Alex Hagen-Zanker

Further developments of a fuzzy set map comparison approach

Fuzzy set map comparison offers a novel approach to map comparison.The approach is specifically aimed at categorical raster maps and applies fuzzy set techniques, accounting for fuzziness of location and fuzziness of category, to create a similarity map as well as an overall similarity statistic: the Fuzzy Kappa. To date, the calculation of the Fuzzy Kappa (or K-fuzzy) has not been formally derived, and the documented procedure was only valid for cases without fuzziness of category. Furthermore, it required an infinitely large, edgeless map. This paper presents the full derivation of the Fuzzy Kappa; the method is now valid for comparisons considering fuzziness of both location and category and does not require further assumptions. This theoretical completion opens opportunities for use of the technique that surpass the original intentions. In particular, the categorical similarity matrix can be applied to highlight or disregard differences pertaining to selected categories or groups of categories and to distinguish between differences due to omission and commission.

Map comparison methods that simultaneously address overlap and structure

Methods for map comparison such as the Kappa and Tau statistics have grown popular in applications of remote sensing accuracy assessment. These methods take pairs of raster maps as sets of paired observations and do not consider spatial structure except for cell-by-cell overlap. In contrast, landscape structure metrics such as mean patch size that are commonly used in landscape ecology do express spatial structure, however without addressing cell-by-cell overlap. This paper introduces a number of comparison methods that consider spatial structure and overlap simultaneously. They achieve this by involving the neighbourhood of a cell in the calculation of similarity at its location. For this, the methods make use of a distance weighted moving window. Two test cases demonstrate that the different comparison methods offer a spatial account of varied aspects of map similarity. It is found that the methods can best be used in conjunction with a visual analysis; they then serve to quantify, reject or confirm hypotheses.

An improved Fuzzy Kappa statistic that accounts for spatial autocorrelation

The Fuzzy Kappa statistic expresses the agreement between two categorical raster maps. The statistic goes beyond cell‐by‐cell comparison and gives partial credit to cells based on the categories found in the neighborhood. When matching categories are found at shorter distances the agreement is higher. Like the well‐established Kappa statistic the Fuzzy Kappa statistic expresses the mean agreement relative to the expected agreement. The model underlying the expected agreement assumes absence of spatial autocorrelation in both compared maps. In reality however, spatial autocorrelation does lower the expected agreement as matching categories become less likely to be found close‐by. Since most maps have some degree of spatial autocorrelation, the calculated expected agreement is generally higher than the true expected agreement. This leads to counterintuitive results when maps that appear to have considerable agreement obtain negative Fuzzy Kappa values. Furthermore, the Fuzzy Kappa may be biased, as it systematically attributes lower agreement to maps with stronger spatial autocorrelation. This paper proposes an improved Fuzzy Kappa statistic that is based on the same local agreement and has the same attractive properties as the original Fuzzy Kappa. The novelty is that the new statistic accounts for spatial autocorrelation, such that the expected Fuzzy Kappa for maps that are not cross‐correlated is equal to zero. The improved statistic is applied on two cases to demonstrate its properties.

Map Comparison Methods for Comprehensive Assessment of Geosimulation Models

A crucial task in the calibration and validation of geosimulation models is to measure the agreement between model and reality. In recent years many map comparison methods have been developed for this purpose. This paper presents a framework to systematically assess different aspects of model performance and express the results relative to a common reference level. Application on a constrained cellular automata model of the Netherlands demonstrates that the framework gives an in-depth account of model performance. It also shows that any performance assessment that does not follow a multi-criteria approach or lacks a reference level results in an unbalanced account and ultimately false conclusions.

Exposure to air pollutants during commuting in London: Are there inequalities among different socio-economic groups?

People with low income often experience higher exposures to air pollutants. We compared the exposure to particulate matter (PM1, PM2.5 and PM10), Black Carbon (BC) and ultrafine particles (PNCs; 0.02-1μm) for typical commutes by car, bus and underground from 4 London areas with different levels of income deprivation (G1 to G4, from most to least deprived). The highest BC and PM concentrations were found in G1 while the highest PNC in G3. Lowest concentrations for all pollutants were observed in G2. We found no systematic relationship between income deprivation and pollutant concentrations, suggesting that differences between transport modes are a stronger influence. The underground showed the highest PM concentrations, followed by buses and a much lower concentrations in cars. BC concentrations in the underground were overestimated due to Fe interference. BC concentrations were also higher in buses than cars because of a lower infiltration of outside pollutants into the car cabin. PNCs were highest in buses, closely followed by cars, but lowest in underground due to the absence of combustion sources. Concentration in the road modes (car and bus) were governed by the traffic conditions (such as traffic flow interruptions) at the specific road section. Exposures were reduced in trains with non-openable windows compared to those with openable windows. People from less income-deprived areas have a predominant use of car, receiving the lowest doses (RDD<1μgh-1) during commute but generating the largest emissions per commuter. Conversely, commuters from high income-deprived areas have a major reliance on the bus, receiving higher exposures (RDD between 1.52 and 3.49μgh-1) while generating less emission per person. These findings suggest an aspect of environmental injustice and a need to incorporate the socioeconomic dimension in life-course exposure assessments.

New Ways of Supporting Decision Making: Linking Qualitative Storylines with Quantitative Modelling

To explore how people will live and work in Europe, what the landscape will look like and what the environmental consequences will be in some 35 years from now, the PRELUDE project (EEA 2007) of the European Environment Agency developed five different land-use scenarios for Europe. The project was carried out according to a Story And Simulation (SAS) approach in which, iteratively, storylines developed in participatory sessions are underpinned by land-use models. Storylines in this context are defined as narratives about future developments in Europe. They provide qualitative information on a broad range of issues in an integrated context.

A Metric of Compactness of Urban Change Illustrated to 22 European Countries

Most metrics of urban spatial structure are snapshots, summarizing spatial structure at one particular moment in time. They are therefore not ideal for the analysis of urban change patterns. This paper presents a new spatio-temporal analytical method for raster maps that explicitly registers changesin patterns. The main contribution is a transition matrix which cross-tabulates the distance to the nearest urbanized location at the beginning and end of the analyzed period. The transition matrix by itself offers a powerful description of urban change patterns from which further metrics can be derived. In particular, a metric that is an indicator of the compactness of urban change is derived. The new metric is applied first to a synthetic dataset demonstrating consistency with existing classifications of urban change patterns. Next, the metric is applied country by country on the European CORINE land cover dataset. The results indicate a striking contrast in change patterns between Western and Eastern European counties. The method can be further elaborated in many different ways and can therefore be the first in a family of spatio-temporal descriptive statistics.

Adaptive zoning for transport mode choice modeling

Adaptive zoning is a recently introduced method for improving computer modeling of spatial interactions and movements in the transport network. Unlike traditional zoning, where geographic locations are defined by one single universal plan of discrete land parcels or ‘zones’ for the study area, adaptive zoning establishes a compendium of different zone plans, each of which is applicable to one journey origin or destination only. These adaptive zone plans are structured to represent strong spatial interactions in proportionately more detail than weaker ones. In recent articles, it has been shown that adaptive zoning improves, by a large margin, the scalability of models of spatial interaction and road traffic assignment. This article confronts the method of adaptive zoning with an application of the scale and complexity for which it was intended, namely an application of mode choice modeling that at the same time requires a large study area and a fine-grained zone system. Our hypothesis is that adaptive zoning can significantly improve the accuracy of mode choice modeling because of its enhanced sensitivity to the geographic patterns and scales of spatial interaction. We test the hypothesis by investigating the performance of three alternative models: (1) a spatially highly detailed model that is permissible to the maximum extent by available data, but requires a high computational load that is generally out of reach for rapid turnaround of policy studies; (2) a mode choice model for the same area, but reducing the computational load by 90% by using a traditional zone system consisting of fewer zones; and (3) a mode choice model that also reduces the computational load by 90%, but based on adaptive zoning instead. The tests are carried out on the basis of a case study that uses the dataset from the London Area Transport Survey. Using the first model as a benchmark, it is found that for a given computational load, the model based on adaptive zoning contains about twice the amount of information of the traditional model, and model parameters on adaptive zoning principles are more accurate by a factor of six to eight. The findings suggest that adaptive zoning has a significant potential in enhancing the accuracy of mode choice modeling at the city or city-region scale.

Adaptive Zoning for Efficient Transport Modelling in Urban Models

Transport modelling and in particular transport assignment is a well-known bottleneck in computation cost and time for urban system models. The use of Transport Analysis Zones (TAZ) implies a trade-off between computation time and accuracy: practical computational constraints can lead to concessions to zone size with severe repercussions for the quality of the transport representation in urban models. This paper investigates how a recently developed geographical topology called adaptive zoning can be used to obtain more favorable trade-offs between computational cost and accuracy than traditional TAZ. Adaptive zoning was developed specifically for representing spatial interactions; it makes use of a nested zone hierarchy to adapt the model resolution as a function of both the origin and destination location. In this paper the adaptive zoning method is tied to an approach to trip assignment that uses high spatial accuracy (small zones) at one end of the route and low spatial accuracy (large zones) at the other end of the route. Opportunistic use of either the first or second half of such routes with asymmetric accuracy profiles leads to a method of transport assignment that is more accurate than traditional TAZ based assignment at reduced computational cost. The method is tested and demonstrated on the well-known Chicago Regional test problem. Compared with an assignment using traditional zoning, an adaptive-zoning-based assignment that uses the same computation time reduces the bias in travel time by a factor 16 and link level traffic volume RMSE by a factor 6.4.

A Framework of Map Comparison Methods to Evaluate Geosimulation Models from a Geospatial Perspective

Geosimulation is a form of microsimulation that seeks to understand geographical patterns and dynamics as the outcome of micro-level geographical processes. Geosimulation has been applied to understand such diverse systems as lake ecology, traffic congestion and urban growth. A crucial task common to these applications is to express the agreement between model and reality and hence the confidence one can have in model results. Such evaluation requires a geospatial perspective; it is not sufficient if micro-level interactions are realistic. Importantly, interactions should be such that meso- and macro- level patterns emerging from the model are realistic. In recent years, a host of map comparison methods have been developed, which address different aspects of the agreement between model and reality. This paper places such methods in a framework to systematically assess breadth and width of model performance. The framework expresses agreement at the continuum of spatial scales ranging from local to whole landscape and separately addresses agreement in structure and presence. A common reference level makes different performance metrics mutually comparable and guides the interpretation of results. The framework is applied for the evaluation of a constrained cellular automata model of the Netherlands. The case demonstrates that a performance assessment lacking either a multi-criteria and multi-scale perspective or a reference level would result in an unbalanced account and ultimately false conclusions.