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Chapter 8 introduces methods for the evaluation of uncertainty associated with spatial analysis. Errors may be stochastic (random) or systematic (caused by a consistent shift away from an accepted or true value). The root mean square error (RMSE) measure is commonly used to quantify errors. Statistical methods for evaluating the uncertainty of analysis can be non-spatial (mean, standard deviation, standard error, probability modelling of confidence intervals, sensitivity analysis, error propagation assessment), or spatial (residual mapping, confidence interval mapping). Spatial error can be mapped and modelled using geographically weighted regression to increase the reliability of predictive models. A validation exercise can evaluate the uncertainty associated with digital maps by systematically comparing them to an independent ground referencing dataset by means of an error (or confusion) matrix. Comparisons yield metrics such as the producer, user and overall accuracy of the map.
Chapter 9 highlights the powerful influence of digital maps and the outputs of spatial analysis in society, and the associated need to present and communicate and interpret them responsibly. It illustrates how decisions made by an analyst when producing a map have important implications for the message conveyed by that map, e.g. through cartographic design principles, colours and symbols selected to represent features. Organisational or institutional uptake of spatial analysis depends on costs associated with hardware, software and human resources, alongside the extent to which spatial analysis has a proven practical impact on the work, tasks and jobs of employees. Spatial information and the results of spatial analysis are increasingly available through spatial data infrastructures, web atlases, web viewers and online repositories such as Google Earth. This increases their influence in society.
Chapter 7 introduces models as concise quantitative accounts of patterns and relationships between different components of natural ‘systems’. Model development is broken down into the four stages of observation, measurement, experimentation and theory development. Models uncover statistical relationships between coastal structure (response) variables, and function (driving) variables. Structure refers to the observable features of coastal landscapes e.g. the sizes, shapes and configurations of components. Function refers to the interactions between these features, e.g. flows of materials or organisms between them. Explanatory models construct an explanation for an observed pattern using empirical data, while predictive models generate a new observation by applying a statistical model to data. Statistical inference enables statements to be made about large populations of data samples on the basis smaller samples. Regression is a statistical technique for measuring the relationship between two or more variables. Where each data point is a location, a geographically weighted regression can utilise the spatial structure of the process of interest to improve the relationship modelled.
Chapter 6 introduces geostatistical techniques that characterise the spatial structure of a dataset. Spatial dependence is a fundamental property of most data because of Tobler’s First Law of Geography: “everything is related to everything else, but near things are more related than distant things”. Positive spatial dependence means that geographically nearby values of a variable tend to be similar. Spatial autocorrelation is the correlation between paired values of a single variable related to their relative position. Practical reasons to measure spatial autocorrelation include evaluating the statistical validity of spatial analysis, incorporating autocorrelation into models and guiding the design of sampling schemes for data collection. Measures of spatial autocorrelation reveal the nature and dimensions of spatial structure in a dataset (e.g. the join-count test, the Geary’s C and Moran’s I statistics and the semi-variogram and spatial autocovariance functions). Spatial interpolation techniques use similar principles to estimate unknown values of a variable on the basis of known point values using methods such as inverse distance weighting, spline and kriging.
Chapter 5 introduces monitoring as a technique that enables changes in coastal landscapes to be identified and evaluated over time. To assess change, it is necessary to have a baseline dataset recording the historic configuration of coastal features against which change can be measured. Baseline datasets should be reliable and in a comparable frame of reference, and may include maps, aerial photographs of satellite images. It is only possible to attribute the difference between a contemporary map and a historical one to coastal change that has occurred if the magnitude of the difference exceeds the uncertainty associated with both the mapping and comparison methods. Coastal change can be measured using raster and vector datasets. The success of a change detection exercise depends largely on the nature of the change being observed and the pairing of this with a suitable technique for its detection. Sources of error in change detection include the data used, its format and georeferencing, comparison of information in different frames of reference (projections, datums) and inaccuracies in digitising (vector) and classification (raster).
Chapter 1 defines spatial analysis as a collection of statistical techniques that explicitly use the spatial referencing associated with each data value. It outlines how an observational scientist treats the world as a ‘natural laboratory’ by interrogating environmental processes along gradients of natural variation to invoke experimental variability. Interrogations can treat location as place and space for this purpose. Processes such as diffusion, dispersal, marine species interactions and environmental controls produce spatial patterns in coastal environments that are spatially autocorrelated (their characteristics at proximate locations are more similar than their distant counterparts). This makes it desirable to analyse them using spatial methods. Coastal spatial analysis incorporates many disciplines that contribute distinct tools and methods for analysis, e.g. landscape ecology and coastal morphodynamics. Coastal environments present some unique challenges to their analysis, particularly regarding tides and weather.
Chapter 4 outlines how digital maps are valuable datasets to be explored for patterns and interrogated for clues as to how and why landscape features are arranged in space. Maps can inform scientific debate and management decision making. The spatial dimensions of a processes or feature of interest define the scope of a geographical area for spatial analysis. Historical maps made from a variety of field techniques represent baseline information against which coastal change can be assessed. Remote sensing represents a key contemporary source of spatial information derived from a sensor that is not in close proximity to the feature of interest. Optical remote sensing is commonly used to map shallow water coastal environments because light in the visible portion of the electromagnetic spectrum penetrates water. Remote sensing images need to be pre-processed to account for the effects of the atmosphere, water surface and water column before they can be interpreted to make coastal maps. LiDAR and sonar are forms of active remote sensing also applied in coastal environments to map water depths, which can also be estimated from satellite images and field data.
Chapter 3 introduces basic geometric operations with spatial data, including measurement of distance, area, proximity, buffer, distance decay, overlay and the application of contextual operators. Different spatial datasets can be linked through their locations or attributes. Spatial point patterns can be explored to see whether they are clustered, dispersed or spatially structured. Inferential statistical methods test the significance of patterns detected (e.g. the significance of a cluster or ‘hotpot’ of points). Raster datasets can be analysed with contextual operators, trend surface analysis and map algebra. Conditional statements use Boolean logic to query spatial data. This forms the basis of multi-criteria decision analysis for coastal management. Exploratory spatial data analysis detects patterns using statistical tools and techniques.
Chapter 2 presents the spatial data matrix as the most efficient structure for storage and analysis of data on different characteristics at different locations. Global Positioning Systems (GPS) help to locate a position on the Earth, and are commonly used for adding locational information to data. Different spatial datasets can be presented in the same frame of reference using a geographic coordinate system or projection (e.g. azimuthal, conical or cylindrical). To undertake spatial analysis, phenomena must first be conceptualised and represented as either raster (grid cells) or vector (point, line polygon) data. Important characteristics of spatial data are its measurement level, map scale and associated topological information. Nominal, ordinal, interval and ratio are the four levels of measurement for populating the spatial data matrix; they hold different amounts of information and determine what analysis can be performed. Map scale refers to the ratio between a distance represented on a map and the same distance on the ground. Spatial data topology governs how information is stored, spatial data are most commonly stored in a hierarchical GIS database.