Del Sarto, G. ORCID: https://orcid.org/0009-0006-3257-6903, Bröcker, J. ORCID: https://orcid.org/0000-0002-0864-6530, Flandoli, F. ORCID: https://orcid.org/0000-0003-2837-3784 and Kuna, T. (2024) Variational techniques for a one-dimensional energy balance model. Nonlinear Processes in Geophysics, 31 (1). pp. 137-150. ISSN 1607-7946 doi: https://doi.org/10.5194/npg-31-137-2024

Weisheimer, A., Baker, L. H. ORCID: https://orcid.org/0000-0003-0738-9488, Bröcker, J., Garfinkel, C. I., Hardiman, S. C., Hodson, D. L. R. ORCID: https://orcid.org/0000-0001-7159-6700, Palmer, T. N., Robson, J. I. ORCID: https://orcid.org/0000-0002-3467-018X, Scaife, A. A., Screen, J. A., Shepherd, T. G. ORCID: https://orcid.org/0000-0002-6631-9968, Smith, D. N. and Sutton, R. T. ORCID: https://orcid.org/0000-0001-8345-8583 (2024) The signal-to-noise paradox in climate forecasts: revisiting our understanding and identifying future priorities. Bulletin of the American Meteorological Society, 105 (3). E651-E659. ISSN 1520-0477 doi: https://doi.org/10.1175/BAMS-D-24-0019.1

de Melo Viríssimo, F. ORCID: https://orcid.org/0000-0002-2905-3478, Stainforth, D. A. ORCID: https://orcid.org/0000-0001-6476-733X and Bröcker, J. ORCID: https://orcid.org/0000-0002-0864-6530 (2024) The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34 (1). 013136. ISSN 1089-7682 doi: https://doi.org/10.1063/5.0180870

Bröcker, J. ORCID: https://orcid.org/0000-0002-0864-6530, Charlton-Perez, A. J. ORCID: https://orcid.org/0000-0001-8179-6220 and Weisheimer, A. ORCID: https://orcid.org/0000-0002-7231-6974 (2023) A statistical perspective on the signal–to–noise paradox. Quarterly Journal of the Royal Meteorological Society, 149 (752). pp. 911-923. ISSN 1477-870X doi: https://doi.org/10.1002/qj.4440

Bröcker, J. (2023) Existence and uniqueness for variational data assimilation in continuous time. Mathematical Control & Related Fields, 13 (1). pp. 94-115. ISSN 2156-8472 doi: https://doi.org/10.3934/mcrf.2021050

Carigi, G. ORCID: https://orcid.org/0000-0001-7611-8230, Bröcker, J. and Kuna, T. (2023) Exponential ergodicity for a stochastic two-layer quasi-geostrophic model. Stochastics and Dynamics, 23 (2). 2350011. ISSN 1793-6799 doi: https://doi.org/10.1142/S0219493723500119

Bröcker, J. (2023) Testing the reliability of forecasting systems. Journal of Applied Statistics, 50 (1). pp. 106-130. ISSN 1360-0532 doi: https://doi.org/10.1080/02664763.2021.1981833

Bröcker, J. ORCID: https://orcid.org/0000-0002-0864-6530 (2022) Uniform calibration tests for forecasting systems with small lead time. Statistics and Computing, 32. 102. ISSN 0960-3174 doi: https://doi.org/10.1007/s11222-022-10144-9

Charlton-Perez, A. J. ORCID: https://orcid.org/0000-0001-8179-6220, Bröcker, J. ORCID: https://orcid.org/0000-0002-0864-6530, Karpechko, A. Y. ORCID: https://orcid.org/0000-0003-0902-0414, Lee, S. H. ORCID: https://orcid.org/0000-0003-0986-0093, Sigmond, M. ORCID: https://orcid.org/0000-0003-2191-9756 and Simpson, I. R. ORCID: https://orcid.org/0000-0002-2915-1377 (2021) A minimal model to diagnose the contribution of the stratosphere to tropospheric forecast skill. Journal of Geophysical Research: Atmospheres, 126 (24). ISSN 2169-8996 doi: https://doi.org/10.1029/2021JD035504

Bröcker, J. and Bouallègue, Z. B. (2020) Stratified rank histograms for ensemble forecast verification under serial dependence. Quarterly Journal of the Royal Meteorological Society, 146 (729). pp. 1976-1990. ISSN 0035-9009 doi: https://doi.org/10.1002/qj.3778

Charlton-Perez, A. J. ORCID: https://orcid.org/0000-0001-8179-6220, Bröcker, J., Stockdale, T. N. and Johnson, S. (2019) When and where do ECMWF seasonal forecast systems exhibit anomalously low signal‐to‐noise ratio? Quarterly Journal of the Royal Meteorological Society, 145 (725). pp. 3466-3478. ISSN 1477-870X doi: https://doi.org/10.1002/qj.3631

Cafaro, C. ORCID: https://orcid.org/0000-0001-8063-4887, Frame, T. H. A. ORCID: https://orcid.org/0000-0001-6542-2173, Methven, J. ORCID: https://orcid.org/0000-0002-7636-6872, Roberts, N. and Bröcker, J. (2019) The added value of convection-permitting ensemble forecasts of sea breeze compared to a Bayesian forecast driven by the global ensemble. Quarterly Journal of the Royal Meteorological Society, 145 (721). pp. 1780-1798. ISSN 1477-870X doi: https://doi.org/10.1002/qj.3531

Bröcker, J. (2019) What is the correct cost functional for variational data assimilation? Climate Dynamics, 52 (1-2). pp. 389-399. ISSN 0930-7575 doi: https://doi.org/10.1007/s00382-018-4146-y

Bröcker, J. (2018) Assessing the reliability of ensemble forecasting systems under serial dependence. Quarterly Journal of the Royal Meteorological Society, 144 (717). pp. 2666-2675. ISSN 1477-870X doi: https://doi.org/10.1002/qj.3379

Oljača, L., Bröcker, J. and Kuna, T. (2018) Almost sure error bounds for data assimilation in dissipative systems with unbounded observation noise. SIAM Journal on Applied Dynamical Systems, 17 (4). pp. 2882-2914. ISSN 1536-0040 doi: https://doi.org/10.1137/17M1162305

Bröcker, J. and Del Magno, G. (2017) Asymptotic stability of the optimal filter for random chaotic maps. Nonlinearity, 30 (5). pp. 1809-1833. ISSN 1361-6544 doi: https://doi.org/10.1088/1361-6544/aa639c

Bröcker, J. (2017) Existence and uniqueness for four-dimensional variational data assimilation in discrete time. SIAM Journal of Applied Dynamical Systems, 16 (1). pp. 361-374. ISSN 1536-0040 doi: https://doi.org/10.1137/16M1068918

Mallia-Parfitt, N. and Bröcker, J. (2016) Assessing the performance of data assimilation algorithms which employ linear error feedback. Chaos, 26 (10). 103109. ISSN 1089-7682 doi: https://doi.org/10.1063/1.4965029

Siegert, S., Bröcker, J. and Kantz, H. (2015) Skill of data-based predictions versus dynamical models. In: Chavez, M., Ghil, M. and Urrutia-Fucugauchi, J. (eds.) Extreme Events — Observations, Modeling, and Economics. John Wiley & Sons, Inc, pp. 35-50. ISBN 9781119157014

Messner, J. W., Zeileis, A., Broecker, J. and Mayr, G. J. (2014) Probabilistic wind power forecasts with an inverse power curve transformation and censored regression. Wind Energy, 17 (11). pp. 1753-1766. ISSN 1099-1824 doi: https://doi.org/10.1002/we.1666

Bröcker, J. (2014) Assessing the performance of dynamical trajectory estimates. Physical Review E, 89 (6). 062919. ISSN 1550-2376 doi: https://doi.org/10.1103/PhysRevE.89.062919

Bröcker, J. (2014) Resolution and discrimination - two sides of the same coin. Quarterly Journal of the Royal Meteorological Society, 141 (689). pp. 1277-1282. ISSN 1477-870X doi: https://doi.org/10.1002/qj.2434

Ho, C. K., Hawkins, E. ORCID: https://orcid.org/0000-0001-9477-3677, Shaffrey, L. ORCID: https://orcid.org/0000-0003-2696-752X, Bröcker, J., Hermanson, L., Murphy, J. M., Smith, D. M. and Eade, R. (2013) Examining reliability of seasonal to decadal sea surface temperature forecasts: the role of ensemble dispersion. Geophysical Research Letters, 40 (21). pp. 5770-5775. ISSN 0094-8276 doi: https://doi.org/10.1002/2013GL057630

Gundermann, J., Kantz, H. and Bröcker, J. (2013) Crooks' fluctuation theorem for a process on a two dimensional fluid field. Physical Review Letters, 110 (23). 234502. ISSN 0031-9007 doi: https://doi.org/10.1103/PhysRevLett.110.234502

Bröcker, J. (2012) Evaluating raw ensembles with the continuous ranked probability score. Quarterly Journal of the Royal Meteorological Society, 138 (667). pp. 1611-1617. ISSN 1477-870X doi: https://doi.org/10.1002/qj.1891

Bröcker, J. and Szendro, I. G. (2012) Sensitivity and out-of-sample error in continuous time data assimilation. Quarterly Journal of the Royal Meteorological Society, 138 (664). pp. 785-801. ISSN 1477-870X doi: https://doi.org/10.1002/qj.940

Bröcker, J. (2012) Estimating reliability and resolution of probability forecasts through decomposition of the empirical score. Climate Dynamics, 39 (3-4). pp. 655-667. ISSN 0930-7575 doi: https://doi.org/10.1007/s00382-011-1191-1

Siegert, S., Bröcker, J. and Kantz, H. (2012) Rank histograms of stratified Monte-Carlo ensembles. Monthly Weather Review, 140 (12). pp. 1558-1571. ISSN 0027-0644 doi: https://doi.org/10.1175/MWR-D-11-00302.1

Bröcker, J., Siegert, S. and Kantz, H. (2011) Comment on ``Conditional Exceedance Probabilities''. Monthly Weather Review, 139 (10). pp. 3322-3324. ISSN 0027-0644 doi: https://doi.org/10.1175/2011MWR3658.1

Siegert, S., Bröcker, J. and Kantz, H. (2011) Predicting outliers in ensemble forecasts. Quarterly Journal of the Royal Meteorological Society, 137 (660). pp. 1887-1897. ISSN 1477-870X doi: https://doi.org/10.1002/qj.868

Broecker, J. (2011) Probability forecasts. In: Jolliffe, I.T. and Stephenson, D. B. (eds.) Forecast verification : a practitioner's guide in atmospheric science. 2nd ed. Wiley-Blackwell, Oxford, pp. 119-139. ISBN 9780470660713

Bröcker, J. and Kantz, H. (2011) The concept of exchangeability in ensemble forecasting. Nonlinear Processes in Geophysics, 18 (1). pp. 1-5. ISSN 1023-5809 doi: https://doi.org/10.5194/npg-18-1-2011

Bröcker, J. (2010) On variational data assimilation in continuous time. Quarterly Journal of the Royal Meteorological Society, 136 (652). pp. 1906-1919. ISSN 1477-870X doi: https://doi.org/10.1002/qj.695

Bröcker, J. (2010) Regularized logistic models for probabilistic forecasting and diagnostics. Monthly Weather Review, 138 (2). pp. 592-604. ISSN 0027-0644 doi: https://doi.org/10.1175/2009MWR3126.1

Bröcker, J., Engster, D. and Parlitz, U. (2009) Probabilistic evaluation of time series models : a comparison of several approaches. Chaos, 19 (4). ISSN 1089-7682

Bröcker, J. (2009) Reliability, sufficiency, and the decomposition of proper scores. Quarterly Journal of the Royal Meteorological Society, 135 (643). 1512 - 1519. ISSN 1477-870X doi: https://doi.org/10.1002/qj.456

Bröcker, J. and Smith, L. A. (2008) From ensemble forecasts to predictive distribution functions. Tellus Series A: Dynamic Meteorology and Oceanography, 60 (4). pp. 663-678. ISSN 1600-0870 doi: https://doi.org/10.1111/j.1600-0870.2008.00333.x

Bröcker, J. (2008) On reliability analysis of multi-categorical forecasts. Nonlinear Processes in Geophysics, 15 (4). pp. 661-673. ISSN 1023-5809 doi: https://doi.org/10.5194/npg-15-661-2008

Hallerberg, S., Bröcker, J. and Kantz, H. (2008) Prediction of extreme events. In: Donner, R. V. and Barbosa, S. M. (eds.) Nonlinear time series analysis in the geosciences : applications in climatology, geodynamics, and solar-terrestrial physics. Lecture notes in earth sciences, 112. Springer, Berlin ; London, pp. 35-59. ISBN 9783540789376