Alex Lenkoski

Combining forecasts from multiple numerical weather prediction (NWP) models has shown substantial benefit over the use of individual forecast products. Although combination, in a broad sense, is widely used in meteorological forecasting, systematic studies of combination methodology in meteorology are scarce. In this article, we study several combination methods, both state-of-the-art and of our own making, with a particular emphasis on situations where one seeks to predict when a particular event of interest will occur. Such time-to-event forecasts require particular methodology and care. We conduct a careful comparison of the different combination methods through an extensive simulation study, where we investigate the conditions under which the combined forecast will outperform the individual forecasting products. Further, we investigate the performance of the methods in a case study modelling the time to the first hard freeze in Norway and parts of Fennoscandia.

This report describes the research related to use case 2 within pilot ♯6 of the FAME project: Embedding Climatic Predictions in Property Insurance Products. In a changing climate, it is expected that the frequency and/or intensity of nat ural disasters will change. This has impacts on several sectors of the economy, perhaps the most obvious being disaster-related damages and losses affecting the profitability of insurance companies. To explore and quantify this link, we analyze the impact of major natural disasters on the volatility of insurance stocks. Our working hypothesis is that the value at risk (VaR) of these stocks increases in the wake of a disaster as a result of an expected spike in claims, loss in value of assets held by insurers, etc. To test this hypothesis, we analyze data on the economic losses associated with major disasters in Europe since January 2000, and we build a statistical model to model their effect on the volatility (and thereby VaR) of the different stock prices. For storms, one of the two most damaging types of disasters in Europe, we also calculate projections of a loss index based on climate model simulations of daily maximum wind speeds, and we analyze how the regionally aggregated loss index is projected to change in the future. Combined with the statistical model that links storm losses to the VaR of insurance stocks, these loss index projections could give us an idea about climate-related changes in VaR. Our analysis, however, does not show a clear and unequivocal link between nat ural disasters and insurance stock volatility. While some major disasters are followed by a drop in the price of certain insurance stocks, the signal is inconsistent and not statistically significant. This is in line with other studies in the literature, which find a significant link only for some regions and some types of disasters, but it leads us to conclude that a robust projection of climate-related changes in VaR cannot be obtained with the data at hand.

This report describes the research related to use case 1 within pilot ♯6 of the FAME project: Embedding Climatic Predictions in Property Insurance Products. For a dataset with house value statistics over a high-resolution grid over California (USA), a hedonic regression model was fitted that explains the median house value over a grid cell through factors like population density, median income, and ocean proximity. Additional variability can be explained by a component in the regression model that quantifies the reduction in house value due to frequent episodes with extreme heat at this grid cell. Daily mean temperature simulations from several regional climate models are then statistically further downscaled to the resolution of the house price grid, and the projected increase in the number of days per year with excessive heat over the next decades is studied. When combining this information with the fitted regression model, the associated projected decrease of house values can be calculated.

A transition to renewable energy is needed to mitigate climate change. In Europe, this transition has been led by wind energy, which is one of the fastest growing energy sources. However, energy demand and production are sensitive to meteorological conditions and atmospheric variability at multiple time scales. To accomplish the required balance between these two variables, critical conditions of high demand and low wind energy supply must be considered in the design of energy systems. We describe a methodology for modeling joint distributions of meteorological variables without making any assumptions about their marginal distributions. In this context, Gaussian copulas are used to model the correlated nature of cold and weak-wind events. The marginal distributions are modeled with logistic regressions defining two sets of binary variables as predictors: four large-scale weather regimes (WRs) and the months of the extended winter season. By applying this framework to ERA5 data, we can compute the joint probabilities of co-occurrence of cold and weak-wind events on a high-resolution grid (0.2◦).Our results show that (a) WRs must be considered when modeling cold and weak-wind events, (b) it is essential to account for the correlations between these events when modeling their joint distribution, (c) we need to analyze each month separately, and (d) the highest estimated number of days with compound events are associated with the negative phase of the North Atlantic Oscillation (3 days on average over Finland, Ireland, and Lithuania in January, and France and Luxembourg in February) and the Scandinavian blocking pattern (3 days on average over Ireland in January and Denmark in February). This information could be relevant for application in sub-seasonal to seasonal forecasts of such events

Agricultural food production and natural ecological systems depend on a range of seasonal climate indicators that describe seasonal patterns in climatological conditions. This article proposes a probabilistic forecasting framework for predicting the end of the freeze-free season, or the time to a mean daily near-surface air temperature below 0°C (referred to here as hard freeze). The forecasting framework is based on the multimodel seasonal forecast ensemble provided by the Copernicus Climate Data Store and uses techniques from survival analysis for time-to-event data. The original mean daily temperature forecasts are statistically postprocessed and downscaled with a mean and variance correction of each model system before the time-to-event forecast is constructed. In a case study for a region in Fennoscandia covering Norway for the period 1993–2020, the proposed forecasts are found to outperform a climatology forecast from an observation-based data product at locations where the average predicted time to hard freeze is less than 40 days after the initialization date of the forecast on October 1.

There is an increasing demand for high-quality seasonal weather forecasts from a broad range of stakeholders. However, the numerical weather prediction (NWP) output on which these forecasts are based require substantial postprocessing, as they are subject to systematic errors in both mean and spread. In order to validate any proposed post-processing methodology, the research community would benefit from a benchmark dataset on which more sophisticated methods can quickly be developed and tested. We supply a multi-model, multi-variable global dataset using five forecasting systems from the Copernicus climate data store (CDS) which can help serve these purposes. Our dataset is constructed using a straightforward anomaly standardization methodology with a leave-year-out cross validation design. In addition, validating observations from the ERA5 dataset are supplied, enabling rapid verification of system performance. The goal of this dataset is to save the research community the substantial investment in time necessary to create a usable baseline for their own investigations and also to create a standard benchmark dataset to which different research groups can compare results.

Seasonal weather forecasts are crucial for long-term planning in many practical situations and skillful forecasts may have substantial economic and humanitarian implications. Current seasonal forecasting models require statistical postprocessing of the output to correct systematic biases and unrealistic uncertainty assessments. We propose a multivariate postprocessing approach using covariance tapering, combined with a dimension reduction step based on principal component analysis for efficient computation. Our proposed technique can correctly and efficiently handle nonstationary, non-isotropic and negatively correlated spatial error patterns, and is applicable on a global scale. Further, a moving average approach to marginal postprocessing is shown to flexibly handle trends in biases caused by global warming, and short training periods. In an application to global sea surface temperature forecasts issued by the Norwegian climate prediction model, our proposed methodology is shown to outperform known reference methods. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

In economic applications, model averaging has found principal use in examining the validity of various theories related to observed heterogeneity in outcomes such as growth, development, and trade. Though often easy to articulate, these theories are imperfectly captured quantitatively. A number of different proxies are often collected for a given theory and the uneven nature of this collection requires care when employing model averaging. Furthermore, if valid, these theories ought to be relevant outside of any single narrowly focused outcome equation. We propose a methodology which treats theories as represented by latent indices, these latent processes controlled by model averaging on the proxy level. To achieve generalizability of the theory index our framework assumes a collection of outcome equations. We accommodate a flexible set of generalized additive models, enabling non-Gaussian outcomes to be included. Furthermore, selection of relevant theories also occurs on the outcome level, allowing for theories to be differentially valid. Our focus is on creating a set of theory-based indices directed at understanding a country’s potential risk of macroeconomic collapse. These Sovereign Risk Indices are calibrated across a set of different “collapse” criteria, including default on sovereign debt, heightened potential for high unemployment or inflation and dramatic swings in foreign exchange values. The goal of this exercise is to render a portable set of country/year theory indices which can find more general use in the research community.

Seasonal forecasting has became a critical area of development in numerical weather prediction. Reliable forecasts beyond the two week time period are necessary for a number of industrial and societal planning applications and new approaches are being developed to extend the useful range of numerical weather prediction output. We investigate the performance of one such system, the UK Met Office’s GloSea5 system, an ensemble system with the novel feature that ensemble members are initiated in a rolling and staggered manner. Focusing on summer surface temperatures, we show that individual model runs from this system do not exhibit skill beyond the two-week time horizon and indeed substantially under-perform climatological forecasts at longer lead times. However, when combining the ensemble system and applying the Rapid Adjustment of Forecast Trajectories (RAFT) methodology to the individual runs, we show that the combined forecast can achieve performance which is always at least on par with climatology and in many circumstances exhibits modest outperformance.

Modern weather forecasts are commonly issued as consistent multi‐day forecast trajectories with a time resolution of 1–3 hours. Prior to issuing, statistical post‐processing is routinely used to correct systematic errors and misrepresentations of the forecast uncertainty. However, once the forecast has been issued, it is rarely updated before it is replaced in the next forecast cycle of the numerical weather prediction (NWP) model. This paper shows that the error correlation structure within the forecast trajectory can be utilized to substantially improve the forecast between the NWP forecast cycles by applying additional post‐processing steps each time new observations become available. The proposed rapid adjustment is applied to temperature forecast trajectories from the UK Met Office's convective‐scale ensemble MOGREPS‐UK. MOGREPS‐UK is run four times daily and produces hourly forecasts for up to 36 hours ahead. Our results indicate that the rapidly adjusted forecast from the previous NWP forecast cycle outperforms the new forecast for the first few hours of the next cycle, or until the new forecast itself can be rapidly adjusted, suggesting a new strategy for updating the forecast cycle.

The skill of a typical NWP forecast decreases over time, so that forecasts from more recent model runs are generallyconsideredtobemoreskillfulandgivemoreaccuratepredictions.Somepost-processingtechniquesstill make use of older model runs through time-lagging or blending, but with very little relevance, as the newer model runs are preferred. At the same time, technological advances make observations become available in very short time frames and in increasing amounts. We propose a new method, Rapid Adjustment of Forecast Trajectories (RAFT), which works in combination with traditional statistical post-processing techniques and uses short-term observations to improve older forecast runs. As a result, older forecasts match or even surpass the skill of the forecasts from the newest model run. Relying on the inherent correlation structure of the forecast errors between lead times, RAFT updates the tail of a forecast trajectory while the first part verifies. The adaptive regression approach takes into account changesinpredictabilityandlocalpatterns,whilebeingcomputationallyefficient.WewillpresentRAFTversions forhourlysurfacetemperatureand10mwindspeedforecastsfromtheUKMetOffice’sMOGREPS-UKensemble.

This paper investigates the role of model uncertainty in explaining the different findings in the literature regarding the determinants of government expenditure and its components. In particular, we systematically assess the evidentiary support for nine different theories using a novel model averaging method that allows for endogeneity. Our results suggest that the government size and its components are explained by multiple mechanisms that work simultaneously but differ in their impact and importance. Hence, policy makers should avoid relying on any particular model to make policy decisions. More precisely, for general government total expenditure we find decisive evidence for the demography theory and a strong evidence for the globalization and political institution theory. In the case of central government total expenditure, we find that income inequality and macroeconomic policy play a decisive role in addition to demography.

Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate prior for inverse covariance matrices satisfying graphical constraints. While it is straightforward to posit the unnormalized densities, the normalizing constants of these distributions have been known only for graphs that are chordal, or decomposable. Up until now, it was unknown whether the normalizing constant for a general graph could be represented explicitly, and a considerable body of computational literature emerged that attempted to avoid this apparent intractability. We close this question by providing an explicit representation of the G-Wishart normalizing constant for general graphs.

Spatial maps of extreme precipitation are a critical component of flood estimation in hydrological modeling, as well as in the planning and design of important infrastructure. This is particularly relevant in countries, such as Norway, that have a high density of hydrological power generating facilities and are exposed to significant risk of infrastructure damage due to flooding. In this work, we estimate a spatially coherent map of the distribution of extreme hourly precipitation in Norway, in terms of return levels, by linking generalized extreme value (GEV) distributions with latent Gaussian fields in a Bayesian hierarchical model. Generalized linear models on the parameters of the GEV distribution are able to incorporate location-specific geographic and meteorological information and thereby accommodate these effects on extreme precipitation. Our model incorporates a Bayesian model averaging component that directly assesses model uncertainty in the effect of the proposed covariates. Gaussian fields on the GEV parameters capture additional unexplained spatial heterogeneity and overcome the sparse grid on which observations are collected. Our framework is able to appropriately characterize both the spatial variability of the distribution of extreme hourly precipitation in Norway and the associated uncertainty in these estimates.

Dust storms in the earth’s major desert regions significantly influence microphysical weather processes, the CO22-cycle and the global climate in general. Recent increases in the spatio-temporal resolution of remote sensing instruments have created new opportunities to understand these phenomena. However, the scale of the data collected and the inherent stochasticity of the underlying process pose significant challenges, requiring a careful combination of image processing and statistical techniques. Using satellite imagery data, we develop a statistical model of atmospheric transport that relies on a latent Gaussian Markov random field (GMRF) for inference. In doing so, we make a link between the optical flow method of Horn and Schunck and the formulation of the transport process as a latent field in a generalized linear model. We critically extend this framework to satisfy the integrated continuity equation, thereby incorporating a flow field with nonzero divergence, and show that such an approach dramatically improves performance while remaining computationally feasible. Effects such as air compressibility and satellite column projection hence become intrinsic parts of this model. We conclude with a study of the dynamics of dust storms formed over Saharan Africa and show that our methodology is able to accurately and coherently track storm movement, a critical problem in this field.

Shape from texture refers to the extraction of 3D information from 2D images with irregular texture. This paper introduces a statistical framework to learn shape from texture where convex texture elements in a 2D image are represented through a point process. In a first step, the 2D image is preprocessed to generate a probability map corresponding to an estimate of the unnormalized intensity of the latent point process underlying the texture elements. The latent point process is subsequently inferred from the probability map in a non-parametric, model free manner. Finally, the 3D information is extracted from the point pattern by applying a locally scaled point process model where the local scaling function represents the deformation caused by the projection of a 3D surface onto a 2D image.

Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent developments provide a direct way to sample from the G-Wishart distribution, which allows for more efficient algorithms for model selection than previously possible. Still, estimating Gaussian graphical models with more than a handful of variables remains a nearly infeasible task. Here, we propose two novel algorithms that use the direct sampler to more efficiently approximate the posterior distribution of the Gaussian graphical model. The first algorithm uses conditional Bayes factors to compare models in a Metropolis–Hastings framework. The second algorithm is based on a continuous time Markov process. We show that both algorithms are substantially faster than state-of-the-art alternatives. Finally, we show how the algorithms may be used to simultaneously estimate both structural and functional connectivity between subcortical brain regions using resting-state functional magnetic resonance imaging.

Economic modeling in the presence of endogeneity is subject to model uncertainty at both the instrument and covariate level. We propose a Two-Stage Bayesian Model Averaging (2SBMA) methodology that extends the Two-Stage Least Squares (2SLS) estimator. By constructing a Two-Stage Unit Information Prior in the endogenous variable model, we are able to efficiently combine established methods for addressing model uncertainty in regression models with the classic technique of 2SLS. To assess the validity of instruments in the 2SBMA context, we develop Bayesian tests of the identification restriction that are based on model averaged posterior predictive p-values. A simulation study showed that 2SBMA has the ability to recover structure in both the instrument and covariate set, and substantially improves the sharpness of resulting coefficient estimates in comparison to 2SLS using the full specification in an automatic fashion. Due to the increased parsimony of the 2SBMA estimate, the Bayesian Sargan test had a power of 50% in detecting a violation of the exogeneity assumption, while the method based on 2SLS using the full specification had negligible power. We apply our approach to the problem of development accounting, and find support not only for institutions, but also for geography and integration as development determinants, once both model uncertainty and endogeneity have been jointly addressed.

The G-Wishart distribution is the conjugate prior for precision matrices that encode the conditional independence of a Gaussian graphical model. Although the distribution has received considerable attention, posterior inference has proven computationally challenging, in part owing to the lack of a direct sampler. In this note, we rectify this situation. The existence of a direct sampler offers a host of new possibilities for the use of G-Wishart variates. We discuss one such development by outlining a new transdimensional model search algorithm—which we term double reversible jump—that leverages this sampler to avoid normalizing constant calculation when comparing graphical models. We conclude with two short studies meant to investigate our algorithm’s validity.

The Gaussian Graphical Model (GGM) is a popular tool for incorporating sparsity into joint multivariate distributions. The G-Wishart distribution, a conjugate prior for precision matrices satisfying general GGM constraints, has now been in existence for over a decade. However, due to the lack of a direct sampler, its use has been limited in hierarchical Bayesian contexts, relegating mixing over the class of GGMs mostly to situations involving standard Gaussian likelihoods. Recent work has developed methods that couple model and parameter moves, first through reversible jump methods and later by direct evaluation of conditional Bayes factors and subsequent resampling. Further, methods for avoiding prior normalizing constant calculations–a serious bottleneck and source of numerical instability–have been proposed. We review and clarify these developments and then propose a new methodology for GGM comparison that blends many recent themes. Theoretical developments and computational timing experiments reveal an algorithm that has limited computational demands and dramatically improves on computing times of existing methods. We conclude by developing a parsimonious multivariate stochastic volatility model that embeds GGM uncertainty in a larger hierarchical framework. The method is shown to be capable of adapting to swings in market volatility, offering improved calibration of predictive distributions.