Statistical post-processing of forecasts for extremes using bivariate brown-resnick processes with an application to wind gusts

Baldauf, M., Seifert, A., Förstner, J, Majewski, D., Raschendorfer, M., Reinhardt, T.: Operational convective-scale numerical weather prediction with the COSMO model. Mon. Wea. Rev. 139, 3887–3905 (2011)

Berg, C., Christensen, J.P.R., Ressel, P.: Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions. Springer, New York (1984)

Brasseur, O.: Development and application of a physical approach to estimating wind gusts. Mon. Wea. Rev. 129(1), 5–25 (2001)

Brown, B.M., Resnick, S.I.: Extreme values of independent stochastic processes. J. Appl. Probab. 14(4), 732–739 (1977)

Chilès, J.P., Delfiner, P.: : Geostatistics Modeling Spatial Uncertainty, 2nd edn. Wiley, Hoboken (2012)

Clark, I., Basinger, K.L., Harper, W.V.: MUCK-a novel approach to co-kriging. In: Geostatistical, sensitivity, and uncertainty methods for ground-water flow and radionuclide transport modeling. Battelle Press, San Francisco (1989)

Coles, S.: Regional modelling of extreme storms via max-stable processes. J. R. Statist. Soc. Ser. B 55, 797–816 (1993)

Coles, S.: An Introduction to Statistical Modeling of Extreme Values. Springer, London (2001)

Coles, S., Tawn, J.: Modelling extremes of the areal rainfall process. J. R. Statist. Soc. Ser. B 58, 329–347 (1996)

Conradsen, K., Nielsen, L.B., Prahm, L.P.: Review of Weibull statistics for estimation of wind speed distributions. J. Clim. Appl. Meteorol. 23, 1173–1183 (1984)

Cooley, D., Naveau, P., Poncet, P.: Variograms for Spatial Max-Stable Random Fields. In: Dependence in Probability and Statistics, pp 373–390. Springer, New York (2006)

Dombry, C., Éyi-Minko, F., Ribatet, M.: Conditional simulation of max-stable processes. Biometrika 100(1), 111–124 (2013)

Dombry, C., Engelke, S., Oesting, M.: Exact simulation of max-stable processes. Biometrika 103(2), 303–317 (2016)

Engelke, S., Malinowski, A., Kabluchko, Z., Schlather, M.: Estimation of Hüsler–Reiss distributions and Brown–Resnick processes. J. R. Statist. Soc. Ser. B 77(1), 239–265 (2015)

Friederichs, P., Thorarinsdottir, T.L.: Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction. Environmetrics 23(7), 579–594 (2012)

Gebhardt, C., Theis, S., Paulat, M., Ben Bouallègue, Z.: Uncertainties in COSMO-DE precipitation forecasts introduced by model perturbations and variation of lateral boundaries. Atmos. Res. 100(2), 168–177 (2011)

Gelfand, A.E., Diggle, P., Guttorp, P., Fuentes, M.: Handbook of Spatial Statistics. CRC Press, Boca Raton (2010)

Genton, M.G., Padoan, S.A., Sang, H.: Multivariate max-stable spatial processes. Biometrika 102(1), 215–230 (2015)

Gneiting, T., Raftery, A.E.: Strictly proper scoring rules, prediction, and estimation. J. Amer. Statist. Assoc. 102(477), 359–378 (2007)

Gneiting, T., Kleiber, W., Schlather, M.: Matérn cross-covariance functions for multivariate random fields. J. Amer. Statist. Assoc. 105(491), 1167–1177 (2010)

Guttorp, P., Gneiting, T.: Studies in the history of probability and statistics XLIX on the Matérn correlation family. Biometrika 93(4), 989–995 (2006)

Handcock, M.S., Wallis, J.R.: An approach to statistical spatial-temporal modeling of meteorological fields. J. Amer. Statist. Assoc. 89(426), 368–378 (1994)

Huser, R., Davison, A.C.: Space-time modelling of extreme events. J. R. Statist. Soc. Ser. B 76(2), 439–461 (2014)

Kabluchko, Z.: Extremes of independent Gaussian processes. Extremes 14(3), 285–310 (2011)

Kabluchko, Z., Schlather, M., de Haan, L.: Stationary max-stable fields associated to negative definite functions. Ann. Probab. 37(5), 2042–2065 (2009)

Leadbetter, M.R., Lindgren, G., Rootzén, H.: Extremes and Related Properties of Random Sequences and Processes. Springer, New York (1983)

Molchanov, I., Stucki, K.: Stationarity of multivariate particle systems. Stochastic. Process. Appl. 123(6), 2272–2285 (2013)

Papritz, A., Künsch, H., Webster, R.: On the pseudo cross-variogram. Math. Geol. 25(8), 1015–1026 (1993)

Pavia, E.G., O’Brien, J.J.: Weibull statistics of wind speed over the ocean. J. Clim. Appl. Meteorol. 25, 1324–1332 (1986)

Peralta, C., Ben Bouallégue, Z., Theis, S.E., Gebhardt, C., Buchhold, M.: Accounting for initial condition uncertainties in COSMO-DE-EPS. J. Geophys. Res. 117, D07,108 (2012)

Ribatet, M.: Spatial extremes: Max-stable processes at work. J. Soc. Fr. Stat. 154(2), 156–177 (2013)

Schilling, R.L., Song, R., Vondraček, Z.: Bernstein Functions: Theory and Applications. Gruyter, Berlin (2010)

Schlather, M., Tawn, J.A.: A dependence measure for multivariate and spatial extreme values: Properties and inference. Biometrika 90(1), 139–156 (2003)

Sloughter, J.M.L., Raftery, A.E., Gneiting, T., Fraley, C.: Probabilistic quantitative precipitation forecasting using Bayesian model averaging. Mon. Wea. Rev. 135, 3209–3220 (2007)

Smith, R.L.: Maximum likelihood estimation in a class of nonregular cases. Biometrika 72(1), 67–90 (1985)

Smith, R.L.: Max–stable processes and spatial extremes, unpublished manuscript (1990)

Stein, M.L.: Interpolation of Spatial Data: Some Theory for Kriging Springer Series in Statistics. Springer, New York (1999)

Zhang, H.: Inconsistent estimation and asymptotically equal interpolations in model-based geostatistics. J. Amer. Statist. Assoc. 99(465), 250–261 (2004)