Quantifying uncertainty in remote sensing-based urban land-use mapping

Highlights

• A morphology-based approach to infer urban land use from RS data is adopted.

• The method's impact on the uncertainty in the derived land-use maps is quantified.

• Errors in impervious surface estimation have a strong impact on the uncertainty.

• Uncertainty is highest in mixed residential-employment zones.

• LU uncertainty needs to be addressed to improve calibration of urban growth models.

Abstract

Land-use/land-cover information constitutes an important component in the calibration of many urban growth models. Typically, the model building involves a process of historic calibration based on time series of land-use maps. Medium-resolution satellite imagery is an interesting source for obtaining data on land-use change, yet inferring information on the use of urbanised spaces from these images is a challenging task that is subject to different types of uncertainty. Quantifying and reducing the uncertainties in land-use mapping and land-use change model parameter assessment are therefore crucial to improve the reliability of urban growth models relying on these data. In this paper, a remote sensing-based land-use mapping approach is adopted, consisting of two stages: (i) estimating impervious surface cover at sub-pixel level through linear regression unmixing and (ii) inferring urban land use from urban form using metrics describing the spatial structure of the built-up area, together with address data. The focus lies on quantifying the uncertainty involved in this approach. Both stages of the land-use mapping process are subjected to Monte Carlo simulation to assess their relative contribution to and their combined impact on the uncertainty in the derived land-use maps. The robustness to uncertainty of the land-use mapping strategy is addressed by comparing the most likely land-use maps obtained from the simulation with the original land-use map, obtained without taking uncertainty into account. The approach was applied on the Brussels-Capital Region and the central part of the Flanders region (Belgium), covering the city of Antwerp, using a time series of SPOT data for 1996, 2005 and 2012. Although the most likely land-use map obtained from the simulation is very similar to the original land-use map – indicating absence of bias in the mapping process – it is shown that the errors related to the impervious surface sub-pixel fraction estimation have a strong impact on the land-use map's uncertainty. Hence, uncertainties observed in the derived land-use maps should be taken into account when using these maps as an input for modelling of urban growth.

Introduction

The world's urban areas, subject to rapid expansion, are expected to take in all the population growth in the next four decades, leading to a total urban population projection for 2050 that equals the world's total population of 2002 (United Nations, 2012). More than ever, effective urban management and planning are crucial in tackling the many social, economic and ecological challenges cities are faced with. Models of land-use change and urban growth are tools to support urban planning and management, since they are useful to analyse the way socio-economic, technological and biophysical forces influence the spatial structure and change of urban processes (Herold et al., 2005, Verburg et al., 2004). Furthermore, they also allow exploring the impact of different scenario conditions on future land-use changes (Verburg et al., 2004).

The performance of these models strongly depends on the availability and quality of different types of data for parameterisation, calibration and validation (Herold et al., 2005). Next to socio-economic data, most of these models require data on topography, road infrastructure, as well as detailed information on land-use/land-cover change. The latter is usually obtained from visual or machine-based interpretation of historic time series of aerial photographs or satellite imagery, complemented with ancillary information. While there exists a clear relationship between the spectral reflectance values of remote sensing data and the physical characteristics of the built-up environment, inferring information on the use of urban areas from remotely sensed imagery is not an easy task. Since urban analysis relies on functional nomenclatures (Longley, 2002), some studies have tried to establish a connection between form (land cover) and function (land use) by investigating the spatial structure of urban areas. In this context, spatial metrics have proven useful to quantify the structural characteristics and growth patterns of the built-up area (Herold et al., 2005). While some studies used categorical land-cover maps as a starting point for describing built-up patterns (Barnsley and Barr, 1996, Herold et al., 2003), Van de Voorde et al. (2011) presented a method for extracting residential and employment related urban land-use patterns from medium-resolution satellite imagery by (a) estimating the fraction of impervious surface cover for each pixel, (b) defining a set of spatial metrics describing the density and the spatial distribution of impervious surface cover within each street block based on these fractions, and (c) relating the “spatial metric signature” of each street block to its functional properties. The method was first tested on the Greater Dublin Area. A sequence of land-use maps covering a period of more than two decades was produced and used as an input for historic calibration of the MOLAND¹ urban growth model for Dublin.

One of the difficulties in land-use change and urban growth modelling is the uncertainty that is present in the land-use maps that are used as input for the modelling, and the impact this uncertainty has on the calibration process and, consequently, on the reliability of future land-use predictions. Often little or no attention is paid to the propagation of uncertainty in models driven by remote sensing data and to its possible effects on these models’ output (Crosetto et al., 2001), although previous research has clearly demonstrated the importance of investigating and quantifying errors when dealing with land-use/land-cover maps. Burnicki et al. (2007) assessed the accuracy associated with land-cover change maps by investigating the interaction between the classification errors within a time-series. It was found that the complex interactions between patterns of change and patterns of error significantly affect the detection of real land-cover changes and the quantification of the level of error present in the final change map. In Canters et al. (2002), analysis of the uncertainty in a land-cover map and in a DEM, as well as their combined impact on the outcome of a structural classification of landscape types showed that the latter was mostly affected by uncertainty in the land-cover classification and that the spatial pattern of uncertainty in the land-cover map had a strong impact on the uncertainty in the landscape map that was finally obtained. The assessment of uncertainty is situated within the closely related areas of uncertainty analysis and sensitivity analysis (Crosetto et al., 2001, Crosetto and Tarantola, 2001, Helton, 1993). Uncertainty analysis allows investigating the way uncertainty in input data and model parameters propagates through the model and affects the model output, while sensitivity analysis determines how much each individual source of uncertainty contributes to the output uncertainty (Crosetto et al., 2001). A distinction can be made between four formal approaches to evaluate uncertainty and sensitivity: differential analysis, Monte Carlo simulation, response surface methodology and the (extended) Fourier amplitude sensitivity test (Crosetto et al., 2001, Helton, 1993). Of these techniques, Monte Carlo simulation is the most popular one, because of its ease of implementation, its wide applicability and its full coverage of the range of each input variable (Crosetto et al., 2001, Crosetto and Tarantola, 2001, Helton, 1993). In GIS-related research, it has become a frequently used technique to analyse the magnitude and the spatial pattern of uncertainty by producing error-sensitised versions of data input and model outcomes (e.g. Burnicki et al., 2007, Canters et al., 2002, Davis and Keller, 1997, De Clercq et al., 2009, Emmi and Horton, 1995, Fisher, 1991, Zhou et al., 2003).

This paper presents a remote sensing-based approach for urban land-use mapping based on an extension of the method proposed by Van de Voorde et al. (2011) and focuses on the characterisation of uncertainty in the land-use mapping process. The adopted land-use mapping approach consists of the following, two-stage remote sensing data processing chain: (i) sub-pixel estimation of impervious surface cover for each urban pixel and (ii) application of a multi-layer perceptron (MLP) approach to infer urban land use from urban form, based on the spatial arrangement of impervious surface cover fractions at street-block level. To model uncertainty in the proportion of impervious surface cover, use is made of a first-order autoregressive model (Heuvelink, 1998), incorporating spatial correlation observed in the fractional errors. To deal with uncertainty associated with the land-use classification, a Bayesian approach is proposed, combining information on the confusion between land-use classes, obtained from the error matrix, with local uncertainty information produced by the MLP classifier in the form of activation levels. The confusion matrix allows comparing the model output with ground truth, but inherently has a non-spatial and general character (Foody, 2002, van der Wel et al., 1998). This is counterbalanced by incorporating information derived from the output unit activation levels of the MLP, which have been recognised as an indication of uncertainty (Foody, 2000, Liu et al., 2004, McIver and Friedl, 2001). In order to assess the impact of uncertainty in both stages of the land-use mapping process, a Monte Carlo simulation is carried out, showing the contribution of uncertainty in impervious surface mapping and in MLP land-use classification, as well as the combined impact of both types of uncertainty on the land-use maps obtained for each date in the time series. Also, the robustness to uncertainty of the adopted land-use mapping strategy is assessed through a comparison of the most likely land-use map obtained from the simulation with the original classification result, obtained without taking uncertainty into account.