Estimation of soil moisture in the root-zone from remote sensing data

Field-based soil moisture measurements are cumbersome. Thus, remote sensing techniques are needed because allows field and landscape-scale mapping of soil moisture depth-averaged through the root zone of existing vegetation. The objective of the study was to evaluate the accuracy of an empirical relationship to calculate soil moisture from remote sensing data of irrigated soils of the Apodi Plateau, in the Brazilian semiarid region. The empirical relationship had previously been tested for irrigated soils in Mexico, Egypt, and Pakistan, with promising results. In this study, the relationship was evaluated from experimental data collected from a cotton field. The experiment was carried out in an area of 5 ha with irrigated cotton. The energy balance and evaporative fraction (Λ) were measured by the Bowen ratio method. Soil moisture (θ) data were collected using a PR2 - Profile Probe (Delta-T Devices Ltd). The empirical relationship was tested using experimentally collected Λ and θ values and was applied using the Λ values obtained from the Surface Energy Balance Algorithm for Land (SEBAL) and three TM - Landsat 5 images. There was a close correlation between measured and estimated θ values (p<0.05, R² = 0.84) and there were no significant differences according to the Student t-test (p<0.01). The statistical analyses showed that the empirical relationship can be applied to estimate the root-zone soil moisture of irrigated soils, i.e. when the evaporative fraction is greater than 0.45.

Estimation of water percolation by different methods using TDR

Detailed knowledge on water percolation into the soil in irrigated areas is fundamental for solving problems of drainage, pollution and the recharge of underground aquifers. The aim of this study was to evaluate the percolation estimated by time-domain-reflectometry (TDR) in a drainage lysimeter. We used Darcy's law with K(θ) functions determined by field and laboratory methods and by the change in water storage in the soil profile at 16 points of moisture measurement at different time intervals. A sandy clay soil was saturated and covered with plastic sheet to prevent evaporation and an internal drainage trial in a drainage lysimeter was installed. The relationship between the observed and estimated percolation values was evaluated by linear regression analysis. The results suggest that percolation in the field or laboratory can be estimated based on continuous monitoring with TDR, and at short time intervals, of the variations in soil water storage. The precision and accuracy of this approach are similar to those of the lysimeter and it has advantages over the other evaluated methods, of which the most relevant are the possibility of estimating percolation in short time intervals and exemption from the predetermination of soil hydraulic properties such as water retention and hydraulic conductivity. The estimates obtained by the Darcy-Buckingham equation for percolation levels using function K(θ) predicted by the method of Hillel et al. (1972) provided compatible water percolation estimates with those obtained in the lysimeter at time intervals greater than 1 h. The methods of Libardi et al. (1980), Sisson et al. (1980) and van Genuchten (1980) underestimated water percolation.

Bi-planar 2D-to-3D registration in Fourier domain for stereoscopic X-ray motion tracking

In this paper we present a new method to track bonemovements in stereoscopic X-ray image series of the kneejoint. The method is based on two different X-ray imagesets: a rotational series of acquisitions of the stillsubject knee that will allow the tomographicreconstruction of the three-dimensional volume (model),and a stereoscopic image series of orthogonal projectionsas the subject performs movements. Tracking the movementsof bones throughout the stereoscopic image series meansto determine, for each frame, the best pose of everymoving element (bone) previously identified in the 3Dreconstructed model. The quality of a pose is reflectedin the similarity between its simulated projections andthe actual radiographs. We use direct Fourierreconstruction to approximate the three-dimensionalvolume of the knee joint. Then, to avoid the expensivecomputation of digitally rendered radiographs (DRR) forpose recovery, we reformulate the tracking problem in theFourier domain. Under the hypothesis of parallel X-raybeams, we use the central-slice-projection theorem toreplace the heavy 2D-to-3D registration of projections inthe signal domain by efficient slice-to-volumeregistration in the Fourier domain. Focusing onrotational movements, the translation-relevant phaseinformation can be discarded and we only consider scalarFourier amplitudes. The core of our motion trackingalgorithm can be implemented as a classical frame-wiseslice-to-volume registration task. Preliminary results onboth synthetic and real images confirm the validity ofour approach.

Revisiting Field Capacity (FC): variation of definition of FC and its estimation from pedotransfer functions

Taking into account the nature of the hydrological processes involved in in situ measurement of Field Capacity (FC), this study proposes a variation of the definition of FC aiming not only at minimizing the inadequacies of its determination, but also at maintaining its original, practical meaning. Analysis of FC data for 22 Brazilian soils and additional FC data from the literature, all measured according to the proposed definition, which is based on a 48-h drainage time after infiltration by shallow ponding, indicates a weak dependency on the amount of infiltrated water, antecedent moisture level, soil morphology, and the level of the groundwater table, but a strong dependency on basic soil properties. The dependence on basic soil properties allowed determination of FC of the 22 soil profiles by pedotransfer functions (PTFs) using the input variables usually adopted in prediction of soil water retention. Among the input variables, soil moisture content θ (6 kPa) had the greatest impact. Indeed, a linear PTF based only on it resulted in an FC with a root mean squared residue less than 0.04 m³ m-3 for most soils individually. Such a PTF proved to be a better FC predictor than the traditional method of using moisture content at an arbitrary suction. Our FC data were compatible with an equivalent and broader USA database found in the literature, mainly for medium-texture soil samples. One reason for differences between FCs of the two data sets of fine-textured soils is due to their different drainage times. Thus, a standardized procedure for in situ determination of FC is recommended.

Estimation of field capacity from ring infiltrometer-drainage data

Field capacity (FC) is a parameter widely used in applied soil science. However, its in situ method of determination may be difficult to apply, generally because of the need of large supplies of water at the test sites. Ottoni Filho et al. (2014) proposed a standardized procedure for field determination of FC and showed that such in situ FC can be estimated by a linear pedotransfer function (PTF) based on volumetric soil water content at the matric potential of -6 kPa [θ(6)] for the same soils used in the present study. The objective of this study was to use soil moisture data below a double ring infiltrometer measured 48 h after the end of the infiltration test in order to develop PTFs for standard in situ FC. We found that such ring FC data were an average of 0.03 m³ m- 3 greater than standard FC values. The linear PTF that was developed for the ring FC data based only on θ(6) was nearly as accurate as the equivalent PTF reported by Ottoni Filho et al. (2014), which was developed for the standard FC data. The root mean squared residues of FC determined from both PTFs were about 0.02 m³ m- 3. The proposed method has the advantage of estimating the soil in situ FC using the water applied in the infiltration test.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Iowa in Motion, Planning Ahead State Transportation Plan, May 8, 2012

According to 23 CFR § 450.214(a), “The State shall develop a long-range statewide transportation plan, with a minimum 20-year forecast period at the time of adoption, that provides for the development and implementation of the multimodal transportation system for the State.” The state transportation plan (Plan) is a document that will address this requirement and serve as a transportation investment guide between now and 2040. Iowa’s most recent plan was developed by the Iowa Department of Transportation and adopted in 1997 through a planning process called Iowa in Motion. Much of Iowa in Motion has been implemented and this Plan, "Iowa in Motion – Planning Ahead," will build on the success of its predecessor. The Plan projects the demand for transportation infrastructure and services to 2040 based on consideration of social and economic changes likely to occur during this time. Iowa’s economy and the need to meet the challenges of the future will continue to place pressure on the transportation system. With this in mind, the Plan will provide direction for each transportation mode, and will support a renewed emphasis on efficient investment and prudent, responsible management of our existing transportation system. In recent years, the Iowa DOT has branded this philosophy as stewardship. As Iowa changes and the transportation system evolves, one constant will be that the safe and efficient movement of Iowans and our products is essential for stable growth in Iowa’s economy. Iowa’s extensive multimodal and multijurisdictional transportation system is a critical component of economic development and job creation throughout the state.

Estimation of the correlation structure of crustal velocity heterogeneity from seismic reflection data

Numerous sources of evidence point to the fact that heterogeneity within the Earth's deep crystalline crust is complex and hence may be best described through stochastic rather than deterministic approaches. As seismic reflection imaging arguably offers the best means of sampling deep crustal rocks in situ, much interest has been expressed in using such data to characterize the stochastic nature of crustal heterogeneity. Previous work on this problem has shown that the spatial statistics of seismic reflection data are indeed related to those of the underlying heterogeneous seismic velocity distribution. As of yet, however, the nature of this relationship has remained elusive due to the fact that most of the work was either strictly empirical or based on incorrect methodological approaches. Here, we introduce a conceptual model, based on the assumption of weak scattering, that allows us to quantitatively link the second-order statistics of a 2-D seismic velocity distribution with those of the corresponding processed and depth-migrated seismic reflection image. We then perform a sensitivity study in order to investigate what information regarding the stochastic model parameters describing crustal velocity heterogeneity might potentially be recovered from the statistics of a seismic reflection image using this model. Finally, we present a Monte Carlo inversion strategy to estimate these parameters and we show examples of its application at two different source frequencies and using two different sets of prior information. Our results indicate that the inverse problem is inherently non-unique and that many different combinations of the vertical and lateral correlation lengths describing the velocity heterogeneity can yield seismic images with the same 2-D autocorrelation structure. The ratio of all of these possible combinations of vertical and lateral correlation lengths, however, remains roughly constant which indicates that, without additional prior information, the aspect ratio is the only parameter describing the stochastic seismic velocity structure that can be reliably recovered.

Proof of concept for microarray-based detection of DNA-binding oncogenes in cell extracts.

The function of DNA-binding proteins is controlled not just by their abundance, but mainly at the level of their activity in terms of their interactions with DNA and protein targets. Moreover, the affinity of such transcription factors to their target sequences is often controlled by co-factors and/or modifications that are not easily assessed from biological samples. Here, we describe a scalable method for monitoring protein-DNA interactions on a microarray surface. This approach was designed to determine the DNA-binding activity of proteins in crude cell extracts, complementing conventional expression profiling arrays. Enzymatic labeling of DNA enables direct normalization of the protein binding to the microarray, allowing the estimation of relative binding affinities. Using DNA sequences covering a range of affinities, we show that the new microarray-based method yields binding strength estimates similar to low-throughput gel mobility-shift assays. The microarray is also of high sensitivity, as it allows the detection of a rare DNA-binding protein from breast cancer cells, the human tumor suppressor AP-2. This approach thus mediates precise and robust assessment of the activity of DNA-binding proteins and takes present DNA-binding assays to a high throughput level.

Cardiovascular risk estimation and eligibility for statins in primary prevention comparing different strategies

Recommendations for statin use for primary prevention of coronary heart disease (CHD) are based on estimation of the 10-year CHD risk. It is unclear which risk algorithm and guidelines should be used in European populations. Using data from a population-based study in Switzerland, we first assessed 10-year CHD risk and eligibility for statins in 5,683 women and men 35 to 75 years of age without cardiovascular disease by comparing recommendations by the European Society of Cardiology without and with extrapolation of risk to age 60 years, the International Atherosclerosis Society, and the US Adult Treatment Panel III. The proportions of participants classified as high-risk for CHD were 12.5% (15.4% with extrapolation), 3.0%, and 5.8%, respectively. Proportions of participants eligible for statins were 9.2% (11.6% with extrapolation), 13.7%, and 16.7%, respectively. Assuming full compliance to each guideline, expected relative decreases in CHD deaths in Switzerland over a 10-year period would be 16.4% (17.5% with extrapolation), 18.7%, and 19.3%, respectively; the corresponding numbers needed to treat to prevent 1 CHD death would be 285 (340 with extrapolation), 380, and 440, respectively. In conclusion, the proportion of subjects classified as high risk for CHD varied over a fivefold range across recommendations. Following the International Atherosclerosis Society and the Adult Treatment Panel III recommendations might prevent more CHD deaths at the cost of higher numbers needed to treat compared with European Society of Cardiology guidelines.

Bayesian estimation of speciation and extinction from incomplete fossil occurrence data.

The temporal dynamics of species diversity are shaped by variations in the rates of speciation and extinction, and there is a long history of inferring these rates using first and last appearances of taxa in the fossil record. Understanding diversity dynamics critically depends on unbiased estimates of the unobserved times of speciation and extinction for all lineages, but the inference of these parameters is challenging due to the complex nature of the available data. Here, we present a new probabilistic framework to jointly estimate species-specific times of speciation and extinction and the rates of the underlying birth-death process based on the fossil record. The rates are allowed to vary through time independently of each other, and the probability of preservation and sampling is explicitly incorporated in the model to estimate the true lifespan of each lineage. We implement a Bayesian algorithm to assess the presence of rate shifts by exploring alternative diversification models. Tests on a range of simulated data sets reveal the accuracy and robustness of our approach against violations of the underlying assumptions and various degrees of data incompleteness. Finally, we demonstrate the application of our method with the diversification of the mammal family Rhinocerotidae and reveal a complex history of repeated and independent temporal shifts of both speciation and extinction rates, leading to the expansion and subsequent decline of the group. The estimated parameters of the birth-death process implemented here are directly comparable with those obtained from dated molecular phylogenies. Thus, our model represents a step towards integrating phylogenetic and fossil information to infer macroevolutionary processes.

Zonation for 3D aquifer characterization based on joint inversions of multimethod crosshole geophysical data

Predictive groundwater modeling requires accurate information about aquifer characteristics. Geophysical imaging is a powerful tool for delineating aquifer properties at an appropriate scale and resolution, but it suffers from problems of ambiguity. One way to overcome such limitations is to adopt a simultaneous multitechnique inversion strategy. We have developed a methodology for aquifer characterization based on structural joint inversion of multiple geophysical data sets followed by clustering to form zones and subsequent inversion for zonal parameters. Joint inversions based on cross-gradient structural constraints require less restrictive assumptions than, say, applying predefined petro-physical relationships and generally yield superior results. This approach has, for the first time, been applied to three geophysical data types in three dimensions. A classification scheme using maximum likelihood estimation is used to determine the parameters of a Gaussian mixture model that defines zonal geometries from joint-inversion tomograms. The resulting zones are used to estimate representative geophysical parameters of each zone, which are then used for field-scale petrophysical analysis. A synthetic study demonstrated how joint inversion of seismic and radar traveltimes and electrical resistance tomography (ERT) data greatly reduces misclassification of zones (down from 21.3% to 3.7%) and improves the accuracy of retrieved zonal parameters (from 1.8% to 0.3%) compared to individual inversions. We applied our scheme to a data set collected in northeastern Switzerland to delineate lithologic subunits within a gravel aquifer. The inversion models resolve three principal subhorizontal units along with some important 3D heterogeneity. Petro-physical analysis of the zonal parameters indicated approximately 30% variation in porosity within the gravel aquifer and an increasing fraction of finer sediments with depth.

Estimation of the noisy component of anatomical backgrounds.

The knowledge of the relationship that links radiation dose and image quality is a prerequisite to any optimization of medical diagnostic radiology. Image quality depends, on the one hand, on the physical parameters such as contrast, resolution, and noise, and on the other hand, on characteristics of the observer that assesses the image. While the role of contrast and resolution is precisely defined and recognized, the influence of image noise is not yet fully understood. Its measurement is often based on imaging uniform test objects, even though real images contain anatomical backgrounds whose statistical nature is much different from test objects used to assess system noise. The goal of this study was to demonstrate the importance of variations in background anatomy by quantifying its effect on a series of detection tasks. Several types of mammographic backgrounds and signals were examined by psychophysical experiments in a two-alternative forced-choice detection task. According to hypotheses concerning the strategy used by the human observers, their signal to noise ratio was determined. This variable was also computed for a mathematical model based on the statistical decision theory. By comparing theoretical model and experimental results, the way that anatomical structure is perceived has been analyzed. Experiments showed that the observer's behavior was highly dependent upon both system noise and the anatomical background. The anatomy partly acts as a signal recognizable as such and partly as a pure noise that disturbs the detection process. This dual nature of the anatomy is quantified. It is shown that its effect varies according to its amplitude and the profile of the object being detected. The importance of the noisy part of the anatomy is, in some situations, much greater than the system noise. Hence, reducing the system noise by increasing the dose will not improve task performance. This observation indicates that the tradeoff between dose and image quality might be optimized by accepting a higher system noise. This could lead to a better resolution, more contrast, or less dose.

Influence of magnetic field strength and image registration strategy on voxel-based morphometry in a study of Alzheimer's disease.

Multi-centre data repositories like the Alzheimer's Disease Neuroimaging Initiative (ADNI) offer a unique research platform, but pose questions concerning comparability of results when using a range of imaging protocols and data processing algorithms. The variability is mainly due to the non-quantitative character of the widely used structural T1-weighted magnetic resonance (MR) images. Although the stability of the main effect of Alzheimer's disease (AD) on brain structure across platforms and field strength has been addressed in previous studies using multi-site MR images, there are only sparse empirically-based recommendations for processing and analysis of pooled multi-centre structural MR data acquired at different magnetic field strengths (MFS). Aiming to minimise potential systematic bias when using ADNI data we investigate the specific contributions of spatial registration strategies and the impact of MFS on voxel-based morphometry in AD. We perform a whole-brain analysis within the framework of Statistical Parametric Mapping, testing for main effects of various diffeomorphic spatial registration strategies, of MFS and their interaction with disease status. Beyond the confirmation of medial temporal lobe volume loss in AD, we detect a significant impact of spatial registration strategy on estimation of AD related atrophy. Additionally, we report a significant effect of MFS on the assessment of brain anatomy (i) in the cerebellum, (ii) the precentral gyrus and (iii) the thalamus bilaterally, showing no interaction with the disease status. We provide empirical evidence in support of pooling data in multi-centre VBM studies irrespective of disease status or MFS.

Prospective and retrospective motion correction in diffusion magnetic resonance imaging of the human brain.

Diffusion-weighting in magnetic resonance imaging (MRI) increases the sensitivity to molecular Brownian motion, providing insight in the micro-environment of the underlying tissue types and structures. At the same time, the diffusion weighting renders the scans sensitive to other motion, including bulk patient motion. Typically, several image volumes are needed to extract diffusion information, inducing also inter-volume motion susceptibility. Bulk motion is more likely during long acquisitions, as they appear in diffusion tensor, diffusion spectrum and q-ball imaging. Image registration methods are successfully used to correct for bulk motion in other MRI time series, but their performance in diffusion-weighted MRI is limited since diffusion weighting introduces strong signal and contrast changes between serial image volumes. In this work, we combine the capability of free induction decay (FID) navigators, providing information on object motion, with image registration methodology to prospectively--or optionally retrospectively--correct for motion in diffusion imaging of the human brain. Eight healthy subjects were instructed to perform small-scale voluntary head motion during clinical diffusion tensor imaging acquisitions. The implemented motion detection based on FID navigator signals is processed in real-time and provided an excellent detection performance of voluntary motion patterns even at a sub-millimetre scale (sensitivity≥92%, specificity>98%). Motion detection triggered an additional image volume acquisition with b=0 s/mm2 which was subsequently co-registered to a reference volume. In the prospective correction scenario, the calculated motion-parameters were applied to perform a real-time update of the gradient coordinate system to correct for the head movement. Quantitative analysis revealed that the motion correction implementation is capable to correct head motion in diffusion-weighted MRI to a level comparable to scans without voluntary head motion. The results indicate the potential of this method to improve image quality in diffusion-weighted MRI, a concept that can also be applied when highest diffusion weightings are performed.