Uncertainty in Geographic Information: House of Cards? Michael F. Goodchild University of California Santa Barbara

Transcription

1 Uncertainty in Geographic Information: House of Cards? Michael F. Goodchild University of California Santa Barbara

2 Starting points All geospatial data leave the user to some extent uncertain about the state of the real world missing data positional and attribute errors uncertain definitions of classes and terms missing metadata projection unspecified horizontal or vertical datum cartographic license

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5 Uncertainty is endemic All geographic information leaves some degree of uncertainty about conditions in the real world x the Greenwich Meridian the Equator standard time z definitions of terms errors of measurement

6 Starting points Some applications will be impacted, some will not for any given data set at least one application can be found where uncertainty matters knowing whether data are fit for use Our perspective on these issues has changed in the past two decades from error to uncertainty from top-down to bottom-up data production

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13 Precision: Definitions of terms the number of significant digits used to report a measurement should never be more than is justified by the accuracy of the measuring device internal precision of the computer single precision arithmetic 1 part in 10 7 double precision 1 part in relative to the Earth's dimensions, single precision is about a meter resolution, double is about the size of an atom no GIS should ever need more than single precision a GIS's internal precision is effectively infinite hard to persuade designers to drop those spurious digits

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16 Scale Relationship between measurement of distance on a map and measurement on the ground 1:24,000 is larger than 1:250,000 A map used for digitizing or scanning always has a scale a geospatial database never has scale but we have complex conventions Scale as a useful surrogate for map contents, resolution, accuracy scale of original map a useful item of geospatial metadata

17 Resolution The minimum distance over which change is recorded 0.5mm for a paper map Positional accuracy set by national map accuracy standards to roughly 0.5mm

18 Accuracy The difference between a measurement and the truth problems of defining truth for some geospatial variables, e.g. soil class if two people classified the same site would they agree? Uncertainty of definition is a form of inaccuracy, along with: variation between observers or measuring instruments temporal change loss of information on e.g. projection, datum transformation of datum map registration digitizing error imperfect fit of the data model, e.g. heterogeneous polygons, transition zones instead of boundaries fuzziness of many geographic concepts transformation of coordinate system, projection, data model, e.g. raster/vector conversion

19 Truth Often a source of higher accuracy circularity - accuracy is the difference between a measurement and a source of higher accuracy? What identifies a source as having higher accuracy? larger scale more recent cost more, took longer to make, more careful more accurate measuring instrument certified by an expert earlier in the chain reality-map-database (less processing)

20 The problem Uncertainty is endemic in geospatial data even a 1:1 mapping would not create a perfect representation of reality All GIS products are therefore subject to uncertainty what is the plus or minus on estimates of length, area, counts of objects, positions, attributes, viewsheds, buffer zones,... GIS products are often used in decision-making by people who do not have intimate knowledge of the methods used to collect, digitize or process the data results are often presented and used visually rather than numerically Computer (GIS) output carries a false sense of credibility

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22 Topology vs geometry Which property does this pole lie in? Which side of the street is this house? Do these two streets connect?

23 Acres > Totals

24 Data types The area-class map soil maps vegetation cover type land use Boundaries surrounding areas of uniform type what s the accuracy issue?

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27 The area class map Assigns every location x to a class Mark and Csillag term c = f(x) a nominal field (or perhaps ordinal) classified scene soil map, vegetation cover map, land use map Need to model uncertainty in this type of map

28 Uncertainty modeling Area-class maps are made by a long and complex process involving many stages, some partially subjective Maps of the same theme for the same area will not be the same level of detail, generalization vague definitions of classes variation among observers measuring instrument error different classifiers, training sites different sensors

29 Error and uncertainty Error: true map plus distortion systematic measurements disturbed by stochastic effects accuracy (deviation from true value) precision (deviation from mean value) variation ascribed to error Uncertainty: differences reflect uncertainty about the real world no true map possible consensus map combining maps can improve estimates

30 Models of uncertainty Determine effects of uncertainty/variation/error on results of analysis if there is known variation, the results of a single analysis cannot be claimed to be correct uncertainty analysis an essential part of GIS error model the preferred term

31 Traditional error analysis Measurements subject to distortion z' = z + δz Propagate through transformations r = f(z) r + δr = f(z + δz) But f is rarely known complex compilation and interpretation complex spatial dependencies between elements of resulting data set

32 Spatial dependence In true values z In errors e cov(e i,e j ) a decreasing positive function of distance geostatistical framework Scale effects, generalization as convolutions of z

33 If this were not true If Tobler s First Law of Geography did not apply to errors in maps If errors were statistically independent If relative errors were as large as absolute errors Errors in derived products would be impossibly large e.g. slope e.g. length Shapes would be unrecognizable

34 Realization A single instance from an error model an error model must be stochastic Monte Carlo simulation The Gaussian distribution metaphor scalar realizations a Gaussian distribution for maps an entire map as a realization

35 The area class map Field of nominal values c(x), n>1 spatially autocorrelated in raster, count of i,i joins greater than expected In vector, collection of discrete objects nodes, edges, areas in coverage model polygons in shapefile model

36 A collection of discrete objects Three conflicts with the observed nature of areaclass maps In repeated mappings, positions, attributes, and numbers of objects will vary (topological variation) Positional uncertainties will vary widely depending on boundary clarity Confusion of attributes will vary within polygons may be greatest in the center contrary to the egg-yolk model

37 suburban core land use type urban

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40 Model {p 1,p 2,,p n } correlation in neighboring cell outcomes posterior probabilities equal to priors 80% sand, 20% inclusions of clay no knowledge of correlations

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50 Topographic data Definition problems sand dunes trees buildings Classic measurement error model measured elevation = truth + error error spatially autocorrelated

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55 z'(x) = z(x) + δz(x)

56 Glyphs indicating wind direction, magnitude, and uncertainty (Pang, 2001)

57 Representation of estimated water balance surplus/deficit (using a mesh surface) and uncertainty in the estimates (using bars above and below the surface). The bars depict the range of a set of model predictions with those predictions above the mean in purple and those below the mean in orange. Fauerbach, Edsall, Barnes, MacEachren animation

58 Options for uncertainty Ignore Present parameters Present simulations confidence intervals

59 Point symbol sets depicting uncertainty with variation in (a) saturation (colors vary from saturated green, bottom, to unsaturated, top); (b) crispness of symbol edge middle; and (c) transparency of symbol right.

60 Alternative depictions of data (inorganic nitrogen in Chesapeake Bay) and uncertainty of data interpolated from sparse point samples. Left view shows bivariate depiction in which dark=more nitrogen and certainty is depicted with a diverging color scheme (blue = most certain and red = most uncertain). Right view depicts data in both panels (dark = more nitrogen), with the right panel showing the results of interactive focusing on the most certain data.

61 Communication of uncertainty Producer to user abilities Metadata standards parameters of complex models Assertion: all knowledge of uncertainty can be expressed in a suitable simulation model equally likely realizations

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63 The "five-fold way" Positional accuracy Attribute accuracy Logical consistency Completeness Lineage Federal Geographic Data Committee Spatial Data Transfer Standard Content Standard for Digital Geospatial Metadata

64 Metadata Data about data handling instructions catalog entry fitness for use What is known about data quality a measure of the success of spatial data quality research much progress has been made FGDC CSDGM 1994 ISO DDI EML

65 Web 2.0 Dominated by user-generated content Bottom-up supply of geospatial data What are the issues?

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70 CSDGM, ISO Do they match the state of research? early 1990s SDTS discussions of 1980s the five-fold way positional accuracy attribute accuracy logical consistency completeness lineage Do they represent a user perspective? committees staffed by data producers production control mechanisms?

71 Producer or user? Producer-centric details of the production process: the measurement and compilation systems used tests of data quality conducted under carefully controlled conditions formal specifications of data set contents User-centric effects of uncertainties on specific uses of the data, from simple queries to complex analyses simple descriptions of quality that are readily understood by non-expert users tools to enable the user to determine the effects of quality on results

72 Increasing complexity Self-documentation notes to oneself A colleague brief description Another discipline, language, culture ideal metadata/data ratio?

73 complexity of metadata social distance

74 Seven issues Areas in which research has moved beyond the standards Accuracy of Spatial Databases 1989 Measurements from Maps books 1000 journal articles

75 1. Decoupling the representative fraction Ratio of distance on the map to distance on the ground no flat map of a curved surface can have a constant RF RF as a surrogate positional accuracy spatial resolution map content RF undefined for digital data inherited from source maps extended by convention aerial photographs (RF of the photographic plate) digital orthoimagery (positional accuracy)

76 2. Accuracy or uncertainty? Accuracy a true value z exists a measured value z* CSDGM ISO error z*-z RMSE theory of measurement error error propagation Uncertainty accuracy 85 7 vagueness in definitions no truth perhaps a consensus? lack of replicability uncertainty 0 0 Change of paradigm around 1992

77 3. Objects and fields A fundamental distinction 1992 appears nowhere in the standards Discrete object conceptualization an empty table top occupied by discrete, countable objects points, lines, areas, volumes Continuous field conceptualization a mapping from location x to value z a single-valued function of location

78 z'(x) = z(x) + δz(x)

79 Separability Phenomenon conceptualized as a field impossible to separate positional and attribute accuracy interval/ratio (elevation) nominal (land cover class)

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81 4. Granularity Metadata definable at any level individual vertex point, line, area layer geodatabase Metadata as a form of generalization economies of scale Spatial non-stationarity Multiple lineages

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84 5. Collection-level metadata Describing the properties of entire collections The Geospatial One-Stop There will always be more than one one-stop how to know where to look?

85 GOS coverage, 1/06

86 6. Spatial dependence Tobler s First Law nearby things are more similar than distant things applies to errors relative accuracy almost always better than absolute accuracy covariances as important as variances

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88 Marginal or joint properties? Visualization of marginal properties Analytic functions respond to joint properties slope area Joint properties must be described at a higher level relative errors of vertex positions described at level of vertex collection

89 Cross-correlation How are errors on Layer 1 related to errors on Layer 2? Error as an issue in interoperability what happens if I superimpose these layers? Two layers will almost always not fit depends on lineage of each how bad is the misfit? will it affect my analysis? Binary metadata the ability of a pair of data sets to interoperate not available from either s unary metadata If GIS is about overlay then binary metadata are essential

90 The way forward Reopen the metadata debate an unpopular move it s hard enough to persuade people to provide metadata a standard before its time standards should emerge only after research is complete It s our responsibility the research task does not end with journal publication metadata standards express the state of our research Many other issues not related to data quality possible allies

91 References My CV and papers Book list Conference series: International Symposium on Spatial Data Quality (ISSDQ) biennial, Hong Kong May 2013 Accuracy (International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences) biennial, Brazil July 2012