial; NeighborsVariable Weighted Distance REQ � POP � DIST / RESspatial; NeighborsMinimum Distance (circle) REQ � POP � DIST / RESspatial

REQ, per capita resource requirement; POP, urban population; RES, ecosystem resource production per unit area; DIST, distanceDIST may be nonlinearly weighted (for example, a polynomial function of distance, based on a road network) to account for transportation costs.“Neighbors” indicates that the spatial search for the next pixel is dependent on pixel values adjacent to the EF at the current iteration.

Figure 2. A comparison of EF areas resulting from dif-ferent methodologies. Some of the values for the UShighest EF are too small to be shown on the chart. Theimportance of spatial heterogeneity is particularly evidentin the contrasting patterns of food and water between thePhoenix average EF (nonspatially explicit) and the Phoe-nix contiguous EF (spatially explicit).


including agricultural usage, as computed using val-ues from the highest-yielding area in the UnitedStates.

The spatial footprints needed to supply water tothe 20 largest US cities varied in size in correspon-dence with climatic variations (Figure 3 B, C). Wa-ter EFs, both with and without agricultural interac-tion, often appear to be linear because they followelevational, latitudinal, and longitudinal gradientsin precipitation and evapotranspiration. The maxi-mum population supportable by the total amountof runoff in the contiguous 48 states is 4.69 billionpeople; however, when water usage for agricultureis taken into account, that figure drops precipitouslyto 674 million.

The nonspatial EF required to generate a sustain-able food supply for Phoenix was 11,000 km2 (Fig-ure 2). When the spatial distribution of resources isconsidered, the minimum area contiguous to thecity needed for the total food consumption is278,000 km2. The maximum population support-able by agricultural production in the contiguous 48states is 1.26 billion. Food EFs for the 20 largest UScities varied with agricultural production (Figure

3D). The minimum area needed to supply Phoenixwith food resources is 850 km2, as computed fromvalues for the four highest-yielding US counties.

The nonspatial area required to assimilate thecarbon emitted from Phoenix is 1,324,000 km2, butthe corresponding figure for the spatially explicitcontiguous model is 584,000 km2 (Figure 2). Thefootprint for carbon assimilation is by far the largestEF of the three resources evaluated, regardless ofmethod. The minimum area that would be neededto assimilate the carbon emitted from Phoenix is117,000 km2. The United States which is able toassimilate carbon for the emissions of 62.9 millionpeople, cannot absorb all of the carbon emittedfrom the 20 largest US cities and hence is a netexporter of carbon.

Our analysis of the 20 largest US cities showedthat location had a striking influence in relationto regional environment (Tables 1 and 3). Onlyone city (Seattle) had a water EF smaller than thecity area after accounting for agricultural interac-tion, while five cities (Chicago, Cleveland, De-troit, Minneapolis, and St. Louis) had smallerfood EFs than their respective city areas. The

Figure 3. (A) Ecological footprints for the Central Arizona Project (CAP) Canal. The minimum-area water-only EF isshown in black, and the EF for water with agricultural interaction is shown in dark gray; the entire CAP watershed includesboth of these EFs plus the light gray area. (B) EFs for renewable water. (C) EFs for water including agricultural interaction.(D) EFs for agricultural food production. The EFs for each city are nonoverlapping and are shown in different shades ofgray. A breakdown of the color scheme is given in Table 1.


water EFs (including agricultural interaction) forthe 20 largest US metropolitan areas are on av-erage two times larger than their food EFs. Citypopulation size is more highly correlated to EFareas than is city area, and water EFs are morestrongly correlated to city population and cityarea than are food EFs (Table 4). There was atrend for EF size to be related to city populationand city area; this relationship was strongest forcarbon assimilation. The most striking examplesof competition for resources were found for waterEFs with agricultural interaction (with the stron-gest competition between San Diego and Los An-geles) and agriculture EFs in the Northeast and onthe West Coast of the United States (Figure 3 C, D).

If we expand the EF for Phoenix to the whole ofthe lower 48 states, the influence of regional het-erogeneity on different ecosystem services becomesevident (Figure 4). The curves are steeper for areasthat generate more ecosystem services and wherethe highest proportion of resources are appropri-ated first, then they level off as less productive areaswith lower population densities are incorporated.

The interesting pattern that emerges from this con-sideration of regional heterogeneity reflects re-gional differences—for instance, between the aridwest and the mesic east regions. These differencesare especially striking for carbon and water. Aspredicted, the response is nonlinear and shows theinfluence of spatial heterogeneity and the effects

Table 3. Minimum-Area (Contiguous) EFs for the 20 largest US Metropolitan Areas

MetropolitanArea Water EF (km2)

Water withAgriculturalInteractionEF (km2)

Food Production EF(km2)

CarbonAssimilationEF (km2)

I C I C I C I

New York, NY 11,700 11,700 76,200 76,200 68,400 68,400 1,301,400Los Angeles, CA 22,800 22,800 69,400 69,400 294,800 294,800 1,540,100Chicago, IL 10,400 10,400 71,000 71,000 5800 5800 540,600Washington, DC 6800 6800 42,500 42,500 20,100 20,100 477,100San Francisco, CA 5200 5200 17,500 17,500 242,600 80,200 402,000Philadelphia, PA 5700 5900 37,300 29,300 18,900 29,200 347,500Boston, MA 3400 3400 20,500 29,500 24,300 80,500 368,400Detroit, MI 7200 7200 43,500 54,500 7900 7900 351,800Dallas, TX 10,400 10,400 54,400 54,400 37,400 37,400 303,300Houston, TX 8100 8200 48,500 44,400 117,800 106,700 247,900Miami, FL 5900 5900 33,300 33,300 67,200 67,200 226,100Atlanta, GA 2700 2700 16,400 16,400 48,300 37,600 232,200Seattle, WA 800 800 3400 3400 21,000 61,700 224,300Cleveland, OH 2900 2900 17,300 17,300 5400 5900 193,000Minneapolis, MN 4400 4400 22,700 22,700 3700 3700 180,900San Diego, CA 4100 19,800 26,700 125,300 169,300 169,800 182,300St. Louis, MO 4200 4200 21,200 24,700 2400 2400 144,300Pittsburgh, PA 3100 3100 14,700 20,700 10,900 8900 157,800Phoenix, AZ 10,300 10,300 50,900 50,900 277,100 313,800 583,800Tampa, FL 3000 3000 17,500 18,200 49,600 38,600 121,200

I, independent; C, resource competition (nonoverlapping)Note that the EF area for carbon assimilation under competition is greater than the available area (contiguous US).

Table 4. Relationship between EFs forEcosystem Services and City Population and CityArea for the 20 Largest US Metropolitan Areas

Ecosystem ServiceCityPopulation

CityArea

Water 0.5247 0.0938Water with Agricultural

Interaction 0.5417 0.2077Food 0.0747 0.0460Carbon Assimilation 0.8625 0.3485

Values are linear regression r2.


that arise when different ecosystem services areevaluated.

DISCUSSION

The urban funnel model of human–ecological in-teractions reveals the disparity in terms of scale andlocation between the appropriated ecosystems andthe urban ecosystem itself. Although the model canbe used to study the ways in which wild or ruralecosystems change in response to urbanization, italso suggests how approaches that incorporatesome aspects of human socioeconomic systems canhelp us to understand the impact of human prac-tices on ecological systems. Socioeconomic institu-tions can act to buffer the effect of small-scale en-vironmental heterogeneities by implementingtechnological solutions (such as efficient machin-ery) and creating transport networks that effec-tively remove local ecological constraints. However,we cannot expect attempts to integrate human sys-tems and ecosystem processes to be productive ifthe scales of interaction are not identified correctly.Much of the historical confusion and frustrationthat has arisen when such attempts were tried atthe scale of the city may well be the result of tryingto integrate two systems that operate at differentscales. The urban funnel model is one approach thatcan be applied to resolve these disparatities of scale,using EF analysis to estimate the constraining scale.

Our modification of the EF calculation improveson the traditional method by taking a spatially ex-plicit approach. It allowed us to make a quantitativedetermination of the appropriate scale of human–ecosystem interaction by using several spatially ex-

plicit algorithms for three distinct ecological re-sources. In addition, our method incorporates adistance-weighted distribution of these resources,arrived at by dividing the resources by distancefrom the city; thus we can identify an entire spec-trum of contiguous footprints that show how re-source return decreases as distance from the cityincreases. Using this methodology, the effect of dis-tance, and therefore transportation costs, could becontrolled by multiplying distance by a constant.We believe that this is a good start toward thedevelopment of EFs that realistically incorporatetransportation.

In an attempt to improve on the accuracy of EFestimation, we modeled the interaction that existsbetween water and food because modern agricul-tural production is highly dependent on the watersupplied via irrigation. In fact, actual water con-sumption for crops is probably intermediate be-tween the two EF values. There is some double-counting involved in our estimates of crop waterusage, because at least part of that amount is alsoaccounted for in the subtraction of actual evapo-transpiration. However, even though our inclusionof the interaction term creates EF values that arelarger than actual water consumption, our figureprobably still represents a conservative estimate be-cause our calculations did not include the high de-mands for water to produce livestock, an essentialelement of the typical nonvegetarian diet (Klohnand Appelgren 1997). Wackernagel and Silverstein(2000) suggest that a conservative estimate of indi-cators be used to quantify sustainability, and ourcalculation of a minimum EF is in agreement withtheir recommendation. However, perhaps the mostimportant result of our calculation is the findingthat the capacities of terrestrial ecosystems to assim-ilate gaseous waste may be more limiting to hu-mans than any constraint on their resource produc-tion.

A comparison of the water and food footprintsreveals that there are distinctions between the sizeof the areas needed to supply individual resources.In both cases, the mean values of the nonspatial EFsfor the US and Phoenix differed by up to two ordersof magnitude (Figure 1). Similarly, a comparison ofnonspatial and spatially explicit EFs shows the im-portant influence of the heterogeneity of resources.For example, if we examine the nonspatial averagefor Phoenix, we see that water is the limiting re-source: 11,000 km2 is needed to supply food,102,000 km2 for water, and 709,000 km2 for waterwith agricultural interaction. However, spatially ex-plicit methods show just the reverse, with foodrequiring approximately 30 times as much land

Figure 4. Differences between ecosystem services andthe influence of spatial heterogeneity are evident in thenonlinear EF area versus supportable population as theEF is expanded from Phoenix to include the entire lower48 US states. The area required for the assimilation ofcarbon emissions is shown on the right y-axis.


area as water and five times as much area as waterwhen agricultural interaction is included.

Further modifications to our model could gener-ate an even more realistic estimate of the area re-quired to meet the demands of resource consump-tion and waste assimilation. For example, thisanalysis might be improved by the incorporation oftemporal heterogeneity. Renewable water re-sources may be spatially or temporally inaccessibleas a result of physical constraints or the inability tocollect all surface runoff (for example, due to waterretention in dams and reservoirs) (Postel and others1996). Desert soils such as those associated withPhoenix, are highly impermeable, and runoff in theSonoran Desert occurs most commonly in the formof infrequent but intense events, often as flooding.This may lead to a greater instantaneous actualrunoff than would be expected from an annualaverage, since the effects of evapotranspiration arereduced. Also, the potential discount or augment-ing effect inherent to living in a city can alter theper capita use of resources. An analytical approachto these issues would make the estimates moreaccurate, but it would also decrease the useful sim-plicity inherent in the EF.

It is important to consider that remote, externalecosystems within the EF are not immune to theeffects of the human appropriation of ecosystemservices. Even though our calculation of the renew-able water supply incorporates transpiration byvegetation, the complete removal of the remainingwater would have severe ecological effects. For ex-ample, fishes, riparian trees and birds, insects, andother fauna are also dependent on the ecosystemservices supplied by intact aquatic ecosystems witha minimum instream flow. Human appropriation ofthat flow could impair the functioning of entireecosystems (Holling 1986). The realistic conse-quences of the human appropriation, through di-rect and indirect feedback mechanisms, include al-terations to the ecosystem structure, function, anddynamics of these systems, resulting in decreasedproductivity and lowered resilience (Peterson andothers 1998; Rockstrom and others 1999).

As a solution to this dilemma, instead of appro-priating all of the available resources in the EF forhuman use, we propose that some minimum levelof ecosystem resources be reserved for ecosystemfunctioning in the interests of maintaining biodiver-sity and ecosystem integrity. We can easily modifyour analysis to make a proportion of resources un-available for human appropriation so that it re-mains in the ecosystem. This modification offers ameans of controlling for the tradeoff between hu-man appropriation and ecosystem requirements. If

we could identify the relevant parameters by ana-lyzing the ecosystems within the EF and modelingtheir resilience or sustainability, we might be able toapply the EF concept to ecosystem management.

Currently, there is no EF analysis designed tomodel the changes in ecosystem dynamics that re-sult from human appropriation, but we have begunto identify some methods that could be used todetermine the requirements essential for the main-tainence of ecosystem structure. For example, weused a conservative value for NEP/NPP of 0.01(Agren and Bosatta 1996). However, other investi-gators have used NEP/NPP values ranging from0.15 (Kolchugina and Vinson 1993) to 0.24 (Turnerand others 1995), and young forests that are ac-tively sequestering carbon may temporarily haveeven higher rates. The incorporation of temporalityas a factor in ecosystem parameters could help toreconcile EF analysis with ecosystem dynamics.

EF analysis is a potentially useful heuristic deviceto portray the sustainability of human systems inrelation to the production of ecosystem services(Wackernagel 1999; Deutsch and others 2000). Ourown work is in line with the intentions of Deutschand others (2000), who use the EF to examine theinteraction of humans and nature. As Wackernagel(1999) states, “[The EF] is one of the few ecologicalmeasures that compares human demand to ecolog-ical supply.” Our analysis does not include any pol-icy recommendations for sustainable management.Instead, our investigation focuses on coarse-scalehuman–ecological dynamics that may help us tounderstand the human socioecological system andits interaction with other ecosystems. As the com-puter revolution continues to transform human in-stitutions, the evaluation of EFs in alternative cur-rencies (such as information or technology) can beexpected to provide further insight into the dynam-ics of human–environment interactions. The powerof the EF lies in its ability to convey an easilyunderstood message about the interaction betweenan urban system and its environment, and ourmodification of traditional EF analysis improves onthe method by allowing more accurate estimates ofthe scales of that interaction.

An integration of human and nonhuman ecolog-ical processes should incorporate multiple scales.Because there are scale-related differences betweenthe urban and regional landscapes, we need to de-fine and understand the urban ecosystem in termsof interactions among separate natural and humanecosystems. Ecologists can answer questions aboutthe effect of human practices on native ecologicalprocesses. Social scientists can predict how humanswill invade the landscape. But even if our environ-


mental policy is directed toward some goal of sus-taining native processes, this policy will ultimatelybe enacted through a concatenation of economic,institutional, and political forces. Our conceptualmodel provides the framework needed to relate thesocial dynamics localized within a city to broader,regional ecological processes.

Despite its evident advantages, EF analysis hasalso been subjected to strong criticism. For example,van den Bergh and Verbruggen (1999) cited severalproblems with the traditional EF concept and ques-tioned both its heuristic utility and its applicabilityto planning. Among the major criticisms are itsinherent assumptions that land has one exclusiveuse, resources are distributed homogeneously, andtransportation networks should be used to redis-tribute appropriated resources. More recently, a thejournal Ecological Economics (2000; 32:341–394) pre-sented a forum debating the pros and cons of theEF. Problems related to trade, social and ecologicaldynamics, and spatial scale have all been obstaclesto its full acceptance. One of the main bones ofcontention concerns the interpretation of the EF inscience versus policy. Thus far, practitioners of thebasic and applied—or alternatively, biological andsocial—sciences have been unable to come to anagreement about the details and purposes of the EF.

Although these concerns are valid, we believethat several of these divisive issues can be resolved.In particular, the importance of spatial location andthe heterogeneous distribution of resources, hasgenerally been overlooked, but these factors couldbe useful in reconciling some of the arguments. Forexample, rather than viewing trade as a pitfall ofthe EF, we think that a regional, spatially explicit EFwould allow the necessity for trade to be factoredinto the analysis. Spatial heterogeneity in the dis-tribution of resources has further implications forthe results of EF analyses. By computing individual,spatially explicit EFs simultaneously for various re-sources based on where the resources actually oc-cur, we can avoid the assumption that land has onlyone use. When EFs are calculated for multiple eco-system services, the EFs for a particular resourcemay overlap different resources and need not cor-respond to, or even occur at the same magnitude asthe EFs for other resources. Our results show howthe spatial competition for resources generally in-creases EF size, but they also indicate, perhaps sur-prisingly, that competition can decrease the EF incertain situations.

Although our EF is computed in a spatially ex-plicit manner, it is incorrect to assume that it rep-resents the area from which the ecosystem servicesare actually acquired. For example, trade and trans-

portation redistribute resources drawn from distanthinterlands. In addition, transportation introducescosts (losses due to inefficiencies) that are not in-corporated in our analysis, except for those ac-counted for by water evaporation during transportalong the CAP canal to Phoenix. Redundancy alsoexists with ecosystem services; no single location iscritical for the supply of any single resource. Thisredundancy both increases the stability of resourceimportation at large scales and reduces the per-ceived feedback from ecosystem services at localscales.

By factoring transportation into our analysis ofmultiple cities, we indirectly consider the effect ofregional heterogeneity, thereby incorporating eco-system dynamics. This aspect of our analysis raisesthe question of whether it is more ecologically sus-tainable for a city to exist in an area of higher orlower potential for resource production—that is,allowing for differing levels of ecosystem resilienceto disturbances caused by the human appropriationof ecosystem services. By analogy to the Leibig-Sprengel Law of the Minimum, determining thesize of the area required to supply the individualresources needed to support urban growth can helpto identify the environmental factors that have thegreatest impact on that growth; however, analysis iscomplicated by the use of imported and nonrenew-able resources.

The spatially heterogeneous EF is consistent withother concepts in biology. Some social organisms,such as ants and bees, utilize ecosystem servicesderived from the environment beyond the colony’sprimary residence. Similarly, the home ranges andmigrations of animals are dependent on the avail-ability of environmental resources. Limitations totheir local availability affect and may ultimatelyconstrain the growth of the organism. In like fash-ion, if the internal resources of a city are notenough to support its needs, resources producedelsewhere need to be obtained. However, since theEFs of two cities cannot overlap, competition forcesthe city to either import resources from distantareas or expand its EF into less productive areas.

The conceptual basis of this analysis can be linkedto the related multidisciplinary ideas of ecologicalneighborhoods, ecological field theory, and meteo-rologically defined footprints. Addicott and others(1987) defined the three properties of the ecologicalneighborhood as “an ecological process, a time scaleappropriate to that process, and an organism’s ac-tivity or influence during that time period” andhypothesized that they are responsible for the spa-tial and temporal patterning of environments. Stud-ies taking this approach commonly focused on den-


sity-dependent competitive processes; for example,the concept of the ecological neighborhood hasbeen applied and tested empirically with plants,where neighborhood interactions ranged from ab-sent to important in influencing the growth ofplants under competition (Silander and Pacala1985; Pacala and Silander 1990). Similarly, ecolog-ical field theory quantifies plant spatial influencesas variable regions around individual plants (Wuand others 1985; Walker and others 1989). Anotherform of footprint analysis has been used in meteo-rology (Wilson and Swaters 1991); in this type ofanalysis, an estimate is made of the upwind sourcearea that influences measurements at a downwindsampling point. This is the area where the diffusionof airborne particles occurs; the footprint is depen-dent on the particle properties and wind patterns.As is also seen with the spatially explicit EF, thespatial distribution of factors external to the localscale is important, in ecological neighborhoods andmeteorological footprints.

In general, the competition for resources increasesthe EF; however, EFs can also shrink due to interur-ban competition because a competing city’s EF mayforce the focal EF out of a high-production, but iso-lated, region, into an area where there is higher pro-duction of ecosystem services (Table 3). This phenom-enon did not occur in the water-only EF, but itappeared twice in the water EF with agricultural in-teraction due to the increased competition for re-sources. It occurred five times in the food EFs for the20 largest US cities, and the total EF area of all 20 citieswas smaller under the competition condition thanindependently. Because the algorithm computed EFsfor cities in order of population, the largest cities wereless affected by spatial competition for resources thanthe smaller ones. Competition among the 20 citiesincreased the water footprints by 10%–20%; San Di-ego had the largest increase in the EFs for all resourcesdue to the influence of competition. Incorporatingadditional cities within the same region increases thedegree of competition and consequently the size ofthe EF.

Our results highlight several characteristics of hu-man–ecosystem interaction that were captured bythe urban funnel model, with its emphasis on thedisparity of scales between cities and external eco-systems. First, the incorporation of the spatial het-erogeneity of resources had a profound effect onthe EF analysis when compared to nonspatial EFs.The EFs resulting from the various methods showdramatic contrasts that reflect the local biogeo-physical environment. Second, the algorithms weused for our analysis of a spatially heterogeneousEF suggested some improved methods of EF analy-

sis, that may help to address some of the issuesraised by its critics. Third, we found that the specificresource used in the calculation can have a largeeffect on the EF analysis; this finding underscoresthe important influence of city location on the in-teraction with local ecosystem services. Fourth, themodel allowed us to address the interactions be-tween ecosystem services; these interactions playan important role in socio ecological dynamics, butthey have often been overlooked.

We humans are unique in our capacity to directlyaffect an extremely wide range of scales, yet it isprimarily at the larger scales that we are ecologi-cally constrained. For the modern city, which canderive all of the requirements needed to sustainhuman habitation from external, sources, theremay be no strong or constraining feedback thatoperates at an internal or local ecological level. Theurban funnel model is a promising first step towardthe design of conceptual and analytical models thatincorporate the appropriation of external resources.Finally, we believe that the inclusion of spatial in-formation in models of complex dynamic processcan enhances our understanding of the interactionsbetween humans and the ecosystems upon whichthey depend.

ACKNOWLEDGMENTS

We appreciate the constructive comments of JohnBriggs, Diane Hope, Amy Nelson, Weixing Zhu, theArizone State University (ASU) Landscape Ecologyand Modeling laboratory, the ASU Ecosystems/Desert Stream laboratory, and the ASU GeographicInformation Systems laboratory. Carl Folke and twoanonymous reviewers provided useful and criticalsuggestions. This work was supported by the Na-tional Science Foundation, grant number DEB-97-14833, in support of the Central Arizona–PhoenixLong-Term Ecological Research (CAP LTER)project.

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