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Spatial Interpolators to generate
Population Density Surfaces in the
Brazilian Amazon: problems and
perspectives
Silvana Amaral
Antonio Miguel V. Monteiro
Gilberto Câmara
José A. Quintanilha
Introduction
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Brazilian Amazonia – 5 million km2, 4 million of forest
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Deforestation rate 15.787 km2/year
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Environment x Life quality
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Urban Population 1970 – 35.5%, 2000 - 70%
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Health, education and urban equipments - precarious
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Planning – consider the human dimension
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POPULATION – subject and object of the
transformations ?
GEOINFO – Dez/2002
Introduction
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Geographic phenomena – computing representation
models to socio-economic data
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Individual
Area
Continuous phenomena in space
Area– discrete region phenomena, homogenous unit
Unit – arbitrary as the census sector – do NOT
represent the spatial distribution of the variable.
Modifiable Area Unit Problem (MAUP) – temporal
series???
GEOINFO – Dez/2002
Introduction
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Surface Models – alternatives to Area restrictions
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Demographic Density – continuous phenomenon
Objective: to estimate distribution in detail (as better as possible)
Advantage: manipulation and analysis - Area independent
Data storage and accessibility in Global Database
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Census Data – Municipal boundaries or census sector
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Land use and coverage evolution in Amazonia
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Territorial divisions
Regular grid for spatial models
Population pressure – Population density gradient
GEOINFO – Dez/2002
Introduction
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Objective – discuss the principal spatial
interpolation techniques used to represent
Population at density surfaces and indicate
the more suitable methods to represent
population in the Amazonia Region.
GEOINFO – Dez/2002
To represent Population in Amazonia…
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Data availability
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Census Data (10 years)
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Inter-census – counting based on sampling
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Statistic estimates – PNAD – UF, metropolitan region,
for urban population in the N region
only
Spatial Reference
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Municipal limits – up to 2000 census, (analogical maps),
official territorial limit (IBGE) – municipal
2000 census – digital census sector (just to the urban area –
mun. > 25,000 inhabitants)
GEOINFO – Dez/2002
To represent Population in Amazonia…
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Census Zone
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Surveyed area - 1 month:
350 rural residences
250 urban
Amazonia – vast areas and
heterogeneous
Alta Floresta d’Oeste (RO)
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165 km2 and regular boundaries –
settlements
435 km2 in forested areas
GEOINFO – Dez/2002
To represent Population in Amazonia…
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Region Heterogeneity
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Municipal Dimension: Raposa (MA) - 64 km2,
Altamira (PA) – 160,000 km2
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Municipal Area: Average = 6,770 km2, Stand. Dev.=14,000 km2
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RO – 52 municipios – average area of 4,600 km2
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AM - 62 municipios – average area of 25,800 km2
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Municipal area influences the census zone dimension
GEOINFO – Dez/2002
To represent Population in Amazonia…
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Process complexity -> spatial distribution
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Rondônia: migrants, INCRA settlements, urban nuclei along the
road axis and population at rural zone.
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Amazonas: lower urban nuclei density, concentrated in Manaus.
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Tendencies:
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Dispersion from metropolis,
Increasing relative participation of cities up to 100,000 inhab.
Population growing at 20,000 inhab. nuclei
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Dispersal population at rural zone and along river sides
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Forest continuous – demographic emptiness
GEOINFO – Dez/2002
Population Models
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Human Dispersion:
Important at
regional projects LBA and LUCC
More frequent
representation:
Thematic Maps
GEOINFO – Dez/2002
Population Models
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Demographic
Density instead of
Total Population
2000
Visualization:
Intervals and criteria
Highlight: Densely
populated regions
and Demographic
emptiness
GEOINFO – Dez/2002
Population Models
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Surface Interpolation Techniques - “Models” –
two groups:
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Considering only one variable – POPULATION:
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Area Weighted, Kriging, Tobler Pycnophylatic, Martin’s
Population Centroids
Considering auxiliary variables, human presence
indicators:
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Dasimetric method, Intelligent Interpolators and variants
GEOINFO – Dez/2002
“Univariate” Population Models
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Area Weighted
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Population Density proportional to the intersection
between original zones and grid cells.
Sharp limits in the boundaries and constant values inside
the units.
Error increases with:
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more clustered distribution,
smaller destiny regions compared to the origin regions
At the Amazonia region –> raster representation of the
Population Density (previous map)
GEOINFO – Dez/2002
“Univariate” Population Models
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Kriging
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Interpolation for spatial random process. It estimates
the occurrence of an event in a certain place based on
the occurrence in other places.
The variable values are dependent of the distance
between them, a function describes this spatial
distribution.
Using Municipal centres as sample points, taking the
demographic density (log) –> a gaussian function can
model the population spatial distribution
GEOINFO – Dez/2002
Spatial Representation - “Univariate”
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Kriging
Imprecision for
modeling
Population
volume
Manaus ->
Pará
Empty areas
RO
 Synoptic vision
 General
Tendency
GEOINFO – Dez/2002
“Univariate” Population Models
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Tobler Pycnophylatic
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Based on the Geometric
centroids of the census unit
Smooth surface ~ “average
filter”
Weighted by the centroid distance, concentric demographic
density function
Population value for the entirely surface (there is NO zeros)
 Consider the adjacent values and maintain the Population
volume
GEOINFO – Dez/2002
“Univariate” Population Models
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Tobler Pycnophylatic
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Ex: Global Demography
Project, 9km grid, 1994.
Manaus ->
Municipal Data
Pará
Homogeneous region,
diffuse boundaries
RO – smaller municipios,
interpolator effect.
Better results – smaller
units (census zone) and
high populated areas.
GEOINFO – Dez/2002
RO
“Univariate” Population Models
Based on Kernel
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Martin’s Centroids Weighted
Census mapping - UK
Adaptive Kernel: point density
define the populated area
extension
Distance decay function:
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Weight for each cell – redistribute
the total counting
Function shape – affects the
distribution of the population over
areas
Rebuild the distribution geography, maintaining areas without
population at the final surface.
GEOINFO – Dez/2002
“Univariate” Population Models
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Kernel – 2000
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Municipal centres centroids
Gradient at high
populated areas
Demographic
emptiness preserved
Better results:
additional centroids
(districts and RS
images), and smaller
units and densely
populated regions
GEOINFO – Dez/2002
“Multivariate” Population Models
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Auxiliary variables - human
presence indicators - to distribute
population
Dasimetric Method – Remote
Sensing classified images –
weights to disaggregate
Intelligent Interpolators: Spatial
information from other sources to
guide the interpolation
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A weighted surface map the original
data on the final surface
Predictors variables x interest variables
GEOINFO – Dez/2002
Land use categories
High housing
Low housing
Industry
Open space
Probabilities by raster cell detail
Weights
10
5
1
1
Probability
No intervals
n total weights of
zone
Zonal data to microdata
1483
Data element
100
50
10
Data element
“Multivariate” Population Models
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Intelligent Interpolators :
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Ex: LandScan –1km grid,
1995
Population Model: land
use, roads proximity,
night-time lights =>
probability coefficients
Population at risk:
information for emergency
response for natural
disasters or anthropogenic
GEOINFO – Dez/2002
“Multivariate” Population Models
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Intelligent Interpolators - Variants:
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Clever SIM – besides the auxiliary variables, neural
network to:
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understand the relations between predictors variables and
population
generate the surface.
Crucial: variable selection and interactions – ”model”
Availability and quality of the auxiliary data ->
responsible for the final density surface precision
GEOINFO – Dez/2002
Perspectives
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Density Surfaces in Amazonia:
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Interpolator Methods – characteristics e restrictions
Adaptive Approach – based on scale of analysis and phenomena
complexity
Scaling Top-Down
Amazonia Legal:
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“Multivariate” models : heterogeneities
“Univariate” Models: Tobler – related to the sampling unit;
Martin – additional centroids; Kriging – general tendencies
=>OK
Kriging including barriers (further)
GEOINFO – Dez/2002
Perspectives
Macro-zones: Spatial-Temporal Subdivision:
I. Oriental and South Amazonia: “deforestation arc”
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Martin’s Centroids Weighted– villages, districts, night-time lights
II. Central Amazonia : Pará, new axis region
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“Multivariate” Model - intelligent Interpolators
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Scenarios Analyze as BR-163 paving
III. Occidental Amazonia : “Nature rhythm”
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“Multivariate” Model – Disaggregating by land use (e.g.)
GEOINFO – Dez/2002
Finally
Scale – Census Zones
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Tobler Pycnophylatic or Martin’s Centroids Weighted
The interpolation procedure should be defined according to
the analysis of land use and settlement process in the region
– different characteristics considering capital, frontier,
ranching, etc.
To be continued:
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Define and execute an experimental procedure to generate
population density surface for the Amazonia region, following
the approach proposed, with data validation and analysis of
results.
GEOINFO – Dez/2002
Some results
Population Density Surface - Kriging
GEOINFO – Dez/2002
Some results
Population Density Surface - Kriging
GEOINFO – Dez/2002