Assessing Sustainability in Real Urban Systems: The Greater

Jul 9, 2012 - Office of Research and Development, National Risk Management Research Laboratory, Sustainable Technology Division, U.S. Environmental ...
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Assessing Sustainability in Real Urban Systems: The Greater Cincinnati Metropolitan Area in Ohio, Kentucky, and Indiana Alejandra M. Gonzalez-Mejía,†,‡,∥ Tarsha N. Eason,§ Heriberto Cabezas,§ and Makram T. Suidan*,†,⊥ †

College of Engineering & Applied Science, Environmental Program, University of Cincinnati, 2901 Woodside Drive, Cincinnati Ohio 45221, United States ‡ Research Fellow, Oak Ridge Institute for Science and Education § Office of Research and Development, National Risk Management Research Laboratory, Sustainable Technology Division, U.S. Environmental Protection Agency, 26 W. Martin Luther King Drive, Cincinnati, Ohio 45268, United States ⊥ Faculty of Engineering and Architecture, American University of Beirut, Beirut, Lebanon S Supporting Information *

ABSTRACT: Urban systems have a number of factors (i.e., economic, social, and environmental) that can potentially impact growth, change, and transition. As such, assessing and managing these systems is a complex challenge. While, tracking trends of key variables may provide some insight, identifying the critical characteristics that truly impact the dynamic behavior of these systems is difficult. As an integrated approach to evaluate real urban systems, this work contributes to the research on scientific techniques for assessing sustainability. Specifically, it proposes a practical methodology based on the estimation of dynamic order, for identifying stable and unstable periods of sustainable or unsustainable trends with Fisher Information (FI) metric. As a test case, the dynamic behavior of the City, Suburbs, and Metropolitan Statistical Area (MSA) of Cincinnati was evaluated by using 29 social and 11 economic variables to characterize each system from 1970 to 2009. Air quality variables were also selected to describe the MSA’s environmental component (1980−2009). Results indicate systems dynamic started to change from about 1995 for the social variables and about 2000 for the economic and environmental characteristics.

1. INTRODUCTION The purpose of a sustainability analysis is to gather information that would allow policy makers to manage systems with the goal of encouraging desirable economic and social tendencies while maintaining long-term environmental responsibility that leads to sustainability. Considering that approximately 93.7% of the U.S. population lives in urbanized areas,1 it is pertinent to assess the sustainability of urban systems. Such assessment involves identifying critical aspects of these important systems that support a human population over time, and maintain the system’s functionality without undergoing drastic changes in its condition. One key feature of real systems is that they are dynamic and characterized by changes in behavior over time, toward or away from a sustainable path. In accordance with the most quoted definition of sustainable development,2 this sustainable path relates to finding a state of socio-economic organization that promotes and integrates intergenerational equity, economic viability, and environmental stewardship. However, determining movement that is in accordance with a desirable trajectory is a complicated endeavor. Hence, there is a premium on sustainability metrics that can evaluate the behavior of complex, multidimensional dynamic systems such as regional and urban areas. Some common sustainability measures include Ecological © 2012 American Chemical Society

footprint, green net regional product, and emergy analyses. Respectively, these quantify ecological impacts of human activity, the economic well-being or welfare, and the flow of available energy through the system. Each of these measures track specific aspects of a system and are three of the four metrics used in an interdisciplinary approach to evaluate a multivariate regional system.3 The fourth measure is Fisher Information (FI) index, which captures a fundamental aspect of the sustainability of a system, its dynamic order. Although all of these metrics were used as a portfolio of measures characterizing and assessing the system; FI was selected for this work, because it has the advantage of collapsing and concurrently evaluating multiple variables that describe the system’s trajectory over time.4 Moreover, FI locates changes in this trajectory for determining stable and unstable regimes, which might represent sustainable or unsustainable periods in a dynamic system.5 FI has been applied to derive fundamental equations of physics and thermodynamics.6 It has been used to study both Received: Revised: Accepted: Published: 9620

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modeled and real systems to include multicompartment food webs and pseudoeconomies,7−9 and socio-political instability.10 It has been devised as a sustainability metric,11 which was subsequently used to characterize the dynamic behavior of regional ecosystems.12 Additionally, FI has been used to assess urban systems13 and optimize control of dynamic model systems for sustainable environmental management.14 Accordingly, this paper presents a methodology for assessing dynamic order and sustainability from social, economic, and environmental aspects of real urban systems over time based on the computation and interpretation of FI. As a test case, a rigorous study of the Metropolitan Statistical Area of Cincinnati, its suburbs, and City is performed to demonstrate this method and also to address limitations in data such as quantity, quality, and a technique of reconciling diverse units. Case Study: Cincinnati Metropolitan Statistical Area, Suburbs, and City. Cincinnati was incorporated as a city in 1819,15 and formally included in the Cincinnati, OH−KY, Standard Metropolitan Area (SMA) constituted by Hamilton County, OH; Campbell County, KY; and Kenton County, KY in 1950.16 Today, the City of Cincinnati is strongly connected by social and economic relations with 12 additional counties, and is a part of the Cincinnati−Middletown, OH−KY−IN Metropolitan Statistical Area (MSA).17 This area located at the southwest corner of Ohio and connected with Kentucky and Indiana is among the most populated and dense MSAs (ranked #37) in the U.S., with a 8.1% increase in population for the first decade of the new millennium.18 Cincinnati, like many of the “rust belt” cities, was a hub for manufacturing and industry since the 19th century and suffered economically in the 1960s and 1970s when industry began moving out of the region resulting in great decreases in population and economic activity.19 As an example, the city of Cincinnati had decreased in population by nearly 25% in 2009 with respect to 1970 (Figure 1c, Supporting Information (SI) Table S1b). However, it has worked to revitalize itself boasting a rich heritage of education, sports, arts, and culture, and serving as the headquarters of a number of Fortune 1000 companies including Procter & Gamble, Kroger, Macy’s, Fifth Third Bancorp, Western & Southern Financial Group and American Financial Group. Combined, these companies generate nearly $200 billion dollars in revenue annually.20 Other characteristics of the area relate to housing occupancy and air quality. In 2010, this MSA had a rental vacancy rate of 12.0% and a homeowner vacancy rate of 4.0%.21 Moreover, Cincinnati was cataloged in 2011, the ninth most polluted MSA by year-round fine particles (PM2.5) and the 16th most polluted MSA by ozone in the U.S.22 Although there have been significant changes in the MSA, the transformation is very much counterbalanced by the economic, social, and environmental conditions of this area. While there is a sense of the general condition of Cincinnati, it is well-known that a single picture in time is not useful for a diagnosis. A natural question at this point is whether the overall conditions are better (toward a sustainable path) or worse. And, what are the underlying drivers of change in Cincinnati? Answers to such questions provide insight pertinent to research, planning, and management. Accordingly, this work aims to investigate the dynamic changes in the condition of the city, the surrounding suburbs, and the MSA over time. Thus, data series from 29 social and 11 economic variables were selected to characterize each system (i.e., city, suburbs, and MSA) from 1970 to 2009. Further, nine air quality variables to

Figure 1. Social component, subcomponent social distribution. (a) Cincinnati Metropolitan Statistical Area (MSA), OH−KY−IN. (b) Cincinnati Suburban Area, OH−KY−IN. (c) City of Cincinnati, OH. The city and suburbs of Cincinnati have the opposite growing dynamic

describe the environmental component of the overall MSA (1980−2009). FI, a measure of system order and stability, was used perform an assessment of the dynamic behavior and sustainable trends of each system’s trajectory. By applying this novel approach, nonintuitive characteristics among these variables were found as potential drivers of sustainability in the systems under study (i.e., MSA, suburbs, and city). Further, the methods demonstrated in this work 9621

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minimum of 50 000 inhabitants. The population in a MSA resides in a central county or adjacent counties, and commutes within this county and/or adjacent counties. The U.S. Census Bureau uses statistical methods to geographically delineate a metropolitan area; however, during the period of the study, the definite region has transitioned over time. The MSA’s boundaries used for the present work are the divisions noted as of December first, 2009.25 Accordingly, in order to maintain a constant area of study, the variables describing the system each year (1970, 1980, 1990, and 2000) were adjusted to match the 2009 area U.S. Census definition; then covering a time period of 39 years. Hence, as illustrated in SI Figure S1, the Cincinnati OH−KY−-IN MSA consists of the following counties: Dearborn, and Ohio, IN; Boone, Campbell, Gallatin, Grant, Kenton, and Pendleton, KY; and Brown, Butler, Clermont, Hamilton, and Warren, OH for the entire period of study. The city of Cincinnati was delimited according to the census tracts from the six outline maps26 for the years 1970, 1980, 1990, and 2000. The city division defined in the 2009 American Community Survey (ACS) 1-Year Estimates27 corresponds the 2000 U.S. Census Bureau boundaries and was used to set the 2009 geographic boundaries. And, the area included in a MSA that it is not within the city boundaries is designated “suburbs” or suburban area (SUBS). From Latin “sub”, which means, close to, and “urbanus”, or city, suburban communities have been growing primarily due to effective transportation since the second half of the last century.19 Today, this residential area in the Cincinnati MSA is connected by road to Kentucky by I-71 and to Indiana by I-74. 2.2. Data. In order to characterize the dynamic behavior of the urban systems under study, data were collected in accordance with the predetermined geographical boundaries. Given a specified geographic unit (e.g., City of Cincinnati or MSA, OH−KY−IN), time series describing the systems were extracted from the decennial US census of 1970, 1980, 1990, and 2000.28 Since current U.S. census data were not readily available at the time of the study, data from the U.S. census, and ACS estimates were used for the year 2009 from the Census Bureau’s Population Estimates Program, which provides information for populations of more than 65 000 inhabitants in the years between censuses. In the Supporting Information, Table S1 consolidates the original social and economic variables for each system: MSA, city, and suburbs. These time series were selected based on the profiles (social, economic, housing and demographic data tables) established by the U.S. Census in the ACS27 and data availability for the period of study (1970−2009). Further, these variables were divided into two main components (social and economic) and seven subcomponents (social distribution, age distribution, household type, educational attainment, housing occupancy, employment status and poverty, and income) which represent main social and economic characteristics of a system over time. Thus, the social component includes the population distribution by social structure (i.e., inhabitants or households), individuals’ gender, age, and school completion (i.e., high school or college degree). The economic component is characterized by the number of inhabitants below the poverty line, civilians employed, housing-units (occupied), and annual average income of households and families (SI Table S1). Due to data availability issues, the environmental component is only used in the assessment of the Cincinnati, MSA. The environmental component is represented by 9 air quality variables extracted from the Air Quality Statistics Report, which

afford the ability to identify sustainable tendencies reflected as periods of stability and change that otherwise are very difficult to determine, particularly, for time varying multidimensional systems.

2. MATERIALS AND METHODS Fisher Information (FI), a key method in information theory, was developed by the statistician Ronald Fisher23 as a statistical measure of the amount or quality of information obtainable data in an effort to estimate the value of an unknown parameter. With a rich history in mathematical statistics, FI has since been adapted into a measure of dynamic order and formulated into a means of evaluating system behavior over time.6,12,24 It may be computed over time to assess order and stability changes and to compare the dynamic behavior of different systems with respect to desirable conditions that describe a sustainable trajectory.5 The basis of the FI computation is representing the condition (trajectory) of the system through time. Within a statistical mechanics framework, a dynamic system may be described by the dimensions (variables, y(t)) that characterize the condition (state) of the system and time. This framework affords the ability to represent the system dynamically as a trajectory in phase space where a vector of m dimensions describes all the possible states of the system. From this depiction, a continuous Fisher Information I(t) is defined as a function of the phase space tangential velocity (s′(t)) and acceleration (s″(t)),4 and evaluated for a window of size l moving the calculation one time step at a time. Equations 1, and 2, are used to compute the Fisher Information in eq 3. I(ti) =

1 l

∫t

ti + l

(s″(ti))2 (s′(ti))4

i

dt (1)

m

s′(ti) =

∑ (y′(ti))2 (2)

1

s″(ti) =

1 s′(ti)

m

∑ y′(ti)y″(ti) 1

(3)

More details on the derivation of FI from its original form may be found in the work by Mayer et al.4 As noted in previous work,5,12,24 high FI values over time are related to orderly and “sustainable” regimes and low or zero FI values are associated with disorderly or “unsustainable” periods of a system. However, these statements refer to the degree of change in the system’s trajectory at a particular time, or the overall change for the entire period of study, which is a true indicator of trends. Further, inflection points (where the trajectory of the system changes direction) denote gains or losses in FI that may lead to a regime shift. Another key point to consider is that while a system is sustainable and functioning well, it may not be in a humanly preferred condition. Accordingly, an analyst using FI to evaluate system behavior must also consider the trends that are desirable for the system so as to know what conditions or regimes should be maintained or attained. In this work, FI was computed numerically and interpreted in accordance with the approach described in ref 5. 2.1. Area and Period of Study. According to the U.S. Office of Management and Budget (OMB), a Metropolitan Statistical Area (MSA) is a region with a strong social and economic connection to at least one urbanized area with a 9622

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consolidates annual values for criteria pollutants related to national standards for air quality (carbon monoxide, nitrogen dioxide, ozone, sulfur dioxide, and particulate matter smaller than 10 μm) as shown in Figure 5b and SI Table S2. Thus, these time series show the highest concentration reported during the year by all monitoring sites in the Cincinnati OH− KY−IN MSA (1980−2009).29 Because all 49 variables have different units (e.g., inhabitants, families, U.S. dollars, concentration) are not comparable to each other. Each datum of a series was divided by its first value in time (1970 for social and economic values and 1980 for air quality data). Consequently, these units-less ratios allows us to see changes in an area of study from a reference value over time,30 and it assigns the same grade of importance to each variable;31 thereby, meeting the scientific basis for computing sustainability metrics,32 FI index for this research. Since the data for the socio-economic variables collected were compiled primarily from sources that report every decade, there were only 5 original data points for the period of study, and 30 for the air quality time series. A Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) embodied in a Matlab algorithm, was used to interpolate between the original data points. PCHIP locates values of an underlying interpolating function at intermediate points and uses a different cubic polynomial on each subinterval, with a continuous first derivative, (necessary for FI calculations), and a piecewise continuous linear second derivative (inadequate for FI computations). PCHIP was selected because it preserves both the shape of the data on intervals where the data is monotonic, and at points where the data has a local extreme.33 The only concern with the approach is that the second derivative is not continuous resulting in “jumps” at the subinterval edges. In order to avoid these types of anomalies, these new data (generated with PCHIP) were then fitted to nth degree polynomials, the best fit selected was the tenth degree polynomial (Figures 1a−c, 2b, 3b, and 4b,c), for the MSA, suburbs, and City of Cincinnati, respectively. The main criterion for the selection of the polynomials fit of the time series was the coefficient of determination (R2) and studentized residuals (see SI Figure S2a-b). 2.3. Approach. This section provides a description of the procedure used to evaluate the dynamic behavior of the urban systems understudy. First, the variable time series characterizing each geographic unit (i.e., City, suburbs, and MSA) were processed as described in the previous segment. From the data, FI was computed numerically using eqs 1, 2, and 3, by integrating over one year, moving the calculation one day at a time. Then, a mean FI (denoted by ⟨FI⟩) was computed using a moving average of three years (1095 days) as a high frequency filter, which allows to focus on trends in the system’s trajectory and not minor fluctuations.12 Further, three methods were applied to thoroughly examine the FI results and aid in the evaluation and interpretation of the dynamic behavior of the system. These include locating the maxima and minima in the FI result over the entire evaluation period, establishing criteria to detect outliers, and computing Spearman Rank Order (SRO) correlation coefficients to assess pertinent relationships between FI results. 2.3.1. Local Fisher Information Maximum(s). A graph of FI vs time can be inspected to find local maxima and minima. These data points determine when changes in a subcomponent or component occurred and whether they reflect or precede a change in the overall system. Once these local maxima and

Figure 2. Cincinnati Metropolitan Statistical Area (MSA), OH-KY-IN. (a) Annual Fisher Information (3 years filter) for social and economic variables (ISE), social component (IS) and economic component (IE) separately. (b) Economic subcomponents: Housing Occupancy and Income. After the year 2000, ISE and IE peaks (Figure 2a) correspond to a change in the growth rate of the variables in Figure 2b, which shows economic drivers for the Cincinnati MSA.

minima are detected, the time when they occurred may denote a change of regime or direction in the system trajectory. 2.3.2. Establishing Criteria for Detecting Outliers. In order to detect deviation from the typical behavior of the system and differentiate atypical variations from significant change, an arithmetic mean of FI (i.e., ⟨I⟩1970 2009) and standard deviation (i.e., ⟨SD⟩1970 ) for all FI results for each system are computed over 2009 the entire period of evaluation (39 years). Hence, if a FI variation is greater than the arithmetic mean plus two standard 1970 deviations (⟨I⟩1970 2009 + 2⟨SD⟩2009), it is considered as a local maximum/minimum or outlier, following Chebyshev’s inequality,34 which is applicable to an arbitrary statistical distribution. Additionally, FI and SD might be recalculated between (and after or before) local maxima (or minimums) in order to determine if there were other important changes. This method, allows scanning for changes that could be overshadowed by large FI peaks (e.g., regime shifts). 2.3.3. Spearman Rank Order Correlation (SROC) nonparametric test. In order to explore underlying variables which may be drivers of the dynamic behavior of the system, a Spearman Rank Order correlation (SROC) test was used to 9623

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Figure 3. Cincinnati Suburban Area, OH−KY−IN. (a) Annual Fisher Information (3 years filter) for social and economic variables (ISE), social component (IS) and economic component (IE) separately. (b) Social subcomponent: type of household. After the year 1995, the higher IS peak (Figure 3a) correspond to a change in the growth rate of the variables in Figure 3b, which shows social drivers for the suburbs of Cincinnati OH−KY−IN

find the strength of association between all possible pairs of FI results. Applying this approach, we are able to compare changes in the trajectory of each system for all components (social and economic), and subcomponents (e.g., social distribution). Identification of these drivers not only provides information on their influence on system dynamics, but also may provide insight on variables that should be monitored and managed. The advantage of this test is in its rank comparison, and the fact that FI pairs do not have to be linearly related with a normal distribution about the regression and constant variance.35 Consequently, it was selected because the variation in the FI over time is more important than the absolute value of FI. Finally, the degree of correlation was assessed for these pairs to determine the “strength” of their linear relationships: strong ([±1.0; ± 0.9]), moderate ([±0.6; ± 0.8), weak ([±0.6; ± 0.8) relation, low ([−0.6; 0.6]) or no significant statistical relation at all (Tables 1 and 2).

Figure 4. City of Cincinnati, OH. (a) Annual Fisher Information (3 years filter) for social and economic variables (ISE), social component (IS) and economic component (IE) separately. (b) Social subcomponent: type of household. (c) Economic subcomponents: housing occupancy and income. After the year 1995, the higher IS peak (Figure 4a) correspond to a change in the growth rate of the variables in Figure 4b, which shows social drivers for the city of Cincinnati OH. Around the years 1980 and 2000 there is a change of direction (decreasing rate) in the variables of Housing Occupancy and Income (except for vacant housing units), which shows economic 9624

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show the identification of the local FI maxima, which are above the line marking of the arithmetic mean plus two times the standard deviation (SD) of FI over the entire period of study 1970 (mean + 2SD = ⟨I⟩1970 2009 + 2⟨SD⟩2009). Tables 1a−c provide a summary of the SROC results for each system describing the strength of association between pairs to include the socioeconomic system (ISE), components (e.g., IS) and subcomponents (e.g., IS- social distribution). Table 2 is a consolidation of the SROC results for comparing and relating all three geographical areas. A detailed discussion of each area is provided in the following sections highlighting key relationships, patterns and potential drivers of dynamic change in each system. This comparative analysis may provide insight on tendencies of behavior that differentiate the internal dynamic of the MSA.

Figure 4. continued drivers for the City of Cincinnati. These changes correspond to IE and ISE peaks in Figure 4a.

3. RESULTS The FI results computed from all of the social and economic variables (ISE) describing each system (i.e., MSA, the suburbs, SUBS, and the City of Cincinnati) are provided in Figures 2a, 3a, and 4a. Also plotted in each graph is the FI computed for the group of variables in the social and economic components separately (denoted as IS and IE, respectively). Figures 2b, 3b, and 4b,c present the social or economic subcomponents (e.g., social distribution and income) for each area understudy. Accordingly, Figures 2a (MSA), 3a (SUBS), and 4a (CITY)

Table 1. Summary of the Spearman Rank Order Correlation (SROC) results of the Fisher Information for the Components and Subcomponents Describing (a) Cincinnati Metropolitan Statistical Area (MSA), (b) Suburban Area (SUBS), and (c) the City of Cincinnati (CITY)

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Table 2. (a) SROC Results of the Social and Economic Variables (ISE), Social Variables (IS), and Economic Variables (IE) for Each Geographical Area (MSA, SUBS, and CITY); (b) SROC Results for Environmental Component Air Quality Variables (IAQ) for Cincinnati MSA, OH−KY−INa

a

The dynamic behavior of the MSA is strongly correlated to the suburbs and the city. The Economic component is the main driver in the overall MSA, the suburbs and City of Cincinnati.

3.1. Cincinnati Metropolitan Statistical Area (MSA) OH−KY−IN. Figure 2a shows that the Cincinnati MSA social and economic (ISE) variables are relatively stable for the first 3 decades of study with a local FI maximum between 2002 and 2005. The economic component (IE) is stable from 1973 to 2001, and has a peak in the FI from 2002 to 2005. In contrast, the social component (IS) has a significant local FI maximum from 1998 to 2000, a couple years before the important change for the Cincinnati MSA (IE and ISE). Thus, this system’s trajectory started to change direction at approximately 1995 for social variables, and around 2000 for economic variables. Additionally, in the Summary of the Spearman Rank Order Correlation (SROC), FI results for the components and subcomponents describing Cincinnati MSA (Table 1a), social and economic variables (ISE) and its social component (IS) are correlated to social distribution (subcomponent). In order to find social drivers, we look at the social distribution variables in Figure 1a, where the decrease in the growth rate of households and families after 1995 corresponds to the system’s trajectory change identified by the IS peak in Figure 2a. This analysis suggests that a possible driver is stagnant social characteristics for the last 15 years of study, which represents an undesirable condition for a developing urban system.

In Table 1a subcomponents such as, housing occupancy and income are identified as variables with key economic patterns. A net increase in the growth rate of economic variables (Figure 2b) might describe the steady period of the first 3 decades of study. The change of direction in the system’s trajectory after 2000 (ISE and IE peak in Figure 1a) can be attributed to a deceleration in the growth rate of income, and to the exponential rate at which housing units became vacant in the last 9 years of this study (Figure 2b). Note that in Figure 2a, there are other high values of FI at the beginning or end of the evaluation period for the individual components IE and IS. These FI peaks might represent a very short stable state (more related to the management of data) not relevant for this study. 3.2. Cincinnati Suburbs OH−KY−IN. As the MSA, the suburban area of Cincinnati presents a stable period in the first 30 years understudy, with a local FI maximum for social and economic variables (ISE) and its economic component (IE) around 2003, and for the social component (IS) at 1999 (Figure 3a). The IS peak in Figure 3a might indicate that since 1995 important changes started to happen for the social subcomponents, social distribution and type of household (Table 1b), and after 2000 (IE peak in Figure 3a), for the 9626

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economic subcomponent income (Table 1b). Therefore, the change of direction for the suburbs’ trajectory might be dominated by the decline in the income growth rate, and the growth rate decrease in the majority of household types (e.g., Married and male-headed families) after 1999 (Figure 3b). Further, note that Figure 2a (MSA) resembles the shape of IS, IE and ISE in Figure 3a (SUBS). Thus, trends in the variables describing the suburban area are correlated to changes in the trajectory of the overall Cincinnati MSA (Table 2). The difference between both systems’ dynamics is that the FI local maximum around 1999 for the social component (IS) is smaller for the suburbs (Figure 3a) than for the MSA (Figure 2a), which suggests that the decline of social variables (e.g., households and families) is more evident in the overall MSA (Figure 1a) than in the suburban area of Cincinnati (Figure 1b). 3.3. City of Cincinnati, OH. According Figure 4a, social and economic variables of Cincinnati City (ISE) and its economic component (IE) remain practically stable for the entire period of study (1970−2009), except for a small IE peak at 1980, and another relative local ISE maximum around 2004. In contrast, the social component (IS) (CITY) reported the highest FI value from 1999 to 2003. Additionally, social and economic drivers of change were identified with FI for the City of Cincinnati. Thus, the IS peak might indicate the start of a stagnant period after 1999 (Figure 4a), for the majority variables of the subcomponent type of household (Figure 4b), which has the strongest association to the social component (Table 1c). Consequently, the decline of the City of Cincinnati might be governed by the decrease and stabilization in the growth rate of all types of families (e.g., Married and maleheaded families) at the end of the 90s (Figure 4b). Further, economic changes in Cincinnati city were smaller compared to its MSA. For instance, the rate of housing vacancy was higher in the MSA (Figure 2b) than in the city of Cincinnati (Figure 4c), and while the rate growth of housing occupancy fairly increased for the entire period of study in the MSA (Figure 2b), it remained relatively stable or decreasing at a slow pace in the city of Cincinnati (Figure 4c). 3.4. The Effect of Air Quality in the Cincinnati MSA, OH−KY−IN (1980−2009). FI was recomputed from 1980 to 2009 for the individual components (social − IS, economic − IE, and air quality − IAQ), as well as for the three components (ISEAQ) in order to incorporate an environmental dimension in the Cincinnati MSA, OH−KY−IN. The results of this calculation are plotted in Figure 5a and the time series of nine air quality variables in Figure 5b. Note that Figure 5a is a dual axis with the scale of IS, IE, and ISEAQ values showing on the left axis and the IAQ scale on the right. The FI of the air quality variables is relatively stable from 1980 to 2002 and peaks around 2005. SROC analysis revealed no significant correlations between the overall system (ISEAQ) and each component (IS, IE, IAQ), as illustrated in Figure 5a and reported in Table 2. However, the trends in each component reflect what may be termed a “crescendo effect” as IS peaks in 2003 followed by successive peaks in IE, IAQ and increasing order in the overall system around 2006, 2007, and 2009, respectively. These peaks indicate a change in system trajectory (and possible regime shift) in the components of the system preceding increasing stability in the overall system and may provide insight on leading indicators of sustainability in the MSA. Figure 5a also shows that the most significant changes for the overall system (ISEAQ) occurred before 1990 and near the

Figure 5. Effect of the Environmental component in the Cincinnati MSA, OH−KY−IN. (a) Annual Fisher Information (3 years filter) for social (IS), economic (IE), air quality (IAQ), and all components (ISEAQ). Right axis: Fisher Information for air quality variables only, IAQ. Left axis: Fisher Information for components: social − IS, economic − IE, and the three components − ISEAQ. (b) Environmental component: air quality variables. Air quality time series, measurement in the year: for carbon monoxide, the second highest 1 h (CO 1 h 2nd max), and the second highest nonoverlapping 8 h average (CO 8 h 2nd max); for nitrogen dioxide, the 98th percentile of the daily max 1 h (NO2 98th %ile); for ozone, the second highest daily max 1 h (O3 1 h 2nd max), and the fourth highest daily max 8 h average (O3 8 h 4th max); for sulfur dioxide, the 99th percentile of the daily max 1 h (SO2 99th %ile), and the second highest 24 h average (SO2 24 h 2nd max); for particulate matter smaller than 10 μm, the second highest 24 h average (PM10 24 h 2nd max), and the 24 h average (PM10 24 h). Please note that the maximum concentration allowed by the U.S. National Ambient Air Quality Standards is marked by a dashed double dotted line (standard). 9627

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growth of income, which increased only half compared to past decades, and the vacancy rate of housing units that increased in 7 years as much as it did in the previous 32 years (Figures 2b, 3b, and 4c). Although, the overall air quality of the Cincinnati MSA has improved with in average 71% reduction for all the variables from 1980 to 2009, ozone and sulfur dioxide levels did not reach the National Air Quality Standards during this period (Figure 5b and SI Table S2). Because the City of Cincinnati, its suburban area, and overall MSA appear to be moving away from sustainability during the period of the study, this analysis clearly demonstrates that trends in key variables characterizing these systems cannot continue at the current rate.

end of the study period, when the concentration in air quality pollutants were changing dramatically or were at the lowest in general (Figure 5b), pointing to a desirable trend for the MSA.

4. DISCUSSION The novel and practical methodology presented in this research facilitates the identification of social, economic, and environmental drivers of change in real urban systems. Data series from forty social and economic variables were selected to characterize each system (i.e., city, suburbs, and MSA), from 1970 to 2009, as well as nine air quality variables for the overall MSA (1980−2009). FI, a measure of system order and stability, was used perform an assessment of the dynamic behavior these real urban systems and a diagnosis of sustainable trends. This study is not a cause and effect analysis; it is focused on subcomponents and components of the system that changed at the same time, before or after the others, indicating characteristic features of Cincinnati that are very difficult to otherwise see by inspecting the individual forty nine variables over four and three decades. We do not intend to explain the possible causes of a change, rather to locate the most significant deviation(s) of the system’s trajectory, and whether after this shift the new path is described by sustainable (i.e., desirable growth rate) or unsustainable trends (i.e., increase on air pollutants concentration). This tool will help stakeholders to decide how to invest or allocate resources among the selected variables for management, planning, or further research. In this work, two trends were found for the three areas understudy, one for the first three decades, and the second for the last ten years of study (Figures 2a, 3a, and 4a). Further, we noted that the dynamic behavior of the MSA is strongly correlated to the suburbs and the city, and the economic component is a key driver in the three areas of this study (MSA, suburbs and City). Cincinnati, part of the U.S. metropolis model that had risen due to transportation factors (new highways and automobiles) and federal aid (low taxes compared to the city), has had favorable housing trends in the postwar World War II era.19 In the 1970s, 1980s, and 1990s (first 3 decades of this study), Cincinnati continued the tendency of regionalization, focusing in its neighborhoods; in contrast to the city, which remained inactive after working hours. In general, while the growth rate of total population, households and families increased in the suburban area, it decreased in the City of Cincinnati (Figure 1). This might indicate that the net migration toward the suburbs in the 39 years of study is dominating the overall MSA dynamic for Cincinnati OH−KY−IN (Table 2). The first period is defined by steady population growth in the suburbs and MSA, and decline in the city (Figure 1). There is also an increasing rate of housing vacancy (greater than the housing occupancy), and a parallel rate of income rise in the suburbs and overall MSA, while there has been a stationary rate for both in the city (Figures 2b, 3b, and 4c). For this reason, major constructions such as: the Central Riverfront Park, Paul Brown Stadium and the Great American Ball Park, as well as the reconstruction of the Fountain Square Plaza and the opening of the Rosenthal Center for Contemporary Art in 2003, were intended to revitalized the city.15 Nevertheless, there was no sign of change in the dynamic regime of the city in the first decade of the 21st century (Figures 1c, 4b,c). After that, for the second regime of study, the current situation (until 2009), the most unsustainable trends for the MSA, suburban area, and city of Cincinnati are the rate of

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ASSOCIATED CONTENT

S Supporting Information *

(1) A map of the three areas of study (Figure S1 , City of Cincinnati, suburbs, and MSA boundaries), (2) the goodness of the polynomial fit for social and economic (Figure S2a) and air quality variables (Figure S2b), and (3) Tables of the social and economic time series describing the systems of study, Cincinnati MSA (Table S1a), City (Table S1b), and suburban area (Table S1c). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

Phone: +011-961-1-347952; e-mail: [email protected]. Present Address ∥

U.S. Environmental Protection Agency, Office of Research and Development, National Risk Management Research Laboratory, Sustainable Technology Division, 26 W. Martin Luther King Drive, Cincinnati, Ohio 45268, United States Notes

The authors declare no competing financial interest.

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REFERENCES

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