Abstract not found

Continuously indexed Gaussian fields (GFs) is the most important ingredient in spatial statistical modelling and geo-statistics. The specification through the covariance function gives an intuitive interpretation of its properties. On the computational side, GFs are hampered with the big-n problem, since the cost of factorising dense matrices is cubic in the dimension. Although the computational power today is alltime-high, this fact seems still to be a computational bottleneck in applications. Along with GFs, there is the class of Gaussian Markov random fields (GMRFs) which are discretely indexed. The Markov property makes the involved precision matrix sparse which enables the use of numerical algorithms for sparse matrices, that for fields in R 2 only use the square-root of the time required by general algorithms. The specification of a GMRF is through its full conditional distributions but its marginal properties are not transparent in such a parametrisation. In this paper, we show that using an approximate stochastic weak solution to (linear) stochastic partial differential equations (SPDEs), we can, for some GFs in the Matérn class, provide an explicit link, for any triangulation of R d, between GFs and GMRFs. The consequence is that we can take the best from the two worlds and do the modelling using GFs but do the computations using GMRFs. Perhaps more importantly,

Forecast ensembles typically show a spread-skill relationship, but they are also often underdispersive, and therefore uncalibrated. Bayesian model averaging (BMA) is a statistical postprocessing method for forecast ensembles that generates calibrated probabilistic forecast products for weather quantities at individual sites. This paper introduces the Spatial BMA technique, which combines BMA and the geostatistical output perturbation (GOP) method, and extends BMA to generate calibrated probabilistic forecasts of whole weather fields simultaneously, rather than just weather events at individual locations. At any site individually, Spatial BMA reduces to the original BMA technique. The Spatial BMA method provides statistical ensembles of weather field forecasts that take the spatial structure of observed fields into account and honor the flow-dependent information contained in the dynamical ensemble. The members of the Spatial BMA ensemble are obtained by dressing the weather field forecasts from the dynamical ensemble with simulated spatially correlated error fields, in proportions that correspond to the BMA weights for the member models in the dynamical ensemble. Statistical ensembles of any size can be

An important potential outcome of anthropogenic climate change is a possible collapse of the Atlantic meridional overturning circulation (AMOC). Assessing the risk of an AMOC collapse is of considerable interest since it may result in major temperature and precipitation changes and a shift in terrestrial ecosystems. One key source of uncertainty in AMOC predictions is uncertainty about background ocean vertical diffusivity (Kv), a key model parameter. Kv cannot be directly observed but can be inferred by combining climate model output with observations on the oceans (so called “tracers”). In this work, we combine information from multiple tracers, each observed on a spatial grid. Our two stage approach emulates the computationally expensive climate model using a flexible hierarchical model to connect the tracers. We then infer Kv using our emulator and the observations via a Bayesian approach, accounting for observation error and model discrepancy. We utilize kernel mixing and matrix identities in our Gaussian process model to considerably reduce the computational burdens imposed by the large data sets. We find that our approach is flexible, reduces identifiability issues, and enables inference about Kv based on large data sets. We use the resulting inference about Kv to improve probabilistic projections of the AMOC.

Abstract not found

Much recent work has concerned sparse approximations to speed up the Gaussian process regression from the unfavorable O(n 3) scaling in computational time to O(nm 2). Thus far, work has concentrated on models with one covariance function. However, in many practical situations additive models with multiple covariance functions may perform better, since the data may contain both long and short length-scale phenomena. The long length-scales can be captured with global sparse approximations, such as fully independent conditional (FIC), and the short length-scales can be modeled naturally by covariance functions with compact support (CS). CS covariance functions lead to naturally sparse covariance matrices, which are computationally cheaper to handle than full covariance matrices. In this paper, we propose a new sparse Gaussian process model with two additive components: FIC for the long length-scales and CS covariance function for the short length-scales. We give theoretical and experimental results and show that under certain conditions the proposed model has the same computational complexity as FIC. We also compare the model performance of the proposed model to additive models approximated by fully and partially independent conditional (PIC). We use real data sets and show that our model outperforms FIC and PIC approximations for data sets with two additive phenomena. 1

Forecast ensembles typically show a spread–skill relationship, but they are also often underdispersive, and therefore uncalibrated. Bayesian model averaging (BMA) is a statistical postprocessing method for forecast ensembles that generates calibrated probabilistic forecast products for weather quantities at individual sites. This paper introduces the spatial BMA technique, which combines BMA and the geostatistical output perturbation (GOP) method, and extends BMA to generate calibrated probabilistic forecasts of whole weather fields simultaneously, rather than just weather events at individual locations. At any site individually, spatial BMA reduces to the original BMA technique. The spatial BMA method provides statistical ensembles of weather field forecasts that take the spatial structure of observed fields into account and honor the flow-dependent information contained in the dynamical ensemble. The members of the spatial BMA ensemble are obtained by dressing the weather field forecasts from the dynamical ensemble with simulated spatially correlated error fields, in proportions that correspond to the BMA weights for the member models in the dynamical ensemble. Statistical ensembles of any size can be generated at minimal computational cost. The spatial BMA technique was applied to 48-h forecasts of surface temperature over the Pacific Northwest in 2004, using the University of Washington mesoscale ensemble. The spatial BMA ensemble generally outperformed the BMA and GOP ensembles and showed much better verification results than the raw ensemble, both at individual sites, for weather field forecasts, and for forecasts of composite quantities, such as average temperature in National Weather Service forecast zones and minimum temperature along the Interstate 90 Mountains to Sound Greenway. 1.

Banerjee for helpful discussions and Dr. Sally Bushhouse for permitting and facilitating our analysis of the Minnesota

test for stationarity of spatio-temporal random fields on planar and spherical domains

A class of covariate-dependent spatiotemporal covariance functions