GRIDS AS USEFUL TOOL FOR REBUILDING TIME SERIES Claude GRASLAND (Univ. Paris Diderot) Nicolas LAMBERT (CNRS-RIATE) Hélène MATHIAN (CNRS- Géographie-cités)

SPECIFIC PROBLEM HOW IS IT POSSIBLE TO ANALYZE EVOLUTIONS WHEN TERRITORIAL DIVISIONS ARE CHANGING ?

HOW IS IT POSSIBLE TO COMBINE DATA AVAILABLE GENERAL PROBLEM GEOM1 GEOM1 x GEOM2 GEOM2 HOW IS IT POSSIBLE TO COMBINE DATA AVAILABLE ON TWO DIFFERENT GEOMETRIES ?

SOLUTION n°1 : TRANSFER DATA BY GRID SOLUTION V1_GRID GEOM1xV1 Auxilliary attribute GRID GEOM2xV2

SOLUTION n°2 : GRIDDING + SMOOTHING V1_GRID GEOM1xV1 POT_V1 Ancillary variable GRID POT_V2 / POT_V1 V2_GRID GEOM2xV2 POT_V2

GRIDDING + SMOOTHING

TEST AREA : South-Western France

OBJECTIVE : Annual growth rate of population 1990-2006 GEOM1 55 Arrondissements GEOM2 52 Zones d’emploi ??? ???

AN EXACT BUT NOT INTERESTING SOLUTION : Aggregation at first common level

ANCILLARY VARIABLE 100 000 Grid points Grid of population 1km x 1km From EEA ANCILLARY VARIABLE 100 000 Grid points

ESTIMATION OF TARGET INDICATOR POP90 / ARRD POP90 /GRID POT (POP90) Gauss 20 km POP00/GRID ANNUAL GROWTH RATE 1990-2006 Gauss 20 km POP06/ GRID POP06 / ZEMP POT (POP06) Gauss 20 km

ESTIMATION OF RESIDUAL « NOISE » POP06 / ARRD POP06/GRID* POT (POP06)* Gauss 20 km POP00/GRID POT(POP06) * ____________ POT (POPO6) POP06/GRID POP06 / ZEMP POT (POP06) Gauss 20 km

Smooth 10 km GOOD SPATIAL RESOLUTION … … BUT HIGH LEVEL OF NOISE Increase of population 1990 - 2006 Noise introduced by the method (%) 0.25 0.5 0.75 1.0 -5% -1% +1% +5%

Smooth 40 km LOW SPATIAL RESOLUTION … … BUT LOW LEVEL OF NOISE Increase of population 1990 - 2006 Noise introduced by the method (%) 0.25 0.5 0.75 1.0 -5% -1% +1% +5%

Smooth 20 km GOOD COMPROMISE BETWEEN SPATIAL RESOLUTION AND NOISE Increase of population 1990 - 2006 Noise introduced by the method (%) 0.25 0.5 0.75 1.0 -5% -1% +1% +5%

SYNTHESIS : Signal & Noise Max Noise < 5% Mean Noise < 1% Gaussian Smooth > 22 km

CONCLUSION & PERSPECTIVES Smooth + Grid CONCLUSION & PERSPECTIVES

Longer Time Series

Multilevel spatial analysis

Cross Border Analysis

Modifiable Area Unit Progress

Thank you for your attention ! Grasland, Mathian, Vincent, 2000, Statistical Journal of UN-ECE Grasland, Madelin, 2007, ESPON 3.4.3, MAUP