**Derivation of a Nationally Consistent Urban Intensity Index**

**BACKGROUND**

-   The USGS's NAWQA Program has been investigating biological,
    chemical, and physical responses to urbanization across the US
    since 1999. This Program has completed studies in 9 metropolitan
    areas: ATL, BIR, BOS, DEN, DFW, MGB, POR, RAL, and SLC.

-   NAWQA Program studies examine responses to urbanization along a
    gradient of urbanization defined by and urban intensity index (UII:
    McMahon and Cuffney 2000, Coles et al. 2003, Tate et al. 2005).

-   The UII provides an *a priori* measure of urban intensity that is
    used to select basins that represent levels of urbanization from "0"
    (essentially reference conditions) to "100" (maximum urbanization in
    the study area) within an area of relatively homogeneous national
    environmental characteristics (e.g., elevation, ecoregion, soils,
    etc.).

-   These UII's are based on a compilation of multiple census, land use,
    and infrastructure characteristics that are associated with changes
    in population density.

-   A multimetric index (i.e., index derived from multiple variables) is
    used to characterize urban intensity because many of the GIS-derived
    urbanization characteristics (e.g., census variables) are estimated
    from data compiled at variable spatial scales. Using multiple
    variables (e.g., census, nlcd, infrastructure) that are associated
    with population density tends to compensate for errors in individual
    variables as is commonly done for biological indices (IBI, ICI refs
    here).

-   The UII's that have been developed in the Program are specific to
    each study, that is, they include variables that have been deemed
    important to the characterization of urbanization within each study
    (e.g., Atlanta or Denver metropolitan area) rather then for
    characterization of urbanization nationally. Consequently, the
    variables used to develop UII's are not consistent among studies and
    vary in the number of variables that comprise the index (5-40).

-   The relation between population density and variables that have been
    incorporated into study-specific UII's (e.g., road density) varies
    across the country. That is, the rate of change in road density as a
    function of population density is not the same in Atlanta as it is
    in Salt Lake City.

-   The purpose of this paper is to derive a nationally consistent UII
    that can be used to compare urban intensity among the 9 NAWQA
    Program urban studies. This index will utilize a consistent set of
    variables and will make adjustments for differences in the rates at
    which UII variables change as a function of population density.

**HYPOTHESIS**

A nationally consistent multimetric urban intensity index can be derived
for the 9 NAWQA Program urban studies. This index will be based on a
consistent set of census, nlcd, and infrastructure variables associated
with changes in population density in all studies and adjusted for
differences among studies in the rate at which the variables respond to
changes in population density.

**APPROACH**

The study-specific UIIs are all derived from variables that are
correlated with 2000 population density. Therefore, use population
density to scale these UIIs in each SU to the full range of population
density observed across all SUs.

Synopsis of procedure for producing nationally-scaled UII's

1.  Select a subset of census, nlcd, and infrastructure variables that
    can be used to characterize environmental changes associated with
    changes in population density (POPDEN00). Sixty-six census, 21 nlcd
    (11 basin-scale and 10 stream buffer variables, including the
    aggregate of nlcd classes '4', '5', and '7' as a "background" nlcd
    class) and 6 infrastructure variables were considered. Variables
    should have the following characteristics for consideration in the
    construction of the EUSE_UII:

    a.  Variables must exhibit a correlation (Spearman rho) of \|ρ\| ≥
        0.7 with POPDEN00.

    b.  Variables must display a relatively linear response across the
        full range of population density (e.g., PPRURAL and PPURBAN were
        not suitable because they only respond over a portion of the
        range in population density).

![](media/image1.wmf){width="3.625in" height="2.0625in"}

c.  Variables must be capable of being expressed as an increasing value
    across the range of population density in order to extrapolate a
    value for the maximum population density encountered in the 9 EUSE
    studies (2174.5).

d.  Only census, nlcd, and infrastructure variables that could be
    readily derived from nationally available GIS coverages and that
    were not dependent upon the mix of sites were considered. For this
    reason fragstats and SEI variables were not considered for the
    EUSE_UII.

e.  If variables that were in the same class (census, nlcd, or
    infrastructure) had essentially the same response among sites (e.g.,
    P_NLCD1_2, P_NLCD1_B2 and NLCD_IS), only one variable (e.g.,
    P_NLCD1_2) was used in the index to represent the group of related
    variables.

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2.  Review of the 93 census, nlcd, and infrastructure variables lead to
    a consideration of 9 variables (HUDEN, PPRURAL, P_NLCD1_2,
    P_NLCD1_4+5+7, NLCD_IS, P_NLCD1_B2, P_NLCD1_B4+5+7, ROADDEN,
    RDTRDEN).

3.  The 9 variables for consideration in the EUSE_UII were examined in
    greater detail by plotting then against POPDEN00.

4.  There was a close correspondence between RDTRDEN and ROADDEN RDTRDEN
    was dropped from the index.

5.  P_NLCD1_2 and P_NLCD1_B2 were compared on a SU-by-SU basis and
    P_NLCD1_B2 was deemed to be redundant and dropped from the index.

6.  The variable PPRURAL did not respond across the entire range of
    POPDEN (see graphs in 1b above) so it was eliminated from the index
    calculations.

7.  The variable NLCD_IS was closely related to P_NLCD1_2 so it was
    eliminated from the index and P_NLCD1_2 was retained.

8.  The variable P_NLCD1_B4+5+7 was closely related to P_NLCD1_4+5+7 so
    it was eliminated from the index and P_NLCD1_4+5+7 was retained.

9.  The relation between P_NLCD1_4+5+7 and POPDEN00 was relatively weak
    and variable, so this variable was eliminated from the index.

10. Elimination of RDTRDEN, P_NLCD1_B2, P_NLCD1_4+5+7, NLCD_IS,
    P_NLCD1_B4+5+7 and PPRURAL left four variables for consideration in
    calculating EUSE_UII: HUDEN, P_NLCD1_2, P_NLCD1_4+5+7, ROADDEN.

11. The EUSE_UII was calculated two ways:

    a.  Conversion of individual variables to the national range of
        POPDEN00 values. This was done by using linear regression to
        predict the value of the variable at the highest level of
        POPDEN00 observed among the 9 EUSE studies, 2174.5 in WMIC.
        Regression equations were developed for each variable and Study
        Unit after log conversion of variables (log(X+1)). The observed
        values were then expressed as a percentage of the maximum
        predicted value after conversion back to the original
        untransformed values. The average percentage for the three
        variables were calculated for each site and the average was
        range standardized over all sites to produce an EUSE_UII value
        that ranged from 0 to 100.\
        \
        Linear regressions were calculated by assuming that the
        intercept was 0.\
        \
        The EUSE_UII index was compared to the original SU UII's.

    b.  Calculation of individual UII's for each SU. A SU_EUSE_UII was
        calculated based on the range standardized values of the three
        variables (HUDEN, P_NLCD1_2, ROADDEN) that comprise the
        EUSE_UII. The range standardized values of the variables are
        averaged and the result is range standardized to produce an
        index that varies from 0 to 100 for each SU. This SU_EUSE_UII is
        then regressed against POPDEN00 (intercept = 0) to get an
        equation that is used to predict the SU_EUSE_UII value at the
        maximum POPDEN00 observed over the 9 EUSE studies (2174.5,
        WMIC). The SU_EUSE_UII indices are then expressed as a
        percentage of the value expected at the maximum POPDEN00 for
        each SU. These percentages are then range standardized to
        produce an index (EUSE_UII\*) that ranges from 0 to 100.\
        \
        The SU_EUSE_UII was compared to the SU_UII and the EUSE_UII\*
        was compared to the EUSE_UII.

**MAJOR FINDINGS\
**

1.  The EUSE_UII's produced by standardizing the individual variables to
    max POPDEN00 produce indices that are less variable across the range
    of POPDEN00 than are the original SU_UII's.

![](media/image2.wmf){width="4.864583333333333in"
height="3.3958333333333335in"}

2.  There is a strong correspondence between the EUSE_UII's and the
    SU_UII's for all SU's except SPLT, TRIN, and WMIC. The SPLT, TRIN,
    and WMIC all have more sites located at the lower end of urban
    intensity using the EUSE_UII than the SU_UII (see graphs in
    worksheet "Index_Intcp_0" in the workbook "Nat_Scaled_UII_B.xls").\
    \
    \
    ![](media/image3.wmf){width="4.250694444444444in"
    height="3.0034722222222223in"}\
    \
    \
    ![](media/image4.wmf){width="4.623611111111111in"
    height="3.267361111111111in"}

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12. Derivation of the UII using by standardizing the individual
    variables (EUSE_UII) or standardizing the index derived from the
    individual variables for each SU (EUSE_UII\*) resulted in virtually
    identical indices.\
    \
    ![](media/image5.wmf){width="5.447916666666667in"
    height="3.3854166666666665in"}

    a.  Recommendation is to use the EUSE_UII (a better acronym is
        needed!) based on standardizing the 3-variables (HUDEN,
        P_NLCD1_2, ROADEN) derived from regression with the intercepts
        set to 0 (i.e., the index values in column "Q" of worksheet
        "Index_Intcp_0" in workbook "Nat_Scaled_UII_B.xls."

**CONTRIBUTIONS AND POLICY IMPLICATIONS**

-   The proposed work will provide a measure of urban intensity that is
    comparable among the 9 urban studies (i.e., the index will express
    equivalent change in the index relative to changes in population
    density for all 9 urban studies).

-   The development of a nationally consistent index will describe the
    regional differences in urban responses that exist among the 9 urban
    study areas (i.e., confirm that changes in "key" urban variables,
    such as road density, differ among regions of the country when
    expressed as a function of population density). This has important
    management and policy implications because it establishes that
    landscape changes (e.g., urban land cover, housing density, and road
    density) resulting from increasing population density vary across
    the country. This suggests that management and policy needs to be
    tailored to local conditions in order to adequately address effects
    of urbanization.

-   Provide an example of how regionally different responses to
    urbanization can be addressed to produce a consistent indication of
    changes in urban intensity.

-   The derivation of a nationally consistent urban intensity index is
    critical to the comparison of responses (physical, chemical, and
    biological) to urbanization across the country.

**SCHEDULE**

-   A draft journal article will be completed in FY 07.

-   This paper will lay the groundwork for the development of: (1) a
    "true" national index of urban intensity that can be applied outside
    of the context of these 9 urban studies (Falcone 2008) and (2)
    response-based indices of urban intensity that will select landscape
    variables on the basis of their association with physical, chemical,
    and biological changes rather than with population density.

**REFERENCES**

Coles, J. F., T. F. Cuffney, G. McMahon. 2004. The effects of
urbanization on the biological, physical, and chemical characteristics
of coastal New England streams. U.S. Geological Survey Professional
Paper 1695. U.S. Geological Survey, Reston, Virginia.

Cuffney, T. F., H. Zappia, E. M. P. Giddings, and J. F. Coles. 2005.
Effects of urbanization on benthic macroinvertebrate assemblages in
contrasting environmental settings: Boston, Massachusetts; Birmingham,
Alabama; and Salt Lake City, Utah. Pages 361--407 *in* L. R. Brown, R.
H. Gray, R. M. Hughes, and M. R. Meador (editors). Effects of
urbanization on stream ecosystems. Symposium 47. American Fisheries
Society, Bethesda, Maryland.

McMahon, G., and T. F. Cuffney. 2000. Quantifying urban intensity in
drainage basins for assessing stream ecological conditions. Journal of
the American Water Resources Association 36:1247--1261.

Tate, C. M., T. F. Cuffney, G. McMahon, E. M. P. Giddings, J. F. Coles,
and H. Zappia. 2005. Use of an urban intensity index to assess urban
effects on streams in three contrasting environmental settings, Pages
291--315 *in* L. R. Brown, R. H. Gray, R. M. Hughes, and M. R. Meador
(editors). Effects of urbanization on stream ecosystems. Symposium 47.
American Fisheries Society, Bethesda, Maryland.