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.

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.