Nearest neighbor methods for testing reflexivity

Nearest neighbor (NN) methods are widely employed for drawing inferences about spatial point patterns of two or more classes. We introduce a method for testing reflexivity in the NN structure (i.e., NN reflexivity) based on a contingency table which will be called reflexivity contingency table (RCT) henceforth. The RCT is based on the NN relationships among the data points and was used for testing niche specificity in literature, but we demonstrate that it is actually more appropriate for testing the NN reflexivity pattern. We derive the asymptotic distribution of the entries of the RCT under random labeling and introduce tests of reflexivity based on these entries. We also consider Pielou’s approach on RCT and show that it is not appropriate for completely mapped spatial data. We determine the appropriate null hypotheses and the underlying conditions/assumptions required for all tests considered. We investigate the finite sample performance of the tests in terms of empirical size and power by extensive Monte Carlo simulations and illustrate the methods on two real-life ecological data sets.     

Fourth-corner correlation is a score test statistic in a log-linear trait–environment model that is useful in permutation testing

Ecologists wish to understand the role of traits of species in determining where each species occurs in the environment. For this, they wish to detect associations between species traits and environmental variables from three data tables, species count data from sites with associated environmental data and species trait data from data bases. These three tables leave a missing part, the fourth-corner. The fourth-corner correlations between quantitative traits and environmental variables, heuristically proposed 20 years ago, fill this corner. Generalized linear (mixed) models have been proposed more recently as a model-based alternative. This paper shows that the squared fourth-corner correlation times the total count is precisely the score test statistic for testing the linear-by-linear interaction in a Poisson log-linear model that also contains species and sites as main effects. For multiple traits and environmental variables, the score test statistic is proportional to the total inertia of a doubly constrained correspondence analysis. When the count data are over-dispersed compared to the Poisson or when there are other deviations from the model such as unobserved traits or environmental variables that interact with the observed ones, the score test statistic does not have the usual chi-square distribution. For these types of deviations, row- and column-based permutation methods (and their sequential combination) are proposed to control the type I error without undue loss of power (unless no deviation is present), as illustrated in a small simulation study. The issues for valid statistical testing are illustrated using the well-known Dutch Dune Meadow data set.     

A graphical assessment and spatial clustering of the Deepwater Horizon oil spill impact on Laughing Gulls

The Deepwater Horizon oil spill occurred in the Gulf of Mexico on April 20, 2010. Considered the largest accidental marine oil spill in history, oil flowed for three months and approximately five million barrels of oil spilled through by mid-July 2010. In this article, we analyze bird data to assess the impact of the oil spill on the Gulf wildlife. Particularly, we want to determine in which regions Laughing Gulls were mostly affected by the oil spill, and whether those regions spatially shifted throughout the year 2010. Though our data sets have some limitations to apply statistical analysis methods, we obtained very interesting results. Our analyses showed the general consistency of the results based on two population data sets (from the 2011 Data Expo and from the eBird community) and justified the use of both publicly available data sets. We showed that the closer the surface oil spill area approached to the Laughing Gulls habitats, the more significant clusters of bird cases were observed.     

Investigating the link between $$\hbox {PM}_{2.5}$$ and atmospheric profile variables via penalized functional quantile regression

Fine particulate matter (\(\hbox {PM}_{2.5}\)) events negatively affect the health of numerous persons globally each year. Previous works have described the association between air pollution and surface-level meteorological conditions; however, there has been less focus on the task of linking air pollution events with meteorological conditions at higher levels of the atmosphere. Working within the functional data framework, we develop a penalized functional quantile regression (PFQR) procedure to model conditional quantiles of a continuous response based on a functional covariate, with the ability to penalize selected derivatives of the estimated coefficient function. Our aim is to investigate the relationship between atmospheric profile variables (APVs), assumed to be functional, and key quantiles of the conditional distribution of surface-level \(\hbox {PM}_{2.5}\). Via a simulation study, we find that the performance of our PFQR procedure compares favorably to other related approaches. We conclude with an analysis of \(\hbox {PM}_{2.5}\) data at two Southeastern US locations, Columbia, SC and Tampa, FL, where we estimate the coefficient functions for the APVs corresponding to both ‘typical’ and ‘high’ \(\hbox {PM}_{2.5}\) events. As we believe that the true coefficient functions are smooth and may be exactly zero over subsets of their domains, we impose penalties on the 0th and 2nd derivatives. Our analysis indicates that the corresponding atmospheric conditions differ between the two locations, and that the conditions differ seasonally within location.     

Comparing canopy leaf temperature of three Central European tree species based on simultaneous confidence bands for penalized splines

Temperature is an important physical factor that is known to strongly affect biodiversity as well as ecosystems and their functioning. However, research in this area is still relatively limited; this may also be attributed to the multitude of influencing factors and the complexity of the statistics involved. This study analyzes the differences between the surface temperature of three Central European broadleaf tree species. A better understanding of these differences may help to elucidate the role of microclimate in biodiversity. We consider a time series of high-resolution thermal images taken from a meteorological observation tower and calculate mean canopy leaf temperatures for beech, ash and maple (Fagus silvatica, Fraxinus excelsior and Acer pseudoplatanus). In a first step, comparable image areas are extracted from the thermal image sections of the crown of each tree species avoiding shadow areas, branches, etc. We used an automatic segmentation technique, the Otsu thresholding. Extracted canopy leaf temperature values were then processed and the resulting temperature profiles estimated by O’Sullivan penalized splines. For comparing the differences in canopy leaf temperature over time, we propose the construction of simultaneous confidence bands. The analyses show that there are significant—though small—differences in canopy surface temperature between the three tree species.     

Estimation bias under model selection for distance sampling detection functions

Many simulation studies have examined the properties of distance sampling estimators of wildlife population size. When assumptions hold, if distances are generated from a detection model and fitted using the same model, they are known to perform well. However, in practice, the true model is unknown. Therefore, standard practice includes model selection, typically using model comparison tools like Akaike Information Criterion. Here we examine the performance of standard distance sampling estimators under model selection. We compare line and point transect estimators with distances simulated from two detection functions, hazard-rate and exponential power series (EPS), over a range of sample sizes. To mimic the real-world context where the true model may not be part of the candidate set, EPS models were not included as candidates, except for the half-normal parameterization. We found median bias depended on sample size (being asymptotically unbiased) and on the form of the true detection function: negative bias (up to 15% for line transects and 30% for point transects) when the shoulder of maximum detectability was narrow, and positive bias (up to 10% for line transects and 15% for point transects) when it was wide. Generating unbiased simulations requires careful choice of detection function or very large datasets. Practitioners should collect data that result in detection functions with a shoulder similar to a half-normal and use the monotonicity constraint. Narrow-shouldered detection functions can be avoided through good field procedures and those with wide shoulder are unlikely to occur, due to heterogeneity in detectability.     

Experimental assessment of characteristic turbulent scales in two-phase flow of hydraulic jump: from bottom to free surface

A hydraulic jump is a turbulent shear flow with a free-surface roller. The turbulent flow pattern is characterised by the development of instantaneous three-dimensional turbulent structures throughout the air–water column up to the free surface. The length and time scales of the turbulent structures are key information to describe the turbulent processes, which is of significant importance for the improvement of numerical models and physical measurement techniques. However, few physical data are available so far due to the complexity of the measurement. This paper presents an investigation of a series of characteristic turbulent scales for hydraulic jumps, covering the length and time scales of turbulent flow structures in bubbly flow, on free surface and at the impingement point. The bubbly-flow turbulent scales are obtained for Fr = 7.5 with 3.4 × 10⁴ < Re < 1.4 × 10⁵ in both longitudinal and transverse directions, and are compared with the free-surface scales. The results highlight three-dimensional flow patterns with anisotropic turbulence field. The turbulent structures are observed with different length and time scales respectively in the shear flow region and free-surface recirculation region. The bubbly structures next to the roller surface and the free-surface fluctuation structures show comparable length and time scales, both larger than the scales of vortical structures in the shear flow and smaller than the scales of impingement perimeter at the jump toe. A decomposition of physical signals indicates that the large turbulent scales are related to the unsteady motion of the flow in the upper part of the roller, while the high-frequency velocity turbulence dominates in the lower part of the roller. Scale effects cannot be ignored for Reynolds number smaller than 4 × 10⁴, mainly linked to the formation of large eddies in the shear layer. The present study provides a comprehensive assessment of turbulent scales in hydraulic jump, including the analyses of first data set of longitudinal bubbly-flow integral scales and transverse jump toe perimeter integral scales.     

Modeling and data assessment of longitudinal salinity in a low-gradient estuarine river

Continuous data of vertical-profile salinity were analyzed for four stations located successively upriver in a macrotidal estuary, the lower St. Johns River (Northeast Florida, USA). The data analysis confirmed well-mixed salinity conditions in the river with at most 1.3 ppt of vertical variability at Dames Point (river km 20), where the main variations of salinity are along the longitudinal axis of the river. Given the well-mixed salinity conditions and dominant horizontal structure of salinity variations in the river, we present and apply a barotropic, two-dimensional modeling approach for hydrodynamic-salinity transport simulation in the lower St. Johns River. When properly forced by offshore surge, high-resolution wind fields and freshwater river inflows, the model replicated the salinity measurements remarkably well, including the separation into tidal and sub-tidal components. The data and model results show that, at times, offshore winds and surge can be more influential on longitudinal salinity variations than local winds over the river. We demonstrate the importance of using proper boundary conditions to force the model relative to the minimal sensitivity of the model to parameter adjustment of horizontal mixing and uncertainty-based perturbation of wind and inflow forcings.     

Direct measurements of the drag force over aligned arrays of cubes exposed to boundary-layer flows

Wind tunnel measurements of the total drag force for aligned arrays of cubes exposed to two different boundary-layer flows at three flow velocities are discussed. The drag force for eight different building packing densities λ _p (from 0.028 to 1) is measured with a standard load cell generating a novel dataset. Different λ _p are reproduced by increasing the number of buildings on the same lot area; this represents a real situation that an urban planner is faced with when a lot area of a given (fixed) size is allocated to the development of new built areas. It is assumed that the surrounding terrain is uniform and there is a transition from a given roughness (smooth) to a new roughness (rough). The approaching flow will adjust itself over the new surface within a distance that in general may be larger than the horizontal length covered by the array. We investigate the region where the flow adjustment occurs. The wide range of packing densities allowed us to analyse in detail the evolution of the drag force. The drag force increases with increasing packing densities until it reaches a maximum at an intermediate packing density (λ _p  = 0.25 in our case) followed by a slight decrease at larger packing densities. The value of the drag force depends on the flow adjustment along the array which is evaluated by introducing the parameter “drag area” to retrieve information about the drag distribution at different λ _p . Results clearly suggest a change of the distribution of the drag force, which is found to be relatively uniform at low packing densities, while most of the force acts on first rows of the arrays at large packing densities. The drag area constitutes the basis for the formulation of a new adjustment length scale defined as the ratio between the volume of the air within the array and the drag area. The proposed adjustment length scale automatically takes into account the change in drag distribution along the array for a better parameterization of urban effects in dispersion models.     

A mathematical model for type II profile of concentration distribution in turbulent flows

This paper presents a mathematical model to investigate type II profile of suspension concentration distribution (i.e., the concentration profile where the maximum concentration appears at some distance above the bed surface) in a steady, uniform turbulent flow through open-channels. Starting from the mass and momentum conservation equations of two-phase flow, a theoretical model has been derived. The distribution equation is derived considering the effects of fluid lift force, drag force, particle inertia, particle–particle interactions, particle velocity fluctuations and drift diffusion. The equation is solved numerically and is compared with available experimental data as well as with other models existing in the literature. Good agreement between the observed value and computed result, and minimum error in comparison to other models indicate that the present model can be applied in predicting particle concentration distribution for type II profile for a wide range of flow conditions. The proposed model is also able to show the transition from type I profile to type II profile.