Areal Interpolation Methods using Land Cover and Street Data. Jeff Bourdier GIS Master s s Project Summer 2006

Transcription

1 Areal Interpolation Methods using Land Cover and Street Data Jeff Bourdier GIS Master s s Project Summer 2006

2 Objective The areal interpolation problem Some variable (here, population) is known in a given set of polygons (source zones) That variable must be estimated for a different set of overlying polygons (target zones) Examples Environmental impact assessment Emergency response Marketing analysis

3 Objective Ideal solution Location of each residence Number of residents at each residence Count residents in each target zone Such data is rarely available In practice, solutions typically assume a homogeneous population distribution Throughout each source zone Throughout each control zone Along each street segment in each source zone

4 Objective Greater accuracy is possible Readily available data Land cover Street network More sophisticated techniques Use of street-weighting versus area-weighting Variations in residential intensity Low (Single-family housing) High (Multi-family housing)

5 Literature Review Goodchild and Lam (1980) Formally defined areal interpolation problem Proposed simple area-weighted method Assumes homogeneous population distribution throughout each source zone Can be formulated in two ways

6 Literature Review v t = s w ts u s v t = population of target zone t u s = population of source zone s w ts = a ts / σ s (area weight) a ts = area of intersection between t and s σ s = area of s d s = u s / σ s area) v t = s a ts d s (population density of s in people per unit

7 Literature Review Goodchild and others (1993) Globally constrained (GC) regression method Introduced control zones: third set of polygons with homogeneous population distributions = c b tc = area of intersection between t and control zone c d c = population density of c,, determined by regression analysis of: a sc = area of intersection between s and c v u t s = c b a tc sc d d c c

8 Literature Review Dasymetric method Based on idea by Wright (1936) Formulated by Fisher and Langford (1996) Intersects residential areas with source zones Effectively eliminates uninhabited areas from each source zone Inhabited portions of each source zone could be thought of as control zones Formulated as in GC regression method, except that d c = u s / a sc

9 Literature Review Simple street-weighted method Concept used by O Neill O and others (1992) to estimate population in transit service area Formulated by Xie (1995) and Reibel and Bufalino (2005) Same as simple area-weighted method, except: a ts = total length of street segments in area of intersection between t and s σ s = total length of street segments in s d s = population density of s in people per unit length

10 Literature Review Parcel-based approach Used by Biba and Curtin (In Review) to estimate population in transit service area More accurate than simple area- and street- weighting Data on number of residents at each parcel unavailable; assumption must be made Parcel data not as readily available as street or land cover data

11 Literature Review Raster-based techniques Tobler (1979) introduced pycnophylactic constraint: calculated population must equal actual population Mennis (2003) allocated population to cells based on urban class Centroid-based approaches Inverse distance weighting (Warntz( 1964; Martin 1989; Moon and Farmer 2001) Gaussian model (Clark 1951; Wang and Zhou 1999)

12 Literature Review Remote sensing (RS) approaches Correlation of reflectance with population density via regression analysis (Lo 1995; Harvey 2002) Comparison of RS methods to street-based methods Street buffer more accurately identified residential areas than unsupervised classification (Epstein and others 2002) Population growth more accurately predicted by increase in street length than increase in residential areas (Qiu( and others 2003)

13 Data Sources Collin County selected as study area Source and target zones chosen to satisfy three criteria: Population known in each Incongruent boundaries Equal granularities Source zones = census tracts (ESRI 2006) Target zones = ZIP Code Tabulation Areas (ZCTAs( ZCTAs) ) (U.S. Census Bureau 2006) TIGER/Line Data on roads (ESRI 2006) Control zones based on residential land use (NCTCOG 2006)

14 Census tracts (source zones) and ZIP Code Tabulation Areas (target zones) for Collin County. Source: ESRI and the U.S. Census Bureau.

15 Auxiliary spatial data for Collin County: (A) areas of residential land use, used to determine control zones, and (B) the street network. Source: The NCTCOG and ESRI.

16 Methodology Target zone (ZCTA) populations are estimated using total of ten techniques Existing methods Simple area-weighted Dasymetric GC regression Simple street-weighted Street-weighted versions of existing methods Dasymetric GC regression New techniques, both area- and street-weighted Locally constrained (LC) regression Equation solution

17 Methodology Control zone definition GC regression Residential land use polygons aggregated based on residential intensity r to make two zones r = 1 (low residential intensity) r = 2 (high residential intensity) LC regression and equation solution The two zones above are intersected with source zones Each control zone has two ancillary properties Residential intensity, p c, equal to some value of r Source zone that contains it, q c, equal to some value of s

18 Methodology Formulation of new methods similar to dasymetric except calculation of d c If q c contains only one class of residential intensity, then d c = u s / a sc ; otherwise, depends on method LC regression Pycnophylactic constraint imposed on each source zone Ratio of population densities (low to high) determined as in GC regression and applied to each source zone

19 Methodology Equation solution For each source zone, two equations can be written: u s = c a sc d c u s = c a s c d c s = source zone of primary interest s' = some secondary source zone c and c' independently index control zones

20 Methodology Since no more than 2 control zones intersect each source zone: u = a d + s sc 1 c1 sc2 c2 c 1 = control zone with low residential intensity in s c 2 = control zone with high residential intensity in s Likewise for c' 1 and c' 2 in s' a d u s = as c d + a d 1 c1 s c2 c2

21 Methodology Assume: Therefore: d c = d c = 1ss δ 1 1 d c = d c = 2ss δ 2 2 u s = asc ss + asc 2ss δ δ u s = as c ss + as c 2ss δ δ Two equations, two unknowns If there are n s source zones, then for each source zone, n s 1 such pairs of equations can be solved

22 w qc s Methodology n q s= 1 d c = n \ q s \ q c w s c s= 1 = inverse distance from centroid of q c to centroid of s,, raised to some exponent Backslash (\)( ) means exclude (an equation cannot be solved with itself) c s w δ q c p s c q c s

23 Results Error measures Percent error calculated for each target zone 100 ( vˆ v ) t = predicted value of v vˆt t Percent error useful for comparison of error distributions Mean percent error not useful for comparison across methods v t t

24 Results Mean absolute percent error (Goodchild( and Lam 1980; Goodchild and others 1993) MAPE = 100 v t t vt n t = number of target zones ˆ n t v t

25 Results Population-weighted mean absolute percent error (Qiu( and others 2003) PWMAPE = 100 vˆ t v t t v t t

26 Results Root mean squared error (Fisher and Langford 1996; Reibel and Bufalino 2005) RMSE = ( vˆ v ) t t n t t 2

27 Results Determination of appropriate exponent in area- weighted equation solution method R M S E M i n : P W M A P E M i n : M A P E M i n : Exponent chosen: 1

28 Results Determination of appropriate exponent in street- weighted equation solution method R M S E M i n : P W M A P E M i n :? M A P E M i n :? Exponent chosen: 5

29 Box plots of percent errors for (A) area-weighted and (B) street-weighted methods.

30 (A) Target zones and associated percent errors by the street-weighted equation solution method. Indeterminate zones are not entirely within the study area, so their estimated populations cannot be compared with their actual populations to assess accuracy. (B) Source zones. The two with thick outlines encapsulate the two target zone outliers.

31 Results Error measures of target zone population estimates by areal interpolation methods. Method With All Target Zones Without Outliers MAPE PWMAPE RMSE MAPE PWMAPE RMSE Area-weighted Simple GC Regression Dasymetric LC Regression Equation solution Street-weighted Simple GC Regression Dasymetric LC Regression Equation solution

32 Conclusions Residential population more correlated with street lengths than with areas Street-weighted equation solution method most accurate overall Dasymetric most accurate area-weighted technique GC regression least accurate overall Exponents in equation solution method suggest neighborhood effects of population density significant for areas but not streets Illustration of two adjacent source zones with comparable lot sizes but a sharp difference in the part of the lot that faces the street.

33 Conclusions Ideas for refinement of equation solution method Use more than two classes of residential intensity Omit solutions leading to unrealistic population densities (negative, backwards ) Generalize determination of exponent(s) Simpler dasymetric method about as accurate

34 References Biba,, S., and K. M. Curtin. In Review. A New Method for Determining g the Population with Walking Access to Transit. International Journal of Geographical Information Science. Clark, Colin Urban Population Densities. Journal of the Royal Statistical Society. Series A (General) 114 (4): Eicher,, Cory L., and Cynthia A. Brewer Dasymetric Mapping and Areal Interpolation: Implementation and Evaluation. Cartography and Geographic Information Science 28 (2): Environmental Systems Research Institute (ESRI) Census 2000 TIGER/Line Data and Census Tract Demographics (SF1). Geography Network.. Redlands, CA. Epstein, Jeanne, Karen Payne, and Elizabeth Kramer Techniques for Mapping Suburban Sprawl. Photogrammetric Engineering and Remote Sensing 68 (9): Fisher, Peter F., and Mitchel Langford Modeling Sensitivity to Accuracy in Classified d Imagery: A Study of Areal Interpolation by Dasymetric Mapping. Professional Geographer 48 (3): Goodchild,, Michael F., and Nina Siu-ngan Lam Areal Interpolation: A Variant of the Traditional Spatial Problem. Geo-Processing 1 (3): Goodchild,, M. F., L. Anselin,, and U. Deichmann A Framework for the Areal Interpolation of Socioeconomic Data. Environment and Planning A 25 (3): Harvey, J. T Estimating Census District Populations from m Satellite Imagery: Some Approaches and Limitations. International Journal of Remote Sensing 23 (10): Lo, C. P Automated Population and Dwelling Unit Estimation ion from High-resolution Satellite Images: A GIS Approach. International Journal of Remote Sensing 16 (1): Martin, David Mapping Population Data from Zone Centroid Locations. Transactions of the Institute of British Geographers, New Series 14 (1): Mennis,, Jeremy Generating Surface Models of Population Using Dasymetric Mapping. Professional Geographer 55 (1):

35 References Moon, Zola K., and Frank L. Farmer Population Density Surface: S A New Approach to an Old Problem. Society and Natural Resources 14 (1): North Central Texas Council of Governments (NCTCOG) Land d Use GIS Data Clearinghouse.. Arlington, TX. O'Neill, Wende A., R. Douglas Ramsey, and JaChing Chou Analysis of Transit Service Areas Using Geographic Information Systems. Transportation Research Record 1364: Qiu,, Fang, Kevin L. Woller, and Ronald Briggs Modeling Urban Population Growth from Remotely Sensed Imagery and TIGER GIS Road Data. Photogrammetric Engineering and Remote Sensing 69 (9): Reibel,, Michael, and Michael E. Bufalino Street-weighted Interpolation Techniques for Demographic Count Estimation in Incompatible Zone Systems. Environment and Planning A 37 (1): Tobler,, Waldo R Smooth Pycnophylactic Interpolation for Geographical Regions. Journal of the American Statistical Association 74 (367): U.S. Census Bureau ZIP Code Tabulation Areas (ZCTAs( ZCTAs) ) 2000 and Census 2000 gazetteer of ZCTAs. Census Bureau Geography.. Washington, DC. Wang, Fahui,, and Yixing Zhou Modelling Urban Population Densities in Beijing : 90: Suburbanisation and its Causes. Urban Studies 36 (2): Warntz,, William A New Map of the Surface of Population Potentials for the United States, Geographical Review 54 (2): Wright, John K A Method of Mapping Densities of Population with Cape Cod as an Example. Geographical Review 26 (1): Xie, Yichun The Overlaid Network Algorithms for Areal Interpolation Problem. Computers, Environment and Urban Systems 19 (4):

36 Questions?