Search Results

You are looking at 1 - 10 of 10 items for

  • Author or Editor: Mathieu Vrac x
  • All content x
Clear All Modify Search
Mathieu Vrac and Petra Friederichs

Abstract

Statistical methods to bias correct global or regional climate model output are now common to get data closer to observations in distribution. However, most bias correction (BC) methods work for one variable and one location at a time and basically reproduce the temporal structure of the models. The intervariable, spatial, and temporal dependencies of the corrected data are usually poor compared to observations. Here, the authors propose a novel method for multivariate BC. The empirical copula–bias correction (EC–BC) combines a one-dimensional BC with a shuffling technique that restores an empirical multidimensional copula. Several BC methods are investigated and compared to high-resolution reference data over the French Mediterranean basin: notably, (i) a 1D BC method applied independently to precipitation and temperature fields, (ii) a recent conditional correction approach developed for producing correct two-dimensional intervariable structures, and (iii) the EC–BC method.

Assessments are realized in terms of intervariable, spatial, and temporal dependencies, and an objective evaluation using the integrated quadratic distance (IQD) is presented. As expected, the 1D methods cannot produce correct multidimensional properties. The conditional technique appears efficient for intervariable properties but not for spatial and temporal dependencies. EC–BC provides realistic dependencies in all respects: intervariable, spatial, and temporal. The IQD results are clearly in favor of EC–BC. As many BC methods, EC–BC relies on a stationarity assumption and is only able to reproduce patterns inherited from historical data. However, because of its ease of coding, its speed of application, and the quality of its results, the EC–BC method is a very good candidate for all needs in multivariate bias correction.

Full access
Mathieu Vrac and Pradeebane Vaittinada Ayar

Abstract

Statistical downscaling models (SDMs) and bias correction (BC) methods are commonly used to provide regional or debiased climate projections. However, most SDMs are utilized in a “perfect prognosis” context, meaning that they are calibrated on reanalysis predictors before being applied to GCM simulations. If the latter are biased, SDMs might suffer from discrepancies with observations and therefore provide unrealistic projections. It is then necessary to study the influence of applying bias correcting to large-scale predictors for SDMs, since it can have impacts on the local-scale simulations: such an investigation for daily temperature and precipitation is the goal of this study. Hence, four temperature and three precipitation SDMs are calibrated over a historical period. First, the SDMs are forced by historical predictors from two GCMs, corrected or not corrected. The two types of simulations are compared with reanalysis-driven SDM outputs to characterize the quality of the simulations. Second, changes in basic statistical properties of the raw GCM projections and those of the SDM simulations—driven by bias-corrected or raw predictors from GCM future projections—are compared. Third, the stationarity of the SDM changes brought by the BC of the predictors is investigated. Changes are computed over a historical (1976–2005) and future (2071–2100) time period and compared to assess the nonstationarity. Overall, BC can have impacts on the SDM simulations, although its influence varies from one SDM to another and from one GCM to another, with different spatial structures, and depends on the considered statistical properties. Nevertheless, corrected predictors generally improve the historical projections and can impact future evolutions with potentially strong nonstationary behaviors.

Full access
Mathieu Vrac, Alain Chédin, and Edwin Diday

Abstract

This work focuses on the clustering of a large dataset of atmospheric vertical profiles of temperature and humidity in order to model a priori information for the problem of retrieving atmospheric variables from satellite observations. Here, each profile is described by cumulative distribution functions (cdfs) of temperature and specific humidity. The method presented here is based on an extension of the mixture density problem to this kind of data. This method allows dependencies between and among temperature and moisture to be taken into account, through copula functions, which are particular distribution functions, linking a (joint) multivariate distribution with its (marginal) univariate distributions. After a presentation of vertical profiles of temperature and humidity and the method used to transform them into cdfs, the clustering method is detailed and then applied to provide a partition into seven clusters based, first, on the temperature profiles only; second, on the humidity profiles only; and, third, on both the temperature and humidity profiles. The clusters are statistically described and explained in terms of airmass types, with reference to meteorological maps. To test the robustness and the relevance of the method for a larger number of clusters, a partition into 18 classes is established, where it is shown that even the smallest clusters are significant. Finally, comparisons with more classical efficient clustering or model-based methods are presented, and the advantages of the approach are discussed.

Full access
Henning W. Rust, Mathieu Vrac, Benjamin Sultan, and Matthieu Lengaigne

Abstract

Senegal is particularly vulnerable to precipitation variability. To investigate the influence of large-scale circulation on local-scale precipitation, a full spatial–statistical description of precipitation occurrence and amount for Senegal is developed. These regression-type models have been built on the basis of daily records at 137 locations and were developed in two stages: (i) a baseline model describing the expected daily occurrence probability and precipitation amount as spatial fields from monsoon onset to offset, and (ii) the inclusion of weather types defined from the NCEP–NCAR reanalysis 850-hPa winds and 925-hPa relative humidity establishing the link to the synoptic-scale atmospheric circulation. During peak phase, the resulting types appear in two main cycles that can be linked to passing African easterly waves. The models allow the investigation of the spatial response of precipitation occurrence and amount to a discrete set of preferred states of the atmospheric circulation. As such, they can be used for drought risk mapping and the downscaling of climate change projections.

Necessary choices, such as filtering and scaling of the atmospheric data (as well as the number of weather types to be used), have been made on the basis of the precipitation models' performance instead of relying on external criteria. It could be demonstrated that the inclusion of the synoptic-scale weather types lead to skill on the local and daily scale. On the interannual scale, the models for precipitation occurrence and amount capture 26% and 38% of the interannual spatially averaged variability, corresponding to Pearson correlation coefficients of rO = 0.52 and ri = 0.65, respectively.

Full access
Elsa Bernard, Philippe Naveau, Mathieu Vrac, and Olivier Mestre

Abstract

One of the main objectives of statistical climatology is to extract relevant information hidden in complex spatial–temporal climatological datasets. To identify spatial patterns, most well-known statistical techniques are based on the concept of intra- and intercluster variances (like the k-means algorithm or EOFs). As analyzing quantitative extremes like heavy rainfall has become more and more prevalent for climatologists and hydrologists during these last decades, finding spatial patterns with methods based on deviations from the mean (i.e., variances) may not be the most appropriate strategy in this context of studying such extremes. For practitioners, simple and fast clustering tools tailored for extremes have been lacking. A possible avenue to bridging this methodological gap resides in taking advantage of multivariate extreme value theory, a well-developed research field in probability, and to adapt it to the context of spatial clustering. In this paper, a novel algorithm based on this plan is proposed and studied. The approach is compared and discussed with respect to the classical k-means algorithm throughout the analysis of weekly maxima of hourly precipitation recorded in France (fall season, 92 stations, 1993–2011).

Full access
Henning W. Rust, Mathieu Vrac, Matthieu Lengaigne, and Benjamin Sultan

Abstract

The comparison of circulation patterns (CPs) obtained from reanalysis data to those from general circulation model (GCM) simulations is a frequent task for model validation, downscaling of GCM simulations, or other climate change–related studies. Here, the authors suggest a set of measures to quantify the differences between CPs. A combination of clustering using Gaussian mixture models with a set of related difference measures allows for taking cluster size and shape information into account and thus provides more information than the Euclidean distances between cluster centroids. The characteristics of the various distance measures are illustrated with a simple simulated example. Subsequently, a five-component Gaussian mixture to define circulation patterns for the North Atlantic region from reanalysis data and GCM simulations is used. CPs are obtained independently for the NCEP–NCAR reanalysis and the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40), as well as for twentieth-century simulations from 14 GCMs of the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) database. After discussing the difference of CPs based on spherical and nonspherical clusters for the reanalysis datasets, the authors give a detailed evaluation of the cluster configuration for two GCMs relative to NCEP–NCAR. Finally, as an illustration, the capability of reproducing the NCEP–NCAR probability density function (pdf) defining the Greenland anticyclone CP is evaluated for all 14 GCMs, considering that the size and shape of the underlying pdfs complement the commonly used Euclidean distance of CPs’ mean values.

Full access
Geraldine Wong, Douglas Maraun, Mathieu Vrac, Martin Widmann, Jonathan M. Eden, and Thomas Kent

Abstract

Precipitation is highly variable in space and time; hence, rain gauge time series generally exhibit additional random small-scale variability compared to area averages. Therefore, differences between daily precipitation statistics simulated by climate models and gauge observations are generally not only caused by model biases, but also by the corresponding scale gap. Classical bias correction methods, in general, cannot bridge this gap; they do not account for small-scale random variability and may produce artifacts. Here, stochastic model output statistics is proposed as a bias correction framework to explicitly account for random small-scale variability. Daily precipitation simulated by a regional climate model (RCM) is employed to predict the probability distribution of local precipitation. The pairwise correspondence between predictor and predictand required for calibration is ensured by driving the RCM with perfect boundary conditions. Wet day probabilities are described by a logistic regression, and precipitation intensities are described by a mixture model consisting of a gamma distribution for moderate precipitation and a generalized Pareto distribution for extremes. The dependence of the model parameters on simulated precipitation is modeled by a vector generalized linear model. The proposed model effectively corrects systematic biases and correctly represents local-scale random variability for most gauges. Additionally, a simplified model is considered that disregards the separate tail model. This computationally efficient model proves to be a feasible alternative for precipitation up to moderately extreme intensities. The approach sets a new framework for bias correction that combines the advantages of weather generators and RCMs.

Full access
Colin Manning, Martin Widmann, Emanuele Bevacqua, Anne F. Van Loon, Douglas Maraun, and Mathieu Vrac

Abstract

Compound events are extreme impacts that depend on multiple variables that need not be extreme themselves. In this study, we analyze soil moisture drought as a compound event of precipitation and potential evapotranspiration (PET) on multiple time scales related to both meteorological drought and heat waves in wet, transitional, and dry climates in Europe during summer. Drought indices that incorporate PET to account for the effect of temperature on drought conditions are sensitive to global warming. However, as evapotranspiration (ET) is moisture limited in dry climates, the use of such drought indices has often been criticized. We therefore assess the relevance of the contributions of both precipitation and PET to the estimation of soil moisture drought. Applying a statistical model based on pair copula constructions to data from FluxNet sites in Europe, we find at all sites that precipitation exerts the main control over soil moisture drought. At wet sites PET is additionally required to explain the onset, severity, and persistence of drought events over different time scales. At dry sites, where ET is moisture limited in summer, PET does not improve the estimation of soil moisture. In dry climates, increases in drought severity measured by indices incorporating PET may therefore not indicate further drying of soil but the increased availability of energy that can contribute to other environmental hazards such as heat waves and wildfires. We therefore highlight that drought indices including PET should be interpreted within the context of the climate and season in which they are applied in order to maximize their value.

Open access
Aglaé Jézéquel, Vivian Dépoues, Hélène Guillemot, Amélie Rajaud, Mélodie Trolliet, Mathieu Vrac, Jean-Paul Vanderlinden, and Pascal Yiou

Abstract

Extreme event attribution (EEA) proposes scientific diagnostics on whether and how a specific weather event is (or is not) different in the actual world from what it could have been in a world without climate change. This branch of climate science has developed to the point where European institutions are preparing the ground for an operational attribution service. In this context, the goal of this article is to explore a panorama of scientist perspectives on their motivations to undertake EEA studies. To do so, we rely on qualitative semi-structured interviews of climate scientists involved in EEA, on peer-reviewed social and climate literature discussing the usefulness of EEA, and on reports from the EUCLEIA project (European Climate and Weather Events: Interpretation and Attribution), which investigated the possibility of building an EEA service. We propose a classification of EEA’s potential uses and users and discuss each of them. We find that, first, there is a plurality of motivations and that individual scientists disagree on which one is most useful. Second, there is a lack of solid, empirical evidence to back up any of these motivations.

Open access
Pascal Yiou, Julien Cattiaux, Davide Faranda, Nikolay Kadygrov, Aglae Jézéquel, Philippe Naveau, Aurelien Ribes, Yoann Robin, Soulivanh Thao, Geert Jan van Oldenborgh, and Mathieu Vrac
Free access