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2019 | OriginalPaper | Buchkapitel

Verification Metrics for Hydrological Ensemble Forecasts

verfasst von : François Anctil, Maria-Helena Ramos

Erschienen in: Handbook of Hydrometeorological Ensemble Forecasting

Verlag: Springer Berlin Heidelberg

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Abstract

This chapter reviews the most commonly used verification metrics for measuring the performance of hydrological ensemble forecasts. It links metrics to the different attributes of forecast quality and discusses the links between verification variables, metrics, and applications in a broad perspective. It provides an overview of the use of these metrics in forecast evaluation studies and general insights into what forecasters, practitioners, and end-users should consider when applying verification measures in the practice of hydrological ensemble forecasting.

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Literatur
Zurück zum Zitat M. Abaza, F. Anctil, V. Fortin, R. Turcotte, A comparison of the Canadian global and regional meteorological ensemble prediction systems for short-term hydrological forecasting. Mon. Weather Rev. 141, 3462–3472 (2013). Corrigendum. Mon. Weather Rev. 142, 2561–2562CrossRef M. Abaza, F. Anctil, V. Fortin, R. Turcotte, A comparison of the Canadian global and regional meteorological ensemble prediction systems for short-term hydrological forecasting. Mon. Weather Rev. 141, 3462–3472 (2013). Corrigendum. Mon. Weather Rev. 142, 2561–2562CrossRef
Zurück zum Zitat M. Abaza, F. Anctil, V. Fortin, R. Turcotte, Sequential streamflow assimilation for short-term hydrological ensemble forecasting. J. Hydrol. 519, 2692–2706 (2014)CrossRef M. Abaza, F. Anctil, V. Fortin, R. Turcotte, Sequential streamflow assimilation for short-term hydrological ensemble forecasting. J. Hydrol. 519, 2692–2706 (2014)CrossRef
Zurück zum Zitat L. Alfieri, F. Pappenberger, F. Wetterhall, T. Haiden, D. Richardson, P. Salamon, Evaluation of ensemble streamflow predictions in Europe. J. Hydrol. 517, 913–922 (2014)CrossRef L. Alfieri, F. Pappenberger, F. Wetterhall, T. Haiden, D. Richardson, P. Salamon, Evaluation of ensemble streamflow predictions in Europe. J. Hydrol. 517, 913–922 (2014)CrossRef
Zurück zum Zitat C. Alvarez-Garreton, D. Ryu, A.W. Western, C.-H. Su, W.T. Crow, D.E. Robertson, C. Leahy, Improving operational flood ensemble prediction by the assimilation of satellite soil moisture: comparison between lumped and semi-distributed schemes. Hydrol. Earth Syst. Sci. 19, 1659–1676 (2015)CrossRef C. Alvarez-Garreton, D. Ryu, A.W. Western, C.-H. Su, W.T. Crow, D.E. Robertson, C. Leahy, Improving operational flood ensemble prediction by the assimilation of satellite soil moisture: comparison between lumped and semi-distributed schemes. Hydrol. Earth Syst. Sci. 19, 1659–1676 (2015)CrossRef
Zurück zum Zitat F. Anctil, C. Michel, C. Perrin, V. Andréassian, A soil moisture index as an auxiliary ANN input for stream flow forecasting. J. Hydrol. 286, 155–167 (2004)CrossRef F. Anctil, C. Michel, C. Perrin, V. Andréassian, A soil moisture index as an auxiliary ANN input for stream flow forecasting. J. Hydrol. 286, 155–167 (2004)CrossRef
Zurück zum Zitat J.L. Anderson, A method for producing and evaluating probabilistic forecasts from ensemble model integrations. J. Clim. 9, 1518–1530 (1996)CrossRef J.L. Anderson, A method for producing and evaluating probabilistic forecasts from ensemble model integrations. J. Clim. 9, 1518–1530 (1996)CrossRef
Zurück zum Zitat F. Atger, Verification of intense precipitation forecasts from single models and ensemble prediction systems. Nonlinear Process. Geophys. 8, 401–417 (2001)CrossRef F. Atger, Verification of intense precipitation forecasts from single models and ensemble prediction systems. Nonlinear Process. Geophys. 8, 401–417 (2001)CrossRef
Zurück zum Zitat L. Baringhaus, C. Franz, On a new multivariate two-sample test. J. Multivar. Anal. 88(1), 190–206 (2004)CrossRef L. Baringhaus, C. Franz, On a new multivariate two-sample test. J. Multivar. Anal. 88(1), 190–206 (2004)CrossRef
Zurück zum Zitat J.C. Bartholmes, J. Thielen, M.H. Ramos, S. Gentilini, The European Flood Alert System EFAS – part 2: statistical skill assessment of probabilistic and deterministic operational forecasts. Hydrol. Earth Syst. Sci. 13(2), 141–153 (2009)CrossRef J.C. Bartholmes, J. Thielen, M.H. Ramos, S. Gentilini, The European Flood Alert System EFAS – part 2: statistical skill assessment of probabilistic and deterministic operational forecasts. Hydrol. Earth Syst. Sci. 13(2), 141–153 (2009)CrossRef
Zurück zum Zitat M.A. Boucher, J.P. Laliberté, F. Anctil, An experiment on the evolution of an ensemble of neural networks for streamflow forecasting. Hydrol. Earth Syst. Sci. 14, 603–612 (2010)CrossRef M.A. Boucher, J.P. Laliberté, F. Anctil, An experiment on the evolution of an ensemble of neural networks for streamflow forecasting. Hydrol. Earth Syst. Sci. 14, 603–612 (2010)CrossRef
Zurück zum Zitat F. Bourgin, M.-H. Ramos, G. Thirel, V. Andréassian, Investigating the interactions between data assimilation and post-processing in hydrological ensemble forecasting. J. Hydrol. 519, 2775–2784 (2014)CrossRef F. Bourgin, M.-H. Ramos, G. Thirel, V. Andréassian, Investigating the interactions between data assimilation and post-processing in hydrological ensemble forecasting. J. Hydrol. 519, 2775–2784 (2014)CrossRef
Zurück zum Zitat A.A. Bradley, T. Hashino, S.S. Schwartz, Distributions-oriented verification of probability forecasts for small data samples. Weather Forecast. 18, 903–917 (2003)CrossRef A.A. Bradley, T. Hashino, S.S. Schwartz, Distributions-oriented verification of probability forecasts for small data samples. Weather Forecast. 18, 903–917 (2003)CrossRef
Zurück zum Zitat D. Brochero, F. Anctil, C. Gagné, Simplifying a hydrological ensemble prediction system with a backward greedy selection of members, part I: optimization criteria. Hydrol. Earth Syst. Sci. 15, 3307–3325 (2011)CrossRef D. Brochero, F. Anctil, C. Gagné, Simplifying a hydrological ensemble prediction system with a backward greedy selection of members, part I: optimization criteria. Hydrol. Earth Syst. Sci. 15, 3307–3325 (2011)CrossRef
Zurück zum Zitat J.D. Brown, M. He, S. Regonda, L. Wu, H. Lee, D.-J. Seo, Verification of temperature, precipitation, and streamflow forecasts from the NOAA/NWS Hydrologic Ensemble Forecast Service (HEFS): 2. Streamflow verification. J. Hydrol. 519, 2847–2868 (2014)CrossRef J.D. Brown, M. He, S. Regonda, L. Wu, H. Lee, D.-J. Seo, Verification of temperature, precipitation, and streamflow forecasts from the NOAA/NWS Hydrologic Ensemble Forecast Service (HEFS): 2. Streamflow verification. J. Hydrol. 519, 2847–2868 (2014)CrossRef
Zurück zum Zitat T.M. Carpenter, K.P. Georgakakos, Impacts of parametric and radar rainfall uncertainty on the ensemble streamflow simulations of a distributed hydrologic model. J. Hydrol. 298, 202–221 (2004)CrossRef T.M. Carpenter, K.P. Georgakakos, Impacts of parametric and radar rainfall uncertainty on the ensemble streamflow simulations of a distributed hydrologic model. J. Hydrol. 298, 202–221 (2004)CrossRef
Zurück zum Zitat B. Casati, L.J. Wilson, D.B. Stephenson, Forecast verification: current status and future directions. Meteorol. Appl. 15(1), 3–18 (2008)CrossRef B. Casati, L.J. Wilson, D.B. Stephenson, Forecast verification: current status and future directions. Meteorol. Appl. 15(1), 3–18 (2008)CrossRef
Zurück zum Zitat M.P. Clark, A.G. Slater, Probabilistic quantitative precipitation estimation in complex terrain. J. Hydrometeorol. 7, 3–22 (2006)CrossRef M.P. Clark, A.G. Slater, Probabilistic quantitative precipitation estimation in complex terrain. J. Hydrometeorol. 7, 3–22 (2006)CrossRef
Zurück zum Zitat H. Cloke, F. Pappenberger, Evaluating forecasts of extreme events for hydrological applications: an approach for screening unfamiliar performance measures. Meteorol. Appl. 15, 181–197 (2008)CrossRef H. Cloke, F. Pappenberger, Evaluating forecasts of extreme events for hydrological applications: an approach for screening unfamiliar performance measures. Meteorol. Appl. 15, 181–197 (2008)CrossRef
Zurück zum Zitat C. Corradini, F. Melone, L. Ubertini, A semi-distributed adaptive model for real-time flood forecasting. Water Resour. Bull. 22, 1031–1038 (1986)CrossRef C. Corradini, F. Melone, L. Ubertini, A semi-distributed adaptive model for real-time flood forecasting. Water Resour. Bull. 22, 1031–1038 (1986)CrossRef
Zurück zum Zitat J. Demargne, J.D. Brown, Y. Liu, D.-J. Seo, L. Wu, Z. Toth, Y. Zhu, Diagnostic verification of hydrometeorological and hydrologic ensembles. Atmos. Sci. Lett. 11(2), 114–122 (2010)CrossRef J. Demargne, J.D. Brown, Y. Liu, D.-J. Seo, L. Wu, Z. Toth, Y. Zhu, Diagnostic verification of hydrometeorological and hydrologic ensembles. Atmos. Sci. Lett. 11(2), 114–122 (2010)CrossRef
Zurück zum Zitat F.M. Fan, W. Collischonn, A. Meller, L.C.M. Botelho, Ensemble streamflow forecasting experiments in a tropical basin: the São Francisco River case study. J. Hydrol. 519, 2906–2919 (2014)CrossRef F.M. Fan, W. Collischonn, A. Meller, L.C.M. Botelho, Ensemble streamflow forecasting experiments in a tropical basin: the São Francisco River case study. J. Hydrol. 519, 2906–2919 (2014)CrossRef
Zurück zum Zitat V. Fortin, M. Abaza, A. Anctil, R. Turcotte, Why should ensemble spread match the RMSE of the ensemble mean? J. Hydrometeorol. 15, 1708–1713 (2014)CrossRef V. Fortin, M. Abaza, A. Anctil, R. Turcotte, Why should ensemble spread match the RMSE of the ensemble mean? J. Hydrometeorol. 15, 1708–1713 (2014)CrossRef
Zurück zum Zitat K.J. Franz, T.S. Hogue, M. Barik, Assessment of SWE data assimilation for ensemble streamflow predictions. J. Hydrol. 519(Part D), 2737–2746 (2014)CrossRef K.J. Franz, T.S. Hogue, M. Barik, Assessment of SWE data assimilation for ensemble streamflow predictions. J. Hydrol. 519(Part D), 2737–2746 (2014)CrossRef
Zurück zum Zitat T. Gneiting, A.E. Raftery, Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association 102, 359–378 (2007)CrossRef T. Gneiting, A.E. Raftery, Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association 102, 359–378 (2007)CrossRef
Zurück zum Zitat T. Gneiting, F. Balabdaoui, A.E. Raftery, Probabilistic forecasts, calibration and sharpness. J. R. Stat. Soc. Ser. B Stat. Methodol. 69, 243–268 (2007)CrossRef T. Gneiting, F. Balabdaoui, A.E. Raftery, Probabilistic forecasts, calibration and sharpness. J. R. Stat. Soc. Ser. B Stat. Methodol. 69, 243–268 (2007)CrossRef
Zurück zum Zitat I.J. Good, Rational decisions. J. R. Stat. Soc. 14, 107–114 (1952) I.J. Good, Rational decisions. J. R. Stat. Soc. 14, 107–114 (1952)
Zurück zum Zitat T. Hamill, Interpretation of rank histograms for verifying ensemble forecasts. Mon. Weather Rev. 129, 550–560 (2001)CrossRef T. Hamill, Interpretation of rank histograms for verifying ensemble forecasts. Mon. Weather Rev. 129, 550–560 (2001)CrossRef
Zurück zum Zitat T.M. Hamill, S.J. Colucci, Verification of Eta RSM short-range ensemble forecasts. Mon. Weather Rev. 125, 1312–1327 (1997)CrossRef T.M. Hamill, S.J. Colucci, Verification of Eta RSM short-range ensemble forecasts. Mon. Weather Rev. 125, 1312–1327 (1997)CrossRef
Zurück zum Zitat T. Hashino, A.A. Bradley, S.S. Schwartz, Evaluation of bias-correction methods for ensemble streamflow volume forecasts. Hydrol. Earth Syst. Sci. 11, 939–950 (2007)CrossRef T. Hashino, A.A. Bradley, S.S. Schwartz, Evaluation of bias-correction methods for ensemble streamflow volume forecasts. Hydrol. Earth Syst. Sci. 11, 939–950 (2007)CrossRef
Zurück zum Zitat H. Hersbach, Decomposition of the continuous ranked probability score for ensemble prediction systems. Weather Forecast. 15, 559–570 (2000)CrossRef H. Hersbach, Decomposition of the continuous ranked probability score for ensemble prediction systems. Weather Forecast. 15, 559–570 (2000)CrossRef
Zurück zum Zitat H. Holt, J. Pullen, C. Bishop, Urban and ocean ensembles for improved meteorological and dispersion modeling of the coastal zone. Tellus 61A, 232–249 (2009)CrossRef H. Holt, J. Pullen, C. Bishop, Urban and ocean ensembles for improved meteorological and dispersion modeling of the coastal zone. Tellus 61A, 232–249 (2009)CrossRef
Zurück zum Zitat P.K. Kitanidis, R.L. Bras, Real-time forecasting with a conceptual hydrologic model. 2. Applications and results. Water Resour. Res. 16(6), 1034–1044 (1980)CrossRef P.K. Kitanidis, R.L. Bras, Real-time forecasting with a conceptual hydrologic model. 2. Applications and results. Water Resour. Res. 16(6), 1034–1044 (1980)CrossRef
Zurück zum Zitat F. Laio, S. Tamea, Verification tools for probabilistic forecasts of continuous hydrological variables. Hydrol. Earth Syst. Sci. 11(4), 1267–1277 (2007)CrossRef F. Laio, S. Tamea, Verification tools for probabilistic forecasts of continuous hydrological variables. Hydrol. Earth Syst. Sci. 11(4), 1267–1277 (2007)CrossRef
Zurück zum Zitat K. Liechti, M. Zappa, F. Fundel, U. Germann, The potential of radar-based ensemble forecasts for flash-flood early warning in the southern Swiss Alps. Hydrol. Earth Syst. Sci. 17, 3853–3869 (2013)CrossRef K. Liechti, M. Zappa, F. Fundel, U. Germann, The potential of radar-based ensemble forecasts for flash-flood early warning in the southern Swiss Alps. Hydrol. Earth Syst. Sci. 17, 3853–3869 (2013)CrossRef
Zurück zum Zitat Y. Liu, J.D. Brown, J. Demargne, D.-J. Seo, A wavelet-based approach to assessing timing errors in hydrologic predictions. J. Hydrol. 397(3–4), 210–224 (2011)CrossRef Y. Liu, J.D. Brown, J. Demargne, D.-J. Seo, A wavelet-based approach to assessing timing errors in hydrologic predictions. J. Hydrol. 397(3–4), 210–224 (2011)CrossRef
Zurück zum Zitat S.J. Mason, A model for assessment of weather forecast. Aust. Meteorol. Mag. 30, 291–303 (1982) S.J. Mason, A model for assessment of weather forecast. Aust. Meteorol. Mag. 30, 291–303 (1982)
Zurück zum Zitat S. Matte, M.-A. Boucher, V. Boucher, T.-C. Fortier Filion, Moving beyond the cost–loss ratio: economic assessment of streamflow forecasts for a risk-averse decision maker. Hydrol. Earth Syst. Sci. 21, 2967–2986 (2017)CrossRef S. Matte, M.-A. Boucher, V. Boucher, T.-C. Fortier Filion, Moving beyond the cost–loss ratio: economic assessment of streamflow forecasts for a risk-averse decision maker. Hydrol. Earth Syst. Sci. 21, 2967–2986 (2017)CrossRef
Zurück zum Zitat D.N. Moriasi, J.G. Arnold, M.W. Van Liew, R.L. Bingner, R.D. Harmel, T.L. Veith, Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE 50, 885–900 (2007)CrossRef D.N. Moriasi, J.G. Arnold, M.W. Van Liew, R.L. Bingner, R.D. Harmel, T.L. Veith, Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE 50, 885–900 (2007)CrossRef
Zurück zum Zitat A.H. Murphy, A new vector partition of the probability score. J. Appl. Meteorol. 12(4), 595–600 (1973)CrossRef A.H. Murphy, A new vector partition of the probability score. J. Appl. Meteorol. 12(4), 595–600 (1973)CrossRef
Zurück zum Zitat A. Murphy, What is a good forecast? An essay on the nature of goodness in weather forecasting. Weather Forecast. 8(2), 281–293 (1993)CrossRef A. Murphy, What is a good forecast? An essay on the nature of goodness in weather forecasting. Weather Forecast. 8(2), 281–293 (1993)CrossRef
Zurück zum Zitat T. Palmer, R. Buizza, R. Hagedorn, A. Lawrence, M. Leutbecher, L. Smith, Ensemble prediction: a pedagogical perspective. ECMWF Newsl. 106, 10–17 (2005). ECMWF, Reading T. Palmer, R. Buizza, R. Hagedorn, A. Lawrence, M. Leutbecher, L. Smith, Ensemble prediction: a pedagogical perspective. ECMWF Newsl. 106, 10–17 (2005). ECMWF, Reading
Zurück zum Zitat F. Pappenberger, K. Scipal, R. Buizza, Hydrological aspects of meteorological verification. Atmos. Sci. Lett. 9, 43–52 (2008)CrossRef F. Pappenberger, K. Scipal, R. Buizza, Hydrological aspects of meteorological verification. Atmos. Sci. Lett. 9, 43–52 (2008)CrossRef
Zurück zum Zitat F. Pappenberger, M.H. Ramos, H.L. Cloke, F. Wetterhall, L. Alfieri, K. Bogner, A. Mueller, P. Salamon, How do I know if my forecasts are better? Using benchmarks in hydrological ensemble prediction. J. Hydrol. 522, 697–713 (2015)CrossRef F. Pappenberger, M.H. Ramos, H.L. Cloke, F. Wetterhall, L. Alfieri, K. Bogner, A. Mueller, P. Salamon, How do I know if my forecasts are better? Using benchmarks in hydrological ensemble prediction. J. Hydrol. 522, 697–713 (2015)CrossRef
Zurück zum Zitat W.W. Peterson, T.G. Birdsall, W.C. Fox, The theory of signal detectability. Trans. IRE Prof. Group Inf. Theory 2–4, 171–212 (1954)CrossRef W.W. Peterson, T.G. Birdsall, W.C. Fox, The theory of signal detectability. Trans. IRE Prof. Group Inf. Theory 2–4, 171–212 (1954)CrossRef
Zurück zum Zitat M.H. Ramos, T. Mathevet, J. Thielen, F. Pappenberger, Communicating uncertainty in hydro-meteorological forecasts: mission impossible? Meteorol. Appl. 17, 223–235 (2010)CrossRef M.H. Ramos, T. Mathevet, J. Thielen, F. Pappenberger, Communicating uncertainty in hydro-meteorological forecasts: mission impossible? Meteorol. Appl. 17, 223–235 (2010)CrossRef
Zurück zum Zitat A. Randrianasolo, M.H. Ramos, G. Thirel, V. Andreassian, E. Martin, Comparing the scores of hydrological ensemble forecasts issued by two different hydrological models. Atmos. Sci. Lett. 11(2), 100–107 (2010)CrossRef A. Randrianasolo, M.H. Ramos, G. Thirel, V. Andreassian, E. Martin, Comparing the scores of hydrological ensemble forecasts issued by two different hydrological models. Atmos. Sci. Lett. 11(2), 100–107 (2010)CrossRef
Zurück zum Zitat B. Renard, D. Kavetski, G. Kuczera, M. Thyer, S.W. Franks, Understanding predictive uncertainty in hydrologic modeling: the challenge of identifying input and structural errors. Water Resour. Res. 46, W05521 (2010)CrossRef B. Renard, D. Kavetski, G. Kuczera, M. Thyer, S.W. Franks, Understanding predictive uncertainty in hydrologic modeling: the challenge of identifying input and structural errors. Water Resour. Res. 46, W05521 (2010)CrossRef
Zurück zum Zitat D.S. Richardson, Skill and relative economic value of ECMWF ensemble prediction system. Q. J. R. Meteorol. Soc. 126, 649–667 (2000)CrossRef D.S. Richardson, Skill and relative economic value of ECMWF ensemble prediction system. Q. J. R. Meteorol. Soc. 126, 649–667 (2000)CrossRef
Zurück zum Zitat E. Roulin, Skill and relative economic value of medium-range hydrological ensemble predictions. Hydrol. Earth Syst. Sci. 11, 725–737 (2007)CrossRef E. Roulin, Skill and relative economic value of medium-range hydrological ensemble predictions. Hydrol. Earth Syst. Sci. 11, 725–737 (2007)CrossRef
Zurück zum Zitat E. Roulin, S. Vannitsem, Post-processing of medium-range probabilistic hydrological forecasting: impact of forcing, initial conditions and model errors. Hydrol. Process. 29(6), 1434–1449 (2015)CrossRef E. Roulin, S. Vannitsem, Post-processing of medium-range probabilistic hydrological forecasting: impact of forcing, initial conditions and model errors. Hydrol. Process. 29(6), 1434–1449 (2015)CrossRef
Zurück zum Zitat M.S. Roulston, L.A. Smith, Evaluating probabilistic forecasts using information theory. Mon. Weather Rev. 130, 1653–1660 (2002)CrossRef M.S. Roulston, L.A. Smith, Evaluating probabilistic forecasts using information theory. Mon. Weather Rev. 130, 1653–1660 (2002)CrossRef
Zurück zum Zitat D.L. Shrestha, D.E. Robertson, J.C. Bennett, Q.J. Wang, Improving precipitation forecasts by generating ensembles through postprocessing. Mon. Weather Rev. 143, 3642–3663 (2015)CrossRef D.L. Shrestha, D.E. Robertson, J.C. Bennett, Q.J. Wang, Improving precipitation forecasts by generating ensembles through postprocessing. Mon. Weather Rev. 143, 3642–3663 (2015)CrossRef
Zurück zum Zitat G. Székely, M. Rizzo, A new test for multivariate normality. J. Multivar. Anal. 1(93), 58–80 (2005)CrossRef G. Székely, M. Rizzo, A new test for multivariate normality. J. Multivar. Anal. 1(93), 58–80 (2005)CrossRef
Zurück zum Zitat O. Talagrand, R. Vautard, B. Strauss, Evaluation of probabilistic prediction systems, in Workshop on Predictability, ed. by for Medium-Range Weather Forecasts, E. C., Shinfield Park, Reading (1997), pp. 1–25 O. Talagrand, R. Vautard, B. Strauss, Evaluation of probabilistic prediction systems, in Workshop on Predictability, ed. by for Medium-Range Weather Forecasts, E. C., Shinfield Park, Reading (1997), pp. 1–25
Zurück zum Zitat A. Thiboult, F. Anctil, M.-A. Boucher, Accounting for three sources of uncertainty in ensemble hydrological forecasting. Hydrol. Earth Syst. Sci. 20, 1809–1825 (2016)CrossRef A. Thiboult, F. Anctil, M.-A. Boucher, Accounting for three sources of uncertainty in ensemble hydrological forecasting. Hydrol. Earth Syst. Sci. 20, 1809–1825 (2016)CrossRef
Zurück zum Zitat J.-A. Velázquez, F. Anctil, C. Perrin, Performance and reliability of multimodel hydrological ensemble simulations based on seventeen lumped models and a thousand catchments. Hydrol. Earth Syst. Sci. 14, 2303–2317 (2010)CrossRef J.-A. Velázquez, F. Anctil, C. Perrin, Performance and reliability of multimodel hydrological ensemble simulations based on seventeen lumped models and a thousand catchments. Hydrol. Earth Syst. Sci. 14, 2303–2317 (2010)CrossRef
Zurück zum Zitat J.S. Verkade, M.G.F. Werner, Estimating the benefits of single value and probability forecasting for flood warning. Hydrol. Earth Syst. Sci. 15, 3751–3765 (2011)CrossRef J.S. Verkade, M.G.F. Werner, Estimating the benefits of single value and probability forecasting for flood warning. Hydrol. Earth Syst. Sci. 15, 3751–3765 (2011)CrossRef
Zurück zum Zitat J.S. Verkade, J.D. Brown, P. Reggiani, A.H. Weerts, Post-processing ECMWF precipitation and temperature ensemble reforecasts for operational hydrologic forecasting at various spatial scales. J. Hydrol. 501, 73–91 (2013)CrossRef J.S. Verkade, J.D. Brown, P. Reggiani, A.H. Weerts, Post-processing ECMWF precipitation and temperature ensemble reforecasts for operational hydrologic forecasting at various spatial scales. J. Hydrol. 501, 73–91 (2013)CrossRef
Zurück zum Zitat N. Voisin, F. Pappenberger, D.P. Lettenmaier, R. Buizza, J.C. Schaake, Application of a medium-range global hydrologic probabilistic forecast scheme to the Ohio River Basin. Weather Forecast. 26, 425–446 (2011)CrossRef N. Voisin, F. Pappenberger, D.P. Lettenmaier, R. Buizza, J.C. Schaake, Application of a medium-range global hydrologic probabilistic forecast scheme to the Ohio River Basin. Weather Forecast. 26, 425–446 (2011)CrossRef
Zurück zum Zitat A.S. Weigend, S. Shi, Predicting daily probability distributions of S&P500 returns. J. Forecast. 19, 375–392 (2000)CrossRef A.S. Weigend, S. Shi, Predicting daily probability distributions of S&P500 returns. J. Forecast. 19, 375–392 (2000)CrossRef
Zurück zum Zitat S.V. Weijs, R. van Nooijen, N. van de Giesen, Kullback–Leibler divergence as a forecast skill score with classic reliability–resolution–uncertainty decomposition. Mon. Weather Rev. 138, 3387–3399 (2010)CrossRef S.V. Weijs, R. van Nooijen, N. van de Giesen, Kullback–Leibler divergence as a forecast skill score with classic reliability–resolution–uncertainty decomposition. Mon. Weather Rev. 138, 3387–3399 (2010)CrossRef
Zurück zum Zitat K. Werner, J.S. Verkade, T.C. Pagano, Application of hydrological forecast verification information, in Handbook of Hydrometeorological Ensemble Forecasting, ed. by Q. Duan, F. Pappenberger, J. Thielen, A. Wood, H. Cloke, J. Schaake (Springer, Berlin/Heidelberg, 2016), 22p. https://doi.org/10.1007/978-3-642-40457-3_7-1 K. Werner, J.S. Verkade, T.C. Pagano, Application of hydrological forecast verification information, in Handbook of Hydrometeorological Ensemble Forecasting, ed. by Q. Duan, F. Pappenberger, J. Thielen, A. Wood, H. Cloke, J. Schaake (Springer, Berlin/Heidelberg, 2016), 22p. https://​doi.​org/​10.​1007/​978-3-642-40457-3_​7-1
Zurück zum Zitat D.S. Wilks, Statistical Methods in the Atmospheric Sciences: An Introduction (Academic, 2011), Amsterdam, 676p D.S. Wilks, Statistical Methods in the Atmospheric Sciences: An Introduction (Academic, 2011), Amsterdam, 676p
Zurück zum Zitat A.W. Wood, A. Kumar, D.P. Lettenmaier, A retrospective assessment of National Centers for Environmental Prediction climate model–based ensemble hydrologic forecasting in the western United States. J. Geophys. Res. Atmos. 110, D04105 (2005). https://doi.org/10.1029/2004JD004508CrossRef A.W. Wood, A. Kumar, D.P. Lettenmaier, A retrospective assessment of National Centers for Environmental Prediction climate model–based ensemble hydrologic forecasting in the western United States. J. Geophys. Res. Atmos. 110, D04105 (2005). https://​doi.​org/​10.​1029/​2004JD004508CrossRef
Zurück zum Zitat I. Zalachori, M.H. Ramos, R. Garçon, T. Mathevet, J. Gailhard, Statistical processing of forecasts for hydrological ensemble prediction: a comparative study of different bias correction strategies. Adv. Sci. Res. 8, 135–141 (2012)CrossRef I. Zalachori, M.H. Ramos, R. Garçon, T. Mathevet, J. Gailhard, Statistical processing of forecasts for hydrological ensemble prediction: a comparative study of different bias correction strategies. Adv. Sci. Res. 8, 135–141 (2012)CrossRef
Metadaten
Titel
Verification Metrics for Hydrological Ensemble Forecasts
verfasst von
François Anctil
Maria-Helena Ramos
Copyright-Jahr
2019
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-39925-1_3