Burn-scar persistence in satellite imagery is treated as a lifetime process and modelled within a doubly censored Weibull framework arising from the finite temporal extent of satellite archives. Episodes may appear doubly censored in calendar time because the Landsat record spans a limited analysis window, so that for some pixels neither the true ignition time nor the full recovery are directly observed. On the persistence-time scale used for inference, incomplete episodes contribute as right-censored lifetimes within a unified likelihood formulation. A robust weighted-likelihood estimator with Huber-type influence weights downweights atypically long-lived scars without excluding any observations, thereby limiting the impact of outliers while preserving the central structure of the persistence distribution. The framework is applied to NDVI-based burn-scar persistence derived from Landsat surface-reflectance time series at Monitoring Trends in Burn Severity (MTBS) sampling locations within a large interior-Alaska fire scar, yielding a sample of 90 persistence episodes comprising fully observed and right-censored lifetimes. Weibull parameters are estimated under both maximum likelihood and weighted likelihood, with parametric bootstrap resampling used to obtain confidence intervals. Agreement between model-based and empirical survival behavior is assessed using Kaplan–Meier and Turnbull estimators and a Weibull probability plot. The fitted model indicates a median persistence of approximately 2.7–2.9 years and a 90th-percentile persistence of roughly five to six years, with the Weibull shape parameter consistently exceeding one, indicating an increasing recovery hazard over time. The proposed framework combines interpretability and robustness under censoring and generalizes naturally to other persistence-type environmental processes observed under incomplete monitoring.
Changes in mean precipitation and the frequency and intensity of extreme precipitation represent one of the most consequential aspects of anthropogenic climate change. This study evaluates a set of statistical distributions for modeling trends across the full precipitation spectrum (low, medium, and extreme daily quantiles). Modeling with a single flexible distribution ensures statistical consistency, thereby avoiding the artificial separation and discontinuity inherent in multi-model approaches. We used time as a covariate for dry-day frequency and sea surface temperature for the wet-day distribution parameters. We applied the methodology to a dense network of over 900 meteorological stations in France, offering a wide variety of climatic regimes, allowing for a robust conclusion. We employed a multi-criterion approach to select the best model, in the first step using the Akaike Information Criterion, and then based on their ability to flexibly capture trends across low, medium, and extreme precipitation quantiles. Our findings highlight that three-parameter distributions (generalized gamma and extended generalized Pareto distribution), particularly with evolving shape parameters, are essential for accurately capturing observed differential changes across the full precipitation spectrum, a flexibility that the two-parameter gamma distribution notably lacked. Although AIC generally favored generalized gamma, both generalized gamma and the extended generalized Pareto distribution demonstrated robust performance. This research underscores the critical need for a multi-criterion model identification framework in nonstationary trend analysis to provide reliable insights essential for hydrological and climate impact assessments.
A critical question in climate science is whether climate model simulations are statistically consistent with observations. If simulations and observations are treated as realizations of Vector Autoregressive (VAR) models, then deciding that simulations and observations came from the same process is equivalent to deciding that the parameters of the respective VAR models are equal. This framework has been developed in parts 1–5 of this series of papers, including extensions to account for annual cycles and radiative forcing. However, the associated tests have been derived under the restriction of equal noise covariances. Previous studies have only allowed unequal noise variances in univariate settings. This paper presents a general test of parameter equality that applies to multivariate models, incorporates external forcing, and does not assume equal noise covariances. Monte Carlo experiments indicate that the test statistic is well approximated by a chi-squared distribution for large degrees of freedom, but that this distribution underestimates upper quantiles when the degrees of freedom are small. This bias can be partially compensated by adopting a more stringent significance level (e.g., using a 1 % level to achieve a nominal 5 % Type I error rate). Applying the method to monthly 2 m-temperature from an observational data set and climate model simulations aggregated over five regional domains reveals that most climate models tested differ significantly from the observational data set, both in their transfer coefficients for radiative forcing and in their AR coefficients, indicating differences in the representation of both internal and forced variability.
The rapid expansion of the French offshore wind sector requires a critical reassessment of structural durability in the face of evolving marine conditions driven by climate change. Traditional design methodologies, which rely on the assumption of stationary environmental conditions, are no longer adequate. This study introduces a novel statistical framework to assess future changes in significant wave height by employing non-stationary Generalized Extreme Value (GEV) models applied to monthly maxima. This approach aims to reduce uncertainty and provide robust design tools adapted to the non-stationary conditions of the future. Based on CMIP6 climate models and reanalysis data, results reveal a projected trend towards a more pronounced seasonal contrast along the French Atlantic and English Channel coasts under future scenarios (SSP1-2.6 and SSP5-8.5), whereas the French Mediterranean Sea exhibits results that are more difficult to interpret, due to a weaker increase of extremes and large uncertainties (inter-model spread). Projections indicate more intense winters and calmer summers, along with a shift in the seasonal cycle. Overall, the multi-model ensemble suggests an increase in the design levels for extreme sea states. The research concludes by defining a new methodology for calculating an equivalent design level over the structure's operational lifespan. This tool is deemed essential for ensuring the resilience and economic viability of future offshore wind farms in a changing climate.
The nonparametric estimation of the power spectral density of uniformly-spaced data with missing samples is revisited. Classical estimators, such as the standard periodogram and the Lomb-Scargle periodogram, are biased when samples are missing. The classical method to obtain an asymptotically-unbiased estimator is to take the finite Fourier transform of the standard unbiased estimator of the autocorrelation function. However, the latter estimator is not necessarily positive semidefinite, so its finite Fourier transform can yield negative power spectral density values at some frequencies. To avoid this problem, Gao et al. (2021) have proposed taking the absolute value of the finite Fourier transform of the standard unbiased estimator of the autocorrelation function to estimate the power spectral density of data with missing samples. We show that the estimator of power spectral density proposed by Gao et al. (2021) is even more biased than classical estimators and should not be used for quantitative analysis of spectral characteristics such as spectral slope in log-log space. We illustrate this using both synthetic data from fractional Brownian processes and actual data from a laboratory experiment of decaying turbulence in an active grid-generated air flow, to which we apply synthetic Bernoulli and batch-Bernoulli sampling functions to simulate missing samples. In fact, negative values of power spectral density estimates for particular realizations of a random process with missing samples should be retained, so that when sufficiently averaged the estimate will be nonnegative, and will not contain the bias induced from taking absolute values as Gao et al. (2021) propose. It is also proposed here to use the circular unbiased estimator of the autocorrelation function, the finite Fourier transform of which yields a power spectral density estimator identical to the standard periodogram estimator in the absence of missing samples. Its advantages are reduced variance and reduced computing memory usage compared to the finite Fourier transform of the standard unbiased estimator of the autocorrelation function. Both power spectral density estimators, when sufficiently averaged, are able to recover the -5/3 spectral slope of the decaying turbulence data even when 50 % of the data are missing. A Matlab implementation of the proposed estimator is provided.
An understanding of Earth's past climate can help put current and future changes into historical context. Widely used tree ring-based drought atlases generally target the Palmer Drought Severity Index or other metrics of soil moisture and/or drought risk. These indices reflect contemporaneous meteorological conditions, and it is possible to extract information about temperature and precipitation given the existing reconstructions. Here, we present a fully Bayesian inverse method that infers a joint posterior for monthly mean temperature and precipitation given tree ring-based PDSI reconstructions from the North American Drought Atlas. The method is skillful at reconstructing early twentieth century conditions when compared to instrumental measurements from the CRU TS dataset. Moreover, the reconstructions can capture the complex temporal and multivariate covariance structure between monthly regional temperatures and precipitation. By reconstructing regional temperature and precipitation for the last millennium, we identify the driest and wettest years and decades in each region. Our results highlight the unique nature of the 1930s Dust Bowl drought in central Kansas and the late twentieth century pluvial in the North American southwest.
Fine-scale oceanic fronts are ubiquitous and ephemeral physical features that separate contrasting water masses, creating significant heterogeneity in the physical seascape and plankton distributions. Because phytoplankton community composition (PCC) is a key driver of marine ecosystem functioning, understanding the extent to which fine-scale fronts influence PCC is a critical challenge. However, studying PCC across and within fronts is particularly difficult due to data scarcity and high biophysical variability. We developed a tailored statistical model to characterize PCC within an oceanic front we studied in the Mediterranean Sea. We modeled the frontal community as a finite mixture model with three components: two communities of adjacent water masses and a potential front-adapted community. Each component was further considered as a discrete mixture of an unknown number of multivariate Gaussian sub-components. First, we used an Expectation–Maximization algorithm to estimate the Gaussian parameters and determine the optimal number of sub-components based on in situ datasets of the PCC within a frontal zone and its adjacent water masses. Second, a hierarchical Bayesian approach was applied to estimate the weight of all components within the frontal dataset. Our analysis suggests that within the front a new community component, distinct from those in adjacent water masses, accounts for 70 % of the frontal community, indicating that a specific phytoplankton community can emerge in fine-scale oceanic fronts. Despite the limited number of frontal observations, our Bayesian modelling approach provides statistical evidence of the front's influence on phytoplankton community composition, effectively overcoming data scarcity and high variability.
Accurate modelling of extreme precipitation is vital for predicting future risks and informing adaptation strategies. Here, we compare and evaluate six different extreme value statistical models for hourly to 48 h extreme precipitation in southern Germany, with a primary focus on duration-dependent Generalized Extreme Value (dGEV) distributions. To assess model performance, particularly in capturing tail behavior, we utilize the 50-member single model initial-condition large ensemble of the Canadian Regional Climate Model version 5 for the period 1980–2019. The large sample size of 2000 simulated years enables a robust sampling of extreme quantiles. Using a sub-sampling strategy with 30 to 100 years, we compare the efficacy of Bayesian methodology, in particular Bayesian hierarchical models, against frequentist models (L-moments and Maximum Likelihood Estimation – MLE) in representing the tail risk of 100-year return levels based on limited sample sizes. Hierarchical models allow us to give special emphasis on the dimensionality of the GEV shape parameter, a critical factor for tail behavior. Our findings reveal that a shape parameter varying over durations but fixed across space is beneficial for the prediction of the 100-year return level. The resulting Intensity-Duration-Frequency (IDF) curve shows the highest accuracy and smallest confidence intervals proving its robustness. Compared to the standard GEV estimated by L-moments, our proposed model can reduce the relative error of the 100-year return level from 18.1 % to 8.8 % based on a 30-year sample size. Furthermore, our analysis reveals fundamental limitations of the Anderson-Darling test for extreme value model selection, demonstrating its poor correlation with predictive skill for upper quantiles – a critical finding for climate risk applications.
Soil moisture–temperature coupling (SM–T) significantly influences the frequency and amplitude of heat extremes. It describes how variations in soil moisture affect surface air temperature conditions and vice versa. This study aims to determine the spatial extent and duration of SM–T in southern and central Sweden, an area increasingly recognized as a coupling hot spot, during the extreme warm conditions between May and August 2018 (MJJA 2018). The assessment of coupling is based on a multi-correlation overlay analysis of key coupling variables: surface soil moisture, evaporative fraction, and daily maximum 2 m temperature from four different simulations of the coupled regional climate model WRF-CTSM, along with a merged gridded GLEAM-E-OBS observational–reanalysis dataset. These datasets demonstrate robust precision in representing the magnitude and variability of the key coupling variables during the MJJA 2018 compared to in situ observations, though the precise timing and duration of the coupling are challenging to reproduce at the local scale. WRF-CTSM provides a more realistic depiction of the key coupling variables and their interactions when recent CTSM advancements are incorporated. On average, across the study region and all five datasets, SM–T persisted for 22 d throughout the MJJA period. The atmospheric leg alone (involving daily evaporative fraction and maximum 2 m temperature), averaged across datasets, contributed 92 % to the regional coupling duration.
We present a novel flexible bi-level spatiotemporal clustering algorithm to extract events based on their intensity and spatiotemporal structures. Our algorithm consists of using (i) a novel space-time k-means clustering to obtain spatiotemporally coherent intensity clusters, and (ii) a density-based spatial clustering of applications with noise (DBSCAN) to spatiotemporally section the intensity clusters into individual events. We discuss the development of the algorithm, the selection, tuning and meaning of the parameters within each step, as well as its validation. Finally, we apply the algorithm to a spatiotemporal drought index, standardized vapor pressure deficit drought index (SVDI), over the continental United States (US) from 1980–2021 and show that it captures historical drought events over the continental United States and their spatiotemporal extents.
Stochastic weather generators are efficient statistical models producing synthetic weather series by replicating key statistical properties without the computational cost of physical models. However, for applications requiring temperature simulation over a large area, challenges arise due to non-stationarity over time and spatial-temporal dependencies. This paper introduces a daily stochastic weather generator for temperature with arbitrary spatial resolution. The non-stationarity issue is addressed using a decomposition method to separate deterministic terms (trends and seasonality), from the stochastic part representing the underlying climate variability. We extend the existing local decomposition method to extrapolate to any point in space. The spatial-temporal dependence is modeled through a Gaussian field with a non-separable covariance function, accommodating complex interactions between time and space. Our generator, calibrated on a few French weather stations, is validated using several spatio-temporal indicators. First, we evaluate the generator's performance at the fitting stations, comparing simulated and observed indicators. Subsequently, we compare our spatial simulations to a high resolution gridded observation dataset. Results demonstrate that the proposed generator accurately captures the observed spatio-temporal statistics, even for extreme events such as large scale persistent heat waves.
We present a lightweight stochastic weather generator (SWG) based on a multisite hidden Markov model (HMM) trained on a large area with French weather station data. Our model captures spatiotemporal precipitation patterns with a strong emphasis on seasonality and the accurate reproduction of dry and wet spell distributions. The hidden states serve as interpretable large-scale weather regimes, learned directly from the data without requiring exogenous inputs. Compared to existing approaches, it offers a robust balance between interpretability and performance, particularly for extremes. The model architecture enables seamless integration of additional weather variables. Finally, we demonstrate its application to future climate scenarios, highlighting how parameter evolution and extreme event distributions can be analyzed in a changing climate.
Studies that investigate the effects of meteorological fluctuations on varying multi-disciplinary outcomes often depend on analysis of high-frequency sensor data from automatic monitoring stations in different locations. The validation of such spatial time series requires attention given that they are susceptible to multiple forms of error. Existing validation techniques tend to cater to detection of only one form of outlier in isolation, lack robustness, or fail to optimally leverage the strong between-series correlation that often prevails in high-frequency meteorological data exhibiting multiple seasonalities. To address these shortcomings, two adaptations were made to an existing procedure, for more powerful outlier detection in strongly correlated high-frequency time series, using a distributional approach. The modified technique was tested in a simulation study and was also applied to a real univariate spatial set of hourly air temperature series from the South African Air Quality Information System. In both instances, the effectiveness of the technique in detecting outliers was assessed relative to procedures lacking either or both adaptations. The results show the modified procedure to be most comprehensive in the simultaneous detection of multiple forms of error, including solitary spikes, shifts in the series mean, and irregularities in the diurnal pattern. Furthermore, the method is generalizable to any set of time series displaying a similar correlation structure.
Forecasting rainfall into the next season remains highly challenging and is normally presented in terms of probabilities rather than the expected rainfall as measured by rain gauges. I show here that, in favourable cases, for the selected times of the year and selected geographical regions, it is possible to obtain useful quantitative forecasts of rainfall with a series of relatively simple steps. One such instance explored in this work is the prediction of austral springtime rainfall in SE Australia regions predominantly based on the surrounding ocean surface temperatures during the winter. In the first stage, I search for predictors by exploring correlations between the target rainfall and ocean surface temperatures at earlier times. In addition to standard ocean climate indicators such as El Niño or the Indian Ocean Dipole, other typical patterns of variation are captured in terms of the temperatures of selected ocean areas. When characteristic patterns of correlation are discovered, they are included in the predictor selection in the form of expansion in terms of the empirical orthogonal functions (EOFs). EOF expansions can provide very strong signals. For example, in the case of the Indian Ocean, during the winter, the dominant EOF shows a stronger correlation with future rainfall than the commonly used Indian Ocean Dipole. The technical part of the forecast model is provided by deep learning artificial neural networks, where I use the information sources with the strongest correlation in relation to the historical rainfall data as the inputs. The networks are trained on past rainfall data, and the output is a quantitative forecast based on the current state of the predictors. The resulting hindcasts appear to be accurate for September and October and less reliable for November. I also present model forecasts for rainfall during the 2024 austral spring in the selected SE Australia regions.
Drought is one of the recurring natural phenomena affecting the socio-economic and environmental well-being of southern Ethiopia's society. The availability of insufficient ground-based rainfall observatory networks is limiting drought-monitoring and early-warning investigations. The main objective of this study is to analyze spatial and temporal drought characteristics using high-resolution satellite-based rainfall products for the 1991–2022 period in the Southern Nations, Nationalities, and Peoples (SNNP) region of Ethiopia. The satellite-based rainfall product used in this study was selected after the evaluation of three satellite products, namely the Africa Rainfall Climatology version 2 (ARC2), the Climate Hazards Group InfraRed Precipitation with Stations (CHIRPS), and the Tropical Applications of Meteorology using SATellite and ground-based observations (TAMSAT), against station-based rainfall for the study area space and time domains. The statistical metrics of correlation coefficient (CORR), bias (BIAS), percent bias (PBIAS), mean error (ME), mean absolute error (MAE), root mean square error (RMSE), and Nash–Sutcliffe efficiency coefficient (NSE) were used to compare and evaluate the satellite rainfall products. Accordingly, the CHIRPS shows the highest CORR of 0.96 and the highest BIAS of 1.02, which is very near to the perfect value (BIAS = 1), followed by the TAMSAT. Hence, the CHIRPS-based satellite rainfall product was used to assess the spatio-temporal patterns of meteorological drought based on the 3-month and 12-month standardized precipitation index (SPI). The results successfully grasped the known historical and recent droughts of 2022, 2021, 2015, 2014, 2010, 2009, and 2000. A high intensity and a high severity of drought were noted in the SPI-3, while the least occurrences of extreme events were recorded in the SPI-12. Additionally, severe drought situations were detected in the drought-prone areas in the southern and southeastern parts of the SNNP region. Finally, the study concludes that, to construct grid-based drought-monitoring tools for the development of early-warning systems, the CHIRPS rainfall product can be used as an additional source of information.
In the study of the global climate, ocean temperature estimates use sea surface temperature (SST) anomalies instead of marine air temperature (MAT) anomalies. A key question to ask is whether biases result from this choice. In this article we employ hierarchical statistical models to investigate spatiotemporal differences between SST and MAT and their anomalies in the tropical Pacific. The analysis uses observations from the Tropical Atmosphere Ocean (TAO) buoy network and the ERA5 data product. Our spatiotemporal modeling approach accounts for missing data in the observation network and allows for full uncertainty quantification. Our findings indicate evidence that SST and MAT are interchangeable in the tropical Pacific when we calculate seasonally adjusted monthly anomalies.
The aim of this study is to provide a probabilistic gust analysis for the region of Germany that is calibrated with station observations and with an interpolation to unobserved locations. To this end, we develop a spatial Bayesian hierarchical model (BHM) for the post-processing of surface maximum wind gusts from the COSMO-REA6 reanalysis. Our approach uses a non-stationary extreme value distribution for the gust observations at the top level, with parameters that vary according to a linear model using COSMO-REA6 predictor variables. To capture spatial patterns in surface extreme wind gust behavior, the regression coefficients are modeled as 2-dimensional Gaussian random fields with a constant mean and an isotropic covariance function that depends only on the distance between locations. In addition, we include an elevation offset in the distance metric for the covariance function to account for differences in topography. This allows us to include data from mountaintop stations in the training process and to utilize all available information. The training of the BHM is carried out with an independent data set from which the data at the station to be predicted are excluded. We evaluate the spatial prediction performance at the withheld station using Brier score and quantile score, including their decomposition, and compare the performance of our BHM to climatological forecasts and a non-hierarchical, spatially constant baseline model. This is done for 109 weather stations in Germany. Compared to the spatially constant baseline model, the spatial BHM significantly improves the estimation of local gust parameters. It shows up to 5 % higher skill for prediction quantiles and provides a particularly improved skill for extreme wind gusts. In addition, the BHM improves the prediction of threshold levels at most of the stations. Although a spatially constant approach already provides high skill, our BHM further improves predictions and improves spatial consistency.
This paper presents a pioneering study on the inference of boxplot-valued data using both Bayesian and frequentist approaches within a multivariate framework. This approach leverages complex yet intuitive representations to make large datasets more manageable and enhance their interpretability, which is invaluable in the age of big data. Boxplot-valued data are particularly important due to their ability to capture the inherent variability and distributional characteristics of complex datasets. In our study, we propose novel methodologies for parameter estimation and density estimation for boxplot-valued data and apply these techniques to climatological data. Specifically, we utilize data from the Berkeley Earth Surface Temperature Study, which aggregates 1.6 billion temperature reports from 16 pre-existing archives affiliated with the Lawrence Berkeley National Laboratory. Our methods are validated through extensive simulations comparing the efficiency and accuracy of Bayesian and frequentist estimators. We demonstrate the practical applicability of our approach by analyzing summer average temperatures across various European countries. The proposed techniques provide robust tools for analyzing complex data structures, offering valuable insights into climatic trends and variations. Our study highlights the advantages and limitations of each inferential method, offering guidance for future research and applications in the field of climatology.
By the end of 2023, renewable sources covered 63.4 % of the total electric-power demand of Chile, and, in line with the global trend, photovoltaic (PV) power showed the most dynamic increase. Although Chile's Atacama Desert is considered to be the sunniest place on Earth, PV power production, even in this area, can be highly volatile. Successful integration of PV energy into the country's power grid requires accurate short-term PV power forecasts, which can be obtained from predictions of solar irradiance and related weather quantities. Nowadays, in weather forecasting, the state-of-the-art approach is the use of ensemble forecasts based on multiple runs of numerical weather prediction models. However, ensemble forecasts still tend to be uncalibrated or biased, thus requiring some form of post-processing. The present work investigates probabilistic forecasts of solar irradiance for regions III and IV in Chile. For this reason, eight-member short-term ensemble forecasts of solar irradiance for the calendar year 2021 are generated using the Weather Research and Forecasting (WRF) model; these are then calibrated using the benchmark ensemble model output statistics (EMOS) method based on a censored Gaussian law and its machine-learning-based distributional regression network (DRN) counterpart. Furthermore, we also propose a neural-network-based post-processing method, resulting in improved eight-member ensemble predictions. All forecasts are evaluated against station observations for 30 locations in the study area, and the skill of post-processed predictions is compared to the raw WRF ensemble. Our case study confirms that all studied post-processing methods substantially improve both the calibration of probabilistic forecasts and the accuracy of point forecasts. Among the methods tested, the corrected ensemble exhibits the best overall performance. Additionally, the DRN model generally outperforms the corresponding EMOS approach.
A number of recent climate studies have used univariate parametric statistical models to estimate return periods of extreme weather events based on the method of maximum likelihood. Using simulations over multiple training datasets, we find that using maximum likelihood gives predictions of extreme return levels that are exceeded more often than expected. For instance, when using the generalised extreme value distribution (GEVD) with 50 annual data values, fitted using maximum likelihood, we find that 200-year return levels are exceeded more than twice as often as expected; i.e. they are exceeded in more than 1 in 100 simulated years. This bias, which we refer to as a predictive coverage probability (PCP) bias, would be expected to lead to unreliable predictions. We review the theory related to Bayesian prediction using right Haar priors which gives an objective way to incorporate parameter uncertainty into predictions for some statistical models and which eliminates the bias. We consider a number of commonly used parametric statistical models and give the right Haar priors in each case. Where possible, we give analytical solutions for the resulting predictions. Where analytical solutions are not possible, we apply either an asymptotic approximation for the Bayesian prediction integral or ratio of uniforms sampling. For the fully parameterised GEVD and the generalised Pareto distribution with a known location parameter, neither of which have a right Haar prior, we test a number of methods and find one that gives big reductions in the PCP bias relative to maximum likelihood predictions. Finally, we revisit the De Bilt extreme temperature example considered in a number of previous studies and generate revised, and shorter, estimates for the return period of the 2018 heatwave. Software for fitting predictive distributions with parameter uncertainty has been developed by the first author and will be available as an R package.
