A Bayesian Model to Study Spatio-temporal Variability of Latent Heat Flux and its Trend

AbstractThis paper talks about two models. First model is presented to study space-time variability of latent heat flux, where latent heat flux has been decomposed into three periodic terms, spatio-temporal process term, long term trend and a term due to covariates. And the second model is presented to characterize the long term trend and its possible causes. For both the models Bayesian approach was adopted. The method presented is particularly useful for characterizing environmental spatio- temporal processes variability. The model parameters were sampled using a Markov chain Monte Carlo simulation technique. The models were used for studying latent heat flux components in the Indian Ocean for the period of January 1985 to April 2010. The results showed that in LHF variability, dominant factors were annual variability, spatio-temporal variability and variability due to covariates. Further it has been found that the long term positive trend of LHF is dominated by the increase in wind speed. In some regions of Indian Ocean, increase in sea surface temperature has also been the cause for increase in LHF

Spatio-temporal Statistical Modeling: Climate Impacts due to Bioenergy Crop Expansion

abstract: Large-scale cultivation of perennial bioenergy crops (e.g., miscanthus and switch- grass) offers unique opportunities to mitigate climate change through avoided fossil fuel use and associated greenhouse gas reduction. Although conversion of existing agriculturally intensive lands (e.g., maize and soy) to perennial bioenergy cropping systems has been shown to reduce near-surface temperatures, unintended consequences on natural water resources via depletion of soil moisture may offset these benefits. In the effort of the cross-fertilization across the disciplines of physics-based modeling and spatio-temporal statistics, three topics are investigated in this dissertation aiming to provide a novel quantification and robust justifications of the hydroclimate impacts associated with bioenergy crop expansion. Topic 1 quantifies the hydroclimatic impacts associated with perennial bioenergy crop expansion over the contiguous United States using the Weather Research and Forecasting Model (WRF) dynamically coupled to a land surface model (LSM). A suite of continuous (2000–09) medium-range resolution (20-km grid spacing) ensemble-based simulations is conducted. Hovmöller and Taylor diagrams are utilized to evaluate simulated temperature and precipitation. In addition, Mann-Kendall modified trend tests and Sieve-bootstrap trend tests are performed to evaluate the statistical significance of trends in soil moisture differences. Finally, this research reveals potential hot spots of suitable deployment and regions to avoid. Topic 2 presents spatio-temporal Bayesian models which quantify the robustness of control simulation bias, as well as biofuel impacts, using three spatio-temporal correlation structures. A hierarchical model with spatially varying intercepts and slopes display satisfactory performance in capturing spatio-temporal associations. Simulated temperature impacts due to perennial bioenergy crop expansion are robust to physics parameterization schemes. Topic 3 further focuses on the accuracy and efficiency of spatial-temporal statistical modeling for large datasets. An ensemble of spatio-temporal eigenvector filtering algorithms (hereafter: STEF) is proposed to account for the spatio-temporal autocorrelation structure of the data while taking into account spatial confounding. Monte Carlo experiments are conducted. This method is then used to quantify the robustness of simulated hydroclimatic impacts associated with bioenergy crops to alternative physics parameterizations. Results are evaluated against those obtained from three alternative Bayesian spatio-temporal specifications.Dissertation/ThesisDoctoral Dissertation Statistics 201

Investigating the thermal state of permafrost with Bayesian inverse modeling of heat transfer

Long-term measurements of permafrost temperatures do not provide a complete picture of the Arctic subsurface thermal regime. Regions with warmer permafrost often show little to no long-term change in ground temperature due to the uptake and release of latent heat during freezing and thawing. Thus, regions where the least warming is observed may also be the most vulnerable to permafrost degradation. Since direct measurements of ice and liquid water contents in the permafrost layer are not widely available, thermal modeling of the subsurface plays a crucial role in understanding how permafrost responds to changes in the local energy balance. In this work, we first analyze trends in observed air and permafrost temperatures at four sites within the continuous permafrost zone, where we find substantial variation in the apparent relationship between long-term changes in permafrost temperatures (0.02–0.16 K yr−1) and air temperature (0.09–0.11 K yr−1). We then apply recently developed Bayesian inversion methods to link observed changes in borehole temperatures to unobserved changes in latent heat and active layer thickness using a transient model of heat conduction with phase change. Our results suggest that the degree to which recent warming trends correlate with permafrost thaw depends strongly on both soil freezing characteristics and historical climatology. At the warmest site, a 9 m borehole near Ny-Ålesund, Svalbard, modeled active layer thickness increases by an average of 13 ± 1 cm K−1 rise in mean annual ground temperature. In stark contrast, modeled rates of thaw at one of the colder sites, a borehole on Samoylov Island in the Lena River delta, appear far less sensitive to temperature change, with a negligible effect of 1 ± 1 cm K−1. Although our study is limited to just four sites, the results urge caution in the interpretation and comparison of warming trends in Arctic boreholes, indicating significant uncertainty in their implications for the current and future thermal state of permafrost.</p

On Simplified Bayesian Modeling for Massive Geostatistical Datasets: Conjugacy and Beyond

With continued advances in Geographic Information Systems and related computational technologies, researchers in diverse fields like forestry, environmental health, climate sciences etc. have growing interests in analyzing large scale data sets measured at a substantial number of geographic locations. Geostatistical models used to capture the space varying relationships in such data are often accompanied by onerous computations which prohibit the analysis of large scale spatial data sets. Less burdensome alternatives proposed recently for analyzing massive spatial datasets often lead to inaccurate inference or require slow sampling process. Bayesian inference, while attractive for accommodating uncertainties through their hierarchical structures, can become computationally onerous for modeling massive spatial data sets because of their reliance on iterative estimation algorithms. My dissertation research aims at developing computationally scalable Bayesian geostatistical models that provide valid inference through highly accelerated sampling process. We also study the asymptotic properties of estimators in spatial analysis.In Chapter 2 and 3, we develop conjugate Bayesian frameworks for analyzing univariate and multivariate spatial data. We propose a conjugate latent Nearest-Neighbor Gaussian Process (NNGP) model in Chapter 2, which uses analytically tractable posterior distributions to obtain posterior inferences, including the large dimensional latent process. In Chapter 3, we focus on building conjugate Bayesian frameworks for analyzing multivariate spatial data. We utilize Matrix-Normal Inverse-Wishart(MNIW) prior to propose conjugate Bayesian frameworks and algorithms that can incorporate a family of scalable spatial modeling methodologies.In Chapter 4, we pursue general Bayesian modeling methodologies beyond a conjugate Bayesian hierarchical modeling. We build scalable versions of a hierarchical linear model of coregionalization (LMC) and spatial factor models, and propose a highly accelerated block update MCMC algorithm. Using the proposed Bayesian LMC model, we extend scalable modeling strategies for a single process into multivariate process cases. All proposed frameworks are tested on simulated data and fit to real data sets with observed locations numbering in the millions. Our contribution is to offer practicing scientists and spatial analysts practical and flexible scalable hierarchical models for analyzing massive spatial data sets.In Chapter 5, we investigate the asymptotic properties of the estimators in spatial analysis. We formally establish results on the identifiability and consistency of the nugget in spatial models based upon the Gaussian process within the framework of in-fill asymptotics, i.e. the sample size increases within a sampling domain that is bounded. We establish the identifiability of parameters in the Matern covariance function and the consistency of their maximum likelihood estimators in the presence of discontinuities due to the nugget

Bayesian inferences of the thermal properties of a wall using temperature and heat flux measurements

The assessment of the thermal properties of walls is essential for accurate building energy simulations that are needed to make effective energy-saving policies. These properties are usually investigated through in-situ measurements of temperature and heat flux over extended time periods. The one-dimensional heat equation with unknown Dirichlet boundary conditions is used to model the heat transfer process through the wall. In [F. Ruggeri, Z. Sawlan, M. Scavino, R. Tempone, A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions, Bayesian Analysis 12 (2)(2017) 407-433], it was assessed the uncertainty about the thermal diffusivity parameter using different synthetic data sets. In this work, we adapt this methodology to an experimental study conducted in an environmental chamber, with measurements recorded every minute from temperature probes and heat flux sensors placed on both sides of a solid brick wall over a five-day period. The observed time series are locally averaged, according to a smoothing procedure determined by the solution of a criterion function optimization problem, to fit the required set of noise model assumptions. Therefore, after preprocessing, we can reasonably assume that the temperature and the heat flux measurements have stationary Gaussian noise and we can avoid working with full covariance matrices. The results show that our technique reduces the bias error of the estimated parameters when compared to other approaches. Finally, we compute the information gain under two experimental setups to recommend how the user can efficiently determine the duration of the measurement campaign and the range of the external temperature oscillation

2016 International Land Model Benchmarking (ILAMB) Workshop Report

As earth system models (ESMs) become increasingly complex, there is a growing need for comprehensive and multi-faceted evaluation of model projections. To advance understanding of terrestrial biogeochemical processes and their interactions with hydrology and climate under conditions of increasing atmospheric carbon dioxide, new analysis methods are required that use observations to constrain model predictions, inform model development, and identify needed measurements and field experiments. Better representations of biogeochemistryclimate feedbacks and ecosystem processes in these models are essential for reducing the acknowledged substantial uncertainties in 21st century climate change projections

Modeling and analysis of actual evapotranspiration using data driven and wavelet techniques

Large-scale mining practices have disturbed many natural watersheds in northern Alberta, Canada. To restore disturbed landscapes and ecosystems’ functions, reconstruction strategies have been adopted with the aim of establishing sustainable reclaimed lands. The success of the reconstruction process depends on the design of reconstruction strategies, which can be optimized by improving the understanding of the controlling hydrological processes in the reconstructed watersheds. Evapotranspiration is one of the important components of the hydrological cycle; its estimation and analysis are crucial for better assessment of the reconstructed landscape hydrology, and for more efficient design. The complexity of the evapotranspiration process and its variability in time and space has imposed some limitations on previously developed evapotranspiration estimation models. The vast majority of the available models estimate the rate of potential evapotranspiration, which occurs under unlimited water supply condition. However, the rate of actual evapotranspiration (AET) depends on the available soil moisture, which makes its physical modeling more complicated than the potential evapotranspiration. The main objective of this study is to estimate and analyze the AET process in a reconstructed landscape. Data driven techniques can model the process without having a complete understanding of its physics. In this study, three data driven models; genetic programming (GP), artificial neural networks (ANNs), and multilinear regression (MLR), were developed and compared for estimating the hourly eddy covariance (EC)-measured AET using meteorological variables. The AET was modeled as a function of five meteorological variables: net radiation (Rn), ground temperature (Tg), air temperature (Ta), relative humidity (RH), and wind speed (Ws) in a reconstructed landscape located in northern Alberta, Canada. Several ANN models were evaluated using two training algorithms of Levenberg-Marquardt and Bayesian regularization. The GP technique was employed to generate mathematical equations correlating AET to the five meteorological variables. Furthermore, the available data were statistically analyzed to obtain MLR models and to identify the meteorological variables that have significant effect on the evapotranspiration process. The utility of the investigated data driven models was also compared with that of HYDRUS-1D model, which is a physically based model that makes use of conventional Penman-Monteith (PM) method for the prediction of AET. HYDRUS-1D model was examined for estimating AET using meteorological variables, leaf area index, and soil moisture information. Furthermore, Wavelet analysis (WA), as a multiresolution signal processing tool, was examined to improve the understanding of the available time series temporal variations, through identifying the significant cyclic features, and to explore the possible correlation between AET and the meteorological signals. WA was used with the purpose of input determination of AET models, a priori. The results of this study indicated that all three proposed data driven models were able to approximate the AET reasonably well; however, GP and MLR models had better generalization ability than the ANN model. GP models demonstrated that the complex process of hourly AET can be efficiently modeled as simple semi-linear functions of few meteorological variables. The results of HYDRUS-1D model exhibited that a physically based model, such as HYDRUS-1D, might perform on par or even inferior to the data driven models in terms of the overall prediction accuracy. The developed equation-based models; GP and MLR, revealed the larger contribution of net radiation and ground temperature, compared to other variables, to the estimation of AET. It was also found that the interaction effects of meteorological variables are important for the AET modeling. The results of wavelet analysis demonstrated the presence of both small-scale (2 to 8 hours) and larger-scale (e.g. diurnal) cyclic features in most of the investigated time series. Larger-scale cyclic features were found to be the dominant source of temporal variations in the AET and most of the meteorological variables. The results of cross wavelet analysis indicated that the cause and effect relationship between AET and the meteorological variables might vary based on the time-scale of variation under consideration. At small time-scales, significant linear correlations were observed between AET and Rn, RH, and Ws time series, while at larger time-scales significant linear correlations were observed between AET and Rn, RH, Tg, and Ta time series