Boundary-preserving Lamperti-splitting scheme for some Stochastic Differential Equations

We propose and analyse an explicit boundary-preserving scheme for the strong approximations of some SDEs with non-globally Lipschitz drift and diffusion coefficients whose state-space is bounded. The scheme consists of a Lamperti transform followed by a Lie--Trotter splitting. We prove $L^{p}(\Omega)$-convergence of order $1$, for every $p \in \mathbb{N}$, of the scheme and exploit the Lamperti transform to confine the numerical approximations to the state-space of the considered SDE. We provide numerical experiments that confirm the theoretical results and compare the proposed Lamperti-splitting scheme to other numerical schemes for SDEs.Comment: 17 pages, 3 figure

Hardware Simulation for Testing IEC 61131-3

Testing of control code written in IEC 61131-3 has long been a strenuous manual process. The focus in this master's thesis is on building a simulator of an Alfa Laval separator to enable testing of control code. In this particular case, the control code being tested is written and executed in a soft PLC called TwinCAT. The simulator for testing code is written in C#. When testing code, automated tests are preferred because it enables easy regression testing. For this purpose a testing tool using a customized script language has been developed. Testing with a simulator is also beneficial because errors can be found early in the development process, thus reducing the number of errors left to be found when testing on hardware. Comparison tests show that the simulator performs sufficiently well for testing of control code

Temporal Characteristics of P-band Tomographic Radar Backscatter of a Boreal Forest

Temporal variations in synthetic aperture radar (SAR) backscatter over forests are of concern for any SAR mission with the goal of estimating forest parameters from SAR data. In this article, a densely sampled, two-year long time series of P-band (420 to 450 MHz) boreal forest backscatter, acquired by a tower-based radar, is analyzed. The experimental setup provides time series data at multiple polarizations. Tomographic capabilities allow the separation of backscatter at different heights within the forest. Temporal variations of these multi-polarimetric, tomographic radar observations are characterized and quantified. The mechanisms studied are seasonal variations, effects of freezing conditions, diurnal variations, effects of wind and the effects of rainfall on backscatter. An emphasis is placed on upper-canopy backscatter, which has been shown to be a robust proxy for forest biomass. The canopy backscatter was most sensitive to freezing conditions but was more stable than ground-level backscatter and full-forest backscatter during non-frozen conditions. The analysis connects tree water transport mechanisms and P-band radar backscatter for the first time. The presented results are useful for designing boreal forest parameter estimation algorithms, using data from P-band SARs, that are robust to temporal variations in backscatter. The results also present new forest remote sensing opportunities using P-band radars

Boreal Forest Properties from TanDEM-X Data Using Interferometric Water Cloud Model and Implications for a Bistatic C-Band Mission

Data from TanDEM-X in single-pass and bistatic interferometric mode together with the interferometric water cloud model (IWCM) can provide estimates of forest height and stem volume (or the related above-ground biomass) of boreal forests with high accuracy. We summarize results from two boreal test sites using two approaches, i.e., 1) based on model calibration using reference insitu stands, and 2) based on minimization of a cost function. Both approaches are based on inversion of IWCM, which models the complex coherence and backscattering coefficient of a homogeneous forest layer, which includes gaps where free-space wave propagation is assumed. A digital terrain model of the ground is also needed. IWCM is used to estimate forest height or stem volume, since the two variables are assumed to be related through an allometric equation. A relationship between the fractional area of gaps, the area-fill, and stem volume is also required to enable model inversion. The accuracy of the stem volume estimate in the two sites varies between 16% and 21% for height of ambiguity <100 m. The results clearly show the importance of using summer-time acquisitions. Based on the TanDEM-X results at X-band, C-band data from the ERS-1/ERS-2 tandem mission are revisited to investigate the potential of a future bistatic C-band interferometric mission. Out of nine ERS-1/ERS-2 pairs, only one pair was found to be acquired at summer temperatures, without precipitation and with high coherence. A simulated bistatic phase height is shown to give approximately the same sensitivity to stem volume as TanDEM-X

The effect of audio recordings and photographs of autistic and typical children on social judgments

In a counterbalanced, 2x2 mixed factorial design, 61 randomly assigned participants rated two audio recordings and two photographs of autistic or typical children. The hypothesis was that participants would judge autistic children most negatively when listening to audio recordings of them, but that they would judge photographs of autistic and typical children similarly. The two-way mixed ANOVA found a statistically significant main effect for the autistic versus typical child, but no statistically significant main effect for type of medium (recording vs. picture) nor interaction effect. This points to autistic children being judged more negatively in comparison to their typical peers, although it is unclear how those judgments are being determined, and has implications for diagnosis and therapeutic success

A Tower-Based Radar Study of Temporal Coherence of a Boreal Forest at P-, L-, and C-Bands and Linear Cross Polarization

Cross-polarized temporal coherence observations of a boreal forest, acquired using a tower-based radar, are presented in this article. Temporal coherence is analyzed with respect to frequency, temporal baseline, time of day of observation, season, meteorological variables, and biophysical variables. During the summer, P- and L-band temporal coherence exhibited diurnal cycles, which appeared to be due to high rates of transpiration and convective winds during the day. During the winter, freeze-thaw cycles and precipitation resulted in decorrelation. At temporal baselines of seconds to hours, a high temporal coherence was observed even at C-band. The best observation times of the day were midnight and dawn. Temporal coherence is the main limitation of accuracy in interferometric and tomographic forest applications. The observations from this experiment will allow for better spaceborne SAR mission designs for forest applications, better temporal decorrelation modeling, and more accurate forest parameter estimation algorithms using interferometric and tomographic SAR data

Retrieval of forest stem volume using VHF SAR

The ability to retrieve forest stem volume using CARABAS (coherent all radio band sensing) SAR images (28–60 MHz) has been investigated. The test site is a deciduous mixed forest on the island of Öland in southern Sweden. The images have been radiometrically calibrated using an array of horizontal dipoles. The images exhibit a clear discrimination between the forest and open fields. The results show that the dynamic range of the backscattering coefficient among the forest stands is higher than what has been found with conventional SAR using microwave frequencies. The backscatter increases with increasing radar frequency. This work shows an advantage compared to higher frequencies for stem volume estimation in dense forests

Positivity-preserving schemes for some nonlinear stochastic PDEs

We introduce a positivity-preserving numerical scheme for a class of nonlinear stochastic heat equations driven by a purely time-dependent Brownian motion. The construction is inspired by a recent preprint by the authors where one-dimensional equations driven by space-time white noise are considered. The objective of this paper is to illustrate the properties of the proposed integrators in a different framework, by numerical experiments and by giving convergence results

Polarimetric-interferometric boreal forest scattering model for BIOMASS end-to-end simulator

A polarimetric-interferometric forward model (FM) for extended covariance matrix modeling is presented. The FM has been designed to be used within the end-to-end simulator for BIOMASS, a new ESA satellite mission aiming at the global mapping of above-ground forest biomass with P-band synthetic aperture radar (SAR). The FM uses linear regression models for prediction of backscatter intensity and HH-VV correlation coefficient, and the random volume over ground (RVoG) model for the prediction of the interferometric correlation coefficients. For boreal forest, parameter values for these sub-models have been derived using polarimetric-interferometric SAR data acquired within the BioSAR 2007 campaign over the Swedish test site Remningstorp. The FM is evaluated qualitatively in a boreal forest scenario through a side-by-side comparison with BioSAR 2007 data. The general agreement is good, although there are regions with structures which cannot be reproduced by the model, probably due to insufficient forest description by the input parameters