Quantifying uncertainty in remotely sensed land cover maps

Remotely sensed land cover maps are increasingly used as inputs into environmental simulation models whose outputs inform decisions and policy-making. Risks associated with these decisions are dependent on model output uncertainty, which is in turn affected by the uncertainty of land cover inputs. This article presents a method of quantifying the uncertainty that results from potential mis-classification in remotely sensed land cover maps. In addition to quantifying uncertainty in the classification of individual pixels in the map, we also address the important case where land cover maps have been upscaled to a coarser grid to suit the users’ needs and are reported as proportions of land cover type. The approach is Bayesian and incorporates several layers of modelling but is straightforward to implement. First, we incorporate data in the confusion matrix derived from an independent field survey, and discuss the appropriate way to model such data. Second, we account for spatial correlation in the true land cover map, using the remotely sensed map as a prior. Third, spatial correlation in the mis-classification characteristics is induced by modelling their variance. The result is that we are able to simulate posterior means and variances for individual sites and the entire map using a simple Monte Carlo algorithm. The method is applied to the Land Cover Map 2000 for the region of England and Wales, a map used as an input into a current dynamic carbon flux model.

Continuous sky view factor maps from high resolution urban digital elevation models

This paper presents a new method to calculate sky view factors (SVFs) from high resolution urban digital elevation models using a shadow casting algorithm. By utilizing weighted annuli to derive SVF from hemispherical images, the distance light source positions can be predefined and uniformly spread over the whole hemisphere, whereas another method applies a random set of light source positions with a cosine-weighted distribution of sun altitude angles. The 2 methods have similar results based on a large number of SVF images. However, when comparing variations at pixel level between an image generated using the new method presented in this paper with the image from the random method, anisotropic patterns occur. The absolute mean difference between the 2 methods is 0.002 ranging up to 0.040. The maximum difference can be as much as 0.122. Since SVF is a geometrically derived parameter, the anisotropic errors created by the random method must be considered as significant.

Modelling of urban sensible heat flux at multiple spatial scales : a demonstration using airborne hyperspectral imagery of Shanghai and a temperature–emissivity separation approach

Urbanization related alterations to the surface energy balance impact urban warming (‘heat islands’), the growth of the boundary layer, and many other biophysical processes. Traditionally, in situ heat flux measures have been used to quantify such processes, but these typically represent only a small local-scale area within the heterogeneous urban environment. For this reason, remote sensing approaches are very attractive for elucidating more spatially representative information. Here we use hyperspectral imagery from a new airborne sensor, the Operative Modular Imaging Spectrometer (OMIS), along with a survey map and meteorological data, to derive the land cover information and surface parameters required to map spatial variations in turbulent sensible heat flux (QH). The results from two spatially-explicit flux retrieval methods which use contrasting approaches and, to a large degree, different input data are compared for a central urban area of Shanghai, China: (1) the Local-scale Urban Meteorological Parameterization Scheme (LUMPS) and (2) an Aerodynamic Resistance Method (ARM). Sensible heat fluxes are determined at the full 6 m spatial resolution of the OMIS sensor, and at lower resolutions via pixel aggregation and spatial averaging. At the 6 m spatial resolution, the sensible heat flux of rooftop dominated pixels exceeds that of roads, water and vegetated areas, with values peaking at ∼ 350 W m− 2, whilst the storage heat flux is greatest for road dominated pixels (peaking at around 420 W m− 2). We investigate the use of both OMIS-derived land surface temperatures made using a Temperature–Emissivity Separation (TES) approach, and land surface temperatures estimated from air temperature measures. Sensible heat flux differences from the two approaches over the entire 2 × 2 km study area are less than 30 W m− 2, suggesting that methods employing either strategy maybe practica1 when operated using low spatial resolution (e.g. 1 km) data. Due to the differing methodologies, direct comparisons between results obtained with the LUMPS and ARM methods are most sensibly made at reduced spatial scales. At 30 m spatial resolution, both approaches produce similar results, with the smallest difference being less than 15 W m− 2 in mean QH averaged over the entire study area. This is encouraging given the differing architecture and data requirements of the LUMPS and ARM methods. Furthermore, in terms of mean study QH, the results obtained by averaging the original 6 m spatial resolution LUMPS-derived QH values to 30 and 90 m spatial resolution are within ∼ 5 W m− 2 of those derived from averaging the original surface parameter maps prior to input into LUMPS, suggesting that that use of much lower spatial resolution spaceborne imagery data, for example from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) is likely to be a practical solution for heat flux determination in urban areas.

On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.

Daily thin-ice thickness maps from modis thermal infrared imagery

Accurate knowledge of ice-production rates within the marginal ice zones of the Arctic Ocean requires monitoring of the thin-ice distribution within polynyas. The thickness of the ice layer controls the heat loss and hence the new-ice formation. An established thinice algorithm using high-resolution MODIS data allows deriving the ice-thickness distribution within polynyas. The average uncertainty is ±4.7 cm for ice thicknesses below 0.2 m. In this study, the ice-thickness distributions within the Laptev Sea polynya for the two winter seasons 2007/08 and 2008/09 are calculated. Then, a new method is applied to determine a daily MODIS thin-ice product.

The Mesolithic-Neolithic transition in the Channel Islands: maritime and terrrestrial perspectives

This paper investigates the Mesolithic-Neolithic transition in the Channel Islands. It presents a new synthesis of all known evidence from the islands c. 5000-4300 BC, including several new excavations as well as find spot sites that have not previously been collated. It also summarises – in English – a large body of contemporary material from north-west France. The paper presents a new high-resolution sea level model for the region, shedding light on the formation of the Channel Islands from 9000-4000 BC. Through comparison with contemporary sites in mainland France, an argument is made suggesting that incoming migrants from the mainland and the small indigenous population of the islands were both involved in the transition. It is also argued that, as a result of the fact the Channel Islands witnessed a very different trajectory of change to that seen in Britain and Ireland c. 5000-3500 BC, this small group of islands has a great deal to tell us about the arrival of the Neolithic more widely.