Uranium-series isotopes are an emerging tool to characterize weathering and soil forming processes in the Critical Zone, the dynamic region of earth's surface where bedrock, water, soil, and life chemically and physically interact to support ecosystems. Understanding controls on the U-series composition of soils across a range of lithologies and climate is critical to applying existing mass balance models of U-series isotopes to calculate soil formation rates in these systems. This study seeks to understand the behavior of U-series isotopes in soil profiles in the semi-arid complex volcanic terrain of the Valles Caldera, NM. (²³⁴U/²³⁸U) measured in soils ranged from 0.90 to 1.56 and (²³⁰Th/²³⁸U) values ranged from 0.48 to 1.39. Significant ²³⁰Th enrichment in upper soil profiles was interpreted as evidence of mixing with ²³⁰Th-enriched volcanic ash and significant ²³⁴U enrichment in one soil profile was interpreted as evidence of addition of U to soils from ²³⁴U-enriched soil solutions. A simple U isotope mass balance model was applied to estimate soil residence time based on U addition, which yielded a minimum residence time of ~10ka. Evidence of past episodic mixing of volcanic ash in these soils suggests modeling soil formation using a mass balance approach is problematic, and future applications of existing models in other heterogeneous volcanic soils should be applied cautiously. U-series isotopes have also shown promise as a tracer of residence time in shallow groundwater and streams. In this study, (²³⁴U/²³⁸U) in dissolved U is used to trace seasonal variation in source water contributions to streamflow in a small (3.29km²), headwater catchment in the Jemez River Basin Critical Zone Observatory within the Valles Caldera. Systematically lower (²³⁴U/²³⁸U) values in dissolved U were observed in spring and stream waters in conjunction with greater contributions of longer residence time waters during snowmelt ((²³⁴U/²³⁸U) ranged 1.7 to 2.8) vs. dry seasons ((²³⁴U/²³⁸U) ranged 1.9 to 3.1). The lower (²³⁴U/²³⁸U) values in longer residence time waters were attributed to progressive depletion of easily-weathered ²³⁴U with increasing duration of water rock interaction. Further studies with more quantitative age tracers, such as ³H, could help to establish (²³⁴U/²³⁸U) values as a powerful tracer of water sources and residence time in streamwaters at the catchment scale.

No description available.

No description available.

No description available.

We investigate conditions for the ergodicity of threshold autoregressive time series by embedding the time series in a general state Markov chain and apply a FosterLyapunov drift condition to demonstrate ergodicity of the Markov chain. We are particularly interested in demonstrating V uniform ergodicity where the test function V () is a function of a norm on the statespace. In this dissertation we provide conditions under which the general state space chain may be approximated by a simpler system, whether deterministic or stochastic, and provide conditions on the simpler system which imply V uniform ergodicity of the general state space Markov chain and thus the threshold autoregressive time series embedded in it. We also examine conditions under which the general state space chain may be classified as transient. Finally, in some cases we provide conditions under which central limit theorems will exist for the V uniformly ergodic general state space chain.

Nagrinėjamos dvi funkcijos. Darbe nustatyta, kad esant papildomiems reikalavimams, šios funkcijos turi be galo daug nulių atitinkamoje juostoje ir pusplokštumoje. / The two functions are analytically continuable to the whole complex plane. It is prove that the functions have infinitely many zeros in the strop and in the half-plane.

No description available.

The State Space Model (SSM) encompasses the class of multivariate linear models, in particular, regression models with fixed, time-varying and random parameters, time series models, unobserved components models and combinations thereof. The well-known Kalman Filter (KF) provides a unifying tool for conducting statistical inferences with the SSM. A major practical problem with the KF concerns its initialization when either the initial state or the regression parameter (or both) in the SSM are diffuse. In these situations, it is common practice to either apply the KF to a transformation of the data which is functionally independent of the diffuse parameters or else initialize the KF with an arbitrarily large error covariance matrix. However neither approach is entirely satisfactory. The data transformation required in the first approach can be computationally tedious and furthermore it may not preserve the state space structure. The second approach is theoretically and numerically unsound. Recently however, De Jong (1991) has developed an extension of the KF, called the Diffuse Kalman Filter (DKF) to handle these diffuse situations. The DKF does not require any data transformation. The thesis contributes further to the theoretical and computational aspects of con ducting statistical inferences using the DKF. First, we demonstrate the appropriate initialization of the DKF for the important class of time-invariant SSM’s. This result is useful for maximum likelihood statistical inference with the SSM. Second, we derive and compare alternative pseudo-likelihoods for the diffuse SSM. We uncover some interesting characteristics of the DKF and the diffuse likelihood with the class of ARMA models. Third, we propose an efficient implementation of the DKF, labelled the collapsed DKF (CDKF). The latter is derived upon sweeping out some columns of the pertinent matrices in the DKF after an initial number of iterations. The CDKF coincides with the KF in the absence of regression effects in the SSM. We demonstrate that in general the CDKF is superior in practicality and performance to alternative algorithms proposed in the literature. Fourth, we consider maximum likelihood estimation in the SSM using an EM (Expectation-Maximization) approach. Through a judicious choice of the complete data, we develop an CDKF-EM algorithm which does not require the evaluation of lag one state error covariance matrices for the most common estimation exercise required for the SSM, namely the estimation of the covariance matrices of the disturbances in the SSM. Last we explore the topic of diagnostic testing in the SSM. We discuss and illustrate the recursive generation of residuals and the usefulness of the latters in pinpointing likely outliers and points of structural change.

No description available.

No description available.