Why Does It Always Rain on Me? A Spatio-Temporal Analysis of Precipitation in Austria


  • Nikolaus Umlauf Universität Innsbruck
  • Georg Mayr Universität Innsbruck
  • Jakob Messner Universität Innsbruck
  • Achim Zeileis Universität Innsbruck




It is popular belief that the weather is “bad” more frequently on weekends than on other days of the week and this is often perceived to be associated with an increased chance of rain. In fact, the meteorological literature does report some evidence for such human-induced weekly cycles although these findings are not undisputed. To contribute to this discussion, a modern data-driven approach using structured additive regression models
is applied to a newly available high-quality data set for Austria. The analysis investigates how an ordered response of rain intensities is influenced by a (potential) weekend effect while adjusting for spatio-temporal structure using spatially varying effects of overall level and seasonality patterns. The underlying data are taken from the HOMSTART project which provides daily precipitation quantities over a period of more than 60 years and a dense net
of more than 50 meteorological stations all across Austria.


Akima, H., Gebhardt, A., Petzoldt, T., and Mächler, M. (2009). akima: Interpolation of irregularly spaced data [Computer software manual]. (R package version 0.5-4, http://CRAN.R-project.org/package=akima)

Barmet, P., Kuster, T., Muhlbauer, A., and Lohmann, U. (2009). Weekly cycle in particulate matter versus weekly cycle in precipitation over Switzerland. Journal of Geophysical Research, 114(D5), 1–7.

Bäumer, D., and Vogel, B. (2007). An unexpected pattern of distinct weekly periodicities in climatological variables in Germany. Geophysical Research Letters, 34(L03819), 1–4.

Belitz, C., Brezger, A., Kneib, T., and Lang, S. (2009). BayesX: Software for Bayesian inference in structured additive regression models [Computer software manual]. (Version 2.0.1, http://www.stat.uni-muenchen.de/bayesx/)

Bivand, R. S., Pebesma, E. J., and Gómez-Rubio, V. (2008). Applied spatial data analysis with R. New York: Springer-Verlag. (http://www.asdar-book.org/)

Brezger, A., Kneib, T., and Lang, S. (2005). BayesX: Analyzing Bayesian structured additive regression models. Journal of Statistical Software, 14(11), 1–22. (http://www.jstatsoft.org/v14/i11/)

Brezger, A., and Lang, S. (2006). Generalized structured additive regression based on Bayesian P-splines. Computational Statistics & Data Analysis, 50, 947–991.

Cehak, K. (1982). Note on the dependence of precipitation on the day of the week in a medium industrialized city. Archives for Meteorology, Geophysics, and Bioclimatology Series B, 30(3), 247–251.

Cryer, J. D., and Chan, K.-S. (2008). Time series analysis with applications in R. Springer-Verlag.

Eilers, P. H. C., and Marx, B. D. (1996). Flexible smoothing using B-splines and penalized likelihood. Statistical Science, 11, 89–121.

Fahrmeir, L., Kneib, T., and Lang, S. (2004). Penalized structured additive regression for space time data: A Bayesian perspective. Statistica Sinica, 14, 731–761.

Fahrmeir, L., Kneib, T., and Lang, S. (2009). Regression – Modelle, Methoden und Anwendungen (2nd ed.). Berlin: Springer-Verlag.

Fahrmeir, L., and Tutz, G. (2001). Multivariate statistical modelling based on generalized linear models. New York: Springer-Verlag.

Frei, C., and Schär, C. (1998). A precipitation climatology of the Alps from highresolution rain-gauge observations. International Journal of Climatology, 18(8), 873–900.

Hendricks Franssen, H. J. (2008). Comment on “An unexpected pattern of distinct weekly periodicities in climatological variables in Germany” by Dominique Bäumer and Bernhard Vogel. Geophysical Research Letters, 35(L05802), 1–3.

Hunsberger, S., Albert, P. S., Follmann, D. A., and Suh, E. (2002). Parametric and semiparametric approaches to testing for seasonal trend in serial count data. Biostatistics, 3(3), 289–298.

Kamman, E. E., and Wand, M. P. (2003). Geoadditive models. Applied Statistics, 52, 1–18.

Kneib, T., and Fahrmeir, L. (2006). Structured additive regression for multicategorical space-time data: A mixed model approach. Biometrics, 62, 109–118.

Laux, P., and Kunstmann, H. (2008). Detection of regional weekly weather cycles across Europe. Environmental Research Letters, 3(4), 044005.

Lewin-Koh, N. J., and Bivand, R. (2011). maptools: Tools for feading and handling spatial objects [Computer software manual]. (R package version 0.8-10, http://CRAN.R-project.org/package=maptools)

Lin, X., and Zhang, D. (1999). Inference in generalized additive mixed models by using smoothing splines. Journal of the Royal Statistical Society B, 61, 381–400.

Nemec, J., Chimani, B., Gruber, C., and Auer, I. (2011). Ein neuer Datensatz homogenisierter Tagesdaten [O¨ GM Bulletin]. (2011/1), 19–20. (http://www.meteorologie.at/docs/OEGM bulletin 2011 1.pdf)

Nemec, J., Gruber, C., Chimani, B., and Auer, I. (2011). Trends in extreme temperature indices in Austria based on a new homogenised dataset of daily minimum and maximum temperature series. (submitted to International Journal of Climatology)

R Development Core Team. (2011). R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria. (ISBN 3-900051-07-

, http://www.R-project.org/)

Ruppert, D., Wand, M. P., and Carrol, R. J. (2003). Semiparametric regression. New York: Cambridge University Press.

Schultz, D. M., Mikkonen, S., Laaksonen, A., and Richman, M. B. (2007). Weekly precipitation cycles? Lack of evidence from United States surface stations. Geophysical Research Letters, 34(22), 2–5.

Stein, M. L. (1999). Interpolation of spatial data: Some theory of kriging. New York: Springer-Verlag.

Stjern, C. W. (2011). Weekly cycles in precipitation in a polluted region of Europe. Atmospheric Chemistry and Physics Discussions, 11(1), 1777–1801.

Umlauf, N., Lang, S., Kneib, T., and Zeileis, A. (2011). Structured additive regression models: An R interface to BayesX [Computer software manual]. (R package version 0.1-1/r242, http://bayesr.R-Forge.R-project.org/)

Wand, M. P. (2003). Smoothing and mixed models. Computational Statistics, 18, 223–249.

Wood, S. N. (2006). Generalized additive models: An introduction with R. Boca Raton: Chapman & Hall/CRC.

Zeileis, A., and Grothendieck, G. (2005). zoo: S3 infrastructure for regular and irregular time series. Journal of Statistical Software, 14(6), 1–27. (http://www.jstatsoft.org/v14/i06/)

Zeileis, A., Hornik, K., and Murrell, P. (2009). Escaping RGBland: Selecting colors for statistical graphics. Computational Statistics & Data Analysis, 53(9), 3259–3270.




How to Cite

Umlauf, N., Mayr, G., Messner, J., & Zeileis, A. (2016). Why Does It Always Rain on Me? A Spatio-Temporal Analysis of Precipitation in Austria. Austrian Journal of Statistics, 41(1), 81–92. https://doi.org/10.17713/ajs.v41i1.190