The scale matcher: A framework for assessing scale compatibility of environmental data and models

Many organisations collect spatial data at a range of scales for a variety of purposes. Scientists apply new environmental knowledge either by improving existing simulation models or developing new ones. Technological advances, and the increasing availability of both models and the data required to run them, are potentially putting better information in the hands of environmental policy analysts, decision makers and land managers to solve environmental problems. A review of the literature, however, shows that each of this trio of Data–Model--Problem is scale dependent, and that this scale dependence can be very significant, potentially leading to the generation of information that is misleading or simply invalid. The research objective is to contribute to the area of spatial modelling by investigating how a best practice of applying environmental data and models, which considers the effects of scale, might be achieved. It is proposed that a systematic framework (dubbed the 'Scale Matcher') can be developed to identify and match the scale requirements of a problem with the scale limitations of spatial data and models. A bottom-up approach is taken by breaking scale into its constituent parts (extent, accuracy and precision), each of which is then analysed in some depth to understand the various ways in which scale can impact on data and simulation models. Each component of scale is quantified by identifying suitable metrics from the literature. Two new indices that take into account attribute imprecision are introduced. Spatial confusion measures the degree of overlap of the attribute values between mapunits. Colour purity measures the proportion of a map that is incorrectly shaded due to within-mapunit imprecision. Both measures can be calculated for continuous and categorical, raster and vector data, providing there is a parametric or empirical estimate of the distribution of sub-mapunit variability. The Scale Matcher comprises a set of 11 comparisons, derived from a systematic match between each combination of the scale components of data, model, and problem. Each match is named and described. In some cases the matches are simple comparisons of the relevant metrics. Others require the combination of data variability and model sensitivity to be investigated. By randomly simulating data and model imprecision and inaccuracy, sensitivity analysis can then be used to identify scales over which scale effects are minor or stable. The Scale Matcher procedure is specified in a flowchart format that leads the user through the relevant sequence of matches. Listing the results as a set of scale assumptions helps to draw attention to them making users more aware of the limitations of spatial modelling. The Scale Matcher is evaluated by assessing scale compatibility in a case study of nitrate leaching vulnerability. Some hypothetical examples are used to verify other routes through the procedure. The case study requires the development of some new representations of soil imprecision and inaccuracy, and loosely coupling a sensitivity analysis tool with a geographic information system. It was concluded that the scale-matching framework successfully broke down the scale issue into a series of comparisons, which, if performed should give the user more confidence in the scale validity of model output for a given problem.UnpublishedAalders, H. J. G. L. (1999). "The registration of quality in a GIS". In W. Shi, M. F. Goodchild & P. Fisher (eds), International Symposium on Spatial Data Quality. Hong Kong pp. 23-32. Addiscott, T. M. (1993). "Simulation modelling and soil behaviour". Geoderma. 60: 15-40. Addiscott, T. M. (1998). "Modelling concepts and their relation to the scale of the problem". Nutrient Cycling in Agroecosystems. 50: 239-245. Addiscott, T. M. & Wagenet, R. J. (1985). "Concepts of solute leaching in soils: a review of modelling approaches". Journal of Soil Science. 36: 411-424. AGI (1996). "GIS dictionary". Accessed: 15 June 2001. URL: http://www.geo.ed.ac.uk/agidict/welcome.html Alker, R. (1969). "A typology of ecological fallacies". In M. Dogan & M. Rokkan (eds), Quantitative Ecological Analysis in the Social Sciences. MIT Press. Cambridge, MA. Altman, D. G. & Bland, J. M. (1983). "Measurement in medicine: the analysis of method comparison studies". The Statistician. 32: 307-317. Amrhein, C. G. (1995). "Searching for the elusive aggregation effect: evidence from statistical simulations". Environment and Planning A. 27: 105-119. Amrhein, C. G. & Griffith, D. A. (1994). "Errors in spatial databases: a summary of results from several research projects". International Symposium on the Spatial Accuracy of Natural Resource Databases. ASPRS Williamsburg, Virginia pp. 214-226. Atkinson, P. M. (1997). "Scale and spatial dependence". In P. R. van Gardingen, G. M. Foody & P. J. Curran (eds), Scaling-up: from Cell to Landscape. Society for experimental biology seminar series Cambridge University Press. Cambridge pp. 35-60. Band, L. E. (1993). "Effect of land surface representation on forest, water and carbon budgets". Journal of Hydrology. 150: 749-772. Barringer, J. & Lilburne, L. (2000). "Developing fundamental data layers to support environmental modelling in New Zealand: progress and problems". 4th International Conference on Integrating GIS and Environmental Modeling (GIS/EM4). Banff, Canada. Barringer, J. R. F. & Lilburne, L. R. (1997). "An evaluation of digital elevation models for upgrading New Zealand land resource inventory slope data". In R. T. Pascoe (ed.), GeoCornputation 97 (incl. SIRC 97). Spatial Information Research Centre, University of Otago Dunedin, NZ pp. 109--116. Barry, R. G. (1992). Mountain weather and climate. 2nd edn. Routledge. London. Batty, M. (1974). "Spatial entropy". Geographical Analysis. 6: 1-31. Becker, A. & Braun, P. (1999). "Disaggregation, aggregation and spatial scaling in hydrological modelling". Journal of Hydrology. 217: 239-252. Bedward, M., Keith, D. A. & Pressey, R. L. (1992). "Homogeneity analysis: assessing the utility of classifications and maps of natural resources". Australian Journal of Ecology. 17: 133-139. Bekesi, G. & McConchie, J. (1999). "Groundwater recharge modelling using the Monte Carlo technique, Manawatu region, New Zealand". Journal of Hydrology. 224: 137-148. Bergstrom, S. & Graham, L. P. (1998). "On the scale problem in hydrological modelling". Journal of Hydrology. 211: 253-265. Bian, L. (1997). "Multiscale nature of spatial data in scaling up environmental models". In D. A. Quattrochi & M. F. Goodchild (eds), Scale in Remote Sensing and GIS. Lewis Publishers. Boca Raton pp. 13-26. Bian, L. & Walsh, S. J. (1993). "Scale dependencies of vegetation and topography in a mountainous environment of Montana". Professional Geographer. 45(1): 1-11. Bloschl, G. (1999). "Scaling issues in snow hydrology". Hydrological Processes. 13: 2149-2175. Bloschl, G. & Sivapalan, M. (1995). "Scale issues in hydrological modelling: a review". Hydrological Processes. 9(3/4): 9-48. Boldocchi, D. D. & Meyers, T. P. (1998). "On using eco-physiological, micrometeorological and biochemical theory to evaluate carbon dioxide, water vapor and gaseous deposition fluxes over vegetation". Agricultural and Forest Meteorology. 90: 1-26. Bouma, J., Booltink, H. W. G. &. Finke, P. A. (1996). "Use of soil survey data for modeling solute transport in the vadose zone". Journal of Environmental Quality. 25: 519-526. Brasington, J. & Richards, K. (1998), "Interactions between model predictions, parameters and DTM scales for topmodel". Computers and Geosciences. 24(4): 299-314. Brassel, K., Bucher, F., Stephan, E.-M. & Vckovski, A. (1995). "Completeness". In S. C. Guptill & J. L. Morrison (eds), Elements of Spatial Data Quality. Elsevier. Oxford pp. 81-107. Bresnahan, P. A. & Miller, D. R. (1997). "Choice of data scale: predicting resolution error in a regional evapotranspiration model". Agricultural and Forest Meteorology. 84: 97-113. Brooks, R. J. & Tobias, A. M. (1996). "Choosing the best model: level of detail, complexity, and model performance". Mathematical and Computing Modelling. 24(4): 1-14. Brown, D. G., Bian, L. & Walsh, S. J. (1993). "Response of a distributed watershed erosion model to variations in input data aggregation levels". Computers and Geosciences. 19(4): 499-509. Burden, R. J. (1982). "Nitrogen contamination of New Zealand aquifers: a review". New Zealand Journal of Science. 25: 205-220. Burrough, P. A. (1989). "Modelling land qualities in space and time: the role of geographical information systems". In J. Bouma & A. Bregt (eds), Land Qualities in Space and Time. Pudoc. Wageningen, the Netherlands pp. 45-59. Burrough, P. A. (1996). "Opportunities and limitations of GIS-based modeling of solute transport at the regional scale". Application of GIS to the Modeling of Non-point Source Pollutants in the Vadose Zone. SSSA Special Publication 48 Soil Science Society of America. Madison, Wisconsin pp. 19-38. Burrough, P. A. & McDonnell, R. A. (1998). Principles of geographic information systems. Spatial Information Systems 2nd edn. Oxford University Press. Oxford. Caldwell, M. M., Matson, P. A., Wessman, C. & Gamon, J. (1993). "Prospects for scaling". In J. R. Ehleringer & C. B. Field (eds), Scaling Physiological Processes: Leaf to Globe. Academic Press. San Diego pp. 223-230. CAMASE (1996). "The CAMASE register of agro-ecosystems models". Accessed: Nov. 2001. URL: http://www.agralin.nl/camase/ Canters, F., Eerens, H. & Veroustraete, F. (1999). "Estimation of land-cover proportions from aggregated medium-resolution satellite data". In K. Lowell & A. Jaton (eds), Spatial Accuracy Assessment: Land Information Uncertainty in Natural Resources. Ann Arbor Press. Michigan pp. 263-270. Cao, C. & Lam, N. S.-N. (1997). "Understanding the scale and resolution effects in remote sensing and GIS". In D. A. Quattrochi & M. F. Goodchild (eds), Scale in Remote Sensing and GIS. Lewis Publishers. Boca Raton pp. 57-72. CartoCorner (n.d.). "Glossary of cartographic terms". Accessed: 15 June 2001. URL: http://atlas.gc.ca/english/carto/cartglos.htrnl Carver, S. J. & Brunsdon, C. F. (1994). "Vector to raster conversion error and feature complexity: an empirical study using simulated data". International Journal of Geographical Information Systems. 8(3): 261-270. Century (2000). "Century model". Accessed: 21 Aug. 2001. URL: http://eco.wiz.uni-kassel.de/modeLdb/mdb/century.html Chrisman, N. R. (1991). "The error component in spatial data". In D. J. Maguire, M. F. Goodchild & D. W. Rhind (eds), Geographical Information Systems: Principles and Applications. Vol. 1 Longman Group UK Ltd. Marlow, UK pp. 165-174. Church, M. & Mark, D. M. (1980). "On size and scale in geomorphology". Progress in Physical Geography. 4: 342-390, Clarke, R. T. (1973). "A review of some mathematical models used in hydrology, with observations on their calibration and use". Journal of Hydrology. 19: 1— 20. Clayden, B. & Webb, T. H. (1994). "Criteria for defining the soilform - the fourth category of the New Zealand soil classification". Technical Report Landcare Research science series no. 3. Landcare Research. Cline, D., Elder, K. & Bales, R. (1998). "Scale effects in a distributed snow water equivalence and snowmelt model for mountain basins". Hydrological Processes. 12: 1527-1536. Congalton, R. G. (1991). "A review of assessing the accuracy of classifications of remotely sensed data". Remote Sensing of the Environment. 37: 35-46. Costanza, R. & Maxwell, T. (1994). "Resolution and predictability: an approach to the scaling problem". Landscape Ecology. 9(1): 47-57. Crosetto, M., Tarantola, S. & Saltelli, A. (2000). "Sensitivity and uncertainty analysis in spatial modelling based on GIS". Agriculture, Ecosystems and Environment. 81: 71-79. Curran, P. J., Foody, G. M. & van Gardingen, P. R. (1997). "Scaling up". In P. R. van Gardingen, G. M. Foody & P. J. Curran (eds), Scaling-up: from Cell to Landscape. Society for experimental biology seminar series Cambridge University Press. Cambridge pp. 1-5. de Boer, D. H. (1992). "Hierarchies and spatial scale in process geomorphology: a review". Geomorphology. 4: 303-318. de Vries, W., Kros, J., van der Salm, C., Groenenberg, J. E. & Reinds, G. J. (1998). "The use of upscaling procedures in the application of soil acidification models at different scales". Nutrient Cycling in Agroecosystems. 50: 223-236. Deutsch, C. V. & Journel, A. G. (1992). GSLIB: Geostatistical software library and user's guide. Oxford University Press. New York. Di, H. J. & Aylmore, L. A. G. (1997). "Modeling the probabilities of groundwater contamination by pesticides". Soil Science Society of America Journal. 61: 17-23. Drummond, J. (1995). "Positional accuracy". In S. Guptill & J. Morrison (eds), Elements of Spatial Data Quality. Elsevier. Oxford pp. 31--58. Duckham, M. (1999). "Implementing an object-oriented error-sensitive GIS". In K. Lowell & A. Jaton (eds), Spatial Accuracy Assessment: Land Information Uncertainty in Natural Resources. Ann Arbor Press. Michigan pp. 209-215. Ehlschlaeger, C. R. & Goodchild, M. F. (1994). "Dealing with uncertainty in categorical coverage maps: defining, visualising, and managing errors". In N. R. Adam, B. K. Bhargava & Y. Yesha (eds), Third International Conference on Information and Knowledge Management (CIKM94). ACM Press Gaithersburg, MD pp. 86-91. Ehlschlaeger, C. R., Shortridge, A. M. & Goodchild, M. F. (1997). "Visualizing spatial data uncertainty using animation". Computers and Geosciences. 23(4): 387-395. ERDAS (1997). "ERDAS field guide". ERDAS. Georgia, USA. ESRI (1991). "ARC/INFO". ESRI. Redlands, CA. Everett, J. & Simonett, D. S. (1976). "Principles, concepts and philosophical problems in remote sensing". In J. Lintz & D. S. Simonett (eds), Remote Sensing of the Environment. Addison-Wesley. Reading, MA pp. 85-127. Finke, P. A., Wladis, D., Kros, J., Pebesma, E. J. & Reinds, G. J. (1999). "Quantification and simulation of errors in categorical data for uncertainty analysis of soil acidification modelling". Geoderma. 93(3-4): 177-194. Finn, J. T. (1993). "Use of the average mutual information index in evaluating classification error and consistency". International Journal of Geographical Information Systems. 7(4): 349-366. Finnerty, B. D., Smith, M. B., Seo, D.-J., Koren, V. I. & Moglen, G. (1997). "Sensitivity of the Sacramento soil moisture accounting model to space-time scale precipitation inputs from NEXRAD". Journal of Hydrology. 203(1-4): 21-38. Fisher, P. F. (1991a). "First experiments in viewshed uncertainty: the accuracy of the viewshed area". Photogrammetric Engineering and Remote Sensing. 57(10): 1321-1327. Fisher, P. F. (1991b). "Modelling soil map-unit inclusions by monte carlo simulation". International Journal of Geographical Information Systems. 5(2): 193— 208. Fisher, P. F. (1991c). "Spatial data sources and data problems". In D. J. Maguire, M. F. Goodchild & D. W. Rhind (eds), Geographical Information Systems: Principles and Applications. Vol. 1 Longman. Marlow, UK pp. 175-189. Fisher, P. F. (1994). "Animation and sound for the visualization of uncertain spatial information". In H. M. Hearnshaw & D. J. Unwin (eds), Visualization in Geographical Information Systems. John Wiley & Sons. London pp. 181— 185. Fisher, P. F., Abrahart, R. J. & Herbinger, W. (1997). "The sensitivity of two distributed non-point source pollution models to the spatial arrangement of the landscape". Hydrological Processes. 11: 241-252. Floate, M. & Cossens, G. (1992). "Land resources". In M. Floate (ed.), Guide to Tussock Grassland Farming. AgResearch. Invermay pp. 23-37. Florinsky, I. V. (1998). "Accuracy of local topographic variables derived from digital elevation models". International Journal of Geographical Information Systems. 12(1): 47-61. Florinsky, I. V. & Kuryakova, G. A. (2000). "Determination of grid size for digital terrain modelling in landscape investigations - exemplified by soil moisture distribution at a micro-scale". International Journal of Geographical Information Systems. 14(8): 815-832. Foody, G. M. (1992). "On the classification for chance agreement in image classification accuracy assessment". Photogrammetric Engineering and Remote Sensing. 58(10): 1459-1460. Foody, G. M. & Curran, P. J. (1994). "Scale and environmental remote sensing". In G. M. Foody & P. J. Curran (eds), Environmental Remote Sensing from Regional to Global Scales. John Wiley & Sons. New York pp. 223-232. Fotheringham, A. S. (1989). "Scale-independent spatial analysis". In NI. F. Goodchild & S. Gopal (eds), Accuracy of Spatial Databases. Taylor & Francis. London pp. 221-228. Fotheringham, A. S. & Wong, D. W. S. (1991). "The modifiable area unit problem in multivariate statistical analysis". Environment and Planning A. 23: 1025- 1044. Fridland, V. M. (1976). Pattern of the soil cover. Keterpress Enterprises. Jerusalem. Frohn, R. C. (1998). Remote sensing for landscape ecology: new metrics for monitoring, modeling, and assessment of ecosystems. Lewis Publishers. Boca Raton, Fuhlendorf, S. D. & Smeins, F. E. (1996). "Spatial scale influence on longterm temporal patterns of a semi-arid grassland". Landscape Ecology. 11(2): 107- 113. Gallant, J. C., Hutchinson, M. F. & Wilson, J. P. (2000). "Future directions for terrain analysis". In J. P. Wilson & J. C. Gallant (eds), Terrain Analysis: Principles and Applications. John Wiley & Sons. New York pp. 423-427. GAO (1979). "Guidelines for model evaluation". Technical Report PAD-79-17. US General Accounting Office. Gao, J. (1997). "Resolution and accuracy of terrain representation by grid DEMs at a micro-scale". International Journal of Geographical Information Science. 11(2): 199-212. Gardner, R. H. & Turner, M. G. (1990). "Future directions in quantitative landscape ecology". In M. G. Turner & R. H. Gardner (eds), Quantitative Methods in Landscape Ecology: the Analysis and Interpretation of Landscape Heterogeneity. Springer-Verlag. New York pp. 519-525. Goodchild, M. F. (1993). "Data models and data quality: problems and prospects". In M. Goodchild, B. Parks & L. Steyaert (eds), Environmental Modeling with GIS. Oxford University Press. pp. 94-103. Goodchild, M. F. (1995). "Attribute accuracy". In S. Guptill & J. Morrison (eds), Elements of Spatial Data Quality. Elsevier. Oxford pp. 59-79. Goodchild, M. F. (2000). "Communicating the results of accuracy assessment: metadata, digital libraries, and assessing fitness for use". In H. T. Mowrer & R. Congalton (eds), Quantifying Spatial Uncertainty in Natural Resources: Theory and Applications for GM and Remote Sensing. Ann Arbor Press. Chelsea, Michigan pp. 3-15. Goodchild, M. F., Chih-Chang, L. & Leung, Y. (1994). "Visualizing fuzzy maps". In H. M. Hearnshaw & D. J. Unwin (eds), Visualization in Geographical Information Systems. John Wiley & Sons. London pp. 158-167. Goodchild, M. F., Guoqing, S. & Shiren, Y. (1992). "Development and test of an error model for categorical data". International Journal of Geographical Information Systems. 6(2): 87-104. Goodchild, M. F. & Proctor, -J. (1997). "Scale in a digital geographic world". Geographical and Environmental Modelling. 1(1): 5-23. Goodchild, M. F. & Quattrochi, D. A. (1997). "Introduction: scale, multiscaling, remote sensing and GIS". In D. A. Quattrochi & M. F. Goodchild (eds), Scale in Remote Sensing and GIS. Lewis Publishers. Boca Raton pp. 1-11. Grayson, R. B., Bloschl, G., Barling, R. D. & Moore, I. D. (1993). "Process, scale and constraints to hydrological modelling in GIS". HydroGIS 93: Application of Geographical Information Systems in Hydrology and Water Resources. IAHS Publication 211 Vienna. Griffin, C. B. (1995). "Data quality issues affecting GIS use for environmental problem-solving". Environmental Problem Solving with Geographic Information Systems. Cincinnati, Ohio. Guptill, S. C. & Morrison, J. L. (eds) (1995). Elements of spatial data quality. Elsevier. Oxford. Hamby, D. M. (1994). "A review of techniques for parameter sensitivity analysis of environmental models". Environmental Monitoring and Assessment. 32: 135 - 154. Harding, R. J., Blyth, E. M. & Taylor, C. M. (1997). "Issues in the aggregation of surface fluxes from a heterogeneous landscape: from sparse canopies up to the GCM grid scale". In P. R. van Gardingen, G. M. Foody & P. J. Curran (eds), Scaling-up: from Cell to Landscape. Society for experimental biology seminar series Cambridge University Press. Cambridge pp. 229-251. Hartshorne, J. (1997). "Assessing the influence of digital terrain model characteristics on tropical slope stability analysis". In Z. Kemp (ed.), Innovations in GIS 4. Taylor & Francis. London pp. 198-214. Harvey, D. W. (1969). Explanation in geography. Edward Arnold. London. Haynes, R. J. (1995). "Soil structural breakdown and compaction in New Zealand soils". Technical paper 95/5. towards sustainable agriculture. MAF Policy. Helton, J. C. (1993). "Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal". Reliability Engineering and System Safety. 42: 327-367. Heuvelink, G. B. M. (1996). "Identification of field attribute error under different models of spatial variation". International Journal of Geographical Information Systems. 10(8): 921-935. Heuvelink, G. B. M. (1998a). Error propagation in environmental modelling with GIS. Research Monographs in Geographical Information Science Taylor & Francis. London. Heuvelink, G. B. M