1. Nationwide Indicators and Their Integration, Evaluation, and Visualization Worldwide UNEP Initiative Collaboration G. P. Patil Yannis FermantzisSonia Rodriguez Charles Taillie Lan Wang G. P. Patil, Director Center for Statistical Ecology and Environmental Statistics Department of Statistics The Pennsylvania State University University Park, PA

2. ON THE FORMULATION OF NATIONWIDE HUMAN ENVIRONMENT INDEX: VISUALIZATION, EVALUATION AND VALIDATION —In Preparation— Under the Auspices of UNEP Science Advisory Board Chair: Mario Molina, Nobel Laureate Manuscript 1 Proposed Human Environment Index in Light of Average Ranking and Rescaling Protocols By Ganapati P. Patil, Lan Wang and Charles Taillie Manuscript 2 Proposed Human Environment Index in Light of Quantiles and Clusters Protocols By Ganapati Patil, Lan Wang and Caterina Pisani Manuscript 3 Proposed Human Environment Index in Light of Visualization Tools By Ganapati Patil, Ioannis Fermantzis, and Lan Wang Manuscript 4 Proposed Human Environment Index in Light of Fuzzy Analysis Tools By Ganapati Patil and Charles Taillie Under the Auspices of UNEP Science Advisory Board Chair: Mario Molina, Nobel Laureate

3. —In Planning Stages— Manuscript 5 Proposed Human Environment Index in Light of Available GIS Information and Remote Sensing Data Manuscript 6 Proposed Human Environment Index in Light of Voronoi Diagrams and Geospatial Statistics Tools Manuscript 7 Proposed Human Environment Index in Light of National Groups and Neighborhoods Manuscript 8 Proposed Human Environment Index in Light of OECD Environmental Indicators for OECD Countries And a Website for Display and Interaction with Stakeholders

4. ENLIGHTENING HIGHLIGHTS ENLIGHTENED The law of human life, living, and human life cycle lies in supportive land, air, and water (LAW). Ancient scriptures express it very well: “…when the land is not livable, when the air is not breathable, when the water is not drinkable, man shall perish…” The worldwide human perception of the above comes through intuitive perspective of green land, blue sky, and clean water. Now that nationwide data have become available worldwide to help consider perceptive measures of greenness of land, blueness of sky, and cleanness of water, it is now possible to attempt to formulate and quantify a composite human environment index as a simple, elegant, and defensible societal instrument for national citizenry to discuss, debate and deal with human-environment interface in a public policy and planning arena. A most important purpose that such a human environment index is expected to serve is to help stimulate national and international dialogue leading to indepth policy discussion and debate essential for sustainable environment and development. G. P. Patil, Member UNEP Science Advisory Board

5. ENLIGHTENING HIGHLIGHTS ENLIGHTENED A major purpose of this study is to explore, investigate, and evaluate the proposed human environment index in light of any alternatives based on the concepts, methods, and tools available in the literature of individual indicators and integrated indicators. For human species and humanity, each of the environmental component land, air, and water is as important as another, and it is not possible to speak of one being more important than the other. This leads to the concept of equal importance of each component, and to the concept of equal weight to each component –a concept potentially useful in the construction of a composite indicator. The three basic individual component indicators are essentially uncorrelated and orthogonal in light of their largely uncorrelated columns. Therefore, their unweighted sum/average has no danger of allotting inadvertent importance to one over the other. Each basic individual component indicator is a bonafide fractional proportion between zero and one. It is dimensionless, being a ratio of a part to the whole in the same units. The unweighted sum/average does not involve adding apples and oranges. And this approach can be satisfactory as long as the parts and the wholes represent satisfactory entities for which commensurate data are available, nationwide and worldwide. Beauty lies in the eyes of the beholder. And that makes the difference. Indicators choice and their composites therefore become crucial when we view the environment in terms of landview, skyview, and waterview involving air, water, food, and shelter for the life support system for the humanity as we have known. G. P. Patil, Member UNEP Science Advisory Board

6. HUMAN ENVIRONMENT INDEX LAND, AIR, WATER INDICATORS for land - % of undomesticated land, i.e. total land area - domesticated (permanent corps and pastures, built up areas, roads, etc.) for air - % of renewable energy resources, i.e. hydro, solar, wind, geothermal for water - % of population with access to safe drinking water RANKCOUNTRYLANDAIRWATERHEI 1Sweden69.0135.241000.68 2Finland76.4619.05980.65 3Norway27.3863.981000.64 5Iceland1.7980.251000.61 13Austria40.5729.851000.57 22Switzerland30.1728.101000.53 39Spain32.637.741000.47 45France28.346.501000.45 47Germany32.562.101000.45 51Portugal34.6214.29820.44 52Italy23.356.891000.43 59Greece21.593.20980.41 61Belgium21.840.001000.41 64Netherlands19.431.071000.40 77Denmark9.835.041000.38 78United Kingdom12.641.131000.38 81Ireland9.251.991000.37

7. Figure 1. Example of perfect positive and perfect negative correlation between two coordinates (variables).

8. Figure 2. Top and Bottom 20 Countries based on their HEI

9. Figure 3. Air – Land distribution of Top and Bottom 20 Countries according to their HEI

10. Figure 4. Water – Land distribution of Top and Bottom 20 Countries according to their HEI

11. Figure 5. Water – Air distribution of Top and Bottom 20 Countries according to their HEI

12. Bivariate L-A L10142 31199 4664 A Bivariate L-W L6713 121334 72425 W Bivariate A-W A636 81417 112749 W Figure 6. Absolute frequency distribution of bivariate data representations.

13. Figure 7. Countries that rank in the highest category in both AIR and WATER in the bivariate AIR-WATER distribution do not rank very high in LAND

14. Figure 8. Countries that rank in the highest category in both LAND and AIR in the bivariate LAND-AIR distribution do not rank very high in WATER.

15. Figure 9.Countries that rank in the highest category in both LAND and WATER in the bivariate LAND-WATER distribution do not rank very high in AIR.

16. Figure 10. Absolute frequency distribution of trivariate data representation.

17. Figure 11. 3D Scatterplot for the LandAirWater dataset. Notice the tendency of records (countries).

18. Figure 12. PCP showing the relationship between one of the trivariate scheme classes (Land oriented) and the LandAirWater indicators.

19. Figure 13. PCP showing the relationship between one of the trivariate scheme classes (Water oriented) and the LandAirWater indicators.

23. We address the question of ranking a collection of objects when a suite of indicator values is available for each member of the collection. The objects can be represented as a cloud of points in indicator space, but the different indicators (coordinate axes) typically convey different comparative messages and there is no unique way to rank the objects. A conventional solution is to assign a composite numerical score to each object by combining the indicator information in some fashion. Consciously or otherwise, every such composite involves judgements (often arbitrary or controversial) about tradeoffs or substitutability between indicators. Environmental Indicators: Comparisons and Rankings without Integration---Some Statistical and Visual Tools

24. Rather than trying to impose a unique ranking, we take the view that the relative positions in indicator space determine only a partial ordering and that a given pair of objects may not be inherently comparable. Working with Hasse diagrams of the partial order, we study the collection of all rankings that are compatible with the partial order (admissible rankings). In this way, an interval of possible ranks is assigned to each object. The intervals can be very wide, however. Noting that ranks near the ends of each interval are infrequent under admissible rankings, a probability distribution is obtained over the interval of possible ranks. This distribution turns out to be unimodal (in fact, log-concave) and the original partial order is represented by stochastic ordering of probability distributions.

25. Our approach to ranking is in analogy with the crisp number to interval number to fuzzy number succession in fuzzy analysis. In fact, the crisp comparisons between comparable pairs of objects in the partial order can be extended to fuzzy comparisons between any pair of objects. By counting admissible rankings, we can assign a numerical degree or grade to the truth of the relation x < y for given objects x and y. The grade lies between 0 and 1, and equals 1 exactly when x < y is true in the original partial order.

26. Finally, the objects under comparison may be spatially referenced, for example: countries across a continent, watersheds within a region, census tracts in a metropolitan area. Echelon analysis shows how spatial connectivity changes as levels are accumulated in the Hasse diagram.

27. Hasse Diagram (all countries)

28. Hasse Diagram (W Europe)

37. Consider a situation in which one indicator column is the same as another indicator column, because the second indicator value is the same as the first indicator value. It is clear from the following figure that the second column does not add information/ discrimination to the first column. This is the situation when there is a strong underlying correlation between the two indicators. Recently, Landscape Ecology has discovered that some fifty landscape fragmentation pattern indicators amount to essentially five to ten indicators. MORE INDICATORS DO NOT NECESSARILY MEAN MORE INFORMATION AND MORE DISCRIMINATION

38. indicator two/ column two indicator one/column one

39. Quantile Method: Consumer Report Approach