Variational Downscaling, Fusion and Assimilation of Hydrometeorological States via Regularized Estimation

Improved estimation of hydrometeorological states from down-sampled observations and background model forecasts in a noisy environment, has been a subject of growing research in the past decades. Here, we introduce a unified framework that ties together the problems of downscaling, data fusion and data assimilation as ill-posed inverse problems. This framework seeks solutions beyond the classic least squares estimation paradigms by imposing proper regularization, which are constraints consistent with the degree of smoothness and probabilistic structure of the underlying state. We review relevant regularization methods in derivative space and extend classic formulations of the aforementioned problems with particular emphasis on hydrologic and atmospheric applications. Informed by the statistical characteristics of the state variable of interest, the central results of the paper suggest that proper regularization can lead to a more accurate and stable recovery of the true state and hence more skillful forecasts. In particular, using the Tikhonov and Huber regularization in the derivative space, the promise of the proposed framework is demonstrated in static downscaling and fusion of synthetic multi-sensor precipitation data, while a data assimilation numerical experiment is presented using the heat equation in a variational setting

Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models

We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the geophysics literature, with state-space algorithms from the statistics literature. Our algorithms address a variety of estimation scenarios, including on-line and off-line state and parameter estimation. We take a Bayesian perspective, for which the goal is to generate samples from the joint posterior distribution of states and parameters. The key benefit of our approach is the use of ensemble Kalman methods for dimension reduction, which allows inference for high-dimensional state vectors. We compare our methods to existing ones, including ensemble Kalman filters, particle filters, and particle MCMC. Using a real data example of cloud motion and data simulated under a number of nonlinear and non-Gaussian scenarios, we show that our approaches outperform these existing methods

Core surface magnetic field evolution 2000-2010

We present new dedicated core surface field models spanning the decade from 2000.0 to 2010.0. These models, called gufm-sat, are based on CHAMP, Ørsted and SAC-C satellite observations along with annual differences of processed observatory monthly means. A spatial parametrization of spherical harmonics up to degree and order 24 and a temporal parametrization of sixth-order B-splines with 0.25 yr knot spacing is employed. Models were constructed by minimizing an absolute deviation measure of misfit along with measures of spatial and temporal complexity at the core surface. We investigate traditional quadratic or maximum entropy regularization in space, and second or third time derivative regularization in time. Entropy regularization allows the construction of models with approximately constant spectral slope at the core surface, avoiding both the divergence characteristic of the crustal field and the unrealistic rapid decay typical of quadratic regularization at degrees above 12. We describe in detail aspects of the models that are relevant to core dynamics. Secular variation and secular acceleration are found to be of lower amplitude under the Pacific hemisphere where the core field is weaker. Rapid field evolution is observed under the eastern Indian Ocean associated with the growth and drift of an intense low latitude flux patch. We also find that the present axial dipole decay arises from a combination of subtle changes in the southern hemisphere field morpholog

A Data Assimilation Framework that Uses the Kullback-Leibler Divergence

The process of integrating observations into a numerical model of an evolving dynamical system, known as data assimilation, has become an essential tool in computational science. These methods, however, are computationally expensive as they typically involve large matrix multiplication and inversion. Furthermore, it is challenging to incorporate a constraint into the procedure, such as requiring a positive state vector. Here we introduce an entirely new approach to data assimilation, one that satisfies an information measure and uses the unnormalized Kullback-Leibler divergence, rather than the standard choice of Euclidean distance. Two sequential data assimilation algorithms are presented within this framework and are demonstrated numerically. These new methods are solved iteratively and do not require an adjoint. We find them to be computationally more efficient than Optimal Interpolation (3D-Var solution) and the Kalman filter whilst maintaining similar accuracy. Furthermore, these Kullback-Leibler data assimilation (KL-DA) methods naturally embed constraints, unlike Kalman filter approaches. They are ideally suited to systems that require positive valued solutions as the KL-DA guarantees this without need of transformations, projections, or any additional steps. This Kullback-Leibler framework presents an interesting new direction of development in data assimilation theory. The new techniques introduced here could be developed further and may hold potential for applications in the many disciplines that utilize data assimilation, especially where there is a need to evolve variables of large-scale systems that must obey physical constraints

Experimental Evolution of Phenotypic Plasticity for Stress Resistance in the Nematode Caenorhabditis remanei

Many organisms can acclimate to new environments through phenotypic plasticity, a complex trait that can be heritable, be subject to selection, and evolve. However, the rate and genetic basis of plasticity evolution remain largely unknown. Experimentally evolved populations of the nematode Caenorhabditis remanei were created by selecting for stress resistance under different environmental conditions. This resource was used to address key questions about how phenotypic plasticity evolves and what the genetic basis of plasticity is. Here, I highlight ways in which a fuller understanding of the environmental context influences our interpretation of the evolution of phenotypic plasticity. In a population selected to withstand heat stress, an apparent case of genetic assimilation did not show correlated changes in global gene regulation. However, further investigation revealed that the induced plasticity was not fixed across environments, but rather the threshold for the response was shifted over evolutionary time. Similarly, the past environment experienced by populations can play a role in directing the multivariate response to selection. Correlated responses to selection between traits and across environments were examined. The pattern of covariation in the evolutionary response among traits differed depending on the environment in which selection occurred, indicating that there exists variation in pleiotropy across the stress response network that is highly sensitive to the external environment. To understand how the patterns of pleiotropy are altered by environment and evolution, there is a pressing need to determine the structure of the molecular networks underlying plastic phenotypes. Using RNA-sequencing, the structure of the gene regulatory network is examined for a subset of evolved populations from one environment. Key modules within this network were identified that are strong candidates for the evolution of phenotypic plasticity in this system. Together, the data presented in this dissertation provide a comprehensive view of the myriad ways in which the environment shapes the genetic architecture of stress response phenotypes and directs the evolution of phenotypic plasticity. Additionally, the structure of transcriptional network provides valuable insight into the genetic basis of adaptation to environmental change and the evolution of phenotypic plasticity. This dissertation includes both previously published and co-authored material

Large Scale Inverse Problems

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation &amp Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences