Statistical modeling of spatially stratified heterogeneous data

Spatial statistics is an important methodology for geospatial data analysis. It has evolved to handle spatially autocorrelated data and spatially (locally) heterogeneous data, which aim to capture the first and second laws of geography, respectively. Examples of spatially stratified heterogeneity (SSH) include climatic zones and land-use types. Methods for such data are relatively underdeveloped compared to the first two properties. The presence of SSH is evidence that nature is lawful and structured rather than purely random. This induces another “layer” of causality underlying variations observed in geographical data. In this article, we go beyond traditional cluster-based approaches and propose a unified approach for SSH in which we provide an equation for SSH, display how SSH is a source of bias in spatial sampling and confounding in spatial modeling, detect nonlinear stochastic causality inherited in SSH distribution, quantify general interaction identified by overlaying two SSH distributions, perform spatial prediction based on SSH, develop a new measure for spatial goodness of fit, and enhance global modeling by integrating them with an SSH q statistic. The research advances statistical theory and methods for dealing with SSH data, thereby offering a new toolbox for spatial data analysis

Spatiotemporally representative and cost-efficient sampling design for validation activities in wanglang experimental site

Altres ajuts: EC Copernicus Global Land Service (CGLOPS-1, 199494-JRC.Spatiotemporally representative Elementary Sampling Units (ESUs) are required for capturing the temporal variations in surface spatial heterogeneity through field measurements. Since inaccessibility often coexists with heterogeneity, a cost-efficient sampling design is mandatory. We proposed a sampling strategy to generate spatiotemporally representative and cost-efficient ESUs based on the conditioned Latin hypercube sampling scheme. The proposed strategy was constrained by multi-temporal Normalized Difference Vegetation Index (NDVI) imagery, and the ESUs were limited within a sampling feasible region established based on accessibility criteria. A novel criterion based on the Overlapping Area (OA) between the NDVI frequency distribution histogram from the sampled ESUs and that from the entire study area was used to assess the sampling efficiency. A case study inWanglang National Nature Reserve in China showed that the proposed strategy improves the spatiotemporally representativeness of sampling (mean annual OA = 74.7%) compared to the single-temporally constrained (OA = 68.7%) and the random sampling (OA = 63.1%) strategies. The introduction of the feasible region constraint significantly reduces in-situ labour-intensive characterization necessities at expenses of about 9% loss in the spatiotemporal representativeness of the sampling. Our study will support the validation activities in Wanglang experimental site providing a benchmark for locating the nodes of automatic observation systems (e.g., LAINet) which need a spatially distributed and temporally fixed sampling design

Dynamics of bidisperse suspensions under stokes flows: linear shear flow and eedimentation

Sedimenting and sheared bidisperse homogeneous suspensions of non-Brownian particles are investigated by numerical simulations in the limit of vanishing small Reynolds number and negligible inertia of the particles. The numerical approach is based on the solution of the three-dimensional Stokes equations forced by the presence of the dispersed phase. Multi-body hydrodynamic interactions are achieved by a low order multipole expansion of the velocity perturbation. The accuracy of the model is validated on analytic solutions of generic flow configurations involving a pair of particles. The first part of the paper aims at investigating the dynamics of monodisperse and bidisperse suspensions embedded in a linear shear flow. The macroscopic transport properties due to hydrodynamic and non hydrodynamic interactions (short range repulsion force) show good agreement with previous theoretical and experimental works on homogeneous monodisperse particles. Increasing the volumetric concentration of the suspension leads to an enhancement of particle fluctuations and self-diffusion. The velocity fluctuation tensor scales linearly up to 15% concentration. Multi-body interactions weaken the correlation of velocity fluctuations and lead to a diffusion like motion of the particles. Probability density functions show a clear transition from Gaussian to exponential tails while the concentration decreases. The behavior of bidisperse suspensions is more complicated, since the respective amount of small and large particles modifies the overall response of the flow. Our simulations show that, for a given concentration of both species, when the size ratio varies from 1 to 2.5, the fluctuation level of the small particles is strongly enhanced. A similar trend is observed on the evolution of the shear induced self-diffusion coefficient. Thus for a fixed and total concentration, increasing the respective volume fraction of large particles can double the velocity fluctuation of small particles. In the second part of the paper, the sedimentation of a single test particle embedded in a suspension of monodisperse particles allows the determination of basic hydrodynamic interactions involved in a bidisperse suspension. Good agreement is achieved when comparing the mean settling velocity and fluctuations levels of the test sphere with experiments. Two distinct behaviors are observed depending on the physical properties of the particle. The Lagrangian velocity autocorrelation function has a negative region when the test particle has a settling velocity twice as large as the reference velocity of the surrounding suspension. The test particle settles with a zig-zag vertical trajectory while a strong reduction of horizontal dispersion occurs. Then, several configurations of bidisperse settling suspensions are investigated. Mean velocity depends on concentration of both species, density ratio and size ratio. Results are compared with theoretical predictions at low concentration and empirical correlations when the assumption of a dilute regime is no longer valid. For particular configurations, a segregation instability sets in. Columnar patterns tend to collect particles of the same species and eventually a complete separation of the suspension is observed. The instability threshold is compared with experiments in the case of suspensions of buoyant and heavy spheres. The basic features are well reproduced by the simulation model

On the question of instabilities upstream of cylindrical bodies

In an attempt to understand the unsteady vortical phenomena in perturbed stagnation regions of cylindrical bodies, a critical review of the theoretical and experimental evidence was made. Current theory is revealed to be incomplete, incorrect, or inapplicable to the phenomena observed experimentally. The formalistic approach via the principle of exchange of instabilities should most likely be replaced by a forced-disturbance approach. Also, many false conclusions were reached by ignoring that treatment of the base and perturbed flows in Hiemenz coordinate eta is asymptotic in nature. Almost surely the techniques of matched asymptotic expansions are expected to be used to capture correctly the diffusive and vorticity amplifying processes of the disturbances regarding the mean-flow boundary layer and outer potential field as eta and y/diameter approach infinity. The serious uncertainties in the experiments are discussed in detail

Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence

We consider the closure problem for turbulence in the dry convective atmospheric boundary layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large plumes in the well mixed middle part up to the inversion that separates the CBL from the stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02) that additionally includes a term for background turbulence. Thus an exact solution is derived and all higher order moments (HOMs) are explained by second order moments, correlation coefficients and the skewness. The solution provides a proof of the extended universality hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi- normality of FOM). This refined hypothesis states that CBL turbulence can be considered as result of a linear interpolation between the Gaussian and the very skewed turbulence regimes. Although the extended universality hypothesis was confirmed by results of field measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained unexplained. These are now answered by the new model including the reasons of the universality of the functional form of the HOMs, the significant scatter of the values of the coefficients and the source of the magic of the linear interpolation. Finally, the closures 61 predicted by the model are tested against measurements and LES data. Some of the other issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area coverage parameters of plumes (so called filling factors) with HOM will be discussed also

Wave propagation in periodic composites: higher-order asymptotic analysis versus plane-wave expansion method

This work is devoted to a comparison of different methods determining stop-bands i

LANDSAT-D investigations in snow hydrology

Work undertaken during the contract and its results are described. Many of the results from this investigation are available in journal or conference proceedings literature - published, accepted for publication, or submitted for publication. For these the reference and the abstract are given. Those results that have not yet been submitted separately for publication are described in detail. Accomplishments during the contract period are summarized as follows: (1) analysis of the snow reflectance characteristics of the LANDSAT Thematic Mapper, including spectral suitability, dynamic range, and spectral resolution; (2) development of a variety of atmospheric models for use with LANDSAT Thematic Mapper data. These include a simple but fast two-stream approximation for inhomogeneous atmospheres over irregular surfaces, and a doubling model for calculation of the angular distribution of spectral radiance at any level in an plane-parallel atmosphere; (3) incorporation of digital elevation data into the atmospheric models and into the analysis of the satellite data; and (4) textural analysis of the spatial distribution of snow cover