Thomas H. Meyer

On modeling animal movements using Brownian motion with measurement error

Modeling animal movements with Brownian motion (or more generally by a Gaussian process) has a long tradition in ecological studies. The recent Brownian bridge movement model (BBMM), which incorporates measurement errors, has been quickly adopted by ecologists because of its simplicity and tractability. We discuss some nontrivial properties of the discrete-time stochastic process that results from observing a Brownian motion with added normal noise at discrete times. In particular, we demonstrate that the observed sequence of random variables is not Markov. Consequently the expected occupation time between two successively observed locations does not depend on just those two observations; the whole path must be taken into account. Nonetheless, the exact likelihood function of the observed time series remains tractable; it requires only sparse matrix computations. The likelihood-based estimation procedure is described in detail and compared to the BBMM estimation.

Triple-Hot-Film Anemometer Performance in Cases-99 and A Comparison With Sonic Anemometer Measurements

Two levels of triple-hot-film and sonic anemometers were deployed on a 5.5-m towerduring the Cooperative Atmospheric Surface Exchange Study (CASES-99) in October1999. Each triple-hot-film probe was collocated 50 mm from the sonic sensing path ona common boom. Various problems with using triple-hot-films in the atmosphere toresolve wind components are addressed including the derivation of a yaw angle correction using the collocated sensors. It was found that output voltage drift due to changes in environmental temperature could be monitored and corrected using an automated system. Non-unique solutions to heat transfer equations can be resolved using a collocated sonic anemometer. Multi-resolution decomposition of the hot-film data was used to estimate appropriate day and night averaging periods for turbulent flux measurements in and near the roughness sub-layer. Finally, triple-hot-film measurements of mean wind magnitude (M), turbulent kinetic energy (TKE), sensible heat flux (H), and local friction velocity (u*) are compared to those of the collocated CSAT3 sonic anemometers. Overall, the mean wind magnitudes measured by the triple-hot-film and the collocated sonic sensorswere close, consistent and independent of stability or proximity to the ground. The turbulent statistics, TKE, u*, and H, measured by the two sensor systems were reasonably close together at z = 5 m. However, the ratio of sonic measurement/hot-film measurement decreased toward the ground surface, especially during stable conditions.

A DYNAMIC LAGRANGIAN, FIELD-SCALE MODEL OF DUST DISPERSION FROM AGRICULTURE TILLING OPERATIONS

Dust exposure in and near farm fields is of increasing concern for human health and may soon be facing new emissions regulations. Dust plumes of this nature have rarely been documented due to the unpredictable nature of the dust plumes and the difficulties of accurately sampling the plumes. This article presents a dynamic random-walk model that simulates the field-scale PM10 (particle diameter <10 µm) dust dispersion from an agriculture disking operation. The major improvements over traditional plume models are that it can simulate moving sources and plume meander. The major inputs are the friction velocity (u*), wind direction in the simulation period, atmospheric stability, and source strength (µg s-1). In each time step of the model simulation, three instantaneous wind velocities (x, y, and z directions) are produced based on friction velocity, mean wind speed, and atmospheric stability. The computational time step is 0.025 times the Lagrangian time scale. The resulting instantaneous wind vectors transport all the individual particles. The particle deposition algorithm calculates if a particle is deposited based on the particle settling speed and vertical wind velocity when it touches the ground surface. The particle mass based concentration in 3-D can be obtained at any instant by counting the particle numbers in a unit volume and then converting to mass based on the particle size and density. Simulations from this model are verified by comparison with dust dispersion and plume concentrations obtained by an elastic backscatter LIDAR. The simulated plume spread parameters (s y, s z) at downplume distances up to 160 m were within ±73% of those measured with a remote aerosol LIDAR. Cross-correlations between a modeled plume and LIDAR measurements of the actual plume were as high as 0.78 near the ground and decreased to 0.65 at 9 m above ground, indicating close pattern similarity between the modeled and measured plumes at lower heights but decreasing with elevation above the ground.

A Comparison of Lagrangian Model Estimates to Light Detection and Ranging (LIDAR) Measurements of Dust Plumes from Field Tilling

Abstract A Lagrangian particle model has been adapted to examine human exposures to particulate matter ≤ 10 µm (PM10) in agricultural settings. This paper reports the performance of the model in comparison to extensive measurements by elastic LIDAR (light detection and ranging). For the first time, the LIDAR measurements allowed spatially distributed and time dynamic measurements to be used to test the predictions of a field-scale model. The model outputs, which are three-dimensional concentration distribution maps from an agricultural disking operation, were compared with the LIDAR-scanned images. The peak cross-correlation coefficient and the offset distance of the measured and simulated plumes were used to quantify both the intensity and location accuracy. The appropriate time averaging and changes in accuracy with height of the plume were examined. Inputs of friction velocity, Monin–Obukhov length, and wind direction (1 sec) were measured with a three-axis sonic anemometer at a single point in the field (at 1.5-m height). The Lagrangian model of Wang et al. predicted the near-field concentrations of dust plumes emitted from a field disking operation with an overall accuracy of approximately 0.67 at 3-m height. Its average offset distance when compared with LIDAR measurements was approximately 38 m, which was 6% of the average plume moving distance during the simulation periods. The model is driven by weather measurements, and its near-field accuracy is highest when input time averages approach the turbulent flow time scale (3–70 sec). The model accuracy decreases with height because of smoothing and errors in the input wind field, which is modeled rather than measured at heights greater than the measurement anemometer. The wind steadiness parameter (S) can be used to quantify the combined effects of wind speed and direction on model accuracy.

Distribution models for Panicum virgatum (Poaceae) reveal an expanded range in present and future climate regimes in the northeastern United States

PREMISE OF THE STUDY Expanded area cultivated with the bioenergy crop Panicum virgatum (switchgrass) could alter the genetics of native populations through gene flow, so understanding current and future species distribution is a first step toward estimating ecological impacts. We surveyed switchgrass distribution in the northeastern United States and generated statistical models to address hypotheses about current distribution relative to historical records and responses to climate change. METHODS Surveys were conducted on 1600 km of road verges along environmental gradients. Switchgrass abundance became the training data for two multivariate generalized linear models that generated maps representing the probability of switchgrass in road verges. Models were evaluated and the superior model was used with variables from three climate change scenarios for 2050 and 2099. KEY RESULTS Switchgrass populations were found in 41% of roadside plots and up to 188 km from the coast. The environmental variables temperature, urban areas, and sandy soils were positively correlated with switchgrass presence, while elevation, soil pH, and distance to the coast were negatively correlated. The model without spatial autocorrelation performed better. Models and maps incorporating climate change predictions showed a sharp northward shift in suitable habitat. CONCLUSIONS Switchgrass populations in the northeastern United States occur on inland road verges, supporting the idea that species distribution has expanded relative to historical descriptions of a restricted coastal habitat. The optimal model showed that mean temperature, elevation, and urban development were important in switchgrass distribution today, and climate change will increase suitable habitat for future bioenergy production and wild populations.

A moving-resting process with an embedded Brownian motion for animal movements

Animal movements are of great importance in studying home ranges, migration routes, resource selection, and social interactions. The Global Positioning System provides relatively continuous animal tracking over time and long distances. Nevertheless, the continuous trajectory of an animal’s movement is usually only observed at discrete time points. Brownian bridge models have been used to model movement of an animal between two observed locations within a reasonably short time interval. Assuming that animals are in perpetual motion, these models ignore inactivity such as resting or sleeping. Using the latest developments in applied probability, we propose a moving–resting process model where an animal is assumed to alternate between a moving state, during which it moves in a Brownian motion, and a resting state, during which it does not move. Theoretical properties of the process are studied as a first step towards more realistic models for animal movements. Analytic expressions are derived for the distribution of one increment and two consecutive increments, and are validated with simulations. The induced bridge model conditioning on the starting and end points is used to compute an animal’s probability of occurrence in an observation area during the time of observation, which has wide applications in wildlife behavior research.

An accuracy assessment of global navigation wildlife-tracking collars in the southern clilean Patagonia

En el Parque Nacional Torres del Paine hemos evaluado la precision de tres tipos de collares diferentes. Los collares utilizan los sistemas de navegacion global mediante satelites (GNSS) y se utilizan en el seguimiento de la fauna salvaje. La evaluacion fue determinada comparando las posiciones del collar en relacion con coordenadas de control establecidas previamente y con posiciones muy precisas. Las coordenadas de control las establecimos utilizando receptores portadores de observacion GNSS de doble frecuencia y comparando estas posiciones de alta precision con las de relativamente baja precision, de frecuencia unica, de un solo codigo de seguimiento en dos escenarios: (i) pruebas estacionarias: tres collares de tres fabricantes diferentes fueron evaluados mediante marcadores de control permanente, y (ii) pruebas itinerantes: el collar de un fabricante se evaluo en ambientes utilizados por animales portadores de collar. Estos ambientes incluyen tres tipos de habitats con topografia y copas de los arboles que pudieran aumentar la obstruccion del contacto con los satelites. Los resultados estacionarios muestran que incluso en condiciones ideales, hay diferencias estadisticamente significativas en la precision media de la posicion entre los collares, pero que estas diferencias son pequenas en comparacion con el tamano de los rangos de hogar de los tipos de animales a los que se les equiparia con collar. La evaluacion del muestreo itinerante demostro que bajo el cielo abierto, los errores promedio fueron consistentes con las afrmaciones del fabricante, pero que las distancias del error medio y el fallo de corregir los errores (fallo en la coleccion de posiciones en horarios establecidos) aumento con segun se incrementa la obstruccion del cielo.

Fast algorithms using minimal data structures for common topological relationships in large, irregularly spaced topographic data sets

Digital terrain models (DTMs) typically contain large numbers of postings, from hundreds of thousands to billions. Many algorithms that run on DTMs require topological knowledge of the postings, such as finding nearest neighbors, finding the posting closest to a chosen location, etc. If the postings are arranged irregularly, topological information is costly to compute and to store. This paper offers a practical approach to organizing and searching irregularly spaced data sets by presenting a collection of efficient algorithms (O(N),O(lgN)) that compute important topological relationships with only a simple supporting data structure. These relationships include finding the postings within a window, locating the posting nearest a point of interest, finding the neighborhood of postings nearest a point of interest, and ordering the neighborhood counter-clockwise. These algorithms depend only on two sorted arrays of two-element tuples, holding a planimetric coordinate and an integer identification number indicating which posting the coordinate belongs to. There is one array for each planimetric coordinate (eastings and northings). These two arrays cost minimal overhead to create and store but permit the data to remain arranged irregularly.

POSITION ERRORS CAUSED BY GPS HEIGHT OF INSTRUMENT BLUNDERS

Abstract Height of instrument (HI) blunders in GPS measurements cause position errors. These errors can be pure vertical, pure horizontal, or a mixture of both. There are different error regimes depending on whether both the base and the rover both have HI blunders, if just the base has an HI blunder, or just the rover has an HI blunder. The resulting errors are on the order of 30 cm for receiver separations of 1000 km for an HI blunder of 2 m. Given the complicated nature of the errors, we believe it would be difficult, if not impossible, to detect such errors by visual inspection. This serves to underline the necessity to enter GPS HIs correctly.