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.

Deglaciation of the Caucasus Mountains, Russia/Georgia, in the 21st century observed with ASTER satellite imagery and aerial photograpy

Changes in the map area of 498 glaciers located on the Main Caucasus ridge (MCR) and on Mt. Elbrus in the Greater Caucasus Mountains (Russia and Georgia) were assessed using multispectral ASTER and panchromatic Landsat imagery with 15 m spatial resolution in 1999/2001 and 2010/2012. Changes in recession rates of glacier snouts between 1987–2001 and 2001–2010 were investigated using aerial photography and ASTER imagery for a sub-sample of 44 glaciers. In total, glacier area decreased by 4.7 ± 2.1% or 19.2 ± 8.7 km2 from 407.3 ± 5.4 km2 to 388.1 ± 5.2 km2. Glaciers located in the central and western MCR lost 13.4 ± 7.3 km2 (4.7 ± 2.5%) in total or 8.5 km2 (5.0 ± 2.4%) and 4.9 km2 (4.1 ± 2.7%) respectively. Glaciers on Mt. Elbrus, although located at higher elevations, lost 5.8 ± 1.4 km2 (4.9 ± 1.2%) of their total area. The recession rates of valley glacier termini increased between 1987–2000/01 and 2000/01–2010 (2000 for the western MCR and 2001 for the central MCR and Mt.~Elbrus) from 3.8 ± 0.8, 3.2 ± 0.9 and 8.3 ± 0.8 m yr−1 to 11.9 ± 1.1, 8.7 ± 1.1 and 14.1 ± 1.1 m yr−1 in the central and western MCR and on Mt. Elbrus respectively. The highest rate of increase in glacier termini retreat was registered on the southern slope of the central MCR where it has tripled. A positive trend in summer temperatures forced glacier recession, and strong positive temperature anomalies in 1998, 2006, and 2010 contributed to the enhanced loss of ice. An increase in accumulation season precipitation observed in the northern MCR since the mid-1980s has not compensated for the effects of summer warming while the negative precipitation anomalies, observed on the southern slope of the central MCR in the 1990s, resulted in stronger glacier wastage.

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.