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Statistical modeling and interpolation of space–time processes has gained increasing relevance over the last few years. However, real world data often exhibit characteristics that challenge conventional methods such as nonstationarity and temporal misalignment. For example, high frequency solar irradiance data are typically observed at fine temporal scales, but at sparse spatial sampling, so space–time interpolation is necessary to support solar energy studies. The nonstationarity and phase misalignment of such data challenges extant approaches. We propose random elastic space–time (REST) prediction, a novel method that addresses temporally-varying phase misalignment by combining elastic alignment and conventional kriging techniques. Moreover, uncertainty in both amplitude and phase alignment can be readily quantified in a conditional simulation framework, whereas conventional space–time methods only address am- plitude uncertainty. We illustrate our approach on a challenging solar irradiance dataset, where our method demonstrates superior predictive distributions compared to existing geostatistical and functional data analytic techniques. 

We present a novel space‐time Bayesian hierarchical model (BHM) to reconstruct annual Sea Surface Temperature (SST) over a large domain based on SST at limited proxy (i.e., sediment core) locations. The model is tested in the equatorial Pacific. The BHM leverages Principal Component Analysis to identify dominant space‐time modes of contemporary variability of the SST field at the proxy locations and employs these modes in a Gaussian process framework to estimate SSTs across the entire domain. The BHM allows us to model the mean field and covariance, varying in space and time in the process layers of the hierarchy. Using the Markov Chain Monte Carlo (MCMC) method and suitable priors on the model parameters, posterior distributions of the model parameters and, consequently, posterior distributions of the SST fields and the attendant uncertainties are obtained for any desired year. The BHM is calibrated and validated in the contemporary period (1854–2014) and subsequently applied to reconstruct SST fields during the Holocene (0–10 ka). Results are consistent with prior inferences of La Niña‐like conditions during the Holocene. This modeling framework opens exciting prospects for modeling and reconstruction of other fields, such as precipitation, drought indices, and vegetation. 

Abstract Snowpack in mountainous areas often provides water storage for summer and fall, especially in the Western United States. In situ observations of snow properties in mountainous terrain are limited by cost and effort, impacting both temporal and spatial sampling, while remote sensing estimates provide more complete spacetime coverage. Spatial estimates of fractional snow covered area (fSCA) at 30m are available every 16 days from the series of multispectral scanning instruments on Landsat platforms. Daily estimates at 463m spatial resolution are also available from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument on the Terra satellite. Fusing Landsat and MODIS fSCA images creates high resolution daily spatial estimates of fSCA that are needed for various uses: to support scientists and managers interested in energy and water budgets for water resources and to understand the movement of animals in a changing climate. Here, we propose a new machine learning approach conditioned on MODIS fSCA, as well as a set of physiographic features, and fit to Landsat fSCA over a portion of the Sierra Nevada USA. The predictions are daily 30m fSCA. The approach relies on two stages of spatially‐varying models. The first classifies fSCA into three categories and the second yields estimates within (0, 100) percent fSCA. Separate models are applied and fitted within sub‐regions of the study domain. Compared with a recently‐published machine learning model (Rittger, Krock, et al., 2021), this approach uses spatially local (rather than global) random forests, and improves the classification error of fSCA by 16%, and fractionally‐covered pixel estimates by 18%. 

Lévy processes are useful tools for analysis and modeling of jump‐diffusion processes. Such processes are commonly used in the financial and physical sciences. One approach to building new Lévy processes is through subordination, or a random time change. In this work, we discuss and examine a type of multiply subordinated Lévy process model that we term a deep variance gamma (DVG) process, including estimation and inspection methods for selecting the appropriate level of subordination given data. We perform an extensive simulation study to identify situations in which different subordination depths are identifiable and provide a rigorous theoretical result detailing the behavior of a DVG process as the levels of subordination tend to infinity. We test the model and estimation approach on a data set of intraday 1‐min cryptocurrency returns and show that our approach outperforms other state‐of‐the‐art subordinated Lévy process models. 

Abstract. Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through the inclusion of cross-domain terms in the background error covariance matrix.When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work, we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari–Cohn localization function; the within-component localization functions are standard Gaspari–Cohn with different localization radii, while the cross-localization function is newly constructed. The functions produce positive semidefinite localization matrices which are suitable for use in both Kalman filters and variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate and weakly coupled analogs of all four functions in a simple experiment with the bivariate Lorenz 96 system. In our experiments, the multivariate Gaspari–Cohn function leads to better performance than any of the other multivariate localization functions.