Abstract
The climate change dispute is about changes over time of environmental characteristics (such as rainfall). Some people say that a possible change is not so much in the mean but rather in the extreme phenomena (that is, the average rainfall may not change much but heavy storms may become more or less frequent). The paper studies changes over time in the probability that some high threshold is exceeded. The model is such that the threshold does not need to be specified, the results hold for any high threshold. For simplicity a certain linear trend is studied depending on one real parameter. Estimation and testing procedures (is there a trend?) are developed. Simulation results are presented. The method is applied to trends in heavy rainfall at 18 gauging stations across Germany and The Netherlands. A tentative conclusion is that the trend seems to depend on whether or not a station is close to the sea.
Article PDF
Similar content being viewed by others
References
AghaKouchak, A., Nasrollahi, N.: Semi-parametric and parametric inference of extreme value models for rainfall data. Water Resour. Manage. 24, 1229–1249 (2010)
Alexander, L.V., Zhang, X., Peterson, T.C., Caesar, J., Gleason, B., Klein Tank, A.M.G., Haylock, M., Collins, D., Trewin, B., Rahimzadeh, F., Tagipour, A., Rupa Kumar, K., Revadekar, J., Griffiths, G., Vincent, L., Stephenson, D.B., Burn, J., Aguilar, E., Brunet, M., Taylor, M., New, M., Zhai, P., Rusticucci, M., Vazquez-Aguirre, J.L.: Global observed changes in daily climate extremes of temperature and precipitation. J. Geophys. Res. 111, D05109 (2006)
Allen, M.R., Ingram, W.J.: Constraints on future changes in climate and the hydrologic cycle. Nature 419, 224–232 (2002)
Buishand, T.A., de Haan, L., Zhou, C: On spatial extremes: with application to a rainfall problem. Ann. Appl. Statist. 2, 624–642 (2008)
Burauskaite-Harju, A., Grimvall, A., von Brömssen, C.: Analysing trends in precipitation extremes for a network of stations. Int. J. Climatol. 32, 86–94 (2012)
Caeiro, F., Gomes, M.I., Pestana, D.: Direct reduction of bias of the classical Hill estimator. Revstat 3, 113–136 (2005)
Cai, J., de Haan, L., Zhou, C.: Bias correction in extreme value statisticswith index around zero. Extremes 16, 173–201 (2013)
Chavez-Demoulin, V.: Two problems in environmental statistics: capture-recapture analysis and smooth extremal models, PhD Thesis. Department of mathematics, swiss federal institute of technology, Lausanne (1999)
Coles, S.: An introduction to statistical modeling of extreme values. Springer Verlag (2001)
Davison, A.C., Ramesh, N.: Local likelihood smoothing of sample extremes. J.R. Statist. Soc. B 62, 191–208 (2000)
Davison, A.C., Smith, R.L.: Models for exceedances over high thresholds (with discussion). J. R. Statist. Soc. B 52, 393–442 (1990)
de Haan, L.: Fighting the arch-enemy with mathematics. Statist. Neerlandica 44, 45–68 (1990)
de Haan, L., Ferreira, A.: Extreme value theory: an introduction. Springer (2006)
Drees, H., Ferreira, A., de Haan, L.: On maximum likelihood estimation of the extreme value index. Ann. Appl. Probab. 14, 1179–1201 (2004)
Gaetan, C., Grigoletto, M.: Smoothing sample extremes with dynamic models. Extremes 7, 221–236 (2004)
Gomes, M.I., de Haan, L., Henriques Rodrigues, L.: Tail index estimation through accommodation of bias in the weighted log-excesses. J. Roy. Statist. Soc. Ser. B 70, 31–52 (2008)
Groisman, P.Y., Knight, R.W., Easterling, D.R., Karl, T.R., Hegerl, G.C., Razuvaev, V.N.: Trends in intense precipitation in the climate record. J. Climate 18, 1326–1350 (2005)
Hall, P., Tajvidi, N.: Nonparametric analysis of temporal trend when fitting parametric models to extreme-value data. Statist. Sci. 15, 153–167 (2000)
Hanel, M., Buishand, T.A., Ferro, C.A.T.: A nonstationary index flood model for precipitation extremes in transient regional climate model simulations. J. Geophys. Res. 114, (D15107) (2009)
Hill, B.M.: A simple general approach to inference about the tail of a distribution. Ann. Statist. 3, 1163–1174 (1975)
Klein Tank, A.M.G., Können, G.P.: Trends in indices of daily temperature and precipitation extremes in Europe, 1946-99. J. Climate 16, 3665–3680 (2003)
Kottek, M., Grieser, J., Christoph, B., Rudolph, B., Rubel, F.: World map of the Köppen-Geiger climate classification updated. Meteorol. Z. 15, 259–263 (2006)
Lenderink, G., van Meijgaard, E., Selten, F.: Intense coastal rainfall in The Netherlands in response to high sea surface temperatures: analysis of the event of august 2006 from the perspective of a changing climate. Clim. Dyn. 32, 19–33 (2009)
Mannshardt-Shamseldin, E.C., Smith, R.L., Sain, S.R., Mearns, L.O., Cooley, D.: Downscaling extremes: a comparison of extreme value distributions in point-source and gridded precipitation data. Ann. Appl. Statist. 4, 484–502 (2010)
Pauli, F., Coles, S.G.: Penalized likelihood inference in extreme value analyses. J. Appl. Stat. 28, 547–560 (2001)
Peel, M., Finlayson, B.L., McMahon, T.A.: Updated world map of the Kop̈pen-Geiger climate classification. Hydrol. Earth Syst. Sci. 11, 1633–1644 (2007)
Pickands, J.: The two-dimensional Poisson process and extremal processes. J. Appl. Probab. 8, 745–756 (1971)
Pickands, J.: Statistical inference using extreme order statistics. Ann. Statist. 3, 119–131 (1975)
Rao, C.R.: Linear statistical inference and its applications. Wiley, New York (1973)
Resnick, S.I.: Tail equivalence and its applications. J. Appl. Prob. 8, 135–156 (1971)
Serfling, R.J.: Approximation theorems of mathematical statistics. Wiley series in probability and statistics. Wiley, New York (2002)
Smith, R.L.: Estimating tails of probability distributions. Ann. Statist. 15, 1174–1207 (1987)
Smith, R.L.: Extreme value analysis of environmental time series: an application to trend detection in ground-level ozone. Stat. Sci. 4, 367–393 (1989)
Tomassini, L., Jacob, D.: Spatial analysis of trends in extreme precipitation events in highresolution climate model results and observations for Germany. J. Geophys. Res. 3, D1211 (2009)
Yee, T.W., Stephenson, A.G: Vector generalized linear and additive extreme value models. Extremes 10, 1–19 (2007)
Zhou, C.: Existence and consistency of the maximum likelihood estimator for the extreme value index. J. Multivar. Anal. 100, 794–815 (2009)
Zolina, O., Simmer, C., Belyaev, K., Kapala, A., Gulev, S.: Improving estimates of heavy and extreme precipitation using daily records from European rain gauges. J. Hydrometeorol. 10, 701–716 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
de Haan, L., Tank, A.K. & Neves, C. On tail trend detection: modeling relative risk. Extremes 18, 141–178 (2015). https://doi.org/10.1007/s10687-014-0207-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10687-014-0207-8