Spatial Modeling

Brenning, A. (2005): Climatic and geomorphological controls of rock glaciers in the Andes of Central Chile: Combining statistical modelling and field mapping. Ph.D. dissertation, Mathematisch-Naturwissenschaftliche Fakultät II, Humboldt-Universität zu Berlin. Electronic publication, urn:nbn:de:kobv:11-10049648

by Alexander Brenning

Brenning A, Trombotto D. 2006. Logistic regression modeling of rock glacier and glacier distribution: topographic and climatic controls in the semi-arid Andes. Geomorphology, 81(1-2): 141-154.

by Alexander Brenning

Logistic regression is applied to a random sample of surface points in the semi-arid Andes of Santiago and Mendoza... more Logistic regression is applied to a random sample of surface points in the semi-arid Andes of Santiago and Mendoza (Chile/Argentina, 32° 45′–34° 30′ S, 12 000 km2 above 3000 m a.s.l.) to identify local and regional controls on rock glacier and glacier distribution. The study area is among the areas with the greatest abundance of rock glaciers worldwide. The explanatory variables used for model selection are related to local and regional morphometric and climatic characteristics. The models achieve a very good fit (area under the ROC curve 0.84 for rock glaciers and 0.95 for glaciers) and are able to reproduce the regional distribution pattern. Model results are used to determine the optimal morphographic and climatic niche of rock glaciers and glaciers in the study area, and help explain the presence of low-elevation rock glaciers under favorable topoclimatic conditions.

Boeckli L, Brenning A, Gruber S, Noetzli J. 2012. A statistical approach to modelling permafrost distribution in the European Alps or similar mountain ranges. The Cryosphere, 6: 125-140.

by Alexander Brenning

Estimates of permafrost distribution in mountain regions are important for the assessment of climate change effects on... more Estimates of permafrost distribution in mountain regions are important for the assessment of climate change effects on natural and human systems. In order to make permafrost analyses and the establishment of guidelines for e.g. construction or hazard assessment comparable and compatible between regions, one consistent and traceable model for the entire Alpine domain is required. For the calibration of statistical models, the scarcity of suitable and reliable information about the presence or absence of permafrost makes the use of large areas attractive due to the larger data base available.

We present a strategy and method for modelling permafrost distribution of entire mountain regions and provide the results of statistical analyses and model calibration for the European Alps. Starting from an integrated model framework, two statistical sub-models are developed, one for debris-covered areas (debris model) and one for steep bedrock (rock model). They are calibrated using rock glacier inventories and rock surface temperatures. To support the later generalization to surface characteristics other than those available for calibration, so-called offset terms have been introduced into the model that allow doing this in a transparent and traceable manner.

For the debris model a generalized linear mixed-effect model (GLMM) is used to predict the probability of a rock glacier being intact as opposed to relict. It is based on the explanatory variables mean annual air temperature (MAAT), potential incoming solar radiation (PISR) and the mean annual sum of precipitation (PRECIP), and achieves an excellent discrimination (area under the receiver-operating characteristic, AUROC = 0.91). Surprisingly, the probability of a rock glacier being intact is positively associated with increasing PRECIP for given MAAT and PISR conditions. The rock model is based on a linear regression and was calibrated with mean annual rock surface temperatures (MARST). The explanatory variables are MAAT and PISR. The linear regression achieves a root mean square error (RMSE) of 1.6 °C. The final model combines the two sub-models and accounts for the different scales used for model calibration.

The modelling approach provides a theoretical basis for estimating mountain permafrost distribution over larger mountain ranges and can be expanded to more surface types and sub-models than considered, here. The analyses performed with the Alpine data set further provide quantitative insight into larger-area patterns as well as the model coefficients for a later spatial application. The transfer into a map-based product, however, requires further steps such as the definition of offset terms that usually contain a degree of subjectivity.

Boeckli, L., A. Brenning, S. Gruber, J. Noetzli, 2012. Permafrost distribution in the European Alps: calculation and evaluation of an index map and summary statistics. The Cryosphere Discussions, 6, 849-891, doi:10.5194/tcd-6-849-2012

by Alexander Brenning

The objective of this study is the production of an Alpine Permafrost Index Map (APIM) covering the entire European... more The objective of this study is the production of an Alpine Permafrost Index Map (APIM) covering the entire European Alps. A unified statistical model that is based on Alpine-wide permafrost observations is used for debris and bedrock surfaces across the entire Alps. The explanatory variables of the model are mean annual air temperatures, potential incoming solar radiation and precipitation. Offset terms were applied to make model predictions for topographic and geomorphic conditions that differ from the terrain features used for model fitting. These offsets are based on literature review and involve some degree of subjective choice during model building. The assessment of the APIM is challenging because limited independent test data are available for comparison and these observations represent point information in a spatially highly variable topography. The APIM provides an index that describes the spatial distribution of permafrost and comes together with an interpretation key that helps to assess map uncertainties and to relate map contents to their actual expression in terrain. The map can be used as a first resource to estimate permafrost conditions at any given location in the European Alps in a variety of contexts such as research and spatial planning.

Results show that Switzerland likely is the country with the largest permafrost area in the Alps, followed by Italy, Austria, France and Germany. Slovenia and Liechtenstein may have marginal permafrost areas. In all countries the permafrost area is expected to be larger than the glacier-covered area.

The permafrost index map with an approximate grid spacing of 30 m is available at the webpage of the Department of Geography, University of Zurich.

Landscape metrics in the analysis of urban land use patterns: A case study in a Spanish metropolitan area

by André Botequilha-Leitão

21st century fisheries management: A spatiotemporally explicit tariff-based approach combining multiple drivers and incentivising responsible fishing.

by Edward Codling

Multikriteriálne rozhodovanie pomocou fuzzy množín v prostredí GIS a jeho využitie v archeologickej predikcii (Multicriteria Decision Making Using Fuzzy Sets in GIS Environment and Its Application in the Archaeological Prediction)

by Tibor Lieskovský

Published in:Geodetický a kartografický obzor, ročník 57/99, 2011, číslo 8

Modelling of uncertainty in multicriteria decision making in prediction of archaeological sites in Slovakia.... more Modelling of uncertainty in multicriteria decision making in prediction of archaeological sites in Slovakia. Description of the
basic concept of fuzzy sets focusing on the possibility of its use in modelling uncertainty in spatial analysis. A few parameters
(slope, distance from watercourses, soil suitability, distance from fl uvial deposits, etc.) enter into the process of deciding
about appropriateness, or inadequacy of potential localities for the archaeological site. Representation of all the factors
implies a degree of uncertainty. To eliminate the impact of uncertain factors or inaccurate data are all parameters chosen by
appropriately modelled fuzzy sets. A practical solution of the spatial analysis using principles of fuzzy logic and fuzzy sets is
realized in the ArcGIS 10 software environment.

Spatio-temporal dynamics of neocortical excitation and inhibition during human sleep.

by Nima Dehghani

Grouping genetic operators for the delineation of functional areas based on spatial interaction

by José M. Casado-Díaz

Martínez-Bernabeu, L.; Flórez-Revuelta, F. y Casado-Díaz, J.M. (2012) “Grouping genetic operators for the delineation of functional areas based on spatial interaction”, Expert Systems with Applications, Volume 39, Issue 8, 15 June 2012, Pages 6754–6766 - doi:10.1016/j.eswa.2011.12.026.

The delineation of functional economic areas, or market areas, is a combinatorial optimisation problem, defined as the... more The delineation of functional economic areas, or market areas, is a combinatorial optimisation problem, defined as the partition of a given set of indivisible spatial units (covering a territory) into regions with high cohesion and self-containment —in terms of spatial interaction data: flows— under constraints of size, self-containment and/or continuity, typicaly solved with greedy methods. An evolutionary algorithm with many tailored operators for the delimitation of Labour Market Areas was recently proposed. This algorithm allowed finding better solutions but was very time consuming, this hampering its use in large real-world problems.
In this paper we present several group-based mutation operators featuring general unary and binary operations over disjoint groups, tailored to tackle with that problem. A comparative analysis of our approach with a greedy algorithm and the previous evolutionary proposals shows that our algorithm always gives better results concerning both quality and time consumed (except for the greedy), and is able to tackle with large real-world problems in reasonable time.

Keywords: functional areas, local market, evolutionary algorithm, grouping problem, regionalisation, combinatorial optimisation

Models of Spatial Competition: A critical review

by Ricardo Biscaia

FEP Working Paper, nº 411 - Jointly with Isabel Mota

Breaking down an early Neolithic palimpsest site: some notes on the concept of Percolation Theory and the understanding of spatial pattern formation.

by Hans Peeters

In: F. Niccolucci & H. Sormon (eds.): Beyond the artifact. Computer Applications in Archaeology and Quantitative Methods, Prato 2004. Oxford (Archaeopress/Archaeolingua), 423-428.

Debt, interest rates, and integration of financial markets

by Peter Claeys

doi:10.1016/j.econmod.2011.05.009

It is commonly believed that higher budget deficits raise interest rates. However, these crowding out effects of... more It is commonly believed that higher budget deficits raise interest rates. However, these crowding out effects of increasing public debt have usually been found to be small or non-existent. One explanation is that on globalised bond markets interest rate differentials are offset due to financial integration. This paper tests crowding out, and measures the degree of integration of government bond markets, using spatial modelling techniques. Our main finding is that the crowding out effect of public debt on domestic long term interest rates is small: a 1% increase in the debt ratio pushes up domestic rates by 2 pp at most. Financial integration implies an important spillover effect via international bond markets, but only between OECD, and in particular EU, countries. The feedback effect from these markets on long term interest rates is as important as the domestic crowding out effect of higher public debt. Emerging markets are not as well integrated into international capital markets, causing a stronger crowding out effect.

Ambient Compass: One approach to model spatial relations

by Petr Aksenov

Reasoning over spatial relations for context-aware distributed user interfaces

by Petr Aksenov

Uncertainty propagation in chained web based modeling services: the case of eHabitat

by Gregoire Dubois

Skøien, J., M. Schulz, G. Dubois, R. Jones, G.B.M. Heuvelink, D. Cornford (2011). Uncertainty propagation in chained web based modeling services: the case of eHabitat.  In: “Innovation in sharing environmental observations and information. Proceedings of EnviroInfo 2011, 25th International Conference Environmental Informatics”. W. Pillmann, S. Schade and P. Smits (Eds), pp: 46-58, 5-7 October 2011, Ispra, Italy.

eHabitat is a Web Processing Service (WPS) designed to compute the likelihood of finding ecosystems with similar... more eHabitat is a Web Processing Service (WPS) designed to compute the likelihood of finding ecosystems with similar conditions. Starting from a reference area, typically a protected area, one can compute for each pixel of a region of interest the probability to find a combination of a set of predefined environmental indicators that is similar to the one observed in the reference area using the Mahalanobis distances to the mean and covariance of these indicators. Inputs to the WPS are thus the reference polygon and a set of environmental indicators, typically thematic geospatial “layers”, which can be discovered using standardised catalogues. The outputs can be tailored to specific end user needs in terms of data format and data resolution. Because these input layers can range from geophysical data captured through remote sensing to socio-economical indicators, eHabitat is exposed to a broad range of different types and levels of uncertainties which are inevitably propagated through the service (see e.g. Heuvelink, 1998). Potentially chained to other services to perform ecological forecasting, for example, eHabitat would be an additional component further propagating uncertainties from a potentially long chain of model services. Such a configuration of distributed data and model services as envisaged by initiatives such as the “Model Web” from the Group on Earth Observations, to be of any use to policy or decision makers, requires from users clear information on data uncertainties. The development of such an Uncertainty-Enabled Model Web is the scope of the UncertWEB project which is promoting interoperability between data and models with quantified uncertainty and building a framework on existing open, international standards. It is the objective of this paper to illustrate a few key ideas behind UncertWeb using eHabitat to discuss the main types of uncertainties the WPS has to deal with and to present the benefits of the use of the UncertWeb framework.

Confronting uncertainty in model-based geostatistics using Markov Chain Monte Carlo simulation

by Budiman Minasny

This paper demonstrates the use of Markov Chain Monte Carlo (MCMC) simulation for parameter inference in model-based... more This paper demonstrates the use of Markov Chain Monte Carlo (MCMC) simulation for parameter inference in model-based soil geostatistics. We implemented the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm to jointly summarize the posterior distribution of variogram parameters and the coefficients of a linear spatial model, and derive estimates of predictive uncertainty. The DREAM method runs multiple different Markov chains in parallel and jumps in each chain are generated from a discrete proposal distribution containing a fixed multiple of the difference of the states of
randomly chosen pairs of other chains. This approach automatically scales the orientation and scale of the proposal distribution, and is especially designed to maintain detailed balance and ergodicity, thereby generating an exact approximation of the posterior probability density function (pdf) of the parameters of the linear model and variogram. This approach is tested using three different data sets from Australia involving
variogram estimation of soil thickness, kriging of soil pH, and spatial prediction of soil organic carbon content.
The results showed some advantages of MCMC over the conventional method of moments and residual maximum likelihood (REML) estimation. The posterior pdf derived with MCMC conveys important information about parameter uncertainty, multi-dimensional parameter correlation, and thus how many significant parameters are warranted by the calibration data. Parameter uncertainty constitutes only a small
part of total prediction uncertainty for the case studies considered here. The prediction accuracies using MCMC and REML are similar. The variogram estimated using conventional approaches (method of moments, and without simulation) lies within the 95% prediction uncertainty interval of the posterior distribution
derived with DREAM. Altogether our results show that conventional kriging and regression-kriging still
remain a viable option for production mapping.

Geographic parthenogenesis in a consumer-resource model for sexual reproduction.

by Yixian Song

Stefan Scheu and Barbara Drossel

The phenomenon of geographic parthenogenesis is closely tied to the question of why sexual reproduction is the... more The phenomenon of geographic parthenogenesis is closely tied to the question of why sexual reproduction is the dominant mode of reproduction in animals and plants. Geographic parthenogenesis describes the fact that many species reproduce asexually at the boundaries of their range. We present a mathematical model that derives the dominance of sexuals at the center and the dominance of asexuals at the boundary of a species' range from exactly the same mechanism. Our model is based on a set of resources that regrow slowly and that can be consumed only by those individuals that have a suitable genotype. Genotype is implemented by a multilocus model with two alleles at each locus, and with free recombination during production of sexual offspring. The model is tailored to seasonal species with intermittent mixis and low survival of offspring, such as Daphnia and aphids. Several patches of resources are arranged in a row, with a gradient of those parameters that typically vary through the range of species. By letting sexually and asexually reproducing populations compete, we obtain the typical patterns of geographic parthenogenesis.

Temporal patterns of resource usage in an ecological model for sexual reproduction and geographic parthenogenesis

by Yixian Song

Co-authored with Barbara Drossel and Stefan Scheu

Questions: How are the prevalence of sexual reproduction and the phenomenon of geographic
parthenogenesis related... more Questions: How are the prevalence of sexual reproduction and the phenomenon of geographic
parthenogenesis related to resource availability? What is the pattern in space of resource and
consumer dynamics?
Mathematical methods: A population dynamics model with structured resources in short
supply, including a spatial gradient of consumer mortality and resource diversity. Species are
modelled using quantitative genetics, combined with random mating for sexuals and clonal
reproduction for asexuals.
Key assumptions: Resources are limited and re-grow slowly. Only a few consumer genotypes
can co-exist locally. The twofold cost of sex is incurred once per season.
Conclusions: The advantage of sexual reproduction is due to the ability of the sexual
population to generate offspring that can use resources that have not been exploited for some
time. Resource use of the sexual population, therefore, changes continuously. This advantage
is most significant at the centre of a species’ range.

Modelling trade offs between public and private conservation policies

by Ascelin Gordon

published in 'Biological Conservation' in 2011

To reduce global biodiversity loss, there is an urgent need to determine the most efficient allocation of conservation... more To reduce global biodiversity loss, there is an urgent need to determine the most efficient allocation of conservation resources. Recently, there has been a growing trend for many governments to supplement public ownership and management of reserves with incentive programs for conservation on private land. At the same time, policies to promote conservation on private land are rarely evaluated in terms of their ecological consequences. This raises important questions, such as the extent to which private land con- servation can improve conservation outcomes, and how it should be mixed with more traditional public land conservation. We address these questions, using a general framework for modelling environmental policies and a case study examining the conservation of endangered native grasslands to the west of Mel- bourne, Australia. Specifically, we examine three policies that involve: (i) spending all resources on cre- ating public conservation areas; (ii) spending all resources on an ongoing incentive program where private landholders are paid to manage vegetation on their property with 5-year contracts; and (iii) split- ting resources between these two approaches. The performance of each strategy is quantified with a veg- etation condition change model that predicts future changes in grassland quality. Of the policies tested, no one policy was always best and policy performance depended on the objectives of those enacting the policy. This work demonstrates a general method for evaluating environmental policies and highlights the utility of a model which combines ecological and socioeconomic processes.

Assessing the impacts of biodiversity offset policies

by Ascelin Gordon

published in Environmental Modelling & Software

In response to the increasing loss of native vegetation and biodiversity, a growing number of countries have adopted... more In response to the increasing loss of native vegetation and biodiversity, a growing number of countries have adopted “offsetting” policies that seek to balance local habitat destruction by restoring, enhancing and/or protecting similar but separate habitat. Although these policies often have a stated aim of producing a “net gain” or “no net loss” in environmental benefits, it is challenging to determine the potential impacts of a policy and if, or when, it will achieve its objectives. In this paper we address these questions with a general approach that uses predictive modelling under uncertainty to quantify the ecological impacts of different offset policies. This is demonstrated with a case study to the west of Melbourne, Australia where a proposed expansion of Melbourne’s urban growth boundary would result in a loss of endangered native grassland, requiring offsets to be implemented as compensation. Three different offset policies were modelled: i) no restrictions on offset location, ii) offset locations spatially restricted to a strategically de␣ned area and iii) offset locations spatially and temporally restricted, requiring all offsets to be implemented before commencing development. The ecological impact of the policies was determined with a system model that predicts future changes in the extent and condition of native grassland. The case study demonstrates how relative and absolute policy performance can be quanti␣ed in relation to best and worst-case scenarios. The study also shows that the ecological bene␣ts of being temporally and spatially strategic in choosing offsets locations are substantially greater than being spatially strategic alone. We also show that even with considerable uncertainties in the system model predicting future grassland condition, the performance of the three offset policies can still be differentiated. Finally, we show the extent to which a policy achieves a “net gain” is dependent on the baseline against which policy performance is measured. The quantitative framework presented here can also be used to evaluate other offset policies or extended to deal with different types of environmental policies.