Modelling Spatial Compositional Data: Reconstructions of past land cover and uncertainties

In this paper, we construct a hierarchical model for spatial compositional data, which is used to reconstruct past land-cover compositions (in terms of coniferous forest, broadleaved forest, and unforested/open land) for five time periods during the past $6\,000$ years over Europe. The model consists of a Gaussian Markov Random Field (GMRF) with Dirichlet observations. A block updated Markov chain Monte Carlo (MCMC), including an adaptive Metropolis adjusted Langevin step, is used to estimate model parameters. The sparse precision matrix in the GMRF provides computational advantages leading to a fast MCMC algorithm. Reconstructions are obtained by combining pollen-based estimates of vegetation cover at a limited number of locations with scenarios of past deforestation and output from a dynamic vegetation model. To evaluate uncertainties in the predictions a novel way of constructing joint confidence regions for the entire composition at each prediction location is proposed. The hierarchical model's ability to reconstruct past land cover is evaluated through cross validation for all time periods, and by comparing reconstructions for the recent past to a present day European forest map. The evaluation results are promising and the model is able to capture known structures in past land-cover compositions

Pollen-Based Maps of Past Regional Vegetation Cover in Europe Over 12 Millennia-Evaluation and Potential

Realistic and accurate reconstructions of past vegetation cover are necessary to study past environmental changes. This is important since the effects of human land-use changes (e.g. agriculture, deforestation and afforestation/reforestation) on biodiversity and climate are still under debate. Over the last decade, development, validation, and application of pollen-vegetation relationship models have made it possible to estimate plant abundance from fossil pollen data at both local and regional scales. In particular, the REVEALS model has been applied to produce datasets of past regional plant cover at 1 degrees spatial resolution at large subcontinental scales (North America, Europe, and China). However, such reconstructions are spatially discontinuous due to the discrete and irregular geographical distribution of sites (lakes and peat bogs) from which fossil pollen records have been produced. Therefore, spatial statistical models have been developed to create continuous maps of past plant cover using the REVEALS-based land cover estimates. In this paper, we present the first continuous time series of spatially complete maps of past plant cover across Europe during the Holocene (25 time windows covering the period from 11.7 k BP to present). We use a spatial-statistical model for compositional data to interpolate REVEALS-based estimates of three major land-cover types (LCTs), i.e., evergreen trees, summer-green trees and open land (grasses, herbs and low shrubs); producing spatially complete maps of the past coverage of these three LCTs. The spatial model uses four auxiliary data sets-latitude, longitude, elevation, and independent scenarios of past anthropogenic land-cover change based on per-capita land-use estimates ("standard" KK10 scenarios)-to improve model performance for areas with complex topography or few observations. We evaluate the resulting reconstructions for selected time windows using present day maps from the European Forest Institute, cross validate, and compare the results with earlier pollen-based spatially-continuous estimates for five selected time windows, i.e., 100 BP-present, 350-100 BP, 700-350 BP, 3.2-2.7 k BP, and 6.2-5.7 k BP. The evaluations suggest that the statistical model provides robust spatial reconstructions. From the maps we observe the broad change in the land-cover of Europe from dominance of naturally open land and persisting remnants of continental ice in the Early Holocene to a high fraction of forest cover in the Mid Holocene, and anthropogenic deforestation in the Late Holocene. The temporal and spatial continuity is relevant for land-use, land-cover, and climate research

Pollen-Based Maps of Past Regional Vegetation Cover in Europe Over 12 Millennia-Evaluation and Potential

Realistic and accurate reconstructions of past vegetation cover are necessary to study past environmental changes. This is important since the effects of human land-use changes (e.g. agriculture, deforestation and afforestation/reforestation) on biodiversity and climate are still under debate. Over the last decade, development, validation, and application of pollen-vegetation relationship models have made it possible to estimate plant abundance from fossil pollen data at both local and regional scales. In particular, the REVEALS model has been applied to produce datasets of past regional plant cover at 1 degrees spatial resolution at large subcontinental scales (North America, Europe, and China). However, such reconstructions are spatially discontinuous due to the discrete and irregular geographical distribution of sites (lakes and peat bogs) from which fossil pollen records have been produced. Therefore, spatial statistical models have been developed to create continuous maps of past plant cover using the REVEALS-based land cover estimates. In this paper, we present the first continuous time series of spatially complete maps of past plant cover across Europe during the Holocene (25 time windows covering the period from 11.7 k BP to present). We use a spatial-statistical model for compositional data to interpolate REVEALS-based estimates of three major land-cover types (LCTs), i.e., evergreen trees, summer-green trees and open land (grasses, herbs and low shrubs); producing spatially complete maps of the past coverage of these three LCTs. The spatial model uses four auxiliary data sets-latitude, longitude, elevation, and independent scenarios of past anthropogenic land-cover change based on per-capita land-use estimates ("standard" KK10 scenarios)-to improve model performance for areas with complex topography or few observations. We evaluate the resulting reconstructions for selected time windows using present day maps from the European Forest Institute, cross validate, and compare the results with earlier pollen-based spatially-continuous estimates for five selected time windows, i.e., 100 BP-present, 350-100 BP, 700-350 BP, 3.2-2.7 k BP, and 6.2-5.7 k BP. The evaluations suggest that the statistical model provides robust spatial reconstructions. From the maps we observe the broad change in the land-cover of Europe from dominance of naturally open land and persisting remnants of continental ice in the Early Holocene to a high fraction of forest cover in the Mid Holocene, and anthropogenic deforestation in the Late Holocene. The temporal and spatial continuity is relevant for land-use, land-cover, and climate research

3D morphological variability in foraminifera unravel environmental changes in the Baltic Sea entrance over the last 200 years

Human activities in coastal areas have intensified over the last 200 years, impacting also high-latitude regions such as the Baltic Sea. Benthic foraminifera, protists often with calcite shells (tests), are typically well preserved in marine sediments and known to record past bottom-water conditions. Morphological analyses of marine shells acquired by microcomputed tomography (µCT) have made significant progress toward a better understanding of recent environmental changes. However, limited access to data processing and a lack of guidelines persist when using open-source software adaptable to different microfossil shapes. This study provides a post-data routine to analyze the entire test parameters: average thickness, calcite volume, calcite surface area, number of pores, pore density, and calcite surface area/volume ratio. A case study was used to illustrate this method: 3D time series (i.e., 4D) of Elphidium clavatum specimens recording environmental conditions in the Baltic Sea entrance from the period early industrial (the 1800s) to present-day (the 2010 s). Long-term morphological trends in the foraminiferal record revealed that modern specimens have ∼28% thinner tests and ∼91% more pores than their historic counterparts. However, morphological variability between specimens and the BFAR (specimens cm−2 yr−1) in E. clavatum were not always synchronous. While the BFAR remained unchanged, morphological variability was linked to natural environmental fluctuations in the early industrial period and the consequences of anthropogenic climate change in the 21st century. During the period 1940–2000 s, the variations in BFAR were synchronous with morphological variability, revealing both the effects of the increase in human activities and major hydrographic changes. Finally, our interpretations, based on E. clavatum morphological variations, highlight environmental changes in the Baltic Sea area, supporting those documented by the foraminiferal assemblages

Creating spatially continuous maps of past land cover from point estimates: A new statistical approach applied to pollen data

International audienceReliable estimates of past land cover are critical for assessing potential effects of anthropogenic land-cover changes on past earth surface-climate feedbacks and landscape complexity. Fossil pollen records from lakes and bogs have provided important information on past natural and human-induced vegetation cover. However, those records provide only point estimates of past land cover, and not the spatially continuous maps at regional and sub-continental scales needed for climate modelling. We propose a set of statistical models that create spatially continuous maps of past land cover by combining two data sets: 1) pollen-based point estimates of past land cover (from the REVEALS model) and 2) spatially continuous estimates of past land cover, obtained by combining simulated potential vegetation (from LPJ-GUESS) with an anthropogenic land-cover change scenario (KK10). The proposed models rely on statistical methodology for compositional data and use Gaussian Markov Random Fields to model spatial dependencies in the data. Land-cover reconstructions are presented for three time windows in Europe: 0.05, 0.2, and 6 ka years before present (BP). The models are evaluated through cross-validation, deviance information criteria and by comparing the reconstruction of the 0.05 ka time window to the present-day land-cover data compiled by the European Forest Institute (EFI). For 0.05 ka, the proposed models provide reconstructions that are closer to the EFI data than either the REVEALS-or LPJ-GUESS/KK10-based estimates; thus the statistical combination of the two estimates improves the reconstruction. The reconstruction by the proposed models for 0.2 ka is also good. For 6 ka, however, the large differences between the REVEALS-and LPJ-GUESS/KK10-based estimates reduce the reliability of the proposed models. Possible reasons for the increased differences between REVEALS and LPJ-GUESS/KK10 for older time periods and further improvement of the proposed models are discussed

Reconstruction of Past European Land Cover Based on Fossil Pollen Data : Gaussian Markov Random Field Models for Compositional Data

The aim of this thesis is to develop statistical models to reconstruct past land cover composition and human land use based on fossil pollen records over Europe for different time periods over the past 6000 years. Accurate maps of past land cover and human land use are needed when studying the interaction between climate and land surface, and the effects of human land use on past climate. Existing land cover maps are mainly simulations from dynamic vegetation models and anthropogenic land cover change scenarios. Pollen records is an alternative to existing land cover estimates that might give better insight into past land cover. The pollen counts are extracted from lake and bog sediments and used to estimate the three land cover compositions; coniferous forest, broadleaved forest, and unforested land for grid cells surrounding the lakes and bogs.In this thesis, first, a statistical model is developed to interpolate transformedpollen based land cover compositions (PbLCC) with spatial dependency modelledusing a Gaussian Markov random Field (GMRF). The mean structure is modelled using a regression on different sets of covariates including elevation and model based vegetation estimates. The model is fitted using Integrated NestedLaplace Approximation. The results indicated the existence of spatial dependence structure in the PbLCC and the possibility of reconstructing past land cover from PbLCC. If the compositional data is over-dispersed, the transformed Gaussian model might underestimate the uncertainties. To capture the variation in the composition correctly, a Bayesian hierarchical model (BHM) for Dirichlet observations of a GMRF is developed. The model is estimated using MCMC with sparse precision matrix of the GMRF being used for computational efficiency. Comparison between the Dirichlet and Gaussian models showed the advantages of the Dirichlet in describing the PbLCC. The large discrepancies in the model based estimates used as covariates could affect the Dirichlet models ability to reconstruct past land cover. To assess this concern a sensitivity study was performed, showing that the results are robust to the choice of covariates. Finally, the BHM is extended to reconstruct past human land use by combing the PbLCC with anthropogenic land cover change estimates. This extension aims at decomposing the PbLCC into past natural land cover and human land use

A Fully Automated Segmentation of Knee Bones and Cartilage Using Shape Context and Active Shape Models

In this master's thesis a fully automated method is presented for seg- menting bones and cartilage in magnetic resonance imaging (MRI) of the knee. The knee joint is the most complex joint in the human body and supports the weight of the whole body. This complexity and acute task of the knee joint leads to a disabling disease called Osteoarthritis among the adult population. The disease leads to loss of cartilage and torn cartilage cannot be repaired unless surgical techniques are used. Therefore, one of the important parts of nding the disease and planning the knee surgery is to segment bones and cartilages in MRI. The segmentation method is based on Statistical Shape Model (SSM) and Active Shape Model (ASM) built from a MICCAI 2010 Grand chal- lenge training database. First, all the data are represented by points and faces. A Shape context algorithm is applied on 60 data sets to obtain consistent landmarks. The mentioned consistent landmarks and Princi- pal Component Analysis are used to build a Statistical Shape Model. The resulting model is used to automatically segment femur and tibia bones and femur and tibia cartilages with Active Shape model. The algorithm is tested on the remaining 40 MRI data sets provided by the Grand challenge 2010, and compared with six other submitted papers

Modulus of continuity and its application in classifying the smoothness of images.

The problems of de-blurring, de-noising, compression and segmenta- tion are fundamental problems in image processing. Each of these prob- lems can be formulated as a problem to find some approximation of an initial image. To find this approximation one needs to specify the ap- proximation space and in what space the error between the image and its approximation should be calculated. Using the space of Bounded Variation, BV, became very popular in the last decade. However it was later proved that for a rich variety of nat- ural images it is more effective to use spaces of smooth functions that are called Besov spaces instead of BV. In the previous papers two methods for classifying the smoothness of images were suggested. The DeVore’s method based on the wavelet transform and Carasso’s method based on singular integrals are reviewed. The classical definition of Besov spaces is based on the modulus of continuity. In this master thesis a new method is suggested for classifying the smoothness of images based on this definition. The developed method was applied to some images to classify the smoothness of them