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Verification of Meteorological Forecasts for Hydrological Applications

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Handbook of Hydrometeorological Ensemble Forecasting

Abstract

This chapter illustrates how verification is conducted with operational meteorological ensemble forecasts. It focuses on the main aspects of importance to hydrological applications, such as verification of point and spatial precipitation forecasts, verification of temperature forecasts, verification of extreme meteorological events, and feature-based verification.

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References

  • C. Accadia, S. Mariani, M. Casaioli, A. Lavagnini, Sensitivity of precipitation forecast skill scores to bilinear interpolation and a simple nearest-neighbor average method on high-resolution verification grids. Weather Forecast. 18, 918–932 (2003)

    Article  Google Scholar 

  • A. AghaKouchak, N. Nasrollahi, J. Li, B. Imam, S. Sorooshian, Geometrical characterization of precipitation patterns. J. Hydrometeorol. 12(2), 274–285 (2010). https://doi.org/10.1175/2010JHM1298.1

    Article  Google Scholar 

  • G.D. Alexander, J.A. Weinman, J.L. Schols, The use of digital warping of microwave integrated vapor imagery to improve forecasts of marine extratropical cyclones. Mon. Weather Rev. 126, 1469–1496 (1998)

    Article  Google Scholar 

  • L. Alfieri, D. Velasco, J. Thielen, Flash flood detection through a multi-stage probabilistic warning system for heavy precipitation events. Adv. Geosci. 29, 69–75 (2011). https://doi.org/10.5194/adgeo-29-69-2011. www.adv-geosci.net/29/69/2011/

    Article  Google Scholar 

  • L. Alfieri, P. Burek, E. Dutra, B. Krzeminski, D. Muraro, J. Thielen, F. Pappenberger, GloFAS – global ensemble streamflow forecasting and flood early warning. Hydrol. Earth Syst. Sci. 13, 141–153 (2012)

    Google Scholar 

  • T. Anderson, D. Darling, Asymptotic theory of certain goodness of fit criteria based on stochastic processes. Ann. Math. Stat. 23, 193–212 (1952)

    Article  Google Scholar 

  • F. Atger, Verification of intense precipitation forecasts from single models and ensemble prediction systems. Nonlinear Processes Geophys. 8, 401–417 (2001)

    Article  Google Scholar 

  • 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, 141–153 (2009)

    Article  Google Scholar 

  • W.M. Briggs, R.A. Levine, Wavelets and field forecast verification. Mon. Weather Rev. 125, 1329–1341 (1997)

    Article  Google Scholar 

  • B.G. Brown, E. Gilleland, E.E. Ebert, Forecasts of spatial fields, in Forecast Verification, ed. by I. Jolliffe, D.B. Stephenson. The Atrium, Southern Gate, Chichester, UK (2011), pp. 95–117

    Chapter  Google Scholar 

  • R. Bullock, Development and implementation of MODE time domain object-based verification, in 24th Conference on Weather and Forecasting, Seattle, 24–27 Jan 2011. American Meteorological Society

    Google Scholar 

  • N. Bussieres, W. Hogg, The objective analysis of daily rainfall by distance weighting schemes on a mesoscale grid. Atmosphere–Ocean 27, 521–541 (1989)

    Article  Google Scholar 

  • B. Casati, New developments of the intensity-scale technique within the spatial verification methods inter-comparison project. Weather Forecast. 25(1), 113–143 (2010). https://doi.org/10.1175/2009WAF2222257.1

    Article  Google Scholar 

  • B. Casati, G. Ross, D.B. Stephenson, A new intensity-scale approach for the verification of spatial precipitation forecasts. Meteorol. Appl. 11, 141–154 (2004)

    Article  Google Scholar 

  • G.J. Ciach, W.F. Krajewski, On the estimation of radar rainfall error variance. Adv. Water Resour. 22, 585–595 (1999)

    Article  Google Scholar 

  • R. Cifelli, V. Chandrasekar, Dual-polarization radar rainfall estimation, in Rainfall: State of the Science, ed. by Y.M. Tistek, M. Gebremichael. American Geophysical Union, Washington, DC (2010), pp. 105–125. doi:10.1029/2010GM000930

    Google Scholar 

  • H.L. Cloke, C. Jeffers, F. Wetterhall, T. Byrne, J. Lowe, F. Pappenberger, Climate impacts on river flow: projections for the Medway catchment, UK, with UKCP09 and CATCHMOD. Hydrol. Process. (2010). https://doi.org/10.1002/hyp.776

    Article  Google Scholar 

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

    Book  Google Scholar 

  • C. Davis, B. Brown, R.G. Bullock, Object-based verification of precipitation forecasts. Part I: methodology and application to mesoscale rain areas. Mon. Weather Rev. 134(7), 1772–1784 (2006a). https://doi.org/10.1175/MWR3145.1

    Article  Google Scholar 

  • C. Davis, B. Brown, R.G. Bullock, Object-based verification of precipitation forecasts. Part II: application to convective rain systems. Mon. Weather Rev. 134(7), 1785–1795 (2006b). https://doi.org/10.1175/MWR3146.1

    Article  Google Scholar 

  • C. Davis, B. Brown, R.G. Bullock, J. Halley Gotway, The method for object-based diagnostic evaluation (MODE) applied to numerical forecasts from the 2005 NSSL/SPC spring program. Weather Forecast. 24(5), 1252–1267 (2009). https://doi.org/10.1175/2009WAF2222241.1

    Article  Google Scholar 

  • F.X. Diebold, R.S. Mariano, Comparing predictive accuracy. J. Bus. Econ. Stat. 13, 253–263 (1995)

    Google Scholar 

  • L. Duc, K. Saito, H. Seko, Spatial-temporal fractions verification for high-resolution ensemble forecasts. Tellus A 65, 18171 (2013). https://doi.org/10.3402/tellusa.v65i0.18171

    Article  Google Scholar 

  • J.D. Duda, X. Wang, F. Kong, M. Xue, Using varied microphysics to account for uncertainty in warm-season QPF in a convection-allowing ensemble. Mon. Weather Rev. 142, 2198–2219 (2014)

    Article  Google Scholar 

  • E. Dutra, M. Diamantakis, I. Tsonevsky, E. Zsoter, F. Wetterhall, T. Stockdale, D. Richardson, F. Pappenberger, The extreme forecast index at the seasonal scale. Atmos. Sci. Lett. 14(4), 256–262 (2013)

    Article  Google Scholar 

  • E.E. Ebert, Fuzzy verification of high resolution gridded forecasts: a review and proposed framework. Meteorol. Appl. 15, 51–64 (2008). https://doi.org/10.1002/met.25. Available at http://www.ecmwf.int/newsevents/meetings/workshops/2007/jwgv/METspecialissueemail.pdf

    Article  Google Scholar 

  • E.E. Ebert, J.L. McBride, Verification of precipitation in weather systems: determination of systematic errors. J. Hydrol. 239, 179–202 (2000)

    Article  Google Scholar 

  • E.E. Ebert, U. Damrath, W. Wergen, M.E. Baldwin, The WGNE assessment of short-term quantitative precipitation forecasts. Bull. Am. Meteorol. Soc. 84, 481–492 (2003)

    Article  Google Scholar 

  • E. Ebert, L. Wilson, A. Weigel, M. Mittermaier, P. Nurmi, P. Gill, M. Göber, S. Joslyn, B. Brown, T. Fowler, A. Watkins, Progress and challenges in forecast verification. Meteorol. Appl. 20, 130–139 (2013). https://doi.org/10.1002/met.1392

    Article  Google Scholar 

  • EUMETNET, ODYSSEY, the OPERA Data Centre (2014), http://www.eumetnet.eu/odyssey-opera-data-centre. Viewed 10 Apr 2014

  • C.A.T. Ferro, D.B. Stephenson, Extremal dependence: improved verification measures for deterministic forecasts of rare binary events. Weather Forecast. 26, 699–713 (2011). https://doi.org/10.1175/WAF-D-10-05030.1

    Article  Google Scholar 

  • V. Fortin, M. Abaza, F. Anctil, R. Turcotte, Why should ensemble spread match the RMSE of the ensemble mean? J. Hydrometeorol. 15, 1708–1713 (2016)

    Article  Google Scholar 

  • W.A. Gallus Jr., Application of object-based verification techniques to ensemble precipitation forecasts. Weather Forecast. 25, 144–158 (2009)

    Article  Google Scholar 

  • A. Ghelli, A. Garcia-Mendez, F. Prates, M. Dahoui, Extreme weather events in summer 2010: how did the ECMWF forecasting systems perform? ECMWF Newsl. 125, 7–11 (2010)

    Google Scholar 

  • R. Giacomini, H. White, Tests of conditional predictive ability. Econometrica 74, 1545–1578 (2006)

    Article  Google Scholar 

  • E. Gilleland, Spatial forecast verification: Baddeley’s delta metric applied to the ICP test cases. Weather Forecast. 26, 409–415 (2011). https://doi.org/10.1175/WAF-D-10-05061.1

    Article  Google Scholar 

  • E. Gilleland, Testing competing precipitation forecasts accurately and efficiently: the spatial prediction comparison test. Mon. Weather Rev. 141(1), 340–355 (2013). https://doi.org/10.1175/MWR-D-12-00155.1

    Article  Google Scholar 

  • E. Gilleland, T.C.M. Lee, J. Halley Gotway, R.G. Bullock, B.G. Brown, Computationally efficient spatial forecast verification using Baddeley’s Delta image metric. Mon. Weather Rev. 136(5), 1747–1757 (2008). https://doi.org/10.1175/2007MWR2274.1

    Article  Google Scholar 

  • E. Gilleland, D. Ahijevych, B.G. Brown, B. Casati, E.E. Ebert, Intercomparison of spatial forecast verification methods. Weather Forecast. 24(5), 1416–1430 (2009). https://doi.org/10.1175/2009WAF2222269.1

    Article  Google Scholar 

  • E. Gilleland, Coauthors, Spatial forecast verification: Image warping. NCAR Technical Note NCAR/TN-482+STR (2010). doi:10.5065/D62805JJ

    Google Scholar 

  • E. Gilleland, D.A. Ahijevych, B.G. Brown, E.E. Ebert, Verifying forecasts spatially. Bull. Am. Meteorol. Soc. 91(10), 1365–1373 (2010a). https://doi.org/10.1175/2010BAMS2819.1

    Article  Google Scholar 

  • E. Gilleland, L. Chen, M. DePersio, G. Do, K. Eilertson, Y. Jin, E.K. Lang, F. Lindgren, J. Lindström, R.L. Smith, C. Xia, Spatial forecast verification: image warping. NCAR Tech. Note (2010b), NCAR/TN-482 + STR doi:10.5065/D62805JJ

    Google Scholar 

  • E. Gilleland, J. Lindström, F. Lindgren, Analyzing the image warp forecast verification method on precipitation fields from the ICP. Weather Forecast. 25(4), 1249–1262 (2010c). https://doi.org/10.1175/2010WAF2222365.1

    Article  Google Scholar 

  • T. Gneiting, R. Ranjan, Comparing density forecasts using threshold- and quantile-weighted scoring rules. J. Bus. Econ. Stat. 29(3), 411–422 (2011)

    Article  Google Scholar 

  • M. Goeber, E. Zsoter, D.S. Richardson, Could a perfect model ever satisfy the forecaster? On grid box mean versus point verification. Meteorol. Appl. 15, 359–365 (2008)

    Article  Google Scholar 

  • T. Haiden, M. Rodwell, D. Richardson, A. Okagaki, T. Robinson, T. Hewson, Intercomparison of global model precipitation forecast skill in 2010/11 using the SEEPS score. Mon. Weather Rev. 140, 2720–2733 (2012)

    Article  Google Scholar 

  • T. Haiden, L. Magnusson, I. Tsonevsky, F. Wetterhall, L. Alfieri, F. Pappenberger, P. de Rosnay, J. Muñoz-Sabater, G. Balsamo, C. Albergel, R. Forbes, T. Hewson, S. Malardel, D. Richardson, ECMWF forecast performance during the June 2013 flood in Central Europe. Technical Memorandum No. 723, European Centre for Medium Range Weather Forecasts, Reading, England, vol 723 (2014)

    Google Scholar 

  • T.M. Hamill, J. Juras, Measuring forecast skill: is it real skill or is it the varying climatology? Q. J. Roy. Meteorol. Soc. 132, 2905–2923 (2006)

    Article  Google Scholar 

  • A.S. Hering, M.G. Genton, Comparing spatial predictions. Technometrics 53, 414–425 (2011)

    Article  Google Scholar 

  • R.N. Hoffman, Z. Liu, J.-F. Louis, C. Grassotti, Distortion representation of forecast errors. Mon. Weather Rev. 123, 1758–2770 (1995)

    Article  Google Scholar 

  • G.J. Huffman, R.F. Adler, D.T. Bolvin, G. Gu, E.J. Nelkin, K.P. Bowman, Y. Hong, E.F. Stocker, D.B. Woff, The TRMM multi-satellite precipitation analysis: quasi-global, multi-year, combined-sensor precipitation estimates at fine scale. J. Hydrometeorol. 8, 38–55 (2007)

    Article  Google Scholar 

  • G.J. Huffman, D.T. Bolvin, D. Braithwaite, K. Hsu, R. Joyce, P. Xie, S.H. Yoo, NASA global precipitation measurement (GPM) integrated multi-satellite retrievals for GPM (IMERG), in Algorithm Theoretical Basis Document, Version 4.1. NASA, Greenbelt, MD (2013)

    Google Scholar 

  • IPWG, International Precipitation Working Group: Data and Products (2016), http://www.isac.cnr.it/~ipwg/data.html. Viewed 18 June 2016

  • J. Jenkner, C. Frei, C. Schwierz, Quantile-based short-range QPF evaluation over Switzerland. Meteorol. Z. 17, 827–848 (2008)

    Article  Google Scholar 

  • C. Keil, G.C. Craig, A displacement-based error measure applied in a regional ensemble forecasting system. Mon. Weather Rev. 135, 3248–3259 (2007). https://doi.org/10.1175/MWR3457.1

    Article  Google Scholar 

  • C. Keil, G.C. Craig, A displacement and amplitude score employing an optical flow technique. Weather Forecast. 24(5), 1297–1308 (2009). doi:10.1175/2009WAF2222247.1

    Article  Google Scholar 

  • C. Kidd, V. Levizzani, Status of satellite precipitation retrievals. Hydrol. Earth Syst. Sci. 15, 1109–1116 (2011)

    Article  Google Scholar 

  • S.A. Lack, G.L. Limpert, N.I. Fox, An object-oriented multiscale verification scheme. Weather Forecast. 25(1), 79–92 (2010). https://doi.org/10.1175/2009WAF2222245.1

    Article  Google Scholar 

  • F. Lalaurette, Early detection of abnormal weather conditions using a probabilistic extreme forecast index. Q. J. Roy. Meteorol. Soc. 129(594), 3037–3057 (2003)

    Article  Google Scholar 

  • S.M. Lazarus, C.M. Ciliberti, J.D. Horel, K.A. Brewster, Near-real-time applications of a mesoscale analysis system to complex terrain. Weather Forecast. 17, 971–1000 (2002)

    Article  Google Scholar 

  • S. Lerch, Verification of Probabilitsic Forecasts for Rare and Extreme Events (Ruprecht-Karls-Universitaet Heidelberg, Heidelberg, 2012)

    Google Scholar 

  • S. Lerch, T.L. Thorarinsdottir, Comparison of nonhomogeneous regression models for probabilistic wind speed forecasting. Tellus A 65, 21206 (2013)

    Article  Google Scholar 

  • C. Marsigli, A. Montani, T. Pacagnella, A spatial verification method applied to the evaluation of high-resolution ensemble forecasts. Meteorol. Appl. 15, 125–143 (2008)

    Article  Google Scholar 

  • C.F. Mass, D. Ovens, K. Westrick, B.A. Colle, Does increasing horizontal resolution produce more skillful forecasts? Bull. Am. Meteorol. Soc. 83, 407–430 (2002)

    Article  Google Scholar 

  • J.L. McBride, E.E. Ebert, Verification of quantitative precipitation forecasts from operational numerical weather prediction models over Australia. Weather Forecast. 15, 103–121 (2000)

    Article  Google Scholar 

  • R. Merz, G. Blöschl, A process typology of regional floods, Water Resour. Res. 39, 1340 (2003). doi:10.1029/2002WR001952, 12

    Google Scholar 

  • A. Micheas, N.I. Fox, S.A. Lack, C.K. Wikle, Cell identification and verification of QPF ensembles using shape analysis techniques. J. Hydrol. 344, 105–116 (2007)

    Article  Google Scholar 

  • J.R. Minder, P.W. Mote, J.D. Lundquist, Surface temperature lapse rates over complex terrain: lessons from the Cascade Mountains. J. Geophys. Res. Atmos. 115(D14) (2010). https://doi.org/10.1029/2009JD013493

  • M. Mittermaier, N. Roberts, Intercomparison of spatial forecast verification methods: identifying skillful spatial scales using the fractions skill score. Weather Forecast. 25, 343–354 (2010)

    Article  Google Scholar 

  • M. Mittermaier, N. Roberts, S.A. Thompson, A long‐term assessment of precipitation forecast skill using the Fractions Skill Score. Meteorol. Appl. 20, 176–186 (2013)

    Article  Google Scholar 

  • F. Molteni, R. Buizza, T.N. Palmer, T. Petroliagis, The ECMWF ensemble prediction system: methodology and validation. Q. J. Roy. Meteorol. Soc. 122, 73–119 (1996)

    Article  Google Scholar 

  • J.E. Nash, J.V. Sutcliffe, River flow forecasting through conceptual models. Part I: a discussion of principles. J. Hydrol. 10, 282–290 (1970)

    Article  Google Scholar 

  • R. North, M. Trueman, M. Mittermaier, M.J. Rodwell, An assessment of the SEEPS and SEDI metrics for the verification of 6 h forecast precipitation accumulations. Meteorol. Appl. 20, 164–175 (2013)

    Article  Google Scholar 

  • NWS, Advanced Hydrologic Prediction Service (2014), http://water.weather.gov/precip/about.php. Viewed 10 Apr 2014

  • 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)

    Article  Google Scholar 

  • T. Petroliagis, P. Pinson, Early indication of extreme winds utilising the Extreme Forecast Index, ECMWF Newsletter No. 132 – Summer 2012, 2012

    Google Scholar 

  • R.-D. Reiss, M. Thomas, Statistical Analysis of Extreme Values: With Applications to Insurance, Finance, Hydrology and Other Fields, 3rd edn. (Birkhäuser, Basel, 2007), 530pp

    Google Scholar 

  • N.M. Roberts, H.W. Lean, Scale-selective verification of rainfall accumulations from high-resolution forecasts of convective events. Mon. Wea. Rev. 136, 78–96 (2008)

    Article  Google Scholar 

  • M.J. Rodwell, D.S. Richardson, T.D. Hewson, T. Haiden, A new equitable score suitable for verifying precipitation in numerical weather prediction. Q. J. Roy. Meteorol. Soc. 136, 1344–1363 (2010)

    Google Scholar 

  • Ø. Saetra, H. Hersbach, J.-R. Bidlot, D.S. Richardson, Effects of observation errors on the statistics for ensemble spread and reliability. Mon. Weather Rev. 132, 1487–1501 (2004)

    Article  Google Scholar 

  • B.R.J. Schwedler, M.E. Baldwin, Diagnosing the sensitivity of binary image measures to bias, location, and event frequency within a forecast verification framework. Weather Forecast. 26, 1032–1044 (2011). https://doi.org/10.1175/WAF-D-11-00032.1

    Article  Google Scholar 

  • D.J. Seo, J.P. Breidenbach, Real-time correction of spatially nonuniform bias in radar rainfall data using rain gauge measurements. J. Hydrometeorol. 3, 93–111 (2002)

    Article  Google Scholar 

  • R. Steinacker, C. Häberli, W. Pöttschacher, A transparent method for the analysis and quality evaluation of irregularly distributed and noisy observational data. Mon. Weather Rev. 128, 2303–2316 (2000)

    Article  Google Scholar 

  • D.B. Stephenson, B. Casati, C.A.T. Ferro, C.A. Wilson, The extreme dependency score: a non-vanishing measure for forecasts of rare events. Meteorol. Appl. 15, 41–50 (2008). https://doi.org/10.1002/met.53

    Article  Google Scholar 

  • J. Thielen-del Pozo, J. Bartholmes, M.-H. Ramos, A. de Roo, The European Flood Alert System. Part 1: concept and development. Hydrol. Earth Syst. Sci. 13, 125–140 (2009)

    Article  Google Scholar 

  • I. Tsonevsky,D.S. Richardson, D.S, Application of the new EFI products to a case of early snowfall in Central Europe. ECMWF Newsletter 133, Autumn 2012, p. 4, 2012

    Google Scholar 

  • H. Wernli, M. Paulat, M. Hagen, C. Frei, SAL – a novel quality measure for the verification of quantitative precipitation forecasts. Mon. Weather Rev. 136, 4470–4487 (2008)

    Article  Google Scholar 

  • T. Weusthoff, F. Ament, M. Arpagaus, M.W. Rotach, Assessing the benefits of convection-permitting models by neighborhood verification: examples from MAP D-PHASE. Mon. Weather Rev. 138, 3418–3433 (2010)

    Article  Google Scholar 

  • D.S. Wilks, Statistical Methods in the Atmospheric Sciences, 3rd edn. (Academic, Amsterdam, 2011), 704 pp

    Google Scholar 

  • WMO, Recommendations for the Verification and Intercomparison of QPFs and PQPFs from Operational NWP Models – Revision 2, WMO/TD-No.1485 WWRP 2009-1 (2008)

    Google Scholar 

  • WMO, Manual on the Global Data-Processing and Forecasting System (GDPFS). WMO-no.485, World Meteorological Organization, Geneva, vol 485 (2014)

    Google Scholar 

  • J. Wolff, M. Harrold, T.A. Fowler, J. Halley Gotway, L. Nance, B.G. Brown, Beyond the basics: evaluating model-based precipitation forecasts using traditional, spatial, and object-based methods. Weather Forecast. 29, 1451–1472 (2014)

    Article  Google Scholar 

  • P. Zacharov, D. Rezacova, Using the fractions skill score to assess the relationship between an ensemble QPF spread and skill. Atmos. Res. 94, 684–693 (2009)

    Article  Google Scholar 

  • M. Zimmer, H. Wernli, Verification of quantitative precipitation forecasts on short time-scales: a fuzzy approach to handle timing errors with SAL. Meteorol. Z. 20, 95–105 (2011)

    Article  Google Scholar 

  • E. Zsótér, Recent developments in extreme weather forecasting. ECMWF Newsl. 107(107), 8–17 (2006)

    Google Scholar 

  • E. Zsótér, F. Pappenberger, D. Richardson, Sensitivity of model climate to sampling configurations and the impact on the Extreme Forecast Index. Meteorol. Appl. (2014). https://doi.org/10.1002/met.1447

    Article  Google Scholar 

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Gilleland, E., Pappenberger, F., Brown, B., Ebert, E., Richardson, D. (2019). Verification of Meteorological Forecasts for Hydrological Applications. In: Duan, Q., Pappenberger, F., Wood, A., Cloke, H., Schaake, J. (eds) Handbook of Hydrometeorological Ensemble Forecasting. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39925-1_4

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