Univ.-Prof. Dr. Henning Rust

Bildquelle: Andreas Wannenmacher, FU Berlin

Freie Universität Berlin

Institut für Meteorologie

Professor für Statistische Meteorologie (DINP), Leiter der AG Statistische Meteorologie. Gefördert aus Mitteln der Exzellenzinitiative der Deutschen Forschungsgemeinschaft.

Adresse Carl-Heinrich-Becker-Weg 6-10
Raum 283/285 (Neubau)
12165 Berlin
Telefon +49 (0)30 838-71147
Fax +49 (0)30 838-471147
E-Mail henning.rust@met.fu-berlin.de

Reseach interests

  • Stochastic precipitation models

  • Stochastic Parametrisations

  • Extreme convective events

  • Decadal prediction

  • Forecast verification
  • Statistical modelling (Circulation patterns: definition and comparison, Extreme value statistics, Statistical downscaling)

  • Time series analysis, Long-range dependence

Associated activities

since 2015

Member of the Management Board of the DFG graduate school Natural Hazards and Risks in a Changing World


Guest editor for Meteorologische Zeitschrift, special issue: Verification and process oriented validation of the MiKlip decadal prediction system.

since 2013

Member of the scientific advisory board of Statistical regionalisation models intercomparisons and hydrological impacts projects (StaRMIP), a French national research project, coordinated by M. Vrac, LSCE, Gif-sur-Yvette, France


Member of the Steering Group of MiKlip, Germany's national initiative on decadal prediction


Guest editor for Nonlinear Processes in Geophysics (EGU), special issue: Extreme events: Nonlinear dynamics and time series analysis.


Academic positions

since 09/2015

Professor for Statistical Meteorology at the Freie Universitat Berlin (DINP), Institut für Meteorologie (FUB-IfM), Berlin, Germany. Co-leader of the working group Climate diagnostics and extreme meteorological events (CliDia) with U. Ulbrich

10/2013 - 08/2015

Assistant Professor at the FUB-IfM, Berlin, Germany. Co-leader of the working group Climate diagnostics and extreme meteorological events (CliDia) with U. Ulbrich. Coordinator of the validation activities for MiKlip, a joint research project for the development of a decadal prediction system funded by the Federal Ministry of Education and Research (BMBF)

01/2012 - 09/2013

Senior researcher and lecturer at the FUB-IfM. Coordinator of the validation activities for MiKlip. From 12/2012 to 09/2013 on partial parental leave with 50% workload

02/2011 - 12/2011

Research associate (Post-Doc) and lecturer at the FUB-IfM. Stochastic modelling of precipitation at sub-daily time scales a project within the initiative Scaling cascades in complex systems from the Centre for scientific computing (CSC) at FUB

12/2009 - 01/2011

Parental leave and associated scientist at the Laboratoire des Sciences du Climat et de l'Environnement (LSCE), Gif-sur-Yvette, France

06/2008 - 11/2009

Research associate (Post-Doc) in the project Regionalisation of precipitation and hydrological and agricultural impact of climate change on vulnerable regions (REGYNA) at the LSCE

10/2006 - 05/2008

Research associate (Post-Doc) in the project Extreme Events:
Causes and Consequences (E2C2) at the University of Potsdam,
Nonlinear Dynamics Group (AGNLD), Potsdam, Germany

09/2002 - 09/2006

Research associate (PhD) in the project Scaling and Trend Analy-
sis in Hydro-meteorological Time Series at the Potsdam Institute
for Climate Impact Research (PIK), Potsdam, Germany

04/2002 - 08/2002

Research associate at the International Centre for Integrative
Studies (ICIS), Maastricht, The Netherlands

Academic education


PhD in Theoretical Physics (summa cum laude) from the University
of Potsdam, Germany, thesis: Detection of long-range dependence - Applications in climatology and hydrology. In cooperation
with the Potsdam Institute for Climate Impact Research,
supervisor Prof. Dr. H.-J. Schellnhuber.


Diplom in Physics (very good) from the Albert-Ludwigs-
Universitat Freiburg, Germany, thesis: Model selection and pa-
rameter estimation in dynamic systems - Two applications (in
. In cooperation with the Institute of Plant Biochemistry
and the Freiburg Centre of Data Analysis and Modelling
(FDM), supervisor Prof. Dr. J. Timmer.


BSc with Honours in Physics from the Brock University,
St. Catharines, Ontario, Canada, thesis: Characterization of
DMPC/DHPC mixtures by 31P and 2H solid state NMR, supervisor
Prof. Dr. E. Sternin. Graduation with the Distinguished
Graduation Student Award for Physics

10/1997 - 05/1998

Studies of physics at the Brock University, St. Catharines, Ontario,

10/1994 - 05/2001

Studies of physics at the Albert-Ludwigs-Universitat Freiburg,


German (native), English (proficient), French and Italian (intermediate conversational)

Computer skills

Profound knowledge in environments for statistical computing
and graphics, such as R and Matlab, as well as in Unix/Linux
based operating systems and high performance computing (MPI,
OpenMP, job scheduling systems). Good knowledge in highlevel
programming languages (Java, C/C++), and in script languages
(Perl and Bash). Excellent command of word processing
(LATEX, Writer, Word), spread sheet applications (Calc, Excel),
vector/bitmap graphics manipulation and version control

Regular teaching activities

Meteorology Master (MSc.)

  • Introduction to Weather and Climate
A course for Meteorology minor students and Environmental Earth Sciences major students (lecture 2hrs/week, computer lab, 2hrs/week, seminar 2hrs/week, written/oral exams), open to students from Humboldt University, Berlin. Language: English.
  • Statistische Klimatologie (Statistical climatology)
(lecture 2hrs/week computer lab, 2hrs/week, regular assignments, oral exams). Language: German. Skript, Folien
  • Seminar Wetter- und Klimadiagnose (Weather and climate diagnostics)
A seminar for Meteorology major students: block on Spatio-temporal variability (lecture 1×2h and computer lab 1×2h), associated seminar (2hrs/week), exams (written/oral). Language: German/English.
  • Meteorologische Extremereignisse (Meteorological extreme events)
block on Extreme value statistics (lecture 2×2h and computer lab 2×2h), associated seminar (2hrs/week), exams  (written/oral). Language: German. Skript, Folien

Meteoroloy Bachelor (BSc.)

  • Angewandte Statistik (Applied statistics)
A course for Meteorology major students (lecture 2hrs/week, computer lab 2hrs/week), exams (written). Language: German. Skript, Folien

Extracurricular seminars

R-Gespräche, a seminar series for researchers and master students at the FUB-IfM. Talks address specific problems or classes of problems from meteorology and present ways to solve these with R, an environment for statistical computing and graphics. (bi-weekly, 2h) Language: German/English, Internal Website


  • Hauptkomponentenanalyse: A short primer on principal components analysis (PCA), in German. Script, Folien
  • Spectral Analysis of Stochastic Processes: A course given at the E2C2/GIACS Advanced School in Comorova, Romania in 2007. Script


PhD theses

  • Spatio-temporal response of extreme precipitation to climate change and decadal climate variability, Madlen Fischer , within the graduate research school Natural Hazards and Risks in a Changing World, started in October 2015
  • Identifying hydrological extreme episodes from large scale patterns, Christos Vagenas, within the EU-project BINGO, started in September 2015
  • Indices for blocking phenomena: New approaches, Andy Richling (partially funded by DWD, Development and testing of a blocking index for Europe, started in 2014)
  • Identification, decadal prediction and regionalisation of winter storms over Europe, Tim Kruschke (funded by BMBF, MiKlip, 2011-2015)

Diploma theses

Master's theses

I have been designing and supervising Master's theses at the FUB-IfM, topics include:

  • Stochastic precipitation models: do they conserve the intensity duration relation? (in progress)
  • Quantifying the respresentation of the intertropical convergence zone in general circulation models (in progress)

I have been co-supervising Master's theses with the following topics:

  • The potential predictability of March-April-May seasonal rainfall over East Africa using ITCZ indices (A visiting student from Kenya)
  • Quantifying the meteorological impact on ozone driven and traffic driven NO2 concentration urban canyons
  • Statistical downscaling of wind gusts with artifical neural networks

Bachelor's theses

I have been designing, supervising and evaluating Bachelor's theses at the FUB-IfM, topics include:

  • Temperature change conditioned on circulation patterns (in progress)
  • Geostrophic wind from triangles of Gauge-based pressure records as a proxy for storminess (in progress)
  • Probabilistic evaluation of frost days in the MiKlip decadal prediction system
  • Comparison of high resolution precipitation records from a Hellmann rain gauge and a tipping bucket

I have been co-supervising Bachelor's theses with the following topics:

  • The NAO-PNA-relation in the MPI Earth System Model (in progress)
  • Spatio-temporal relation between the wind over the North Sea and wind induced water level in Cuxhaven
  • Are ticks sensitive to meteorological conditions?
  • The climate change impact on the atmospheric excitation of polar motion

Ongoing projects

BINGO -- Bringing INnovation to onGOing Water Management – A better Future under Climate Change

The project aims at providing practical knowledge and tools to water managers affected by climate change to better cope with climate projections and near-term climate predictions (decadal predictions). The work package led by the Institute of Meteorology of Freie Universität Berlin will particularly address hydrological extreme conditions within climate change scenarios and decadal climate predictions, focusing on six representative areas across Europe.

Homepage: www.projectbingo.eu

Project Scientists: Christos Vagenas, Edmund Meredith, Agbeko K. Kpogo-Nuwoklo

Natural Hazards and Risks in a Changing World 

A graduate research school with the University of Potsdam, Potsdam Institute for Climate Impact Research (PIK), Helmholtz Centre Potsdam German Research Centre for Geosciences GFZ.

  • I1: Natural hazards in a changing climate – What causes the variability?, A project together with Uwe Ulbrich, Project scientist: Thomas Moran

Effects of extreme teleconnection indices on climate parameters of Central Europe based on RCM simulations

A project together with Uwe Ulbrich.

Project scientist: Eftychia Rousi 


A project together with the German Weather Service (DWD).

Project scientist: Andy Richling

Coupling a multiscale stochastic precipitation model to large scale atmospheric flow is part of the Collaborative Research Center SFB1114: Scaling Cascades in Complex Systems. A stochastic precipitation model is investigated for means to be linked to atmospheric flow via the use of the Dynamic State Index (DSI). The project is carried out together with Peter Nevir (Theoretical Meteorology). Project scientists are Annette Müller and Christoph Ritschel.

MiKlip II (Mittelfristige Klimaprognose, second phase, since 2015) is the German initiative for decadal climate prediction funded by the Ministry of Education and Research (BMBF), a research alliance in 5 modules:

  • ECO: Coordination of the process-oriented validation and forecast verification activities in MiKlip II (Module E). Development and Implementation of a drift correction framework
  • CALIBRATION: Re-Calibration of probabilistic decadal forecast
  • STOC: Storm-ocean interaction on decadal timescales


Finished projects


MiKlip (Mittelfristige Klimaprognose,since 2011) is the German initiative for decadal climate prediction funded by the Ministry of Education and Research (BMBF), a research alliance with 35 projects in 5 modules (about 150 people involved): I am coordinating the evaluation and validation activities (MiKlip Module E) which are distributed over 11 projects (about 40 scientists). As such I am a member of the MiKlip steering committee. Besides coordinating this research alliance, setting guidelines for forecast verification approaches, organising workshops, maintaining a communication platform, I contribute to the following projects within MiKlip:

  • EnsDiVal: I am leading the evaluation of probabilistic forecasts of winter storm frequencies (Tim Kruschke) and frost days (Igor Kröner), an analysis of a potential systematic dependence of temperature forecast skill on height (Madlen Fischer), the development of a reliability diagram plugin for the central evaluation system (CES, Andreas Dobler), the development of a new set of indices to describe cyclone and winter storm densities (Bruno Schyska) and the representation of the AAO in the MiKlip system (Stella Babian). I furthermore design and author explanatory material for forecast verification tools.
  • INTEGRATION: I am involved in the design and test of the essential plugin MurCSS of the CES (Christopher Kadow, Sebastian Illing, Oliver Kunst). MurCSS implements the Module E guidelines for forecast verification on decadal time scales.
  • StepClim: I suggested the use of generalised linear and additive models for extreme convective event probabilities dependent on CAPE and wind shear and I am actively involved in the current analyses (Peter Groenemeijer, Georg Pistotnik @ ESSL).
  • VESPA: I am supporting the analysis of skill dependence on the Atlantic Multidecadal Variability (Ines Höschel), the time series analysis of NAO and PNA (Alexander Pasternack), testing for a relation between NAO and PNA (Franz Landrock).
2012/2013 The relation between large scale circulation indices and European temperatures and precipitation, together with the German Weather Service (DWD). The result is used in the DWD's operational climate monitoring (Andy Richling).
Climate change and adaptation in Ethiopia, together with the PotsdamInstitute for Climate Impact Research (PIK) and financed by the GermanMinistry of Foreign Affairs. Bias correction for temperature andprecipitation from GCMs/RCMs (Tim Kruschke, Madlen Fischer).
2008/2009 Regionalisation of precipitation, and hydrological and agricultural impact of climate change on vulnerable regions (REGYNA), a French national project led by B. Sultan. I participated during my post-doc at the LSCE, Gif-sur-Yvette, France: development of a novel probabilistic assessment scheme for circulation patterns, precipitation modelling and downscaling with GLMs.
2007/2008 Modelling extreme precipitation. A case study for the UK, funded by a DAAD-BC travel grant. Several visits to the Climatic Research Unit (CRU) in Norwich, UK. Extreme value models including the annual cycle
and vector generalised models to link extreme precipitation to large scale flow indices.
Extreme events, causes and consequences (E2C2), a Specific TargetedResearch Project (STREP) by the European Commission (FP-6) led byM. Ghil. I contributed with work to long-range dependence and its effecton extreme value statistics during my post-doc at the University of Potsdam, Germany.
2002-2006 Scaling and trend analysis in hydro-meteorological time series, a project with stakeholders from Hydrology, funded by the German Ministry of Education and Research (BMBF). I developed a novel test on long-range dependence and analysed trends in extreme values during my PhD project at the PIK.


ResearcherID: F-2961-2013

In preparation

H. W. Rust, M. Fischer, T. Kruschke, U.  Ulbrich: Verifying decadal air temperature predictions against various reanalyses (to be submitted to Meteorol. Z.)

H. W. Rust, B. Schyska, T. Kruschke, U. Ulbrich: A new framework for the qualitative description of spatial cyclone distrubution (to be submitted to Tellus)

A. Pasternack, H. W. Rust, J. Bhend, M. Liniger, W. A. Müller: Decadal Forecast Recalibration – A Parametric Strategy Accounting for Drift, Conditional Bias and Ensemble Spread


  M. Fischer, H. W. Rust, U. Ulbrich: Seasonality in extreme  precipitation - Using Extreme value statistics to describe the annual cycle in German daily precipitation extremes, submitted to Meteorol. Z.

  M. Fischer, H. W. Rust, U. Ulbrich: A spatial and seasonal description of extreme precipitation return-levels: A case study. submitted to Spatial Statistics

  C. Ritschel, H.W. Rust, U. Ulbrich: Precipitation extremes on multiple time scales -- Bartlett-Lewis Rectangular Pulse Model and Intensity-Duration-Frequency curves, submitted to Hydrol. Earth Syst. Sci.


M. Walz, T. Kruschke, H. W. Rust, G. Leckebusch, U. Ulbrich: Quantifying the extremity of windstorms for regions featuring infrequent events, Atmos. Sci. Lett.(accepted, Mai 2017)

Published in peer-reviewed journals


S. Babian, H. W. Rust, K. Prömmel, J. Grieger, U. Cubasch: Representation of Antarctic Oscillation and related precipitation in the MPI Earth System Model, Meteorol. Z., 2016, 767-774, DOI: 10.1127/metz/2016/0661

J. Marotzke, W. A. Müller, F. S. E. Vamborg, P. Becker, U. Cubasch, H. Feldmann, F. Kaspar, C. Kottmeier, C. Marini, I. Polkova, K. Prömmel, H. W. Rust, D. Stammer, U. Ulbrich, C. Kadow, A. Köhl, J. Kröger, T. Kruschke, J. G. Pinto, H. Pohlmann, M. Reyers, M. Schröder, F. Sienz, C. Timmreck, M. Ziese: MiKlip - a National Research Project on Decadal Climate Prediction, Bulletin of the American Meteorological Society, 2016, DOI: 10.1175/BAMS-D-15-00184.1.

Otero Felipe, N., Sillmann, J., Schnell, J. L., Rust, H. W., Butler, T. M.:  Synoptic and meteorological drivers of extreme ozone concentrations over Europe. - Environ. Res. Lett., 11, 2, 024005, 2016. DOI: 10.1088/1748-9326/11/2/024005


T. Kruschke, H. W. Rust, C. Kadow, W. Müller, H. Pohlmann, G. C. Leckebusch, U. Ulbrich: Probabilistic evaluation of decadal predictions for Northern Hemisphere winter storms, Meteorol. Z., 2015, DOI: 10.1127/metz/2015/0641

C. Kadow, S. Illing, O. Kunst, H. W. Rust, H. Pohlmann, W. Müller, U. Cubasch: Evaluation of forecasts by accuracy and spread in the MiKlip decadal climate prediction system, Meteorol. Z., 2015, DOI: 10.1127/metz/2015/0639

H. W. Rust, A. Richling, P. Bissolli, U. Ulbrich: Linking teleconnection patterns to European temperature – a multiple linear regression model. Meteorol. Z., 24, 411 - 423, 2015

H.W. Rust, T. Kruschke, A. Dobler, M. Fischer, U. Ulbrich. Discontinous daily temperatures in the WATCH forcing data sets. J. Hydrometeorol. 16(1):465-472, 2015, DOI: 10.1175/JHM-D-14-0123.1


T. Kruschke, H. W. Rust, C. Kadow, G.C. Leckebusch, U. Ulbrich: Evaluating decadal predictions of northern hemispheric cyclone frequenciesTellus A 66, 22830, 2014, DOI: 10.3402/tellusa.v66.22830

V. Guemas, L. Auger, F.J. Doblas-Reyes, H.W. Rust, A. Ribes: Dealing with data dependencies when applying statistical hypothesis tests for climate time series. Bull. Amer. Meteorol. Soc., 95 (11), 1666-1667, 2014, See also related article.


H. W. Rust, M. Vrac, B. Sultan and M. Lengaigne: Mapping weather type influence on Senegal precipitation based on a spatio-temporal statistical model. J. Climate, 26, 8189-8209, 2013


D. Maraun, T.J. Osborn, H. W. Rust: The influence of synoptic airflow on UK daily precipitation extremes. Part II: regional climate model and EOBS data validation. Clim. Dyn. 39:287-301, 2012


P. Yiou, B. D. Malamud, H. W. Rust: Preface "Extreme Events: Nonlinear Dynamics and Time Series Analysis". Nonlin. Processes Geophys., 18, 895-897, 2011

M. Ghil, P. Yiou, S. Hallegatte, B. D. Malamud, P. Naveau, A. Soloviev, P. Friederichs, V. Keilis-Borok, D. Kondrashov, V. Kossobokov, O. Mestre, C. Nicolis, H. W. Rust, P. Shebalin, M. Vrac, A. Witt, I. Zaliapin: Extreme Events: Dynamics, Statistics and Prediction. Nonlin. Proc. Geophys., 18, 295-350, 2011

D. Maraun, H. W. Rust, T.J. Osborn: The Influence of Synoptic Airflow on UK Daily Precipitation Extremes. PartI: Observed Spatio-Temporal Relations. Clim. Dyn., 36:261-275, 2011


H. W. Rust, M. Vrac, M. Lengaigne, B. Sultan: Quantifying Differences in Circulation Patterns Based on Probabilistic Models. J. Climate, 23:6573-6589, 2010

P. Yiou, E. Bard, P. Dandin, B. Legras, P. Naveau, H. W. Rust, L. Terray, M. Vrac: Statistical Issues about Solar-Climate Relations. Clim. Past., 6:565-573, 2010

D. Maraun, F. Wetterhall, A.M. Ireson, R.E. Chandler, E.J. Kendon, M. Widmann, S. Brienen, H. W.Rust, T. Sauter, M. Themeßl,V.K.C. Venema, K.P. Chun, C.M. Goodess, R.G. Jones, C. Onof, M. Vrac, I. Thiele-Eich: Precipitation Downscaling under Climate Change. Recent Developements to Bridge the Gap between Dynamical Models and the End User. Rev. Geophys., 48, RG3003, 2010

D. Maraun, H. W. Rust, T.J. Osborn: Synoptic airflow and UK daily precipitation extremes. Development and validation of a vector generalised linear model. Extremes, 13(2):133-153, 2010


H. W. Rust, D. Maraun, T.J. Osborn: Modelling Seasonality in Extreme Precipitation: A UK Case Study. Europ. Phys. J. Special Topics, 174:91-97, 2009

H. W. Rust: The Effect of Long-Range Dependence on Modelling Extremes with the Generalised Extreme Value Distribution. Europ. Phys. J. Special Topics, 174:99-111, 2009

D. Maraun, H. W. Rust, T.J. Osborn: The Annual Cycle of Heavy Precipitation Across the United Kinddom: A Model Based on Extreme Value Statistics. Int. J. Climatol., 29(12):1731-1744, 2009

2008 and ealier

H. W. Rust, O. Mestre, V.K.C Venema: Fewer Jumps, Less Memory: Homogenized Temperature Records and Long Memory. J. Geophys. Res., 113:D19110, 2008

V.K.C Venema, S. Bachner, H. W. Rust, C. Simmer: Statistical Characteristics of Surrogate Data based on Geophysical Measurements. Nonlin. Proc. Geophys., 13:449-466, 2006

M. Kallache, H. W. Rust, J.P. Kropp: Trend assessment: Applications for hydrology and climate research. Nonlin. Proc. Geophys., 12:201-210, 2005

D. Maraun, H. W. Rust, J. Timmer: Tempting Long-Memory - On the Interpretation of DFA Results. Nonlin. Proc. Geophys.,11:495-503, 2004

D. Maraun, W. Horbelt, H. W. Rust, J. Timmer, F. Drepper, H.P. Happersberger: Identification of Rate Constants and Non-Observable Absorption Spectra in Nonlinear Biochemical Dynamics. Int. J. Bif. Chaos, 14:(6)2081-2092, 2004

H.U. Voss, H. W. Rust, W. Horbelt, J. Timmer: A combined approach for the indentification of continuous non-linear systems. Int. J. Adapt. Contr. Signal. Process., 17:335-352, 2003

J. Timmer, H. W. Rust, W. Horbelt, H.U. Voss: Parametric, Nonparametric and Parametric Modelling of a Chaotic Circuit Time Series. Phys. Lett. A, 274:123-134, 2000


In monographs and conference proceedings 

Rousi, E., Ulbrich, U., Rust, H. W., & Anagnostolpoulou, C.: An NAO Climatology in Reanalysis Data with the Use of Self-organizing Maps, in Perspectives on Atmospheric Sciences (pp. 719-724), Springer International Publishing, 2017.

M. Fischer ,H. W. Rust, U. Ulbrich: Seasonal Extreme Value Statistics for Precipitation in Germany, EVAN 2013: Proceedings of the 1st International Short Conference on Advances in Extreme Value Analysis and Application to Natural Hazards, Forschungsinstitut Wasser und Umwelt (fwu) der Universität Siegen 144-152,  2014

H. W. Rust, M. Kallache, H.-J. Schellnhuber and J. P. Kropp: Confidence Intervals for Flood Return Level Estimation using a Bootstrap Approach, in J. Kropp and H.J. Schellnhuber (Eds.): In Extremis: Disruptive Events and Correlations in Hydrology and Climate, Springer, 2011

M. Kallache, H. W. Rust, H. Lange and J. Kropp: Extreme Value Analysis for Non-Stationary Data, in J. Kropp and H.J. Schellnhuber (Eds.): In Extremis: Disruptive Events and Correlations in Hydrology and Climate, Springer, 2011

M. Kallache, H. W. Rust, H.-J. Schellnhuber and J. P. Kropp: Trend Assessment of Correlated Data, Complexity and Integrated Resources Management, Transactions of the 2nd Biennial Meeting of the International Environmental Modelling and Software Society, iEMSs, Manno, Switzerland, 2004

H. U. Voss, M. Peifer, W. Horbelt, H. W. Rust and J. Timmer: Parametric, Nonparametric and Parametric Modeling of a Chaotic Circuit Time Series, NOLTA-Proceedings, 2:713-716, 2000

PhD Thesis

Detection of Long-Range Dependence – Applications in Climatology and Hydrology; H. W. Rust, 2007. Potsdam University, Potsdam, Germany.



Software package farima for the environment for statistical computing R: Algorithms and tools for parameter estimation and model selection for long-memory processes. H. W. Rust, 2007

gaussDiff (also available on CRAN)

Software package gaussDiff for the environment for statistical computing R: A set of difference measures for multivariate Gaussian probability distributions. H. W. Rust, 2007