Visualizing And Communicating Uncertainty In Spatial Analyses

Defining Uncertainty in Spatial Data

Uncertainty in spatial data refers to the lack of complete knowledge regarding the precise locations and attributes of geographic features. This uncertainty stems from the inherent variability and errors associated with measuring and depicting real-world phenomena. Defining and quantifying uncertainty is essential for properly interpreting spatial datasets and analyses.

Key types of spatial uncertainty include:

Positional uncertainty – error in the recorded locations of features
Attribute uncertainty – error in numerical or categorical descriptions of features
Temporal uncertainty – error related to when a feature was measured or mapped

Uncertainty may be represented numerically through statistical metrics like variance, standard deviation, confidence intervals, and error bands. It can also be communicated visually using techniques like fuzzy boundaries, transparency, and color schemes.

Table of Contents

Sources of Uncertainty

Measurement and Processing Errors

During data collection and processing, many technical factors introduce randomness and imprecision in measurements. Sensor noise and limitations, digitization errors, interpolation uncertainty, and geospatial model oversights can manifest as uncertainty.

For example, satellite imagery and aerial photos contain positional errors from camera precision limitations, image processing artifacts, and terrain displacement. Field measurements using GPS involve variability in coordinate accuracy and precision due to atmospheric effects, baseline distances, and device specifications.

Data Quality Issues

Data quality issues stemming from the data lifecycle processes can propagate uncertainty. These may include data gaps from incomplete sampling, classification errors during manual digitization, varying precision and accuracy across datasets, data entry mistakes, outdated sources, and inadequate metadata documentation.

Integrating datasets collected at different times using different methods can compound uncertainty in unpredictable ways. Assumptions made during harmonization of semantics, schemas, formats, and resolutions also introduce ambiguity.

Assumptions and Generalizations

All spatial data involves assumptions and generalizations that simplify real-world complexity. Cartographic generalization smooths map features and displaces locations for legibility. Categorization of continuous phenomena into discrete classes adds abstraction. Default parameter settings, data model choices, and algorithm determinations embed subjectivity.

Projections that transform the Earth’s three-dimensional surface introduce well-defined distortions but also some positional uncertainty. Even the definition of apparently crisp features like roads, shorelines, and jurisdiction boundaries contain some latent vagueness in their real-world manifestation.

Communicating Uncertainty Visually

Visual representations provide intuitive ways to encapsulate uncertainty and display its magnitude and spatial structure. By mapping quality metrics, confidence intervals, and error distributions, users can evaluate fitness for use and understand where analysis results are less reliable.

Using Transparency and Blurring

Transparency and blurring alter features’ opacity, edges, and sharpness to integrate uncertainty into the visual variable of texture. Fading polygon boundaries conveys probabilistic regions with gradated transitions. Blurring suggests areas of lower confidence by disrupting crisp definitions.

These techniques maintain overall feature location and extent while signaling imprecision. They can reveal spatial patterns in uncertainty – whether concentrated in certain areas or uniformly distributed. Used judiciously, transparency prevents hard boundaries from falsely implying precision.

Employing Color Schemes

Color schemes encode uncertainty metrics using intuitive gradients. Sequential single-hue schemes gracefully transition from darker shades for low uncertainty to lighter shades indicating higher uncertainty. Diverging schemes pivot transparency around an anchor color representing mean uncertainty level.

Categorical color schemes allocate distinct hues to tiered uncertainty classes. These delineate concentrated regions of high and low reliability for comparison. Color lightness and saturation can further embellish differences. schemes avoid sharp distinctions between categories to acknowledge their inherent vagueness.

Adding Elements Like Error Bars

Graphical elements visually manifest uncertainty statistics for specific features and locations. Error bars, brackets, and ovals orient according to directional variability while encoding magnitude through length and diameter. Isarithmic lines and topographic-style shading patterns detail spatial gradations in uncertainty.

These embellishments quantitatively communicate positional accuracy ranges, variance of attributes, confidence interval widths, or other precision metrics. They localize vagueness amidst broader map patterns since numbers lack intrinsic spatial relationships. Labels further annotate the meaning and implications of graphical uncertainty descriptors.

Best Practices for Visualizing Uncertainty

Effective visualization both exposes the presence of uncertainty and provides contextual details for reasoning about its impacts. Adhering to cartographic design principles fosters interpretable displays suited to user objectives and tasks.

Choosing Appropriate Visual Encodings

Matching visual encodings like transparency, color schemes, error bars, and blurring to data properties and analysis aims enables meaningful representations. Consider dimensionality – whether conveying linear variance, radial spread, or multidirectional ambiguity. Also factor in data density and feature types needing embellishment.

Assess visual channel capacity to avoid encodings that introduce clutter or hide patterns. For example, transparency can mask trends in dense datasets. Evaluate perceptual properties like figure-ground separation, visual salience of markings, and discrimination of steps in color schemes.

Providing Context for Interpretation

Supplement uncertainty visualizations with descriptive detail, keys, coordinated displays, and interactive functionality. Metadata, statistical summaries, quality reports, and guidelines for handling uncertainty aid pragmatic understanding. Legends unpack meaning of visual encodings and their scoping parameters or data attribute linkages.

Linked multidimensional views, like coordinated choropleth maps and correlation plots, furnish richer contextual insight. Dynamism through tooltips, details-on-demand, and user filtering exposes uncertainty specifics alongside field measurements. Providing actionable protocols for reconciling uncertainty with analysis objectives improves usability.

Testing on Target Audiences

Evaluate visualizations with user groups who will leverage the uncertain spatial analyses in applied scenarios. Solicit feedback on confusion points, connotations of design choices, and relevance of uncertainty information to decisions and tasks. Assess interpretability, navigation challenges, and influence on risk tolerance.

Iteratively pilot refined versions to gauge mental models, assess resonance of visual metaphors, and collect trustworthiness judgments. Quantitative user studies help rate efficacy for improving comprehension and calibration of uncertainty considerations. Customize final displays for audience specialties and objectives through participatory design.

Example Code for Visualizing Positional Accuracy

This Python code excerpt generates a choropleth map with polygon shading to denote positional accuracy grades assessed during quality control checks on street centerline locations. Darker transparency indicates larger deviations between recorded and ground-truthed coordinates. An interactive tooltip presents statistic details on demand.

#Import geospatial and data visualization libraries
import geopandas as gpd
import matplotlib.pyplot as plt

#Load vector dataset, assign column with accuracy estimate
lines = gpd.read_file('./centerlines.shp') 
lines['accuracy'] = lines['qc_grade'] 

#Define shading scheme based on accuracy
shade = [-1.5, -1, -0.5, 0, 0.5]  
colors = ['lightgrey', 'grey', 'dimgrey', 'black']
cmap = plt.matplotlib.colors.ListedColormap(colors)

#Plot map with polygon alpha channel scaled by accuracy  
lines.plot(column='accuracy', cmap=cmap, alpha=0.7)

#Add interactive tooltips showing statistic summaries
tooltip = lines['qc_report']  
plt.gca().set_interactive(True)
def show_stats(hover_data):
    #Display report excerpt on hover 
    label = tooltip[hover_data['index']] 
    plt.tooltip(label) 

plt.connect('motion_notify_event', show_stats)
plt.show()

This example demonstrates geospatial visualization techniques to embed quantified uncertainty within an interactive choropleth map. The alpha channel makes accuracy variability visible through polygon transparency, while color choices and legends facilitate interpretation. Details-on-demand via tooltips provide further statistical context to support understanding and analysis.