Rainfall spatial predictions: a two-part model and its assessment

Spatial prediction of hourly rainfall via radar calibration is addressed. The change of support problem (COSP), arising when the spatial supports of different data sources do not coincide, is faced in a non-Gaussian setting; in fact, hourly rainfall in Emilia-Romagna region, in Italy, is characterized by abundance of zero values and right-skeweness of the distribution of positive amounts. Rain gauge direct measurements on sparsely distributed locations and hourly cumulated radar grids are provided by the ARPA-SIMC Emilia-Romagna. We propose a three-stage Bayesian hierarchical model for radar calibration, exploiting rain gauges as reference measure. Rain probability and amounts are modeled via linear relationships with radar in the log scale; spatial correlated Gaussian effects capture the residual information. We employ a probit link for rainfall probability and Gamma distribution for rainfall positive amounts; the two steps are joined via a two-part semicontinuous model. Three model specifications differently addressing COSP are presented; in particular, a stochastic weighting of all radar pixels, driven by a latent Gaussian process defined on the grid, is employed. Estimation is performed via MCMC procedures implemented in C, linked to R software. Communication and evaluation of probabilistic, point and interval predictions is investigated. A non-randomized PIT histogram is proposed for correctly assessing calibration and coverage of two-part semicontinuous models. Predictions obtained with the different model specifications are evaluated via graphical tools (Reliability Plot, Sharpness Histogram, PIT Histogram, Brier Score Plot and Quantile Decomposition Plot), proper scoring rules (Brier Score, Continuous Rank Probability Score) and consistent scoring functions (Root Mean Square Error and Mean Absolute Error addressing the predictive mean and median, respectively). Calibration is reached and the inclusion of neighbouring information slightly improves predictions. All specifications outperform a benchmark model with incorrelated effects, confirming the relevance of spatial correlation for modeling rainfall probability and accumulation.

Spatial and temporal characterisation of ground deformation recorded by geodetic techniques

A critical point in the analysis of ground displacements time series is the development of data driven methods that allow the different sources that generate the observed displacements to be discerned and characterised. A widely used multivariate statistical technique is the Principal Component Analysis (PCA), which allows reducing the dimensionality of the data space maintaining most of the variance of the dataset explained. Anyway, PCA does not perform well in finding the solution to the so-called Blind Source Separation (BSS) problem, i.e. in recovering and separating the original sources that generated the observed data. This is mainly due to the assumptions on which PCA relies: it looks for a new Euclidean space where the projected data are uncorrelated. The Independent Component Analysis (ICA) is a popular technique adopted to approach this problem. However, the independence condition is not easy to impose, and it is often necessary to introduce some approximations. To work around this problem, I use a variational bayesian ICA (vbICA) method, which models the probability density function (pdf) of each source signal using a mix of Gaussian distributions. This technique allows for more flexibility in the description of the pdf of the sources, giving a more reliable estimate of them. Here I present the application of the vbICA technique to GPS position time series. First, I use vbICA on synthetic data that simulate a seismic cycle (interseismic + coseismic + postseismic + seasonal + noise) and a volcanic source, and I study the ability of the algorithm to recover the original (known) sources of deformation. Secondly, I apply vbICA to different tectonically active scenarios, such as the 2009 L'Aquila (central Italy) earthquake, the 2012 Emilia (northern Italy) seismic sequence, and the 2006 Guerrero (Mexico) Slow Slip Event (SSE).

Trial history biases the spatial programming of antisaccades

The historical context in which saccades are made influences their latency and error rates, but less is known about how context influences their spatial parameters. We recently described a novel spatial bias for antisaccades, in which the endpoints of these responses deviate towards alternative goal locations used in the same experimental block, and showed that expectancy (prior probability) is at least partly responsible for this 'alternate-goal bias'. In this report we asked whether trial history also plays a role. Subjects performed antisaccades to a stimulus randomly located on the horizontal meridian, on a 40° angle downwards from the horizontal meridian, or on a 40° upward angle, with all three locations equally probable on any given trial. We found that the endpoints of antisaccades were significantly displaced towards the goal location of not only the immediately preceding trial (n - 1) but also the penultimate (n - 2) trial. Furthermore, this bias was mainly present for antisaccades with a short latency of <250 ms and was rapidly corrected by secondary saccades. We conclude that the location of recent antisaccades biases the spatial programming of upcoming antisaccades, that this historical effect persists over many seconds, and that it influences mainly rapidly generated eye movements. Because corrective saccades eliminate the historical bias, we suggest that the bias arises in processes generating the response vector, rather than processes generating the perceptual estimate of goal location.

Probability inundation map for a scenario combining storm surge and sea-level rise

Coastal managers require reliable spatial data on the extent and timing of potential coastal inundation, particularly in a changing climate. Most sea level rise (SLR) vulnerability assessments are undertaken using the easily implemented bathtub approach, where areas adjacent to the sea and below a given elevation are mapped using a deterministic line dividing potentially inundated from dry areas. This method only requires elevation data usually in the form of a digital elevation model (DEM). However, inherent errors in the DEM and spatial analysis of the bathtub model propagate into the inundation mapping. The aim of this study was to assess the impacts of spatially variable and spatially correlated elevation errors in high-spatial resolution DEMs for mapping coastal inundation. Elevation errors were best modelled using regression-kriging. This geostatistical model takes the spatial correlation in elevation errors into account, which has a significant impact on analyses that include spatial interactions, such as inundation modelling. The spatial variability of elevation errors was partially explained by land cover and terrain variables. Elevation errors were simulated using sequential Gaussian simulation, a Monte Carlo probabilistic approach. 1,000 error simulations were added to the original DEM and reclassified using a hydrologically correct bathtub method. The probability of inundation to a scenario combining a 1 in 100 year storm event over a 1 m SLR was calculated by counting the proportion of times from the 1,000 simulations that a location was inundated. This probabilistic approach can be used in a risk-aversive decision making process by planning for scenarios with different probabilities of occurrence. For example, results showed that when considering a 1% probability exceedance, the inundated area was approximately 11% larger than mapped using the deterministic bathtub approach. The probabilistic approach provides visually intuitive maps that convey uncertainties inherent to spatial data and analysis.

Probability sampling protocol of classification maps from spaceborne/airborne image

To deliver sample estimates provided with the necessary probability foundation to permit generalization from the sample data subset to the whole target population being sampled, probability sampling strategies are required to satisfy three necessary not sufficient conditions: (i) All inclusion probabilities be greater than zero in the target population to be sampled. If some sampling units have an inclusion probability of zero, then a map accuracy assessment does not represent the entire target region depicted in the map to be assessed. (ii) The inclusion probabilities must be: (a) knowable for nonsampled units and (b) known for those units selected in the sample: since the inclusion probability determines the weight attached to each sampling unit in the accuracy estimation formulas, if the inclusion probabilities are unknown, so are the estimation weights. This original work presents a novel (to the best of these authors' knowledge, the first) probability sampling protocol for quality assessment and comparison of thematic maps generated from spaceborne/airborne Very High Resolution (VHR) images, where: (I) an original Categorical Variable Pair Similarity Index (CVPSI, proposed in two different formulations) is estimated as a fuzzy degree of match between a reference and a test semantic vocabulary, which may not coincide, and (II) both symbolic pixel-based thematic quality indicators (TQIs) and sub-symbolic object-based spatial quality indicators (SQIs) are estimated with a degree of uncertainty in measurement in compliance with the well-known Quality Assurance Framework for Earth Observation (QA4EO) guidelines. Like a decision-tree, any protocol (guidelines for best practice) comprises a set of rules, equivalent to structural knowledge, and an order of presentation of the rule set, known as procedural knowledge. The combination of these two levels of knowledge makes an original protocol worth more than the sum of its parts. The several degrees of novelty of the proposed probability sampling protocol are highlighted in this paper, at the levels of understanding of both structural and procedural knowledge, in comparison with related multi-disciplinary works selected from the existing literature. In the experimental session the proposed protocol is tested for accuracy validation of preliminary classification maps automatically generated by the Satellite Image Automatic MapperT (SIAMT) software product from two WorldView-2 images and one QuickBird-2 image provided by DigitalGlobe for testing purposes. In these experiments, collected TQIs and SQIs are statistically valid, statistically significant, consistent across maps and in agreement with theoretical expectations, visual (qualitative) evidence and quantitative quality indexes of operativeness (OQIs) claimed for SIAMT by related papers. As a subsidiary conclusion, the statistically consistent and statistically significant accuracy validation of the SIAMT pre-classification maps proposed in this contribution, together with OQIs claimed for SIAMT by related works, make the operational (automatic, accurate, near real-time, robust, scalable) SIAMT software product eligible for opening up new inter-disciplinary research and market opportunities in accordance with the visionary goal of the Global Earth Observation System of Systems (GEOSS) initiative and the QA4EO international guidelines.

Modelled spatial and seasonal distribution of Blue Whiting (Micromesistius poutassou) larvae in the North-East Atlantic (1951 to 2005)

Blue whiting (Micromesistius poutassou, http://www.marinespecies.org/aphia.php?p=taxdetails&id=126439) is a small mesopelagic planktivorous gadoid found throughout the North-East Atlantic. This data contains the results of a model-based analysis of larvae captured by the Continuous Plankton Recorder (CPR) during the period 1951-2005. The observations are analysed using Generalised Additive Models (GAMs) of the the spatial, seasonal and interannual variation in the occurrence of larvae. The best fitting model is chosen using the Aikaike Information Criteria (AIC). The probability of occurrence in the continous plankton recorder is then normalised and converted to a probability distribution function in space (UTM projection Zone 28) and season (day of year). The best fitting model splits the distribution into two separate spawning grounds north and south of a dividing line at 53 N. The probability distribution is therefore normalised in these two regions (ie the space-time integral over each of the two regions is 1). The modelled outputs are on a UTM Zone 28 grid: however, for convenience, the latitude ("lat") and longitude ("lon") of each of these grid points are also included as a variable in the NetCDF file. The assignment of each grid point to either the Northern or Southern component (defined here as north/south of 53 N), is also included as a further variable ("component"). Finally, the day of year ("doy") is stored as the number of days elapsed from and included January 1 (ie doy=1 on January 1) - the year is thereafter divided into 180 grid points.

Mach Bands: multi-scale spatial filtering and co-operative coding of edges and bars

Perception of Mach bands may be explained by spatial filtering ('lateral inhibition') that can be approximated by 2nd derivative computation, and several alternative models have been proposed. To distinguish between them, we used a novel set of ‘generalised Gaussian’ images, in which the sharp ramp-plateau junction of the Mach ramp was replaced by smoother transitions. The images ranged from a slightly blurred Mach ramp to a Gaussian edge and beyond, and also included a sine-wave edge. The probability of seeing Mach Bands increased with the (relative) sharpness of the junction, but was largely independent of absolute spatial scale. These data did not fit the predictions of MIRAGE, nor 2nd derivative computation at a single fine scale. In experiment 2, observers used a cursor to mark features on the same set of images. Data on perceived position of Mach bands did not support the local energy model. Perceived width of Mach bands was poorly explained by a single-scale edge detection model, despite its previous success with Mach edges (Wallis & Georgeson, 2009, Vision Research, 49, 1886-1893). A more successful model used separate (odd and even) scale-space filtering for edges and bars, local peak detection to find candidate features, and the MAX operator to compare odd- and even-filter response maps (Georgeson, VSS 2006, Journal of Vision 6(6), 191a). Mach bands are seen when there is a local peak in the even-filter (bar) response map, AND that peak value exceeds corresponding responses in the odd-filter (edge) maps.

Spatial pattern analysis of beta-amyloid (A beta) deposits in Alzheimer disease by linear regression

The spatial patterns of discrete beta-amyloid (Abeta) deposits in brain tissue from patients with Alzheimer disease (AD) were studied using a statistical method based on linear regression, the results being compared with the more conventional variance/mean (V/M) method. Both methods suggested that Abeta deposits occurred in clusters (400 to <12,800 mu m in diameter) in all but 1 of the 42 tissues examined. In many tissues, a regular periodicity of the Abeta deposit clusters parallel to the tissue boundary was observed. In 23 of 42 (55%) tissues, the two methods revealed essentially the same spatial patterns of Abeta deposits; in 15 of 42 (36%), the regression method indicated the presence of clusters at a scale not revealed by the V/M method; and in 4 of 42 (9%), there was no agreement between the two methods. Perceived advantages of the regression method are that there is a greater probability of detecting clustering at multiple scales, the dimension of larger Abeta clusters can be estimated more accurately, and the spacing between the clusters may be estimated. However, both methods may be useful, with the regression method providing greater resolution and the V/M method providing greater simplicity and ease of interpretation. Estimates of the distance between regularly spaced Abeta clusters were in the range 2,200-11,800 mu m, depending on tissue and cluster size. The regular periodicity of Abeta deposit clusters in many tissues would be consistent with their development in relation to clusters of neurons that give rise to specific neuronal projections.

Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges

Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding. © 2012 ARVO.

Spatial relationships between diffuse prion protein deposits and neuronal perikarya in variant Creutzfeldt-Jakob disease

Two morphological types of prion protein (PrPsc) deposit occur in the cerebral cortex of cases of variant Creutzfeldt-Jakob disease (vCJD), viz., diffuse and florid deposits. The objective of this study was to determine whether diffuse-type PrPsc deposits in areas of the cerebral cortex in six cases of the variant form of CJD (vCJD) were spatially correlated with neurons and whether diffuse deposit size was related to the number of adjacent neurons contributing PrPsc. In cortical gyri, density of surviving neurons was 5.38-12.15 per 50 × 200 µm sample field, neurons being distributed randomly, regularly or were clustered relative to the pia mater. Density of neurons embedded within diffuse deposits, however, was three to eight times their overall density in the section. In addition, diffuse deposit area was positively correlated with the number of embedded neurons. The frequency distribution of diffuse deposits with 0, 1, 2, 3, …, n, embedded neurons did not deviate from a Poisson distribution. These results suggest: (1) diffuse deposits in vCJD develop in situ as a result of the formation of PrPsc in relation to clusters of neurons, (2) size of a diffuse deposit is determined by the number of adjacent neurons which develop PrPsc, and (3) the probability that PrPsc is formed in relation to one neuron is independent of that of its neighbour.

On the eigenvalues of the spatial sign covariance matrix in more than two dimensions

Acknowledgments Alexander Dürre was supported in part by the Collaborative Research Grant 823 of the German Research Foundation. David E. Tyler was supported in part by the National Science Foundation grant DMS-1407751. A visit of Daniel Vogel to David E. Tyler was supported by a travel grant from the Scottish Universities Physics Alliance. The authors are grateful to the editors and referees for their constructive comments.

Strong inference from transect sign surveys : combining spatial autocorrelation and misclassification occupancy models to quantify the detectability of a recovering carnivore

Funding — Forest Enterprise Scotland and the University of Aberdeen provided funding for the project. The Carnegie Trust supported the lead author, E. McHenry, in this research through the award of a tuition fees bursary.

Data to Decision in a Dynamic Ocean: Robust Species Distribution Models and Spatial Decision Frameworks

Human use of the oceans is increasingly in conflict with conservation of endangered species. Methods for managing the spatial and temporal placement of industries such as military, fishing, transportation and offshore energy, have historically been post hoc; i.e. the time and place of human activity is often already determined before assessment of environmental impacts. In this dissertation, I build robust species distribution models in two case study areas, US Atlantic (Best et al. 2012) and British Columbia (Best et al. 2015), predicting presence and abundance respectively, from scientific surveys. These models are then applied to novel decision frameworks for preemptively suggesting optimal placement of human activities in space and time to minimize ecological impacts: siting for offshore wind energy development, and routing ships to minimize risk of striking whales. Both decision frameworks relate the tradeoff between conservation risk and industry profit with synchronized variable and map views as online spatial decision support systems.

For siting offshore wind energy development (OWED) in the U.S. Atlantic (chapter 4), bird density maps are combined across species with weights of OWED sensitivity to collision and displacement and 10 km2 sites are compared against OWED profitability based on average annual wind speed at 90m hub heights and distance to transmission grid. A spatial decision support system enables toggling between the map and tradeoff plot views by site. A selected site can be inspected for sensitivity to a cetaceans throughout the year, so as to capture months of the year which minimize episodic impacts of pre-operational activities such as seismic airgun surveying and pile driving.

Routing ships to avoid whale strikes (chapter 5) can be similarly viewed as a tradeoff, but is a different problem spatially. A cumulative cost surface is generated from density surface maps and conservation status of cetaceans, before applying as a resistance surface to calculate least-cost routes between start and end locations, i.e. ports and entrance locations to study areas. Varying a multiplier to the cost surface enables calculation of multiple routes with different costs to conservation of cetaceans versus cost to transportation industry, measured as distance. Similar to the siting chapter, a spatial decisions support system enables toggling between the map and tradeoff plot view of proposed routes. The user can also input arbitrary start and end locations to calculate the tradeoff on the fly.

Essential to the input of these decision frameworks are distributions of the species. The two preceding chapters comprise species distribution models from two case study areas, U.S. Atlantic (chapter 2) and British Columbia (chapter 3), predicting presence and density, respectively. Although density is preferred to estimate potential biological removal, per Marine Mammal Protection Act requirements in the U.S., all the necessary parameters, especially distance and angle of observation, are less readily available across publicly mined datasets.

In the case of predicting cetacean presence in the U.S. Atlantic (chapter 2), I extracted datasets from the online OBIS-SEAMAP geo-database, and integrated scientific surveys conducted by ship (n=36) and aircraft (n=16), weighting a Generalized Additive Model by minutes surveyed within space-time grid cells to harmonize effort between the two survey platforms. For each of 16 cetacean species guilds, I predicted the probability of occurrence from static environmental variables (water depth, distance to shore, distance to continental shelf break) and time-varying conditions (monthly sea-surface temperature). To generate maps of presence vs. absence, Receiver Operator Characteristic (ROC) curves were used to define the optimal threshold that minimizes false positive and false negative error rates. I integrated model outputs, including tables (species in guilds, input surveys) and plots (fit of environmental variables, ROC curve), into an online spatial decision support system, allowing for easy navigation of models by taxon, region, season, and data provider.

For predicting cetacean density within the inner waters of British Columbia (chapter 3), I calculated density from systematic, line-transect marine mammal surveys over multiple years and seasons (summer 2004, 2005, 2008, and spring/autumn 2007) conducted by Raincoast Conservation Foundation. Abundance estimates were calculated using two different methods: Conventional Distance Sampling (CDS) and Density Surface Modelling (DSM). CDS generates a single density estimate for each stratum, whereas DSM explicitly models spatial variation and offers potential for greater precision by incorporating environmental predictors. Although DSM yields a more relevant product for the purposes of marine spatial planning, CDS has proven to be useful in cases where there are fewer observations available for seasonal and inter-annual comparison, particularly for the scarcely observed elephant seal. Abundance estimates are provided on a stratum-specific basis. Steller sea lions and harbour seals are further differentiated by ‘hauled out’ and ‘in water’. This analysis updates previous estimates (Williams & Thomas 2007) by including additional years of effort, providing greater spatial precision with the DSM method over CDS, novel reporting for spring and autumn seasons (rather than summer alone), and providing new abundance estimates for Steller sea lion and northern elephant seal. In addition to providing a baseline of marine mammal abundance and distribution, against which future changes can be compared, this information offers the opportunity to assess the risks posed to marine mammals by existing and emerging threats, such as fisheries bycatch, ship strikes, and increased oil spill and ocean noise issues associated with increases of container ship and oil tanker traffic in British Columbia’s continental shelf waters.

Starting with marine animal observations at specific coordinates and times, I combine these data with environmental data, often satellite derived, to produce seascape predictions generalizable in space and time. These habitat-based models enable prediction of encounter rates and, in the case of density surface models, abundance that can then be applied to management scenarios. Specific human activities, OWED and shipping, are then compared within a tradeoff decision support framework, enabling interchangeable map and tradeoff plot views. These products make complex processes transparent for gaming conservation, industry and stakeholders towards optimal marine spatial management, fundamental to the tenets of marine spatial planning, ecosystem-based management and dynamic ocean management.

GIS technologies and spatial organization patterns among hunter-gatherers: an archaeological case study from Southern Patagonia (southern South America)

This paper discusses some aspects of hunter-gatherer spatial organization in southern South Patagonia, in later times to 10,000 cal yr BP. Various methods of spatial analysis, elaborated with a Geographic Information System (GIS) were applied to the distributional pattern of archaeological sites with radiocarbon dates. The shift in the distributional pattern of chronological information was assessed in conjunction with other lines of evidence within a biogeographic framework. Accordingly, the varying degrees of occupation and integration of coastal and interior spaces in human spatial organization are explained in association with the adaptive strategies hunter-gatherers have used over time. Both are part of the same human response to changes in risk and uncertainty variability in the region in terms of resource availability and environmental dynamics.

Spatial modeling of data with excessive zeros applied to reindeer pellet-group counts

We analyze a real data set pertaining to reindeer fecal pellet-group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi-Poisson hierarchical generalized linear model (HGLM), zero-inflated Poisson (ZIP), and hurdle models. The quasi-Poisson HGLM allows for both under- and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi-Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi-Poisson HGLM with spatial random effects.