arXiv subjects

Stefan Siegert

Publications and source records attributed to Stefan Siegert.

11 recordsLinked to original sources

arXiv2025

A curated UK rain radar data set for training and benchmarking nowcasting models

This paper documents a data set of UK rain radar image sequences for use in statistical modeling and machine learning methods for nowcasting. The main dataset contains 1,000 randomly sampled sequences of length 20 steps (15-minute increments) of 2D radar intensity fields of dimension 40x40 (at 5km spatial resolution). Spatially stratified sampling ensures spatial homogeneity despite removal of clear-sky cases by threshold-based truncation. For each radar sequence, additional atmospheric and geographic features are made available, including date, location, mean elevation, mean wind direction and speed and prevailing storm type. New R functions to extract data from the binary "Nimrod" radar data format are provided. A case study is presented to train and evaluate a simple convolutional neural network for radar nowcasting, including self-contained R code.

physics.ao-ph↗

arXiv2025

Discrete Gaussian Vector Fields On Meshes

Though the underlying fields associated with vector-valued environmental data are continuous, observations themselves are discrete. For example, climate models typically output grid-based representations of wind fields or ocean currents, and these are often downscaled to a discrete set of points. By treating the area of interest as a two-dimensional manifold that can be represented as a triangular mesh and embedded in Euclidean space, this work shows that discrete intrinsic Gaussian processes for vector-valued data can be developed from discrete differential operators defined with respect to a mesh. These Gaussian processes account for the geometry and curvature of the manifold whilst also providing a flexible and practical formulation that can be readily applied to any two-dimensional mesh. We show that these models can capture harmonic flows, incorporate boundary conditions, and model non-stationary data. Finally, we apply these models to downscaling stationary and non-stationary gridded wind data on the globe, and to inference of ocean currents from sparse observations in bounded domains.

stat.ME↗

arXiv2024

DustNet: skillful neural network predictions of Saharan dust

Suspended in the atmosphere are millions of tonnes of mineral dust which interacts with weather and climate. Accurate representation of mineral dust in weather models is vital, yet remains challenging. Large scale weather models use high power supercomputers and take hours to complete the forecast. Such computational burden allows them to only include monthly climatological means of mineral dust as input states inhibiting their forecasting accuracy. Here, we introduce DustNet a simple, accurate and super fast forecasting model for 24-hours ahead predictions of aerosol optical depth AOD. DustNet trains in less than 8 minutes and creates predictions in 2 seconds on a desktop computer. Created by DustNet predictions outperform the state-of-the-art physics-based model on coarse 1 x 1 degree resolution at 95% of grid locations when compared to ground truth satellite data. Our results show DustNet has a potential for fast and accurate AOD forecasting which could transform our understanding of dust impacts on weather patterns.

physics.geo-ph↗

arXiv2022

Spatial forecast postprocessing: The Max-and-Smooth approach

Numerical weather forecasts can exhibit systematic errors due to simplifying model assumptions and computational approximations. Statistical postprocessing is a statistical approach to correcting such biases. A statistical postprocessing model takes input data from a numerical forecast model, and outputs a parametric predictive distribution of a real-world observation, with model parameters learned from past forecast-observation pairs. In this paper we develop and discuss methods for postprocessing of gridded data. We show that estimates of postprocessing parameters on a spatial grid can be improved by Bayesian hierarchical modelling with spatial priors. We use the "Max-and-Smooth" approach [Hrafnkelsson et al., 2021] to approximate a fully Bayesian inference in two steps. First we calculate maximum-likelihood estimates (MLEs) of postprocessing parameters at individual grid points. Second we smooth the MLEs using a measurement error model with a spatial prior. Our approach provides the theoretical basis for the parameter smoothing approach by Kharin et al. [2017], and simplifies and generalises the Bayesian hierarchical modelling approach by Moeller et al. [2015]. A new derivation of Max-and-Smooth is presented. The method is applicable to arbitrary postprocessing models, as illustrated on Model Output Statistics, Logistic Regression, and Nonhomogeneous Gaussian Regression. We report consistent improvements in forecast accuracy, calibration, and probabilistic skill in postprocessing of temperature and precipitation forecasts.

stat.ME↗

arXiv2021

Approximate Bayesian inference for analysis of spatio-temporal flood frequency data

Extreme floods cause casualties, and widespread damage to property and vital civil infrastructure. We here propose a Bayesian approach for predicting extreme floods using the generalized extreme-value (GEV) distribution within gauged and ungauged catchments. A major methodological challenge is to find a suitable parametrization for the GEV distribution when covariates or latent spatial effects are involved. Other challenges involve balancing model complexity and parsimony using an appropriate model selection procedure, and making inference using a reliable and computationally efficient approach. Our approach relies on a latent Gaussian modeling framework with a novel multivariate link function designed to separate the interpretation of the parameters at the latent level and to avoid unreasonable estimates of the shape and time trend parameters. Structured additive regression models are proposed for the four parameters at the latent level. For computational efficiency with large datasets and richly parametrized models, we exploit an accurate and fast approximate Bayesian inference approach. We applied our proposed methodology to annual peak river flow data from 554 catchments across the United Kingdom (UK). Our model performed well in terms of flood predictions for both gauged and ungauged catchments. The results show that the spatial model components for the transformed location and scale parameters, and the time trend, are all important. Posterior estimates of the time trend parameters correspond to an average increase of about $1.5\%$ per decade and reveal a spatial structure across the UK. To estimate return levels for spatial aggregates, we further develop a novel copula-based post-processing approach of posterior predictive samples, in order to mitigate the effect of the conditional independence assumption at the data level, and we show that our approach provides accurate results.

stat.ME↗

arXiv2020

Max-and-Smooth: a two-step approach for approximate Bayesian inference in latent Gaussian models

With modern high-dimensional data, complex statistical models are necessary, requiring computationally feasible inference schemes. We introduce Max-and-Smooth, an approximate Bayesian inference scheme for a flexible class of latent Gaussian models (LGMs) where one or more of the likelihood parameters are modeled by latent additive Gaussian processes. Max-and-Smooth consists of two-steps. In the first step (Max), the likelihood function is approximated by a Gaussian density with mean and covariance equal to either (a) the maximum likelihood estimate and the inverse observed information, respectively, or (b) the mean and covariance of the normalized likelihood function. In the second step (Smooth), the latent parameters and hyperparameters are inferred and smoothed with the approximated likelihood function. The proposed method ensures that the uncertainty from the first step is correctly propagated to the second step. Since the approximated likelihood function is Gaussian, the approximate posterior density of the latent parameters of the LGM (conditional on the hyperparameters) is also Gaussian, thus facilitating efficient posterior inference in high dimensions. Furthermore, the approximate marginal posterior distribution of the hyperparameters is tractable, and as a result, the hyperparameters can be sampled independently of the latent parameters. In the case of a large number of independent data replicates, sparse precision matrices, and high-dimensional latent vectors, the speedup is substantial in comparison to an MCMC scheme that infers the posterior density from the exact likelihood function. The proposed inference scheme is demonstrated on one spatially referenced real dataset and on simulated data mimicking spatial, temporal, and spatio-temporal inference problems. Our results show that Max-and-Smooth is accurate and fast.

stat.ME↗

arXiv2015

Parameter uncertainty in forecast recalibration

Ensemble forecasts of weather and climate are subject to systematic biases in the ensemble mean and variance, leading to inaccurate estimates of the forecast mean and variance. To address these biases, ensemble forecasts are post-processed using statistical recalibration frameworks. These frameworks often specify parametric probability distributions for the verifying observations. A common choice is the Normal distribution with mean and variance specified by linear functions of the ensemble mean and variance. The parameters of the recalibration framework are estimated from historical archives of forecasts and verifying observations. Often there are relatively few forecasts and observations available for parameter estimation, and so the fitted parameters are also subject to uncertainty. This artefact is usually ignored. This study reviews analytic results that account for parameter uncertainty in the widely used Model Output Statistics recalibration framework. The predictive bootstrap is used to approximate the parameter uncertainty by resampling in more general frameworks such as Non-homogeneous Gaussian Regression. Forecasts on daily, seasonal and annual time scales are used to demonstrate that accounting for parameter uncertainty in the recalibrated predictive distributions leads to probability forecasts that are more skilful and reliable than those in which parameter uncertainty is ignored. The improvements are attributed to more reliable tail probabilities of the recalibrated forecast distributions.

stat.AP↗

arXiv2015

A Bayesian framework for verification and recalibration of ensemble forecasts: How uncertain is NAO predictability?

Predictability estimates of ensemble prediction systems are uncertain due to limited numbers of past forecasts and observations. To account for such uncertainty, this paper proposes a Bayesian inferential framework that provides a simple 6-parameter representation of ensemble forecasting systems and the corresponding observations. The framework is probabilistic, and thus allows for quantifying uncertainty in predictability measures such as correlation skill and signal-to-noise ratios. It also provides a natural way to produce recalibrated probabilistic predictions from uncalibrated ensembles forecasts. The framework is used to address important questions concerning the skill of winter hindcasts of the North Atlantic Oscillation for 1992-2011 issued by the Met Office GloSea5 climate prediction system. Although there is much uncertainty in the correlation between ensemble mean and observations, there is strong evidence of skill: the 95% credible interval of the correlation coefficient of [0.19,0.68] does not overlap zero. There is also strong evidence that the forecasts are not exchangeable with the observations: With over 99% certainty, the signal-to-noise ratio of the forecasts is smaller than the signal-to-noise ratio of the observations, which suggests that raw forecasts should not be taken as representative scenarios of the observations. Forecast recalibration is thus required, which can be coherently addressed within the proposed framework.

stat.AP↗

arXiv2015

Evaluating ensemble forecasts by the Ignorance score -- Correcting the finite-ensemble bias

This study considers the application of the Ignorance Score (also known as the Logarithmic Score) in the context of ensemble verification. In particular, we consider the case where an ensemble forecast is transformed to a Normal forecast distribution, and this distribution is evaluated by the Ignorance Score. It is shown that the standard Ignorance score is biased with respect to the ensemble size, such that larger ensembles yield systematically better expected scores. A new estimator of the Ignorance score is derived which is unbiased with respect to the ensemble size. In an application to seasonal climate predictions it is shown that the standard Ignorance score assigns better expected scores to simple climatological ensembles or biased ensembles that have many members, than to physical dynamical and unbiased ensembles with fewer members. By contrast, the new bias-corrected Ignorance score ranks the physical dynamical and unbiased ensembles better than the climatological and biased ones, independent of ensemble size. It is shown that the unbiased estimator has smaller estimator variance and error than the standard estimator, and that it is a fair verification score, which is optimized if the ensemble members are statistically consistent with the observations. The finite ensemble bias of ensemble verification scores is discussed more broadly. It is argued that a bias-correction is appropriate when forecast systems with different ensemble sizes are compared, and when an evaluation of the underlying distribution of the ensemble is of interest; possible applications to unbiased parameter estimation are discussed.

stat.ME↗

arXiv2013

Skill of data based predictions versus dynamical models -- case study on extreme temperature anomalies

We compare probabilistic predictions of extreme temperature anomalies issued by two different forecast schemes. One is a dynamical physical weather model, the other a simple data model. We recall the concept of skill scores in order to assess the performance of these two different predictors. Although the result confirms the expectation that the (computationally expensive) weather model outperforms the simple data model, the performance of the latter is surprisingly good. More specifically, for some parameter range, it is even better than the uncalibrated weather model. Since probabilistic predictions are not easily interpreted by the end user, we convert them into deterministic yes/no statements and measure the performance of these by ROC statistics. Scored in this way, conclusions about model performance partly change, which illustrates that predictive power depends on how it is quantified.

stat.AP↗

arXiv2013

Variance estimation for Brier Score decomposition

The Brier Score is a widely-used criterion to assess the quality of probabilistic predictions of binary events. The expectation value of the Brier Score can be decomposed into the sum of three components called reliability, resolution, and uncertainty which characterize different forecast attributes. Given a dataset of forecast probabilities and corresponding binary verifications, these three components can be estimated empirically. Here, propagation of uncertainty is used to derive expressions that approximate the sampling variances of the estimated components. Variance estimates are provided for both the traditional estimators, as well as for refined estimators that include a bias correction. Applications of the derived variance estimates to artificial data illustrate their validity, and application to a meteorological prediction problem illustrates a possible use case. The observed increase of variance of the bias-corrected estimators is discussed.

stat.ME↗