Validation in Weather Forecasting

  • Susanne TheisEmail author
  • Michael Baldauf
Part of the Simulation Foundations, Methods and Applications book series (SFMA)


Numerical simulations are the core technique in forecasting the weather. The simulation calculates a weather forecast by use of an atmospheric model, which is implemented on a computer. The model itself can be partitioned into various complexity levels, and these can be associated with respective validation concepts. The proper design and implementation of the ‘dynamical core’ (i.e.,  partial differential equations and their numerical solver) is tested via comparison to idealized test cases. In a subsequent development step, ‘parameterizations’ are added, and then the simulation is considered a serious attempt to forecast the weather. The quality of the forecast is estimated by the retrospective comparison between simulation output and observed weather. In addition, a day-specific estimate of forecast uncertainty is derived via ‘ensemble forecasting’ on a routine basis.


Weather forecasting Dynamical core Parameterizations Ensemble Uncertainty 



We thank Felix Fundel and Ulrich Damrath (DWD) for delivering several verification plots. We also thank Nicole J. Saam and Claus Beisbart for inviting Susanne Theis to the Symposium ‘How to Build Trust in Computer Simulations’ (2015), funded by VolkswagenStiftung.


  1. Adrian, G. (2016). Qualitätsmangement-Handbuch für den Deutschen Wetterdienst (DWD). Deutscher Wetterdienst, Offenbach, Germany. Version 52.Google Scholar
  2. Arakawa, A. (2004). The cumulus parameterization problem: Past, present, and future. Journal of Climate, 17(13), 2493–2525.CrossRefGoogle Scholar
  3. Arakawa, A., & Konor, C. S. (2009). Unification of the anelastic and quasi-hydrostatic systems of equations. Monthly Weather Review, 137(2), 710–726.CrossRefGoogle Scholar
  4. Baldauf, M., & Brdar, S. (2013). An analytic solution for linear gravity waves in a channel as a test for numerical models using the non-hydrostatic, compressible Euler equations. Quarterly Journal of the Royal Meteorological Society, 139, 1977–1989.CrossRefGoogle Scholar
  5. Baldauf, M., Reinert, D., & Zängl, G. (2014). An analytical solution for linear gravity and sound waves on the sphere as a test for compressible, non-hydrostatic numerical models. Quarterly Journal of the Royal Meteorological Society, 140, 1974–1985.Google Scholar
  6. Bauer, P., Thorpe, I., & Brunet, G. (2015). The quiet revolution of numerical weather prediction. Nature, 525, 47–55.CrossRefGoogle Scholar
  7. Bowler, N. E. (2008). Accounting for the effect of observation errors on verification of MOGREPS. Meteorological Applications, 15(1), 199–205.CrossRefGoogle Scholar
  8. Bröcker, J., & Smith, L. A. (2007). Scoring probabilistic forecasts: The importance of being proper. Weather and Forecasting, 22(2), 382–388.CrossRefGoogle Scholar
  9. Bröcker, J., & Smith, L. A. (2008). From ensemble forecasts to predictive distribution functions. Tellus A: Dynamic Meteorology and Oceanography, 60(4).Google Scholar
  10. Casati, B., Wilson, L. J., Stephenson, D. B., Nurmi, P., Ghelli, A., Pocernich, M., et al. (2008). Forecast verification: Current status and future directions. Meteorological Applications, 15(1), 3–18.CrossRefGoogle Scholar
  11. Daley, R. (1994). Atmospheric data analysis. Cambridge, UK: Cambridge University Press.Google Scholar
  12. DWD (2016). Deutscher Wetterdienst: Jahresbericht 2016. Deutscher Wetterdienst, Offenbach, Germany.
  13. Durran, D. R. (1998). Numerical methods for wave equations in geophysical fluid dynamics. New York: Springer.zbMATHGoogle Scholar
  14. Ebert, E. E. (2009). Neighborhood verification: A strategy for rewarding close forecasts. Weather and Forecasting, 24(6), 1498–1510.CrossRefGoogle Scholar
  15. Ehrendorfer, M. (1997). Predicting the uncertainty of numerical weather forecasts: A review. Meteorologische Zeitschrift, 6, 147183.CrossRefGoogle Scholar
  16. Ferro, C. A. T., & Stephenson, D. B. (2011). Extremal dependence indices: Improved verification measures for deterministic forecasts of rare binary events. Weather and Forecasting, 26(5), 699–713.CrossRefGoogle Scholar
  17. Gilleland, E., Ahijevych, D., Brown, B. G., Casati, B., & Ebert, E. E. (2009). Intercomparison of spatial forecast verification methods. Weather and Forecasting, 24(5), 1416–1430.CrossRefGoogle Scholar
  18. Giraldo, F. X., & Restelli, M. (2008). A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases. Journal of Computational Physics, 227(8), 3849–3877.MathSciNetCrossRefGoogle Scholar
  19. Gramelsberger, G. (2010). Conceiving processes in atmospheric models–general equations, subscale parameterizations, and superparameterizations. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 41(3), 233–241.CrossRefGoogle Scholar
  20. Hamill, T. M. (2012). Verification of TIGGE multimodel and ECMWF reforecast-calibrated probabilistic precipitation forecasts over the contiguous United States. Monthly Weather Review, 140(7), 2232–2252.CrossRefGoogle Scholar
  21. Heinze, R., Dipankar, A., Henken, C. C., Moseley, C., Sourdeval, O., Trömel, S., et al. (2017). Large-eddy simulations over Germany using ICON: A comprehensive evaluation. Quarterly Journal of the Royal Meteorological Society, 143(702), 69–100.CrossRefGoogle Scholar
  22. Jablonowski, C., & Williamson, D. L. (2006). A baroclinic instability test case for atmospheric model dynamical cores. Quarterly Journal of the Royal Meteorological Society, 132, 2943–2975.CrossRefGoogle Scholar
  23. Jolliffe, I. T., & Stephenson, D. B. (Eds.). (2011). Forecast verification: A practitioner’s guide in Atmospheric Science (2nd ed.). Wiley.Google Scholar
  24. Kox, T., & Thieken, A. H. (2017). To act or not to act? Factors influencing the general public’s decision about whether to take protective action against severe weather. Weather, Climate, and Society, 9(2), 299–315.CrossRefGoogle Scholar
  25. Kox, T., Gerhold, L., & Ulbrich, U. (2015). Perception and use of uncertainty in severe weather warnings by emergency services in Germany. Atmospheric Research, 158, 292–301.CrossRefGoogle Scholar
  26. Lauritzen, P. H., & Thuburn, J. (2012). Evaluating advection/transport schemes using interrelated tracers, scatter plots and numerical mixing diagnostics. Quarterly Journal of the Royal Meteorological Society, 138, 906–918.Google Scholar
  27. Lazo, J. K., Morss, R. E., & Demuth, J. L. (2009). 300 billion served: Sources, perceptions, uses, and values of weather forecasts. Bulletin of the American Meteorological Society, 90(6), 785–798.CrossRefGoogle Scholar
  28. Lerch, S., Thorarinsdottir, T. L., Ravazzolo, F., & Gneiting, T. (2017). Forecasters dilemma: Extreme events and forecast evaluation. Statistical Science, 32(1), 106–127.MathSciNetCrossRefGoogle Scholar
  29. Leutbecher, M., & Palmer, T. N. (2008). Ensemble forecasting. Journal of Computational Physics, 227, 3515–3539.MathSciNetCrossRefGoogle Scholar
  30. LeVeque, R. J. (1996). High-resolution conservative algorithms for advection in incompressible flow. SIAM Journal on Numerical Analysis, 33, 627–665.MathSciNetCrossRefGoogle Scholar
  31. Long, R. R. (1953). Some aspects of the flow of stratified fluids - Part 1. A theoretical investigation. Tellus, 5(1), 42–58.MathSciNetCrossRefGoogle Scholar
  32. Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2), 130–141.MathSciNetCrossRefGoogle Scholar
  33. Lynch, P. (2008). The ENIAC forecasts: A re-creation. Bulletin of the American Meteorological Society, 89(1), 45–55.CrossRefGoogle Scholar
  34. Ogura, Y., & Phillips, N. A. (1962). Scale analysis of deep and shallow convection in the atmosphere. Journal of the Atmospheric Sciences, 19, 173–179.CrossRefGoogle Scholar
  35. Parker, W. S. (2010). Predicting weather and climate: Uncertainty, ensembles and probability. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 41(3), 263–272.CrossRefGoogle Scholar
  36. Randall, D., Krueger, S., Bretherton, C., Curry, J., Duynkerke, P., Moncrieff, M., et al. (2003). Confronting models with data: The GEWEX cloud systems study. Bulletin of the American Meteorological Society, 84(4), 455–469.CrossRefGoogle Scholar
  37. Robert, A. (1993). Bubble convection experiments with a semi-implicit formulation of the Euler equations. Journal of the Atmospheric Sciences, 50, 1865–1873.CrossRefGoogle Scholar
  38. Skamarock, W. C., & Klemp, J. B. (1992). The stability of time-split numerical methods for the hydrostatic and the nonhydrostatic elastic equations. Monthly Weather Review, 120, 2109–2127.CrossRefGoogle Scholar
  39. Staniforth, A., & White, A. A. (2007). Some exact solutions of geophysical fluid-dynamics equations for testing models in spherical and plane geometry. Quarterly Journal of the Royal Meteorological Society, 133, 1605–1614.CrossRefGoogle Scholar
  40. Stensrud, D. J. (2007). Parameterization schemes: Keys to understanding numerical weather prediction models. Cambridge University Press.Google Scholar
  41. Straka, J. M., Wilhelmson, R. B., Wicker, L. J., Anderson, J. R., & Droegemeier, K. K. (1993). Numerical solutions of a non-linear density current: A benchmark solution and comparisons. International Journal for Numerical Methods in Fluids, 17, 1–22.Google Scholar
  42. Wilhelmson, R., & Ogura, Y. (1972). The pressure perturbation and the numerical modeling of a cloud. Journal of the Atmospheric Sciences, 29, 1295–1307.CrossRefGoogle Scholar
  43. Wilks, D. (2011). Statistical methods in the atmospheric sciences (3rd ed., Vol. 100). Academic Press.Google Scholar
  44. Wilks, D. S., & Hamill, T. M. (2007). Comparison of ensemble-MOS methods using GFS reforecasts. Monthly Weather Review, 135(6), 2379–2390.CrossRefGoogle Scholar
  45. Yanai, M. and Johnson, R. H. (1993). Impacts of cumulus convection on thermodynamic fields. In The representation of cumulus convection in numerical models, number 46 in Meteor. Monogr. (pp. 39–62). American Meteorological Society.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Deutscher WetterdienstOffenbach am MainGermany

Personalised recommendations