Homepage Denis Allard

Directeur de Recherche, HDR  / Senior Researcher

Biostatistics and Spatial Processes (BioSP), INRA, Avignon

Tel:      +33 (0) 4 32 72 21 71
Fax:     +33 (0) 4 32 72 21 82

Member of the Applied Mathematics and Informatics division (MIA) of the french National Institute for Agricultural Research


  Denis Allard                                                                      

News / Vita / WACSgen / Research / Publications / PhD Students  / Teaching  / Professional services / Editorial services




réseau RESSTE network


  • I am the coordinator of the research network on statistics for spatio-temporal data RESSTE (RESeau Statistiques pour Données Spatio-Temporelles). RESSTE is funded by the Applied Mathematcis and Informatics division (MIA) of INRA. It gathers more than 60 researches from about 20 research teams in France and abroad. We organize seminars and workshops and we support all sorts of actions actions in view of developping models and methods for analyzing space-time data. Feel free to contact me if you wish to be on the RESSTE mailing list.


Recent conferences I co-organized:

  • L’Université d’Avignon (UAVP) accueillera les Journées de Statistique 2017 du 29 mai au 2 juin sur le campus Hannah Arendt (anciennement Sainte-Marthe) au centre-ville d’Avignon. L'événement est co-organisé par le laboratoire de mathématique d'Avignon, BioSP, le laboratoire d'Informatique d'Avignon et par l'UMR ESPACE.
  • The 9th edition of the French-Danish Workshop took place in May 2012 in Avignon, France. It was jointly organized by the Biostatistics and Spatial Processes research unit (INRA) and the Dpt. of Mathematics, LANLG (University of Avignon). It was devoted to spatial statistics and image analysis and their applications in biology (agriculture, aquaculture, ecology, economy, environment, health, medicine, ...). Presentations can be found here.


1993 PhD in geostatistics, Paris School of Mines  / Centre de Géostatistique de l'Ecole des Mines de Paris,maintenant Equipe de Géostatistique du Centre de Géoscience de Mines ParisTech
1994 - 1995 Visting Assistant Professor, Department of Statistics, University of Washington, Seattle (WA, USA)

1995 - 1996 Geostatistician, BP Exploration - Subsurface Technology, Londres
since 1996 Researcher, Biostatistics and Spatial Processes (BioSP),  INRA, Avignon
2007 Habilitation à Diriger les Recherches (Université Montpellier II)

2008 Senior Researcher, BioSP, INRA / Directeur de Recherche INRA

2005 - 2011  Head of BioSP / Directeur de l'Unité Biostatistique et Processus Spatiaux

2016  Visiting Professor at Dipartimento di Scienze Ambietali, Informatica e Statistica (DAIS), University Ca'Foscari, Venezia.

Since 2016: Member of board of the INRA Metaprogramme "Adaptation of agriculture and forests to climate change"

Since 09/2017: I am in charge of Innovation, Partnership and Transfer for "Digital Agriculture"

Full vita in English here


WACSgen is a single-site, stationary multivariate weather generator for daily climate variables based on weather-states that uses a Markov chain for modeling the succession of (an unlimited number of) weather states. Conditionally to the weather states, the multivariate variables are modeled using the family of Complete skew-normal distributions. It is described in Flecher et~al. (2010).

Version WACSgen 1.0 is now avaliable to download. Here is the zip file of the R pacakge WACS. Simply download in your owkring directory and install with the usual install command install.packages(,) or from the Rstudio tool. WACS is also available as a package on the R-CRAN repository. Follow this link.

A user guide with a full description of the model, methods and algorithms is accessible here. Feel free to use WCASgen and to contact me for complementary information. Do not forget to make proper reference to WACSgen and the original paper Flecher et~al. (2010).



Half-tapering strategy for conditional simulation with large datasets [with D. Marcotte]

Gaussian conditional realizations are routinely used for risk assessment and planning in a variety of Earth sciences applications. Conditional realizations can be obtained by first creating unconditional realizations that are then post-conditioned by kriging. Many efficient algorithms are available for the first step, so the bottleneck resides in the second step. Instead of doing the conditional simulations with the desired covariance (F approach) or with a tapered covariance (T approach), we propose to use the taper covariance only in the conditioning step (Half-Taper or HT approach). This enables to speed up the computations and to reduce memory requirements for the conditioning step but also to keep the right short scale variations in the realizations. A criterion based on mean square error of the simulation is derived to help anticipate the similarity of HT to F. Moreover, an index is used to predict the sparsity of the kriging matrix for the conditioning step. Some guides for the choice of the taper function are discussed. The distributions of a series of 1D, 2D and 3D scalar response functions are compared for F, T and HT approaches. The distributions obtained indicate a much better similarity to F with HT than with T. A preprint is avalaible here. Publication in SERRA is here.


Multivariate space-time models [with M. Bourotte and E. Porcu]

Multivariate space-time data are increasingly recorded in various scientific disciplines. When analyzing these data, one of the key issue is to describe the multivariate space-time dependencies. In a Gaussian framework, this necessitates to propose relevant models for multivariate space-time covariance functions, mathematically described as matrix-valued covariance functions for which non-negative definiteness must be ensured.  A new flexible parametric class of cross-covariance functions for multivariate space-time Gaussian random fields has been proposed where space-time components belong to the (univariate) Gneiting class of space-time covariance functions, with Matern or Cauchy covariance functions in the spatial dimensions. In this class, the smoothness and the scale parameters can be different for each variable. Sufficient conditions are provided, ensuring that this model is a valid matrix-valued covariance functionfor multivariate space-time random fields. Through a simulation study, it is shown that the parameters of this model can be efficiently estimated using weighted pairwise likelihood, which belongs to class of composite likelihood methods. A preprint is available here. Publication in Spatial Statistics is here.


Variograms for anisotropic random fields [with R. Senoussi and E. Porcu]

The question of building useful and valid models of anisotropic variograms for spatial data that go beyond classical anisotropy models (geometric and zonal models of anisotropy) is rarely addressed. In Allard, Senoussi and Porcu (Math. Geosciences) it is shown that if the regularity parameter is a continuous function of the direction, it must necessarily be constant. Instead, the scale parameter can vary in a continuous or discontinuous fashion with the direction according to a directional mixture representation, which allows to build a very large class of anisotropy models. A turning band algorithm for the simulation of Gaussian anisotropic processes, obtained from the mixture representation, is also presented.


Stochastic Weather Generators [with P. Naveau, P. Ailliot, V. Monbet, M. Bourotte]

A recurrent issue encountered in impact studies is to provide fast and realistic (in a distributional sense) simulations of atmospheric variables like temperatures, precipitation and winds at a few specific locations and at daily or hourly temporal scales. This stochastic inquiry leads to a large variety of so-called Stochastic Weather Generators (SWG) in the hydrological and weather literature. A concise and up-to-date review paper on Weather-states stochastic Weather Generators is available in Ailliot, Allard, Monbet and Naveau (2015).

To simulate multivariate daily time series (minimum and maximum temperatures, global radiation, wind speed and precipitation intensity) at a single site, WACS-Gen, a Weather-state Approach with conditionally multivariate Closed Skew-normal distribution is proposed in Flecher, Naveau, Allard, Brisson (WRR, 2010). WACS-Gen is able to accurately reproduce the statistical properties of these five variables, including time dependence. It takes advantage of two elements. First, the classical wet and dry days dichotomy used in most past weather generators is generalized to multiple weather states using clustering techniques. The transitions among weather states are modeled by a first order Markov chain. Secondly, the vector of our five daily variables of interest is sampled, conditionally on these weather states, from a closed skew-normal distribution, thus allowing to handle non-symmetric behaviors. WACS-Gen is coded in R, and is available upon request by emailing me.

Allard and Bourotte (2014) considers the problem disaggregating daily precipitations into hourly values with a transformed censored latent Gaussian process. Current researches aim at proposing relevant models for multisite, multivariate Stochastic Weather Generators.


Means and covariance functions for spatial compositional data: an axiomatic approach [with T. Marchant]

Our work focuses on the characterization of the central tendency of a sample of compositional data. It provides new results about theoretical properties of means and covariance functions for compositional data, with an axiomatic perspective. Original results that shed new light on the geostatistical modeling of compositional data are presented.As a first result, it is shown that the weighted  arithmetic mean is the only central tendency characteristic verifying a small set of axioms, namely reflexivity and marginal stability. Moreover, the weights must be identical for all components of the compositional vector.This result has deep consequences on the spatial multivariate covariance modeling of compositional data.  In a geostatistical setting,it is shown as a second result that the proportional model of covariance functions (i.e. the product of a covariance matrix and a single correlation function) is the only model that provides identical kriging for all components of the compositional data. As a consequence of these two results, the proportional model of covariance function is the only covariance model compatible with reflexivity and marginal stability. A preprint can be found here.


Combining indicator probabilities [with D. D'Or, R. Froidevaux, A. Communian, P. Renard]

The need of combining in a probabilistic framework different sources of information is a frequent task in geoscience. For example, the probability of occurrence of a certain lithofacies at a given location can easily be computed conditionally on the values observed at other sources of information (sample observations, geophysics, remote sensing, training images). The problem of aggregating these different conditional probability distributions into a single conditional distribution arises as an approximation to the inaccessible genuine conditional probability given all information. Allard, Communian and Renard (2012) makes a formal review of most aggregation methods with a particular focus on their mathematical properties. Exact relationships relating the different methods is emphasized. The case of events with more than 2 possible outcomes is treated in details. It is shown that in this case, equivalence between different aggregation formulas is lost. It is proved that the log-linear pooling formulas with parameters estimated from maximum likelihood are calibrated. These results are illustrated on simulations from two common stochastic models for earth science: the truncated Gaussian model and the Boolean model.

When considering the problem of the spatial prediction of a categorical variable given a set of observations at surrounding locations, a useful approximation of the conditional probability of observing a category at a location is obtained with a particular maximum entropy principle. It leads to a simple combination of sums and products of univariate and bivariate probabilities. This prediction equation can be used for categorical estimation or categorical simulation. In Allard, D'Or and Froideveaux (2011), connections are made to earlier work on prediction of categorical variables. In particular, it is a parameter free, suboptimal, special case of log-linear pooling.


Skew normal random fields [with P. Naveau]

Skewness is often present in a wide range of environmental problems, and modelling it in the spatial context remains a challenging problem. In Allard and Naveau (2007), a new family of skewed random fields based on the multivariate closed skew-normal distribution is proposed. Such fields can be written as the sum of two independent fields; one Gaussian and the other truncated Gaussian. This model contains very few parameters while still incorporating the classical spatial structures used in geostatistics.  Crucially, a high degree of skewness can be induced through the use of a single skewness parameter. It is thus possible to compute the first- and second-order moments of our skewed fields, as well as deriving the properties of the sample variogram and covariance. This leads to a method of moments algorithm to estimate the parameters.


Zones of Abrupt Changes [with Edith Gabriel and J.N. Bacro]

Estimating the zones where a variable under study changes abruptly is a problem encountered in many biological, ecological, agricultural or environmental applications. In Gabriel, Allard and Bacro (2011), a method is proposed for detecting the zones where a spatially correlated variable irregularly sampled in the plane changes abruptly. The general model is that under the null hypothesis the variable is the realization of a stationary Gaussian process with constant expectation. The alternative is that the mean function is discontinuous on some curves in the plane. The general approach is a global aggregation of local tests of the hypothesis of a local constant mean vs. the alternative of the existence of a discontinuity. The theory that links the local and global levels is based on asymptotic distributions of excursion sets of non-stationary khi2 fields. It is thus possible to control the global type I error and to simultaneously estimate the covariance function and the ZACs in the case of an unknown mean. This method is easy to use, to visualise and to interpret. An R set of functions, detecZAC, can be downloaded from Edith Gabriel's homepage.


CART algorithm for spatial data [with Liliane Bel and Avner Bar-Hen]

Classification And Regression Trees (CART) assume independent samples to compute classification rules. This assumption is very practical for estimating  quantities involved in the algorithm and for assessing asymptotic properties of estimators. Unfortunately, in most environmental or ecological applications, the data under study present some amount of spatial correlation. When the sampling scheme is very irregular, a direct application of supervised classification algorithms leads to biased discriminant rules due, for example, to the possible oversampling of some areas. In Bel, Allard, Laurent, Cheddadi  and Bar-Hen (2009), two approaches for taking this spatial dependence into account are considered. The first one  takes into account the irregularity of the sampling by weighting the data according to their spatial pattern using two existing methods based on Voronoï tessellation and regular grid, and one original method based on kriging. The second one uses spatial estimates of the quantities involved in the construction of the discriminant rule at each step of the algorithm.



Full list of publications is here

HDR Thesis can be found here

Book edition
Monestiez, P., Allard, D., Froidevaux, R. (2001) geoENV III Geostatistics for Environmental Applications. Kluwer Academic Publishers, Dordrecht, 540p.

Book reviews (avalaible upon request)

J.-P. Chilès, P. Delfiner: Geostatistics: Modeling Spatial Uncertainty 2nd Edition. Wiley, 2012. Mathematical Geosciences, 2012.  doi:10.1007/s11004-012-9429-y

A.E. Gelfand, P.J. Diggle, M. Fuentes, P. Guttorp (eds.): Handbook of spatial statistics, Chapman & Hall/CRC, Statistics and Computing, 2010. doi:10.1007/s11222-010-9211-2

Some recent or not too old publications

with RESSTE network (2017). Analyzing spatio-temporal data with R: Everything you always wanted to know - but were afraid to ask.     Manuscript accessible here.    Supplementary material is here

Csilléry, K., Kunstler G., Courbaud, B., Allard, D., Lassegues, P., Haslinger, K., Gardiner, G. (In Press) Coupled effects of wind-storms and drought on tree mortality across 115 forest stands from the Western Alps and the Jura mountains. Global Change Biology.  DOI : 10.1111/gcb.13773

Marcotte, D. and Allard, D. (2017) Half-tapering strategy for conditional simulation with large datasets, SERRA (in press). doi: 10.1007/s00477-017-1386-z.    Manuscript accessible here.

Allard, D. and Marchant, T.   (2017) Means and covariance functions for spatial compositional data: an axiomatic approach (In revision).    Manuscript accessible here.

Bourotte M., Allard, D. and Porcu, E.   (2016) A Flexible Class of Non-separable Cross-Covariance Functions for Multivariate Space-Time Data, Spatial Statistics, 18(A), 125-146.    doi: 10.1016/j.spasta.2016.02.004. ArXiv 1510.07840

Zaytsev, V. BIver, P., Wackernagel, H. and Allard, D. (2016) Change-of-Support Models on Irregular Grids for Geostatistical Simulation, Mathematical Geosciences, 48(4): 353-369.    doi: 10.1007/s11004-015-9614-x.

Allard, D. Senoussi, R., Porcu, E. (2015) Anisotropy models for spatial data. Mathematical Geosciences, 48(3): 305-328.    doi: 10.1007/s11004-015-9594-xPreprint accessible here.

Ailliot P., Allard, D., Monbet V. and Naveau, P. (2015)  Stochastic weather generators: an overview of weather type models. Journal de la Société Française de Statistiques, 156(1), 101-103.    Paper accessible here.

Allard, D., Bourotte, M. (2015) Disaggregating daily precipitations into hourly values with a transformed censored latent Gaussian process. Stochastic Environmental Research and Risk Assesment, 29(2), 453-462,    doi: 10.1007/s00477-014-0913-4. Preprint accessible here.

Allard, D., Lopez-Lozano, R. and Baret, F. (2013) Modeling forest canopies with a hierarchical multi-ring Boolean model for estimating Leaf Area Index. Spatial Statistics, 5, 42-56.    doi:10.1016/j.spasta.2013.04.007.    Preprint accessible here.

Renard, P. and Allard, D. (2013)  Connectivity metrics for subsurface flow and transport.  Advances in Water Resources, 51, 168-196.    doi:10.1016/j.advwatres.2011.12.001    Preprint accesstible here.

Girard, R. and Allard, D. (2013) Spatio-temporal propagation of wind power prediction errors. Wind Energy,16, 999-1012.    doi:10.1002/we.1527

Allard, D. Soubeyrand, S.  (2012) Skew-normality for climatic data and dispersal models for plant epidemiology: when application fields drive spatial statistics. Spatial Statistics, 1, 50-64.    doi: 10.1016/j.spasta.2012.03.001.    Preprint accessible here.

Allard, D., Communian, A. and Renard, P. (2012)  Probability aggregation methods in geoscience. Mathematical Geosciences, 44: 545-581.    doi: 10.1007/s11004-012-9396-3.    Preprint accessible here.

Allard, D. (2012)  Modeling spatial and spatio-temporal non Gaussian processes. In  Space-Time Processes and Challenges Related to Environmental Problem,
Eds. Porcu, E., Montero, J.-M. and Schlather M., Lecture Notes in Statistics, Vol. 207, Springer. pp. 141-164.    doi: 10.1007/978-3-642-17086-7_7

Allard, D., D'Or, D. and Froidevaux, R. (2011)  Letter to the Editor: Response to W. Li and C. Zhang,
European Journal of Soil Science, 63, 125-128.  doi: 10.1111/j.1365-2389.2011.01414.x.    Preprint accessible here.

Allard, D., D'Or, D. and Froidevaux, R. (2011) An efficient maximum entropy approach for categorical variable prediction, European Journal of Soil Science, 61, 381-293.    doi:10.1111/j.1365-2389.2011.01362.x. preprint accessible here.

Flecher, C. Allard, D. and Naveau P. (2010) Truncated skew-normal distributions: moments, estimation by weighted moments and application to climatic data.Metron - International Journal of Statistics -- Special Issue on Skew-symmetric and flexible distributions, LXVIII, 331-345.    Prepint is accessible here.

Flecher, C., Naveau P.,  Allard D. and Brisson, N. (2010) A Stochastic Daily Weather Generator for Skewed Data, Water Resource Research, 46, W07519.    doi:10.1029/2009WR008098.     Preprint accessible here.

Gabriel, E., Allard, D. and Bacro, J.-N. (2010) Estimating and testing zones of abrupt change for spatial data, Statistics and Computing21, 107-120.    doi:10.1007/s11222-009-9151-x.    Preprint accessible here.

Flecher, C., Naveau, Ph. and Allard, D. (2009) Estimating the Closed Skew-Normal distributions parameters using weighted moments",  Statistics and Probability Letters, 79, 1977-1984.    doi:10.1016/j.spl.2009.06.004.    Preprint accessible here.

Bel, L., Allard, D., Laurent, J.M., Cheddadi, R. and Bar-Hen, A.  (2009) CART algorithm for spatial data: Application to environmental and ecological data, Computational Statistics and Data Analysis, 53, 3082-3093.    doi:10.1016/j.csda.2008.09.012.     Preprint accessible here.

Garrigues, S., Allard, D., Baret, F. Modeling Temporal Changes in Surface Spatial Heterogeneity over an Agricultural site (2008) Remote Sensing of Environment, 112, 588-602.   doi:10.1016/j.rse.2007.05.014.

Gabriel, E. and Allard, D. Evaluating the Sampling Pattern When Detecting Zones of Abrupt Change (2008)  Environmental and Ecological Statistics, 15, 469-489.    doi:10.1007/s10651-007-0067-3.    Manuscrit accessible ici.

Gabriel, E., Allard, D., Mary, B. & Guérif, M.  (2007) Detecting zones of abrupt change in soil data, with an application to an agricultural field. European Journal of Soil Science, 58, 1273-1284.    doi:10.1111/j.1365-2389.2007.00920.x.

Garrigues, S., Allard, D., Baret, F. & Morisette, J. (2007) Multivariate Quantification of Landscape Spatial Heterogeneity using Variogram Models. Remote Sensing of Environment, 112, 216-230.    doi:10.1016/j.rse.2007.04.017

Garrigues, S., Allard, D., & Baret, F. (2007) Using first and second order variograms for characterizing landscape spatial structures from remote sensing imagery, IEEE TGARS, 45, 1823 - 1834.    doi:10.1109/TGRS.2007.894572

Allard D. & Naveau, P. (2007) A new spatial skew-normal random field model, Communications in Statistics, 36, 1821 - 1834.    doi:10.1080/03610920601126290.    Manuscrit accessible ici.
Allard D., Froidevaux R. & Biver, P. (2006) Conditional Simulation of Multi-Type Non Stationary Markov Object Models Respecting Specified Proportions, Mathematical Geology, 38, 959-986.    doi:10.1007/s11004-006-9057-5.    Manuscit accessible ici.
Allard, D. & Gabriel, E. (2007), Détection de zones de changement abrupts pour des variables non permanentes du sol: vers la définition de zones homogènes ?, in Agriculture de Précision, Guérif, M. and King, D., Coords., Editions Quae, Paris, pp. 165--76.

Garrigues, S., Allard, D., Baret, F. & Weiss, M. (2006) Influence of the spatial heterogeneity on the non linear Estimation of Leaf Area Index from moderate resolution remote sensing data, Remote Sensing of Environment, 105, 286-298.    doi:10.1016/jrse.2006.07.013

Magnussen S., Allard D., & Wulder M. (2006) Poisson Voronoï tiling for finding clusters in spatial point patterns, Scan. J. For. Res., 21, 239-248.    doi:10.1080/02827580600688178

Allard, D. (2006), Validation d'un modèle géostatistique pour l'interpolation : application à un événement pluvieux, in Statistiques Spatiales, Eds. Droesbeke, J.-J. et Lejeune, M., Technip, Paris, pp. 403--414.
Chilès, J.-P. & Allard, D. (2005), Stochastic Simulation of Soil Variation, in Geographic Information Technologies for Environmental Soil-Landscape Modelling, Ed. Grunwald, S., CRC Press, Boca Raton, pp. 289-321.


PhD Students

Edith Gabriel (2001-2004) Détection de zones de changement abrupt dans des données spatiales et application à l'agriculture de précision, Univsersity Montpellier II, ED ISS. Co-supervised with M. Guérif, EMMAH, INRA Avignon. Today, at Laboratoire d'Analyse Non Linéaire et géométrie d'Avignon, Université d'Avignon

Sébastien Garrigues (2001-2004) Hétérogénéité spatiale des surfaces terrestres en télédétection ; caractérisation et influence sur l'estimation des variables biophysiques, ENSA-R. co-supervised with F. Baret, EMMAH INRA Avignon. Today at EMMAH, INRA Avignon

Cédric Flécher (2006-2009 ) Développement de méthodes statistiques pour la mise au point d'un générateur de climat adapté à l'utilisation des scénarii de changement climatique, University Montpellier II, ED SIBAGHE, co-supervised with Ph. Naveau, LSCE, CNRS and N. Brisson AgroClim, INRA Avignon. Today with InBox, Montréal.

Marc Bourotte (2012-2016)  Modèles et algorithmes pour un générateur de temps spatialisé (SWgen) prenant en compte les valeurs extrêmes. Université d'Avignon. Co-supervised with Liliane Bel, AgroParisTech.

Rocardo Carrizo (2015  2018) Spatio-temporal statistical models from stochastic partial derivative equations. co-supervised with Nicolas Desassis, MinesParisTech.

Teaching (mostly in french)

Environmental data analysis, for the Doctoral Program in Environmental Sciences, Universita Ca'Foscari, Venezia, Italy.

Part I: Introduction; Exploratory data analysis; estimation and hypothsis testing; linear model

Part II: Time series; spatial statistics; geostatistics

R scripts

Atelier Statistique de la SFdS: Introduction aux méthodes spatiales et spatio-temporelles, 23 et 24 juin 2016. Présentations "Géostatistique multivariée", "Géostatistique Spatio-temporelle" et script R.

Cargèse Fall School on "statistical and mathematical tools for climate extremes", November 2015.  Slides on Stochastic Weather Generators are here.  Compressed directory for exercises is here

Journées R pour la fédération ECCOREV   Scripts R pour le TD

Pratiques des statistiques paramétriques. Séquence I: statistique inférentielle   Transparents d'introduction; Transparents Inférence et TestsJeu de données du Jura Suisse   Script R pour le TD

Toledo Spring School on Advances And Challenges In Space-time Modelling Of Natural Events. Introduction to Non-Gaussian Random Fields: a Journey Beyond Gaussianity. Slides

Statistiques Spatiales : introduction à la géostatistique (20 h), M2 Biostatistique, Université Montpellier II.     

Polycopié du cours.

Transparents d'introduction

Transparents variogrammes

Transparents krigeage

Transparents simulation

Probabilité et Statistiques (27 h), Centre de Recherche et d'Enseignement en Informatique, Université d'Avignon. Polycopié du cours.

Processus Stochastiques (40 h),Centre de Recherche et d'Enseignement en Informatique. Université d'Avignon


Professional Services

Editorial Services

Reviewers for Acta Mechanica, Annals of Statistics, Annals of Applied Statistics, Biometrics, Biometrika, Chilean Journal of Statistics, Climate Dynamics, Climate Research, Communications in Statistics - Theory and Methods, Computational Statistics and Data Analysis, Computer and Geoscience, Environmental Modelling & Software, Environmental Pollution, European Journal of Soil Science, IEEE Transactions in Geosciences and Remote Sensing, IEEE Transactions on Power Systems, International Journal of Climatology, Journal of African Earth Sciences, Journal of Agricultural, Biological, and Environmental Statistics, Journal of Computational and Applied Mathematics, Journal of Multivariate Analysis, Journal of the Royal Society Interface, Journal of the Royal Statistical Society, Journal for Stochastic Environmental Research and Risk Assessment, Operations Research, Physics Letters A, Probabilistic Engineering Mechanics, Statistics and Probability Letters, Water Resources Research, etc.