1. Agreement at Multiple Resolutions for Real and Categorical Maps Chris Ayres – George Kariuki Kristopher Kuzera cayres@clarku.edu, gkariuki@clarku.edu, kkuzera@clarku.edu GEOG 360 Quantitative Modeling Final Project - Spring 2004 REALMULTIRES, SOFTMULTIRES

2. 2 Lessons Currently, there is no known program available to perform and interpret a MULTIPLE- RESOLUTION ANALYSIS for real and categorical data. Automation of these processes allows for efficient production and replication of methodologies, with a minimization of human error.

3. 3 Multiple Resolution Analysis Multiple resolution analysis compares corresponding pixels of two maps over varying resolutions ranging from fine to coarse. This helps locate spatial patterns within the dataset and allows for ease in interpretability of the data. The analysis can distinguish disagreement of quantity from disagreement of location.

4. 4 Forest 1999 Urban 1971 Multiple Resolution Example Maps of categorical disagreement from fine to coarse resolutions Worcester County, MA

5. 5 MULTIRES Programs 1971 1999 Actual Predicted REALMULTIRES –Real variables SOFTMULTIRES –Categorical variables

6. 6 CharacteristicREAL- MULTIRES SOFT- MULTIRES Performs MULTIPLE RESOLUTION ANALYSIS of three different SOFT-CLASSIFIED OPERATORS to compare two categorical maps. Yes Compares two maps of a common real variable (NDVI, SST) at multiple spatial-resolutions using various components of two measures of accuracy: (1) Root Mean Square Error (RMSE) (2) Mean Absolute Error (MAE) Yes Uses IDRISI to carry out raster functions: CONTRACT, RECLASS, OVERLAY, EXTRACT, WINDOW, CONVERT, TRANSFORM Yes Calculates COEFFICIENTS OF AGREEMENT from generated cross-tabulation matrices of agreement and disagreement. Yes Graphically displays results over all resolutions. Yes

7. 7 NDVI deviation at 1x1 km Null model would predict zero everywhere. Drought Prediction in Southern Africa Actual Map Predicted Map

8. 8 NDVI deviation at 4x4 km Null model would predict zero everywhere. Drought Prediction in Southern Africa Actual Map Predicted Map

9. 9 NDVI deviation at 16x16 km Null model would predict zero everywhere. Drought Prediction in Southern Africa Actual Map Predicted Map

10. 10 Program Implementation: RMSE Perfect Posterior Prior INFORMATION OF QUANTITY Perfect Perfect Posterior Uniform Uniform Global In-Stratum Pixel In-Stratum Global INFORMATION OF LOCATION

11. 11 Program Implementation: MAE Perfect Posterior Prior INFORMATION OF QUANTITY Perfect Perfect Posterior Uniform Uniform Global In-Stratum Pixel In-Stratum Global INFORMATION OF LOCATION

12. 12 Interface for REALMULTIRES Inputs –Working Folder –Actual map –Prediction map –Mask Map –No. of Rows –No. of Cols –Range of resolutions

13. 13 Budget Results: Null versus Prediction

14. 14 REALMULTIRES Automation Benefits Huge time savings –2 WEEKS manually becomes 1½ MINUTES automatically. Minimize Chance of Error, Maximize Efficiency –Repetitive tasks are prone to human error such as typos that could have a big unwanted impact on the results. RMSE and MAE have great potential for accuracy assessment (drought prediction) The two methods are better than regression at giving useful information to evaluate drought prediction in Africa.

15. 15 SOFTMULTIRES Flow Chart Which operator? MULTIPLICATIONCOMPOSITE MINIMUM Calculate minimum values of similar classes at resolutions. (MINIMUM) Create gains and losses maps at resolutions. (ADD / SUBTRACT) Multiply gains and losses over 1 - agreement Multiply each map with every other at resolutions. (MULTIPLY) Calculate minimum values of comparing maps at resolutions. (MINIMUM) Calculate sum of pixels. (EXTRACT) Calculate sum of pixels. (EXTRACT) Calculate sum of pixels. (EXTRACT) Calculate sum of pixels. (EXTRACT) START Read the following variables from input sheet: Comparison Year, Reference Year, Map files, Operators, Number of Categories Create soft-classified resolution maps for each class at each year. (CONTRACT) Read RDC file to determine number of resolutions, rows, and columns. END Sums entered in contingency table at resolutions. Derive statistics from matrices. Graph statistics over resolutions. IDRISI Kilimanjaro Another operator? NOYES

16. 16 SOFTMULTIRES Soft-Classified Operators Soft-classified operators allow for multiple class membership per pixel. The pixels are considered “soft”. Different operators have different interpretations of class membership and location within a pixel. SOFTMULTIRES allows user to choose any or all operators for their analysis. OPERATORAGREEMENTDISAGREEMENT Multiplicationmultiply Minimumminimum Compositeminimummultiply / ratio

17. 17 Coefficients of agreement determine agreement based on the proportions of categories correctly classified. These vary depending on which cells of the cross-tabulation matrix are used for calculation. SOFTMULTIRES derives the above coefficients from generated cross-tabulation matrices. OVERALL COEFFICIENTS OF AGREEMENT CATEGORICAL COEFFICIENTS OF AGREEMENT Overall Proportion CorrectUser’s Accuracy Nishii-TanakaProducer’s Accuracy Cramer’s V Conditional Kappa (by row and column) SOFTMULTIRES Coefficients of Agreement

18. 18 Interface for SOFTMULTIRES Inputs –Comparison map year –Reference map year –Number of Categories (maximum 15) –Operator (Multiplication, Minimum, and/or Composite) –Path Directory –Boolean raster images for each category

19. 19 Cross-Tabulation Matrix

20. 20 Graphical Output

21. 21 SOFTMULTIRES Automation Benefits SOFTMULTIRES allows for simple recreation of methodology for any two categorical maps. SOFTMULTIRES produces many coefficients for ease of interpretability. SOFTMULTIRES reduces processing time. –40 HOURS manually becomes 10 MINUTES automatically. SOFTMULTIRES produces hundreds of maps quickly. 4 reference categories x 4 comparison categories x 10 resolutions x 3 operators = 480 images

22. 22 Lessons Currently, there is no known program available to perform and interpret a MULTIPLE- RESOLUTION ANALYSIS for real and categorical data. Automation of these processes allows for efficient production and replication of methodologies, with a minimization of human error.

23. 23 REALMULTIRES method is based on: Pontius. 2002. Statistical methods to partition effects of quantity and location during comparison of categorical maps at multiple resolutions. Photogrammetric Engineering & Remote Sensing 68(10). pp. 1041-1049. SOFTMULTIRES method is based on: Kuzera, K. and Pontius, R. G. Jr. 2004. Categorical Coefficients of Agreement for Assessing Soft-Classified Maps at Multiple Resolutions. In proceedings TIES 2004. Special thanks to: Clarklabs (www.clarklabs.org) who is incorporating the validation method and the multiple- resolution analysis of categorical maps into the GIS software Idrisi. Ron Eastman who supplied data of NDVI images. Human-Environment Regional Observatory Network for providing Worcester categorical data. Gil Pontius for advising. Olufunmilayo E. Thontteh for collaboration. More information available at the presentation of her Masters Thesis work: “Verification Of Vegetation Index Predictions Using Multiple Resolution Images”. Plugs & Acknowledgements